Daily Papers

Nature is infinitely resolution-free. In the context of this reality, existing diffusion models, such as Diffusion Transformers, often face challenges when processing image resolutions outside of their trained domain. To address this limitation, we conceptualize images as sequences of tokens with dynamic sizes, rather than traditional methods that perceive images as fixed-resolution grids. This perspective enables a flexible training strategy that seamlessly accommodates various aspect ratios during both training and inference, thus promoting resolution generalization and eliminating biases introduced by image cropping. On this basis, we present the Flexible Vision Transformer (FiT), a transformer architecture specifically designed for generating images with unrestricted resolutions and aspect ratios. We further upgrade the FiT to FiTv2 with several innovative designs, includingthe Query-Key vector normalization, the AdaLN-LoRA module, a rectified flow scheduler, and a Logit-Normal sampler. Enhanced by a meticulously adjusted network structure, FiTv2 exhibits 2times convergence speed of FiT. When incorporating advanced training-free extrapolation techniques, FiTv2 demonstrates remarkable adaptability in both resolution extrapolation and diverse resolution generation. Additionally, our exploration of the scalability of the FiTv2 model reveals that larger models exhibit better computational efficiency. Furthermore, we introduce an efficient post-training strategy to adapt a pre-trained model for the high-resolution generation. Comprehensive experiments demonstrate the exceptional performance of FiTv2 across a broad range of resolutions. We have released all the codes and models at https://github.com/whlzy/FiT to promote the exploration of diffusion transformer models for arbitrary-resolution image generation.

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.

Recently, pre-trained vision-language models (e.g., CLIP) have shown great potential in few-shot learning and attracted a lot of research interest. Although efforts have been made to improve few-shot ability of CLIP, key factors on the effectiveness of existing methods have not been well studied, limiting further exploration of CLIP's potential in few-shot learning. In this paper, we first introduce a unified formulation to analyze CLIP-based few-shot learning methods from a perspective of logit bias, which encourages us to learn an effective logit bias for further improving performance of CLIP-based few-shot learning methods. To this end, we disassemble three key components involved in computation of logit bias (i.e., logit features, logit predictor, and logit fusion) and empirically analyze the effect on performance of few-shot classification. Based on analysis of key components, this paper proposes a novel AMU-Tuning method to learn effective logit bias for CLIP-based few-shot classification. Specifically, our AMU-Tuning predicts logit bias by exploiting the appropriate textbf{A}uxiliary features, which are fed into an efficient feature-initialized linear classifier with textbf{M}ulti-branch training. Finally, an textbf{U}ncertainty-based fusion is developed to incorporate logit bias into CLIP for few-shot classification. The experiments are conducted on several widely used benchmarks, and the results show AMU-Tuning clearly outperforms its counterparts while achieving state-of-the-art performance of CLIP-based few-shot learning without bells and whistles.

We present the Stanford Question Answering Dataset (SQuAD), a new reading comprehension dataset consisting of 100,000+ questions posed by crowdworkers on a set of Wikipedia articles, where the answer to each question is a segment of text from the corresponding reading passage. We analyze the dataset to understand the types of reasoning required to answer the questions, leaning heavily on dependency and constituency trees. We build a strong logistic regression model, which achieves an F1 score of 51.0%, a significant improvement over a simple baseline (20%). However, human performance (86.8%) is much higher, indicating that the dataset presents a good challenge problem for future research. The dataset is freely available at https://stanford-qa.com

Knowledge distillation involves transferring soft labels from a teacher to a student using a shared temperature-based softmax function. However, the assumption of a shared temperature between teacher and student implies a mandatory exact match between their logits in terms of logit range and variance. This side-effect limits the performance of student, considering the capacity discrepancy between them and the finding that the innate logit relations of teacher are sufficient for student to learn. To address this issue, we propose setting the temperature as the weighted standard deviation of logit and performing a plug-and-play Z-score pre-process of logit standardization before applying softmax and Kullback-Leibler divergence. Our pre-process enables student to focus on essential logit relations from teacher rather than requiring a magnitude match, and can improve the performance of existing logit-based distillation methods. We also show a typical case where the conventional setting of sharing temperature between teacher and student cannot reliably yield the authentic distillation evaluation; nonetheless, this challenge is successfully alleviated by our Z-score. We extensively evaluate our method for various student and teacher models on CIFAR-100 and ImageNet, showing its significant superiority. The vanilla knowledge distillation powered by our pre-process can achieve favorable performance against state-of-the-art methods, and other distillation variants can obtain considerable gain with the assistance of our pre-process.

Cross-tokenizer knowledge distillation allows a student model to learn from teachers with incompatible vocabularies. Prior work operates on hidden states or logits; the latter is preferred as a drop-in replacement requiring no auxiliary components. Logit-based methods either use only the correct-token probability, missing the full 'dark knowledge' in the teacher's distribution, or operate on the full output distribution, relying on strict token partitioning and/or unprincipled heuristic ranking. We identify two key shortcomings of full-distribution, logit-based methods: (i) an uncommon-token failure, where critical tokens fall into the unmatched subset (e.g., Llama's 1100 multi-digit numerals under digit-splitting Qwen supervision) and are suppressed during training, reducing GSM8k from 12.89 to 2.56 compared to same-tokenizer KD from a weaker teacher; and (ii) over-conservative matching, where strict 1-to-1 matching excludes near-equivalent tokens across surface forms. These failures require distinct remedies: eliminating the partition when critical tokens are misaligned, and refining it when alignment is reliable. We propose X-Token, an approach with two complementary loss formulations targeting these issues. P-KL removes partitioning and aligns the student's distribution with the teacher's via a sparse projection matrix W (initialized from tokenizer-level string rules) to address the uncommon-token failure. H-KL retains the hybrid form while relaxing matching to align each student token with its top-ranked teacher mapping under W. Both objectives share W and extend naturally to multiple teachers. Empirically, on Llama-3.2-1B, X-Token outperforms the current state of the art GOLD by +3.82 average points with a Qwen3-4B teacher and by +0.5 with a Phi-4-Mini teacher. Further, a two-teacher setup (Phi-4-mini + Llama-3B) improves over single-teacher distillation by +1.3 points.

Large language models (LLMs) typically employ greedy decoding or low-temperature sampling for reasoning tasks, reflecting a perceived trade-off between diversity and accuracy. We challenge this convention by introducing top-nsigma, a novel sampling method that operates directly on pre-softmax logits by leveraging a statistical threshold. Our key insight is that logits naturally separate into a Gaussian-distributed noisy region and a distinct informative region, enabling efficient token filtering without complex probability manipulations. Unlike existing methods (e.g., top-p, min-p) that inadvertently include more noise tokens at higher temperatures, top-nsigma maintains a stable sampling space regardless of temperature scaling. We also provide a theoretical analysis of top-nsigma to better understand its behavior. The extensive experimental results across four reasoning-focused datasets demonstrate that our method not only outperforms existing sampling approaches but also surpasses greedy decoding, while maintaining consistent performance even at high temperatures.

We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function piproptoe^{-U} is known up to a normalizing constant, which is an important task in fields such as statistical physics, machine learning, combinatorial optimization, etc. To better address this challenging task when the state space has a large cardinality and the distribution is multi-modal, we propose Masked Diffusion Neural Sampler (MDNS), a novel framework for training discrete neural samplers by aligning two path measures through a family of learning objectives, theoretically grounded in the stochastic optimal control of the continuous-time Markov chains. We validate the efficiency and scalability of MDNS through extensive experiments on various distributions with distinct statistical properties, where MDNS learns to accurately sample from the target distributions despite the extremely high problem dimensions and outperforms other learning-based baselines by a large margin. A comprehensive study of ablations and extensions is also provided to demonstrate the efficacy and potential of the proposed framework.

We characterize the statistical efficiency of knowledge transfer through n samples from a teacher to a probabilistic student classifier with input space mathcal S over labels mathcal A. We show that privileged information at three progressive levels accelerates the transfer. At the first level, only samples with hard labels are known, via which the maximum likelihood estimator attains the minimax rate {|{mathcal S||{mathcal A}|}/{n}}. The second level has the teacher probabilities of sampled labels available in addition, which turns out to boost the convergence rate lower bound to {{|{mathcal S}||{mathcal A}|}/{n}}. However, under this second data acquisition protocol, minimizing a naive adaptation of the cross-entropy loss results in an asymptotically biased student. We overcome this limitation and achieve the fundamental limit by using a novel empirical variant of the squared error logit loss. The third level further equips the student with the soft labels (complete logits) on {mathcal A} given every sampled input, thereby provably enables the student to enjoy a rate {|{mathcal S}|}/{n} free of |{mathcal A}|. We find any Kullback-Leibler divergence minimizer to be optimal in the last case. Numerical simulations distinguish the four learners and corroborate our theory.

With the increasing numbers of publicly available models, there are probably pretrained, online models for most tasks users require. However, current model search methods are rudimentary, essentially a text-based search in the documentation, thus users cannot find the relevant models. This paper presents ProbeLog, a method for retrieving classification models that can recognize a target concept, such as "Dog", without access to model metadata or training data. Differently from previous probing methods, ProbeLog computes a descriptor for each output dimension (logit) of each model, by observing its responses on a fixed set of inputs (probes). Our method supports both logit-based retrieval ("find more logits like this") and zero-shot, text-based retrieval ("find all logits corresponding to dogs"). As probing-based representations require multiple costly feedforward passes through the model, we develop a method, based on collaborative filtering, that reduces the cost of encoding repositories by 3x. We demonstrate that ProbeLog achieves high retrieval accuracy, both in real-world and fine-grained search tasks and is scalable to full-size repositories.

Out-of-distribution (OOD) detection is critical for ensuring the reliability of deep learning models in open-world applications. While post-hoc methods are favored for their efficiency and ease of deployment, existing approaches often underexploit the rich information embedded in the model's logits space. In this paper, we propose LogitGap, a novel post-hoc OOD detection method that explicitly exploits the relationship between the maximum logit and the remaining logits to enhance the separability between in-distribution (ID) and OOD samples. To further improve its effectiveness, we refine LogitGap by focusing on a more compact and informative subset of the logit space. Specifically, we introduce a training-free strategy that automatically identifies the most informative logits for scoring. We provide both theoretical analysis and empirical evidence to validate the effectiveness of our approach. Extensive experiments on both vision-language and vision-only models demonstrate that LogitGap consistently achieves state-of-the-art performance across diverse OOD detection scenarios and benchmarks. Code is available at https://github.com/GIT-LJc/LogitGap.

Most of the existing Out-Of-Distribution (OOD) detection algorithms depend on single input source: the feature, the logit, or the softmax probability. However, the immense diversity of the OOD examples makes such methods fragile. There are OOD samples that are easy to identify in the feature space while hard to distinguish in the logit space and vice versa. Motivated by this observation, we propose a novel OOD scoring method named Virtual-logit Matching (ViM), which combines the class-agnostic score from feature space and the In-Distribution (ID) class-dependent logits. Specifically, an additional logit representing the virtual OOD class is generated from the residual of the feature against the principal space, and then matched with the original logits by a constant scaling. The probability of this virtual logit after softmax is the indicator of OOD-ness. To facilitate the evaluation of large-scale OOD detection in academia, we create a new OOD dataset for ImageNet-1K, which is human-annotated and is 8.8x the size of existing datasets. We conducted extensive experiments, including CNNs and vision transformers, to demonstrate the effectiveness of the proposed ViM score. In particular, using the BiT-S model, our method gets an average AUROC 90.91% on four difficult OOD benchmarks, which is 4% ahead of the best baseline. Code and dataset are available at https://github.com/haoqiwang/vim.

