Daily Papers

On-policy distillation (OPD) provides dense token-level supervision on student-generated trajectories. Although OPD performs strongly when teacher and student belong to the same model family, we find that its effectiveness degrades in cross-family settings even after tokenizer alignment, with substantially stronger external teachers offering little additional improvement. To understand this disconnect, we decompose the cross-family OPD signal into two components: an offset between a low-capability teacher-family reference and the student, and the within-family log-likelihood shift from that reference to the strong teacher. Standard OPD transfers both components together, allowing the offset to dominate the update direction and obscure the changes associated with teacher capability improvements. We propose CompassOPD, which removes this offset and transfers the within-family shift, while a frozen student reference anchors updates to the student's initial policy. Thus, both teacher-side and student-side changes are measured within their respective model families. Experiments across three student families and multiple teacher families show that CompassOPD consistently outperforms standard cross-family OPD, improving average reasoning accuracy by up to 5.50 points. For an MoE teacher, we further construct the reference directly from the teacher checkpoint by reducing expert activation, eliminating the need for a separate reference checkpoint while retaining a 3.43-point gain over OPD.

Mixture-of-Experts (MoE) language models are universally sensitive to demographic content at the routing level, yet exploiting this sensitivity for fairness control is structurally limited. We introduce Fairness-Aware Routing Equilibrium (FARE), a diagnostic framework designed to probe the limits of routing-level stereotype intervention across diverse MoE architectures. FARE reveals that routing-level preference shifts are either unachievable (Mixtral, Qwen1.5, Qwen3), statistically non-robust (DeepSeekMoE), or accompanied by substantial utility cost (OLMoE, -4.4%p CrowS-Pairs at -6.3%p TQA). Critically, even where log-likelihood preference shifts are robust, they do not transfer to decoded generation: expanded evaluations on both non-null models yield null results across all generation metrics. Group-level expert masking reveals why: bias and core knowledge are deeply entangled within expert groups. These findings indicate that routing sensitivity is necessary but insufficient for stereotype control, and identify specific architectural conditions that can inform the design of more controllable future MoE systems.

This study presents PARROT (Persuasion and Agreement Robustness Rating of Output Truth), a robustness focused framework designed to measure the degradation in accuracy that occurs under social pressure exerted on users through authority and persuasion in large language models (LLMs) the phenomenon of sycophancy (excessive conformity). PARROT (i) isolates causal effects by comparing the neutral version of the same question with an authoritatively false version using a double-blind evaluation, (ii) quantifies confidence shifts toward the correct and imposed false responses using log-likelihood-based calibration tracking, and (iii) systematically classifies failure modes (e.g., robust correct, sycophantic agreement, reinforced error, stubborn error, self-correction, etc.) using an eight-state behavioral taxonomy. We evaluated 22 models using 1,302 MMLU-style multiple-choice questions across 13 domains and domain-specific authority templates. Findings show marked heterogeneity: advanced models (e.g., GPT-5, GPT-4.1, Claude Sonnet 4.5) exhibit low "follow rates" (leq 11%, GPT-5: 4\%) and minimal accuracy loss, while older/smaller models show severe epistemic collapse (GPT-4: 80\%, Qwen 2.5-1.5B: 94\%). The danger is not limited to response changes; weak models reduce confidence in the correct response while increasing confidence in the imposed incorrect response. While international law and global knowledge at the domain level exhibit high fragility, elementary mathematics is relatively resilient. Consequently, we argue that the goal of "resistance to overfitting pressure" should be addressed as a primary objective alongside accuracy, harm avoidance, and privacy for safe deployment in the real world.

Direct Preference Optimization is an offline post-SFT method for aligning language models from preference pairs, with strong results in instruction following and summarization. However, DPO's sequence-level implicit reward can be brittle for token-critical structured prediction settings such as medical annotation, which often exhibit (i) low-separation preference pairs, where chosen and rejected completions differ by minimal edit distance (often 1-3 tokens), and (ii) token-importance skew, where sparse semantic tokens (hierarchical labels and evidence Spans) carry disproportionate task importance relative to high-frequency structural tokens (JSON scaffolding). In this regime, standard DPO suffers from margin collapse (insufficient log-probability separation between near-identical preferences), likelihood squeezing (the margin objective shifts the absolute likelihoods of both completions together), and gradient dilution, where uniform sequence-level weighting diffuses learning signal across shared scaffolding while rare, confusable label tokens receive weak, noisy updates. We introduce Token-Adaptive Barrier Preference Optimization (TAB-PO), which augments DPO with token-weighted, reference-adjusted advantages that prioritize high-value semantic tokens, and a conditional token-level barrier that regularizes under-confident tokens balancing SFT-anchored likelihood and preference-driven separation in low-separation, importance-skewed regimes. We evaluate TAB-PO on medical communication annotation, a task requiring joint prediction of hierarchical labels and evidence Spans from patient-provider messages. TAB-PO achieves a ~ 4% relative improvement in micro-F1 over SFT and consistently outperforms recent preference-optimization baselines.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an effective approach for enhancing the reasoning capabilities of Large Language Models (LLMs). Despite its efficacy, RLVR faces a meta-learning bottleneck: it lacks mechanisms for error attribution and experience internalization intrinsic to the human learning cycle beyond practice and verification, thereby limiting fine-grained credit assignment and reusable knowledge formation. We term such reusable knowledge representations derived from past errors as meta-experience. Based on this insight, we propose Meta-Experience Learning (MEL), a novel framework that incorporates self-distilled meta-experience into the model's parametric memory. Building upon standard RLVR, we introduce an additional design that leverages the LLM's self-verification capability to conduct contrastive analysis on paired correct and incorrect trajectories, identify the precise bifurcation points where reasoning errors arise, and summarize them into generalizable meta-experience. The meta-experience is further internalized into the LLM's parametric memory by minimizing the negative log-likelihood, which induces a language-modeled reward signal that bridges correct and incorrect reasoning trajectories and facilitates effective knowledge reuse. Experimental results demonstrate that MEL achieves consistent improvements on benchmarks, yielding 3.92%--4.73% Pass@1 gains across varying model sizes.

Model fusing has always been an important topic, especially in an era where large language models (LLM) and multi-modal language models (MLM) with different architectures, parameter sizes and training pipelines, are being created all the time. In this work, we propose a post-hoc framework, aiming at fusing heterogeneous models off-the-shell, which we call likelihood composition, and the basic idea is to compose multiple models' likelihood distribution when doing a multi-choice visual-question-answering task. Here the core concept, likelihood, is actually the log-probability of the candidate answer. In likelihood composition, we introduce some basic operations: debias, highlight, majority-vote and ensemble. By combining (composing) these basic elements, we get the mixed composition methods: mix-composition. Through conducting comprehensive experiments on 9 VQA datasets and 10 MLMs, we prove the effectiveness of mix-composition compared with simple ensemble or majority-vote methods. In this framework, people can propose new basic composition methods and combine them to get the new mixed composition methods. We hope our proposed likelihood composition can provide a new perspective of fusing heterogeneous models and inspire the exploration under this framework.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

Faced with distribution shift between training and test set, we wish to detect and quantify the shift, and to correct our classifiers without test set labels. Motivated by medical diagnosis, where diseases (targets) cause symptoms (observations), we focus on label shift, where the label marginal p(y) changes but the conditional p(x| y) does not. We propose Black Box Shift Estimation (BBSE) to estimate the test distribution p(y). BBSE exploits arbitrary black box predictors to reduce dimensionality prior to shift correction. While better predictors give tighter estimates, BBSE works even when predictors are biased, inaccurate, or uncalibrated, so long as their confusion matrices are invertible. We prove BBSE's consistency, bound its error, and introduce a statistical test that uses BBSE to detect shift. We also leverage BBSE to correct classifiers. Experiments demonstrate accurate estimates and improved prediction, even on high-dimensional datasets of natural images.

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.

We consider the problem of conformal prediction under covariate shift. Given labeled data from a source domain and unlabeled data from a covariate shifted target domain, we seek to construct prediction sets with valid marginal coverage in the target domain. Most existing methods require estimating the unknown likelihood ratio function, which can be prohibitive for high-dimensional data such as images. To address this challenge, we introduce the likelihood ratio regularized quantile regression (LR-QR) algorithm, which combines the pinball loss with a novel choice of regularization in order to construct a threshold function without directly estimating the unknown likelihood ratio. We show that the LR-QR method has coverage at the desired level in the target domain, up to a small error term that we can control. Our proofs draw on a novel analysis of coverage via stability bounds from learning theory. Our experiments demonstrate that the LR-QR algorithm outperforms existing methods on high-dimensional prediction tasks, including a regression task for the Communities and Crime dataset, an image classification task from the WILDS repository, and an LLM question-answering task on the MMLU benchmark.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates x) of training and testing samples p_tr(x) and p_te(x) are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio p_te(x)/p_tr(x) to weight training samples (reweighted methods) or using the ratio p_tr(x)/p_te(x) to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.

The task of out-of-distribution (OOD) detection is notoriously ill-defined. Earlier works focused on new-class detection, aiming to identify label-altering data distribution shifts, also known as "semantic shift." However, recent works argue for a focus on failure detection, expanding the OOD evaluation framework to account for label-preserving data distribution shifts, also known as "covariate shift." Intriguingly, under this new framework, complex OOD detectors that were previously considered state-of-the-art now perform similarly to, or even worse than the simple maximum softmax probability baseline. This raises the question: what are the latest OOD detectors actually detecting? Deciphering the behavior of OOD detection algorithms requires evaluation datasets that decouples semantic shift and covariate shift. To aid our investigations, we present ImageNet-OOD, a clean semantic shift dataset that minimizes the interference of covariate shift. Through comprehensive experiments, we show that OOD detectors are more sensitive to covariate shift than to semantic shift, and the benefits of recent OOD detection algorithms on semantic shift detection is minimal. Our dataset and analyses provide important insights for guiding the design of future OOD detectors.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

This paper studies the prediction of a target z from a pair of random variables (x,y), where the ground-truth predictor is additive E[z mid x,y] = f_star(x) +g_{star}(y). We study the performance of empirical risk minimization (ERM) over functions f+g, f in F and g in G, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class F is "simpler" than G (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogenous covariate shifts in which the shift in x is much greater than that in y. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Supervised fine-tuning (SFT) is the standard approach for post-training large language models (LLMs), yet it often shows limited generalization. We trace this limitation to its default training objective: negative log likelihood (NLL). While NLL is classically optimal when training from scratch, post-training operates in a different paradigm and could violate its optimality assumptions, where models already encode task-relevant priors and supervision can be long and noisy. To this end, we study a general family of probability-based objectives and characterize their effectiveness under different conditions. Through comprehensive experiments and extensive ablation studies across 7 model backbones, 14 benchmarks, and 3 domains, we uncover a critical dimension that governs objective behavior: the model-capability continuum. Near the model-strong end, prior-leaning objectives that downweight low-probability tokens (e.g., -p, -p^{10}, thresholded variants) consistently outperform NLL; toward the model-weak end, NLL dominates; in between, no single objective prevails. Our theoretical analysis further elucidates how objectives trade places across the continuum, providing a principled foundation for adapting objectives to model capability. Our code is available at https://github.com/GaotangLi/Beyond-Log-Likelihood.

