Daily Papers

Specialist epilepsy expertise is scarce in resource-constrained settings, making LLM-based decision support attractive for frontline clinicians managing longitudinal treatment. Such systems must adapt to local prescribing practice and know when to defer. We study this problem in Ugandan pediatric epilepsy care, predicting anti-seizure medication regimens from longitudinal unstructured clinic notes. Standard prompting achieves non-trivial agreement with physician prescriptions, but neurologist review shows that many errors reflect distribution-miscalibrated prescribing defaults rather than failures to parse the local record. We introduce MANANA, a non-parametric prompt-learning framework that learns local prescribing guidance from a small patient-level training set. MANANA converts observed prescription errors into auditable prompt memories, instantiated in single-agent and multi-agent variants, and improves over classical ML models, direct LLM prompting, and prompt-optimization baselines across two independently collected Ugandan cohorts. We further propose Bayesian prompt averaging, which converts the learned prompt trajectory into prescription likelihoods and an uncertainty-based deferral signal. On the independently collected held-out cohort, this improves visit-level top-3 prescription accuracy by 4-8 percentage points over prompt-optimization baselines and enables selective prediction: the system can auto-handle the most confident half of cases at 95% precision, or the most confident quarter at 99% precision, while deferring lower-confidence cases for specialist review.

Foundational image-language models have generated considerable interest due to their efficient adaptation to downstream tasks by prompt learning. Prompt learning treats part of the language model input as trainable while freezing the rest, and optimizes an Empirical Risk Minimization objective. However, Empirical Risk Minimization is known to suffer from distributional shifts which hurt generalizability to prompts unseen during training. By leveraging the regularization ability of Bayesian methods, we frame prompt learning from the Bayesian perspective and formulate it as a variational inference problem. Our approach regularizes the prompt space, reduces overfitting to the seen prompts and improves the prompt generalization on unseen prompts. Our framework is implemented by modeling the input prompt space in a probabilistic manner, as an a priori distribution which makes our proposal compatible with prompt learning approaches that are unconditional or conditional on the image. We demonstrate empirically on 15 benchmarks that Bayesian prompt learning provides an appropriate coverage of the prompt space, prevents learning spurious features, and exploits transferable invariant features. This results in better generalization of unseen prompts, even across different datasets and domains. Code available at: https://github.com/saic-fi/Bayesian-Prompt-Learning

Recently, vision-language models (e.g. CLIP) have demonstrated remarkable performance in zero-shot anomaly detection (ZSAD). By leveraging auxiliary data during training, these models can directly perform cross-category anomaly detection on target datasets, such as detecting defects on industrial product surfaces or identifying tumors in organ tissues. Existing approaches typically construct text prompts through either manual design or the optimization of learnable prompt vectors. However, these methods face several challenges: 1) handcrafted prompts require extensive expert knowledge and trial-and-error; 2) single-form learnable prompts struggle to capture complex anomaly semantics; and 3) an unconstrained prompt space limits generalization to unseen categories. To address these issues, we propose Bayesian Prompt Flow Learning (Bayes-PFL), which models the prompt space as a learnable probability distribution from a Bayesian perspective. Specifically, a prompt flow module is designed to learn both image-specific and image-agnostic distributions, which are jointly utilized to regularize the text prompt space and improve the model's generalization on unseen categories. These learned distributions are then sampled to generate diverse text prompts, effectively covering the prompt space. Additionally, a residual cross-model attention (RCA) module is introduced to better align dynamic text embeddings with fine-grained image features. Extensive experiments on 15 industrial and medical datasets demonstrate our method's superior performance. The code is available at https://github.com/xiaozhen228/Bayes-PFL.

Recent advances have witnessed the effectiveness of reinforcement learning (RL) finetuning in enhancing the reasoning capabilities of large language models (LLMs). The optimization process often requires numerous iterations to achieve satisfactory performance, resulting in high computational costs due to the need for frequent prompt evaluations under intensive LLM interactions and repeated policy updates. Appropriate online prompt selection methods reduce iteration steps by prioritizing informative prompts during training, while the pipeline's reliance on exhaustive prompt evaluation and subset selection for optimization still incurs substantial computational overhead due to frequent LLM inference calls. Distinguished from these direct evaluate-then-select schemes, this work investigates iterative approximate evaluation for arbitrary prompts and introduces Model Predictive Prompt Selection (MoPPS), a Bayesian risk-predictive framework that online estimates prompt difficulty without requiring costly LLM interactions. Technically, MoPPS models each prompt's success rate as a latent variable, performs streaming Bayesian inference, and employs posterior sampling in a constructed multi-armed bandit machine, enabling sample efficient and adaptive prompt selection. Extensive experiments across mathematics, planning, and vision-based geometry tasks show that MoPPS reliably predicts prompt difficulty and accelerates training with significantly reduced LLM rollouts.

Large language models (LLMs) transfer well to new tasks out-of-the-box simply given a natural language prompt that demonstrates how to perform the task and no additional training. Prompting is a brittle process wherein small modifications to the prompt can cause large variations in the model predictions, and therefore significant effort is dedicated towards designing a painstakingly "perfect prompt" for a task. To mitigate the high degree of effort involved in prompt-design, we instead ask whether producing multiple effective, yet imperfect, prompts and aggregating them can lead to a high quality prompting strategy. Our observations motivate our proposed prompting method, ASK ME ANYTHING (AMA). We first develop an understanding of the effective prompt formats, finding that question-answering (QA) prompts, which encourage open-ended generation ("Who went to the park?") tend to outperform those that restrict the model outputs ("John went to the park. Output True or False."). Our approach recursively uses the LLM itself to transform task inputs to the effective QA format. We apply the collected prompts to obtain several noisy votes for the input's true label. We find that the prompts can have very different accuracies and complex dependencies and thus propose to use weak supervision, a procedure for combining the noisy predictions, to produce the final predictions for the inputs. We evaluate AMA across open-source model families (e.g., EleutherAI, BLOOM, OPT, and T0) and model sizes (125M-175B parameters), demonstrating an average performance lift of 10.2% over the few-shot baseline. This simple strategy enables the open-source GPT-J-6B model to match and exceed the performance of few-shot GPT3-175B on 15 of 20 popular benchmarks. Averaged across these tasks, the GPT-J-6B model outperforms few-shot GPT3-175B. We release our code here: https://github.com/HazyResearch/ama_prompting

As a novel and effective fine-tuning paradigm based on large-scale pre-trained language models (PLMs), prompt-tuning aims to reduce the gap between downstream tasks and pre-training objectives. While prompt-tuning has yielded continuous advancements in various tasks, such an approach still remains a persistent defect: prompt-tuning methods fail to generalize to specific few-shot patterns. From the perspective of distribution analyses, we disclose that the intrinsic issues behind the phenomenon are the over-multitudinous conceptual knowledge contained in PLMs and the abridged knowledge for target downstream domains, which jointly result in that PLMs mis-locate the knowledge distributions corresponding to the target domains in the universal knowledge embedding space. To this end, we intuitively explore to approximate the unabridged target domains of downstream tasks in a debiased manner, and then abstract such domains to generate discriminative prompts, thereby providing the de-ambiguous guidance for PLMs. Guided by such an intuition, we propose a simple yet effective approach, namely BayesPrompt, to learn prompts that contain the domain discriminative information against the interference from domain-irrelevant knowledge. BayesPrompt primitively leverages known distributions to approximate the debiased factual distributions of target domains and further uniformly samples certain representative features from the approximated distributions to generate the ultimate prompts for PLMs. We provide theoretical insights with the connection to domain adaptation. Empirically, our method achieves state-of-the-art performance on benchmarks.

Reinforcement learning enhances the reasoning capabilities of large language models but often involves high computational costs due to rollout-intensive optimization. Online prompt selection presents a plausible solution by prioritizing informative prompts to improve training efficiency. However, current methods either depend on costly, exact evaluations or construct prompt-specific predictive models lacking generalization across prompts. This study introduces Generalizable Predictive Prompt Selection (GPS), which performs Bayesian inference towards prompt difficulty using a lightweight generative model trained on the shared optimization history. Intermediate-difficulty prioritization and history-anchored diversity are incorporated into the batch acquisition principle to select informative prompt batches. The small predictive model also generalizes at test-time for efficient computational allocation. Experiments across varied reasoning benchmarks indicate GPS's substantial improvements in training efficiency, final performance, and test-time efficiency over superior baseline methods.

Prompt optimization improves language models without updating their weights by searching for a better system prompt, but its effectiveness varies widely across tasks. We study what makes a task amenable to prompt optimization. We show that the reward variance across different system prompts can be decomposed into two components: variance among responses, which captures generation stochasticity, and variance among system prompts, which captures differences in system prompt quality. Prompt optimization succeeds when variance among system prompts is sufficiently large, but fails when variance among responses dominates the variance of the system prompts. Surprisingly, we further show that scaling to more user prompts can hurt optimization by reducing variance among system prompts, especially on heterogeneous datasets where different user prompts favor different system prompts. Motivated by this insight, we propose p1, a simple user prompt filtering method that selects a small subset of user prompts with high variance across candidate system prompts. This subset of user prompts allows one to distinguish a good system prompt from a bad one, making system optimization easier. Experiments on reasoning benchmarks show that p1 substantially improves prompt optimization over training on the full dataset and outperforms strong baselines such as GEPA. Notably, training on only two prompts from AIME 24 yields a system prompt that generalizes well to other reasoning benchmarks.

We present prompt distribution learning for effectively adapting a pre-trained vision-language model to address downstream recognition tasks. Our method not only learns low-bias prompts from a few samples but also captures the distribution of diverse prompts to handle the varying visual representations. In this way, we provide high-quality task-related content for facilitating recognition. This prompt distribution learning is realized by an efficient approach that learns the output embeddings of prompts instead of the input embeddings. Thus, we can employ a Gaussian distribution to model them effectively and derive a surrogate loss for efficient training. Extensive experiments on 12 datasets demonstrate that our method consistently and significantly outperforms existing methods. For example, with 1 sample per category, it relatively improves the average result by 9.1% compared to human-crafted prompts.

Recent work finds that retrieval-augmented generation with large language models is prone to be influenced by the order of retrieved documents in the context. However, the lack of in-depth analysis limits the use of this phenomenon for prompt engineering in practice. In this study, we posit that likelihoods serve as an effective gauge for language model performance. Through experiments on two question-answering datasets with a variety of state-of-the-art language models, we reveal correlations between answer accuracy and the likelihood of the question at both the corpus level and the instance level. In addition, we find that question likelihood can also indicate the position of the task-relevant information in the context. Based on these findings, we propose two methods that use question likelihood as a gauge for selecting and constructing prompts that lead to better performance. We demonstrate their effectiveness with experiments. In addition, our likelihood-based methods are efficient, as they only need to compute the likelihood of the input, requiring much fewer language model passes than heuristic prompt engineering methods that require generating responses. Our analysis deepens our understanding of how input prompts affect model performance and provides a promising direction for efficient prompt optimization.

LLMs are highly sensitive to prompt phrasing, yet standard benchmarks typically report performance using a single prompt, raising concerns about the reliability of such evaluations. In this work, we argue for a stochastic method of moments evaluation over the space of meaning-preserving prompt perturbations. We introduce a formal definition of reliable evaluation that accounts for prompt sensitivity, and suggest ReliableEval - a method for estimating the number of prompt resamplings needed to obtain meaningful results. Using our framework, we stochastically evaluate five frontier LLMs and find that even top-performing models like GPT-4o and Claude-3.7-Sonnet exhibit substantial prompt sensitivity. Our approach is model-, task-, and metric-agnostic, offering a recipe for meaningful and robust LLM evaluation.

Certain statistical models are capable of interpreting input strings as instructions, or prompts, and carry out tasks based on them. Many approaches to prompting and pre-training these models involve the automated generation of these prompts. We call these approaches meta-prompting, or prompting to obtain prompts. We propose a theoretical framework based on category theory to generalize and describe them. This framework is flexible enough to account for LLM stochasticity; and allows us to obtain formal results around task agnosticity and equivalence of various meta-prompting approaches. We experiment with meta-prompting in two active areas of model research: creativity and ideation. We find that user preference favors (p < 0.01) the prompts generated under meta-prompting, as well as their corresponding outputs, over a series of hardcoded baseline prompts that include the original task prompt. Using our framework, we argue that meta-prompting is more effective than basic prompting at generating desirable outputs.

Large language models (LLMs) are increasingly deployed as autonomous decision agents in settings with asymmetric error costs: hiring (missed talent vs wasted interviews), medical triage (missed emergencies vs unnecessary escalation), and fraud detection (approved fraud vs declined legitimate payments). The dominant design queries a single LLM for a posterior over states, thresholds "confidence," and acts; we prove this is inadequate for sequential decisions with costs. We propose a Bayesian, cost-aware multi-LLM orchestration framework that treats LLMs as approximate likelihood models rather than classifiers. For each candidate state, we elicit likelihoods via contrastive prompting, aggregate across diverse models with robust statistics, and update beliefs with Bayes rule under explicit priors as new evidence arrives. This enables coherent belief updating, expected-cost action selection, principled information gathering via value of information, and fairness gains via ensemble bias mitigation. In resume screening with costs of 40000 USD per missed hire, 2500 USD per interview, and 150 USD per phone screen, experiments on 1000 resumes using five LLMs (GPT-4o, Claude 4.5 Sonnet, Gemini Pro, Grok, DeepSeek) reduce total cost by 294000 USD (34 percent) versus the best single-LLM baseline and improve demographic parity by 45 percent (max group gap 22 to 5 percentage points). Ablations attribute 51 percent of savings to multi-LLM aggregation, 43 percent to sequential updating, and 20 percent to disagreement-triggered information gathering, consistent with the theoretical benefits of correct probabilistic foundations.