As post-training processes utilize increasingly large datasets and base models continue to grow in size, the computational demands and implementation challenges of existing algorithms are escalating significantly. In this paper, we propose modeling the changes at the logits level during post-training using a separate neural network (i.e., the value network). After training this network on a small base model using demonstrations, this network can be seamlessly integrated with other pre-trained models during inference, enables them to achieve similar capability enhancements. We systematically investigate the best practices for this paradigm in terms of pre-training weights and connection schemes. We demonstrate that the resulting value network has broad transferability across pre-trained models of different parameter sizes within the same family, models undergoing continuous pre-training within the same family, and models with different vocabularies across families. In certain cases, it can achieve performance comparable to full-parameter fine-tuning. Furthermore, we explore methods to enhance the transferability of the value model and prevent overfitting to the base model used during training.

Sampling from a categorical distribution is mathematically simple, but in large-vocabulary decoding, it often triggers extra memory traffic and extra kernels after the LM head. We present FlashSampling, an exact sampling primitive that fuses sampling into the LM-head matmul and never materializes the logits tensor in HBM. The method is simple: compute logits tile-by-tile on chip, add Gumbel noise, keep only one maximizer per row and per vocabulary tile, and finish with a small reduction over tiles. The fused tiled kernel is exact because argmax decomposes over a partition; grouped variants for online and tensor-parallel settings are exact by hierarchical factorization of the categorical distribution. Across H100, H200, B200, and B300 GPUs, FlashSampling speeds up kernel-level decode workloads, and in end-to-end vLLM experiments, it reduces time per output token by up to 19% on the models we test. These results show that exact sampling, with no approximation, can be integrated into the matmul itself, turning a bandwidth-bound postprocessing step into a lightweight epilogue. Project Page: https://github.com/FlashSampling/FlashSampling.

Training modern large language models (LLMs) has become a veritable smorgasbord of algorithms and datasets designed to elicit particular behaviors, making it critical to develop techniques to understand the effects of datasets on the model's properties. This is exacerbated by recent experiments that show datasets can transmit signals that are not directly observable from individual datapoints, posing a conceptual challenge for dataset-centric understandings of LLM training and suggesting a missing fundamental account of such phenomena. Towards understanding such effects, inspired by recent work on the linear structure of LLMs, we uncover a general mechanism through which hidden subtexts can arise in generic datasets. We introduce Logit-Linear-Selection (LLS), a method that prescribes how to select subsets of a generic preference dataset to elicit a wide range of hidden effects. We apply LLS to discover subsets of real-world datasets so that models trained on them exhibit behaviors ranging from having specific preferences, to responding to prompts in a different language not present in the dataset, to taking on a different persona. Crucially, the effect persists for the selected subset, across models with varying architectures, supporting its generality and universality.

We study the problem of determining whether a piece of text has been authored by a human or by a large language model (LLM). Existing state of the art logits-based detectors make use of statistics derived from the log-probability of the observed text evaluated using the distribution function of a given source LLM. However, relying solely on log probabilities can be sub-optimal. In response, we introduce AdaDetectGPT -- a novel classifier that adaptively learns a witness function from training data to enhance the performance of logits-based detectors. We provide statistical guarantees on its true positive rate, false positive rate, true negative rate and false negative rate. Extensive numerical studies show AdaDetectGPT nearly uniformly improves the state-of-the-art method in various combination of datasets and LLMs, and the improvement can reach up to 58%. A python implementation of our method is available at https://github.com/Mamba413/AdaDetectGPT.

Existing studies on preference optimization (PO) have centered on constructing pairwise preference data following simple heuristics, such as maximizing the margin between preferred and dispreferred completions based on human (or AI) ranked scores. However, none of these heuristics has a full theoretical justification. In this work, we develop a novel PO framework that provides theoretical guidance to effectively sample dispreferred completions. To achieve this, we formulate PO as minimizing the negative log-likelihood (NLL) of a probability model and propose to estimate its normalization constant via a sampling strategy. As we will demonstrate, these estimative samples can act as dispreferred completions in PO. We then select contrastive divergence (CD) as the sampling strategy, and propose a novel MC-PO algorithm that applies the Monte Carlo (MC) kernel from CD to sample hard negatives w.r.t. the parameterized reward model. Finally, we propose the OnMC-PO algorithm, an extension of MC-PO to the online setting. On popular alignment benchmarks, MC-PO outperforms existing SOTA baselines, and OnMC-PO leads to further improvement.

This paper proposes a simple method for controllable text generation based on weighting logits with a free-form classifier, namely CAIF sampling. Using an arbitrary text classifier, we adjust a small part of a language model's logits and guide text generation towards or away from classifier prediction. We experimented with toxicity avoidance and sentiment control tasks and showed that the proposed method significantly outperforms recent PPLM, GeDi, and DExperts on PPL and task accuracy metrics based on the external classifier of generated texts. In addition, compared to other approaches, it is easier to implement and tune and has significantly fewer restrictions and requirements.

Many applications involve estimating the mean of multiple binomial outcomes as a common problem -- assessing intergenerational mobility of census tracts, estimating prevalence of infectious diseases across countries, and measuring click-through rates for different demographic groups. The most standard approach is to report the plain average of each outcome. Despite simplicity, the estimates are noisy when the sample sizes or mean parameters are small. In contrast, the Empirical Bayes (EB) methods are able to boost the average accuracy by borrowing information across tasks. Nevertheless, the EB methods require a Bayesian model where the parameters are sampled from a prior distribution which, unlike the commonly-studied Gaussian case, is unidentified due to discreteness of binomial measurements. Even if the prior distribution is known, the computation is difficult when the sample sizes are heterogeneous as there is no simple joint conjugate prior for the sample size and mean parameter. In this paper, we consider the compound decision framework which treats the sample size and mean parameters as fixed quantities. We develop an approximate Stein's Unbiased Risk Estimator (SURE) for the average mean squared error given any class of estimators. For a class of machine learning-assisted linear shrinkage estimators, we establish asymptotic optimality, regret bounds, and valid inference. Unlike existing work, we work with the binomials directly without resorting to Gaussian approximations. This allows us to work with small sample sizes and/or mean parameters in both one-sample and two-sample settings. We demonstrate our approach using three datasets on firm discrimination, education outcomes, and innovation rates.

The use of deep neural networks in real-world applications require well-calibrated networks with confidence scores that accurately reflect the actual probability. However, it has been found that these networks often provide over-confident predictions, which leads to poor calibration. Recent efforts have sought to address this issue by focal loss to reduce over-confidence, but this approach can also lead to under-confident predictions. While different variants of focal loss have been explored, it is difficult to find a balance between over-confidence and under-confidence. In our work, we propose a new loss function by focusing on dual logits. Our method not only considers the ground truth logit, but also take into account the highest logit ranked after the ground truth logit. By maximizing the gap between these two logits, our proposed dual focal loss can achieve a better balance between over-confidence and under-confidence. We provide theoretical evidence to support our approach and demonstrate its effectiveness through evaluations on multiple models and datasets, where it achieves state-of-the-art performance. Code is available at https://github.com/Linwei94/DualFocalLoss

Label smoothing (LS) is a popular regularisation method for training deep neural network classifiers due to its effectiveness in improving test accuracy and its simplicity in implementation. "Hard" one-hot labels are "smoothed" by uniformly distributing probability mass to other classes, reducing overfitting. In this work, we reveal that LS negatively affects selective classification (SC) - where the aim is to reject misclassifications using a model's predictive uncertainty. We first demonstrate empirically across a range of tasks and architectures that LS leads to a consistent degradation in SC. We then explain this by analysing logit-level gradients, showing that LS exacerbates overconfidence and underconfidence by regularising the max logit more when the probability of error is low, and less when the probability of error is high. This elucidates previously reported experimental results where strong classifiers underperform in SC. We then demonstrate the empirical effectiveness of logit normalisation for recovering lost SC performance caused by LS. Furthermore, based on our gradient analysis, we explain why such normalisation is effective. We will release our code shortly.

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

We give the first efficient algorithm for learning halfspaces in the testable learning model recently defined by Rubinfeld and Vasilyan (2023). In this model, a learner certifies that the accuracy of its output hypothesis is near optimal whenever the training set passes an associated test, and training sets drawn from some target distribution -- e.g., the Gaussian -- must pass the test. This model is more challenging than distribution-specific agnostic or Massart noise models where the learner is allowed to fail arbitrarily if the distributional assumption does not hold. We consider the setting where the target distribution is Gaussian (or more generally any strongly log-concave distribution) in d dimensions and the noise model is either Massart or adversarial (agnostic). For Massart noise, our tester-learner runs in polynomial time and outputs a hypothesis with (information-theoretically optimal) error opt + epsilon for any strongly log-concave target distribution. For adversarial noise, our tester-learner obtains error O(opt) + epsilon in polynomial time when the target distribution is Gaussian; for strongly log-concave distributions, we obtain O(opt) + epsilon in quasipolynomial time. Prior work on testable learning ignores the labels in the training set and checks that the empirical moments of the covariates are close to the moments of the base distribution. Here we develop new tests of independent interest that make critical use of the labels and combine them with the moment-matching approach of Gollakota et al. (2023). This enables us to simulate a variant of the algorithm of Diakonikolas et al. (2020) for learning noisy halfspaces using nonconvex SGD but in the testable learning setting.

Because anomalous samples cannot be used for training, many anomaly detection and localization methods use pre-trained networks and non-parametric modeling to estimate encoded feature distribution. However, these methods neglect the impact of position and neighborhood information on the distribution of normal features. To overcome this, we propose a new algorithm, PNI, which estimates the normal distribution using conditional probability given neighborhood features, modeled with a multi-layer perceptron network. Moreover, position information is utilized by creating a histogram of representative features at each position. Instead of simply resizing the anomaly map, the proposed method employs an additional refine network trained on synthetic anomaly images to better interpolate and account for the shape and edge of the input image. We conducted experiments on the MVTec AD benchmark dataset and achieved state-of-the-art performance, with 99.56\% and 98.98\% AUROC scores in anomaly detection and localization, respectively.

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.

An approach to the construction of classifiers from imbalanced datasets is described. A dataset is imbalanced if the classification categories are not approximately equally represented. Often real-world data sets are predominately composed of "normal" examples with only a small percentage of "abnormal" or "interesting" examples. It is also the case that the cost of misclassifying an abnormal (interesting) example as a normal example is often much higher than the cost of the reverse error. Under-sampling of the majority (normal) class has been proposed as a good means of increasing the sensitivity of a classifier to the minority class. This paper shows that a combination of our method of over-sampling the minority (abnormal) class and under-sampling the majority (normal) class can achieve better classifier performance (in ROC space) than only under-sampling the majority class. This paper also shows that a combination of our method of over-sampling the minority class and under-sampling the majority class can achieve better classifier performance (in ROC space) than varying the loss ratios in Ripper or class priors in Naive Bayes. Our method of over-sampling the minority class involves creating synthetic minority class examples. Experiments are performed using C4.5, Ripper and a Naive Bayes classifier. The method is evaluated using the area under the Receiver Operating Characteristic curve (AUC) and the ROC convex hull strategy.

