Daily Papers

Recent advances have shown that sequential fine-tuning (SeqFT) of pre-trained vision transformers (ViTs), followed by classifier refinement using approximate distributions of class features, can be an effective strategy for class-incremental learning (CIL). However, this approach is susceptible to distribution drift, caused by the sequential optimization of shared backbone parameters. This results in a mismatch between the distributions of the previously learned classes and that of the updater model, ultimately degrading the effectiveness of classifier performance over time. To address this issue, we introduce a latent space transition operator and propose Sequential Learning with Drift Compensation (SLDC). SLDC aims to align feature distributions across tasks to mitigate the impact of drift. First, we present a linear variant of SLDC, which learns a linear operator by solving a regularized least-squares problem that maps features before and after fine-tuning. Next, we extend this with a weakly nonlinear SLDC variant, which assumes that the ideal transition operator lies between purely linear and fully nonlinear transformations. This is implemented using learnable, weakly nonlinear mappings that balance flexibility and generalization. To further reduce representation drift, we apply knowledge distillation (KD) in both algorithmic variants. Extensive experiments on standard CIL benchmarks demonstrate that SLDC significantly improves the performance of SeqFT. Notably, by combining KD to address representation drift with SLDC to compensate distribution drift, SeqFT achieves performance comparable to joint training across all evaluated datasets. Code: https://github.com/raoxuan98-hash/sldc.git.

The success of deep neural networks (DNNs) is heavily dependent on the availability of labeled data. However, obtaining labeled data is a big challenge in many real-world problems. In such scenarios, a DNN model can leverage labeled and unlabeled data from a related domain, but it has to deal with the shift in data distributions between the source and the target domains. In this paper, we study the problem of classifying social media posts during a crisis event (e.g., Earthquake). For that, we use labeled and unlabeled data from past similar events (e.g., Flood) and unlabeled data for the current event. We propose a novel model that performs adversarial learning based domain adaptation to deal with distribution drifts and graph based semi-supervised learning to leverage unlabeled data within a single unified deep learning framework. Our experiments with two real-world crisis datasets collected from Twitter demonstrate significant improvements over several baselines.

Multivariate time series forecasting plays a crucial role in various fields such as finance, traffic management, energy, and healthcare. Recent studies have highlighted the advantages of channel independence to resist distribution drift but neglect channel correlations, limiting further enhancements. Several methods utilize mechanisms like attention or mixer to address this by capturing channel correlations, but they either introduce excessive complexity or rely too heavily on the correlation to achieve satisfactory results under distribution drifts, particularly with a large number of channels. Addressing this gap, this paper presents an efficient MLP-based model, the Series-cOre Fused Time Series forecaster (SOFTS), which incorporates a novel STar Aggregate-Redistribute (STAR) module. Unlike traditional approaches that manage channel interactions through distributed structures, e.g., attention, STAR employs a centralized strategy to improve efficiency and reduce reliance on the quality of each channel. It aggregates all series to form a global core representation, which is then dispatched and fused with individual series representations to facilitate channel interactions effectively.SOFTS achieves superior performance over existing state-of-the-art methods with only linear complexity. The broad applicability of the STAR module across different forecasting models is also demonstrated empirically. For further research and development, we have made our code publicly available at https://github.com/Secilia-Cxy/SOFTS.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Deep neural networks have enabled improved image quality and fast inference times for various inverse problems, including accelerated magnetic resonance imaging (MRI) reconstruction. However, such models require a large number of fully-sampled ground truth datasets, which are difficult to curate, and are sensitive to distribution drifts. In this work, we propose applying physics-driven data augmentations for consistency training that leverage our domain knowledge of the forward MRI data acquisition process and MRI physics to achieve improved label efficiency and robustness to clinically-relevant distribution drifts. Our approach, termed VORTEX, (1) demonstrates strong improvements over supervised baselines with and without data augmentation in robustness to signal-to-noise ratio change and motion corruption in data-limited regimes; (2) considerably outperforms state-of-the-art purely image-based data augmentation techniques and self-supervised reconstruction methods on both in-distribution and out-of-distribution data; and (3) enables composing heterogeneous image-based and physics-driven data augmentations. Our code is available at https://github.com/ad12/meddlr.

This paper uncovers a critical yet overlooked phenomenon in multi-modal large language models (MLLMs): detrimental concept drift within chain-of-thought (CoT) reasoning during non-stationary reinforcement fine-tuning (RFT), where reasoning token distributions evolve unpredictably, thereby introducing significant biases in final predictions. To address this, we are pioneers in establishing the theoretical bridge between concept drift theory and RFT processes by formalizing CoT's autoregressive token streams as non-stationary distributions undergoing arbitrary temporal shifts. Leveraging this framework, we propose a novel counterfact-aware RFT that systematically decouples beneficial distribution adaptation from harmful concept drift through concept graph-empowered LLM experts generating counterfactual reasoning trajectories. Our solution, Counterfactual Preference Optimization (CPO), enables stable RFT in non-stationary environments, particularly within the medical domain, through custom-tuning of counterfactual-aware preference alignment. Extensive experiments demonstrate our superior performance of robustness, generalization and coordination within RFT. Besides, we also contributed a large-scale dataset CXR-CounterFact (CCF), comprising 320,416 meticulously curated counterfactual reasoning trajectories derived from MIMIC-CXR. Our code and data are public.

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models, and generalizes previous results on agnostic learning under drift.

Large language models are prone to hallucinating factually incorrect statements. A key source of these errors is exposure to new factual information through supervised fine-tuning (SFT), which can increase hallucinations w.r.t. knowledge acquired during pre-training. In this work, we explore whether SFT-induced hallucinations can be mitigated using established tools from the continual learning literature, since they arise as a by-product of knowledge degradation during training. We propose a self-distillation-based SFT method that facilitates effective factual learning while minimizing hallucinations w.r.t. pre-existing knowledge by regularizing output-distribution drift. We also show that, in settings where new knowledge acquisition is unnecessary, suppressing factual plasticity by freezing parameter groups, can preserve task performance while reducing hallucinations. Lastly, we investigate the mechanism behind SFT-induced hallucinations through three hypotheses: capacity limitations, behavior cloning, and localized interference. Our experiments show that a main driver is interference among overlapping semantic representations, and that self-distillation succeeds by mitigating this interference.

Recent studies suggest that Reinforcement Fine-Tuning (RFT) is inherently more resilient to catastrophic forgetting than Supervised Fine-Tuning (SFT). However, whether RFT (e.g., GRPO) can effectively overcome forgetting in challenging visual continual learning settings, such as class-incremental learning (CIL) and domain-incremental learning (DIL), remains an open problem. Through a pilot study, we confirm that while RFT consistently outperforms SFT, it still suffers from non-negligible forgetting. We empirically trace this bottleneck to Trajectory-level Drift Agnosticism: among candidate rollouts achieving identical task rewards, the KL divergence from the preceding-task policy varies substantially, which strongly correlates with catastrophic forgetting across sequential tasks. Motivated by this insight, we propose Retention-aware Policy Optimization (RaPO), a simple yet effective RFT method that explicitly mitigates forgetting through trajectory-level reward shaping. Specifically, RaPO comprises two core components: (1) Retention Reward that converts trajectory-level distribution drift into a continuous reward signal, preferentially reinforcing knowledge-preserving rollouts within each group; (2) Cross-Task Advantage Normalization (CTAN), which maintains a persistent exponential moving average of reward statistics across task boundaries to stabilize the optimization progress during continual learning. Leveraging the free-form textual generalization of MLLMs, we comprehensively evaluate RaPO across five visual continual learning settings. Extensive experiments demonstrate that RaPO achieves leading performance, substantially reducing catastrophic forgetting while preserving strong plasticity. To the best of our knowledge, this work represents the first systematic exploration of RFT in visual continual learning, offering insights that we hope will inspire future research.

Diffusion and flow models achieve State-Of-The-Art (SOTA) generative performance, yet many practically important behaviors such as fine-grained prompt fidelity, compositional correctness, and text rendering are weakly specified by score or flow matching pretraining objectives. Reinforcement Learning (RL) fine-tuning with external, black-box rewards is a natural remedy, but diffusion RL is often brittle. Trajectory-based methods incur high memory cost and high-variance gradient estimates; forward-process approaches converge faster but can suffer from distribution drift, and hence reward hacking. In this work, we present Centered Reward Distillation (CRD), a diffusion RL framework derived from KL-regularized reward maximization built on forward-process-based fine-tuning. The key insight is that the intractable normalizing constant cancels under within-prompt centering, yielding a well-posed reward-matching objective. To enable reliable text-to-image fine-tuning, we introduce techniques that explicitly control distribution drift: (i) decoupling the sampler from the moving reference to prevent ratio-signal collapse, (ii) KL anchoring to a CFG-guided pretrained model to control long-run drift and align with the inference-time semantics of the pre-trained model, and (iii) reward-adaptive KL strength to accelerate early learning under large KL regularization while reducing late-stage exploitation of reward-model loopholes. Experiments on text-to-image post-training with GenEval and OCR rewards show that CRD achieves competitive SOTA reward optimization results with fast convergence and reduced reward hacking, as validated on unseen preference metrics.

Tool-based Agentic Reinforcement Learning (TARL) has emerged as a promising paradigm for training search agents to interact with external tools for a multi-turn information-seeking process autonomously. However, we identify a critical training instability that leads to catastrophic model collapse: Importance Sampling Distribution Drift(ISDD). In Group Relative Policy Optimization(GRPO), a widely adopted TARL algorithm, ISDD manifests as a precipitous decline in the importance sampling ratios, which nullifies gradient updates and triggers irreversible training failure. To address this, we propose Search Agent Policy Optimization (SAPO), which stabilizes training via a conditional token-level KL constraint. Unlike hard clipping, which ignores distributional divergence, SAPO selectively penalizes the KL divergence between the current and old policies. Crucially, this penalty is applied only to positive tokens with low probabilities where the policy has shifted excessively, thereby preventing distribution drift while preserving gradient flow. Remarkably, SAPO requires only one-line code modification to standard GRPO, ensuring immediate deployability. Extensive experiments across seven QA benchmarks demonstrate that SAPO achieves +10.6\% absolute improvement (+31.5\% relative) over Search-R1, yielding consistent gains across varying model scales (1.5B, 14B) and families (Qwen, LLaMA).

