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May 19

A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning

Test-time scaling seeks to improve the reasoning performance of large language models (LLMs) by adding computational resources. A prevalent approach within the field is sampling-based test-time scaling methods, which enhance reasoning by generating multiple reasoning paths for a given input during inference. However, despite its practical success, the theoretical foundations remain underexplored. In this paper, we provide the first theoretical framework for analyzing sampling-based test-time scaling methods, grounded in the perspective of confidence estimation. Based on the framework, we analyze two dominant paradigms: self-consistency and perplexity, and reveal key limitations: self-consistency suffers from high estimation error while perplexity exhibits substantial modeling error and possible degradation of the estimation error convergence. To address these limitations, we introduce RPC, a hybrid method that leverages our theoretical insights through two key components: Perplexity Consistency and Reasoning Pruning. Perplexity Consistency combines the strengths of self-consistency and perplexity, boosting the convergence rate of estimation error from linear to exponential while preserving model error. Reasoning Pruning prevents degradation by eliminating low-probability reasoning paths. Both theoretical analysis and empirical results across seven benchmark datasets demonstrate that RPC has a strong potential for reducing reasoning error. Notably, RPC achieves reasoning performance comparable to self-consistency while not only enhancing confidence reliability but also reducing sampling costs by 50%. The code and resources are available at https://wnjxyk.github.io/RPC.

LAMDA-NeSy NJU-IRP
·
Oct 17, 2025 7

DataMan: Data Manager for Pre-training Large Language Models

The performance emergence of large language models (LLMs) driven by data scaling laws makes the selection of pre-training data increasingly important. However, existing methods rely on limited heuristics and human intuition, lacking comprehensive and clear guidelines. To address this, we are inspired by ``reverse thinking'' -- prompting LLMs to self-identify which criteria benefit its performance. As its pre-training capabilities are related to perplexity (PPL), we derive 14 quality criteria from the causes of text perplexity anomalies and introduce 15 common application domains to support domain mixing. In this paper, we train a Data Manager (DataMan) to learn quality ratings and domain recognition from pointwise rating, and use it to annotate a 447B token pre-training corpus with 14 quality ratings and domain type. Our experiments validate our approach, using DataMan to select 30B tokens to train a 1.3B-parameter language model, demonstrating significant improvements in in-context learning (ICL), perplexity, and instruction-following ability over the state-of-the-art baseline. The best-performing model, based on the Overall Score l=5 surpasses a model trained with 50% more data using uniform sampling. We continue pre-training with high-rated, domain-specific data annotated by DataMan to enhance domain-specific ICL performance and thus verify DataMan's domain mixing ability. Our findings emphasize the importance of quality ranking, the complementary nature of quality criteria, and their low correlation with perplexity, analyzing misalignment between PPL and ICL performance. We also thoroughly analyzed our pre-training dataset, examining its composition, the distribution of quality ratings, and the original document sources.

  • 6 authors
·
Feb 26, 2025

Bridging Internal Probability and Self-Consistency for Effective and Efficient LLM Reasoning

Recent advancements in large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, single-shot inference often yields unreliable results for complex reasoning tasks, leading researchers to explore multiple reasoning paths through methods such as perplexity and self-consistency. In this paper, we present the first theoretical error decomposition analysis of these techniques, breaking down their error into estimation error and model error. Our analysis reveals a fundamental trade-off: perplexity methods suffer from substantial model error due to the absence of a proper consistency function, while self-consistency exhibits high estimation error due to a slow error convergence rate. To overcome these limitations, we propose Reasoning-Pruning Perplexity Consistency (RPC). This approach combines Perplexity Consistency, which seamlessly integrates LLM perplexity with self-consistency, and Reasoning Pruning, which eliminates low-probability reasoning paths to effectively prevent the degeneration of estimation error reduction. Theoretical analysis demonstrates that RPC not only accelerates the convergence rate of estimation error to an exponential level but also holds strong potential for further reducing model error. Extensive empirical evaluations on seven benchmark datasets confirm that RPC can significantly improve reasoning performance, sample efficiency, and confidence reliability.