This paper proposes a new loss function for adversarial training. Since adversarial training has difficulties, e.g., necessity of high model capacity, focusing on important data points by weighting cross-entropy loss has attracted much attention. However, they are vulnerable to sophisticated attacks, e.g., Auto-Attack. This paper experimentally reveals that the cause of their vulnerability is their small margins between logits for the true label and the other labels. Since neural networks classify the data points based on the logits, logit margins should be large enough to avoid flipping the largest logit by the attacks. Importance-aware methods do not increase logit margins of important samples but decrease those of less-important samples compared with cross-entropy loss. To increase logit margins of important samples, we propose switching one-vs-the-rest loss (SOVR), which switches from cross-entropy to one-vs-the-rest loss for important samples that have small logit margins. We prove that one-vs-the-rest loss increases logit margins two times larger than the weighted cross-entropy loss for a simple problem. We experimentally confirm that SOVR increases logit margins of important samples unlike existing methods and achieves better robustness against Auto-Attack than importance-aware methods.

Recommendation systems (RS) aim to provide personalized content, but they face a challenge in unbiased learning due to selection bias, where users only interact with items they prefer. This bias leads to a distorted representation of user preferences, which hinders the accuracy and fairness of recommendations. To address the issue, various methods such as error imputation based, inverse propensity scoring, and doubly robust techniques have been developed. Despite the progress, from the structural causal model perspective, previous debiasing methods in RS assume the independence of the exogenous variables. In this paper, we release this assumption and propose a learning algorithm based on likelihood maximization to learn a prediction model. We first discuss the correlation and difference between unmeasured confounding and our scenario, then we propose a unified method that effectively handles latent exogenous variables. Specifically, our method models the data generation process with latent exogenous variables under mild normality assumptions. We then develop a Monte Carlo algorithm to numerically estimate the likelihood function. Extensive experiments on synthetic datasets and three real-world datasets demonstrate the effectiveness of our proposed method. The code is at https://github.com/WallaceSUI/kdd25-background-variable.

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

We introduce UnpredictaBench, an evaluation that tests the ability of large language models (LLMs) to capture true underlying distributions. As LLMs are increasingly used as substitutes for other entities (e.g., for humans in economic simulations), the tendency of many models to collapse towards a single plausible answer means a failure to capture the unpredictability of real systems. Recent work on improving output diversity is insufficient for this setting: simulation requires samples that are calibrated to a target distribution, not merely varied outputs. UnpredictaBench isolates a simplified but fundamental version of this problem: sampling outcomes from individual target distributions, including canonical statistical distributions, distributions induced by stochastic programs, and natural-language scenarios that describe random processes. We introduce 448 such problems together with KS@N, a general-purpose evaluation metric that quantifies how well a model outputs approximate black-box target distributions via the Kolmogorov-Smirnov statistical test. This is the rate at which we fail to reject model samples of size N against ground-truth samples, with larger N indicating greater difficulty. Tested across open and proprietary models, we find a large spread in distributional capabilities. For instance, when models generate samples of size 100 (KS@100, our standard metric), scores range from near 0 to over 20%. No model is able to achieve over 40% at KS@100, showing significant headroom in distributional sampling as a capability. Although adding reasoning can somewhat increase scores, we find no immediate solution for this issue. UnpredictaBench shows that even simple distributional simulation remains challenging, making it a necessary first step toward using LLMs as stand-ins for complex systems.

In the presence of noisy labels, designing robust loss functions is critical for securing the generalization performance of deep neural networks. Cross Entropy (CE) loss has been shown to be not robust to noisy labels due to its unboundedness. To alleviate this issue, existing works typically design specialized robust losses with the symmetric condition, which usually lead to the underfitting issue. In this paper, our key idea is to induce a loss bound at the logit level, thus universally enhancing the noise robustness of existing losses. Specifically, we propose logit clipping (LogitClip), which clamps the norm of the logit vector to ensure that it is upper bounded by a constant. In this manner, CE loss equipped with our LogitClip method is effectively bounded, mitigating the overfitting to examples with noisy labels. Moreover, we present theoretical analyses to certify the noise-tolerant ability of LogitClip. Extensive experiments show that LogitClip not only significantly improves the noise robustness of CE loss, but also broadly enhances the generalization performance of popular robust losses.

In knowledge distillation literature, feature-based methods have dominated due to their ability to effectively tap into extensive teacher models. In contrast, logit-based approaches, which aim to distill `dark knowledge' from teachers, typically exhibit inferior performance compared to feature-based methods. To bridge this gap, we present LumiNet, a novel knowledge distillation algorithm designed to enhance logit-based distillation. We introduce the concept of 'perception', aiming to calibrate logits based on the model's representation capability. This concept addresses overconfidence issues in logit-based distillation method while also introducing a novel method to distill knowledge from the teacher. It reconstructs the logits of a sample/instances by considering relationships with other samples in the batch. LumiNet excels on benchmarks like CIFAR-100, ImageNet, and MSCOCO, outperforming leading feature-based methods, e.g., compared to KD with ResNet18 and MobileNetV2 on ImageNet, it shows improvements of 1.5% and 2.05%, respectively.

Recent masked diffusion models (MDMs) have shown competitive performance compared to autoregressive models (ARMs) for language modeling. While most literature has focused on performance enhancing sampling procedures, efficient sampling from MDMs has been scarcely explored. We make the observation that often a given sequence of partially masked tokens determines the values of multiple unknown tokens deterministically, meaning that a single prediction of a masked model holds additional information unused by standard sampling procedures. Based on this observation, we introduce EB-Sampler, a simple drop-in replacement for existing samplers, utilizing an Entropy Bounded unmasking procedure that dynamically unmasks multiple tokens in one function evaluation with predefined approximate error tolerance. We formulate the EB-Sampler as part of a broad family of adaptive samplers for which we provide an error analysis that motivates our algorithmic choices. EB-Sampler accelerates sampling from current state of the art MDMs by roughly 2-3x on standard coding and math reasoning benchmarks without loss in performance. We also validate the same procedure works well on smaller reasoning tasks including maze navigation and Sudoku, tasks ARMs often struggle with.

Large Language Models (LLMs) are increasingly utilized in autonomous decision-making, where they sample options from vast action spaces. However, the heuristics that guide this sampling process remain under-explored. We study this sampling behavior and show that this underlying heuristics resembles that of human decision-making: comprising a descriptive component (reflecting statistical norm) and a prescriptive component (implicit ideal encoded in the LLM) of a concept. We show that this deviation of a sample from the statistical norm towards a prescriptive component consistently appears in concepts across diverse real-world domains like public health, and economic trends. To further illustrate the theory, we demonstrate that concept prototypes in LLMs are affected by prescriptive norms, similar to the concept of normality in humans. Through case studies and comparison with human studies, we illustrate that in real-world applications, the shift of samples toward an ideal value in LLMs' outputs can result in significantly biased decision-making, raising ethical concerns.

In recent years, developing compact and efficient large language models (LLMs) has emerged as a thriving area of research. Traditional Supervised Fine-Tuning (SFT), which relies on singular ground truth labels, often fails to capture token-level dependencies and linguistic diversity. To address these limitations, we propose a logits-based fine-tuning framework that integrates the strengths of supervised learning and knowledge distillation. Our approach constructs enriched training targets by combining teacher logits with ground truth labels, preserving both correctness and linguistic diversity. This ensures more reliable and effective training. We constructed a large-scale 1.2M logits dataset and trained a series of science-focused models. Experimental results demonstrate that our method achieves significant improvements, with accuracy gains of 18% on Mawps and 22.7% on TabMWP. Across nine widely used mathematical benchmarks, our method consistently outperforms prior SFT models, achieving an average improvement of 7.28%. Codes are available at https://github.com/dvlab-research/Logits-Based-Finetuning.

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires O(log n) samples to approach its asymptotic error while the corresponding multiclass logistic regression requires O(n) samples, where n is the feature dimension. To establish it, we present a multiclass H-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes" phenomenon in pre-trained supervised models. Our code is available at https://github.com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

Generalist Anomaly Detection (GAD) aims to train a unified model on an original domain that can detect anomalies in new target domains. Previous GAD methods primarily use only normal samples as references, overlooking the valuable information contained in anomalous samples that are often available in real-world scenarios. To address this limitation, we propose a more practical approach: normal-abnormal-guided generalist anomaly detection, which leverages both normal and anomalous samples as references to guide anomaly detection across diverse domains. We introduce the Normal-Abnormal Generalist Learning (NAGL) framework, consisting of two key components: Residual Mining (RM) and Anomaly Feature Learning (AFL). RM extracts abnormal patterns from normal-abnormal reference residuals to establish transferable anomaly representations, while AFL adaptively learns anomaly features in query images through residual mapping to identify instance-aware anomalies. Our approach effectively utilizes both normal and anomalous references for more accurate and efficient cross-domain anomaly detection. Extensive experiments across multiple benchmarks demonstrate that our method significantly outperforms existing GAD approaches. This work represents the first to adopt a mixture of normal and abnormal samples as references in generalist anomaly detection. The code and datasets are available at https://github.com/JasonKyng/NAGL.

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.

On-Policy Distillation (OPD) trains a student model on its own generative trajectories under dense token-level feedback from a stronger teacher, mitigating both the off-policy distribution shift of Supervised Fine-Tuning (SFT) and the sparse credit assignment of Reinforcement Learning (RL). However, standard OPD faces two coupled limitations. First, it requires direct access to the teacher's token-level logits, excluding a broad class of capable proprietary models from serving as teachers. Second, the token-level logit signal itself is brittle, depending on a narrow overlap of plausible next tokens between teacher and student, and prone to amplifying degenerate patterns such as repetition loops. In this paper, we introduce OmniOPD, a novel framework that addresses both limitations through a logit-free, chunk-level supervision signal. OmniOPD replaces deterministic logit matching with Monte Carlo rollouts that approximate the teacher's local preferences through a continuous semantic similarity metric over multi-token chunks, and concentrates this supervision via a peak-entropy scheduler that audits the student only at its high-uncertainty reasoning forks. A Dirichlet-Multinomial Bayesian prior and a base-model KL anchor further bound the variance of discrete sampling and prevent policy collapse across unaudited tokens. Across competitive benchmarks, OmniOPD surpasses the standard OPD approach by up to +28.64% on math, confirming that chunk-level semantic verification extracts a more reliable learning signal than token-level logit matching, whose high information density is offset by significant noise and brittleness. Furthermore, when paired with stronger black-box teachers such as Claude-4.5-Haiku and Gemini-2.5-Flash, OmniOPD achieves an additional +9.54% relative on math over its open-weight teacher counterpart, advancing the student past the performance of self-exploratory RL.

Various XAI attribution methods have been recently proposed for the transformer architecture, allowing for insights into the decision-making process of large language models by assigning importance scores to input tokens and intermediate representations. One class of methods that seems very promising in this direction includes decomposition-based approaches, i.e., XAI-methods that redistribute the model's prediction logit through the network, as this value is directly related to the prediction. In the previous literature we note though that two prominent methods of this category, namely ALTI-Logit and LRP, have not yet been analyzed in juxtaposition and hence we propose to close this gap by conducting a careful quantitative evaluation w.r.t. ground truth annotations on a subject-verb agreement task, as well as various qualitative inspections, using BERT, GPT-2 and LLaMA-3 as a testbed. Along the way we compare and extend the ALTI-Logit and LRP methods, including the recently proposed AttnLRP variant, from an algorithmic and implementation perspective. We further incorporate in our benchmark two widely-used gradient-based attribution techniques. Finally, we make our carefullly constructed benchmark dataset for evaluating attributions on language models, as well as our code, publicly available in order to foster evaluation of XAI-methods on a well-defined common ground.