We present Vivid-VR, a DiT-based generative video restoration method built upon an advanced T2V foundation model, where ControlNet is leveraged to control the generation process, ensuring content consistency. However, conventional fine-tuning of such controllable pipelines frequently suffers from distribution drift due to limitations in imperfect multimodal alignment, resulting in compromised texture realism and temporal coherence. To tackle this challenge, we propose a concept distillation training strategy that utilizes the pretrained T2V model to synthesize training samples with embedded textual concepts, thereby distilling its conceptual understanding to preserve texture and temporal quality. To enhance generation controllability, we redesign the control architecture with two key components: 1) a control feature projector that filters degradation artifacts from input video latents to minimize their propagation through the generation pipeline, and 2) a new ControlNet connector employing a dual-branch design. This connector synergistically combines MLP-based feature mapping with cross-attention mechanism for dynamic control feature retrieval, enabling both content preservation and adaptive control signal modulation. Extensive experiments show that Vivid-VR performs favorably against existing approaches on both synthetic and real-world benchmarks, as well as AIGC videos, achieving impressive texture realism, visual vividness, and temporal consistency. The codes and checkpoints are publicly available at https://github.com/csbhr/Vivid-VR.

Large language models (LLMs) have shown remarkable potential as autonomous agents, particularly in web-based tasks. However, existing LLM web agents heavily rely on expensive proprietary LLM APIs, while open LLMs lack the necessary decision-making capabilities. This paper introduces WebRL, a self-evolving online curriculum reinforcement learning framework designed to train high-performance web agents using open LLMs. WebRL addresses three key challenges in building LLM web agents, including the scarcity of training tasks, sparse feedback signals, and policy distribution drift in online learning. Specifically, WebRL incorporates 1) a self-evolving curriculum that generates new tasks from unsuccessful attempts, 2) a robust outcome-supervised reward model (ORM), and 3) adaptive reinforcement learning strategies to ensure consistent improvements. We apply WebRL to transform open Llama-3.1 and GLM-4 models into proficient web agents. On WebArena-Lite, WebRL improves the success rate of Llama-3.1-8B from 4.8% to 42.4%, and from 6.1% to 43% for GLM-4-9B. These open models significantly surpass the performance of GPT-4-Turbo (17.6%) and GPT-4o (13.9%) and outperform previous state-of-the-art web agents trained on open LLMs (AutoWebGLM, 18.2%). Our findings demonstrate WebRL's effectiveness in bridging the gap between open and proprietary LLM-based web agents, paving the way for more accessible and powerful autonomous web interaction systems.

Millions of smart meters have been deployed worldwide, collecting the total power consumed by individual households. Based on these data, electricity suppliers offer their clients energy monitoring solutions to provide feedback on the consumption of their individual appliances. Historically, such estimates have relied on statistical methods that use coarse-grained total monthly consumption and static customer data, such as appliance ownership. Non-Intrusive Load Monitoring (NILM) is the problem of disaggregating a household's collected total power consumption to retrieve the consumed power for individual appliances. Current state-of-the-art (SotA) solutions for NILM are based on deep-learning (DL) and operate on subsequences of an entire household consumption reading. However, the non-stationary nature of real-world smart meter data leads to a drift in the data distribution within each segmented window, which significantly affects model performance. This paper introduces NILMFormer, a Transformer-based architecture that incorporates a new subsequence stationarization/de-stationarization scheme to mitigate the distribution drift and that uses a novel positional encoding that relies only on the subsequence's timestamp information. Experiments with 4 real-world datasets show that NILMFormer significantly outperforms the SotA approaches. Our solution has been deployed as the backbone algorithm for EDF's (Electricit\'e De France) consumption monitoring service, delivering detailed insights to millions of customers about their individual appliances' power consumption. This paper appeared in KDD 2025.

Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing the actual ground truth. While the original formulation assumes data exchangeability, some extensions handle non-exchangeable data, which is often the case in many real-world scenarios. In parallel, some progress has been made in conformal methods that provide statistical guarantees for a broader range of objectives, such as bounding the best F_1-score or minimizing the false negative rate in expectation. In this paper, we leverage and extend these two lines of work by proposing non-exchangeable conformal risk control, which allows controlling the expected value of any monotone loss function when the data is not exchangeable. Our framework is flexible, makes very few assumptions, and allows weighting the data based on its relevance for a given test example; a careful choice of weights may result on tighter bounds, making our framework useful in the presence of change points, time series, or other forms of distribution drift. Experiments with both synthetic and real world data show the usefulness of our method.

Non-stationarity of an underlying data generating process that leads to distributional changes over time is a key characteristic of Data Streams. This phenomenon, commonly referred to as Concept Drift, has been intensively studied, and Concept Drift Detectors have been established as a class of methods for detecting such changes (drifts). For the most part, Drift Detectors compare regions (windows) of the data stream and detect drift if those windows are sufficiently dissimilar. In this work, we introduce the Window Dilemma, an observation that perceived drift is a product of windowing and not necessarily the underlying data generating process. Additionally, we highlight that drift detection is ill-posed, primarily because verification of drift events are implausible in practice. We demonstrate these contributions first by an illustrative example, followed by empirical comparisons of drift detectors against a variety of alternative adaptation strategies. Our main finding is that traditional batch learning techniques often perform better than their drift-aware counterparts further bringing into question the purpose of detectors in Stream Classification.

Ocean scientists have been collecting visual data to study marine organisms for decades. These images and videos are extremely valuable both for basic science and environmental monitoring tasks. There are tools for automatically processing these data, but none that are capable of handling the extreme variability in sample populations, image quality, and habitat characteristics that are common in visual sampling of the ocean. Such distribution shifts can occur over very short physical distances and in narrow time windows. Creating models that are able to recognize when an image or video sequence contains a new organism, an unusual collection of animals, or is otherwise out-of-sample is critical to fully leverage visual data in the ocean. The FathomNet2023 competition dataset presents a realistic scenario where the set of animals in the target data differs from the training data. The challenge is both to identify the organisms in a target image and assess whether it is out-of-sample.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and flow-based models. In this paper, we propose a new paradigm called Drifting Models, which evolve the pushforward distribution during training and naturally admit one-step inference. We introduce a drifting field that governs the sample movement and achieves equilibrium when the distributions match. This leads to a training objective that allows the neural network optimizer to evolve the distribution. In experiments, our one-step generator achieves state-of-the-art results on ImageNet at 256 x 256 resolution, with an FID of 1.54 in latent space and 1.61 in pixel space. We hope that our work opens up new opportunities for high-quality one-step generation.

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work focuses on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of optimal transport, where the candidate mappings are restricted to a set of interpretable mappings. We then inspect multiple quintessential use-cases of distribution shift in real-world tabular, text, and image datasets to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

Deep learning has achieved tremendous success with independent and identically distributed (i.i.d.) data. However, the performance of neural networks often degenerates drastically when encountering out-of-distribution (OoD) data, i.e., when training and test data are sampled from different distributions. While a plethora of algorithms have been proposed for OoD generalization, our understanding of the data used to train and evaluate these algorithms remains stagnant. In this work, we first identify and measure two distinct kinds of distribution shifts that are ubiquitous in various datasets. Next, through extensive experiments, we compare OoD generalization algorithms across two groups of benchmarks, each dominated by one of the distribution shifts, revealing their strengths on one shift as well as limitations on the other shift. Overall, we position existing datasets and algorithms from different research areas seemingly unconnected into the same coherent picture. It may serve as a foothold that can be resorted to by future OoD generalization research. Our code is available at https://github.com/ynysjtu/ood_bench.

Real-world data often exhibit extreme imbalances and out-of-distribution (OOD) instances, which significantly biases the model training. While it has been extensively studied in vision and language domains separately, the impact of long-tailed open worlds on multi-modal large language models (MLLMs) has been largely overlooked. In this paper, we first demonstrate the susceptibility and vulnerability of vision-language models to significant biases caused by tail drift and out-of-distribution (OOD) drift during both the pre-training and fine-tuning stages. To eliminate the bias from different sources, we integrate the tailed drift adaptation and OOD drift detection into a unified framework by extending the concept drift theory to multi-modal. Specifically, a T-distribution-based drift adapter is proposed to effectively mitigate the bias induced by the long-tailed problem, which also facilitates the model in distinguishing OOD data through explicit distribution modelling. Extensive experiments show significant improvements in our model's ability to adapt to tailed drift and OOD drift. Moreover, it enhances the efficiency and accuracy of image-text alignment in vision language model pre-training, particularly in the long-tail open world scenario. Furthermore, we create a set of multi-modal datasets called OpenMMlo, specifically tailored for the long-tailed open world scenario, to validate our findings. To foster the development of the multi-modal community, we have made both OpenMMlo datasets and our code publicly available at: https://github.com/Anonymous0Knight/ConceptDriftMLLMs.

While previous distribution shift detection approaches can identify if a shift has occurred, these approaches cannot localize which specific features have caused a distribution shift -- a critical step in diagnosing or fixing any underlying issue. For example, in military sensor networks, users will want to detect when one or more of the sensors has been compromised, and critically, they will want to know which specific sensors might be compromised. Thus, we first define a formalization of this problem as multiple conditional distribution hypothesis tests and propose both non-parametric and parametric statistical tests. For both efficiency and flexibility, we then propose to use a test statistic based on the density model score function (i.e. gradient with respect to the input) -- which can easily compute test statistics for all dimensions in a single forward and backward pass. Any density model could be used for computing the necessary statistics including deep density models such as normalizing flows or autoregressive models. We additionally develop methods for identifying when and where a shift occurs in multivariate time-series data and show results for multiple scenarios using realistic attack models on both simulated and real world data.

Data drift is the change in model input data that is one of the key factors leading to machine learning models performance degradation over time. Monitoring drift helps detecting these issues and preventing their harmful consequences. Meaningful drift interpretation is a fundamental step towards effective re-training of the model. In this study we propose an end-to-end framework for reliable model-agnostic change-point detection and interpretation in large task-oriented dialog systems, proven effective in multiple customer deployments. We evaluate our approach and demonstrate its benefits with a novel variant of intent classification training dataset, simulating customer requests to a dialog system. We make the data publicly available.

Post-training quantization (PTQ) is a practical path to deploy large diffusion models, but quantization noise can accumulate over the denoising trajectory and degrade generation quality. We propose Q-Drift, a principled sampler-side correction that treats quantization error as an implicit stochastic perturbation on each denoising step and derives a marginal-distribution-preserving drift adjustment. Q-Drift estimates a timestep-wise variance statistic from calibration, in practice requiring as few as 5 paired full-precision/quantized calibration runs. The resulting sampler correction is plug-and-play with common samplers, diffusion models, and PTQ methods, while incurring negligible overhead at inference. Across six diverse text-to-image models (spanning DiT and U-Net), three samplers (Euler, flow-matching, DPM-Solver++), and two PTQ methods (SVDQuant, MixDQ), Q-Drift improves FID over the corresponding quantized baseline in most settings, with up to 4.59 FID reduction on PixArt-Sigma (SVDQuant W3A4), while preserving CLIP scores.