Human cognition excels at transcending sensory input and forming latent representations that structure our understanding of the world. Although Large Language Models (LLMs) can produce chain-of-thought reasoning, they lack a principled framework to capture latent structures and model uncertainty, especially in compositional reasoning tasks. We propose Verbalized Probabilistic Graphical Modeling (vPGM), a Bayesian prompting framework that guides LLMs to simulate key principles of Probabilistic Graphical Models (PGMs) in natural language. Unlike many traditional probabilistic methods requiring substantial domain expertise or specialized training, vPGM bypasses expert-driven model design, making it well-suited for scenarios with limited assumptions or scarce data. We evaluated our model on several compositional reasoning tasks, both close-ended and open-ended. Our results indicate that the model effectively enhances confidence calibration and text generation quality.

We present a novel prompt design for Large Language Models (LLMs) tailored to Asynchronous Time Series. Unlike regular time series, which assume values at evenly spaced time points, asynchronous time series consist of timestamped events occurring at irregular intervals, each described in natural language. Our approach effectively utilizes the rich natural language of event descriptions, allowing LLMs to benefit from their broad world knowledge for reasoning across different domains and tasks. This allows us to extend the scope of asynchronous time series analysis beyond forecasting to include tasks like anomaly detection and data imputation. We further introduce Stochastic Soft Prompting, a novel prompt-tuning mechanism that significantly improves model performance, outperforming existing fine-tuning methods such as QLoRA. Through extensive experiments on real world datasets, we demonstrate that our approach achieves state-of-the-art performance across different tasks and datasets.

In this paper, we conduct a comprehensive study of In-Context Learning (ICL) by addressing several open questions: (a) What type of ICL estimator is learned by large language models? (b) What is a proper performance metric for ICL and what is the error rate? (c) How does the transformer architecture enable ICL? To answer these questions, we adopt a Bayesian view and formulate ICL as a problem of predicting the response corresponding to the current covariate, given a number of examples drawn from a latent variable model. To answer (a), we show that, without updating the neural network parameters, ICL implicitly implements the Bayesian model averaging algorithm, which is proven to be approximately parameterized by the attention mechanism. For (b), we analyze the ICL performance from an online learning perspective and establish a O(1/T) regret bound for perfectly pretrained ICL, where T is the number of examples in the prompt. To answer (c), we show that, in addition to encoding Bayesian model averaging via attention, the transformer architecture also enables a fine-grained statistical analysis of pretraining under realistic assumptions. In particular, we prove that the error of pretrained model is bounded by a sum of an approximation error and a generalization error, where the former decays to zero exponentially as the depth grows, and the latter decays to zero sublinearly with the number of tokens in the pretraining dataset. Our results provide a unified understanding of the transformer and its ICL ability with bounds on ICL regret, approximation, and generalization, which deepens our knowledge of these essential aspects of modern language models.

Prompt-based classifiers are an attractive approach for zero-shot classification. However, the precise choice of the prompt template and label words can largely influence performance, with semantically equivalent settings often showing notable performance difference. This discrepancy can be partly attributed to word biases, where the classifier may be biased towards classes. To address this problem, it is possible to optimise classification thresholds on a labelled data set, however, this mitigates some of the advantages of prompt-based classifiers. This paper instead approaches this problem by examining the expected marginal probabilities of the classes. Here, probabilities are reweighted to have a uniform prior over classes, in an unsupervised fashion. Further, we draw a theoretical connection between the class priors and the language models' word prior, and offer the ability to set a threshold in a zero-resource fashion. We show that matching class priors correlates strongly with the oracle upper bound performance and demonstrate large consistent performance gains for prompt settings over a range of NLP tasks.

Large language models (LLMs) solve problems more accurately and interpretably when instructed to work out the answer step by step using a ``chain-of-thought'' (CoT) prompt. One can also improve LLMs' performance on a specific task by supervised fine-tuning, i.e., by using gradient ascent on some tunable parameters to maximize the average log-likelihood of correct answers from a labeled training set. Naively combining CoT with supervised tuning requires supervision not just of the correct answers, but also of detailed rationales that lead to those answers; these rationales are expensive to produce by hand. Instead, we propose a fine-tuning strategy that tries to maximize the marginal log-likelihood of generating a correct answer using CoT prompting, approximately averaging over all possible rationales. The core challenge is sampling from the posterior over rationales conditioned on the correct answer; we address it using a simple Markov-chain Monte Carlo (MCMC) expectation-maximization (EM) algorithm inspired by the self-taught reasoner (STaR), memoized wake-sleep, Markovian score climbing, and persistent contrastive divergence. This algorithm also admits a novel control-variate technique that drives the variance of our gradient estimates to zero as the model improves. Applying our technique to GSM8K and the tasks in BIG-Bench Hard, we find that this MCMC-EM fine-tuning technique typically improves the model's accuracy on held-out examples more than STaR or prompt-tuning with or without CoT.

Fine-tuning continuous prompts for target tasks has recently emerged as a compact alternative to full model fine-tuning. Motivated by these promising results, we investigate the feasibility of extracting a discrete (textual) interpretation of continuous prompts that is faithful to the problem they solve. In practice, we observe a "wayward" behavior between the task solved by continuous prompts and their nearest neighbor discrete projections: We can find continuous prompts that solve a task while being projected to an arbitrary text (e.g., definition of a different or even a contradictory task), while being within a very small (2%) margin of the best continuous prompt of the same size for the task. We provide intuitions behind this odd and surprising behavior, as well as extensive empirical analyses quantifying the effect of various parameters. For instance, for larger model sizes we observe higher waywardness, i.e, we can find prompts that more closely map to any arbitrary text with a smaller drop in accuracy. These findings have important implications relating to the difficulty of faithfully interpreting continuous prompts and their generalization across models and tasks, providing guidance for future progress in prompting language models.

We study adaptive querying for learning user-dependent quantities of interest, such as responses to held-out items and psychometric indicators, within tight question budgets. Classical Bayesian design and computerized adaptive testing typically rely on restrictive parametric assumptions or expensive posterior approximations, limiting their use in heterogeneous, high-dimensional, and cold-start settings. We introduce a persona-induced latent variable model that represents a user's state through membership in a finite dictionary of AI personas, each offering response distributions produced by a large language model. This yields expressive priors with closed-form posterior updates and efficient finite-mixture predictions, enabling scalable Bayesian design for sequential item selection. Experiments on synthetic data and WorldValuesBench demonstrate that persona-based posteriors deliver accurate probabilistic predictions and an interpretable adaptive elicitation pipeline.

Zero-shot learning in prompted vision-language models, the practice of crafting prompts to build classifiers without an explicit training process, has achieved impressive performance in many settings. This success presents a seemingly surprising observation: these methods suffer relatively little from overfitting, i.e., when a prompt is manually engineered to achieve low error on a given training set (thus rendering the method no longer actually zero-shot), the approach still performs well on held-out test data. In this paper, we show that we can explain such performance well via recourse to classical PAC-Bayes bounds. Specifically, we show that the discrete nature of prompts, combined with a PAC-Bayes prior given by a language model, results in generalization bounds that are remarkably tight by the standards of the literature: for instance, the generalization bound of an ImageNet classifier is often within a few percentage points of the true test error. We demonstrate empirically that this holds for existing handcrafted prompts and prompts generated through simple greedy search. Furthermore, the resulting bound is well-suited for model selection: the models with the best bound typically also have the best test performance. This work thus provides a possible justification for the widespread practice of prompt engineering, even if it seems that such methods could potentially overfit the training data.

We introduce a novel framework that transforms the resource-intensive (adversarial) prompt optimization problem into an efficient, amortized inference task. Our core insight is that pretrained, non-autoregressive generative LLMs, such as Diffusion LLMs, which model the joint distribution over prompt-response pairs, can serve as powerful surrogates for prompt search. This approach enables the direct conditional generation of prompts, effectively replacing costly, per-instance discrete optimization with a small number of parallelizable samples. We provide a probabilistic analysis demonstrating that under mild fidelity assumptions, only a few conditional samples are required to recover high-reward (harmful) prompts. Empirically, we find that the generated prompts are low-perplexity, diverse jailbreaks that exhibit strong transferability to a wide range of black-box target models, including robustly trained and proprietary LLMs. Beyond adversarial prompting, our framework opens new directions for red teaming, automated prompt optimization, and leveraging emerging Flow- and Diffusion-based LLMs.

Large language model (LLM) evaluations typically rely on aggregated metrics like accuracy or human preference, averaging across users and prompts. This averaging obscures user- and prompt-specific variations in model performance. To address this, we propose Prompt-to-Leaderboard (P2L), a method that produces leaderboards specific to a prompt. The core idea is to train an LLM taking natural language prompts as input to output a vector of Bradley-Terry coefficients which are then used to predict the human preference vote. The resulting prompt-dependent leaderboards allow for unsupervised task-specific evaluation, optimal routing of queries to models, personalization, and automated evaluation of model strengths and weaknesses. Data from Chatbot Arena suggest that P2L better captures the nuanced landscape of language model performance than the averaged leaderboard. Furthermore, our findings suggest that P2L's ability to produce prompt-specific evaluations follows a power law scaling similar to that observed in LLMs themselves. In January 2025, the router we trained based on this methodology achieved the \#1 spot in the Chatbot Arena leaderboard. Our code is available at this GitHub link: https://github.com/lmarena/p2l.

This paper surveys and organizes research works in a new paradigm in natural language processing, which we dub "prompt-based learning". Unlike traditional supervised learning, which trains a model to take in an input x and predict an output y as P(y|x), prompt-based learning is based on language models that model the probability of text directly. To use these models to perform prediction tasks, the original input x is modified using a template into a textual string prompt x' that has some unfilled slots, and then the language model is used to probabilistically fill the unfilled information to obtain a final string x, from which the final output y can be derived. This framework is powerful and attractive for a number of reasons: it allows the language model to be pre-trained on massive amounts of raw text, and by defining a new prompting function the model is able to perform few-shot or even zero-shot learning, adapting to new scenarios with few or no labeled data. In this paper we introduce the basics of this promising paradigm, describe a unified set of mathematical notations that can cover a wide variety of existing work, and organize existing work along several dimensions, e.g.the choice of pre-trained models, prompts, and tuning strategies. To make the field more accessible to interested beginners, we not only make a systematic review of existing works and a highly structured typology of prompt-based concepts, but also release other resources, e.g., a website http://pretrain.nlpedia.ai/ including constantly-updated survey, and paperlist.

Recent advances on instruction fine-tuning have led to the development of various prompting techniques for large language models, such as explicit reasoning steps. However, the success of techniques depends on various parameters, such as the task, language model, and context provided. Finding an effective prompt is, therefore, often a trial-and-error process. Most existing approaches to automatic prompting aim to optimize individual techniques instead of compositions of techniques and their dependence on the input. To fill this gap, we propose an adaptive prompting approach that predicts the optimal prompt composition ad-hoc for a given input. We apply our approach to social bias detection, a highly context-dependent task that requires semantic understanding. We evaluate it with three large language models on three datasets, comparing compositions to individual techniques and other baselines. The results underline the importance of finding an effective prompt composition. Our approach robustly ensures high detection performance, and is best in several settings. Moreover, first experiments on other tasks support its generalizability.

Large language models are highly sensitive to prompts, but this sensitivity is usually studied through task-relevant instructions, demonstrations, or reasoning cues. In this paper, we study a different form of prompt sensitivity: whether prompts that are semantically unrelated to the task can nevertheless steer model behavior. We call them spurious prompts and show their surprising efficacy. We also propose a simple black-box search procedure for discovering them. Across reasoning and question-answering benchmarks, using models ranging from 0.8B to 27B parameters and spanning three model families, we show that spurious prompts can improve performance, often matching or outperforming standard prompting baselines and task-aware prompt optimization. We further show that they can steer models toward unintended behaviors, such as repeatedly selecting the first answer option, producing incorrect answers, returning an even, prime or small number without explicitly instructing the model to do so. These findings reveal a new kind of prompt sensitivity: LLMs can be systematically steered by prompts that are unrelated to the task they are asked to solve. Our code is available at https://github.com/Batorskq/spurious

Prompt sensitivity, which refers to how strongly the output of a large language model (LLM) depends on the exact wording of its input prompt, raises concerns among users about the LLM's stability and reliability. In this work, we consider LLMs as multivariate functions and perform a first-order Taylor expansion, thereby analyzing the relationship between meaning-preserving prompts, their gradients, and the log probabilities of the model's next token. We derive an upper bound on the difference between log probabilities using the Cauchy-Schwarz inequality. We show that LLMs do not internally cluster similar inputs like smaller neural networks do, but instead disperse them. This dispersing behavior leads to an excessively high upper bound on the difference of log probabilities between two meaning-preserving prompts, making it difficult to effectively reduce to 0. In our analysis, we also show which types of meaning-preserving prompt variants are more likely to introduce prompt sensitivity risks in LLMs. In addition, we demonstrate that the upper bound is strongly correlated with an existing prompt sensitivity metric, PromptSensiScore. Moreover, by analyzing the logit variance, we find that prompt templates typically exert a greater influence on logits than the questions themselves. Overall, our results provide a general interpretation for why current LLMs can be highly sensitive to prompts with the same meaning, offering crucial evidence for understanding the prompt sensitivity of LLMs. Code for experiments is available at https://github.com/ku-nlp/Understanding_the_Prompt_Sensitivity.