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies have observed that LR+GD can find a solution with arbitrarily large step sizes, defying conventional optimization theory. Our work investigates this phenomenon and makes three interconnected key observations about LR+GD with large step sizes. First, we find a remarkably simple explanation of why LR+GD with large step sizes solves the classification problem: LR+GD reduces to a batch version of the celebrated perceptron algorithm when the step size gamma to infty. Second, we observe that larger step sizes lead LR+GD to higher logistic losses when it tends to the perceptron algorithm, but larger step sizes also lead to faster convergence to a solution for the classification problem, meaning that logistic loss is an unreliable metric of the proximity to a solution. Surprisingly, high loss values can actually indicate faster convergence. Third, since the convergence rate in terms of loss function values of LR+GD is unreliable, we examine the iteration complexity required by LR+GD with large step sizes to solve the classification problem and prove that this complexity is suboptimal. To address this, we propose a new method, Normalized LR+GD - based on the connection between LR+GD and the perceptron algorithm - with much better theoretical guarantees.

We introduce a theoretical framework for sampling from unnormalized densities based on a smoothing scheme that uses an isotropic Gaussian kernel with a single fixed noise scale. We prove one can decompose sampling from a density (minimal assumptions made on the density) into a sequence of sampling from log-concave conditional densities via accumulation of noisy measurements with equal noise levels. Our construction is unique in that it keeps track of a history of samples, making it non-Markovian as a whole, but it is lightweight algorithmically as the history only shows up in the form of a running empirical mean of samples. Our sampling algorithm generalizes walk-jump sampling (Saremi & Hyv\"arinen, 2019). The "walk" phase becomes a (non-Markovian) chain of (log-concave) Markov chains. The "jump" from the accumulated measurements is obtained by empirical Bayes. We study our sampling algorithm quantitatively using the 2-Wasserstein metric and compare it with various Langevin MCMC algorithms. We also report a remarkable capacity of our algorithm to "tunnel" between modes of a distribution.

Iterative data generation and model retraining are widely used to align large language models (LLMs). It typically involves a policy model to generate on-policy responses and a reward model to guide training data selection. Direct Preference Optimization (DPO) further enhances this process by constructing preference pairs of chosen and rejected responses. In this work, we aim to scale up the number of on-policy samples via repeated random sampling to improve alignment performance. Conventional practice selects the sample with the highest reward as chosen and the lowest as rejected for DPO. However, our experiments reveal that this strategy leads to a decline in performance as the sample size increases. To address this, we investigate preference data construction through the lens of underlying normal distribution of sample rewards. We categorize the reward space into seven representative points and systematically explore all 21 (C_7^2) pairwise combinations. Through evaluations on four models using AlpacaEval 2, we find that selecting the rejected response at reward position mu - 2sigma rather than the minimum reward, is crucial for optimal performance. We finally introduce a scalable preference data construction strategy that consistently enhances model performance as the sample scale increases.

Reinforcement Learning (RL) for Large Language Models (LLMs) often suffers from training collapse in long-horizon tasks due to exploding gradient variance. To mitigate this, a baseline is commonly introduced for advantage computation; however, traditional value models remain difficult to optimize, and standard group-based baselines overlook sequence heterogeneity. Although classic optimal baseline theory can achieve global variance reduction, it neglects token heterogeneity and requires prohibitive gradient-based computation. In this work, we derive the Optimal Token Baseline (OTB) from first principles, proving that gradient updates should be weighted inversely to their cumulative gradient norm. To ensure efficiency, we propose the Logit-Gradient Proxy that approximates the gradient norm using only forward-pass probabilities. Our method achieves training stability and matches the performance of large group sizes (N=32) with only N=4, reducing token consumption by over 65% across single-turn and tool-integrated reasoning tasks.

Bandits with preference feedback present a powerful tool for optimizing unknown target functions when only pairwise comparisons are allowed instead of direct value queries. This model allows for incorporating human feedback into online inference and optimization and has been employed in systems for fine-tuning large language models. The problem is well understood in simplified settings with linear target functions or over finite small domains that limit practical interest. Taking the next step, we consider infinite domains and nonlinear (kernelized) rewards. In this setting, selecting a pair of actions is quite challenging and requires balancing exploration and exploitation at two levels: within the pair, and along the iterations of the algorithm. We propose MAXMINLCB, which emulates this trade-off as a zero-sum Stackelberg game, and chooses action pairs that are informative and yield favorable rewards. MAXMINLCB consistently outperforms existing algorithms and satisfies an anytime-valid rate-optimal regret guarantee. This is due to our novel preference-based confidence sequences for kernelized logistic estimators.

Current language models demonstrate remarkable proficiency in text generation. However, for many applications it is desirable to control attributes, such as sentiment, or toxicity, of the generated language -- ideally tailored towards each specific use case and target audience. For auto-regressive language models, existing guidance methods are prone to decoding errors that cascade during generation and degrade performance. In contrast, text diffusion models can easily be guided with, for example, a simple linear sentiment classifier -- however they do suffer from significantly higher perplexity than auto-regressive alternatives. In this paper we use a guided diffusion model to produce a latent proposal that steers an auto-regressive language model to generate text with desired properties. Our model inherits the unmatched fluency of the auto-regressive approach and the plug-and-play flexibility of diffusion. We show that it outperforms previous plug-and-play guidance methods across a wide range of benchmark data sets. Further, controlling a new attribute in our framework is reduced to training a single logistic regression classifier.

Polar slice sampling (Roberts & Rosenthal, 2002) is a Markov chain approach for approximate sampling of distributions that is difficult, if not impossible, to implement efficiently, but behaves provably well with respect to the dimension. By updating the directional and radial components of chain iterates separately, we obtain a family of samplers that mimic polar slice sampling, and yet can be implemented efficiently. Numerical experiments in a variety of settings indicate that our proposed algorithm outperforms the two most closely related approaches, elliptical slice sampling (Murray et al., 2010) and hit-and-run uniform slice sampling (MacKay, 2003). We prove the well-definedness and convergence of our methods under suitable assumptions on the target distribution.

How many experimental studies would have come to different conclusions had they been run on larger samples? I show how to estimate the expected number of statistically significant results that a set of experiments would have reported had their sample sizes all been counterfactually increased. The proposed deconvolution estimator is asymptotically normal and adjusts for publication bias. Unlike related methods, this approach requires no assumptions of any kind about the distribution of true intervention treatment effects and allows for point masses. Simulations find good coverage even when the t-score is only approximately normal. An application to randomized trials (RCTs) published in economics journals finds that doubling every sample would increase the power of t-tests by 7.2 percentage points on average. This effect is smaller than for non-RCTs and comparable to systematic replications in laboratory psychology where previous studies enabled more accurate power calculations. This suggests that RCTs are on average relatively insensitive to sample size increases. Research funders who wish to raise power should generally consider sponsoring better-measured and higher quality experiments -- rather than only larger ones.

State-of-the-art distillation methods are mainly based on distilling deep features from intermediate layers, while the significance of logit distillation is greatly overlooked. To provide a novel viewpoint to study logit distillation, we reformulate the classical KD loss into two parts, i.e., target class knowledge distillation (TCKD) and non-target class knowledge distillation (NCKD). We empirically investigate and prove the effects of the two parts: TCKD transfers knowledge concerning the "difficulty" of training samples, while NCKD is the prominent reason why logit distillation works. More importantly, we reveal that the classical KD loss is a coupled formulation, which (1) suppresses the effectiveness of NCKD and (2) limits the flexibility to balance these two parts. To address these issues, we present Decoupled Knowledge Distillation (DKD), enabling TCKD and NCKD to play their roles more efficiently and flexibly. Compared with complex feature-based methods, our DKD achieves comparable or even better results and has better training efficiency on CIFAR-100, ImageNet, and MS-COCO datasets for image classification and object detection tasks. This paper proves the great potential of logit distillation, and we hope it will be helpful for future research. The code is available at https://github.com/megvii-research/mdistiller.

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.

Pretrained models have become standard in both vision and language, yet they typically do not provide reliable measures of confidence. Existing uncertainty estimation methods, such as deep ensembles and MC dropout, are often too computationally expensive to deploy in practice. Evidential Deep Learning (EDL) offers a more efficient alternative, but it requires models to be trained to output evidential quantities from the start, which is rarely true for pretrained networks. To enable EDL-style uncertainty estimation in pretrained models, we propose the Evidential Transformation Network (ETN), a lightweight post-hoc module that converts a pretrained predictor into an evidential model. ETN operates in logit space: it learns a sample-dependent affine transformation of the logits and interprets the transformed outputs as parameters of a Dirichlet distribution for uncertainty estimation. We evaluate ETN on image classification and large language model question-answering benchmarks under both in-distribution and out-of-distribution settings. ETN consistently improves uncertainty estimation over post-hoc baselines while preserving accuracy and adding only minimal computational overhead.

When fitting the learning data of an individual to algorithm-like learning models, the observations are so dependent and non-stationary that one may wonder what the classical Maximum Likelihood Estimator (MLE) could do, even if it is the usual tool applied to experimental cognition. Our objective in this work is to show that the estimation of the learning rate cannot be efficient if the learning rate is constant in the classical Exp3 (Exponential weights for Exploration and Exploitation) algorithm. Secondly, we show that if the learning rate decreases polynomially with the sample size, then the prediction error and in some cases the estimation error of the MLE satisfy bounds in probability that decrease at a polynomial rate.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional 'corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation. Our code is available at https://github.com/martaskrt/fkc-diffusion.

This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.

In natural language processing, a recently popular line of work explores how to best report the experimental results of neural networks. One exemplar publication, titled "Show Your Work: Improved Reporting of Experimental Results," advocates for reporting the expected validation effectiveness of the best-tuned model, with respect to the computational budget. In the present work, we critically examine this paper. As far as statistical generalizability is concerned, we find unspoken pitfalls and caveats with this approach. We analytically show that their estimator is biased and uses error-prone assumptions. We find that the estimator favors negative errors and yields poor bootstrapped confidence intervals. We derive an unbiased alternative and bolster our claims with empirical evidence from statistical simulation. Our codebase is at http://github.com/castorini/meanmax.

We show that a GPT-3 model can learn to express uncertainty about its own answers in natural language -- without use of model logits. When given a question, the model generates both an answer and a level of confidence (e.g. "90% confidence" or "high confidence"). These levels map to probabilities that are well calibrated. The model also remains moderately calibrated under distribution shift, and is sensitive to uncertainty in its own answers, rather than imitating human examples. To our knowledge, this is the first time a model has been shown to express calibrated uncertainty about its own answers in natural language. For testing calibration, we introduce the CalibratedMath suite of tasks. We compare the calibration of uncertainty expressed in words ("verbalized probability") to uncertainty extracted from model logits. Both kinds of uncertainty are capable of generalizing calibration under distribution shift. We also provide evidence that GPT-3's ability to generalize calibration depends on pre-trained latent representations that correlate with epistemic uncertainty over its answers.

Traditional knowledge distillation focuses on aligning the student's predicted probabilities with both ground-truth labels and the teacher's predicted probabilities. However, the transition to predicted probabilities from logits would obscure certain indispensable information. To address this issue, it is intuitive to additionally introduce a logit-level loss function as a supplement to the widely used probability-level loss function, for exploiting the latent information of logits. Unfortunately, we empirically find that the amalgamation of the newly introduced logit-level loss and the previous probability-level loss will lead to performance degeneration, even trailing behind the performance of employing either loss in isolation. We attribute this phenomenon to the collapse of the classification head, which is verified by our theoretical analysis based on the neural collapse theory. Specifically, the gradients of the two loss functions exhibit contradictions in the linear classifier yet display no such conflict within the backbone. Drawing from the theoretical analysis, we propose a novel method called dual-head knowledge distillation, which partitions the linear classifier into two classification heads responsible for different losses, thereby preserving the beneficial effects of both losses on the backbone while eliminating adverse influences on the classification head. Extensive experiments validate that our method can effectively exploit the information inside the logits and achieve superior performance against state-of-the-art counterparts.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are discrete. In this paper we find that classical estimators, including the maximum score estimator, (Manski (1975)), loose their attractive statistical properties without point identification. First of all, they are not sharp with the estimator converging to an outer region of the identified set, (Komarova (2013)), and in many discrete designs it weakly converges to a random set. Second, they are not robust, with their distribution limit discontinuously changing with respect to the parameters of the model. We propose a novel class of estimators based on the concept of a quantile of a random set, which we show to be both sharp and robust. We demonstrate that our approach extends from cross-sectional settings to classical static and dynamic discrete panel data models.