  • 7 authors
·
Feb 1, 2025

The Butterfly Effect of Model Editing: Few Edits Can Trigger Large Language Models Collapse

Although model editing has shown promise in revising knowledge in Large Language Models (LLMs), its impact on the inherent capabilities of LLMs is often overlooked. In this work, we reveal a critical phenomenon: even a single edit can trigger model collapse, manifesting as significant performance degradation in various benchmark tasks. However, benchmarking LLMs after each edit, while necessary to prevent such collapses, is impractically time-consuming and resource-intensive. To mitigate this, we propose using perplexity as a surrogate metric, validated by extensive experiments demonstrating changes in an edited model's perplexity are strongly correlated with its downstream task performances. We further conduct an in-depth study on sequential editing, a practical setting for real-world scenarios, across various editing methods and LLMs, focusing on hard cases from our previous single edit studies. The results indicate that nearly all examined editing methods result in model collapse after only few edits. To facilitate further research, we have utilized GPT-3.5 to develop a new dataset, HardEdit, based on those hard cases. This dataset aims to establish the foundation for pioneering research in reliable model editing and the mechanisms underlying editing-induced model collapse. We hope this work can draw the community's attention to the potential risks inherent in model editing practices.

  • 6 authors
·
Feb 14, 2024

Protecting Copyrighted Material with Unique Identifiers in Large Language Model Training

A primary concern regarding training large language models (LLMs) is whether they abuse copyrighted online text. With the increasing training data scale and the prevalence of LLMs in daily lives, two problems arise: 1) false positive membership inference results misled by similar examples; 2) membership inference methods are usually too complex for end users to understand and use. To address these issues, we propose an alternative insert-and-detect methodology, advocating that web users and content platforms employ \textit{unique identifiers} for reliable and independent membership inference. Users and platforms can create their identifiers, embed them in copyrighted text, and independently detect them in future LLMs. As an initial demonstration, we introduce \textbf{ghost sentences} and a user-friendly last-k words test, allowing end users to chat with LLMs for membership inference. Ghost sentences consist primarily of unique passphrases of random natural words, which can come with customized elements to bypass possible filter rules. The last-k words test requires a significant repetition time of ghost sentences~(ge10). For cases with fewer repetitions, we designed an extra perplexity test, as LLMs exhibit high perplexity when encountering unnatural passphrases. We also conduct a comprehensive study on the memorization and membership inference of ghost sentences, examining factors such as training data scales, model sizes, repetition times, insertion positions, wordlist of passphrases, alignment, etc. Our study shows the possibility of applying ghost sentences in real scenarios and provides instructions for the potential application.

  • 4 authors
·
Mar 23, 2024

Queries, Representation & Detection: The Next 100 Model Fingerprinting Schemes

The deployment of machine learning models in operational contexts represents a significant investment for any organisation. Consequently, the risk of these models being misappropriated by competitors needs to be addressed. In recent years, numerous proposals have been put forth to detect instances of model stealing. However, these proposals operate under implicit and disparate data and model access assumptions; as a consequence, it remains unclear how they can be effectively compared to one another. Our evaluation shows that a simple baseline that we introduce performs on par with existing state-of-the-art fingerprints, which, on the other hand, are much more complex. To uncover the reasons behind this intriguing result, this paper introduces a systematic approach to both the creation of model fingerprinting schemes and their evaluation benchmarks. By dividing model fingerprinting into three core components -- Query, Representation and Detection (QuRD) -- we are able to identify sim100 previously unexplored QuRD combinations and gain insights into their performance. Finally, we introduce a set of metrics to compare and guide the creation of more representative model stealing detection benchmarks. Our approach reveals the need for more challenging benchmarks and a sound comparison with baselines. To foster the creation of new fingerprinting schemes and benchmarks, we open-source our fingerprinting toolbox.

  • 5 authors
·
Dec 17, 2024

(Dynamic) Prompting might be all you need to repair Compressed LLMs

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.

  • 5 authors
·
Oct 1, 2023

Weight Pruning Amplifies Bias: A Multi-Method Study of Compressed LLMs for Edge AI