Direct Preference Optimization (DPO) and its variants are increasingly used for aligning language models with human preferences. Although these methods are designed to teach a model to generate preferred responses more frequently relative to dispreferred responses, prior work has observed that the likelihood of preferred responses often decreases during training. The current work sheds light on the causes and implications of this counter-intuitive phenomenon, which we term likelihood displacement. We demonstrate that likelihood displacement can be catastrophic, shifting probability mass from preferred responses to responses with an opposite meaning. As a simple example, training a model to prefer No over Never can sharply increase the probability of Yes. Moreover, when aligning the model to refuse unsafe prompts, we show that such displacement can unintentionally lead to unalignment, by shifting probability mass from preferred refusal responses to harmful responses (e.g., reducing the refusal rate of Llama-3-8B-Instruct from 74.4% to 33.4%). We theoretically characterize that likelihood displacement is driven by preferences that induce similar embeddings, as measured by a centered hidden embedding similarity (CHES) score. Empirically, the CHES score enables identifying which training samples contribute most to likelihood displacement in a given dataset. Filtering out these samples effectively mitigated unintentional unalignment in our experiments. More broadly, our results highlight the importance of curating data with sufficiently distinct preferences, for which we believe the CHES score may prove valuable.

We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance σ^2, while the component means are estimated using a likelihood with variance τ^2, yielding a family of mismatched likelihood functions parameterized by the ratio ρ=τ/σ. We show that the interplay between ρ and the signal-to-noise ratio (SNR) induces a sharp phase diagram. Under correct specification (ρ=1), maximum likelihood recovers the true means, independently of the SNR. However, once the model is misspecified, two different regimes emerge. Under under-smoothing (ρ<1), the estimated Gaussian means are displaced from the truth, and in low SNR this discrepancy grows as the SNR decreases: for every fixed ρ<1, the squared error scales as SNR^{-1}. Under over-smoothing (ρ>1), the fitted likelihood blurs the cluster separation, causing distinct component means to collapse towards the overall mixture center once ρ^2 exceeds a threshold of the form 1 + λ,SNR, where λ depends on the geometry of the true means. We further show that the hard assignment objective arises as the limit τto 0 of the same mismatched likelihood family, and derive corresponding low- and high-SNR results for hard-assignment mean estimation and latent-label recovery. Furthermore, in low SNR, Bayes-optimal clustering is close to random guessing, and the hard-assignment target remains far from the true means. These results show that in low-SNR applications, even mild variance misspecification or hard-assignment procedures can induce substantial bias, whereas in high SNR these effects are largely absent.

PixelCNNs are a recently proposed class of powerful generative models with tractable likelihood. Here we discuss our implementation of PixelCNNs which we make available at https://github.com/openai/pixel-cnn. Our implementation contains a number of modifications to the original model that both simplify its structure and improve its performance. 1) We use a discretized logistic mixture likelihood on the pixels, rather than a 256-way softmax, which we find to speed up training. 2) We condition on whole pixels, rather than R/G/B sub-pixels, simplifying the model structure. 3) We use downsampling to efficiently capture structure at multiple resolutions. 4) We introduce additional short-cut connections to further speed up optimization. 5) We regularize the model using dropout. Finally, we present state-of-the-art log likelihood results on CIFAR-10 to demonstrate the usefulness of these modifications.

Direct Preference Optimization (DPO) and its variants have become increasingly popular for aligning language models with human preferences. These methods aim to teach models to better distinguish between chosen (or preferred) and rejected (or dispreferred) responses. However, prior research has identified that the probability of chosen responses often decreases during training, and this phenomenon is known as likelihood displacement. To tackle this challenge, in this work we introduce \method to controllably shift the distribution of the chosen probability. Then, we show that \method exhibits a fundamental trade-off between improving the chosen probability and sacrificing the reward margin, as supported by both theoretical analysis and experimental validation. Furthermore, we demonstrate the superiority of \method over DPO on downstream tasks such as MT-Bench and a designed win rate experiment. We believe this study shows that the likelihood displacement issue of DPO can be effectively mitigated with a simple, theoretically grounded solution. Our code is available at https://github.com/Meaquadddd/DPO-Shift.

Modern machine learning models deployed in the wild can encounter both covariate and semantic shifts, giving rise to the problems of out-of-distribution (OOD) generalization and OOD detection respectively. While both problems have received significant research attention lately, they have been pursued independently. This may not be surprising, since the two tasks have seemingly conflicting goals. This paper provides a new unified approach that is capable of simultaneously generalizing to covariate shifts while robustly detecting semantic shifts. We propose a margin-based learning framework that exploits freely available unlabeled data in the wild that captures the environmental test-time OOD distributions under both covariate and semantic shifts. We show both empirically and theoretically that the proposed margin constraint is the key to achieving both OOD generalization and detection. Extensive experiments show the superiority of our framework, outperforming competitive baselines that specialize in either OOD generalization or OOD detection. Code is publicly available at https://github.com/deeplearning-wisc/scone.

Do reasoning models have "Aha!" moments? Prior work suggests that models like DeepSeek-R1-Zero undergo sudden mid-trace realizations that lead to accurate outputs, implying an intrinsic capacity for self-correction. Yet, it remains unclear whether such intrinsic shifts in reasoning strategy actually improve performance. Here, we study mid-reasoning shifts and instrument training runs to detect them. Our analysis spans 1M+ reasoning traces, hundreds of training checkpoints, three reasoning domains, and multiple decoding temperatures and model architectures. We find that reasoning shifts are rare, do not become more frequent with training, and seldom improve accuracy, indicating that they do not correspond to prior perceptions of model insight. However, their effect varies with model uncertainty. Building on this finding, we show that artificially triggering extrinsic shifts under high entropy reliably improves accuracy. Our results show that mid-reasoning shifts are symptoms of unstable inference behavior rather than an intrinsic mechanism for self-correction.

We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. Machine learning (ML) systems, however, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to fail silently. This paper explores the problem of building ML systems that fail loudly, investigating methods for detecting dataset shift, identifying exemplars that most typify the shift, and quantifying shift malignancy. We focus on several datasets and various perturbations to both covariates and label distributions with varying magnitudes and fractions of data affected. Interestingly, we show that across the dataset shifts that we explore, a two-sample-testing-based approach, using pre-trained classifiers for dimensionality reduction, performs best. Moreover, we demonstrate that domain-discriminating approaches tend to be helpful for characterizing shifts qualitatively and determining if they are harmful.

Concept shift occurs when the distribution of labels conditioned on the features changes between domains, which can make even a well-tuned ML model miscalibrated on a new domain. Identifying these shifted features provides unique insight into how feature-label relationships differ between domains, considering the difference may be across a scientifically relevant dimension, such as time, disease status, population, etc. In this paper, we propose SGShift, a method for attributing performance degradation under concept shift in tabular data to a sparse set of shifted features. We frame concept shift as a feature selection task to learn the features that can explain performance differences between models in the source and target domain. This framework enables SGShift to adapt powerful statistical tools such as generalized additive models, knockoffs, and absorption towards identifying these shifted features. We conduct extensive experiments in synthetic and real data across various ML models and find SGShift can identify shifted features much more accurately than baseline methods, requires few samples in the shifted domain, and is robust to complex cases of concept shift.

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.

A prominent family of methods for learning data distributions relies on density ratio estimation (DRE), where a model is trained to classify between data samples and samples from some reference distribution. DRE-based models can directly output the likelihood for any given input, a highly desired property that is lacking in most generative techniques. Nevertheless, to date, DRE methods have failed in accurately capturing the distributions of complex high-dimensional data, like images, and have thus been drawing reduced research attention in recent years. In this work we present classification diffusion models (CDMs), a DRE-based generative method that adopts the formalism of denoising diffusion models (DDMs) while making use of a classifier that predicts the level of noise added to a clean signal. Our method is based on an analytical connection that we derive between the MSE-optimal denoiser for removing white Gaussian noise and the cross-entropy-optimal classifier for predicting the noise level. Our method is the first DRE-based technique that can successfully generate images beyond the MNIST dataset. Furthermore, it can output the likelihood of any input in a single forward pass, achieving state-of-the-art negative log likelihood (NLL) among methods with this property. Code is available on the project's webpage in https://shaharYadin.github.io/CDM/ .

Transfer learning with a small amount of target data is an effective and common approach to adapting a pre-trained model to distribution shifts. In some situations, target data labels may be expensive to obtain, so we may only have access to a limited number of target data points. To make the most of a very small target dataset, we propose a lightweight, sample-efficient approach that learns a diverse set of features and adapts to a target distribution by interpolating these features. Our approach, Project and Probe (Pro^2), first learns a linear projection that maps a pre-trained embedding onto orthogonal directions while being predictive of labels in the source dataset. The goal of this step is to learn a variety of predictive features, so that at least some of them remain useful after distribution shift. Pro^2 then learns a linear classifier on top of these projected features using a small target dataset. Theoretically, we find that Pro^2 results in more sample-efficient generalization by inducing a favorable bias-variance tradeoff. Our experiments on four datasets, with multiple distribution shift settings for each, show that Pro^2 improves performance by 5-15% when given limited target data compared to prior methods such as standard linear probing.

Test-time adaptation with pre-trained vision-language models, such as CLIP, aims to adapt the model to new, potentially out-of-distribution test data. Existing methods calculate the similarity between visual embedding and learnable class embeddings, which are initialized by text embeddings, for zero-shot image classification. In this work, we first analyze this process based on Bayes theorem, and observe that the core factors influencing the final prediction are the likelihood and the prior. However, existing methods essentially focus on adapting class embeddings to adapt likelihood, but they often ignore the importance of prior. To address this gap, we propose a novel approach, Bayesian Class Adaptation (BCA), which in addition to continuously updating class embeddings to adapt likelihood, also uses the posterior of incoming samples to continuously update the prior for each class embedding. This dual updating mechanism allows the model to better adapt to distribution shifts and achieve higher prediction accuracy. Our method not only surpasses existing approaches in terms of performance metrics but also maintains superior inference rates and memory usage, making it highly efficient and practical for real-world applications.