The sampling of probability distributions specified up to a normalization constant is an important problem in both machine learning and statistical mechanics. While classical stochastic sampling methods such as Markov Chain Monte Carlo (MCMC) or Langevin Dynamics (LD) can suffer from slow mixing times there is a growing interest in using normalizing flows in order to learn the transformation of a simple prior distribution to the given target distribution. Here we propose a generalized and combined approach to sample target densities: Stochastic Normalizing Flows (SNF) -- an arbitrary sequence of deterministic invertible functions and stochastic sampling blocks. We show that stochasticity overcomes expressivity limitations of normalizing flows resulting from the invertibility constraint, whereas trainable transformations between sampling steps improve efficiency of pure MCMC/LD along the flow. By invoking ideas from non-equilibrium statistical mechanics we derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end, and by which we can compute exact importance weights without having to marginalize out the randomness of the stochastic blocks. We illustrate the representational power, sampling efficiency and asymptotic correctness of SNFs on several benchmarks including applications to sampling molecular systems in equilibrium.

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on the tractability of the normalizing constant, thus are more flexible to parameterize and can model a more expressive family of probability distributions. However, the unknown normalizing constant of EBMs makes training particularly difficult. Our goal is to provide a friendly introduction to modern approaches for EBM training. We start by explaining maximum likelihood training with Markov chain Monte Carlo (MCMC), and proceed to elaborate on MCMC-free approaches, including Score Matching (SM) and Noise Constrastive Estimation (NCE). We highlight theoretical connections among these three approaches, and end with a brief survey on alternative training methods, which are still under active research. Our tutorial is targeted at an audience with basic understanding of generative models who want to apply EBMs or start a research project in this direction.

Despite their widespread use, the mechanisms by which large language models (LLMs) represent and regulate uncertainty in next-token predictions remain largely unexplored. This study investigates two critical components believed to influence this uncertainty: the recently discovered entropy neurons and a new set of components that we term token frequency neurons. Entropy neurons are characterized by an unusually high weight norm and influence the final layer normalization (LayerNorm) scale to effectively scale down the logits. Our work shows that entropy neurons operate by writing onto an unembedding null space, allowing them to impact the residual stream norm with minimal direct effect on the logits themselves. We observe the presence of entropy neurons across a range of models, up to 7 billion parameters. On the other hand, token frequency neurons, which we discover and describe here for the first time, boost or suppress each token's logit proportionally to its log frequency, thereby shifting the output distribution towards or away from the unigram distribution. Finally, we present a detailed case study where entropy neurons actively manage confidence in the setting of induction, i.e. detecting and continuing repeated subsequences.

The goal of two-sample tests is to assess whether two samples, S_P sim P^n and S_Q sim Q^m, are drawn from the same distribution. Perhaps intriguingly, one relatively unexplored method to build two-sample tests is the use of binary classifiers. In particular, construct a dataset by pairing the n examples in S_P with a positive label, and by pairing the m examples in S_Q with a negative label. If the null hypothesis "P = Q" is true, then the classification accuracy of a binary classifier on a held-out subset of this dataset should remain near chance-level. As we will show, such Classifier Two-Sample Tests (C2ST) learn a suitable representation of the data on the fly, return test statistics in interpretable units, have a simple null distribution, and their predictive uncertainty allow to interpret where P and Q differ. The goal of this paper is to establish the properties, performance, and uses of C2ST. First, we analyze their main theoretical properties. Second, we compare their performance against a variety of state-of-the-art alternatives. Third, we propose their use to evaluate the sample quality of generative models with intractable likelihoods, such as Generative Adversarial Networks (GANs). Fourth, we showcase the novel application of GANs together with C2ST for causal discovery.

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample sizes or model misspecification. We introduce a practical and broadly applicable Bayesian conformal approach based on the influence-function Bayesian bootstrap (BB) with data-driven tuning of the Dirichlet concentration parameter, α. By efficiently approximating the Bayesian bootstrap predictive distribution via influence functions and calibrating α to optimize empirical coverage or average log-probability, our method constructs prediction intervals and distributions that are both well-calibrated and sharp. Across a range of regression models and data settings, this Bayesian conformal framework consistently yields improved empirical coverage and log-score compared to standard Bayesian posteriors. Our procedure is fast, easy to implement, and offers a flexible approach for distributional calibration in predictive modeling.

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

Many commercial Large Language Models (LLMs) are often closed-source, limiting developers to prompt tuning for aligning content generation with specific applications. While these models currently do not provide access to token logits, we argue that if such access were available, it would enable more powerful adaptation techniques beyond prompt engineering. In this paper, we propose a token-level probability reweighting framework that, given access to logits and a small amount of task-specific data, can effectively steer black-box LLMs toward application-specific content generation. Our approach views next-token prediction through the lens of supervised classification. We show that aligning black-box LLMs with task-specific data can be formulated as a label noise correction problem, leading to Plugin model -- an autoregressive probability reweighting model that operates solely on logits. We provide theoretical justification for why reweighting logits alone is sufficient for task adaptation. Extensive experiments with multiple datasets, LLMs, and reweighting models demonstrate the effectiveness of our method, advocating for broader access to token logits in closed-source models.

Probing studies what information is encoded in a frozen LLM's layer representations by training a lightweight predictor on top of them. Beyond analysis, probes are often used operationally in probe-then-steer pipelines: a learned concept vector is extracted from a probe and injected via additive activation steering by adding it to a layer representation during the forward pass. The effectiveness of this pipeline hinges on estimating concept vectors that are accurate, directionally stable under ablation, and inexpensive to obtain. Motivated by these desiderata, we propose RAPTOR (Ridge-Adaptive Logistic Probe), a simple L2-regularized logistic probe whose validation-tuned ridge strength yields concept vectors from normalized weights. Across extensive experiments on instruction-tuned LLMs and human-written concept datasets, RAPTOR matches or exceeds strong baselines in accuracy while achieving competitive directional stability and substantially lower training cost; these quantitative results are supported by qualitative downstream steering demonstrations. Finally, using the Convex Gaussian Min-max Theorem (CGMT), we provide a mechanistic characterization of ridge logistic regression in an idealized Gaussian teacher-student model in the high-dimensional few-shot regime, explaining how penalty strength mediates probe accuracy and concept-vector stability and yielding structural predictions that qualitatively align with trends observed on real LLM embeddings.

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

The standard Monte Carlo estimator I_N^{MC} of int fdω relies on independent samples from ω and has variance of order 1/N. Replacing the samples with a determinantal point process (DPP), a repulsive distribution, makes the estimator consistent, with variance rates that depend on how the DPP is adapted to f and ω. We examine two existing DPP-based estimators: one by Bardenet & Hardy (2020) with a rate of O(N^{-(1+1/d)}) for smooth f, but relying on a fixed DPP. The other, by Ermakov & Zolotukhin (1960), is unbiased with rate of order 1/N, like Monte Carlo, but its DPP is tailored to f. We revisit these estimators, generalize them to continuous settings, and provide sampling algorithms.

Supervised fine-tuning (SFT) is a commonly used technique to adapt large language models (LLMs) to downstream tasks. In practice, SFT on a full dataset is computationally expensive and sometimes suffers from overfitting or bias amplification. This facilitates the rise of data curation in SFT, which prioritizes the most valuable data to optimze. This work studies the online batch selection family that dynamically scores and filters samples during the training process. However, existing popular methods often (i) rely merely on the utility of data to select a subset while neglecting other crucial factors like diversity, (ii) rely on external resources such as reference models or validation sets, and (iii) incur extra training time over full-dataset training. To address these limitations, this work develops UDS (Utility-Diversity Sampling), a framework for efficient online batch selection in SFT. UDS leverages the nuclear norm of the logits matrix to capture both data utility and intra-sample diversity, while estimating inter-sample diversity through efficient low-dimensional embedding comparisons with a lightweight memory buffer of historical samples. Such a design eliminates the need for external resources and unnecessary backpropagation, securing computational efficiency. Experiments on multiple benchmarks demonstrate that UDS consistently outperforms state-of-the-art online batch selection methods under varying data budgets, and significantly reduces training time compared to full-dataset fine-tuning. Code is available at https://github.com/gfyddha/UDS.

Generative Language Models (GLMs) have shown impressive performance in tasks such as text generation, understanding, and reasoning. However, the large model size poses challenges for practical deployment. To solve this problem, Quantization-Aware Training (QAT) has become increasingly popular. However, current QAT methods for generative models have resulted in a noticeable loss of accuracy. To counteract this issue, we propose a novel knowledge distillation method specifically designed for GLMs. Our method, called token-scaled logit distillation, prevents overfitting and provides superior learning from the teacher model and ground truth. This research marks the first evaluation of ternary weight quantization-aware training of large-scale GLMs with less than 1.0 degradation in perplexity and no loss of accuracy in a reasoning task.

We propose (G)I-DLE, a new approach to constrained decoding that leverages KL divergence minimization to preserve the intrinsic conditional probability distribution of autoregressive language models while excluding undesirable tokens. Unlike conventional methods that naively set banned tokens' logits to -infty, which can distort the conversion from raw logits to posterior probabilities and increase output variance, (G)I-DLE re-normalizes the allowed token probabilities to minimize such distortion. We validate our method on the K2-Eval dataset, specifically designed to assess Korean language fluency, logical reasoning, and cultural appropriateness. Experimental results on Qwen2.5 models (ranging from 1.5B to 14B) demonstrate that G-IDLE not only boosts mean evaluation scores but also substantially reduces the variance of output quality.

Score- and flow-matching models often rely on preference-based reinforcement learning for two purposes: aligning with subjective preferences and, surprisingly, recovering properties such as visual realism and coherent object structure that matching-based training is intended to learn from the data itself. We argue that this reflects a structural mismatch. Matching losses measure ell_2 regression error on the velocity or score field under training-time marginals, a proxy poorly aligned with the visual and semantic properties that determine sample quality at inference. Given a reward aligned with these properties, RL sidesteps the mismatch by evaluating the model on its own samples and following the reward landscape directly. The challenge is to obtain such a reward without relying on human preferences, which are expensive and conflate data realism with annotator inclinations. We propose Discriminator-Guided RL (DRL). DRL trains a discriminator to separate data from base-model samples in a pretrained representation space and uses its logit as the reward in KL-regularized RL. The pretrained space restricts the discriminator to perceptually meaningful directions, and the logit estimates the log-likelihood ratio between data and model, which is the optimal reward for targeting the data distribution. Across SiT, JiT, REPA, and RAE, DRL reduces guidance-free FID (e.g., 9.38 to 2.62 on SiT) and semantic-space FD (e.g., 88.2 to 19.3 on DINOv3 for SiT), with consistent gains across all backbones, and improves human-preference rewards without training on them. It also yields a better Pareto frontier between preference reward and image fidelity under subsequent preference-based post-training, increasing alignment while reducing low-level artifacts such as oversaturation and excessive brightness.