Prompt engineering has emerged as an indispensable technique for extending the capabilities of large language models (LLMs) and vision-language models (VLMs). This approach leverages task-specific instructions, known as prompts, to enhance model efficacy without modifying the core model parameters. Rather than updating the model parameters, prompts allow seamless integration of pre-trained models into downstream tasks by eliciting desired model behaviors solely based on the given prompt. Prompts can be natural language instructions that provide context to guide the model or learned vector representations that activate relevant knowledge. This burgeoning field has enabled success across various applications, from question-answering to commonsense reasoning. However, there remains a lack of systematic organization and understanding of the diverse prompt engineering methods and techniques. This survey paper addresses the gap by providing a structured overview of recent advancements in prompt engineering, categorized by application area. For each prompting approach, we provide a summary detailing the prompting methodology, its applications, the models involved, and the datasets utilized. We also delve into the strengths and limitations of each approach and include a taxonomy diagram and table summarizing datasets, models, and critical points of each prompting technique. This systematic analysis enables a better understanding of this rapidly developing field and facilitates future research by illuminating open challenges and opportunities for prompt engineering.

Large Language Models (LLMs) have shown remarkable success, and their multimodal expansions (MLLMs) further unlock capabilities spanning images, videos, and other modalities beyond text. However, despite this shift, prompt optimization approaches, designed to reduce the burden of manual prompt crafting while maximizing performance, remain confined to text, ultimately limiting the full potential of MLLMs. Motivated by this gap, we introduce the new problem of multimodal prompt optimization, which expands the prior definition of prompt optimization to the multimodal space defined by the pairs of textual and non-textual prompts. To tackle this problem, we then propose the Multimodal Prompt Optimizer (MPO), a unified framework that not only performs the joint optimization of multimodal prompts through alignment-preserving updates but also guides the selection process of candidate prompts by leveraging earlier evaluations as priors in a Bayesian-based selection strategy. Through extensive experiments across diverse modalities that go beyond text, such as images, videos, and even molecules, we demonstrate that MPO outperforms leading text-only optimization methods, establishing multimodal prompt optimization as a crucial step to realizing the potential of MLLMs.

Large language models (LLMs) have demonstrated impressive capabilities across various tasks, but their performance is highly sensitive to the prompts utilized. This variability poses challenges for accurate assessment and user satisfaction. Current research frequently overlooks instance-level prompt variations and their implications on subjective evaluations. To address these shortcomings, we introduce ProSA, a framework designed to evaluate and comprehend prompt sensitivity in LLMs. ProSA incorporates a novel sensitivity metric, PromptSensiScore, and leverages decoding confidence to elucidate underlying mechanisms. Our extensive study, spanning multiple tasks, uncovers that prompt sensitivity fluctuates across datasets and models, with larger models exhibiting enhanced robustness. We observe that few-shot examples can alleviate this sensitivity issue, and subjective evaluations are also susceptible to prompt sensitivities, particularly in complex, reasoning-oriented tasks. Furthermore, our findings indicate that higher model confidence correlates with increased prompt robustness. We believe this work will serve as a helpful tool in studying prompt sensitivity of LLMs. The project is released at: https://github.com/open-compass/ProSA .

Large Language Models (LLMs) have demonstrated great capabilities in solving a wide range of tasks in a resource-efficient manner through prompting, which does not require task-specific training, but suffers from performance fluctuation when there are multiple prompt candidates. Previous works have introduced gradient-free probability-based prompt selection methods that aim to choose the optimal prompt among the candidates for a given task but fail to provide a comprehensive and fair comparison between each other. In this paper, we propose a unified framework to interpret and evaluate the existing probability-based prompt selection methods by performing extensive experiments on 13 common NLP tasks. We find that all existing methods can be unified into some variant of the method that maximizes the mutual information between the input and the corresponding model output (denoted as MI). Using the finding, we develop several variants of MI and increases the effectiveness of the best prompt selection method from 87.79% to 94.98%, measured as the ratio of the performance of the selected prompt to that of the optimal oracle prompt. Furthermore, we propose a novel calibration method called Calibration by Marginalization (CBM) that is orthogonal to existing methods and helps increase the prompt selection effectiveness of the best method by 99.44%. The code and datasets used in our work will be released at https://github.com/soheeyang/unified-prompt-selection.

Prompt-based learning has shown considerable promise in reformulating various downstream tasks as cloze problems by combining original input with a predetermined template. This approach demonstrates its effectiveness, especially in few-shot learning scenarios, where the model is trained on a scarce amount of data. Despite its successes, the limited templates and text in few-shot prompt-based learning scenarios leave significant room for performance improvement. Moreover, existing methods sometimes resort to model ensembles, which, while effective, could potentially hamper model efficiency due to increased computational demands. To address these issues, we introduce MixPro, an augmentation method designed to augment both the vanilla input text and the templates. We implement this through the token-level, the sentence-level, and the template-level Mixup strategies. The experimental results on five few-shot datasets show that MixPro outperforms other augmentation baselines, improving model performance by an average of 5.08% compared to before augmentation.

Prompts are the interface for eliciting the capabilities of large language models (LLMs). Understanding their structure and components is critical for analyzing LLM behavior and optimizing performance. However, the field lacks a comprehensive framework for systematic prompt analysis and understanding. We introduce PromptPrism, a linguistically-inspired taxonomy that enables prompt analysis across three hierarchical levels: functional structure, semantic component, and syntactic pattern. We show the practical utility of PromptPrism by applying it to three applications: (1) a taxonomy-guided prompt refinement approach that automatically improves prompt quality and enhances model performance across a range of tasks; (2) a multi-dimensional dataset profiling method that extracts and aggregates structural, semantic, and syntactic characteristics from prompt datasets, enabling comprehensive analysis of prompt distributions and patterns; (3) a controlled experimental framework for prompt sensitivity analysis by quantifying the impact of semantic reordering and delimiter modifications on LLM performance. Our experimental results validate the effectiveness of our taxonomy across these applications, demonstrating that PromptPrism provides a foundation for refining, profiling, and analyzing prompts.

Recent advancements in Text-to-Image (T2I) diffusion models have demonstrated impressive success in generating high-quality images with zero-shot generalization capabilities. Yet, current models struggle to closely adhere to prompt semantics, often misrepresenting or overlooking specific attributes. To address this, we propose a simple, training-free approach that modulates the guidance direction of diffusion models during inference. We first decompose the prompt semantics into a set of concepts, and monitor the guidance trajectory in relation to each concept. Our key observation is that deviations in model's adherence to prompt semantics are highly correlated with divergence of the guidance from one or more of these concepts. Based on this observation, we devise a technique to steer the guidance direction towards any concept from which the model diverges. Extensive experimentation validates that our method improves the semantic alignment of images generated by diffusion models in response to prompts. Project page is available at: https://korguy.github.io/

Recently, there has been an increasing interest in automated prompt optimization based on reinforcement learning (RL). This approach offers important advantages, such as generating interpretable prompts and being compatible with black-box foundation models. However, the substantial prompt space size poses challenges for RL-based methods, often leading to suboptimal policy convergence. This paper introduces MultiPrompter, a new framework that views prompt optimization as a cooperative game between prompters which take turns composing a prompt together. Our cooperative prompt optimization effectively reduces the problem size and helps prompters learn optimal prompts. We test our method on the text-to-image task and show its ability to generate higher-quality images than baselines.

While Large Language Models (LLMs) adapt well to downstream tasks after fine-tuning, this adaptability often compromises prompt robustness, as even minor prompt variations can significantly degrade performance. To address this, we propose Prompt-Agnostic Fine-Tuning(PAFT), a simple yet effective approach that dynamically adjusts prompts during fine-tuning. This encourages the model to learn underlying task principles rather than overfitting to specific prompt formulations. PAFT operates in two stages: First, a diverse set of meaningful, synthetic candidate prompts is constructed. Second, during fine-tuning, prompts are randomly sampled from this set to create dynamic training inputs. Extensive experiments across diverse datasets and LLMs demonstrate that models trained with PAFT exhibit strong robustness and generalization across a wide range of prompts, including unseen ones. This enhanced robustness improves both model performance and inference speed while maintaining training efficiency. Ablation studies further confirm the effectiveness of PAFT.

Recent soft prompt research has tried to improve reasoning by inserting trained vectors into LLM inputs, yet whether the gain comes from the learned content or from the act of injection itself has not been carefully separated. We study Random Soft Prompts (RSPs), which drop the training step entirely and append a freshly drawn sequence of random embedding vectors to the input. Each RSP vector is sampled from an isotropic Gaussian fitted to the entrywise mean and variance of the pretrained embedding table; the sequence carries no learned content, and yet reaches accuracy comparable to optimized soft prompts on math reasoning benchmarks in several settings. The mechanism unfolds in two stages: because attention has to absorb a never-seen-before random position, the distribution over the first few generated tokens flattens and reasoning trajectories branch, and as generation continues this influence dilutes naturally so the response commits to a single completion. We show that during inference RSPs lift early-stage token diversity and, combined with temperature sampling, widen Pass@N, the probability that at least one out of N attempts is correct. Beyond inference, we carry the same effect into DAPO training and demonstrate practical gains. Our contributions are: (i) RSP isolates the simplest form of soft prompt -- training-free, freshly resampled -- providing a unified lens for the structural effect of injection that variants otherwise differing in training and form all share; (ii) a theoretical and empirical validation of the underlying mechanism; and (iii) an extension from inference to training.

Recent advancements in vision-language models (VLMs), such as CLIP, have demonstrated substantial success in self-supervised representation learning for vision tasks. However, effectively adapting VLMs to downstream applications remains challenging, as their accuracy often depends on time-intensive and expertise-demanding prompt engineering, while full model fine-tuning is costly. This is particularly true for biomedical images, which, unlike natural images, typically suffer from limited annotated datasets, unintuitive image contrasts, and nuanced visual features. Recent prompt learning techniques, such as Context Optimization (CoOp) intend to tackle these issues, but still fall short in generalizability. Meanwhile, explorations in prompt learning for biomedical image analysis are still highly limited. In this work, we propose BiomedCoOp, a novel prompt learning framework that enables efficient adaptation of BiomedCLIP for accurate and highly generalizable few-shot biomedical image classification. Our approach achieves effective prompt context learning by leveraging semantic consistency with average prompt ensembles from Large Language Models (LLMs) and knowledge distillation with a statistics-based prompt selection strategy. We conducted comprehensive validation of our proposed framework on 11 medical datasets across 9 modalities and 10 organs against existing state-of-the-art methods, demonstrating significant improvements in both accuracy and generalizability. The code is publicly available at https://github.com/HealthX-Lab/BiomedCoOp.

Achieving precise alignment between user intent and generated visuals remains a central challenge in text-to-visual generation, as a single attempt often fails to produce the desired output. To handle this, prior approaches mainly scale the visual generation process (e.g., increasing sampling steps or seeds), but this quickly leads to a quality plateau. This limitation arises because the prompt, crucial for guiding generation, is kept fixed. To address this, we propose Prompt Redesign for Inference-time Scaling, coined PRIS, a framework that adaptively revises the prompt during inference in response to the scaled visual generations. The core idea of PRIS is to review the generated visuals, identify recurring failure patterns across visuals, and redesign the prompt accordingly before regenerating the visuals with the revised prompt. To provide precise alignment feedback for prompt revision, we introduce a new verifier, element-level factual correction, which evaluates the alignment between prompt attributes and generated visuals at a fine-grained level, achieving more accurate and interpretable assessments than holistic measures. Extensive experiments on both text-to-image and text-to-video benchmarks demonstrate the effectiveness of our approach, including a 15% gain on VBench 2.0. These results highlight that jointly scaling prompts and visuals is key to fully leveraging scaling laws at inference-time. Visualizations are available at the website: https://subin-kim-cv.github.io/PRIS.

Frontier reasoning models have exhibited incredible capabilities across a wide array of disciplines, driven by posttraining large language models (LLMs) with reinforcement learning (RL). However, despite the widespread success of this paradigm, much of the literature has been devoted to disentangling truly novel behaviors that emerge during RL but are not present in the base models. In our work, we approach this question from a different angle, instead asking whether comparable reasoning capabilites can be elicited from base models at inference time by pure sampling, without any additional training. Inspired by Markov chain Monte Carlo (MCMC) techniques for sampling from sharpened distributions, we propose a simple iterative sampling algorithm leveraging the base models' own likelihoods. Over different base models, we show that our algorithm offers substantial boosts in reasoning that nearly match and even outperform those from RL on a wide variety of single-shot tasks, including MATH500, HumanEval, and GPQA. Moreover, our sampler avoids the collapse in diversity over multiple samples that is characteristic of RL-posttraining. Crucially, our method does not require training, curated datasets, or a verifier, suggesting broad applicability beyond easily verifiable domains.

Prompting has shown impressive success in enabling large pretrained language models (LMs) to perform diverse NLP tasks, especially when only few downstream data are available. Automatically finding the optimal prompt for each task, however, is challenging. Most existing work resorts to tuning soft prompt (e.g., embeddings) which falls short of interpretability, reusability across LMs, and applicability when gradients are not accessible. Discrete prompt, on the other hand, is difficult to optimize, and is often created by "enumeration (e.g., paraphrasing)-then-selection" heuristics that do not explore the prompt space systematically. This paper proposes RLPrompt, an efficient discrete prompt optimization approach with reinforcement learning (RL). RLPrompt formulates a parameter-efficient policy network that generates the desired discrete prompt after training with reward. To overcome the complexity and stochasticity of reward signals by the large LM environment, we incorporate effective reward stabilization that substantially enhances the training efficiency. RLPrompt is flexibly applicable to different types of LMs, such as masked (e.g., BERT) and left-to-right models (e.g., GPTs), for both classification and generation tasks. Experiments on few-shot classification and unsupervised text style transfer show superior performance over a wide range of existing finetuning or prompting methods. Interestingly, the resulting optimized prompts are often ungrammatical gibberish text; and surprisingly, those gibberish prompts are transferrable between different LMs to retain significant performance, indicating LM prompting may not follow human language patterns.