The recent trend towards Personalized Federated Learning (PFL) has garnered significant attention as it allows for the training of models that are tailored to each client while maintaining data privacy. However, current PFL techniques primarily focus on modeling the conditional distribution heterogeneity (i.e. concept shift), which can result in suboptimal performance when the distribution of input data across clients diverges (i.e. covariate shift). Additionally, these techniques often lack the ability to adapt to unseen data, further limiting their effectiveness in real-world scenarios. To address these limitations, we propose a novel approach, FedGMM, which utilizes Gaussian mixture models (GMM) to effectively fit the input data distributions across diverse clients. The model parameters are estimated by maximum likelihood estimation utilizing a federated Expectation-Maximization algorithm, which is solved in closed form and does not assume gradient similarity. Furthermore, FedGMM possesses an additional advantage of adapting to new clients with minimal overhead, and it also enables uncertainty quantification. Empirical evaluations on synthetic and benchmark datasets demonstrate the superior performance of our method in both PFL classification and novel sample detection.

With the increase in availability of large pre-trained language models (LMs) in Natural Language Processing (NLP), it becomes critical to assess their fit for a specific target task a priori - as fine-tuning the entire space of available LMs is computationally prohibitive and unsustainable. However, encoder transferability estimation has received little to no attention in NLP. In this paper, we propose to generate quantitative evidence to predict which LM, out of a pool of models, will perform best on a target task without having to fine-tune all candidates. We provide a comprehensive study on LM ranking for 10 NLP tasks spanning the two fundamental problem types of classification and structured prediction. We adopt the state-of-the-art Logarithm of Maximum Evidence (LogME) measure from Computer Vision (CV) and find that it positively correlates with final LM performance in 94% of the setups. In the first study of its kind, we further compare transferability measures with the de facto standard of human practitioner ranking, finding that evidence from quantitative metrics is more robust than pure intuition and can help identify unexpected LM candidates.

Training Data Attribution (TDA) seeks to trace a model's predictions back to its training data. The gold standard for TDA relies on causal interventions, observing how a model changes when data is added or removed, but repeated retraining is computationally challenging for Large Language Models (LLMs). Consequently, most approaches approximate this effect in the parameter space using gradients. However, tracking gradients across billions of parameters is not only prohibitively expensive but relies on local approximations. In this work, we propose a shift: rather than estimating parameter changes, we model the functional effect of training data in the activation space. We introduce STRIDE (Steering-based Training Data Influence Decomposition), a framework that formulates TDA as a sparse recovery problem in the spirit of compressive sensing. STRIDE learns lightweight "steering operators" that mimic the behavioral shift caused by training on data subsets. By measuring how these operators perturb test predictions, we recover individual training example influences via sparse linear decomposition. STRIDE achieves state-of-the-art for LLM pre-training attribution while being an order of magnitude (13times) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative analysis.

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

Ensuring the quality and integrity of medical images is crucial for maintaining diagnostic accuracy in deep learning-based Computer-Aided Diagnosis and Computer-Aided Detection (CAD) systems. Covariate shifts are subtle variations in the data distribution caused by different imaging devices or settings and can severely degrade model performance, similar to the effects of adversarial attacks. Therefore, it is vital to have a lightweight and fast method to assess the quality of these images prior to using CAD models. AdverX-Ray addresses this need by serving as an image-quality assessment layer, designed to detect covariate shifts effectively. This Adversarial Variational Autoencoder prioritizes the discriminator's role, using the suboptimal outputs of the generator as negative samples to fine-tune the discriminator's ability to identify high-frequency artifacts. Images generated by adversarial networks often exhibit severe high-frequency artifacts, guiding the discriminator to focus excessively on these components. This makes the discriminator ideal for this approach. Trained on patches from X-ray images of specific machine models, AdverX-Ray can evaluate whether a scan matches the training distribution, or if a scan from the same machine is captured under different settings. Extensive comparisons with various OOD detection methods show that AdverX-Ray significantly outperforms existing techniques, achieving a 96.2% average AUROC using only 64 random patches from an X-ray. Its lightweight and fast architecture makes it suitable for real-time applications, enhancing the reliability of medical imaging systems. The code and pretrained models are publicly available.

Leveraging the models' outputs, specifically the logits, is a common approach to estimating the test accuracy of a pre-trained neural network on out-of-distribution (OOD) samples without requiring access to the corresponding ground truth labels. Despite their ease of implementation and computational efficiency, current logit-based methods are vulnerable to overconfidence issues, leading to prediction bias, especially under the natural shift. In this work, we first study the relationship between logits and generalization performance from the view of low-density separation assumption. Our findings motivate our proposed method MaNo which (1) applies a data-dependent normalization on the logits to reduce prediction bias, and (2) takes the L_p norm of the matrix of normalized logits as the estimation score. Our theoretical analysis highlights the connection between the provided score and the model's uncertainty. We conduct an extensive empirical study on common unsupervised accuracy estimation benchmarks and demonstrate that MaNo achieves state-of-the-art performance across various architectures in the presence of synthetic, natural, or subpopulation shifts.

For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback-Leibler (K-L) divergence, the closest distribution is called the "information projection." The estimation risk of the maximum likelihood estimator (MLE) is defined as the expectation of K-L divergence between the information projection and the predictive distribution with plugged-in MLE. Here, the asymptotic expansion of the risk is derived up to n^{-2}-order, and the sufficient condition on the risk for the Bayes error rate between the true distribution and the information projection to be lower than a specified value is investigated. Combining these results, the "p-n criterion" is proposed, which determines whether the MLE is sufficiently close to the information projection for the given model and sample. In particular, the criterion for an exponential family model is relatively simple and can be used for a complex model with no explicit form of normalizing constant. This criterion can constitute a solution to the sample size or model acceptance problem. Use of the p-n criteria is demonstrated for two practical datasets. The relationship between the results and information criteria is also studied.

Estimating the test performance of a model, possibly under distribution shift, without having access to the ground-truth labels is a challenging, yet very important problem for the safe deployment of machine learning algorithms in the wild. Existing works mostly rely on information from either the outputs or the extracted features of neural networks to estimate a score that correlates with the ground-truth test accuracy. In this paper, we investigate -- both empirically and theoretically -- how the information provided by the gradients can be predictive of the ground-truth test accuracy even under distribution shifts. More specifically, we use the norm of classification-layer gradients, backpropagated from the cross-entropy loss after only one gradient step over test data. Our intuition is that these gradients should be of higher magnitude when the model generalizes poorly. We provide the theoretical insights behind our approach and the key ingredients that ensure its empirical success. Extensive experiments conducted with various architectures on diverse distribution shifts demonstrate that our method significantly outperforms current state-of-the-art approaches. The code is available at https://github.com/Renchunzi-Xie/GdScore

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.

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.

Likelihood approximations for images are not trivial to compute and can be useful in many applications. We examine the use of Contrastive Language-Image Pre-training (CLIP) to assess the likelihood of images and captions. We introduce Whitened CLIP, a novel transformation of the CLIP latent space via an invertible linear operation. This transformation ensures that each feature in the embedding space has zero mean, unit standard deviation, and no correlation with all other features, resulting in an identity covariance matrix. We show that the whitened embeddings statistics can be well approximated as a standard normal distribution, thus, the log-likelihood is estimated simply by the square Euclidean norm in the whitened embedding space. The whitening procedure is completely training-free and performed using a pre-computed whitening matrix, hence, is very fast. We present several preliminary experiments demonstrating the properties and applicability of these likelihood scores to images and captions.

In open-world scenarios, where both novel classes and domains may exist, an ideal segmentation model should detect anomaly classes for safety and generalize to new domains. However, existing methods often struggle to distinguish between domain-level and semantic-level distribution shifts, leading to poor out-of-distribution (OOD) detection or domain generalization performance. In this work, we aim to equip the model to generalize effectively to covariate-shift regions while precisely identifying semantic-shift regions. To achieve this, we design a novel generative augmentation method to produce coherent images that incorporate both anomaly (or novel) objects and various covariate shifts at both image and object levels. Furthermore, we introduce a training strategy that recalibrates uncertainty specifically for semantic shifts and enhances the feature extractor to align features associated with domain shifts. We validate the effectiveness of our method across benchmarks featuring both semantic and domain shifts. Our method achieves state-of-the-art performance across all benchmarks for both OOD detection and domain generalization. Code is available at https://github.com/gaozhitong/MultiShiftSeg.

System log anomaly detection is critical for maintaining the reliability of large-scale software systems, yet traditional methods struggle with the heterogeneous and evolving nature of modern log data. Recent advances in Large Language Models (LLMs) offer promising new approaches to log understanding, but a systematic comparison of LLM-based methods against established techniques remains lacking. In this paper, we present a comprehensive benchmark study evaluating both LLM-based and traditional approaches for log anomaly detection across four widely-used public datasets: HDFS, BGL, Thunderbird, and Spirit. We evaluate three categories of methods: (1) classical log parsers (Drain, Spell, AEL) combined with machine learning classifiers, (2) fine-tuned transformer models (BERT, RoBERTa), and (3) prompt-based LLM approaches (GPT-3.5, GPT-4, LLaMA-3) in zero-shot and few-shot settings. Our experiments reveal that while fine-tuned transformers achieve the highest F1-scores (0.96-0.99), prompt-based LLMs demonstrate remarkablezero-shot capabilities (F1: 0.82-0.91) without requiring any labeled training data -- a significant advantage for real-world deployment where labeled anomalies are scarce. We further analyze the cost-accuracy trade-offs, latency characteristics, and failure modes of each approach. Our findings provide actionable guidelines for practitioners choosing log anomaly detection methods based on their specific constraints regarding accuracy, latency, cost, and label availability. All code and experimental configurations are publicly available to facilitate reproducibility.

Knowledge probing assesses to which degree a language model (LM) has successfully learned relational knowledge during pre-training. Probing is an inexpensive way to compare LMs of different sizes and training configurations. However, previous approaches rely on the objective function used in pre-training LMs and are thus applicable only to masked or causal LMs. As a result, comparing different types of LMs becomes impossible. To address this, we propose an approach that uses an LM's inherent ability to estimate the log-likelihood of any given textual statement. We carefully design an evaluation dataset of 7,731 instances (40,916 in a larger variant) from which we produce alternative statements for each relational fact, one of which is correct. We then evaluate whether an LM correctly assigns the highest log-likelihood to the correct statement. Our experimental evaluation of 22 common LMs shows that our proposed framework, BEAR, can effectively probe for knowledge across different LM types. We release the BEAR datasets and an open-source framework that implements the probing approach to the research community to facilitate the evaluation and development of LMs.