Binary classification involves predicting the label of an instance based on whether the model score for the positive class exceeds a threshold chosen based on the application requirements (e.g., maximizing recall for a precision bound). However, model scores are often not aligned with the true positivity rate. This is especially true when the training involves a differential sampling across classes or there is distributional drift between train and test settings. In this paper, we provide theoretical analysis and empirical evidence of the dependence of model score estimation bias on both uncertainty and score itself. Further, we formulate the decision boundary selection in terms of both model score and uncertainty, prove that it is NP-hard, and present algorithms based on dynamic programming and isotonic regression. Evaluation of the proposed algorithms on three real-world datasets yield 25%-40% gain in recall at high precision bounds over the traditional approach of using model score alone, highlighting the benefits of leveraging uncertainty.

Selecting the best response from multiple small-model samples using a stronger scorer is a simple inference-time strategy, but fails when the small model has already committed to incorrect reasoning paths. PRM guided search avoids this by scoring candidate continuations during generation, but requires a reward model trained with step-level labels. We propose Chunk-Level Guided Generation, a training-free alternative that uses an off-the-shelf large language model as a process scorer. At each step, a small model samples k fixed-length candidate chunks, while the larger model scores the candidates using likelihoods without generating any text. The selected chunk is committed before the next step, steering generation before errors can propagate. We instantiate this framework with two selection rules: Likelihood-Guided Selection (LGS), which selects the chunk with the highest length-normalized large-model log-probability, and Contrastive-Guided Selection (CGS), which subtracts the small model's log-probability to favor chunks where the large model's preference diverges from the small model's. We show that scoring variable-length reasoning steps with large-model likelihoods is unreliable due to a systematic length bias that persists even after length normalization, and that fixed-length chunks avoid this confound. On GSM8K, MATH, Minerva Math, AMC23, and AIME24 with Qwen2.5-1.5B guided by Qwen2.5-32B and Llama-3.2-1B guided by Llama-3.1-70B, CGS outperforms majority voting by up to 28 pp and, under matched guidance budgets, matches or outperforms Qwen2.5-Math-PRM-72B guided search on most benchmarks without reward-model training. With Qwen2.5-7B guided by Qwen2.5-72B, CGS reaches 81.8% on MATH and 63.6% on Minerva Math at k=16, surpassing majority voting by 4--6 pp. Finally, Chunk-Level Guided Generation produces substantially shorter reasoning traces than PRM guided search.

Embedding-based collaborative filtering, often coupled with nearest neighbor search, is widely deployed in large-scale recommender systems for personalized content selection. Modern systems leverage multiple implicit feedback signals (e.g., clicks, add to cart, purchases) to model user preferences comprehensively. However, prevailing approaches adopt a feedback-wise modeling paradigm, which (1) fails to capture the structured progression of user engagement entailed among different feedback and (2) embeds feedback-specific information into disjoint spaces, making representations incommensurable, increasing system complexity, and leading to suboptimal retrieval performance. A promising alternative is Ordinal Logistic Regression (OLR), which explicitly models discrete ordered relations. However, existing OLR-based recommendation models mainly focus on explicit feedback (e.g., movie ratings) and struggle with implicit, correlated feedback, where ordering is vague and non-linear. Moreover, standard OLR lacks flexibility in handling feedback-dependent covariates, resulting in suboptimal performance in real-world systems. To address these limitations, we propose Generalized Neural Ordinal Logistic Regression (GNOLR), which encodes multiple feature-feedback dependencies into a unified, structured embedding space and enforces feedback-specific dependency learning through a nested optimization framework. Thus, GNOLR enhances predictive accuracy, captures the progression of user engagement, and simplifies the retrieval process. We establish a theoretical comparison with existing paradigms, demonstrating how GNOLR avoids disjoint spaces while maintaining effectiveness. Extensive experiments on ten real-world datasets show that GNOLR significantly outperforms state-of-the-art methods in efficiency and adaptability.

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.

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classification. It is easily implemented with neural nets since it is equivalent to log-transforming the uncalibrated probabilities, followed by one linear layer and softmax. Experiments demonstrate improved probabilistic predictions according to multiple measures (confidence-ECE, classwise-ECE, log-loss, Brier score) across a wide range of datasets and classifiers. Parameters of the learned Dirichlet calibration map provide insights to the biases in the uncalibrated model.

As LLM benchmarks saturate, the evaluation community has pursued two strategies to increase difficulty: escalating knowledge demands (GPQA, HLE) or removing knowledge entirely in favor of abstract reasoning (ARC-AGI). The first conflates memorization with capability; the second divorces reasoning from the practical contexts in which it matters. We take a different approach. The Grounded Integration Measure (GIM) is a benchmark of 820 original problems (615 public, 205 private) where difficulty comes from integration; individual problems require coordinating multiple cognitive operations (constraint satisfaction, state tracking, epistemic vigilance, audience calibration) over broadly accessible knowledge, so that reasoning stays grounded in realistic tasks without being gated on specialized expertise. Each problem is an original expert-authored composition, majority with rubric-decomposed scoring (median 6 independently judged criteria). A balanced public--private split provides built-in contamination diagnostic. We calibrate a continuous response 2-parameter logistic (2PL) IRT model over >200k prompt-response pairs across 28 models, producing robust ability estimates that correctly order test-configurations even when raw accuracy is distorted by errors or missing data, addressing a common challenge in benchmark reporting. Using this framework, we present a comprehensive leaderboard spanning 22 models and 47 test-configurations (unique model, thinking-level pairs), and conduct what is to our knowledge the most extensive published study of how test-time compute trades off against model capability on a fixed benchmark: 11 models swept across 35 test-configurations. We observe that within-family configuration choices, such as thinking budget and quantization, matter as much as model selection. We release the evaluation framework, calibrated IRT parameters, and all public problems.

Minimum Bayes risk (MBR) decoding outputs the hypothesis with the highest expected utility over the model distribution for some utility function. It has been shown to improve accuracy over beam search in conditional language generation problems and especially neural machine translation, in both human and automatic evaluations. However, the standard sampling-based algorithm for MBR is substantially more computationally expensive than beam search, requiring a large number of samples as well as a quadratic number of calls to the utility function, limiting its applicability. We describe an algorithm for MBR which gradually grows the number of samples used to estimate the utility while pruning hypotheses that are unlikely to have the highest utility according to confidence estimates obtained with bootstrap sampling. Our method requires fewer samples and drastically reduces the number of calls to the utility function compared to standard MBR while being statistically indistinguishable in terms of accuracy. We demonstrate the effectiveness of our approach in experiments on three language pairs, using chrF++ and COMET as utility/evaluation metrics.

A neural network trained on a classification dataset often exhibits a higher vector norm of hidden layer features for in-distribution (ID) samples, while producing relatively lower norm values on unseen instances from out-of-distribution (OOD). Despite this intriguing phenomenon being utilized in many applications, the underlying cause has not been thoroughly investigated. In this study, we demystify this very phenomenon by scrutinizing the discriminative structures concealed in the intermediate layers of a neural network. Our analysis leads to the following discoveries: (1) The feature norm is a confidence value of a classifier hidden in the network layer, specifically its maximum logit. Hence, the feature norm distinguishes OOD from ID in the same manner that a classifier confidence does. (2) The feature norm is class-agnostic, thus it can detect OOD samples across diverse discriminative models. (3) The conventional feature norm fails to capture the deactivation tendency of hidden layer neurons, which may lead to misidentification of ID samples as OOD instances. To resolve this drawback, we propose a novel negative-aware norm (NAN) that can capture both the activation and deactivation tendencies of hidden layer neurons. We conduct extensive experiments on NAN, demonstrating its efficacy and compatibility with existing OOD detectors, as well as its capability in label-free environments.

Objective: To propose and retrospectively validate an integrated framework addressing three barriers to clinical translation of readmission prediction: lack of explainability, absence of deployment reliability infrastructure, and inadequate demographic fairness evaluation. Materials and Methods: We constructed a cohort of 415231 adult admissions from the MIMIC-IV database (30-day readmission prevalence 18.0%), split 70/15/15. Logistic regression, XGBoost, and LightGBM models were trained on 26 features. SHAP provided per-patient explanations. Fairness was evaluated across 16 subgroups using AUC-ROC, false negative rate (FNR), and positive predictive value (PPV). Calibration was assessed using Brier scores and calibration curves. Results: XGBoost achieved AUC-ROC 0.696 (95% CI 0.691-0.701), outperforming or matching the LACE baseline (AUC 0.60-0.68). LightGBM achieved best calibration (Brier 0.146). Prior admissions were the dominant predictor. All subgroups met equity thresholds (delta AUC <= 0.05, delta FNR <= 0.10). Conclusion: This framework delivers competitive performance, clinically actionable explanations, and strong demographic equity. Code is publicly available at https://github.com/Tomisin92/readmission-prediction.

We present a faster algorithm to generate a warm start for sampling an arbitrary logconcave density specified by an evaluation oracle, leading to the first sub-cubic sampling algorithms for inputs in (near-)isotropic position. A long line of prior work incurred a warm-start penalty of at least linear in the dimension, hitting a cubic barrier, even for the special case of uniform sampling from convex bodies. Our improvement relies on two key ingredients of independent interest. (1) We show how to sample given a warm start in weaker notions of distance, in particular q-R\'enyi divergence for q=mathcal{O}(1), whereas previous analyses required stringent infty-R\'enyi divergence (with the exception of Hit-and-Run, whose known mixing time is higher). This marks the first improvement in the required warmness since Lov\'asz and Simonovits (1991). (2) We refine and generalize the log-Sobolev inequality of Lee and Vempala (2018), originally established for isotropic logconcave distributions in terms of the diameter of the support, to logconcave distributions in terms of a geometric average of the support diameter and the largest eigenvalue of the covariance matrix.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

We show that feedforward neural networks with ReLU activation generalize on low complexity data, suitably defined. Given i.i.d. data generated from a simple programming language, the minimum description length (MDL) feedforward neural network which interpolates the data generalizes with high probability. We define this simple programming language, along with a notion of description length of such networks. We provide several examples on basic computational tasks, such as checking primality of a natural number, and more. For primality testing, our theorem shows the following. Suppose that we draw an i.i.d. sample of Theta(N^{delta}ln N) numbers uniformly at random from 1 to N, where deltain (0,1). For each number x_i, let y_i = 1 if x_i is a prime and 0 if it is not. Then with high probability, the MDL network fitted to this data accurately answers whether a newly drawn number between 1 and N is a prime or not, with test error leq O(N^{-delta}). Note that the network is not designed to detect primes; minimum description learning discovers a network which does so.

Large language models (LLMs) are typically personalized via prompt engineering or parameter-efficient fine-tuning such as LoRA. However, writing style can be difficult to distill into a single prompt, and LoRA fine-tuning requires computationally intensive training and infrastructure. We investigate a possible lightweight alternative: steering a frozen LLM with n-gram style priors injected in logit space at decoding time. We train an n-gram model on stylistically distinct corpora -- including Don Quixote, CNN/DailyMail news headlines, and arXiv abstracts -- constructing an interpolated 1-to-3-gram prior over next-token probabilities. During generation we modify the LLM's logits by adding a weighted sum of style log-probabilities from each n-gram order that matches the current context, scaled by a control parameter lambda in [0, 1]. We sweep lambda and style corpora and report style perplexity under the n-gram model, base-model perplexity as a proxy for fluency, Jensen-Shannon (JS) divergence between the original and steered token distributions, and token-overlap statistics. On TinyLlama-1.1B we identify a single narrow regime (for the Don Quixote corpus at lambda=0.1) where style perplexity improves by 24.7% and base-model perplexity improves by 51.4% relative to the frozen model. Outside this regime, and for multi-author corpora such as CNN/DailyMail and arXiv abstracts, even small nonzero lambda values generally result in worse style and fluency, and larger lambda values lead to collapse with extreme perplexities and incoherent text. Logit-space injection of n-gram style priors provides lightweight, tunable style control, but it is fragile: it operates effectively only within a narrow range of low lambda values and is consistently outperformed by prompting and LoRA.