Many recent prompting strategies for large language models (LLMs) query the model multiple times sequentially -- first to produce intermediate results and then the final answer. However, using these methods, both decoder and model are unaware of potential follow-up prompts, leading to disconnected and undesirably wordy intermediate responses. In this work, we address this issue by proposing prompt sketching, a new prompting paradigm in which an LLM does not only respond by completing a prompt, but by predicting values for multiple variables in a template. This way, sketching grants users more control over the generation process, e.g., by providing a reasoning framework via intermediate instructions, leading to better overall results. The key idea enabling sketching with existing, autoregressive models is to adapt the decoding procedure to also score follow-up instructions during text generation, thus optimizing overall template likelihood in inference. Our experiments show that in a zero-shot setting, prompt sketching outperforms existing, sequential prompting schemes such as direct asking or chain-of-thought on 7 out of 8 LLM benchmarking tasks, including state tracking, arithmetic reasoning, and general question answering. To facilitate future use, we release a number of generic, yet effective sketches applicable to many tasks, and an open source library called dclib, powering our sketch-aware decoders.

Recent research has shown that rationales, or step-by-step chains of thought, can be used to improve performance in multi-step reasoning tasks. We reconsider rationale-augmented prompting for few-shot in-context learning, where (input -> output) prompts are expanded to (input, rationale -> output) prompts. For rationale-augmented prompting we demonstrate how existing approaches, which rely on manual prompt engineering, are subject to sub-optimal rationales that may harm performance. To mitigate this brittleness, we propose a unified framework of rationale-augmented ensembles, where we identify rationale sampling in the output space as the key component to robustly improve performance. This framework is general and can easily be extended to common natural language processing tasks, even those that do not traditionally leverage intermediate steps, such as question answering, word sense disambiguation, and sentiment analysis. We demonstrate that rationale-augmented ensembles achieve more accurate and interpretable results than existing prompting approaches--including standard prompting without rationales and rationale-based chain-of-thought prompting--while simultaneously improving interpretability of model predictions through the associated rationales.

Curriculum learning plays a crucial role in enhancing the training efficiency of large language models (LLMs) on reasoning tasks. However, existing methods often fail to adequately account for variations in prompt difficulty or rely on simplistic filtering mechanisms to select prompt datasets within a narrow criterion range, resulting in significant computational waste. In this work, we approach the problem from the perspective of reinforcement learning gradient optimization, offering a systematic and theoretical investigation into how to improve the training efficiency of LLMs. We identify two key factors influencing training efficiency: the selection of training prompts and the allocation of rollout quantities across different prompts. Our theoretical analysis reveals that the sampling distribution of prompts dictates the convergence rate of gradient descent, while the allocation of the rollout quantity influences the consistency and stability of overall gradient updates. Based on these insights, we propose CurES, an efficient training method that accelerates convergence and employs Bayesian posterior estimation to minimize computational overhead. Experiments demonstrate that our CurES outperforms Group Relative Policy Optimization (GRPO) by +3.30 points and +4.82 points with 1.5B and 7B models, respectively. Additionally, CurES exhibits faster convergence compared to baselines, including GRPO.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly "general", i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in black-box prompt learning and Chain-of-Thought prompt tuning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown, opening the door to a cornucopia of possibilities in prompt optimization. We release all the codes in https://github.com/research4pan/Plum.

Prompt engineering has emerged as a powerful technique for optimizing large language models (LLMs) for specific applications, enabling faster prototyping and improved performance, and giving rise to the interest of the community in protecting proprietary system prompts. In this work, we explore a novel perspective on prompt privacy through the lens of membership inference. We develop Prompt Detective, a statistical method to reliably determine whether a given system prompt was used by a third-party language model. Our approach relies on a statistical test comparing the distributions of two groups of model outputs corresponding to different system prompts. Through extensive experiments with a variety of language models, we demonstrate the effectiveness of Prompt Detective for prompt membership inference. Our work reveals that even minor changes in system prompts manifest in distinct response distributions, enabling us to verify prompt usage with statistical significance.

Contrastively trained text-image models have the remarkable ability to perform zero-shot classification, that is, classifying previously unseen images into categories that the model has never been explicitly trained to identify. However, these zero-shot classifiers need prompt engineering to achieve high accuracy. Prompt engineering typically requires hand-crafting a set of prompts for individual downstream tasks. In this work, we aim to automate this prompt engineering and improve zero-shot accuracy through prompt ensembling. In particular, we ask "Given a large pool of prompts, can we automatically score the prompts and ensemble those that are most suitable for a particular downstream dataset, without needing access to labeled validation data?". We demonstrate that this is possible. In doing so, we identify several pathologies in a naive prompt scoring method where the score can be easily overconfident due to biases in pre-training and test data, and we propose a novel prompt scoring method that corrects for the biases. Using our proposed scoring method to create a weighted average prompt ensemble, our method outperforms equal average ensemble, as well as hand-crafted prompts, on ImageNet, 4 of its variants, and 11 fine-grained classification benchmarks, all while being fully automatic, optimization-free, and not requiring access to labeled validation data.

Prompt learning has emerged as an efficient alternative for fine-tuning foundational models, such as CLIP, for various downstream tasks. Conventionally trained using the task-specific objective, i.e., cross-entropy loss, prompts tend to overfit downstream data distributions and find it challenging to capture task-agnostic general features from the frozen CLIP. This leads to the loss of the model's original generalization capability. To address this issue, our work introduces a self-regularization framework for prompting called PromptSRC (Prompting with Self-regulating Constraints). PromptSRC guides the prompts to optimize for both task-specific and task-agnostic general representations using a three-pronged approach by: (a) regulating prompted representations via mutual agreement maximization with the frozen model, (b) regulating with self-ensemble of prompts over the training trajectory to encode their complementary strengths, and (c) regulating with textual diversity to mitigate sample diversity imbalance with the visual branch. To the best of our knowledge, this is the first regularization framework for prompt learning that avoids overfitting by jointly attending to pre-trained model features, the training trajectory during prompting, and the textual diversity. PromptSRC explicitly steers the prompts to learn a representation space that maximizes performance on downstream tasks without compromising CLIP generalization. We perform extensive experiments on 4 benchmarks where PromptSRC overall performs favorably well compared to the existing methods. Our code and pre-trained models are publicly available at: https://github.com/muzairkhattak/PromptSRC.

Autoregressive Large Language Models have transformed the landscape of Natural Language Processing. Pre-train and prompt paradigm has replaced the conventional approach of pre-training and fine-tuning for many downstream NLP tasks. This shift has been possible largely due to LLMs and innovative prompting techniques. LLMs have shown great promise for a variety of downstream tasks owing to their vast parameters and huge datasets that they are pre-trained on. However, in order to fully realize their potential, their outputs must be guided towards the desired outcomes. Prompting, in which a specific input or instruction is provided to guide the LLMs toward the intended output, has become a tool for achieving this goal. In this paper, we discuss the various prompting techniques that have been applied to fully harness the power of LLMs. We present a taxonomy of existing literature on prompting techniques and provide a concise survey based on this taxonomy. Further, we identify some open problems in the realm of prompting in autoregressive LLMs which could serve as a direction for future research.

Recent visual autoregressive (AR) models have shown promising capabilities in text-to-image generation, operating in a manner similar to large language models. While test-time computation scaling has brought remarkable success in enabling reasoning-enhanced outputs for challenging natural language tasks, its adaptation to visual AR models remains unexplored and poses unique challenges. Naively applying test-time scaling strategies such as Best-of-N can be suboptimal: they consume full-length computation on erroneous generation trajectories, while the raster-scan decoding scheme lacks a blueprint of the entire canvas, limiting scaling benefits as only a few prompt-aligned candidates are generated. To address these, we introduce GridAR, a test-time scaling framework designed to elicit the best possible results from visual AR models. GridAR employs a grid-partitioned progressive generation scheme in which multiple partial candidates for the same position are generated within a canvas, infeasible ones are pruned early, and viable ones are fixed as anchors to guide subsequent decoding. Coupled with this, we present a layout-specified prompt reformulation strategy that inspects partial views to infer a feasible layout for satisfying the prompt. The reformulated prompt then guides subsequent image generation to mitigate the blueprint deficiency. Together, GridAR achieves higher-quality results under limited test-time scaling: with N=4, it even outperforms Best-of-N (N=8) by 14.4% on T2I-CompBench++ while reducing cost by 25.6%. It also generalizes to autoregressive image editing, showing comparable edit quality and a 13.9% gain in semantic preservation on PIE-Bench over larger-N baselines.

Large Language Models (LLMs) have shown impressive performance as general purpose agents, but their abilities remain highly dependent on prompts which are hand written with onerous trial-and-error effort. We propose a simple and nonparametric solution to this problem, Automatic Prompt Optimization (APO), which is inspired by numerical gradient descent to automatically improve prompts, assuming access to training data and an LLM API. The algorithm uses minibatches of data to form natural language ``gradients'' that criticize the current prompt. The gradients are then ``propagated'' into the prompt by editing the prompt in the opposite semantic direction of the gradient. These gradient descent steps are guided by a beam search and bandit selection procedure which significantly improves algorithmic efficiency. Preliminary results across three benchmark NLP tasks and the novel problem of LLM jailbreak detection suggest that Automatic Prompt Optimization can outperform prior prompt editing techniques and improve an initial prompt's performance by up to 31\%, by using data to rewrite vague task descriptions into more precise annotation instructions.

This research explores the integration of large language models (LLMs) into scientific data assimilation, focusing on combustion science as a case study. Leveraging foundational models integrated with Retrieval-Augmented Generation (RAG) framework, the study introduces an approach to process diverse combustion research data, spanning experimental studies, simulations, and literature. The multifaceted nature of combustion research emphasizes the critical role of knowledge processing in navigating and extracting valuable information from a vast and diverse pool of sources. The developed approach minimizes computational and economic expenses while optimizing data privacy and accuracy. It incorporates prompt engineering and offline open-source LLMs, offering user autonomy in selecting base models. The study provides a thorough examination of text segmentation strategies, conducts comparative studies between LLMs, and explores various optimized prompts to demonstrate the effectiveness of the framework. By incorporating an external database, the framework outperforms a conventional LLM in generating accurate responses and constructing robust arguments. Additionally, the study delves into the investigation of optimized prompt templates for the purpose of efficient extraction of scientific literature. The research addresses concerns related to hallucinations and false research articles by introducing a custom workflow developed with a detection algorithm to filter out inaccuracies. Despite identified areas for improvement, the framework consistently delivers accurate domain-specific responses with minimal human oversight. The prompt-agnostic approach introduced holds promise for future deliberations. The study underscores the significance of integrating LLMs and knowledge processing techniques in scientific research, providing a foundation for advancements in data assimilation and utilization.

We introduce \`A-la-carte Prompt Tuning (APT), a transformer-based scheme to tune prompts on distinct data so that they can be arbitrarily composed at inference time. The individual prompts can be trained in isolation, possibly on different devices, at different times, and on different distributions or domains. Furthermore each prompt only contains information about the subset of data it was exposed to during training. During inference, models can be assembled based on arbitrary selections of data sources, which we call "\`a-la-carte learning". \`A-la-carte learning enables constructing bespoke models specific to each user's individual access rights and preferences. We can add or remove information from the model by simply adding or removing the corresponding prompts without retraining from scratch. We demonstrate that \`a-la-carte built models achieve accuracy within 5% of models trained on the union of the respective sources, with comparable cost in terms of training and inference time. For the continual learning benchmarks Split CIFAR-100 and CORe50, we achieve state-of-the-art performance.

The recent explosion in the capabilities of large language models has led to a wave of interest in how best to prompt a model to perform a given task. While it may be tempting to simply choose a prompt based on average performance on a validation set, this can lead to a deployment where unexpectedly poor responses are generated, especially for the worst-off users. To mitigate this prospect, we propose Prompt Risk Control, a lightweight framework for selecting a prompt based on rigorous upper bounds on families of informative risk measures. We offer methods for producing bounds on a diverse set of metrics, including quantities that measure worst-case responses and disparities in generation quality across the population of users. In addition, we extend the underlying statistical bounding techniques to accommodate the possibility of distribution shifts in deployment. Experiments on applications such as open-ended chat, medical question summarization, and code generation highlight how such a framework can foster responsible deployment by reducing the risk of the worst outcomes.

Recent prompt optimisation approaches use the generative nature of language models to produce prompts -- even rivaling the performance of human-curated prompts. In this paper, we demonstrate that randomly sampling tokens from the model vocabulary as ``separators'' can be as effective as language models for prompt-style text classification. Our experiments show that random separators are competitive baselines, having less than a 1% difference compared to previous self-optimisation methods and showing a 12% average relative improvement over strong human baselines across nine text classification tasks and eight language models. We further analyse this phenomenon in detail using three different random generation strategies, establishing that the language space is rich with potentially good separators, with a greater than 40% average chance that a randomly drawn separator performs better than human-curated separators. These observations challenge the common assumption that an effective prompt should be human readable or task relevant and establish a strong baseline for prompt optimisation research.

Reinforcement learning (RL) is a central approach for improving reasoning capabilities in large language models (LLMs), where training efficiency depends critically on how problems are sampled during optimization. Existing adaptive curriculum learning methods typically prioritize prompts of intermediate difficulty, treating problem selection as a standard bandit problem with independent arms and overlooking the structured, heterogeneous nature of the task space. In this work, we frame problem sampling as a manifold-structured bandit problem with endogenous non-stationarity: problems are related through the model's latent representation space, and sampling decisions can steer how learning signals evolve across that space. To operationalize this perspective, we introduce Bayesian Manifold Curriculum (BMC), a structure-aware framework that organizes problems into a hierarchical task tree and applies Bayesian learning to guide sampling. Empirically, we find that different sampling strategies induce non-trivial tradeoffs between productivity (learning signal), diversity (coverage of the task manifold), and utility (evaluation relevance). These results show that prioritizing difficulty alone is insufficient for strong downstream performance, highlighting the importance of incorporating structure and type-awareness into problem sampling.