Diffusion models have shown promising ability in generating high-quality time series (TS) data. Despite the initial success, existing works mostly focus on the authenticity of data at the individual level, but pay less attention to preserving the population-level properties on the entire dataset. Such population-level properties include value distributions for each dimension and distributions of certain functional dependencies (e.g., cross-correlation, CC) between different dimensions. For instance, when generating house energy consumption TS data, the value distributions of the outside temperature and the kitchen temperature should be preserved, as well as the distribution of CC between them. Preserving such TS population-level properties is critical in maintaining the statistical insights of the datasets, mitigating model bias, and augmenting downstream tasks like TS prediction. Yet, it is often overlooked by existing models. Hence, data generated by existing models often bear distribution shifts from the original data. We propose Population-aware Diffusion for Time Series (PaD-TS), a new TS generation model that better preserves the population-level properties. The key novelties of PaD-TS include 1) a new training method explicitly incorporating TS population-level property preservation, and 2) a new dual-channel encoder model architecture that better captures the TS data structure. Empirical results in major benchmark datasets show that PaD-TS can improve the average CC distribution shift score between real and synthetic data by 5.9x while maintaining a performance comparable to state-of-the-art models on individual-level authenticity.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Distribution shifts -- where the training distribution differs from the test distribution -- can substantially degrade the accuracy of machine learning (ML) systems deployed in the wild. Despite their ubiquity in the real-world deployments, these distribution shifts are under-represented in the datasets widely used in the ML community today. To address this gap, we present WILDS, a curated benchmark of 10 datasets reflecting a diverse range of distribution shifts that naturally arise in real-world applications, such as shifts across hospitals for tumor identification; across camera traps for wildlife monitoring; and across time and location in satellite imaging and poverty mapping. On each dataset, we show that standard training yields substantially lower out-of-distribution than in-distribution performance. This gap remains even with models trained by existing methods for tackling distribution shifts, underscoring the need for new methods for training models that are more robust to the types of distribution shifts that arise in practice. To facilitate method development, we provide an open-source package that automates dataset loading, contains default model architectures and hyperparameters, and standardizes evaluations. Code and leaderboards are available at https://wilds.stanford.edu.

In federated learning (FL), the data distribution of each client may change over time, introducing both temporal and spatial data heterogeneity, known as concept drift. Data heterogeneity arises from three drift sources: real drift (a shift in the conditional distribution P(y|x)), virtual drift (a shift in the input distribution P(x)), and label drift (a shift in the label distribution P(y)). However, most existing FL methods addressing concept drift primarily focus on real drift. When clients experience virtual or label drift, these methods often fail to selectively retain useful historical knowledge, leading to catastrophic forgetting. A key challenge lies in distinguishing different sources of drift, as they require distinct adaptation strategies: real drift calls for discarding outdated data, while virtual or label drift benefits from retaining historical data. Without explicitly identifying the drift sources, a general adaptation strategy is suboptimal and may harm generalization. To address this challenge, we propose FedDAA, a dynamic clustered FL framework designed to adapt to multi-source concept drift while preserving valuable historical knowledge. Specifically, FedDAA integrates three modules: a cluster number determination module to find the optimal number of clusters; a real drift detection module to distinguish real drift from virtual/label drift; and a concept drift adaptation module to adapt to new data while retaining useful historical information. We provide theoretical convergence guarantees, and experiments show that FedDAA achieves 7.84% to 8.52% accuracy improvements over state-of-the-art methods on Fashion-MNIST, CIFAR-10, and CIFAR-100.

Machine learning models frequently experience performance drops under distribution shifts. The underlying cause of such shifts may be multiple simultaneous factors such as changes in data quality, differences in specific covariate distributions, or changes in the relationship between label and features. When a model does fail during deployment, attributing performance change to these factors is critical for the model developer to identify the root cause and take mitigating actions. In this work, we introduce the problem of attributing performance differences between environments to distribution shifts in the underlying data generating mechanisms. We formulate the problem as a cooperative game where the players are distributions. We define the value of a set of distributions to be the change in model performance when only this set of distributions has changed between environments, and derive an importance weighting method for computing the value of an arbitrary set of distributions. The contribution of each distribution to the total performance change is then quantified as its Shapley value. We demonstrate the correctness and utility of our method on synthetic, semi-synthetic, and real-world case studies, showing its effectiveness in attributing performance changes to a wide range of distribution shifts.

Trajectory prediction models often fail in real-world automated driving due to distributional shifts between training and test conditions. Such distributional shifts, whether behavioural or environmental, pose a critical risk by causing the model to make incorrect forecasts in unfamiliar situations. We propose a self-supervised method that trains a decoder in a post-hoc fashion on the self-supervised task of forecasting the second half of observed trajectories from the first half. The L2 norm of the gradient of this forecasting loss with respect to the decoder's final layer defines a score to identify distribution shifts. Our approach, first, does not affect the trajectory prediction model, ensuring no interference with original prediction performance and second, demonstrates substantial improvements on distribution shift detection for trajectory prediction on the Shifts and Argoverse datasets. Moreover, we show that this method can also be used to early detect collisions of a deep Q-Network motion planner in the Highway simulator. Source code is available at https://github.com/Michedev/forecasting-the-past.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

In machine learning, generalization against distribution shifts -- where deployment conditions diverge from the training scenarios -- is crucial, particularly in fields like climate modeling, biomedicine, and autonomous driving. The emergence of foundation models, distinguished by their extensive pretraining and task versatility, has led to an increased interest in their adaptability to distribution shifts. GPT-4V(ision) acts as the most advanced publicly accessible multimodal foundation model, with extensive applications across various domains, including anomaly detection, video understanding, image generation, and medical diagnosis. However, its robustness against data distributions remains largely underexplored. Addressing this gap, this study rigorously evaluates GPT-4V's adaptability and generalization capabilities in dynamic environments, benchmarking against prominent models like CLIP and LLaVA. We delve into GPT-4V's zero-shot generalization across 13 diverse datasets spanning natural, medical, and molecular domains. We further investigate its adaptability to controlled data perturbations and examine the efficacy of in-context learning as a tool to enhance its adaptation. Our findings delineate GPT-4V's capability boundaries in distribution shifts, shedding light on its strengths and limitations across various scenarios. Importantly, this investigation contributes to our understanding of how AI foundation models generalize to distribution shifts, offering pivotal insights into their adaptability and robustness. Code is publicly available at https://github.com/jameszhou-gl/gpt-4v-distribution-shift.

Anomaly detection (AD) is a crucial machine learning task that aims to learn patterns from a set of normal training samples to identify abnormal samples in test data. Most existing AD studies assume that the training and test data are drawn from the same data distribution, but the test data can have large distribution shifts arising in many real-world applications due to different natural variations such as new lighting conditions, object poses, or background appearances, rendering existing AD methods ineffective in such cases. In this paper, we consider the problem of anomaly detection under distribution shift and establish performance benchmarks on three widely-used AD and out-of-distribution (OOD) generalization datasets. We demonstrate that simple adaptation of state-of-the-art OOD generalization methods to AD settings fails to work effectively due to the lack of labeled anomaly data. We further introduce a novel robust AD approach to diverse distribution shifts by minimizing the distribution gap between in-distribution and OOD normal samples in both the training and inference stages in an unsupervised way. Our extensive empirical results on the three datasets show that our approach substantially outperforms state-of-the-art AD methods and OOD generalization methods on data with various distribution shifts, while maintaining the detection accuracy on in-distribution data.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample (X,Y) drawn from a distribution D and will face a model h and its classification result h(X). Agents can modify X to adapt to h, which will incur a distribution shift on (X,Y). Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of a model by studying how the performance of the model trained on the available source distribution (data) would translate to the performance on its induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bounds for the trade-offs that a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings, including covariate shift and target shift.

We introduce four new real-world distribution shift datasets consisting of changes in image style, image blurriness, geographic location, camera operation, and more. With our new datasets, we take stock of previously proposed methods for improving out-of-distribution robustness and put them to the test. We find that using larger models and artificial data augmentations can improve robustness on real-world distribution shifts, contrary to claims in prior work. We find improvements in artificial robustness benchmarks can transfer to real-world distribution shifts, contrary to claims in prior work. Motivated by our observation that data augmentations can help with real-world distribution shifts, we also introduce a new data augmentation method which advances the state-of-the-art and outperforms models pretrained with 1000 times more labeled data. Overall we find that some methods consistently help with distribution shifts in texture and local image statistics, but these methods do not help with some other distribution shifts like geographic changes. Our results show that future research must study multiple distribution shifts simultaneously, as we demonstrate that no evaluated method consistently improves robustness.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

We study inference-time scaling for diffusion models, where the goal is to adapt a pre-trained model to new target distributions without retraining. Existing guidance-based methods are simple but introduce bias, while particle-based corrections suffer from weight degeneracy and high computational cost. We introduce DriftLite, a lightweight, training-free particle-based approach that steers the inference dynamics on the fly with provably optimal stability control. DriftLite exploits a previously unexplored degree of freedom in the Fokker-Planck equation between the drift and particle potential, and yields two practical instantiations: Variance- and Energy-Controlling Guidance (VCG/ECG) for approximating the optimal drift with minimal overhead. Across Gaussian mixture models, particle systems, and large-scale protein-ligand co-folding problems, DriftLite consistently reduces variance and improves sample quality over pure guidance and sequential Monte Carlo baselines. These results highlight a principled, efficient route toward scalable inference-time adaptation of diffusion models.

Customer Lifetime Value (CLTV) prediction is a critical task in business applications. Accurately predicting CLTV is challenging in real-world business scenarios, as the distribution of CLTV is complex and mutable. Firstly, there is a large number of users without any consumption consisting of a long-tailed part that is too complex to fit. Secondly, the small set of high-value users spent orders of magnitude more than a typical user leading to a wide range of the CLTV distribution which is hard to capture in a single distribution. Existing approaches for CLTV estimation either assume a prior probability distribution and fit a single group of distribution-related parameters for all samples, or directly learn from the posterior distribution with manually predefined buckets in a heuristic manner. However, all these methods fail to handle complex and mutable distributions. In this paper, we propose a novel optimal distribution selection model OptDist for CLTV prediction, which utilizes an adaptive optimal sub-distribution selection mechanism to improve the accuracy of complex distribution modeling. Specifically, OptDist trains several candidate sub-distribution networks in the distribution learning module (DLM) for modeling the probability distribution of CLTV. Then, a distribution selection module (DSM) is proposed to select the sub-distribution for each sample, thus making the selection automatically and adaptively. Besides, we design an alignment mechanism that connects both modules, which effectively guides the optimization. We conduct extensive experiments on both two public and one private dataset to verify that OptDist outperforms state-of-the-art baselines. Furthermore, OptDist has been deployed on a large-scale financial platform for customer acquisition marketing campaigns and the online experiments also demonstrate the effectiveness of OptDist.