Weight pruning is widely advocated for deploying Large Language Models on resource-constrained IoT and edge devices, yet its impact on model fairness remains poorly understood. We conduct a controlled empirical study of three instruction-tuned models (Gemma-2-9b-it, Mistral-7B-Instruct-v0.3, Phi-3.5-mini-instruct) across three pruning methods (Random, Magnitude, Wanda) at four sparsity levels (10-70%) on 12,148 BBQ bias benchmark items with 5 random seeds, totaling 2,368,860 inference records. Our results reveal a Smart Pruning Paradox: activation-aware pruning (Wanda) preserves perplexity nearly perfectly (just 3.5% increase at 50% sparsity for Mistral-7B), yet produces the highest bias amplification, with Stereotype Reliance Score increasing 83.7% and 47-59% of previously unbiased items developing new stereotypical behaviors at 70% sparsity. Random pruning destroys language capability entirely (perplexity exceeding 10^4 and reaching 10^8) but produces only random-chance bias. We further show that unstructured pruning provides zero storage savings and zero inference latency reduction on real edge hardware, undermining the primary motivation for its use in IoT deployment. Of 180 dense-vs-pruned comparisons, 141 (78.3%) are significant (p < 0.05) with mean |h| = 0.305. Published quantization studies report up to 21% of responses flipping between biased and unbiased states; our pruning results show transition rates nearly three times higher (47-59%), suggesting pruning poses a categorically greater risk to alignment than quantization. These findings demonstrate that perplexity-based evaluation provides false assurance of behavioral equivalence, and that IoT deployment pipelines require bias-aware validation before deploying pruned models at the edge.

  • 2 authors
·
May 1

Judging LLMs on a Simplex

Automated evaluation of free-form outputs from large language models (LLMs) is challenging because many distinct answers can be equally valid. A common practice is to use LLMs themselves as judges, but the theoretical properties of this approach are not yet well understood. We show that a geometric framework that represents both judges and candidates as points on a probability simplex can provide helpful insight on what is or is not identifiable using LLM judges. Our theoretical analysis uncovers a "phase transition" in ranking identifiability: for binary scoring systems, true rankings are identifiable even with weak judges under mild assumptions, while rankings become non-identifiable for three or more scoring levels even with infinite data, absent additional prior knowledge. This non-identifiability highlights how uncertainty in rankings stems from not only aleatoric uncertainty (i.e., inherent stochasticity in the data) but also epistemic uncertainty regarding which assumptions hold, an aspect that has received limited attention until now. To integrate both types of uncertainty, we use Bayesian inference to encode assumptions as priors and conduct sensitivity analysis of ranking estimates and credible intervals. Empirical evaluations across multiple benchmarks demonstrate that Bayesian inference yields more accurate rankings and substantially improves coverage rates. These results underscore the importance of taking a more holistic approach to uncertainty quantification when using LLMs as judges.

  • 4 authors
·
May 28, 2025

Internal Knowledge Without External Expression: Probing the Generalization Boundary of a Classical Chinese Language Model

We train a 318M-parameter Transformer language model from scratch on a curated corpus of 1.56 billion tokens of pure Classical Chinese, with zero English characters or Arabic numerals. Through systematic out-of-distribution (OOD) testing, we investigate whether the model can distinguish known from unknown inputs, and crucially, whether it can express this distinction in its generated text. We find a clear dissociation between internal and external uncertainty. Internally, the model exhibits a perplexity jump ratio of 2.39x between real and fabricated historical events (p = 8.9e-11, n = 92 per group), with semi-fabricated events (real figures + fictional events) showing the highest perplexity (4.24x, p = 1.1e-16), demonstrating genuine factual encoding beyond syntactic pattern matching. Externally, however, the model never learns to express uncertainty: classical Chinese epistemic markers appear at lower rates for OOD questions (3.5%) than for in-distribution questions (8.3%, p = 0.023), reflecting rhetorical conventions rather than genuine metacognition. We replicate both findings across three languages (Classical Chinese, English, Japanese), three writing systems, and eight models from 110M to 1.56B parameters. We further show that uncertainty expression frequency is determined entirely by training data conventions, with Classical Chinese models showing a "humility paradox" (more hedging for known topics), while Japanese models almost never hedge. We argue that metacognitive expression -- the ability to say "I don't know" -- does not emerge from language modeling alone and requires explicit training signals such as RLHF.

  • 7 authors
·
Mar 30

Real Money, Fake Models: Deceptive Model Claims in Shadow APIs

Access to frontier large language models (LLMs), such as GPT-5 and Gemini-2.5, is often hindered by high pricing, payment barriers, and regional restrictions. These limitations drive the proliferation of shadow APIs, third-party services that claim to provide access to official model services without regional limitations via indirect access. Despite their widespread use, it remains unclear whether shadow APIs deliver outputs consistent with those of the official APIs, raising concerns about the reliability of downstream applications and the validity of research findings that depend on them. In this paper, we present the first systematic audit between official LLM APIs and corresponding shadow APIs. We first identify 17 shadow APIs that have been utilized in 187 academic papers, with the most popular one reaching 5,966 citations and 58,639 GitHub stars by December 6, 2025. Through multidimensional auditing of three representative shadow APIs across utility, safety, and model verification, we uncover both indirect and direct evidence of deception practices in shadow APIs. Specifically, we reveal performance divergence reaching up to 47.21%, significant unpredictability in safety behaviors, and identity verification failures in 45.83% of fingerprint tests. These deceptive practices critically undermine the reproducibility and validity of scientific research, harm the interests of shadow API users, and damage the reputation of official model providers.