Post-training alignment often reduces LLM diversity, leading to a phenomenon known as mode collapse. Unlike prior work that attributes this effect to algorithmic limitations, we identify a fundamental, pervasive data-level driver: typicality bias in preference data, whereby annotators systematically favor familiar text as a result of well-established findings in cognitive psychology. We formalize this bias theoretically, verify it on preference datasets empirically, and show that it plays a central role in mode collapse. Motivated by this analysis, we introduce Verbalized Sampling, a simple, training-free prompting strategy to circumvent mode collapse. VS prompts the model to verbalize a probability distribution over a set of responses (e.g., ``Generate 5 jokes about coffee and their corresponding probabilities''). Comprehensive experiments show that VS significantly improves performance across creative writing (poems, stories, jokes), dialogue simulation, open-ended QA, and synthetic data generation, without sacrificing factual accuracy and safety. For instance, in creative writing, VS increases diversity by 1.6-2.1x over direct prompting. We further observe an emergent trend that more capable models benefit more from VS. In sum, our work provides a new data-centric perspective on mode collapse and a practical inference-time remedy that helps unlock pre-trained generative diversity.

We propose a general-purpose approach for improving the ability of Large Language Models (LLMs) to intelligently and adaptively gather information from a user or other external source using the framework of sequential Bayesian experimental design (BED). This enables LLMs to act as effective multi-turn conversational agents and interactively interface with external environments. Our approach, which we call BED-LLM (Bayesian Experimental Design with Large Language Models), is based on iteratively choosing questions or queries that maximize the expected information gain (EIG) about the task of interest given the responses gathered previously. We show how this EIG can be formulated in a principled way using a probabilistic model derived from the LLM's belief distribution and provide detailed insights into key decisions in its construction. Further key to the success of BED-LLM are a number of specific innovations, such as a carefully designed estimator for the EIG, not solely relying on in-context updates for conditioning on previous responses, and a targeted strategy for proposing candidate queries. We find that BED-LLM achieves substantial gains in performance across a wide range of tests based on the 20-questions game and using the LLM to actively infer user preferences, compared to direct prompting of the LLM and other adaptive design strategies.

Vision-Language Models (VLMs), such as CLIP, have significantly advanced zero-shot image recognition. However, their performance remains limited by suboptimal prompt engineering and poor adaptability to target classes. While recent methods attempt to improve prompts through diverse class descriptions, they often rely on heuristic designs, lack versatility, and are vulnerable to outlier prompts. This paper enhances prompt by incorporating class-specific concepts. By treating concepts as latent variables, we rethink zero-shot image classification from a Bayesian perspective, casting prediction as marginalization over the concept space, where each concept is weighted by a prior and a test-image conditioned likelihood. This formulation underscores the importance of both a well-structured concept proposal distribution and the refinement of concept priors. To construct an expressive and efficient proposal distribution, we introduce a multi-stage concept synthesis pipeline driven by LLMs to generate discriminative and compositional concepts, followed by a Determinantal Point Process to enforce diversity. To mitigate the influence of outlier concepts, we propose a training-free, adaptive soft-trim likelihood, which attenuates their impact in a single forward pass. We further provide robustness guarantees and derive multi-class excess risk bounds for our framework. Extensive experiments demonstrate that our method consistently outperforms state-of-the-art approaches, validating its effectiveness in zero-shot image classification. Our code is available at https://github.com/less-and-less-bugs/CGBC.

Most popular benchmarks for comparing LLMs rely on a limited set of prompt templates, which may not fully capture the LLMs' abilities and can affect the reproducibility of results on leaderboards. Many recent works empirically verify prompt sensitivity and advocate for changes in LLM evaluation. In this paper, we consider the problem of estimating the performance distribution across many prompt variants instead of finding a single prompt to evaluate with. We introduce PromptEval, a method for estimating performance across a large set of prompts borrowing strength across prompts and examples to produce accurate estimates under practical evaluation budgets. The resulting distribution can be used to obtain performance quantiles to construct various robust performance metrics (e.g., top 95% quantile or median). We prove that PromptEval consistently estimates the performance distribution and demonstrate its efficacy empirically on three prominent LLM benchmarks: MMLU, BIG-bench Hard, and LMentry. For example, PromptEval can accurately estimate performance quantiles across 100 prompt templates on MMLU with a budget equivalent to two single-prompt evaluations. Our code and data can be found at https://github.com/felipemaiapolo/prompt-eval.

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.

We propose a novel prompt design paradigm that challenges conventional wisdom in large language model (LLM) prompting. While conventional wisdom prioritizes well-crafted instructions and demonstrations for in-context learning (ICL), we show that pruning random demonstrations into seemingly incoherent "gibberish" can remarkably improve performance across diverse tasks. Notably, the "gibberish" always matches or surpasses state-of-the-art automatic prompt optimization techniques, achieving substantial gains regardless of LLM alignment. Nevertheless, discovering an effective pruning strategy is non-trivial, as existing attribution methods and prompt compression algorithms fail to deliver robust results, let alone human intuition. In terms of this, we propose a self-discover prompt optimization framework, PromptQuine, an evolutionary search framework that automatically searches for the pruning strategy by itself using only low-data regimes. Much like the emergent complexity in nature--such as symbiosis and self-organization--arising in response to resource constraints, our framework evolves and refines unconventional yet highly effective prompts by leveraging only the tokens present within the context. We demonstrate its effectiveness across classification, multi-choice question answering, generation and math reasoning tasks across LLMs, while achieving decent runtime efficiency. We hope our findings can guide mechanistic studies on in-context learning, and provide a call to action, to pave the way for more open-ended search algorithms for more effective LLM prompting.

We present the Bayesian Linguistic Forecaster (BLF), an agentic system for binary forecasting that achieves state-of-the-art performance on the ForecastBench benchmark. The system is built on three ideas. (1) Linguistic belief state: a semi-structured representation combining numerical probability estimates with natural-language evidence summaries, updated by the LLM at each step of an iterative tool-use loop. This contrasts with the common approach of appending all retrieved evidence to an ever-growing, unstructured context. (2) Hierarchical multi-trial aggregation: running K independent trials and combining them using logit-space averaging shrinkage with a data-dependent prior. (3) Hierarchical calibration: Platt scaling with a hierarchical prior, which avoids over-shrinking extreme predictions for sources with skewed base rates. On 400 questions from the ForecastBench leaderboard, BLF outperforms all the top public methods, including Cassi, GPT-5, Grok~4.20, and Foresight-32B. Careful ablation studies, using mixed effects analysis to control for question variability (which accounts for 62\% of the variance in performance), reveals that all 3 components contribute to the overall gains, but some components matter more than others, depending on the base LLM, and the setting (e.g.\ with or without a crowd prior). All our experiments are based on a robust back-testing framework which we develop, which has a leakage rate below 1.5\%, and may be of independent interest.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

Large language models (LLMs) have demonstrated the capacity to improve summary quality by mirroring a human-like iterative process of critique and refinement starting from the initial draft. Two strategies are designed to perform this iterative process: Prompt Chaining and Stepwise Prompt. Prompt chaining orchestrates the drafting, critiquing, and refining phases through a series of three discrete prompts, while Stepwise prompt integrates these phases within a single prompt. However, the relative effectiveness of the two methods has not been extensively studied. This paper is dedicated to examining and comparing these two methods in the context of text summarization to ascertain which method stands out as the most effective. Experimental results show that the prompt chaining method can produce a more favorable outcome. This might be because stepwise prompt might produce a simulated refinement process according to our various experiments. Since refinement is adaptable to diverse tasks, our conclusions have the potential to be extrapolated to other applications, thereby offering insights that may contribute to the broader development of LLMs.

Leveraging human preferences for steering the behavior of Large Language Models (LLMs) has demonstrated notable success in recent years. Nonetheless, data selection and labeling are still a bottleneck for these systems, particularly at large scale. Hence, selecting the most informative points for acquiring human feedback may considerably reduce the cost of preference labeling and unleash the further development of LLMs. Bayesian Active Learning provides a principled framework for addressing this challenge and has demonstrated remarkable success in diverse settings. However, previous attempts to employ it for Preference Modeling did not meet such expectations. In this work, we identify that naive epistemic uncertainty estimation leads to the acquisition of redundant samples. We address this by proposing the Bayesian Active Learner for Preference Modeling (BAL-PM), a novel stochastic acquisition policy that not only targets points of high epistemic uncertainty according to the preference model but also seeks to maximize the entropy of the acquired prompt distribution in the feature space spanned by the employed LLM. Notably, our experiments demonstrate that BAL-PM requires 33% to 68% fewer preference labels in two popular human preference datasets and exceeds previous stochastic Bayesian acquisition policies.

We introduce Prompt Curriculum Learning (PCL), a lightweight reinforcement learning (RL) algorithm that selects intermediate-difficulty prompts using a learned value model to post-train language models. Since post-training LLMs via RL remains sensitive to batching and prompt selection strategies, we first conduct a series of systematic experiments where we (1) determine the optimal training batch size that balances generation efficiency and gradient quality and (2) establish the importance of focusing on prompts of intermediate difficulty for the policy. We build upon these results to design PCL, which identifies prompts of intermediate difficulty for the current policy in an on-policy manner by using a value model that is concurrently updated based on the current policy. By focusing on informative prompts that yield high effective ratios, PCL achieves either the highest performance or requires significantly less time to reach comparable performance to its counterparts. Compared to rollout-based filtering methods, PCL avoids costly rollouts and achieves 12.1times and 16.9times faster speed on identifying intermediate-difficulty prompts when training on MATH and DeepScaleR, respectively. We further demonstrate that our value model accurately predicts prompt difficulty and allows PCL to focus on progressively more challenging prompts during RL. Our results present a new methodology that delivers improved tradeoff between upper-bound performance and efficiency for reasoning-focused RL.

Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider approximate Bayesian neural networks in a Thompson Sampling framework. To understand the impact of using an approximate posterior on Thompson Sampling, we benchmark well-established and recently developed methods for approximate posterior sampling combined with Thompson Sampling over a series of contextual bandit problems. We found that many approaches that have been successful in the supervised learning setting underperformed in the sequential decision-making scenario. In particular, we highlight the challenge of adapting slowly converging uncertainty estimates to the online setting.

Prompt optimization (PO) offers a practical alternative to fine-tuning large language models (LLMs), enabling performance improvements without altering model weights. Existing methods typically rely on advanced, large-scale LLMs like GPT-4 to generate optimized prompts. However, due to limited downward compatibility, verbose, instruction-heavy prompts from advanced LLMs can overwhelm lightweight inference models and degrade response quality. In this work, we rethink prompt optimization through the lens of interpretable design. We first identify a set of model-agnostic prompt quality merits and empirically validate their effectiveness in enhancing prompt and response quality. We then introduce MePO, a merit-guided, lightweight, and locally deployable prompt optimizer trained on our preference dataset built from merit-aligned prompts generated by a lightweight LLM. Unlike prior work, MePO avoids online optimization reliance, reduces cost and privacy concerns, and, by learning clear, interpretable merits, generalizes effectively to both large-scale and lightweight inference models. Experiments demonstrate that MePO achieves better results across diverse tasks and model types, offering a scalable and robust solution for real-world deployment. Our model and dataset are available at: https://github.com/MidiyaZhu/MePO

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference.

Chain-of-thought (CoT) reasoning in large language models (LLMs) can be formalized as a latent variable problem, where the model needs to generate intermediate reasoning steps. While prior approaches such as iterative reward-ranked fine-tuning (RAFT) have relied on such formulations, they typically apply uniform inference budgets across prompts, which fails to account for variability in difficulty and convergence behavior. This work identifies the main bottleneck in CoT training as inefficient stochastic gradient estimation due to static sampling strategies. We propose GVM-RAFT, a prompt-specific Dynamic Sample Allocation Strategy designed to minimize stochastic gradient variance under a computational budget constraint. The method dynamically allocates computational resources by monitoring prompt acceptance rates and stochastic gradient norms, ensuring that the resulting gradient variance is minimized. Our theoretical analysis shows that the proposed dynamic sampling strategy leads to accelerated convergence guarantees under suitable conditions. Experiments on mathematical reasoning show that GVM-RAFT achieves a 2-4x speedup and considerable accuracy improvements over vanilla RAFT. The proposed dynamic sampling strategy is general and can be incorporated into other reinforcement learning algorithms, such as GRPO, leading to similar improvements in convergence and test accuracy. Our code is available at https://github.com/RLHFlow/GVM.

Recent advancements in text-to-image (T2I) diffusion models have demonstrated remarkable capabilities in generating high-fidelity images. However, these models often struggle to faithfully render complex user prompts, particularly in aspects like attribute binding, negation, and compositional relationships. This leads to a significant mismatch between user intent and the generated output. To address this challenge, we introduce PromptEnhancer, a novel and universal prompt rewriting framework that enhances any pretrained T2I model without requiring modifications to its weights. Unlike prior methods that rely on model-specific fine-tuning or implicit reward signals like image-reward scores, our framework decouples the rewriter from the generator. We achieve this by training a Chain-of-Thought (CoT) rewriter through reinforcement learning, guided by a dedicated reward model we term the AlignEvaluator. The AlignEvaluator is trained to provide explicit and fine-grained feedback based on a systematic taxonomy of 24 key points, which are derived from a comprehensive analysis of common T2I failure modes. By optimizing the CoT rewriter to maximize the reward from our AlignEvaluator, our framework learns to generate prompts that are more precisely interpreted by T2I models. Extensive experiments on the HunyuanImage 2.1 model demonstrate that PromptEnhancer significantly improves image-text alignment across a wide range of semantic and compositional challenges. Furthermore, we introduce a new, high-quality human preference benchmark to facilitate future research in this direction.