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.

Ensuring the reliability and safety of automated decision-making is crucial. It is well-known that data distribution shifts in machine learning can produce unreliable outcomes. This paper proposes a new approach for measuring the reliability of predictions under distribution shifts. We analyze how the outputs of a trained neural network change using clustering to measure distances between outputs and class centroids. We propose this distance as a metric to evaluate the confidence of predictions under distribution shifts. We assign each prediction to a cluster with centroid representing the mean softmax output for all correct predictions of a given class. We then define a safety threshold for a class as the smallest distance from an incorrect prediction to the given class centroid. We evaluate the approach on the MNIST and CIFAR-10 datasets using a Convolutional Neural Network and a Vision Transformer, respectively. The results show that our approach is consistent across these data sets and network models, and indicate that the proposed metric can offer an efficient way of determining when automated predictions are acceptable and when they should be deferred to human operators given a distribution shift.

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous "square-root law" of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the linear impact of order imbalances? Can one entirely explain the volatility of prices as resulting from the flow of uninformed metaorders that mechanically impact them? We introduce a new theoretical framework to describe metaorders with different signs, sizes and durations, which all impact prices as a square-root of volume but with a subsequent time decay. We show that, as in the original propagator model, price diffusion is ensured by the long memory of cross-correlations between metaorders. In order to account for the effect of strongly fluctuating volumes q of individual trades, we further introduce two q-dependent exponents, which allow us to describe how the moments of generalized volume imbalance and the correlation between price changes and generalized order flow imbalance scale with T. We predict in particular that the corresponding power-laws depend in a non-monotonic fashion on a parameter a, which allows one to put the same weight on all child orders or to overweight large ones, a behaviour that is clearly borne out by empirical data. We also predict that the correlation between price changes and volume imbalances should display a maximum as a function of a, which again matches observations. Such noteworthy agreement between theory and data suggests that our framework correctly captures the basic mechanism at the heart of price formation, namely the average impact of metaorders. We argue that our results support the "Order-Driven" theory of excess volatility, and are at odds with the idea that a "Fundamental" component accounts for a large share of the volatility of financial markets.

Risk decision systems in fraud detection and credit scoring operate under structural label absence: ground truth arrives weeks to months after decisions are made. During this blind period, model performance may degrade silently, eroding the governance evidence that justifies automated decisions. Existing drift detection methods either require labels (supervised detectors) or detect statistical change without distinguishing harmful degradation from benign distributional evolution (unsupervised detectors). No existing framework integrates drift detection with governance evidence assessment and operational response. This paper presents a label-free governance monitoring extension to the Governance Drift Toolkit that produces governance alerts rather than statistical alarms. The monitoring architecture applies composite multi-proxy monitoring across four proxy monitors (score distribution, feature drift, prediction entropy, confidence distribution), with governance-calibrated thresholds. Empirical evaluation on the Lending Club credit scoring dataset (1.37M loans, 11 years) demonstrates three findings. First, raw proxy metrics (Feature PSI delta up to 1.84, Score PSI delta up to 0.92) distinguish injected covariate degradation from natural temporal drift in an offline evaluation setting. Second, pure concept drift in P(Y|X) produces exactly zero delta across all proxy metrics in all windows, confirming the irreducible blind spot of label-free monitoring as a structural verification. Third, the composite score provides monotonic severity progression as more monitors trigger (0.583 to 0.833 to 1.000), enabling graduated governance response. Cross-domain comparison with IEEE-CIS fraud detection results shows the detectable/undetectable boundary is consistent across both domains. The toolkit and evaluation code are available as open-source artifacts.

Facing climate change, the already limited availability of drinking water will decrease in the future rendering drinking water an increasingly scarce resource. Considerable amounts of it are lost through leakages in water transportation and distribution networks. Thus, anomaly detection and localization, in particular for leakages, are crucial but challenging tasks due to the complex interactions and changing demands in water distribution networks. In this work, we analyze the effects of anomalies on the dynamics of critical infrastructure systems by modeling the networks employing Bayesian networks. We then discuss how the problem is connected to and can be considered through the lens of concept drift. In particular, we argue that model-based explanations of concept drift are a promising tool for localizing anomalies given limited information about the network. The methodology is experimentally evaluated using realistic benchmark scenarios. To showcase that our methodology applies to critical infrastructure more generally, in addition to considering leakages and sensor faults in water systems, we showcase the suitability of the derived technique to localize sensor faults in power systems.

We study the problem of predicting numeric labels that are constrained to the integers or to a subrange of the integers. For example, the number of up-votes on social media posts, or the number of bicycles available at a public rental station. While it is possible to model these as continuous values, and to apply traditional regression, this approach changes the underlying distribution on the labels from discrete to continuous. Discrete distributions have certain benefits, which leads us to the question whether such integer labels can be modeled directly by a discrete distribution, whose parameters are predicted from the features of a given instance. Moreover, we focus on the use case of output distributions of neural networks, which adds the requirement that the parameters of the distribution be continuous so that backpropagation and gradient descent may be used to learn the weights of the network. We investigate several options for such distributions, some existing and some novel, and test them on a range of tasks, including tabular learning, sequential prediction and image generation. We find that overall the best performance comes from two distributions: Bitwise, which represents the target integer in bits and places a Bernoulli distribution on each, and a discrete analogue of the Laplace distribution, which uses a distribution with exponentially decaying tails around a continuous mean.

This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales r. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade at a constant rate varepsilon_u; iii) On small scales, the even order moments of pairwise velocity Delta u_L follow a two-thirds law (-varepsilon_ur)^{2/3}, while the odd order moments follow a linear scaling langle(Delta u_L)^{2n+1}rangle=(2n+1)langle(Delta u_L)^{2n}ranglelangleDelta u_Lrangler; iv) The scale variation of the velocity distributions was studied for longitudinal velocities u_L or u_L^{'}, pairwise velocity (velocity difference) Delta u_L=u_L^{'}-u_L and velocity sum Sigma u_L=u^{'}_L+u_L. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; v) On small scales, u_L and Sigma u_L can be modeled by a X distribution to maximize the system entropy; vi) On large scales, Delta u_L and Sigma u_L can be modeled by a logistic or a X distribution; vii) the redshift variation of the velocity distributions follows the evolution of the X distribution involving a shape parameter alpha(z) decreasing with time.

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an alternative approach, utilizing neural networks combined with ODE solvers to learn continuous latent representations through parameterized vector fields. Neural Stochastic Differential Equations (Neural SDEs) extend Neural ODEs by incorporating a diffusion term, although this addition is not trivial, particularly when addressing irregular intervals and missing values. Consequently, careful design of drift and diffusion functions is crucial for maintaining stability and enhancing performance, while incautious choices can result in adverse properties such as the absence of strong solutions, stochastic destabilization, or unstable Euler discretizations, significantly affecting Neural SDEs' performance. In this study, we propose three stable classes of Neural SDEs: Langevin-type SDE, Linear Noise SDE, and Geometric SDE. Then, we rigorously demonstrate their robustness in maintaining excellent performance under distribution shift, while effectively preventing overfitting. To assess the effectiveness of our approach, we conduct extensive experiments on four benchmark datasets for interpolation, forecasting, and classification tasks, and analyze the robustness of our methods with 30 public datasets under different missing rates. Our results demonstrate the efficacy of the proposed method in handling real-world irregular time series data.

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.

In stochastic multi-armed bandits, the reward distribution of each arm is assumed to be stationary. This assumption is often violated in practice (e.g., in recommendation systems), where the reward of an arm may change whenever is selected, i.e., rested bandit setting. In this paper, we consider the non-parametric rotting bandit setting, where rewards can only decrease. We introduce the filtering on expanding window average (FEWA) algorithm that constructs moving averages of increasing windows to identify arms that are more likely to return high rewards when pulled once more. We prove that for an unknown horizon T, and without any knowledge on the decreasing behavior of the K arms, FEWA achieves problem-dependent regret bound of mathcal{O}((KT)), and a problem-independent one of mathcal{O}(KT). Our result substantially improves over the algorithm of Levine et al. (2017), which suffers regret mathcal{O}(K^{1/3}T^{2/3}). FEWA also matches known bounds for the stochastic bandit setting, thus showing that the rotting bandits are not harder. Finally, we report simulations confirming the theoretical improvements of FEWA.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

As black-box models increasingly power high-stakes applications, a variety of data-driven explanation methods have been introduced. Meanwhile, machine learning models are constantly challenged by distributional shifts. A question naturally arises: Are data-driven explanations robust against out-of-distribution data? Our empirical results show that even though predict correctly, the model might still yield unreliable explanations under distributional shifts. How to develop robust explanations against out-of-distribution data? To address this problem, we propose an end-to-end model-agnostic learning framework Distributionally Robust Explanations (DRE). The key idea is, inspired by self-supervised learning, to fully utilizes the inter-distribution information to provide supervisory signals for the learning of explanations without human annotation. Can robust explanations benefit the model's generalization capability? We conduct extensive experiments on a wide range of tasks and data types, including classification and regression on image and scientific tabular data. Our results demonstrate that the proposed method significantly improves the model's performance in terms of explanation and prediction robustness against distributional shifts.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

Three key properties that are desired of trustworthy machine learning models deployed in high-stakes environments are fairness, explainability, and an ability to account for various kinds of "drift". While drifts in model accuracy, for example due to covariate shift, have been widely investigated, drifts in fairness metrics over time remain largely unexplored. In this paper, we propose FEAMOE, a novel "mixture-of-experts" inspired framework aimed at learning fairer, more explainable/interpretable models that can also rapidly adjust to drifts in both the accuracy and the fairness of a classifier. We illustrate our framework for three popular fairness measures and demonstrate how drift can be handled with respect to these fairness constraints. Experiments on multiple datasets show that our framework as applied to a mixture of linear experts is able to perform comparably to neural networks in terms of accuracy while producing fairer models. We then use the large-scale HMDA dataset and show that while various models trained on HMDA demonstrate drift with respect to both accuracy and fairness, FEAMOE can ably handle these drifts with respect to all the considered fairness measures and maintain model accuracy as well. We also prove that the proposed framework allows for producing fast Shapley value explanations, which makes computationally efficient feature attribution based explanations of model decisions readily available via FEAMOE.