Distributional shift, or the mismatch between training and deployment data, is a significant obstacle to the usage of machine learning in high-stakes industrial applications, such as autonomous driving and medicine. This creates a need to be able to assess how robustly ML models generalize as well as the quality of their uncertainty estimates. Standard ML baseline datasets do not allow these properties to be assessed, as the training, validation and test data are often identically distributed. Recently, a range of dedicated benchmarks have appeared, featuring both distributionally matched and shifted data. Among these benchmarks, the Shifts dataset stands out in terms of the diversity of tasks as well as the data modalities it features. While most of the benchmarks are heavily dominated by 2D image classification tasks, Shifts contains tabular weather forecasting, machine translation, and vehicle motion prediction tasks. This enables the robustness properties of models to be assessed on a diverse set of industrial-scale tasks and either universal or directly applicable task-specific conclusions to be reached. In this paper, we extend the Shifts Dataset with two datasets sourced from industrial, high-risk applications of high societal importance. Specifically, we consider the tasks of segmentation of white matter Multiple Sclerosis lesions in 3D magnetic resonance brain images and the estimation of power consumption in marine cargo vessels. Both tasks feature ubiquitous distributional shifts and a strict safety requirement due to the high cost of errors. These new datasets will allow researchers to further explore robust generalization and uncertainty estimation in new situations. In this work, we provide a description of the dataset and baseline results for both tasks.

Maximizing the log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward chi^2 divergence, to enhance log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, both in terms of log-likelihood and model parameter estimation.

Deploying LLMs raises two coupled challenges: (1) monitoring - estimating where a model underperforms as traffic and domains drift - and (2) improvement - prioritizing data acquisition to close the largest performance gaps. We test whether an inference-time signal can estimate slice-level accuracy under domain shift. For each response, we compute an output-entropy profile from final-layer next-token probabilities (from top-k logprobs) and summarize it with eleven statistics. A lightweight classifier predicts instance correctness, and averaging predicted probabilities yields a domain-level accuracy estimate. We evaluate on ten STEM reasoning benchmarks with exhaustive train/test compositions (k in {1,2,3,4}; all "10 choose k" combinations), across nine LLMs from six families (3B-20B). Estimates often track held-out benchmark accuracy, and several models show near-monotonic ordering of domains. Output-entropy profiles are thus an accessible signal for scalable monitoring and for targeting data acquisition.

Evaluating the performance of machine learning models under distribution shift is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackle this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings.

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

Test-time compute allocation in large reasoning models (LRMs) is widely used and has applications in mathematical problem solving, code synthesis, and planning. Recent work has addressed this problem by scaling self-consistency and parallel thinking, adding generic ``thinking tokens'' and prompting models to re-read the question before answering. Unfortunately, these approaches either inject task-agnostic tokens or mandate heuristics that do not explain -- and often ignore -- the spontaneous repetition that many LRMs exhibit at the head of their internal chains. In contrast, we analyze and harness the model's tendency to restate the question, which we term the Echo of Prompt (EOP), as a front-loaded, compute-shaping mechanism. We formalize its probabilistic cost by casting echo removal as rejection-based conditioning and defining the Echo Likelihood Gap ΔL as a computable proxy. This provides the missing theoretical link that links early repetition to likelihood gains and downstream accuracy. However, it does not by itself specify how to exploit EOP. Consequently, we develop Echo-Distilled SFT (ED-SFT) to instill an ``echo-then-reason'' pattern through supervised finetuning, and Echoic Prompting (EP) to re-ground the model mid-trace without training. While promising, quantifying benefits beyond verbosity is non-trivial. Therefore, we conduct length and suffix-controlled likelihood analyses together with layer-wise attention studies, showing that EOP increases answer to answer-prefix attention in middle layers, consistent with an attention refocusing mechanism. We evaluate on GSM8K, MathQA, Hendrycks-MATH, AIME24, and MATH-500 under identical decoding settings and budgets, and find consistent gains over baselines. Code is available at https://github.com/hhh2210/echoes-as-anchors.

Software systems often record important runtime information in logs to help with troubleshooting. Log-based anomaly detection has become a key research area that aims to identify system issues through log data, ultimately enhancing the reliability of software systems. Traditional deep learning methods often struggle to capture the semantic information embedded in log data, which is typically organized in natural language. In this paper, we propose LogLLM, a log-based anomaly detection framework that leverages large language models (LLMs). LogLLM employs BERT for extracting semantic vectors from log messages, while utilizing Llama, a transformer decoder-based model, for classifying log sequences. Additionally, we introduce a projector to align the vector representation spaces of BERT and Llama, ensuring a cohesive understanding of log semantics. Unlike conventional methods that require log parsers to extract templates, LogLLM preprocesses log messages with regular expressions, streamlining the entire process. Our framework is trained through a novel three-stage procedure designed to enhance performance and adaptability. Experimental results across four public datasets demonstrate that LogLLM outperforms state-of-the-art methods. Even when handling unstable logs, it effectively captures the semantic meaning of log messages and detects anomalies accurately.

Out-of-distribution (OOD) detection aims to identify test examples that do not belong to the training distribution and are thus unlikely to be predicted reliably. Despite a plethora of existing works, most of them focused only on the scenario where OOD examples come from semantic shift (e.g., unseen categories), ignoring other possible causes (e.g., covariate shift). In this paper, we present a novel, unifying framework to study OOD detection in a broader scope. Instead of detecting OOD examples from a particular cause, we propose to detect examples that a deployed machine learning model (e.g., an image classifier) is unable to predict correctly. That is, whether a test example should be detected and rejected or not is ``model-specific''. We show that this framework unifies the detection of OOD examples caused by semantic shift and covariate shift, and closely addresses the concern of applying a machine learning model to uncontrolled environments. We provide an extensive analysis that involves a variety of models (e.g., different architectures and training strategies), sources of OOD examples, and OOD detection approaches, and reveal several insights into improving and understanding OOD detection in uncontrolled environments.

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.

Large language models fine-tuned for forecasting can be accurate yet poorly calibrated, and their chain-of-thought (CoT) reasoning may not faithfully reflect the evidence behind a forecast. We ask whether internal representations offer a more direct window into both. Working with Eternis-Forecaster 8B on OpenForesight, we train representation-pooling probes on intermediate activations and find they achieve substantially better calibration; a result that also holds for GLM-4.7-Flash and GLM-4.5-Air. We then assess CoT faithfulness through evidence ablation and diversionary injection: removing an influential source in the prompt often changes the model's forecast while leaving the reasoning trace untouched. The same probes function as lie detectors: their activations track behavioral shifts far better than the reasoning trace does, and they also predict the direction of change in 84% of cases, including when the CoT conceals the perturbation's influence. Finally, forced answering reveals that forecasts are largely fixed before reasoning begins: a single pre-reasoning pass recovers the committed answer and confidence, and routing questions by the spread of this pre-set answer distribution saves 30-47% of generated tokens, with no loss of accuracy. Together, these results establish probing internal representations as a practical tool for calibrating, auditing, and triaging language model forecasters and reasoning models more broadly.

Automated checking pipelines increasingly place one language model as the checker and another (or the same one) as the fixer. We ask whether that wiring changes what the checker reports. Measuring false alarms on human-verified-correct ProcessBench traces with the present task held byte-identical, we find that a completed audit -> repair episode already in the model's context lowers false alarms in 15 of 15 model x wording combinations, by 2.8 to 11.5 percentage points against a length-matched non-audit control, a 9 to 25% reduction relative to that control. The direction contradicts what the accumulated-message literature predicts: an episode whose audit reported an error lowers false alarms further still, at all five wordings on the model where that manipulation lands cleanly, though a negativity asymmetry predicts more flagging. Decomposing the episode finds repair content and audit verdict complementary: different components carry the effect on different model families. Signal-detection analysis locates the change in the threshold rather than in discrimination -- the criterion moves in 15 of 15 combinations and survives correction in 13 while d' survives in none, though the d' test is half as sensitive by construction -- and a hand audit of 50 false alarms finds 82% simply wrong, so at this operating point the shift need not be harmful. With reasoning enabled the effect keeps its relative size on both models tested, and the threshold reading holds there too.

In this paper, we suggest a novel method for detecting mortality deceleration. We focus on the gamma-Gompertz frailty model and suggest the subtraction of a penalty in the log-likelihood function as an alternative to traditional likelihood inference and hypothesis testing. Over existing methods, our method offers advantages, such as avoiding the use of a p-value, hypothesis testing, and asymptotic distributions. We evaluate the performance of our approach by comparing it with traditional likelihood inference on both simulated and real mortality data. Results have shown that our approach is more accurate in detecting mortality deceleration and provides more reliable estimates of the underlying parameters. The proposed method is a significant contribution to the literature as it offers a powerful tool for analyzing mortality patterns.

The probabilistic reading of the cumulative accuracy profile (CAP) has a long industry lineage. Falkenstein, Boral and Carty (2000) state, in discrete form, that the default rate at a score percentile equals the portfolio average rate times the local slope of the power curve; van der Burgt (2008, 2019) formalizes this as the continuous identity p(Dmid x) = p_D, dy/dx and imports the continuous form as a working fact; Tasche (2009) analyzes the resulting calibration method; Voloshyn and Voloshyn (2023) substitute Bayes' theorem, f(xmid D)=p(Dmid x) f(x)/p_D, into the area integral and write the Gini as a functional of the calibration curve. The slope itself is already in the lineage (van der Burgt's dy/dx is the ratio of the two cumulative differentials), but it enters as a cited working fact, never as Bayes' theorem. We make that identification explicit and draw out its consequences. First, the CAP slope is Bayes' theorem in cumulative coordinates: the standardized PD it recovers is the posterior probability rescaled by the prior. The weight of the paper then falls on two results this reading unlocks. The odds form places the weight of evidence (the log of the likelihood ratio, i.e. the Bayes factor) and the information value inside one geometry (the weight of evidence at a point is the log of the ratio of the "bad" and "good" CAP slopes). The accuracy ratio, Somers' D_{xy}, and the Gini (2A-1)/(1-p_D) are revealed as one number computed three ways. Run in comparison mode (realized outcomes against model claims), the same identity recovers the reliability diagram in cumulative coordinates, with the sign of the gap between the empirical and model-implied Gini coefficients as a calibration diagnostic. A worked five-band example carries every identity in discrete form, and a kernel-density example extends them to the continuous case.

Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a fundamental difficulty with probabilistic multi-scale models: the intractability of the likelihood function. Chiefly, in cascaded models each intermediary scale introduces extraneous variables that cannot be tractably marginalized out for likelihood evaluation. This issue vanishes by modeling the diffusion process on latent spaces induced by a class of transformations we call hierarchical volume-preserving maps, which decompose spatially structured data in a hierarchical fashion without introducing local distortions in the latent space. We demonstrate that two such maps are well-known in the literature for multiscale modeling: Laplacian pyramids and wavelet transforms. Not only do such reparameterizations allow the likelihood function to be directly expressed as a joint likelihood over the scales, we show that the Laplacian pyramid and wavelet transform also produces significant improvements to the state-of-the-art on a selection of benchmarks in likelihood modeling, including density estimation, lossless compression, and out-of-distribution detection. Investigating the theoretical basis of our empirical gains we uncover deep connections to score matching under the Earth Mover's Distance (EMD), which is a well-known surrogate for perceptual similarity. Code can be found at https://github.com/lihenryhfl/pcdm{this https url}.