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.

In-Context Learning (ICL) emerges as a key feature for Large Language Models (LLMs), allowing them to adapt to new tasks by leveraging task-specific examples without updating model parameters. However, ICL faces challenges with increasing numbers of examples due to performance degradation and quadratic computational costs. In this paper, we propose Logit Arithmetic Reweighting Approach (LARA), a novel framework that enhances ICL by using logit-based ensembling of multiple demonstrations. Our approach divides long input demonstrations into parallelizable shorter inputs to significantly reduce memory requirements, and then effectively aggregate the information by reweighting logits of each group via a non-gradient optimization approach. We further introduce Binary LARA (B-LARA), a variant that constrains weights to binary values to simplify the search space and reduces memory usage by filtering out less informative demonstration groups. Experiments on BBH and MMLU demonstrate that LARA and B-LARA outperform all baseline methods in both accuracy and memory efficiency. We also conduct extensive analysis to show that LARA generalizes well to scenarios of varying numbers of examples from limited to many-shot demonstrations.

Layer-wise normalization (LN) is an essential component of virtually all transformer-based large language models. While its effects on training stability are well documented, its role at inference time is poorly understood. Additionally, LN layers hinder mechanistic interpretability by introducing additional nonlinearities and increasing the interconnectedness of individual model components. Here, we show that all LN layers can be removed from every GPT-2 model with only a small increase in validation loss (e.g. +0.03 cross-entropy loss for GPT-2 XL). Thus, LN cannot play a substantial role in language modeling. We find that the amount of fine-tuning data needed for LN removal grows sublinearly with model parameters, suggesting scaling to larger models is feasible. We release a suite of LN-free GPT-2 models on Hugging Face. Furthermore, we test interpretability techniques on LN-free models. Direct logit attribution now gives the exact direct effect of individual components, while the accuracy of attribution patching does not significantly improve. We also confirm that GPT-2's "confidence neurons" are inactive in the LN-free models. Our work clarifies the role of LN layers in language modeling, showing that GPT-2-class models can function without LN layers. We hope that our LN-free analogs of the GPT-2 family of models will enable more precise interpretability research and improve our understanding of language models.

We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific parameter values, whose prior knowledge is required in theory but quite difficult to estimate in practice; an example is the commonly assumed sub-Gaussian family. We alleviate this issue by instead considering a new general family of sub-exponential distributions, which contains bounded and Gaussian ones. We prove a new lower bound on the expected regret on this family, that is parameterized by the unknown covariance matrix of outcomes, a tighter quantity than the sub-Gaussian matrix. We then construct an algorithm that uses covariance estimates, and provide a tight asymptotic analysis of the regret. Finally, we apply and extend our results to the family of sparse outcomes, which has applications in many recommender systems.

We present a method to integrate Large Language Models (LLMs) and traditional tabular data classification techniques, addressing LLMs challenges like data serialization sensitivity and biases. We introduce two strategies utilizing LLMs for ranking categorical variables and generating priors on correlations between continuous variables and targets, enhancing performance in few-shot scenarios. We focus on Logistic Regression, introducing MonotonicLR that employs a non-linear monotonic function for mapping ordinals to cardinals while preserving LLM-determined orders. Validation against baseline models reveals the superior performance of our approach, especially in low-data scenarios, while remaining interpretable.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

We extend conformal prediction methodology beyond the case of exchangeable data. In particular, we show that a weighted version of conformal prediction can be used to compute distribution-free prediction intervals for problems in which the test and training covariate distributions differ, but the likelihood ratio between these two distributions is known---or, in practice, can be estimated accurately with access to a large set of unlabeled data (test covariate points). Our weighted extension of conformal prediction also applies more generally, to settings in which the data satisfies a certain weighted notion of exchangeability. We discuss other potential applications of our new conformal methodology, including latent variable and missing data problems.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

Human evaluation is the gold-standard for evaluating text generation models. It is also expensive, and to fit budgetary constraints, a random subset of the test data is often chosen in practice. The randomly selected data may not accurately represent test performance, making this approach economically inefficient for model comparison. Thus, in this work, we develop a suite of selectors to get the most informative datapoints for human evaluation while taking the evaluation costs into account. We show that selectors based on variance in automated metric scores, diversity in model outputs, or Item Response Theory outperform random selection. We further develop an approach to distill these selectors to the scenario where the model outputs are not yet available. In particular, we introduce source-based estimators, which predict item usefulness for human evaluation just based on the source texts. We demonstrate the efficacy of our selectors in two common NLG tasks, machine translation and summarization, and show that up to only ~50% of the test data is needed to produce the same evaluation result as the entire data. Our implementations are published in the subset2evaluate package.

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.

Large vision-language models (LVLMs), designed to interpret and respond to human instructions, occasionally generate hallucinated or harmful content due to inappropriate instructions. This study uses linear probing to shed light on the hidden knowledge at the output layer of LVLMs. We demonstrate that the logit distributions of the first tokens contain sufficient information to determine whether to respond to the instructions, including recognizing unanswerable visual questions, defending against multi-modal jailbreaking attack, and identifying deceptive questions. Such hidden knowledge is gradually lost in logits of subsequent tokens during response generation. Then, we illustrate a simple decoding strategy at the generation of the first token, effectively improving the generated content. In experiments, we find a few interesting insights: First, the CLIP model already contains a strong signal for solving these tasks, indicating potential bias in the existing datasets. Second, we observe performance improvement by utilizing the first logit distributions on three additional tasks, including indicting uncertainty in math solving, mitigating hallucination, and image classification. Last, with the same training data, simply finetuning LVLMs improve models' performance but is still inferior to linear probing on these tasks.

Real-world datasets follow an imbalanced distribution, which poses significant challenges in rare-category object detection. Recent studies tackle this problem by developing re-weighting and re-sampling methods, that utilise the class frequencies of the dataset. However, these techniques focus solely on the frequency statistics and ignore the distribution of the classes in image space, missing important information. In contrast to them, we propose FRActal CALibration (FRACAL): a novel post-calibration method for long-tailed object detection. FRACAL devises a logit adjustment method that utilises the fractal dimension to estimate how uniformly classes are distributed in image space. During inference, it uses the fractal dimension to inversely downweight the probabilities of uniformly spaced class predictions achieving balance in two axes: between frequent and rare categories, and between uniformly spaced and sparsely spaced classes. FRACAL is a post-processing method and it does not require any training, also it can be combined with many off-the-shelf models such as one-stage sigmoid detectors and two-stage instance segmentation models. FRACAL boosts the rare class performance by up to 8.6% and surpasses all previous methods on LVIS dataset, while showing good generalisation to other datasets such as COCO, V3Det and OpenImages. We provide the code at https://github.com/kostas1515/FRACAL.

Large language models (LLMs) can be used to generate text data for training and evaluating other models. However, creating high-quality datasets with LLMs can be challenging. In this work, we explore human-AI partnerships to facilitate high diversity and accuracy in LLM-based text data generation. We first examine two approaches to diversify text generation: 1) logit suppression, which minimizes the generation of languages that have already been frequently generated, and 2) temperature sampling, which flattens the token sampling probability. We found that diversification approaches can increase data diversity but often at the cost of data accuracy (i.e., text and labels being appropriate for the target domain). To address this issue, we examined two human interventions, 1) label replacement (LR), correcting misaligned labels, and 2) out-of-scope filtering (OOSF), removing instances that are out of the user's domain of interest or to which no considered label applies. With oracle studies, we found that LR increases the absolute accuracy of models trained with diversified datasets by 14.4%. Moreover, we found that some models trained with data generated with LR interventions outperformed LLM-based few-shot classification. In contrast, OOSF was not effective in increasing model accuracy, implying the need for future work in human-in-the-loop text data generation.

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

The conventional recipe for maximizing model accuracy is to (1) train multiple models with various hyperparameters and (2) pick the individual model which performs best on a held-out validation set, discarding the remainder. In this paper, we revisit the second step of this procedure in the context of fine-tuning large pre-trained models, where fine-tuned models often appear to lie in a single low error basin. We show that averaging the weights of multiple models fine-tuned with different hyperparameter configurations often improves accuracy and robustness. Unlike a conventional ensemble, we may average many models without incurring any additional inference or memory costs -- we call the results "model soups." When fine-tuning large pre-trained models such as CLIP, ALIGN, and a ViT-G pre-trained on JFT, our soup recipe provides significant improvements over the best model in a hyperparameter sweep on ImageNet. The resulting ViT-G model, which attains 90.94% top-1 accuracy on ImageNet, achieved a new state of the art. Furthermore, we show that the model soup approach extends to multiple image classification and natural language processing tasks, improves out-of-distribution performance, and improves zero-shot performance on new downstream tasks. Finally, we analytically relate the performance similarity of weight-averaging and logit-ensembling to flatness of the loss and confidence of the predictions, and validate this relation empirically. Code is available at https://github.com/mlfoundations/model-soups.

Timestep sampling p(t) is a central design choice in Flow Matching models, yet common practice increasingly favors static middle-biased distributions (e.g., Logit-Normal). We show that this choice induces a speed--quality trade-off: middle-biased sampling accelerates early convergence but yields worse asymptotic fidelity than Uniform sampling. By analyzing per-timestep training losses, we identify a U-shaped difficulty profile with persistent errors near the boundary regimes, implying that under-sampling the endpoints leaves fine details unresolved. Guided by this insight, we propose Curriculum Sampling, a two-phase schedule that begins with middle-biased sampling for rapid structure learning and then switches to Uniform sampling for boundary refinement. On CIFAR-10, Curriculum Sampling improves the best FID from 3.85 (Uniform) to 3.22 while reaching peak performance at 100k rather than 150k training steps. Our results highlight that timestep sampling should be treated as an evolving curriculum rather than a fixed hyperparameter.

For learning with noisy labels, the transition matrix, which explicitly models the relation between noisy label distribution and clean label distribution, has been utilized to achieve the statistical consistency of either the classifier or the risk. Previous researches have focused more on how to estimate this transition matrix well, rather than how to utilize it. We propose good utilization of the transition matrix is crucial and suggest a new utilization method based on resampling, coined RENT. Specifically, we first demonstrate current utilizations can have potential limitations for implementation. As an extension to Reweighting, we suggest the Dirichlet distribution-based per-sample Weight Sampling (DWS) framework, and compare reweighting and resampling under DWS framework. With the analyses from DWS, we propose RENT, a REsampling method with Noise Transition matrix. Empirically, RENT consistently outperforms existing transition matrix utilization methods, which includes reweighting, on various benchmark datasets. Our code is available at https://github.com/BaeHeeSun/RENT.

Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional assumptions or model assumptions. One can use conformal prediction with any pre-trained model, such as a neural network, to produce sets that are guaranteed to contain the ground truth with a user-specified probability, such as 90%. It is easy-to-understand, easy-to-use, and general, applying naturally to problems arising in the fields of computer vision, natural language processing, deep reinforcement learning, and so on. This hands-on introduction is aimed to provide the reader a working understanding of conformal prediction and related distribution-free uncertainty quantification techniques with one self-contained document. We lead the reader through practical theory for and examples of conformal prediction and describe its extensions to complex machine learning tasks involving structured outputs, distribution shift, time-series, outliers, models that abstain, and more. Throughout, there are many explanatory illustrations, examples, and code samples in Python. With each code sample comes a Jupyter notebook implementing the method on a real-data example; the notebooks can be accessed and easily run using our codebase.