Machine learning models often experience performance degradation post-deployment due to shifts in data distribution. It is challenging to assess model's performance accurately when labels are missing or delayed. Existing proxy methods, such as drift detection, fail to measure the effects of these shifts adequately. To address this, we introduce a new method, Probabilistic Adaptive Performance Estimation (PAPE), for evaluating classification models on unlabeled data that accurately quantifies the impact of covariate shift on model performance. It is model and data-type agnostic and works for various performance metrics. Crucially, PAPE operates independently of the original model, relying only on its predictions and probability estimates, and does not need any assumptions about the nature of the covariate shift, learning directly from data instead. We tested PAPE on tabular data using over 900 dataset-model combinations created from US census data, assessing its performance against multiple benchmarks. Overall, PAPE provided more accurate performance estimates than other evaluated methodologies.

Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, most Bayesian papers have focused on the retrospective segmentation problem. Here we examine the case where the model parameters before and after the changepoint are independent and we derive an online algorithm for exact inference of the most recent changepoint. We compute the probability distribution of the length of the current ``run,'' or time since the last changepoint, using a simple message-passing algorithm. Our implementation is highly modular so that the algorithm may be applied to a variety of types of data. We illustrate this modularity by demonstrating the algorithm on three different real-world data sets.

The study conducted by Shumailov et al. (2024) demonstrates that repeatedly training a generative model on synthetic data leads to model collapse. This finding has generated considerable interest and debate, particularly given that current models have nearly exhausted the available data. In this work, we investigate the effects of fitting a distribution (through Kernel Density Estimation, or KDE) or a model to the data, followed by repeated sampling from it. Our objective is to develop a theoretical understanding of the phenomenon observed by Shumailov et al. (2024). Our results indicate that the outcomes reported are a statistical phenomenon and may be unavoidable.

Volatility clustering is an important characteristic that has a significant effect on the behavior of stock markets. However, designing robust models for accurate prediction of future volatilities of stock prices is a very challenging research problem. We present several volatility models based on generalized autoregressive conditional heteroscedasticity (GARCH) framework for modeling the volatility of ten stocks listed in the national stock exchange (NSE) of India. The stocks are selected from the auto sector and the banking sector of the Indian economy, and they have a significant impact on the sectoral index of their respective sectors in the NSE. The historical stock price records from Jan 1, 2010, to Apr 30, 2021, are scraped from the Yahoo Finance website using the DataReader API of the Pandas module in the Python programming language. The GARCH modules are built and fine-tuned on the training data and then tested on the out-of-sample data to evaluate the performance of the models. The analysis of the results shows that asymmetric GARCH models yield more accurate forecasts on the future volatility of stocks.

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling for well-known function spaces. The highlight of this paper is that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates in the total variation distance and in the Wasserstein distance of order one. Furthermore, we extend our theory to demonstrate how diffusion models adapt to low-dimensional data distributions. We expect these results advance theoretical understandings of diffusion modeling and its ability to generate verisimilar outputs.

In reinforcement learning an agent interacts with the environment by taking actions and observing the next state and reward. When sampled probabilistically, these state transitions, rewards, and actions can all induce randomness in the observed long-term return. Traditionally, reinforcement learning algorithms average over this randomness to estimate the value function. In this paper, we build on recent work advocating a distributional approach to reinforcement learning in which the distribution over returns is modeled explicitly instead of only estimating the mean. That is, we examine methods of learning the value distribution instead of the value function. We give results that close a number of gaps between the theoretical and algorithmic results given by Bellemare, Dabney, and Munos (2017). First, we extend existing results to the approximate distribution setting. Second, we present a novel distributional reinforcement learning algorithm consistent with our theoretical formulation. Finally, we evaluate this new algorithm on the Atari 2600 games, observing that it significantly outperforms many of the recent improvements on DQN, including the related distributional algorithm C51.

The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [1]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data.

The change in data distribution over time, also known as concept drift, poses a significant challenge to the reliability of online learning methods. Existing methods typically require model retraining or drift detection, both of which demand high computational costs and are often unsuitable for real-time applications. To address these limitations, a lightweight, fast and efficient random vector functional-link network termed Lite-RVFL is proposed, capable of adapting to concept drift without drift detection and retraining. Lite-RVFL introduces a novel objective function that assigns weights exponentially increasing to new samples, thereby emphasizing recent data and enabling timely adaptation. Theoretical analysis confirms the feasibility of this objective function for drift adaptation, and an efficient incremental update rule is derived. Experimental results on a real-world safety assessment task validate the efficiency, effectiveness in adapting to drift, and potential to capture temporal patterns of Lite-RVFL. The source code is available at https://github.com/songqiaohu/Lite-RVFL.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

In this paper, we study the infinite-depth limit of finite-width residual neural networks with random Gaussian weights. With proper scaling, we show that by fixing the width and taking the depth to infinity, the pre-activations converge in distribution to a zero-drift diffusion process. Unlike the infinite-width limit where the pre-activation converge weakly to a Gaussian random variable, we show that the infinite-depth limit yields different distributions depending on the choice of the activation function. We document two cases where these distributions have closed-form (different) expressions. We further show an intriguing change of regime phenomenon of the post-activation norms when the width increases from 3 to 4. Lastly, we study the sequential limit infinite-depth-then-infinite-width and compare it with the more commonly studied infinite-width-then-infinite-depth limit.

In many real-world settings, agents must learn from an offline dataset gathered by some prior behavior policy. Such a setting naturally leads to distribution shift between the behavior policy and the target policy being trained - requiring policy conservatism to avoid instability and overestimation bias. Autoregressive world models offer a different solution to this by generating synthetic, on-policy experience. However, in practice, model rollouts must be severely truncated to avoid compounding error. As an alternative, we propose policy-guided diffusion. Our method uses diffusion models to generate entire trajectories under the behavior distribution, applying guidance from the target policy to move synthetic experience further on-policy. We show that policy-guided diffusion models a regularized form of the target distribution that balances action likelihood under both the target and behavior policies, leading to plausible trajectories with high target policy probability, while retaining a lower dynamics error than an offline world model baseline. Using synthetic experience from policy-guided diffusion as a drop-in substitute for real data, we demonstrate significant improvements in performance across a range of standard offline reinforcement learning algorithms and environments. Our approach provides an effective alternative to autoregressive offline world models, opening the door to the controllable generation of synthetic training data.

We introduce Animate124 (Animate-one-image-to-4D), the first work to animate a single in-the-wild image into 3D video through textual motion descriptions, an underexplored problem with significant applications. Our 4D generation leverages an advanced 4D grid dynamic Neural Radiance Field (NeRF) model, optimized in three distinct stages using multiple diffusion priors. Initially, a static model is optimized using the reference image, guided by 2D and 3D diffusion priors, which serves as the initialization for the dynamic NeRF. Subsequently, a video diffusion model is employed to learn the motion specific to the subject. However, the object in the 3D videos tends to drift away from the reference image over time. This drift is mainly due to the misalignment between the text prompt and the reference image in the video diffusion model. In the final stage, a personalized diffusion prior is therefore utilized to address the semantic drift. As the pioneering image-text-to-4D generation framework, our method demonstrates significant advancements over existing baselines, evidenced by comprehensive quantitative and qualitative assessments.

We develop an econometric framework integrating heavy-tailed Student's t distributions with behavioral probability weighting while preserving infinite divisibility. Using 432{,}752 observations across 86 assets (2004--2024), we demonstrate Student's t specifications outperform Gaussian models in 88.4\% of cases. Bounded probability-weighting transformations preserve mathematical properties required for dynamic pricing. Gaussian models underestimate 99\% Value-at-Risk by 19.7\% versus 3.2\% for our specification. Joint estimation procedures identify tail and behavioral parameters with established asymptotic properties. Results provide robust inference for asset-pricing applications where heavy tails and behavioral distortions coexist.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter-Syntetos-Babai (TSB) method provide simple heuristics but lack a principled generative foundation. Deep learning models address these limitations but often require large datasets and sacrifice interpretability. We introduce TSB-HB, a hierarchical Bayesian extension of TSB. Demand occurrence is modeled with a Beta-Binomial distribution, while nonzero demand sizes follow a Log-Normal distribution. Crucially, hierarchical priors enable partial pooling across items, stabilizing estimates for sparse or cold-start series while preserving heterogeneity. This framework yields a fully generative and interpretable model that generalizes classical exponential smoothing. On the UCI Online Retail dataset, TSB-HB achieves lower RMSE and RMSSE than Croston, SBA, TSB, ADIDA, IMAPA, ARIMA and Theta, and on a subset of the M5 dataset it outperforms all classical baselines we evaluate. The model provides calibrated probabilistic forecasts and improved accuracy on intermittent and lumpy items by combining a generative formulation with hierarchical shrinkage, while remaining interpretable and scalable.

Despite diffusion models' superior capabilities in modeling complex distributions, there are still non-trivial distributional discrepancies between generated and ground-truth images, which has resulted in several notable problems in image generation, including missing object errors in text-to-image generation and low image quality. Existing methods that attempt to address these problems mostly do not tend to address the fundamental cause behind these problems, which is the distributional discrepancies, and hence achieve sub-optimal results. In this paper, we propose a particle filtering framework that can effectively address both problems by explicitly reducing the distributional discrepancies. Specifically, our method relies on a set of external guidance, including a small set of real images and a pre-trained object detector, to gauge the distribution gap, and then design the resampling weight accordingly to correct the gap. Experiments show that our methods can effectively correct missing object errors and improve image quality in various image generation tasks. Notably, our method outperforms the existing strongest baseline by 5% in object occurrence and 1.0 in FID on MS-COCO. Our code is publicly available at https://github.com/UCSB-NLP-Chang/diffusion_resampling.git.

As the number of Internet of Things (IoT) devices and systems have surged, IoT data analytics techniques have been developed to detect malicious cyber-attacks and secure IoT systems; however, concept drift issues often occur in IoT data analytics, as IoT data is often dynamic data streams that change over time, causing model degradation and attack detection failure. This is because traditional data analytics models are static models that cannot adapt to data distribution changes. In this paper, we propose a Performance Weighted Probability Averaging Ensemble (PWPAE) framework for drift adaptive IoT anomaly detection through IoT data stream analytics. Experiments on two public datasets show the effectiveness of our proposed PWPAE method compared against state-of-the-art methods.