Machine learning systems often experience a distribution shift between training and testing. In this paper, we introduce a simple variational objective whose optima are exactly the set of all representations on which risk minimizers are guaranteed to be robust to any distribution shift that preserves the Bayes predictor, e.g., covariate shifts. Our objective has two components. First, a representation must remain discriminative for the task, i.e., some predictor must be able to simultaneously minimize the source and target risk. Second, the representation's marginal support needs to be the same across source and target. We make this practical by designing self-supervised objectives that only use unlabelled data and augmentations to train robust representations. Our objectives give insights into the robustness of CLIP, and further improve CLIP's representations to achieve SOTA results on DomainBed.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Interpretability methods for large language models (LLMs) typically derive directions from textual supervision, which can lack external grounding. We propose using human brain activity not as a training signal but as a coordinate system for reading and steering LLM states. Using the SMN4Lang MEG dataset, we construct a word-level brain atlas of phase-locking value (PLV) patterns and extract latent axes via ICA. We validate axes with independent lexica and NER-based labels (POS/log-frequency used as sanity checks), then train lightweight adapters that map LLM hidden states to these brain axes without fine-tuning the LLM. Steering along the resulting brain-derived directions yields a robust lexical (frequency-linked) axis in a mid TinyLlama layer, surviving perplexity-matched controls, and a brain-vs-text probe comparison shows larger log-frequency shifts (relative to the text probe) with lower perplexity for the brain axis. A function/content axis (axis 13) shows consistent steering in TinyLlama, Qwen2-0.5B, and GPT-2, with PPL-matched text-level corroboration. Layer-4 effects in TinyLlama are large but inconsistent, so we treat them as secondary (Appendix). Axis structure is stable when the atlas is rebuilt without GPT embedding-change features or with word2vec embeddings (|r|=0.64-0.95 across matched axes), reducing circularity concerns. Exploratory fMRI anchoring suggests potential alignment for embedding change and log frequency, but effects are sensitive to hemodynamic modeling assumptions and are treated as population-level evidence only. These results support a new interface: neurophysiology-grounded axes provide interpretable and controllable handles for LLM behavior.

Large Language Models (LLMs) are widely used to evaluate natural language generation tasks as automated metrics. However, the likelihood, a measure of LLM's plausibility for a sentence, can vary due to superficial differences in sentences, such as word order and sentence structure. It is therefore possible that there might be a likelihood bias if LLMs are used for evaluation: they might overrate sentences with higher likelihoods while underrating those with lower likelihoods. In this paper, we investigate the presence and impact of likelihood bias in LLM-based evaluators. We also propose a method to mitigate the likelihood bias. Our method utilizes highly biased instances as few-shot examples for in-context learning. Our experiments in evaluating the data-to-text and grammatical error correction tasks reveal that several LLMs we test display a likelihood bias. Furthermore, our proposed method successfully mitigates this bias, also improving evaluation performance (in terms of correlation of models with human scores) significantly.

We propose a new method for generating realistic datasets with distribution shifts using any decoder-based generative model. Our approach systematically creates datasets with varying intensities of distribution shifts, facilitating a comprehensive analysis of model performance degradation. We then use these generated datasets to evaluate the performance of various commonly used networks and observe a consistent decline in performance with increasing shift intensity, even when the effect is almost perceptually unnoticeable to the human eye. We see this degradation even when using data augmentations. We also find that enlarging the training dataset beyond a certain point has no effect on the robustness and that stronger inductive biases increase robustness.

This paper first answers the question "why do the two most powerful techniques Dropout and Batch Normalization (BN) often lead to a worse performance when they are combined together?" in both theoretical and statistical aspects. Theoretically, we find that Dropout would shift the variance of a specific neural unit when we transfer the state of that network from train to test. However, BN would maintain its statistical variance, which is accumulated from the entire learning procedure, in the test phase. The inconsistency of that variance (we name this scheme as "variance shift") causes the unstable numerical behavior in inference that leads to more erroneous predictions finally, when applying Dropout before BN. Thorough experiments on DenseNet, ResNet, ResNeXt and Wide ResNet confirm our findings. According to the uncovered mechanism, we next explore several strategies that modifies Dropout and try to overcome the limitations of their combination by avoiding the variance shift risks.

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.

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect performance. In this paper, we explore whether the diffusion process can be learned from data. Our work is grounded in Bayesian inference and seeks to improve log-likelihood estimation by casting the learned diffusion process as an approximate variational posterior that yields a tighter lower bound (ELBO) on the likelihood. A widely held assumption is that the ELBO is invariant to the noise process: our work dispels this assumption and proposes multivariate learned adaptive noise (MULAN), a learned diffusion process that applies noise at different rates across an image. Specifically, our method relies on a multivariate noise schedule that is a function of the data to ensure that the ELBO is no longer invariant to the choice of the noise schedule as in previous works. Empirically, MULAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet and reduces the number of training steps by 50%. Code is available at https://github.com/s-sahoo/MuLAN

Converting a pretrained Transformer into a more efficient hybrid model through distillation offers a promising approach to reducing inference costs. However, achieving high-quality generation in distilled models requires careful joint design of both the student architecture and the distillation process. Many prior distillation works evaluate downstream multiple-choice benchmarks by ranking candidate answers with log-likelihood rather than requiring autoregressive generation, which can obscure important differences in model quality. For example, we show that a 7B parameter distilled model that nearly matches its teacher to within 0.2\,pp under log-likelihood scoring actually falls behind by 20.8\,pp when the model must generate answers autoregressively. We propose a Hybrid Kimi Delta Attention (Hybrid-KDA) architecture paired with GenDistill, a multi-stage distillation pipeline, and use generation-based evaluation throughout to guide design decisions. Applying this approach to Qwen3-0.6B, we systematically ablate six design axes: training objective, loss masking, training duration, dataset selection, parameter freezing, and architecture choice. We find that log-likelihood-based evaluation consistently underestimates the gap between teacher and student, and can in some cases reverse the ranking of design choices, meaning that conclusions drawn from perplexity-only evaluation may be misleading. Among the factors we study, dataset selection, completion-only masking, and freezing attention layers during post-training have the largest impact on generation quality. Our best Hybrid-KDA model retains 86--90\% of teacher accuracy on knowledge benchmarks while reducing KV cache memory by up to 75\% and improving time-to-first-token by 2--4times at 128K-token contexts.

While diffusion has drawn considerable recent attention from the language modeling community, continuous diffusion has appeared less scalable than discrete approaches. To challenge this belief we revisit Plaid, a likelihood-based continuous diffusion language model (DLM), and construct RePlaid by aligning the architecture of Plaid with modern discrete DLMs. In this unified setting, we establish the first scaling law for continuous DLMs that rivals discrete DLMs: RePlaid exhibits a compute gap of only 20times compared to autoregressive models, outperforms Duo while using fewer parameters, and outperforms MDLM in the over-trained regime. We benchmark RePlaid against recent continuous DLMs: on OpenWebText, RePlaid achieves a new state-of-the-art PPL bound of 22.1 among continuous DLMs and superior generation quality. These results suggest that continuous diffusion, when trained via likelihood, is a highly competitive and scalable alternative to discrete DLMs. Moreover, we offer theoretical insights to understand the advantage of likelihood-based training. We show that optimizing the noise schedule to minimize the ELBO's variance naturally yields linear cross-entropy (information loss) over time. This evenly distributes denoising difficulty without any case-specific time reparameterization. In addition, we find that optimizing embeddings via likelihood creates structured geometries and drives the most significant likelihood gain.

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.

Large reasoning models enhanced by reinforcement learning with verifiable rewards have achieved significant performance gains by extending their chain-of-thought. However, this paradigm incurs substantial deployment costs as models often exhibit excessive verbosity on simple queries. Existing efficient reasoning methods relying on explicit length penalties often introduce optimization conflicts and leave the generative mechanisms driving overthinking largely unexamined. In this paper, we identify a phenomenon termed length shift where models increasingly generate unnecessary reasoning on trivial inputs during training. To address this, we introduce Dynamic Outlier Truncation (DOT), a training-time intervention that selectively suppresses redundant tokens. This method targets only the extreme tail of response lengths within fully correct rollout groups while preserving long-horizon reasoning capabilities for complex problems. To complement this intervention and ensure stable convergence, we further incorporate auxiliary KL regularization and predictive dynamic sampling. Experimental results across multiple model scales demonstrate that our approach significantly pushes the efficiency-performance Pareto frontier outward. Notably, on the AIME-24, our method reduces inference token usage by 78% while simultaneously increasing accuracy compared to the initial policy and surpassing state-of-the-art efficient reasoning methods.

The goal of the change-point detection is to discover changes of time series distribution. One of the state of the art approaches of the change-point detection are based on direct density ratio estimation. In this work we show how existing algorithms can be generalized using various binary classification and regression models. In particular, we show that the Gradient Boosting over Decision Trees and Neural Networks can be used for this purpose. The algorithms are tested on several synthetic and real-world datasets. The results show that the proposed methods outperform classical RuLSIF algorithm. Discussion of cases where the proposed algorithms have advantages over existing methods are also provided.

Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models. While existing analyses identify that RLVR-induced changes are sparse, they primarily focus on the magnitude of these updates, largely overlooking their direction. In this work, we argue that the direction of updates is a more critical lens for understanding RLVR's effects, which can be captured by the signed, token-level log probability difference Δlog p between the base and final RLVR models. Through statistical analysis and token-replacement interventions, we demonstrate that Δlog p more effectively identifies sparse, yet reasoning-critical updates than magnitude-based metrics (\eg divergence or entropy). Building on this insight, we propose two practical applications: (1) a test-time extrapolation method that amplifies the policy along the learned Δlog p direction to improve reasoning accuracy without further training; (2) a training-time reweighting method that focuses learning on low-probability (corresponding to higher Δlog p) tokens, which improves reasoning performance across models and benchmarks. Our work establishes the direction of change as a key principle for analyzing and improving RLVR.

Reliable detection of out-of-distribution (OOD) samples is crucial for the safe deployment of machine learning models. Neural networks often produce overconfident predictions for inputs that deviate from their training data, leading to significant degradation in performance. While many OOD detection methods focus on the final output layer, they neglect the rich hierarchical information present in intermediate network layers. This paper introduces a novel approach that leverages sparse autoencoders (SAEs) to learn interpretable features from these intermediate activations. We find that in-distribution (ID) and OOD data activate distinct sets of these sparse features. We propose a new OOD score derived from the cosine similarity between the sparse feature activations of a test sample and the mean activations of ID classes. Our post-hoc detection method not only achieves state-of-the-art performance on standard OOD detection benchmarks, but yields interpretable insights into how distribution shift affects learned representations.