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

Masked Diffusion Models (MDMs) offer greater flexibility in decoding order than autoregressive models but require careful planning to achieve high-quality generation. Existing samplers typically adopt greedy heuristics, prioritizing positions with the highest local certainty to decode at each step. Through failure case analysis, we identify a fundamental limitation of this approach: it neglects the downstream impact of current decoding choices on subsequent steps and fails to minimize cumulative uncertainty. In particular, these methods do not fully exploit the non-causal nature of MDMs, which enables evaluating how a decoding decision reshapes token probabilities/uncertainty across all remaining masked positions. To bridge this gap, we propose the Info-Gain Sampler, a principled decoding framework that balances immediate uncertainty with information gain over future masked tokens. Extensive evaluations across diverse architectures and tasks (reasoning, coding, creative writing, and image generation) demonstrate that Info-Gain Sampler consistently outperforms existing samplers for MDMs. For instance, it achieves a 3.6% improvement in average accuracy on reasoning tasks and a 63.1% win-rate in creative writing. Notably, on reasoning tasks it reduces cumulative uncertainty from 78.4 to 48.6, outperforming the best baseline by a large margin. The code will be available at https://github.com/yks23/Information-Gain-Sampler.

We study networked binary classification on a directed acyclic graph (DAG) where each agent observes only a subset of the feature columns of a shared dataset. Agents act sequentially along the DAG: each receives prediction columns from its parents (if any), augments its local features with these columns, fits a logistic predictor by minimizing binary cross-entropy (BCE), and forwards its prediction column to its outgoing neighbors. We ask whether this sequential distributed training procedure achieves information aggregation, meaning that some agent attains small excess loss compared to the best logistic predictor trained with access to all feature columns. This question was studied for linear regression under squared loss by Kearns, Roth, and Ryu (SODA 2026). Extending their guarantees to classification is nontrivial because their analysis relies on quadratic structure that does not directly transfer to BCE with a logistic link. We analyze the resulting sequential logit-passing protocol and prove: (i) an excess loss upper bound of O(M/D) on depth-D paths under the condition that every M contiguous subsequence of M agents collectively observe all features, and (ii) a close lower bound showing instances with excess loss of at least Ω(k/D) where k is the dimension of the feature space. Together, these results identify network depth as a fundamental bottleneck for information aggregation in networked logistic regression.

Machine learning (ML) holds great potential for accurately forecasting treatment outcomes over time, which could ultimately enable the adoption of more individualized treatment strategies in many practical applications. However, a significant challenge that has been largely overlooked by the ML literature on this topic is the presence of informative sampling in observational data. When instances are observed irregularly over time, sampling times are typically not random, but rather informative -- depending on the instance's characteristics, past outcomes, and administered treatments. In this work, we formalize informative sampling as a covariate shift problem and show that it can prohibit accurate estimation of treatment outcomes if not properly accounted for. To overcome this challenge, we present a general framework for learning treatment outcomes in the presence of informative sampling using inverse intensity-weighting, and propose a novel method, TESAR-CDE, that instantiates this framework using Neural CDEs. Using a simulation environment based on a clinical use case, we demonstrate the effectiveness of our approach in learning under informative sampling.

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out, including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.

We investigate how teacher-student capacity relationships modulate knowledge distillation (KD) effectiveness in ResNet-based image classification on CIFAR-10. Across three teacher-student pairs -- R50->R18, R34->R18, and R50->R34 -- we compare Logit-KD and Feature-KD under controlled, reproducible conditions (3 seeds, mean+/-std reported throughout). We report three main findings. First, student capacity is a key moderating factor in distillation gain: R34 students benefit substantially more from KD than R18 students even when teacher-student accuracy gaps are comparable, with the strongest gain of +0.30pp observed for R50->R34 Feature-KD versus +0.18pp for R34->R18 Feature-KD and +0.00pp for R34->R18 Logit-KD. Second, implementation correctness critically affects Feature-KD: a gradient clipping bug that excluded projection layers suppressed Feature-KD performance and produced misleading comparisons with Logit-KD. After correction, Feature-KD matches or outperforms Logit-KD in two of three pairs, reaching 95.55% on R50->R34 against a baseline of 95.25%. Third, input-resolution-aware architecture is a prerequisite for effective distillation: correcting the ResNet stem for 32x32 inputs raises teacher accuracy by over 5pp -- an order of magnitude larger than any KD gain. All code and results are available at github.com/umutonuryasar/kd-capacity-gap.

Authorship verification (AV) is the task of determining whether two texts were written by the same author. In a forensic context, the strength of AV evidence can be quantified using likelihood ratios. Most AV methods are score-based and deriving well-calibrated likelihood ratios from these scores requires a separate calibration model. This, in turn, requires additional amounts of case-relevant data, which is often time-consuming to obtain and prepare. This study proposes two novel normalisation techniques, the Square Root Correction and the Hapax Correction, for deriving likelihood ratios from the AV method LambdaG without the need of a calibration model (Nini et al. 2026). These corrections are designed to mitigate the overestimation of evidential strength that may result from long or highly repetitive texts. Performance is evaluated against logistic regression calibration across fifteen corpora and a range of text lengths (100-9,500 tokens), using the log-likelihood ratio cost (Cllr). The proposed methods achieve performance comparable to logistic regression calibration, with the Hapax Correction outperforming it in approximately 45% of tests (weighted by corpora). Furthermore, performance was more frequently close (within 5%) when the Hapax Correction was outperformed by logistic regression calibration, compared with the reverse comparison. Eliminating the need to train a calibration model reduces data-requirements, time and complexity, thereby increasing the accessibility and transparency of forensic text comparison. This combination of empirical performance and practical advantages supports the adoption of the proposed methods in forensic settings.

Real-world classifiers can benefit from the option of abstaining from predicting on samples where they have low confidence. Such abstention is particularly useful on samples which are close to the learned decision boundary, or which are outliers with respect to the training sample. These settings have been the subject of extensive but disjoint study in the selective classification (SC) and out-of-distribution (OOD) detection literature. Recent work on selective classification with OOD detection (SCOD) has argued for the unified study of these problems; however, the formal underpinnings of this problem are still nascent, and existing techniques are heuristic in nature. In this paper, we propose new plugin estimators for SCOD that are theoretically grounded, effective, and generalise existing approaches from the SC and OOD detection literature. In the course of our analysis, we formally explicate how na\"{i}ve use of existing SC and OOD detection baselines may be inadequate for SCOD. We empirically demonstrate that our approaches yields competitive SC and OOD detection performance compared to baselines from both literatures.

The goal of one-class collaborative filtering (OCCF) is to identify the user-item pairs that are positively-related but have not been interacted yet, where only a small portion of positive user-item interactions (e.g., users' implicit feedback) are observed. For discriminative modeling between positive and negative interactions, most previous work relied on negative sampling to some extent, which refers to considering unobserved user-item pairs as negative, as actual negative ones are unknown. However, the negative sampling scheme has critical limitations because it may choose "positive but unobserved" pairs as negative. This paper proposes a novel OCCF framework, named as BUIR, which does not require negative sampling. To make the representations of positively-related users and items similar to each other while avoiding a collapsed solution, BUIR adopts two distinct encoder networks that learn from each other; the first encoder is trained to predict the output of the second encoder as its target, while the second encoder provides the consistent targets by slowly approximating the first encoder. In addition, BUIR effectively alleviates the data sparsity issue of OCCF, by applying stochastic data augmentation to encoder inputs. Based on the neighborhood information of users and items, BUIR randomly generates the augmented views of each positive interaction each time it encodes, then further trains the model by this self-supervision. Our extensive experiments demonstrate that BUIR consistently and significantly outperforms all baseline methods by a large margin especially for much sparse datasets in which any assumptions about negative interactions are less valid.

Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR) serves as a convenient alternative: the measurement model is fitted to obtain factor scores in the first stage, which are then used to fit the structural model in the subsequent stage. However, naive application of FSR is known to yield biased estimates of structural parameters. In this paper, we develop a generic bias-correction framework for two-stage estimation of parametric statistical models and tailor it specifically to FSR. Unlike existing bias-corrected FSR solutions, the proposed method applies to a broader class of LV models and does not require computing specific types of factor scores. We establish the root-n consistency of the proposed bias-corrected two-stage estimator under mild regularity conditions. To ensure broad applicability and minimize reliance on complex analytical derivations, we introduce a stochastic approximation algorithm for point estimation and a Monte Carlo-based procedure for variance estimation. In a sequence of Monte Carlo experiments, we demonstrate that the bias-corrected FSR estimator performs comparably to the ``gold standard'' one-stage maximum likelihood estimator. These results suggest that our approach offers a straightforward yet effective alternative for estimating LV models.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Natural Language Processing (NLP) for low-resource languages presents significant challenges, particularly due to the scarcity of high-quality annotated data and linguistic resources. The choice of embeddings plays a critical role in enhancing the performance of NLP tasks, such as news classification, sentiment analysis, and hate speech detection, especially for low-resource languages like Marathi. In this study, we investigate the impact of various embedding techniques- Contextual BERT-based, Non-Contextual BERT-based, and FastText-based on NLP classification tasks specific to the Marathi language. Our research includes a thorough evaluation of both compressed and uncompressed embeddings, providing a comprehensive overview of how these embeddings perform across different scenarios. Specifically, we compare two BERT model embeddings, Muril and MahaBERT, as well as two FastText model embeddings, IndicFT and MahaFT. Our evaluation includes applying embeddings to a Multiple Logistic Regression (MLR) classifier for task performance assessment, as well as TSNE visualizations to observe the spatial distribution of these embeddings. The results demonstrate that contextual embeddings outperform non-contextual embeddings. Furthermore, BERT-based non-contextual embeddings extracted from the first BERT embedding layer yield better results than FastText-based embeddings, suggesting a potential alternative to FastText embeddings.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

Randomized controlled trials (RCTs) are considered the gold standard for estimating the average treatment effect (ATE) of interventions. One use of RCTs is to study the causes of global poverty -- a subject explicitly cited in the 2019 Nobel Memorial Prize awarded to Duflo, Banerjee, and Kremer "for their experimental approach to alleviating global poverty." Because the ATE is a population summary, anti-poverty experiments often seek to unpack the effect variation around the ATE by conditioning (CATE) on tabular variables such as age and ethnicity that were measured during the RCT data collection. Although such variables are key to unpacking CATE, using only such variables may fail to capture historical, geographical, or neighborhood-specific contributors to effect variation, as tabular RCT data are often only observed near the time of the experiment. In global poverty research, when the location of the experiment units is approximately known, satellite imagery can provide a window into such factors important for understanding heterogeneity. However, there is no method that specifically enables applied researchers to analyze CATE from images. In this paper, using a deep probabilistic modeling framework, we develop such a method that estimates latent clusters of images by identifying images with similar treatment effects distributions. Our interpretable image CATE model also includes a sensitivity factor that quantifies the importance of image segments contributing to the effect cluster prediction. We compare the proposed methods against alternatives in simulation; also, we show how the model works in an actual RCT, estimating the effects of an anti-poverty intervention in northern Uganda and obtaining a posterior predictive distribution over effects for the rest of the country where no experimental data was collected. We make all models available in open-source software.