Diffusion models are the state of the art in text-to-image generation, but their perceptual variability remains understudied. In this paper, we examine how prompts affect image variability in black-box diffusion-based models. We propose W1KP, a human-calibrated measure of variability in a set of images, bootstrapped from existing image-pair perceptual distances. Current datasets do not cover recent diffusion models, thus we curate three test sets for evaluation. Our best perceptual distance outperforms nine baselines by up to 18 points in accuracy, and our calibration matches graded human judgements 78% of the time. Using W1KP, we study prompt reusability and show that Imagen prompts can be reused for 10-50 random seeds before new images become too similar to already generated images, while Stable Diffusion XL and DALL-E 3 can be reused 50-200 times. Lastly, we analyze 56 linguistic features of real prompts, finding that the prompt's length, CLIP embedding norm, concreteness, and word senses influence variability most. As far as we are aware, we are the first to analyze diffusion variability from a visuolinguistic perspective. Our project page is at http://w1kp.com.

Large language models (LLMs) have played a fundamental role in various natural language processing tasks with powerful prompt techniques. However, in real-world applications, there are often similar prompt components for repeated queries, which causes significant computational burdens during inference. Existing prompt compression and direct fine-tuning methods aim to tackle these challenges, yet they frequently struggle to strike an optimal balance between cost-efficiency and performance effectiveness, especially in complex tasks such as NL2Code. In this paper, we propose a novel method namely PromptIntern to internalize the prompt knowledge into model parameters via progressive fine-tuning. Our method enables LLMs to emulate the human learning process for a new task, where detailed templates and examples in a prompt are gradually internalized and phased out progressively as the model grows accustomed to the task. Extensive experiments demonstrate that our method reduces inference tokens over 90%, speedups inference by 4.2 times, and saves 88.3% monetary cost.

LLM agents increasingly rely on external inference conditions: prompts, tools, memory, SOPs, skills, and harness feedback. These assets can improve task execution without changing model weights, but they are often revised by heuristic reflection or by reusing observed successes and failures as if counts alone were reliable belief. We introduce Bayesian-Agent, a native and cross-harness framework that treats reusable skills and SOPs as hypotheses about whether a frozen model will succeed under a particular prompt, context, and harness environment. Bayesian-Agent records verified trajectory evidence, maintains a feature-conditioned categorical posterior over each skill, and maps posterior state into inspectable actions such as patch, split, compress, retire, and explore. Model-facing prompts receive executable guardrails and failure-mode patches, while posterior summaries remain available for audit. With deepseek-v4-flash, incremental repair improves SOP-Bench from 80\% to 95\%, Lifelong AgentBench from 90\% to 100\%, and RealFin-Bench from 45\% to 65\%. We further evaluate Bayesian-Agent's native backend and optional GenericAgent, mini-swe-agent, and Claude Code backends. The results include positive, negative, saturated, and case-study settings, suggesting that agent skill evolution is best viewed as posterior-guided harness optimization rather than uncalibrated prompt accumulation. The source code is available at https://github.com/DataArcTech/Bayesian-Agent.

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon H with S states, and A actions. The performance of an agent is measured by the regret after interacting with the environment for T episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in H, S, A, and T per state-action pair. For OPSRL we guarantee a high-probability regret bound of order at most mathcal{O}(H^3SAT) ignoring polylog(HSAT) terms. The key novel technical ingredient is a new sharp anti-concentration inequality for linear forms which may be of independent interest. Specifically, we extend the normal approximation-based lower bound for Beta distributions by Alfers and Dinges [1984] to Dirichlet distributions. Our bound matches the lower bound of order Ω(H^3SAT), thereby answering the open problems raised by Agrawal and Jia [2017b] for the episodic setting.

In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

Large language models (LLMs), while transformative for NLP, come with significant computational demands, underlining the need for efficient, training-free compression. Notably, the reliability of perplexity as a benchmark for compressed model efficacy is in question, as our tests using LLaMA-7B and OPT-6.7b reveal a significant performance drop in several realistic downstream tasks, underscoring the disparity between perplexity as a performance indicator and real-world performance. Investigation into the trade-off between resource-intensive post-compression re-training highlights the prospect of prompt-driven recovery as a lightweight adaption tool. However, existing studies, confined mainly to perplexity evaluations and simple tasks, fail to offer unequivocal confidence in the scalability and generalizability of prompting. We tackle this uncertainty in two key ways. First, we uncover the vulnerability of naive prompts in LLM compression as an over-reliance on a singular prompt per input. In response, we propose inference-time dynamic prompting (IDP), a mechanism that autonomously chooses from a set of curated prompts based on the context of each individual input. Second, we delve into a scientific understanding of why ``prompting might be all you need post-LLM compression". Our findings suggest that compression doesn't irretrievably erase LLM model knowledge but displace it, necessitating a new inference path. IDP effectively redirects this path, enabling the model to tap into its inherent yet displaced knowledge and thereby recover performance. Empirical tests affirm the value of IDP, demonstrating an average performance improvement of 1.24% across nine varied tasks spanning multiple knowledge domains.

In any ranking system, the retrieval model outputs a single score for a document based on its belief on how relevant it is to a given search query. While retrieval models have continued to improve with the introduction of increasingly complex architectures, few works have investigated a retrieval model's belief in the score beyond the scope of a single value. We argue that capturing the model's uncertainty with respect to its own scoring of a document is a critical aspect of retrieval that allows for greater use of current models across new document distributions, collections, or even improving effectiveness for down-stream tasks. In this paper, we address this problem via an efficient Bayesian framework for retrieval models which captures the model's belief in the relevance score through a stochastic process while adding only negligible computational overhead. We evaluate this belief via a ranking based calibration metric showing that our approximate Bayesian framework significantly improves a retrieval model's ranking effectiveness through a risk aware reranking as well as its confidence calibration. Lastly, we demonstrate that this additional uncertainty information is actionable and reliable on down-stream tasks represented via cutoff prediction.

Prompt-based learning has been an effective paradigm for large pretrained language models (LLM), enabling few-shot or even zero-shot learning. Black-box prompt search has received growing interest recently for its distinctive properties of gradient-free optimization, proven particularly useful and powerful for model-as-a-service usage. However, the discrete nature and the complexity of combinatorial optimization hinder the efficiency of modern black-box approaches. Despite extensive research on search algorithms, the crucial aspect of search space design and optimization has been largely overlooked. In this paper, we first conduct a sensitivity analysis by prompting LLM, revealing that only a small number of tokens exert a disproportionate amount of influence on LLM predictions. Leveraging this insight, we propose the Clustering and Pruning for Efficient Black-box Prompt Search (ClaPS), a simple black-box search method that first clusters and prunes the search space to focus exclusively on influential prompt tokens. By employing even simple search methods within the pruned search space, ClaPS achieves state-of-the-art performance across various tasks and LLMs, surpassing the performance of complex approaches while significantly reducing search costs. Our findings underscore the critical role of search space design and optimization in enhancing both the usefulness and the efficiency of black-box prompt-based learning.

This paper introduces Bayesian uncertainty modeling using Stochastic Weight Averaging-Gaussian (SWAG) in Natural Language Understanding (NLU) tasks. We apply the approach to standard tasks in natural language inference (NLI) and demonstrate the effectiveness of the method in terms of prediction accuracy and correlation with human annotation disagreements. We argue that the uncertainty representations in SWAG better reflect subjective interpretation and the natural variation that is also present in human language understanding. The results reveal the importance of uncertainty modeling, an often neglected aspect of neural language modeling, in NLU tasks.

The alignment of large language models (LLMs) with human values is critical as these models become increasingly integrated into various societal and decision-making processes. Traditional methods, such as reinforcement learning from human feedback (RLHF), achieve alignment by fine-tuning model parameters, but these approaches are often computationally expensive and impractical when models are frozen or inaccessible for parameter modification. In contrast, prompt optimization is a viable alternative to RLHF for LLM alignment. While the existing literature has shown empirical promise of prompt optimization, its theoretical underpinning remains under-explored. We address this gap by formulating prompt optimization as an optimization problem and try to provide theoretical insights into the optimality of such a framework. To analyze the performance of the prompt optimization, we study theoretical suboptimality bounds and provide insights in terms of how prompt optimization depends upon the given prompter and target model. We also provide empirical validation through experiments on various datasets, demonstrating that prompt optimization can effectively align LLMs, even when parameter fine-tuning is not feasible.

With growing capabilities of large language models, prompting them has become the dominant way to access them. This has motivated the development of strategies for automatically selecting effective language prompts. In this paper, we introduce prompt flatness, a new metric to quantify the expected utility of a language prompt. This metric is inspired by flatness regularization in statistical learning that quantifies the robustness of the model towards its parameter perturbations. We provide theoretical foundations for this metric and its relationship with other prompt selection metrics, providing a comprehensive understanding of existing methods. Empirically, we show that combining prompt flatness with existing metrics improves both performance and sample efficiency. Our metric outperforms the previous prompt selection metrics with an average increase of 5% in accuracy and 10% in Pearson correlation across 6 classification benchmarks.

Prompting is a mainstream paradigm for adapting large language models to specific natural language processing tasks without modifying internal parameters. Therefore, detailed supplementary knowledge needs to be integrated into external prompts, which inevitably brings extra human efforts and computational burdens for practical applications. As an effective solution to mitigate resource consumption, Efficient Prompting Methods have attracted a wide range of attention. We provide mathematical expressions at a high level to deeply discuss Automatic Prompt Engineering for different prompt components and Prompt Compression in continuous and discrete spaces. Finally, we highlight promising future directions to inspire researchers interested in this field.

We consider the problem of recommending relevant content to users of an internet platform in the form of lists of items, called slates. We introduce a variational Bayesian Recurrent Neural Net recommender system that acts on time series of interactions between the internet platform and the user, and which scales to real world industrial situations. The recommender system is tested both online on real users, and on an offline dataset collected from a Norwegian web-based marketplace, FINN.no, that is made public for research. This is one of the first publicly available datasets which includes all the slates that are presented to users as well as which items (if any) in the slates were clicked on. Such a data set allows us to move beyond the common assumption that implicitly assumes that users are considering all possible items at each interaction. Instead we build our likelihood using the items that are actually in the slate, and evaluate the strengths and weaknesses of both approaches theoretically and in experiments. We also introduce a hierarchical prior for the item parameters based on group memberships. Both item parameters and user preferences are learned probabilistically. Furthermore, we combine our model with bandit strategies to ensure learning, and introduce `in-slate Thompson Sampling' which makes use of the slates to maximise explorative opportunities. We show experimentally that explorative recommender strategies perform on par or above their greedy counterparts. Even without making use of exploration to learn more effectively, click rates increase simply because of improved diversity in the recommended slates.

Large Language Models (LLMs) have shown remarkable capabilities, with optimizing their input prompts playing a pivotal role in maximizing their performance. However, while LLM prompts consist of both the task-agnostic system prompts and task-specific user prompts, existing work on prompt optimization has focused on user prompts specific to individual queries or tasks, and largely overlooked the system prompt that is, once optimized, applicable across different tasks and domains. Motivated by this, we introduce the novel problem of bilevel system prompt optimization, whose objective is to design system prompts that are robust to diverse user prompts and transferable to unseen tasks. To tackle this problem, we then propose a meta-learning framework, which meta-learns the system prompt by optimizing it over various user prompts across multiple datasets, while simultaneously updating the user prompts in an iterative manner to ensure synergy between them. We conduct experiments on 14 unseen datasets spanning 5 different domains, on which we show that our approach produces system prompts that generalize effectively to diverse user prompts. Also, our findings reveal that the optimized system prompt enables rapid adaptation even to unseen tasks, requiring fewer optimization steps for test-time user prompts while achieving improved performance.

In many real-world applications, users rely on natural language instructions to guide large language models (LLMs) across a wide range of tasks. These instructions are often complex, diverse, and subject to frequent change. However, LLMs do not always attend to these instructions reliably, and users lack simple mechanisms to emphasize their importance beyond modifying prompt wording or structure. To address this, we present an inference-time method that enables users to emphasize specific parts of their prompt by steering the model's attention toward them, aligning the model's perceived importance of different prompt tokens with user intent. Unlike prior approaches that are limited to static instructions, require significant offline profiling, or rely on fixed biases, we dynamically update the proportion of model attention given to the user-specified parts--ensuring improved instruction following without performance degradation. We demonstrate that our approach improves instruction following across a variety of tasks involving multiple instructions and generalizes across models of varying scales.

Vision-language models (VLMs) have demonstrated remarkable zero-shot performance across various classification tasks. Nonetheless, their reliance on hand-crafted text prompts for each task hinders efficient adaptation to new tasks. While prompt learning offers a promising solution, most studies focus on maximizing the utilization of given few-shot labeled datasets, often overlooking the potential of careful data selection strategies, which enable higher accuracy with fewer labeled data. This motivates us to study a budget-efficient active prompt learning framework. Specifically, we introduce a class-guided clustering that leverages the pre-trained image and text encoders of VLMs, thereby enabling our cluster-balanced acquisition function from the initial round of active learning. Furthermore, considering the substantial class-wise variance in confidence exhibited by VLMs, we propose a budget-saving selective querying based on adaptive class-wise thresholds. Extensive experiments in active learning scenarios across nine datasets demonstrate that our method outperforms existing baselines.