Large language models (LLMs) are routinely pre-trained on billions of tokens, only to start the process over again once new data becomes available. A much more efficient solution is to continually pre-train these models, saving significant compute compared to re-training. However, the distribution shift induced by new data typically results in degraded performance on previous data or poor adaptation to the new data. In this work, we show that a simple and scalable combination of learning rate (LR) re-warming, LR re-decaying, and replay of previous data is sufficient to match the performance of fully re-training from scratch on all available data, as measured by final loss and language model (LM) evaluation benchmarks. Specifically, we show this for a weak but realistic distribution shift between two commonly used LLM pre-training datasets (EnglishrightarrowEnglish) and a stronger distribution shift (EnglishrightarrowGerman) at the 405M parameter model scale with large dataset sizes (hundreds of billions of tokens). Selecting the weak but realistic shift for larger-scale experiments, we also find that our continual learning strategies match the re-training baseline for a 10B parameter LLM. Our results demonstrate that LLMs can be successfully updated via simple and scalable continual learning strategies, matching the re-training baseline using only a fraction of the compute. Finally, inspired by previous work, we propose alternatives to the cosine learning rate schedule that help circumvent forgetting induced by LR re-warming and that are not bound to a fixed token budget.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Open set label shift (OSLS) occurs when label distributions change from a source to a target distribution, and the target distribution has an additional out-of-distribution (OOD) class. In this work, we build estimators for both source and target open set label distributions using a source domain in-distribution (ID) classifier and an ID/OOD classifier. With reasonable assumptions on the ID/OOD classifier, the estimators are assembled into a sequence of three stages: 1) an estimate of the source label distribution of the OOD class, 2) an EM algorithm for Maximum Likelihood estimates (MLE) of the target label distribution, and 3) an estimate of the target label distribution of OOD class under relaxed assumptions on the OOD classifier. The sampling errors of estimates in 1) and 3) are quantified with a concentration inequality. The estimation result allows us to correct the ID classifier trained on the source distribution to the target distribution without retraining. Experiments on a variety of open set label shift settings demonstrate the effectiveness of our model. Our code is available at https://github.com/ChangkunYe/OpenSetLabelShift.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Open-ended scientific discovery with large language models (LLMs) increasingly operates as a long-horizon loop of hypothesis search and verification, where a reward signal guides which hypotheses to test next. A notable recent example is AutoDiscovery, which uses "Bayesian surprise" - the belief shift an LLM undergoes after observing evidence for a hypothesis - as both a discovery metric and a reward for search. We first observe that AutoDiscovery treats surprisal as a static quantity, while surprisal in human reasoning is non-stationary - it is defined relative to beliefs that evolve with experience, a prerequisite for continual scientific discovery. We address this mismatch with evidence-informed LLM beliefs: priors updated with evidence from previous hypotheses to compute non-stationary surprisal for new hypotheses. We compare in-context belief-updating mechanisms and find that embedding-based retrieval-augmented generation over prior discoveries best anticipates eventual posteriors, identifying 37.5% of static surprisals as spurious. We then modify search to avoid these spurious rewards and prioritize hypotheses that remain surprising under non-stationary beliefs. Concretely, we introduce two complementary changes to the original search procedure: belief-update filtering and diversity maximization. Across five discovery domains, our method increases accumulated non-stationary surprisal by 30.62% on average compared to the original search procedure, demonstrating that continual scientific discovery with LLMs requires not only better belief measurement but also search procedures that avoid redundancy and encourage diversity.

Existing bias auditing methods typically rely on model outputs, requiring costly benchmarks or judge models and potentially missing internal shifts that never appear in generated text. We propose a reference-based method that audits bias in hidden-state representations across related model variants, for example before and after fine-tuning. Because fine-tuning reshapes representation geometry, absolute hidden states are not directly comparable, so we encode each sentence by its similarities to a fixed set of anchor sentences, yielding relative representations in a shared comparison space. There we measure how target groups shift in their association with positive and negative attributes, a quantity we call the Representational Bias Shift ΔB. Across three model families and the WildGuardMix, DecodingTrust and ToxiGen benchmarks, ΔB correlates with output-level bias change in 15 of the 18 settings we test, reaching |r| = 0.84 (p < 0.001) under full fine-tuning and becoming more model-dependent under parameter-efficient adaptation. Thresholding ΔB detects checkpoints whose bias increased with ROC AUC between 0.65 and 0.99, and on WildGuardMix and DecodingTrust it separates them better than a SEAT-based baseline for all three families. ΔB is also stable under changes to the anchor set, attribute sets and target templates. Our method requires no task-specific evaluation data and audits a model in about three minutes, using 3-50times less compute than the output-level benchmarks considered here. We view it as complementary to output-based auditing rather than a replacement for it.

Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples -- including those with low likelihood under the base model -- which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens -- those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

Diffusion Language Models (DLMs) have recently emerged as a strong alternative to autoregressive language models (LMs). DLMs offer comparable accuracy with faster inference speed via parallel decoding. However, standard DLM decoding strategies relying on high-confidence tokens encounter an inherent information-theoretic bottleneck that restricts decoding progress and ultimately slows generation. We demonstrate both theoretically and empirically that prioritizing high-confidence tokens is inherently inefficient. High-probability tokens carry negligible information and strictly relying on them limits the effective progress made in each decoding round. We prove that the number of decoding rounds must grow linearly with the sample's total information (negative log-likelihood) and inversely with the per-round information budget, establishing a bits-to-rounds principle. We also propose Explore-Then-Exploit (ETE), a training-free decoding strategy that maximizes information throughput and decoding efficiency. ETE combines cross-block decoding with targeted exploration of high-uncertainty tokens to reshape the conditional distribution and trigger cascades of confident predictions. Experiments verify our theoretical bounds and demonstrate that ETE consistently reduces the required number of decoding rounds compared to confidence-only baselines without compromising generation quality.

Diffusion models have emerged as the de facto choice for generating visual signals. However, training a single model to predict noise across various levels poses significant challenges, necessitating numerous iterations and incurring significant computational costs. Various approaches, such as loss weighting strategy design and architectural refinements, have been introduced to expedite convergence. In this study, we propose a novel approach to design the noise schedule for enhancing the training of diffusion models. Our key insight is that the importance sampling of the logarithm of the Signal-to-Noise ratio (logSNR), theoretically equivalent to a modified noise schedule, is particularly beneficial for training efficiency when increasing the sample frequency around log SNR=0. We empirically demonstrate the superiority of our noise schedule over the standard cosine schedule. Furthermore, we highlight the advantages of our noise schedule design on the ImageNet benchmark, showing that the designed schedule consistently benefits different prediction targets.

Diffusion-based image super-resolution (SR), which aims to reconstruct high-resolution (HR) images from corresponding low-resolution (LR) observations, faces a fundamental trade-off between inference efficiency and reconstruction quality. The state-of-the-art residual-shifting diffusion framework achieves efficient 4-step inference, yet suffers from severe performance degradation in compact sampling trajectories. This is mainly attributed to two core limitations: the inherent suboptimality of unconstrained random Gaussian noise in intermediate steps, which leads to error accumulation and insufficient LR prior guidance, and the initialization bias caused by naive bicubic upsampling. In this paper, we propose LPNSR, a prior-enhanced efficient diffusion framework to address these issues. We first mathematically derive the closed-form analytical solution of the optimal intermediate noise for the residual-shifting diffusion paradigm, and accordingly design an LR-guided multi-input-aware noise predictor to replace random Gaussian noise, embedding LR structural priors into the reverse process while fully preserving the framework's core efficient residual-shifting mechanism. We further mitigate initial bias with a high-quality pre-upsampling network to optimize the diffusion starting point. With a compact 4-step trajectory, LPNSR can be optimized in an end-to-end manner. Extensive experiments demonstrate that LPNSR achieves state-of-the-art perceptual performance on both synthetic and real-world datasets, without relying on any large-scale text-to-image priors. The source code of our method can be found at https://github.com/Faze-Hsw/LPNSR.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

We consider a number of graph kernels and proximity measures including commute time kernel, regularized Laplacian kernel, heat kernel, exponential diffusion kernel (also called "communicability"), etc., and the corresponding distances as applied to clustering nodes in random graphs and several well-known datasets. The model of generating random graphs involves edge probabilities for the pairs of nodes that belong to the same class or different predefined classes of nodes. It turns out that in most cases, logarithmic measures (i.e., measures resulting after taking logarithm of the proximities) perform better while distinguishing underlying classes than the "plain" measures. A comparison in terms of reject curves of inter-class and intra-class distances confirms this conclusion. A similar conclusion can be made for several well-known datasets. A possible origin of this effect is that most kernels have a multiplicative nature, while the nature of distances used in cluster algorithms is an additive one (cf. the triangle inequality). The logarithmic transformation is a tool to transform the first nature to the second one. Moreover, some distances corresponding to the logarithmic measures possess a meaningful cutpoint additivity property. In our experiments, the leader is usually the logarithmic Communicability measure. However, we indicate some more complicated cases in which other measures, typically, Communicability and plain Walk, can be the winners.

Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification, providing calibrated predictive intervals associated with automatic volume measurements. However, this methodology is based on the hypothesis that calibration and test samples are exchangeable, an assumption that is in practice often violated in medical image applications. A weighted formulation of Conformal Prediction can be framed to mitigate this issue, but its empirical investigation in the medical domain is still lacking. A potential reason is that it relies on the estimation of the density ratio between the calibration and test distributions, which is likely to be intractable in scenarios involving high-dimensional data. To circumvent this, we propose an efficient approach for density ratio estimation relying on the compressed latent representations generated by the segmentation model. Our experiments demonstrate the efficiency of our approach to reduce the coverage error in the presence of covariate shifts, in both synthetic and real-world settings. Our implementation is available at https://github.com/benolmbrt/wcp_miccai

This large scale study focuses on quantifying what X-rays diagnostic prediction tasks generalize well across multiple different datasets. We present evidence that the issue of generalization is not due to a shift in the images but instead a shift in the labels. We study the cross-domain performance, agreement between models, and model representations. We find interesting discrepancies between performance and agreement where models which both achieve good performance disagree in their predictions as well as models which agree yet achieve poor performance. We also test for concept similarity by regularizing a network to group tasks across multiple datasets together and observe variation across the tasks. All code is made available online and data is publicly available: https://github.com/mlmed/torchxrayvision