  • 6 authors
·
Mar 2 1

WOUAF: Weight Modulation for User Attribution and Fingerprinting in Text-to-Image Diffusion Models

The rapid advancement of generative models, facilitating the creation of hyper-realistic images from textual descriptions, has concurrently escalated critical societal concerns such as misinformation. Traditional fake detection mechanisms, although providing some mitigation, fall short in attributing responsibility for the malicious use of synthetic images. This paper introduces a novel approach to model fingerprinting that assigns responsibility for the generated images, thereby serving as a potential countermeasure to model misuse. Our method modifies generative models based on each user's unique digital fingerprint, imprinting a unique identifier onto the resultant content that can be traced back to the user. This approach, incorporating fine-tuning into Text-to-Image (T2I) tasks using the Stable Diffusion Model, demonstrates near-perfect attribution accuracy with a minimal impact on output quality. We rigorously scrutinize our method's secrecy under two distinct scenarios: one where a malicious user attempts to detect the fingerprint, and another where a user possesses a comprehensive understanding of our method. We also evaluate the robustness of our approach against various image post-processing manipulations typically executed by end-users. Through extensive evaluation of the Stable Diffusion models, our method presents a promising and novel avenue for accountable model distribution and responsible use.

  • 5 authors
·
Jun 7, 2023 1

RidgeBase: A Cross-Sensor Multi-Finger Contactless Fingerprint Dataset

Contactless fingerprint matching using smartphone cameras can alleviate major challenges of traditional fingerprint systems including hygienic acquisition, portability and presentation attacks. However, development of practical and robust contactless fingerprint matching techniques is constrained by the limited availability of large scale real-world datasets. To motivate further advances in contactless fingerprint matching across sensors, we introduce the RidgeBase benchmark dataset. RidgeBase consists of more than 15,000 contactless and contact-based fingerprint image pairs acquired from 88 individuals under different background and lighting conditions using two smartphone cameras and one flatbed contact sensor. Unlike existing datasets, RidgeBase is designed to promote research under different matching scenarios that include Single Finger Matching and Multi-Finger Matching for both contactless- to-contactless (CL2CL) and contact-to-contactless (C2CL) verification and identification. Furthermore, due to the high intra-sample variance in contactless fingerprints belonging to the same finger, we propose a set-based matching protocol inspired by the advances in facial recognition datasets. This protocol is specifically designed for pragmatic contactless fingerprint matching that can account for variances in focus, polarity and finger-angles. We report qualitative and quantitative baseline results for different protocols using a COTS fingerprint matcher (Verifinger) and a Deep CNN based approach on the RidgeBase dataset. The dataset can be downloaded here: https://www.buffalo.edu/cubs/research/datasets/ridgebase-benchmark-dataset.html

  • 5 authors
·
Jul 9, 2023

Scalable Data Ablation Approximations for Language Models through Modular Training and Merging

Training data compositions for Large Language Models (LLMs) can significantly affect their downstream performance. However, a thorough data ablation study exploring large sets of candidate data mixtures is typically prohibitively expensive since the full effect is seen only after training the models; this can lead practitioners to settle for sub-optimal data mixtures. We propose an efficient method for approximating data ablations which trains individual models on subsets of a training corpus and reuses them across evaluations of combinations of subsets. In continued pre-training experiments, we find that, given an arbitrary evaluation set, the perplexity score of a single model trained on a candidate set of data is strongly correlated with perplexity scores of parameter averages of models trained on distinct partitions of that data. From this finding, we posit that researchers and practitioners can conduct inexpensive simulations of data ablations by maintaining a pool of models that were each trained on partitions of a large training corpus, and assessing candidate data mixtures by evaluating parameter averages of combinations of these models. This approach allows for substantial improvements in amortized training efficiency -- scaling only linearly with respect to new data -- by enabling reuse of previous training computation, opening new avenues for improving model performance through rigorous, incremental data assessment and mixing.

  • 7 authors
·
Oct 21, 2024