Significant work has been recently dedicated to the stochastic delayed bandit setting because of its relevance in applications. The applicability of existing algorithms is however restricted by the fact that strong assumptions are often made on the delay distributions, such as full observability, restrictive shape constraints, or uniformity over arms. In this work, we weaken them significantly and only assume that there is a bound on the tail of the delay. In particular, we cover the important case where the delay distributions vary across arms, and the case where the delays are heavy-tailed. Addressing these difficulties, we propose a simple but efficient UCB-based algorithm called the PatientBandits. We provide both problems-dependent and problems-independent bounds on the regret as well as performance lower bounds.

Out-of-distribution (OOD) prediction is often approached by restricting models to causal or invariant covariates, avoiding non-causal spurious associations that may be unstable across environments. Despite its theoretical appeal, this strategy frequently underperforms empirical risk minimization (ERM) in practice. We investigate the source of this gap and show that such failures naturally arise when only a subset of the true causes of the outcome is observed. In these settings, non-causal spurious covariates can serve as informative proxies for unobserved causes and substantially improve prediction, except under distribution shifts that break these proxy relationships. Consequently, the optimal set of predictive covariates is neither universal nor necessarily exhibits invariant relationships with the outcome across all environments, but instead depends on the specific type of shift encountered. Crucially, we observe that different covariate shifts induce distinct, observable signatures in the covariate distribution itself. Moreover, these signatures can be extracted from unlabeled data in the target OOD environment and used to assess when proxy covariates remain reliable and when they fail. Building on this observation, we propose an environment-adaptive covariate selection (EACS) algorithm that maps environment-level covariate summaries to environment-specific covariate sets, while allowing the incorporation of prior causal knowledge as constraints. Across simulations and applied datasets, EACS consistently outperforms static causal, invariant, and ERM-based predictors under diverse distribution shifts.

For a sequence of random variables (X_1, X_2, ldots, X_n), n geq 1, that are independent and identically distributed with a regularly varying tail with index -alpha, alpha geq 0, we show that the contribution of the maximum term M_n triangleq max(X_1,ldots,X_n) in the sum S_n triangleq X_1 + cdots +X_n, as n to infty, decreases monotonically with alpha in stochastic ordering sense.

Boltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples in thermodynamic equilibrium. The equilibrium distribution is usually defined by an energy function and a thermodynamic state. Here we propose temperature-steerable flows (TSF) which are able to generate a family of probability densities parametrized by a choosable temperature parameter. TSFs can be embedded in generalized ensemble sampling frameworks to sample a physical system across multiple thermodynamic states.

We report the discovery of bimodal structure in the drift rate distribution of upward-drifting burst clusters from the hyperactive repeating fast radio burst FRB 20240114A. Using unsupervised machine learning (UMAP dimensionality reduction combined with HDBSCAN density-based clustering) applied to 233 upward-drifting burst clusters from the FAST telescope dataset, we identify a distinct subpopulation of 45 burst clusters (Cluster C1) with mean drift rates 2.5x higher than typical upward-drifting burst clusters (245.6 vs 98.1 MHz/ms). Gaussian mixture modeling reveals strong evidence for bimodality (delta-BIC = 296.6), with clearly separated modes (Ashman's D = 2.70 > 2) and a statistically significant gap in the distribution (11.3 sigma). Crucially, we demonstrate that this bimodality persists when restricting the analysis to single-component (U1) burst clusters only (delta-BIC = 19.9, Ashman's D = 2.71), confirming that the result is not an artifact of combining single- and multi-component burst clusters with different drift rate definitions. The extreme-drift subpopulation also exhibits systematically lower peak frequencies (-7%), shorter durations (-29%), and distinct clustering in multi-dimensional feature space. These findings are suggestive of two spatially separated emission regions in the magnetosphere, each producing upward-drifting burst clusters with distinct physical characteristics, although confirmation requires observations from additional epochs and sources.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

This article studies the change in the prediction accuracy of a response variable when the number of predictors increases, and all variables follow a multivariate normal distribution. Assuming that the correlations between variables are independently drawn, I show that adding variables leads to globally increasing returns to scale when the mean of the correlation distribution is zero. The speed of learning depends positively on the variance of the correlation distribution. I use simulations to study the more complex case of correlation distributions with a non-zero mean and find a pattern of decreasing returns followed by increasing returns to scale - as long as the variance of correlations is not degenerate, in which case globally decreasing returns emerge. I train a collaborative filtering algorithm using the MovieLens 1M dataset to analyze returns from adding variables in a more realistic setting and find globally increasing returns to scale across 2,000 variables. The results suggest significant scale advantages from additional variables in prediction tasks.

In statistical modelling the biggest threat is concept drift which makes the model gradually showing deteriorating performance over time. There are state of the art methodologies to detect the impact of concept drift, however general strategy considered to overcome the issue in performance is to rebuild or re-calibrate the model periodically as the variable patterns for the model changes significantly due to market change or consumer behavior change etc. Quantitative research is the most widely spread application of data science in Marketing or financial domain where applicability of state of the art reinforcement learning for auto-learning is less explored paradigm. Reinforcement learning is heavily dependent on having a simulated environment which is majorly available for gaming or online systems, to learn from the live feedback. However, there are some research happened on the area of online advertisement, pricing etc where due to the nature of the online learning environment scope of reinforcement learning is explored. Our proposed solution is a reinforcement learning based, true self-learning algorithm which can adapt to the data change or concept drift and auto learn and self-calibrate for the new patterns of the data solving the problem of concept drift. Keywords - Reinforcement learning, Genetic Algorithm, Q-learning, Classification modelling, CMA-ES, NES, Multi objective optimization, Concept drift, Population stability index, Incremental learning, F1-measure, Predictive Modelling, Self-learning, MCTS, AlphaGo, AlphaZero

Real-world large language model deployments (e.g., conversational AI systems, code generation assistants) naturally generate abundant implicit user dissatisfaction (DSAT) signals, as users iterate toward better answers through refinements, corrections, and expressed preferences, while explicit satisfaction (SAT) feedback is scarce. Existing preference learning approaches are poorly aligned with this data profile, as they rely on costly human annotations or assume plentiful positive responses. In this paper, we introduce DRIFT (Dissatisfaction-Refined Iterative preFerence Training), which anchors training on real-world DSAT signals and samples positives dynamically from the evolving policy. Empirically, DRIFT models trained on real-world WildFeedback datasets and synthetic UltraFeedback datasets achieve up to +6.23\% (7B) / +7.61\% (14B) on WildBench Task Score and up to +8.95\% (7B) / +12.29\% (14B) on AlpacaEval2 win rate over base models, outperforming strong baseline methods such as iterative DPO and SPIN. At larger scales, the improvements are particularly pronounced: 14B models trained with DRIFT surpass GPT-4o-mini on WildBench. Further analysis shows that DRIFT also preserves exploratory capacity, yielding more diverse high-reward solutions rather than collapsing to narrow subsets. Theoretically, we demonstrate that this design preserves preference margins and avoids the gradient degeneration. These results show that DRIFT is an effective and scalable recipe for real-world post-training that leverages the most abundant and informative signal. The code and data are available at https://github.com/cacayaya/DRIFT.git.

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes unfeasible. In this work, we use non-parametric bootstrapped uncertainty estimates and SHAP values to provide explainable uncertainty estimation as a technique that aims to monitor the deterioration of machine learning models in deployment environments, as well as determine the source of model deterioration when target labels are not available. Classical methods are purely aimed at detecting distribution shift, which can lead to false positives in the sense that the model has not deteriorated despite a shift in the data distribution. To estimate model uncertainty we construct prediction intervals using a novel bootstrap method, which improves upon the work of Kumar & Srivastava (2012). We show that both our model deterioration detection system as well as our uncertainty estimation method achieve better performance than the current state-of-the-art. Finally, we use explainable AI techniques to gain an understanding of the drivers of model deterioration. We release an open source Python package, doubt, which implements our proposed methods, as well as the code used to reproduce our experiments.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

Understanding how machine learning models respond to distributional shifts is a key research challenge. Mazes serve as an excellent testbed due to varied generation algorithms offering a nuanced platform to simulate both subtle and pronounced distributional shifts. To enable systematic investigations of model behavior on out-of-distribution data, we present maze-dataset, a comprehensive library for generating, processing, and visualizing datasets consisting of maze-solving tasks. With this library, researchers can easily create datasets, having extensive control over the generation algorithm used, the parameters fed to the algorithm of choice, and the filters that generated mazes must satisfy. Furthermore, it supports multiple output formats, including rasterized and text-based, catering to convolutional neural networks and autoregressive transformer models. These formats, along with tools for visualizing and converting between them, ensure versatility and adaptability in research applications.

We propose a general methodology for recovering preference parameters from data on choices and response times. Our methods yield estimates with fast (1/n for n data points) convergence rates when specialized to the popular Drift Diffusion Model (DDM), but are broadly applicable to generalizations of the DDM as well as to alternative models of decision making that make use of response time data. The paper develops an empirical application to an experiment on intertemporal choice, showing that the use of response times delivers predictive accuracy and matters for the estimation of economically relevant parameters.

Adapting to concept drift is a challenging task in machine learning, which is usually tackled using incremental learning techniques that periodically re-fit a learning model leveraging newly available data. A primary limitation of these techniques is their reliance on substantial amounts of data for retraining. The necessity of acquiring fresh data introduces temporal delays prior to retraining, potentially rendering the models inaccurate if a sudden concept drift occurs in-between two consecutive retrainings. In communication networks, such issue emerges when performing traffic forecasting following a~failure event: post-failure re-routing may induce a drastic shift in distribution and pattern of traffic data, thus requiring a timely model adaptation. In this work, we address this challenge for the problem of traffic forecasting and propose an approach that exploits adaptive learning algorithms, namely, liquid neural networks, which are capable of self-adaptation to abrupt changes in data patterns without requiring any retraining. Through extensive simulations of failure scenarios, we compare the predictive performance of our proposed approach to that of a reference method based on incremental learning. Experimental results show that our proposed approach outperforms incremental learning-based methods in situations where the shifts in traffic patterns are drastic.