This study explores the application of anomaly detection (AD) methods in imbalanced learning tasks, focusing on fraud detection using real online credit card payment data. We assess the performance of several recent AD methods and compare their effectiveness against standard supervised learning methods. Offering evidence of distribution shift within our dataset, we analyze its impact on the tested models' performances. Our findings reveal that LightGBM exhibits significantly superior performance across all evaluated metrics but suffers more from distribution shifts than AD methods. Furthermore, our investigation reveals that LightGBM also captures the majority of frauds detected by AD methods. This observation challenges the potential benefits of ensemble methods to combine supervised, and AD approaches to enhance performance. In summary, this research provides practical insights into the utility of these techniques in real-world scenarios, showing LightGBM's superiority in fraud detection while highlighting challenges related to distribution shifts.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift. We introduce the concept of relative signal strength (RSS), a pointwise measure that quantifies the transferability from noisy to clean posterior. Using RSS, we establish nearly matching upper and lower bounds on the excess risk. Our theoretical findings support the simple Noise Ignorant Empirical Risk Minimization (NI-ERM) principle, which minimizes empirical risk while ignoring label noise. Finally, we translate this theoretical insight into practice: by using NI-ERM to fit a linear classifier on top of a self-supervised feature extractor, we achieve state-of-the-art performance on the CIFAR-N data challenge.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation~(NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study it a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

Reconstruction of magnetic resonance imaging (MRI) data has been positively affected by deep learning. A key challenge remains: to improve generalisation to distribution shifts between the training and testing data. Most approaches aim to address this via inductive design or data augmentation. However, they can be affected by misleading data, e.g. random noise, and cases where the inference stage data do not match assumptions in the modelled shifts. In this work, by employing a conditional hyperparameter network, we eliminate the need of augmentation, yet maintain robust performance under various levels of Gaussian noise. We demonstrate that our model withstands various input noise levels while producing high-definition reconstructions during the test stage. Moreover, we present a hyperparameter sampling strategy that accelerates the convergence of training. Our proposed method achieves the highest accuracy and image quality in all settings compared to baseline methods.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Existing denoising generative models rely on solving discretized reverse-time SDEs or ODEs. In this paper, we identify a long-overlooked yet pervasive issue in this family of models: a misalignment between the pre-defined noise level and the actual noise level encoded in intermediate states during sampling. We refer to this misalignment as noise shift. Through empirical analysis, we demonstrate that noise shift is widespread in modern diffusion models and exhibits a systematic bias, leading to sub-optimal generation due to both out-of-distribution generalization and inaccurate denoising updates. To address this problem, we propose Noise Awareness Guidance (NAG), a simple yet effective correction method that explicitly steers sampling trajectories to remain consistent with the pre-defined noise schedule. We further introduce a classifier-free variant of NAG, which jointly trains a noise-conditional and a noise-unconditional model via noise-condition dropout, thereby eliminating the need for external classifiers. Extensive experiments, including ImageNet generation and various supervised fine-tuning tasks, show that NAG consistently mitigates noise shift and substantially improves the generation quality of mainstream diffusion models.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

Dynamic neuroimaging data, such as emission tomography measurements of radiotracer transport in blood or cerebrospinal fluid, often exhibit diffusion-like properties. These introduce distance-dependent temporal delays, scale-differences, and stretching effects that limit the effectiveness of conventional linear modeling and decomposition methods. To address this, we present the shift- and stretch-invariant non-negative matrix factorization framework. Our approach estimates both integer and non-integer temporal shifts as well as temporal stretching, all implemented in the frequency domain, where shifts correspond to phase modifications, and where stretching is handled via zero-padding or truncation. The model is implemented in PyTorch (https://github.com/anders-s-olsen/shiftstretchNMF). We demonstrate on synthetic data and brain emission tomography data that the model is able to account for stretching to provide more detailed characterization of brain tissue structure.

Large pre-trained models such as CLIP or ALIGN offer consistent accuracy across a range of data distributions when performing zero-shot inference (i.e., without fine-tuning on a specific dataset). Although existing fine-tuning methods substantially improve accuracy on a given target distribution, they often reduce robustness to distribution shifts. We address this tension by introducing a simple and effective method for improving robustness while fine-tuning: ensembling the weights of the zero-shot and fine-tuned models (WiSE-FT). Compared to standard fine-tuning, WiSE-FT provides large accuracy improvements under distribution shift, while preserving high accuracy on the target distribution. On ImageNet and five derived distribution shifts, WiSE-FT improves accuracy under distribution shift by 4 to 6 percentage points (pp) over prior work while increasing ImageNet accuracy by 1.6 pp. WiSE-FT achieves similarly large robustness gains (2 to 23 pp) on a diverse set of six further distribution shifts, and accuracy gains of 0.8 to 3.3 pp compared to standard fine-tuning on seven commonly used transfer learning datasets. These improvements come at no additional computational cost during fine-tuning or inference.

Background: Deep learning models are typically trained using stochastic gradient descent or one of its variants. These methods update the weights using their gradient, estimated from a small fraction of the training data. It has been observed that when using large batch sizes there is a persistent degradation in generalization performance - known as the "generalization gap" phenomena. Identifying the origin of this gap and closing it had remained an open problem. Contributions: We examine the initial high learning rate training phase. We find that the weight distance from its initialization grows logarithmically with the number of weight updates. We therefore propose a "random walk on random landscape" statistical model which is known to exhibit similar "ultra-slow" diffusion behavior. Following this hypothesis we conducted experiments to show empirically that the "generalization gap" stems from the relatively small number of updates rather than the batch size, and can be completely eliminated by adapting the training regime used. We further investigate different techniques to train models in the large-batch regime and present a novel algorithm named "Ghost Batch Normalization" which enables significant decrease in the generalization gap without increasing the number of updates. To validate our findings we conduct several additional experiments on MNIST, CIFAR-10, CIFAR-100 and ImageNet. Finally, we reassess common practices and beliefs concerning training of deep models and suggest they may not be optimal to achieve good generalization.

Large language models (LLMs) are widely used as information sources, yet small changes in semantic assumptions can destabilize their beliefs. We introduce P-StaT (Perturbation Stability of Truth), a framework for evaluating belief stability under matched semantic perturbations in both representational and behavioral settings. Across 21 LLMs and three domains, we compare perturbations involving familiar Fictional statements against synthetically generated and unfamiliar Synthetic statements. Unfamiliar Synthetic perturbations generally induce greater epistemic instability than familiar Fictional perturbations, with behavioral belief retraction rates frequently exceeding 0.5 (50%). Finally, exploratory clustering analyses reveal recurring themes among retracted statements, including ambiguity, technical terminology, and obscure concepts. These results show that epistemic familiarity is systematically associated with stability under semantic reframing, suggesting that stability-based analyses can complement accuracy-based benchmarks when evaluating LLM robustness and reliability. Code and data are available at https://github.com/samanthadies/P-StaT.

Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear regression tasks, and different from all the existing literature, we consider a bi-objective prediction task of predicting both the conditional expectation E[Y|X] and the conditional variance Var(Y|X). This additional uncertainty quantification objective provides a handle to (i) better design out-of-distribution experiments to distinguish ICL from in-weight learning (IWL) and (ii) make a better separation between the algorithms with and without using the prior information of the training distribution. Theoretically, we show that the trained Transformer reaches near Bayes-optimum, suggesting the usage of the information of the training distribution. Our method can be extended to other cases. Specifically, with the Transformer's context window S, we prove a generalization bound of mathcal{O}(min{S, T/(n T)}) on n tasks with sequences of length T, providing sharper analysis compared to previous results of mathcal{O}(1/n). Empirically, we illustrate that while the trained Transformer behaves as the Bayes-optimal solution as a natural consequence of supervised training in distribution, it does not necessarily perform a Bayesian inference when facing task shifts, in contrast to the equivalence between these two proposed in many existing literature. We also demonstrate the trained Transformer's ICL ability over covariates shift and prompt-length shift and interpret them as a generalization over a meta distribution.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

Despite a growing interest in diffusion-based language models, existing work has not shown that these models can attain nontrivial likelihoods on standard language modeling benchmarks. In this work, we take the first steps towards closing the likelihood gap between autoregressive and diffusion-based language models, with the goal of building and releasing a diffusion model which outperforms a small but widely-known autoregressive model. We pursue this goal through algorithmic improvements, scaling laws, and increased compute. On the algorithmic front, we introduce several methodological improvements for the maximum-likelihood training of diffusion language models. We then study scaling laws for our diffusion models and find compute-optimal training regimes which differ substantially from autoregressive models. Using our methods and scaling analysis, we train and release Plaid 1B, a large diffusion language model which outperforms GPT-2 124M in likelihood on benchmark datasets and generates fluent samples in unconditional and zero-shot control settings.

Multimodal large language models (MLLMs) have shown promising capabilities but struggle under distribution shifts, where evaluation data differ from instruction tuning distributions. Although previous works have provided empirical evaluations, we argue that establishing a formal framework that can characterize and quantify the risk of MLLMs is necessary to ensure the safe and reliable application of MLLMs in the real world. By taking an information-theoretic perspective, we propose the first theoretical framework that enables the quantification of the maximum risk of MLLMs under distribution shifts. Central to our framework is the introduction of Effective Mutual Information (EMI), a principled metric that quantifies the relevance between input queries and model responses. We derive an upper bound for the EMI difference between in-distribution (ID) and out-of-distribution (OOD) data, connecting it to visual and textual distributional discrepancies. Extensive experiments on real benchmark datasets, spanning 61 shift scenarios empirically validate our theoretical insights.

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data, called Constraint-based causal Discovery from heterogeneous/NOnstationary Data (CD-NOD), to find causal skeleton and directions and estimate the properties of mechanism changes. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a method to determine causal orientations by making use of independent changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. After learning the causal structure, next, we investigate how to efficiently estimate the "driving force" of the nonstationarity of a causal mechanism. That is, we aim to extract from data a low-dimensional representation of changes. The proposed methods are nonparametric, with no hard restrictions on data distributions and causal mechanisms, and do not rely on window segmentation. Furthermore, we find that data heterogeneity benefits causal structure identification even with particular types of confounders. Finally, we show the connection between heterogeneity/nonstationarity and soft intervention in causal discovery. Experimental results on various synthetic and real-world data sets (task-fMRI and stock market data) are presented to demonstrate the efficacy of the proposed methods.

Learning representations that generalize under distribution shifts is critical for building robust machine learning models. However, despite significant efforts in recent years, algorithmic advances in this direction have been limited. In this work, we seek to understand the fundamental difficulty of out-of-distribution generalization with deep neural networks. We first empirically show that perhaps surprisingly, even allowing a neural network to explicitly fit the representations obtained from a teacher network that can generalize out-of-distribution is insufficient for the generalization of the student network. Then, by a theoretical study of two-layer ReLU networks optimized by stochastic gradient descent (SGD) under a structured feature model, we identify a fundamental yet unexplored feature learning proclivity of neural networks, feature contamination: neural networks can learn uncorrelated features together with predictive features, resulting in generalization failure under distribution shifts. Notably, this mechanism essentially differs from the prevailing narrative in the literature that attributes the generalization failure to spurious correlations. Overall, our results offer new insights into the non-linear feature learning dynamics of neural networks and highlight the necessity of considering inductive biases in out-of-distribution generalization.