The basic question-answering format of large language models involves inputting a prompt and receiving a response, and the quality of the prompt directly impacts the effectiveness of the response. Automated Prompt Optimization (APO) aims to break free from the cognitive biases of manually designed prompts and explores a broader design space for prompts. However, existing APO methods suffer from limited flexibility of fixed templates and inefficient search in prompt spaces as key issues. To this end, we propose a Multi-Agent framework Incorporating Socratic guidance (MARS), which utilizes multi-agent fusion technology for automatic planning, with gradual continuous optimization and evaluation. Specifically, MARS comprises seven agents, each with distinct functionalities, which autonomously use the Planner to devise an optimization path that ensures flexibility. Additionally, it employs a Teacher-Critic-Student Socratic dialogue pattern to iteratively optimize the prompts while conducting effective search. We conduct extensive experiments on various datasets to validate the effectiveness of our method, and perform additional analytical experiments to assess the model's advancement as well as the interpretability.

Large Language Models (LLMs) can perform various natural language processing tasks with suitable instruction prompts. However, designing effective prompts manually is challenging and time-consuming. Existing methods for automatic prompt optimization either lack flexibility or efficiency. In this paper, we propose an effective approach to automatically select the optimal prompt for a given input from a finite set of synthetic candidate prompts. Our approach consists of three steps: (1) clustering the training data and generating candidate prompts for each cluster using an LLM-based prompt generator; (2) synthesizing a dataset of input-prompt-output tuples for training a prompt evaluator to rank the prompts based on their relevance to the input; (3) using the prompt evaluator to select the best prompt for a new input at test time. Our approach balances prompt generality-specificity and eliminates the need for resource-intensive training and inference. It demonstrates competitive performance on zero-shot question-answering datasets: GSM8K, MultiArith, and AQuA.

Large language models (LLMs) have demonstrated remarkable performances in various tasks. However, the performance of LLMs heavily depends on the input prompt, which has given rise to a number of recent works on prompt optimization. However, previous works often require the availability of a numeric score to assess the quality of every prompt. Unfortunately, when a human user interacts with a black-box LLM, attaining such a score is often infeasible and unreliable. Instead, it is usually significantly easier and more reliable to obtain preference feedback from a human user, i.e., showing the user the responses generated from a pair of prompts and asking the user which one is preferred. Therefore, in this paper, we study the problem of prompt optimization with human feedback (POHF), in which we aim to optimize the prompt for a black-box LLM using only human preference feedback. Drawing inspiration from dueling bandits, we design a theoretically principled strategy to select a pair of prompts to query for preference feedback in every iteration, and hence introduce our algorithm named automated POHF (APOHF). We apply our APOHF algorithm to various tasks, including optimizing user instructions, prompt optimization for text-to-image generative models, and response optimization with human feedback (i.e., further refining the response using a variant of our APOHF). The results demonstrate that our APOHF can efficiently find a good prompt using a small number of preference feedback instances. Our code can be found at https://github.com/xqlin98/APOHF.

Multi-armed bandits a simple but very powerful framework for algorithms that make decisions over time under uncertainty. An enormous body of work has accumulated over the years, covered in several books and surveys. This book provides a more introductory, textbook-like treatment of the subject. Each chapter tackles a particular line of work, providing a self-contained, teachable technical introduction and a brief review of the further developments; many of the chapters conclude with exercises. The book is structured as follows. The first four chapters are on IID rewards, from the basic model to impossibility results to Bayesian priors to Lipschitz rewards. The next three chapters cover adversarial rewards, from the full-feedback version to adversarial bandits to extensions with linear rewards and combinatorially structured actions. Chapter 8 is on contextual bandits, a middle ground between IID and adversarial bandits in which the change in reward distributions is completely explained by observable contexts. The last three chapters cover connections to economics, from learning in repeated games to bandits with supply/budget constraints to exploration in the presence of incentives. The appendix provides sufficient background on concentration and KL-divergence. The chapters on "bandits with similarity information", "bandits with knapsacks" and "bandits and agents" can also be consumed as standalone surveys on the respective topics.

Neural Temporal Point Processes (TPPs) are the prevalent paradigm for modeling continuous-time event sequences, such as user activities on the web and financial transactions. In real-world applications, event data is typically received in a streaming manner, where the distribution of patterns may shift over time. Additionally, privacy and memory constraints are commonly observed in practical scenarios, further compounding the challenges. Therefore, the continuous monitoring of a TPP to learn the streaming event sequence is an important yet under-explored problem. Our work paper addresses this challenge by adopting Continual Learning (CL), which makes the model capable of continuously learning a sequence of tasks without catastrophic forgetting under realistic constraints. Correspondingly, we propose a simple yet effective framework, PromptTPPOur code is available at {\small \url{ https://github.com/yanyanSann/PromptTPP}}, by integrating the base TPP with a continuous-time retrieval prompt pool. The prompts, small learnable parameters, are stored in a memory space and jointly optimized with the base TPP, ensuring that the model learns event streams sequentially without buffering past examples or task-specific attributes. We present a novel and realistic experimental setup for modeling event streams, where PromptTPP consistently achieves state-of-the-art performance across three real user behavior datasets.

Text-to-image models are powerful for producing high-quality images based on given text prompts, but crafting these prompts often requires specialized vocabulary. To address this, existing methods train rewriting models with supervision from large amounts of manually annotated data and trained aesthetic assessment models. To alleviate the dependence on data scale for model training and the biases introduced by trained models, we propose a novel prompt optimization framework, designed to rephrase a simple user prompt into a sophisticated prompt to a text-to-image model. Specifically, we employ the large vision language models (LVLMs) as the solver to rewrite the user prompt, and concurrently, employ LVLMs as a reward model to score the aesthetics and alignment of the images generated by the optimized prompt. Instead of laborious human feedback, we exploit the prior knowledge of the LVLM to provide rewards, i.e., AI feedback. Simultaneously, the solver and the reward model are unified into one model and iterated in reinforcement learning to achieve self-improvement by giving a solution and judging itself. Results on two popular datasets demonstrate that our method outperforms other strong competitors.

Large language models demonstrate a remarkable capability for learning to solve new tasks from a few examples. The prompt template, or the way the input examples are formatted to obtain the prompt, is an important yet often overlooked aspect of in-context learning. In this work, we conduct a comprehensive study of the template format's influence on the in-context learning performance. We evaluate the impact of the prompt template across models (from 770M to 70B parameters) and 4 standard classification datasets. We show that a poor choice of the template can reduce the performance of the strongest models and inference methods to a random guess level. More importantly, the best templates do not transfer between different setups and even between models of the same family. Our findings show that the currently prevalent approach to evaluation, which ignores template selection, may give misleading results due to different templates in different works. As a first step towards mitigating this issue, we propose Template Ensembles that aggregate model predictions across several templates. This simple test-time augmentation boosts average performance while being robust to the choice of random set of templates.

We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our main contribution, we provide the first sample complexity analysis of TTTS and T3C when coupled with a very natural Bayesian stopping rule, for bandits with Gaussian rewards, solving one of the open questions raised by Russo (2016). We also provide new posterior convergence results for TTTS under two models that are commonly used in practice: bandits with Gaussian and Bernoulli rewards and conjugate priors.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

Large Language Models (LLMs) have demonstrated remarkable problem-solving and basic mathematics abilities. However, their efficacy is highly contingent on the formulation of the prompt. This study endeavors to quantify the influence of incorporating "positive thinking" into the system message of the prompt, then compare that to systematic prompt optimization. We assess the performance of 60 combinations of system message snippets, tested with and without Chain of Thought prompting, across three models with parameters ranging from 7 to 70 billion on the GSM8K dataset. Our findings reveal that results do not universally generalize across models. In most instances, the inclusion of "positive thinking" prompts positively affected model performance. Notably, however, Llama2-70B exhibited an exception when not utilizing Chain of Thought, as the optimal system message was found to be none at all. Given the combinatorial complexity, and thus computation time, of experimenting with hand-tuning prompts for large black-box models, we then compared the performance of the best "positive thinking" prompt against the output of systematic prompt optimization. We show that employing an automated prompt optimizer emerges as the most effective method for enhancing performance, even when working with smaller open-source models. Additionally, our findings reveal that the highest-scoring, automatically-optimized prompt exhibits a degree of peculiarity far beyond expectations.

Recently, multimodal large language models (MLLMs) have received much attention for their impressive capabilities. The evaluation of MLLMs is becoming critical to analyzing attributes of MLLMs and providing valuable insights. However, current benchmarks overlook the problem of prompt sensitivity - minor prompt variations may lead to significant performance fluctuations. Thus, inappropriate prompts may obscure the models' capabilities, underestimating the models' performance. Moreover, different models have different preferences for different prompts, and thus, using the same prompt for all models will cause evaluation bias. This paper analyzes this deficiency in existing benchmarks and further introduces a new evaluation framework named TP-Eval, which introduces a prompt customization method to reduce evaluation biases and tap models' potential. TP-Eval will rewrite the original prompts to different customized prompts for different models. In particular, we propose some well-designed modules for prompt customization tailored to the scenario of MLLM evaluation. Extensive experiments demonstrate the effectiveness of our approach to uncovering models' capabilities, and TP-Eval should benefit the community in developing more comprehensive and convincing MLLM evaluation benchmarks.

Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of thumb, or sometimes brute-force search. Much more appealing is the idea of developing automatic approaches which can optimize the performance of a given learning algorithm to the task at hand. In this work, we consider the automatic tuning problem within the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). The tractable posterior distribution induced by the GP leads to efficient use of the information gathered by previous experiments, enabling optimal choices about what parameters to try next. Here we show how the effects of the Gaussian process prior and the associated inference procedure can have a large impact on the success or failure of Bayesian optimization. We show that thoughtful choices can lead to results that exceed expert-level performance in tuning machine learning algorithms. We also describe new algorithms that take into account the variable cost (duration) of learning experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization on a diverse set of contemporary algorithms including latent Dirichlet allocation, structured SVMs and convolutional neural networks.

We study the task of prompting large-scale language models to perform multi-step reasoning. Existing work shows that when prompted with a chain of thoughts (CoT), sequences of short sentences describing intermediate reasoning steps towards a final answer, large language models can generate new reasoning chains and predict answers for new inputs. A central question is which reasoning examples make the most effective prompts. In this work, we propose complexity-based prompting, a simple and effective example selection scheme for multi-step reasoning. We show that prompts with higher reasoning complexity, i.e., chains with more reasoning steps, achieve substantially better performance on multi-step reasoning tasks over strong baselines. We further extend our complexity-based criteria from prompting (selecting inputs) to decoding (selecting outputs), where we sample multiple reasoning chains from the model, then choose the majority of generated answers from complex reasoning chains (over simple chains). When used to prompt GPT-3 and Codex, our approach substantially improves multi-step reasoning accuracy and achieves new state-of-the-art (SOTA) performance on three math benchmarks (GSM8K, MultiArith, and MathQA) and two BigBenchHard tasks (Date Understanding and Penguins), with an average +5.3 and up to +18 accuracy improvements. Compared with existing example selection schemes like manual tuning or retrieval-based selection, selection based on reasoning complexity is intuitive, easy to implement, and annotation-efficient. Further results demonstrate the robustness of performance gains from complex prompts under format perturbation and distribution shift.

Although soft prompt tuning is effective in efficiently adapting Vision-Language (V&L) models for downstream tasks, it shows limitations in dealing with distribution shifts. We address this issue with Attribute-Guided Prompt Tuning (ArGue), making three key contributions. 1) In contrast to the conventional approach of directly appending soft prompts preceding class names, we align the model with primitive visual attributes generated by Large Language Models (LLMs). We posit that a model's ability to express high confidence in these attributes signifies its capacity to discern the correct class rationales. 2) We introduce attribute sampling to eliminate disadvantageous attributes, thus only semantically meaningful attributes are preserved. 3) We propose negative prompting, explicitly enumerating class-agnostic attributes to activate spurious correlations and encourage the model to generate highly orthogonal probability distributions in relation to these negative features. In experiments, our method significantly outperforms current state-of-the-art prompt tuning methods on both novel class prediction and out-of-distribution generalization tasks.

Highly effective, task-specific prompts are often heavily engineered by experts to integrate detailed instructions and domain insights based on a deep understanding of both instincts of large language models (LLMs) and the intricacies of the target task. However, automating the generation of such expert-level prompts remains elusive. Existing prompt optimization methods tend to overlook the depth of domain knowledge and struggle to efficiently explore the vast space of expert-level prompts. Addressing this, we present PromptAgent, an optimization method that autonomously crafts prompts equivalent in quality to those handcrafted by experts. At its core, PromptAgent views prompt optimization as a strategic planning problem and employs a principled planning algorithm, rooted in Monte Carlo tree search, to strategically navigate the expert-level prompt space. Inspired by human-like trial-and-error exploration, PromptAgent induces precise expert-level insights and in-depth instructions by reflecting on model errors and generating constructive error feedback. Such a novel framework allows the agent to iteratively examine intermediate prompts (states), refine them based on error feedbacks (actions), simulate future rewards, and search for high-reward paths leading to expert prompts. We apply PromptAgent to 12 tasks spanning three practical domains: BIG-Bench Hard (BBH), as well as domain-specific and general NLP tasks, showing it significantly outperforms strong Chain-of-Thought and recent prompt optimization baselines. Extensive analyses emphasize its capability to craft expert-level, detailed, and domain-insightful prompts with great efficiency and generalizability.