We propose a method to easily modify existing offline Recommender Systems to run online using Transfer Learning. Online Learning for Recommender Systems has two main advantages: quality and scale. Like many Machine Learning algorithms in production if not regularly retrained will suffer from Concept Drift. A policy that is updated frequently online can adapt to drift faster than a batch system. This is especially true for user-interaction systems like recommenders where the underlying distribution can shift drastically to follow user behaviour. As a platform grows rapidly like Grubhub, the cost of running batch training jobs becomes material. A shift from stateless batch learning offline to stateful incremental learning online can recover, for example, at Grubhub, up to a 45x cost savings and a +20% metrics increase. There are a few challenges to overcome with the transition to online stateful learning, namely convergence, non-stationary embeddings and off-policy evaluation, which we explore from our experiences running this system in production.

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence, an extension of weak convergence that compares a statistic or process to a sequence of evolving processes. Relative weak convergence retains the essential consequences of classical weak convergence and coincides with it under stationarity. Crucially, it applies in general non-stationary settings where classical weak convergence fails. We establish concrete relative CLTs for random vectors and empirical processes, along with sequential, weighted, and bootstrap variants, that parallel the state-of-the-art in stationary settings. Our framework and results offer simple, plug-in replacements for classical CLTs whenever stationarity is untenable, as illustrated by applications in nonparametric trend estimation and hypothesis testing.

We consider N classical particles interacting via the Coulomb potential in spatial dimension d and in the presence of an external trap, at equilibrium at inverse temperature beta. In the large N limit, the particles are confined within a droplet of finite size. We study smooth linear statistics, i.e. the fluctuations of sums of the form {cal L}_N = sum_{i=1}^N f({bf x}_i), where {bf x}_i's are the positions of the particles and where f({bf x}_i) is a sufficiently regular function. There exists at present standard results for the first and second moments of {cal L}_N in the large N limit, as well as associated Central Limit Theorems in general dimension and for a wide class of confining potentials. Here we obtain explicit expressions for the higher order cumulants of {cal L}_N at large N, when the function f({bf x})=f(|{bf x}|) and the confining potential are both rotationnally invariant. A remarkable feature of our results is that these higher cumulants depend only on the value of f'(|{bf x}|) and its higher order derivatives evaluated exactly at the boundary of the droplet, which in this case is a d-dimensional sphere. In the particular two-dimensional case d=2 at the special value beta=2, a connection to the Ginibre ensemble allows us to derive these results in an alternative way using the tools of determinantal point processes. Finally we also obtain the large deviation form of the full probability distribution function of {cal L}_N.

In contrast to classical reinforcement learning, distributional reinforcement learning algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or arbitrarily complex, a common approach finds approximations within a set of representable, parametric distributions. Typically, this involves a projection of the unconstrained distribution onto the set of simplified distributions. We argue that this projection step entails a strong inductive bias when coupled with neural networks and gradient descent, thereby profoundly impacting the generalization behavior of learned models. In order to facilitate reliable uncertainty estimation through diversity, this work studies the combination of several different projections and representations in a distributional ensemble. We establish theoretical properties of such projection ensembles and derive an algorithm that uses ensemble disagreement, measured by the average 1-Wasserstein distance, as a bonus for deep exploration. We evaluate our algorithm on the behavior suite benchmark and find that diverse projection ensembles lead to significant performance improvements over existing methods on a wide variety of tasks with the most pronounced gains in directed exploration problems.

Out-of-distribution (OOD) detection is crucial to modern deep learning applications by identifying and alerting about the OOD samples that should not be tested or used for making predictions. Current OOD detection methods have made significant progress when in-distribution (ID) and OOD samples are drawn from static distributions. However, this can be unrealistic when applied to real-world systems which often undergo continuous variations and shifts in ID and OOD distributions over time. Therefore, for an effective application in real-world systems, the development of OOD detection methods that can adapt to these dynamic and evolving distributions is essential. In this paper, we propose a novel and more realistic setting called continuously adaptive out-of-distribution (CAOOD) detection which targets on developing an OOD detection model that enables dynamic and quick adaptation to a new arriving distribution, with insufficient ID samples during deployment time. To address CAOOD, we develop meta OOD learning (MOL) by designing a learning-to-adapt diagram such that a good initialized OOD detection model is learned during the training process. In the testing process, MOL ensures OOD detection performance over shifting distributions by quickly adapting to new distributions with a few adaptations. Extensive experiments on several OOD benchmarks endorse the effectiveness of our method in preserving both ID classification accuracy and OOD detection performance on continuously shifting distributions.

Temporal distribution shift (TDS) erodes the long-term accuracy of recommender systems, yet industrial practice still relies on periodic incremental training, which struggles to capture both stable and transient patterns. Existing approaches such as invariant learning and self-supervised learning offer partial solutions but often suffer from unstable temporal generalization, representation collapse, or inefficient data utilization. To address these limitations, we propose ELBO_TDS, a probabilistic framework that integrates seamlessly into industry-scale incremental learning pipelines. First, we identify key shifting factors through statistical analysis of real-world production data and design a simple yet effective data augmentation strategy that resamples these time-varying factors to extend the training support. Second, to harness the benefits of this extended distribution while preventing representation collapse, we model the temporal recommendation scenario using a causal graph and derive a self-supervised variational objective, ELBO_TDS, grounded in the causal structure. Extensive experiments supported by both theoretical and empirical analysis demonstrate that our method achieves superior temporal generalization, yielding a 2.33\% uplift in GMV per user and has been successfully deployed in Shopee Product Search. Code is available at https://github.com/FuCongResearchSquad/ELBO4TDS.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Models for learning probability distributions such as generative models and density estimators behave quite differently from models for learning functions. One example is found in the memorization phenomenon, namely the ultimate convergence to the empirical distribution, that occurs in generative adversarial networks (GANs). For this reason, the issue of generalization is more subtle than that for supervised learning. For the bias potential model, we show that dimension-independent generalization accuracy is achievable if early stopping is adopted, despite that in the long term, the model either memorizes the samples or diverges.

Calibrated uncertainty estimates in machine learning are crucial to many fields such as autonomous vehicles, medicine, and weather and climate forecasting. While there is extensive literature on uncertainty calibration for classification, the classification findings do not always translate to regression. As a result, modern models for predicting uncertainty in regression settings typically produce uncalibrated and overconfident estimates. To address these gaps, we present a calibration method for regression settings that does not assume a particular uncertainty distribution over the error: Calibrating Regression Uncertainty Distributions Empirically (CRUDE). CRUDE makes the weaker assumption that error distributions have a constant arbitrary shape across the output space, shifted by predicted mean and scaled by predicted standard deviation. We detail a theoretical connection between CRUDE and conformal inference. Across an extensive set of regression tasks, CRUDE demonstrates consistently sharper, better calibrated, and more accurate uncertainty estimates than state-of-the-art techniques.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Robustness to natural distribution shifts has seen remarkable progress thanks to recent pre-training strategies combined with better fine-tuning methods. However, such fine-tuning assumes access to large amounts of labelled data, and the extent to which the observations hold when the amount of training data is not as high remains unknown. We address this gap by performing the first in-depth study of robustness to various natural distribution shifts in different low-shot regimes: spanning datasets, architectures, pre-trained initializations, and state-of-the-art robustness interventions. Most importantly, we find that there is no single model of choice that is often more robust than others, and existing interventions can fail to improve robustness on some datasets even if they do so in the full-shot regime. We hope that our work will motivate the community to focus on this problem of practical importance.

We show via a combination of mathematical arguments and empirical evidence that data distributions sampled from diffusion models satisfy a Concentration of Measure Property saying that any Lipschitz 1-dimensional projection of a random vector is not too far from its mean with high probability. This implies that such models are quite restrictive and gives an explanation for a fact previously observed in the literature that conventional diffusion models cannot capture "heavy-tailed" data (i.e. data x for which the norm |x|_2 does not possess a sub-Gaussian tail) well. We then proceed to train a generalized linear model using stochastic gradient descent (SGD) on the diffusion-generated data for a multiclass classification task and observe empirically that a Gaussian universality result holds for the test error. In other words, the test error depends only on the first and second order statistics of the diffusion-generated data in the linear setting. Results of such forms are desirable because they allow one to assume the data itself is Gaussian for analyzing performance of the trained classifier. Finally, we note that current approaches to proving universality do not apply to this case as the covariance matrices of the data tend to have vanishing minimum singular values for the diffusion-generated data, while the current proofs assume that this is not the case (see Subsection 3.4 for more details). This leaves extending previous mathematical universality results as an intriguing open question.

The solar wind speed at Earth is one of the most important parameters regarding the effects of space weather on society. Thus far, most approaches for predicting the solar wind speed produce a single-value time series without uncertainty, or utilize ensemble methods which require custom calibration development. In this study, a method is developed that produces calibrated probabilistic forecasts of the solar wind speed using skew normal distributions and a novel extension of analog ensembles. In our extension, the single-value predictions from a baseline model of the next Δt days are used along with Δwindow hours of recent observations and single-value predictions to create a forecasting scenario vector that is compared against a historical database for outcomes. The baseline model used is the combined Air Force Data Assimilative Photospheric Flux Transport-Wang Sheeley Arge (ADAPT-WSA) model and the WSA point parcel simulation, but the method is directly applicable to other deterministic models including components such as Enlil or the Heliospheric Upwind Extrapolation with time dependence model (HUXt). The approach works notably well on the benchmark of whether observations fall within the p^{th} percentile p% of the time (for p between 0 and 100). Falling back on the mean or median of the predicted distribution as a non-probabilistic prediction yields a direct improvement in root-mean-square error (RMSE) over the original WSA point parcel simulation, and is shown to beat approx 1 solar rotation recurrence for 1-5 day ahead forecasts.

In many application domains (e.g., recommender systems, intelligent tutoring systems), the rewards associated to the actions tend to decrease over time. This decay is either caused by the actions executed in the past (e.g., a user may get bored when songs of the same genre are recommended over and over) or by an external factor (e.g., content becomes outdated). These two situations can be modeled as specific instances of the rested and restless bandit settings, where arms are rotting (i.e., their value decrease over time). These problems were thought to be significantly different, since Levine et al. (2017) showed that state-of-the-art algorithms for restless bandit perform poorly in the rested rotting setting. In this paper, we introduce a novel algorithm, Rotting Adaptive Window UCB (RAW-UCB), that achieves near-optimal regret in both rotting rested and restless bandit, without any prior knowledge of the setting (rested or restless) and the type of non-stationarity (e.g., piece-wise constant, bounded variation). This is in striking contrast with previous negative results showing that no algorithm can achieve similar results as soon as rewards are allowed to increase. We confirm our theoretical findings on a number of synthetic and dataset-based experiments.