We revisit the noisy binary search model of Karp and Kleinberg, in which we have n coins with unknown probabilities p_i that we can flip. The coins are sorted by increasing p_i, and we would like to find where the probability crosses (to within varepsilon) of a target value tau. This generalized the fixed-noise model of Burnashev and Zigangirov , in which p_i = 1{2} pm varepsilon, to a setting where coins near the target may be indistinguishable from it. Karp and Kleinberg showed that Theta(1{varepsilon^2} log n) samples are necessary and sufficient for this task. We produce a practical algorithm by solving two theoretical challenges: high-probability behavior and sharp constants. We give an algorithm that succeeds with probability 1-delta from \[ 1{C_{\tau, \varepsilon}} \cdot \left(\lg n + O(\log^{2/3} n \log^{1/3} 1{\delta} + \log 1{\delta})\right) \] samples, where C_{tau, varepsilon} is the optimal such constant achievable. For delta > n^{-o(1)} this is within 1 + o(1) of optimal, and for delta ll 1 it is the first bound within constant factors of optimal.

Biomedical imaging datasets are often small and biased, meaning that real-world performance of predictive models can be substantially lower than expected from internal testing. This work proposes using generative image editing to simulate dataset shifts and diagnose failure modes of biomedical vision models; this can be used in advance of deployment to assess readiness, potentially reducing cost and patient harm. Existing editing methods can produce undesirable changes, with spurious correlations learned due to the co-occurrence of disease and treatment interventions, limiting practical applicability. To address this, we train a text-to-image diffusion model on multiple chest X-ray datasets and introduce a new editing method RadEdit that uses multiple masks, if present, to constrain changes and ensure consistency in the edited images. We consider three types of dataset shifts: acquisition shift, manifestation shift, and population shift, and demonstrate that our approach can diagnose failures and quantify model robustness without additional data collection, complementing more qualitative tools for explainable AI.

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

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs and GANs cover the target distribution. Finally, we show that the sample quality and likelihood of these models scale smoothly with model capacity and training compute, making them easily scalable. We release our code at https://github.com/openai/improved-diffusion

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood on standard benchmarks. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient realistic-looking synthesis and manipulation of large images. The code for our model is available at https://github.com/openai/glow

Previous work has highlighted that existing post-hoc explanation methods exhibit disparities in explanation fidelity (across 'race' and 'gender' as sensitive attributes), and while a large body of work focuses on mitigating these issues at the explanation metric level, the role of the data generating process and black box model in relation to explanation disparities remains largely unexplored. Accordingly, through both simulations as well as experiments on a real-world dataset, we specifically assess challenges to explanation disparities that originate from properties of the data: limited sample size, covariate shift, concept shift, omitted variable bias, and challenges based on model properties: inclusion of the sensitive attribute and appropriate functional form. Through controlled simulation analyses, our study demonstrates that increased covariate shift, concept shift, and omission of covariates increase explanation disparities, with the effect pronounced higher for neural network models that are better able to capture the underlying functional form in comparison to linear models. We also observe consistent findings regarding the effect of concept shift and omitted variable bias on explanation disparities in the Adult income dataset. Overall, results indicate that disparities in model explanations can also depend on data and model properties. Based on this systematic investigation, we provide recommendations for the design of explanation methods that mitigate undesirable disparities.

Many problems in machine learning are naturally expressed in the language of undirected graphical models. Here, we propose black-box learning and inference algorithms for undirected models that optimize a variational approximation to the log-likelihood of the model. Central to our approach is an upper bound on the log-partition function parametrized by a function q that we express as a flexible neural network. Our bound makes it possible to track the partition function during learning, to speed-up sampling, and to train a broad class of hybrid directed/undirected models via a unified variational inference framework. We empirically demonstrate the effectiveness of our method on several popular generative modeling datasets.

Recent studies have revealed a number of pathologies of neural machine translation (NMT) systems. Hypotheses explaining these mostly suggest there is something fundamentally wrong with NMT as a model or its training algorithm, maximum likelihood estimation (MLE). Most of this evidence was gathered using maximum a posteriori (MAP) decoding, a decision rule aimed at identifying the highest-scoring translation, i.e. the mode. We argue that the evidence corroborates the inadequacy of MAP decoding more than casts doubt on the model and its training algorithm. In this work, we show that translation distributions do reproduce various statistics of the data well, but that beam search strays from such statistics. We show that some of the known pathologies and biases of NMT are due to MAP decoding and not to NMT's statistical assumptions nor MLE. In particular, we show that the most likely translations under the model accumulate so little probability mass that the mode can be considered essentially arbitrary. We therefore advocate for the use of decision rules that take into account the translation distribution holistically. We show that an approximation to minimum Bayes risk decoding gives competitive results confirming that NMT models do capture important aspects of translation well in expectation.

It is believed that in knowledge distillation (KD), the role of the teacher is to provide an estimate for the unknown Bayes conditional probability distribution (BCPD) to be used in the student training process. Conventionally, this estimate is obtained by training the teacher using maximum log-likelihood (MLL) method. To improve this estimate for KD, in this paper we introduce the concept of conditional mutual information (CMI) into the estimation of BCPD and propose a novel estimator called the maximum CMI (MCMI) method. Specifically, in MCMI estimation, both the log-likelihood and CMI of the teacher are simultaneously maximized when the teacher is trained. Through Eigen-CAM, it is further shown that maximizing the teacher's CMI value allows the teacher to capture more contextual information in an image cluster. Via conducting a thorough set of experiments, we show that by employing a teacher trained via MCMI estimation rather than one trained via MLL estimation in various state-of-the-art KD frameworks, the student's classification accuracy consistently increases, with the gain of up to 3.32\%. This suggests that the teacher's BCPD estimate provided by MCMI method is more accurate than that provided by MLL method. In addition, we show that such improvements in the student's accuracy are more drastic in zero-shot and few-shot settings. Notably, the student's accuracy increases with the gain of up to 5.72\% when 5\% of the training samples are available to the student (few-shot), and increases from 0\% to as high as 84\% for an omitted class (zero-shot). The code is available at https://github.com/iclr2024mcmi/ICLRMCMI.

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.

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.

Implicit Neural Representations (INRs) have recently gained attention as a powerful approach for continuously representing signals such as images, videos, and 3D shapes using multilayer perceptrons (MLPs). However, MLPs are known to exhibit a low-frequency bias, limiting their ability to capture high-frequency details accurately. This limitation is typically addressed by incorporating high-frequency input embeddings or specialized activation layers. In this work, we demonstrate that these embeddings and activations are often configured with hyperparameters that perform well on average but are suboptimal for specific input signals under consideration, necessitating a costly grid search to identify optimal settings. Our key observation is that the initial frequency spectrum of an untrained model's output correlates strongly with the model's eventual performance on a given target signal. Leveraging this insight, we propose frequency shifting (or FreSh), a method that selects embedding hyperparameters to align the frequency spectrum of the model's initial output with that of the target signal. We show that this simple initialization technique improves performance across various neural representation methods and tasks, achieving results comparable to extensive hyperparameter sweeps but with only marginal computational overhead compared to training a single model with default hyperparameters.

Counterfactual prompting (i.e., perturbing a single factor and measuring output change) is widely used to evaluate things like LLM bias and CoT faithfulness. But in this work we argue that observed effects cannot be attributed to the targeted factor without accounting for baseline ``meaning-preserving'' modifications to text that establish general model sensitivity. This is because every counterfactual edit is a compound treatment that bundles the variable of interest with incidental surface-form variation; this violates treatment variation irrelevance. We observe prediction flip rates on MedQA of 14.9% when we surgically change patient gender. However, this is statistically indistinguishable from the flip rates induced by simply paraphrasing inputs (14.1%). In this case, it would therefore be unwarranted to conclude that the LLM is especially sensitive to patient gender. To account for this and robustly measure the effects of targeted interventions, we propose a framework in which we compare (via statistical testing) differences observed under target interventions to those induced by paraphrasing inputs. We then use this framework to revisit a analysis done on the MedPerturb dataset, which reported evidence of model sensitivity to patient demographics and stylistic cues. We find that these effects largely dissipate when we account for general model sensitivity, with only 5 of 120 tests reaching statistical significance. Applying the same framework to occupational biography classification, we detect clearly significant directional gender bias, showing that the framework identifies real directional effects even when they are small. We evaluate a range of metrics -- aggregate, per-sample distributional, and regression -- and find that per-sample metrics are dramatically more powerful than aggregate metrics and regression powerfully and uniquely characterizes effect direction and magnitude.

The fluency and factual knowledge of large language models (LLMs) heightens the need for corresponding systems to detect whether a piece of text is machine-written. For example, students may use LLMs to complete written assignments, leaving instructors unable to accurately assess student learning. In this paper, we first demonstrate that text sampled from an LLM tends to occupy negative curvature regions of the model's log probability function. Leveraging this observation, we then define a new curvature-based criterion for judging if a passage is generated from a given LLM. This approach, which we call DetectGPT, does not require training a separate classifier, collecting a dataset of real or generated passages, or explicitly watermarking generated text. It uses only log probabilities computed by the model of interest and random perturbations of the passage from another generic pre-trained language model (e.g, T5). We find DetectGPT is more discriminative than existing zero-shot methods for model sample detection, notably improving detection of fake news articles generated by 20B parameter GPT-NeoX from 0.81 AUROC for the strongest zero-shot baseline to 0.95 AUROC for DetectGPT. See https://ericmitchell.ai/detectgpt for code, data, and other project information.

We consider the problem of support recovery for sparse binary signals from noisy linear measurements. For sparse Gaussian measurement matrices we identify sufficient conditions on the minimal sample size for maximum-likelihood recovery in the high-SNR regime ds/p to infty, where p denotes the signal dimension, s the number of non-zero components of the signal, and d the expected number of non-zero components per row of measurement. Combined with known lower bounds, this yields an information-theoretic threshold of order slog(p/s) / log(ds/p), making explicit the price of measurement sparsity. In particular, we highlight a regime where the sample-complexity loss from measurement sparsity is logarithmic while the computational gain is nearly linear. Second, we study recovery after sparsifying an originally dense Gaussian design: the observations are generated from the dense design, while estimation uses an independently sparsified design and a rescaled response. In the proportional regime s=αp, d=ψp, we prove that, for every fixed target error level δ and every slack varepsilon>0, a sample size of order p/ψ^2 is sufficient for support recovery for arbitrarily small ψ.

We study the probabilistic modeling performed by Autoregressive Large Language Models (LLMs) through the angle of time directionality, addressing a question first raised in (Shannon, 1951). For large enough models, we empirically find a time asymmetry in their ability to learn natural language: a difference in the average log-perplexity when trying to predict the next token versus when trying to predict the previous one. This difference is at the same time subtle and very consistent across various modalities (language, model size, training time, ...). Theoretically, this is surprising: from an information-theoretic point of view, there should be no such difference. We provide a theoretical framework to explain how such an asymmetry can appear from sparsity and computational complexity considerations, and outline a number of perspectives opened by our results.