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific target generative processes, where these local random variables are governed by a higher-level global random variate. The global variable helps memorize the important information from historic episodes while controlling how much the model needs to be adapted to new episodes in a principled Bayesian manner. Within our model framework, the prediction on a novel episode/task can be seen as a Bayesian inference problem. However, a main obstacle in learning with a large/infinite number of local random variables in online nature, is that one is not allowed to store the posterior distribution of the current local random variable for frequent future updates, typical in conventional variational inference. We need to be able to treat each local variable as a one-time iterate in the optimization. We propose a Normal-Inverse-Wishart model, for which we show that this one-time iterate optimization becomes feasible due to the approximate closed-form solutions for the local posterior distributions. The resulting algorithm is more attractive than the MAML in that it is not required to maintain computational graphs for the whole gradient optimization steps per episode. Our approach is also different from existing Bayesian meta learning methods in that unlike dealing with a single random variable for the whole episodes, our approach has a hierarchical structure that allows one-time episodic optimization, desirable for principled Bayesian learning with many/infinite tasks. The code is available at https://github.com/minyoungkim21/niwmeta.

Aligning text-to-image generation with user intent remains challenging, for users who provide ambiguous inputs and struggle with model idiosyncrasies. We propose Adaptive Prompt Elicitation (APE), a technique that adaptively asks visual queries to help users refine prompts without extensive writing. Our technical contribution is a formulation of interactive intent inference under an information-theoretic framework. APE represents latent intent as interpretable feature requirements using language model priors, adaptively generates visual queries, and compiles elicited requirements into effective prompts. Evaluation on IDEA-Bench and DesignBench shows that APE achieves stronger alignment with improved efficiency. A user study with challenging user-defined tasks demonstrates 19.8% higher alignment without workload overhead. Our work contributes a principled approach to prompting that, for general users, offers an effective and efficient complement to the prevailing prompt-based interaction paradigm with text-to-image models.

As large language models (LLMs) have progressed towards more human-like and human--AI communications have become prevalent, prompting has emerged as a decisive component. However, there is limited conceptual consensus on what exactly quantifies natural language prompts. We attempt to address this question by conducting a meta-analysis surveying more than 150 prompting-related papers from leading NLP and AI conferences from 2022 to 2025 and blogs. We propose a property- and human-centric framework for evaluating prompt quality, encompassing 21 properties categorized into six dimensions. We then examine how existing studies assess their impact on LLMs, revealing their imbalanced support across models and tasks, and substantial research gaps. Further, we analyze correlations among properties in high-quality natural language prompts, deriving prompting recommendations. We then empirically explore multi-property prompt enhancements in reasoning tasks, observing that single-property enhancements often have the greatest impact. Finally, we discover that instruction-tuning on property-enhanced prompts can result in better reasoning models. Our findings establish a foundation for property-centric prompt evaluation and optimization, bridging the gaps between human--AI communication and opening new prompting research directions.

Can a diffusion model produce its own "mental average" of a concept-one that is as sharp and realistic as a typical sample? We introduce Diffusion Mental Averages (DMA), a model-centric answer to this question. While prior methods aim to average image collections, they produce blurry results when applied to diffusion samples from the same prompt. These data-centric techniques operate outside the model, ignoring the generative process. In contrast, DMA averages within the diffusion model's semantic space, as discovered by recent studies. Since this space evolves across timesteps and lacks a direct decoder, we cast averaging as trajectory alignment: optimize multiple noise latents so their denoising trajectories progressively converge toward shared coarse-to-fine semantics, yielding a single sharp prototype. We extend our approach to multimodal concepts (e.g., dogs with many breeds) by clustering samples in semantically-rich spaces such as CLIP and applying Textual Inversion or LoRA to bridge CLIP clusters into diffusion space. This is, to our knowledge, the first approach that delivers consistent, realistic averages, even for abstract concepts, serving as a concrete visual summary and a lens into model biases and concept representation.

We introduce and study the problem of detecting whether an agent is updating their prior beliefs given new evidence in an optimal way that is Bayesian, or whether they are biased towards their own prior. In our model, biased agents form posterior beliefs that are a convex combination of their prior and the Bayesian posterior, where the more biased an agent is, the closer their posterior is to the prior. Since we often cannot observe the agent's beliefs directly, we take an approach inspired by information design. Specifically, we measure an agent's bias by designing a signaling scheme and observing the actions they take in response to different signals, assuming that they are maximizing their own expected utility; our goal is to detect bias with a minimum number of signals. Our main results include a characterization of scenarios where a single signal suffices and a computationally efficient algorithm to compute optimal signaling schemes.

We introduce Directional Stimulus Prompting, a novel framework for guiding black-box large language models (LLMs) toward specific desired outputs. Instead of directly adjusting LLMs, our method employs a small tunable policy model (e.g., T5) to generate an auxiliary directional stimulus prompt for each input instance. These directional stimulus prompts act as nuanced, instance-specific hints and clues to guide LLMs in generating desired outcomes, such as including specific keywords in the generated summary. Our approach sidesteps the challenges of direct LLM tuning by optimizing the policy model to explore directional stimulus prompts that align LLMs with desired behaviors. The policy model can be optimized through 1) supervised fine-tuning using labeled data and 2) reinforcement learning from offline or online rewards based on the LLM's output. We assess our method across summarization, dialogue response generation, and chain-of-thought reasoning tasks. Our experiments demonstrate that the framework consistently improves LLMs' (e.g., ChatGPT, Codex, InstructGPT) performance on these supervised tasks using minimal labeled data. Notably, using just 80 dialogues on the MultiWOZ dataset, our approach enhances ChatGPT's performance by an impressive 41.4%, matching or surpassing some fully supervised start-of-the-art models. Additionally, the instance-specific chain-of-thought prompt generated by our approach improves InstructGPT's reasoning accuracy compared to human-crafted or automatically generated prompts. The code and data are publicly available at https://github.com/Leezekun/Directional-Stimulus-Prompting.

Large Language Models (LLMs) have shown impressive capabilities in many scenarios, but their performance depends, in part, on the choice of prompt. Past research has focused on optimizing prompts specific to a task. However, much less attention has been given to optimizing the general instructions included in a prompt, known as a system prompt. To address this gap, we propose SPRIG, an edit-based genetic algorithm that iteratively constructs prompts from prespecified components to maximize the model's performance in general scenarios. We evaluate the performance of system prompts on a collection of 47 different types of tasks to ensure generalizability. Our study finds that a single optimized system prompt performs on par with task prompts optimized for each individual task. Moreover, combining system and task-level optimizations leads to further improvement, which showcases their complementary nature. Experiments also reveal that the optimized system prompts generalize effectively across model families, parameter sizes, and languages. This study provides insights into the role of system-level instructions in maximizing LLM potential.

We present Multi-expert Prompting, a novel enhancement of ExpertPrompting (Xu et al., 2023), designed to improve the large language model (LLM) generation. Specifically, it guides an LLM to fulfill an input instruction by simulating multiple experts, aggregating their responses, and selecting the best among individual and aggregated responses. This process is performed in a single chain of thoughts through our seven carefully designed subtasks derived from the Nominal Group Technique (Ven and Delbecq, 1974), a well-established decision-making framework. Our evaluations demonstrate that Multi-expert Prompting significantly outperforms ExpertPrompting and comparable baselines in enhancing the truthfulness, factuality, informativeness, and usefulness of responses while reducing toxicity and hurtfulness. It further achieves state-of-the-art truthfulness by outperforming the best baseline by 8.69% with ChatGPT. Multi-expert Prompting is efficient, explainable, and highly adaptable to diverse scenarios, eliminating the need for manual prompt construction.

We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements.

Recent developments in large language models have shown advantages in reallocating a notable share of computational resource from training time to inference time. However, the principles behind inference time scaling are not well understood. In this paper, we introduce an analytically tractable model of inference-time scaling: Bayesian linear regression with a reward-weighted sampler, where the reward is determined from a linear model, modeling LLM-as-a-judge scenario. We study this problem in the high-dimensional regime, where the deterministic equivalents dictate a closed-form expression for the posterior predictive mean and variance. We analyze the generalization error when training data are sampled from a teacher model. We draw k inference-time samples and select via softmax at a temperature applied to a quadratic reward. When the reward is not too different from the teacher, the generalization error decreases monotonically with increasing inference time samples k. However, the specific reward that optimizes inference-time selection generally differs from the teacher. In contrast, substantial reward misspecification induces a finite optimal k beyond which more sampling can increase the generalization error. For fixed k, there exists an optimal sampling temperature. We experimentally verify these facts in large language model inference with an additional large language model as a judge. In the "best-of-k" limit with the teacher as reward, we theoretically show that the generalization error decays as Θ(1/k^2) and determine the leading coefficient via extreme value theory. These formulas delineate domains where scaling inference-time computation is provably preferable to collecting more data. Finally, we demonstrate that when task difficulty increases, the previously mentioned advantage of inference-time compute degrades.

The generations of large language models are commonly controlled through prompting techniques, where a user's query to the model is prefixed with a prompt that aims to guide the model's behaviour on the query. The prompts used by companies to guide their models are often treated as secrets, to be hidden from the user making the query. They have even been treated as commodities to be bought and sold. However, there has been anecdotal evidence showing that the prompts can be extracted by a user even when they are kept secret. In this paper, we present a framework for systematically measuring the success of prompt extraction attacks. In experiments with multiple sources of prompts and multiple underlying language models, we find that simple text-based attacks can in fact reveal prompts with high probability.

We present a state-of-the-art model for fine-grained probability estimation of propositions conditioned on context. Recent advances in large language models (LLMs) have significantly enhanced their reasoning capabilities, particularly on well-defined tasks with complete information. However, LLMs continue to struggle with making accurate and well-calibrated probabilistic predictions under uncertainty or partial information. While incorporating uncertainty into model predictions often boosts performance, obtaining reliable estimates of that uncertainty remains understudied. In particular, LLM probability estimates tend to be coarse and biased towards more frequent numbers. Through a combination of human and synthetic data creation and assessment, scaling to larger models, and better supervision, we propose a set of strong and precise probability estimation models. We conduct systematic evaluations across tasks that rely on conditional probability estimation and show that our approach consistently outperforms existing fine-tuned and prompting-based methods by a large margin.

Monocular 3D object detection typically relies on pseudo-labeling techniques to reduce dependency on real-world annotations. Recent advances demonstrate that deterministic linguistic cues can serve as effective auxiliary weak supervision signals, providing complementary semantic context. However, hand-crafted textual descriptions struggle to capture the inherent visual diversity of individuals across scenes, limiting the model's ability to learn scene-aware representations. To address this challenge, we propose Visual-referred Probabilistic Prompt Learning (VirPro), an adaptive multi-modal pretraining paradigm that can be seamlessly integrated into diverse weakly supervised monocular 3D detection frameworks. Specifically, we generate a diverse set of learnable, instance-conditioned prompts across scenes and store them in an Adaptive Prompt Bank (APB). Subsequently, we introduce Multi-Gaussian Prompt Modeling (MGPM), which incorporates scene-based visual features into the corresponding textual embeddings, allowing the text prompts to express visual uncertainties. Then, from the fused vision-language embeddings, we decode a prompt-targeted Gaussian, from which we derive a unified object-level prompt embedding for each instance. RoI-level contrastive matching is employed to enforce modality alignment, bringing embeddings of co-occurring objects within the same scene closer in the latent space, thus enhancing semantic coherence. Extensive experiments on the KITTI benchmark demonstrate that integrating our pretraining paradigm consistently yields substantial performance gains, achieving up to a 4.8% average precision improvement than the baseline. Code is available at https://github.com/AustinLCP/VirPro.

Instruction embedding models have become common among state-of-the-art models, however are evaluated using a single prompt per task. The single-point evaluation ignores a main problem of the instruction-based approach namely: sensitivity to the phrasing of the instruction. We present an empirical study of prompt sensitivity across 6 embedding models, 11 datasets, and 15 task-specific prompts per dataset, a total of 990. We show that reported scores misrepresent the distribution of scores over plausible prompts. The default prompt can both systematically understate or overstate performance. Furthermore, we show that the leaderboard ranking is not robust to prompt selection: by choosing prompts favorably, any model in our study can be promoted to first place. Our findings suggest that single-prompt evaluation is insufficient for instruction-tuned embedding models and that benchmarks should incorporate prompt robustness, either by evaluating over multiple prompts or by reporting sensitivity alongside point estimates.

In many applications of LLMs, natural language responses often have an underlying structure such as representing discrete labels, numerical values, or graphs. Yet, existing decoding and uncertainty estimation methods operate only in language space and largely disregard structural information. We address this by modeling LLM outputs directly in a task-dependent latent structure. By equipping this structure with a dissimilarity measure, we can compute Bayes-optimal responses. These are not selected from sampled generations but are newly synthesized by combining individual responses in the latent space. Across different tasks, Bayes-optimal responses consistently outperform standard decoding methods like beam search. Moreover, quantifying uncertainty via the induced Bayesian risk captures variations in terms of the latent structure and improves alignment with output quality and correctness. Our decision-theoretic framework is applicable to any problem that admits a latent response structure and enables reliable task-aware LLM predictions.

We investigate the generation of minority samples using pretrained text-to-image (T2I) latent diffusion models. Minority instances, in the context of T2I generation, can be defined as ones living on low-density regions of text-conditional data distributions. They are valuable for various applications of modern T2I generators, such as data augmentation and creative AI. Unfortunately, existing pretrained T2I diffusion models primarily focus on high-density regions, largely due to the influence of guided samplers (like CFG) that are essential for high-quality generation. To address this, we present a novel framework to counter the high-density-focus of T2I diffusion models. Specifically, we first develop an online prompt optimization framework that encourages emergence of desired properties during inference while preserving semantic contents of user-provided prompts. We subsequently tailor this generic prompt optimizer into a specialized solver that promotes generation of minority features by incorporating a carefully-crafted likelihood objective. Extensive experiments conducted across various types of T2I models demonstrate that our approach significantly enhances the capability to produce high-quality minority instances compared to existing samplers. Code is available at https://github.com/soobin-um/MinorityPrompt.