Real-world deployment of machine learning models is challenging because data evolves over time. While no model can work when data evolves in an arbitrary fashion, if there is some pattern to these changes, we might be able to design methods to address it. This paper addresses situations when data evolves gradually. We introduce a time-varying propensity score that can detect gradual shifts in the distribution of data which allows us to selectively sample past data to update the model -- not just similar data from the past like that of a standard propensity score but also data that evolved in a similar fashion in the past. The time-varying propensity score is quite general: we demonstrate different ways of implementing it and evaluate it on a variety of problems ranging from supervised learning (e.g., image classification problems) where data undergoes a sequence of gradual shifts, to reinforcement learning tasks (e.g., robotic manipulation and continuous control) where data shifts as the policy or the task changes.

Mining data streams with multi-label outputs poses significant challenges due to evolving distributions, high-dimensional label spaces, sparse label occurrences, and complex label dependencies. Moreover, concept drift affects not only input distributions but also label correlations and imbalance ratios over time, complicating model adaptation. To address these challenges, structured learners are categorized into local and global methods. Local methods break down the task into simpler components, while global methods adapt the algorithm to the full output space, potentially yielding better predictions by exploiting label correlations. This work introduces iHOMER (Incremental Hierarchy Of Multi-label Classifiers), an online multi-label learning framework that incrementally partitions the label space into disjoint, correlated clusters without relying on predefined hierarchies. iHOMER leverages online divisive-agglomerative clustering based on Jaccard similarity and a global tree-based learner driven by a multivariate Bernoulli process to guide instance partitioning. To address non-stationarity, it integrates drift detection mechanisms at both global and local levels, enabling dynamic restructuring of label partitions and subtrees. Experiments across 23 real-world datasets show iHOMER outperforms 5 state-of-the-art global baselines, such as MLHAT, MLHT of Pruned Sets and iSOUPT, by 23\%, and 12 local baselines, such as binary relevance transformations of kNN, EFDT, ARF, and ADWIN bagging/boosting ensembles, by 32\%, establishing its robustness for online multi-label classification.

Using a 100-day symmetric window around the January 2025 U.S. presidential inauguration, non-parametric statistical methods with bootstrap resampling (10,000 iterations) analyze distributional properties and anomalies. Results indicate a statistically significant 3.61\% Indonesian rupiah depreciation post-inauguration, with a large effect size (Cliff's Delta = -0.9224, CI: [-0.9727, -0.8571]). Central tendency shifted markedly, yet volatility remained stable (variance ratio = 0.9061, p = 0.504). Four significant anomalies exhibiting temporal clustering are detected. These findings provide quantitative evidence of political transition effects on emerging market currencies, highlighting implications for monetary policy and currency risk management.

Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that effect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semi-analytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any arbitrary astrophysical system of interest. Here, we adopt that the assigned magnetic turbulence is constrained on a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump -- that has for some special cases long been established -- is a universal feature of stochastic acceleration that emerges around the momentum chi_{rm eq} where acceleration and continuous loss are in equilibrium if the particle's residence time in the system is sufficient at chi_{rm eq}. In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.

Data Drift is the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory that is similar in structure to the neocortex, and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is its independence from training and testing cycle; all the learning takes place online with streaming data and no separate training and testing cycle is required. In sequential learning paradigm, Sequential Probability Ratio Test (SPRT) offers some unique benefit for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each dimension of the data, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

Meta-learning has emerged as an effective methodology to model several real-world tasks and problems due to its extraordinary effectiveness in the low-data regime. There are many scenarios ranging from the classification of rare diseases to language modelling of uncommon languages where the availability of large datasets is rare. Similarly, for more broader scenarios like self-driving, an autonomous vehicle needs to be trained to handle every situation well. This requires training the ML model on a variety of tasks with good quality data. But often times, we find that the data distribution across various tasks is skewed, i.e.the data follows a long-tail distribution. This leads to the model performing well on some tasks and not performing so well on others leading to model robustness issues. Meta-learning has recently emerged as a potential learning paradigm which can effectively learn from one task and generalize that learning to unseen tasks. In this study, we aim to exploit external knowledge of task relations to improve training stability via effective mini-batching of tasks. We hypothesize that selecting a diverse set of tasks in a mini-batch will lead to a better estimate of the full gradient and hence will lead to a reduction of noise in training.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

Dependable visual drone detection is crucial for the secure integration of drones into the airspace. However, drone detection accuracy is significantly affected by domain shifts due to environmental changes, varied points of view, and background shifts. To address these challenges, we present the DrIFT dataset, specifically developed for visual drone detection under domain shifts. DrIFT includes fourteen distinct domains, each characterized by shifts in point of view, synthetic-to-real data, season, and adverse weather. DrIFT uniquely emphasizes background shift by providing background segmentation maps to enable background-wise metrics and evaluation. Our new uncertainty estimation metric, MCDO-map, features lower postprocessing complexity, surpassing traditional methods. We use the MCDO-map in our uncertainty-aware unsupervised domain adaptation method, demonstrating superior performance to SOTA unsupervised domain adaptation techniques. The dataset is available at: https://github.com/CARG-uOttawa/DrIFT.git.

Machine learning systems in fraud detection, credit scoring, and clinical risk assessment operate under delayed ground truth: outcome labels arrive days to months after the decision they evaluate. During this blind period, governance evidence degrades through mechanisms that neither drift detection methods nor governance frameworks adequately address. This paper formalizes an evidence sufficiency model with four dimensions (completeness, freshness, reliability, representativeness) and a decision-readiness gate that quantifies how label latency degrades evidence quality. The model maps three drift types to dimension-specific degradation trajectories. A complementary proxy indicator framework comprising seven measurement categories estimates sufficiency degradation without labels, with explicit coverage mapping and characterized blind spots per drift type. Evaluation on the IEEE-CIS Fraud Detection dataset (~590K transactions) with controlled drift injection shows that composite proxy monitoring detects covariate and mixed drift with 100% detection rate, while concept drift without feature change remains undetected -- consistent with the theoretical impossibility of unsupervised detection when P(X) is unchanged. Blind period simulation confirms monotone sufficiency degradation, with concept drift degrading fastest (S=0.242 at day 60 vs 0.418 for no-drift). The framework contributes a governance sufficiency monitoring instrument; its value lies in translating drift signals into auditable sufficiency assessments with characterized blind spots. Mapping sufficiency levels to governance actions requires deployment-specific calibration beyond this study's scope.

Prior work has analyzed the robustness of visual encoders to image transformations and corruptions, particularly in cases where such alterations are not seen during training. When this occurs, they introduce a form of distribution shift at test time, often leading to performance degradation. The primary focus has been on severe corruptions that, when applied aggressively, distort useful signals necessary for accurate semantic predictions. We take a different perspective by analyzing parameters of the image acquisition process and transformations that may be subtle or even imperceptible to the human eye. We find that such parameters are systematically encoded in the learned visual representations and can be easily recovered. More strikingly, their presence can have a profound impact, either positively or negatively, on semantic predictions. This effect depends on whether there is a strong correlation or anti-correlation between semantic labels and these acquisition-based or processing-based labels. Our code and data are available at: https://github.com/ryan-caesar-ramos/visual-encoder-traces

When facing data with imbalanced classes or groups, practitioners follow an intriguing strategy to achieve best results. They throw away examples until the classes or groups are balanced in size, and then perform empirical risk minimization on the reduced training set. This opposes common wisdom in learning theory, where the expected error is supposed to decrease as the dataset grows in size. In this work, we leverage extreme value theory to address this apparent contradiction. Our results show that the tails of the data distribution play an important role in determining the worst-group-accuracy of linear classifiers. When learning on data with heavy tails, throwing away data restores the geometric symmetry of the resulting classifier, and therefore improves its worst-group generalization.

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of a test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the efficiency and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results. We end with a discussion on general formulations for handling distribution shifts and our observations from comparing with similar approaches from other domains.

This article introduces Regression Discontinuity Design (RDD) with Distribution-Valued Outcomes (R3D), extending the standard RDD framework to settings where the outcome is a distribution rather than a scalar. Such settings arise when treatment is assigned at a higher level of aggregation than the outcome-for example, when a subsidy is allocated based on a firm-level revenue cutoff while the outcome of interest is the distribution of employee wages within the firm. Since standard RDD methods cannot accommodate such two-level randomness, I propose a novel approach based on random distributions. The target estimand is a "local average quantile treatment effect", which averages across random quantiles. To estimate this target, I introduce two related approaches: one that extends local polynomial regression to random quantiles and another based on local Fr\'echet regression, a form of functional regression. For both estimators, I establish asymptotic normality and develop uniform, debiased confidence bands together with a data-driven bandwidth selection procedure. Simulations validate these theoretical properties and show existing methods to be biased and inconsistent in this setting. I then apply the proposed methods to study the effects of gubernatorial party control on within-state income distributions in the US, using a close-election design. The results suggest a classic equality-efficiency tradeoff under Democratic governorship, driven by reductions in income at the top of the distribution.

During 2023, two interesting results were proven about the limit behavior of game dynamics: First, it was shown that there is a game for which no dynamics converges to the Nash equilibria. Second, it was shown that the sink equilibria of a game adequately capture the limit behavior of natural game dynamics. These two results have created a need and opportunity to articulate a principled computational theory of the meaning of the game that is based on game dynamics. Given any game in normal form, and any prior distribution of play, we study the problem of computing the asymptotic behavior of a class of natural dynamics called the noisy replicator dynamics as a limit distribution over the sink equilibria of the game. When the prior distribution has pure strategy support, we prove this distribution can be computed efficiently, in near-linear time to the size of the best-response graph. When the distribution can be sampled -- for example, if it is the uniform distribution over all mixed strategy profiles -- we show through experiments that the limit distribution of reasonably large games can be estimated quite accurately through sampling and simulation.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

Diffusion models have been widely adopted in image generation, producing higher-quality and more diverse samples than generative adversarial networks (GANs). We introduce a latent diffusion model (LDM) for precipitation nowcasting - short-term forecasting based on the latest observational data. The LDM is more stable and requires less computation to train than GANs, albeit with more computationally expensive generation. We benchmark it against the GAN-based Deep Generative Models of Rainfall (DGMR) and a statistical model, PySTEPS. The LDM produces more accurate precipitation predictions, while the comparisons are more mixed when predicting whether the precipitation exceeds predefined thresholds. The clearest advantage of the LDM is that it generates more diverse predictions than DGMR or PySTEPS. Rank distribution tests indicate that the distribution of samples from the LDM accurately reflects the uncertainty of the predictions. Thus, LDMs are promising for any applications where uncertainty quantification is important, such as weather and climate.