Daily Papers

Multimodal learning has demonstrated incredible successes by integrating diverse data sources, yet it often relies on the availability of all modalities - an assumption that rarely holds in real-world applications. Pretrained multimodal models, while effective, struggle when confronted with small-scale and incomplete datasets (i.e., missing modalities), limiting their practical applicability. Previous studies on reconstructing missing modalities have overlooked the reconstruction's potential unreliability, which could compromise the quality of the final outputs. We present SURE (Scalable Uncertainty and Reconstruction Estimation), a novel framework that extends the capabilities of pretrained multimodal models by introducing latent space reconstruction and uncertainty estimation for both reconstructed modalities and downstream tasks. Our method is architecture-agnostic, reconstructs missing modalities, and delivers reliable uncertainty estimates, improving both interpretability and performance. SURE introduces a unique Pearson Correlation-based loss and applies statistical error propagation in deep networks for the first time, allowing precise quantification of uncertainties from missing data and model predictions. Extensive experiments across tasks such as sentiment analysis, genre classification, and action recognition show that SURE consistently achieves state-of-the-art performance, ensuring robust predictions even in the presence of incomplete data.

Transformer-based image restoration methods in adverse weather have achieved significant progress. Most of them use self-attention along the channel dimension or within spatially fixed-range blocks to reduce computational load. However, such a compromise results in limitations in capturing long-range spatial features. Inspired by the observation that the weather-induced degradation factors mainly cause similar occlusion and brightness, in this work, we propose an efficient Histogram Transformer (Histoformer) for restoring images affected by adverse weather. It is powered by a mechanism dubbed histogram self-attention, which sorts and segments spatial features into intensity-based bins. Self-attention is then applied across bins or within each bin to selectively focus on spatial features of dynamic range and process similar degraded pixels of the long range together. To boost histogram self-attention, we present a dynamic-range convolution enabling conventional convolution to conduct operation over similar pixels rather than neighbor pixels. We also observe that the common pixel-wise losses neglect linear association and correlation between output and ground-truth. Thus, we propose to leverage the Pearson correlation coefficient as a loss function to enforce the recovered pixels following the identical order as ground-truth. Extensive experiments demonstrate the efficacy and superiority of our proposed method. We have released the codes in Github.

This paper proposes a new metric to measure the calibration error of probabilistic binary classifiers, called test-based calibration error (TCE). TCE incorporates a novel loss function based on a statistical test to examine the extent to which model predictions differ from probabilities estimated from data. It offers (i) a clear interpretation, (ii) a consistent scale that is unaffected by class imbalance, and (iii) an enhanced visual representation with repect to the standard reliability diagram. In addition, we introduce an optimality criterion for the binning procedure of calibration error metrics based on a minimal estimation error of the empirical probabilities. We provide a novel computational algorithm for optimal bins under bin-size constraints. We demonstrate properties of TCE through a range of experiments, including multiple real-world imbalanced datasets and ImageNet 1000.

A critical barrier to learning an accurate decision rule for outlier detection is the scarcity of outlier data. As such, practitioners often turn to the use of similar but imperfect outlier data from which they might transfer information to the target outlier detection task. Despite the recent empirical success of transfer learning approaches in outlier detection, a fundamental understanding of when and how knowledge can be transferred from a source to a target outlier detection task remains elusive. In this work, we adopt the traditional framework of Neyman-Pearson classification -- which formalizes supervised outlier detection -- with the added assumption that one has access to some related but imperfect outlier data. Our main results are as follows: We first determine the information-theoretic limits of the problem under a measure of discrepancy that extends some existing notions from traditional balanced classification; interestingly, unlike in balanced classification, seemingly very dissimilar sources can provide much information about a target, thus resulting in fast transfer. We then show that, in principle, these information-theoretic limits are achievable by adaptive procedures, i.e., procedures with no a priori information on the discrepancy between source and target outlier distributions.

In contrastive learning, two views of an original image, generated by different augmentations, are considered a positive pair, and their similarity is required to be high. Similarly, two views of distinct images form a negative pair, with encouraged low similarity. Typically, a single similarity measure, provided by a lone projection head, evaluates positive and negative sample pairs. However, due to diverse augmentation strategies and varying intra-sample similarity, views from the same image may not always be similar. Additionally, owing to inter-sample similarity, views from different images may be more akin than those from the same image. Consequently, enforcing high similarity for positive pairs and low similarity for negative pairs may be unattainable, and in some cases, such enforcement could detrimentally impact performance. To address this challenge, we propose using multiple projection heads, each producing a distinct set of features. Our pre-training loss function emerges from a solution to the maximum likelihood estimation over head-wise posterior distributions of positive samples given observations. This loss incorporates the similarity measure over positive and negative pairs, each re-weighted by an individual adaptive temperature, regulated to prevent ill solutions. Our approach, Adaptive Multi-Head Contrastive Learning (AMCL), can be applied to and experimentally enhances several popular contrastive learning methods such as SimCLR, MoCo, and Barlow Twins. The improvement remains consistent across various backbones and linear probing epochs, and becomes more significant when employing multiple augmentation methods.

Solving complex classification tasks using deep neural networks typically requires large amounts of annotated data. However, corresponding class labels are noisy when provided by error-prone annotators, e.g., crowd workers. Training standard deep neural networks leads to subpar performances in such multi-annotator supervised learning settings. We address this issue by presenting a probabilistic training framework named multi-annotator deep learning (MaDL). A ground truth and an annotator performance model are jointly trained in an end-to-end learning approach. The ground truth model learns to predict instances' true class labels, while the annotator performance model infers probabilistic estimates of annotators' performances. A modular network architecture enables us to make varying assumptions regarding annotators' performances, e.g., an optional class or instance dependency. Further, we learn annotator embeddings to estimate annotators' densities within a latent space as proxies of their potentially correlated annotations. Together with a weighted loss function, we improve the learning from correlated annotation patterns. In a comprehensive evaluation, we examine three research questions about multi-annotator supervised learning. Our findings indicate MaDL's state-of-the-art performance and robustness against many correlated, spamming annotators.

Dual-encoder retrievers depend on the principle that relevant documents should score higher than irrelevant ones for a given query. Yet the dominant Noise Contrastive Estimation (NCE) objective, which underpins Contrastive Loss, optimizes a softened ranking surrogate that we rigorously prove is fundamentally oblivious to score separation quality and unrelated to AUC. This mismatch leads to poor calibration and suboptimal performance in downstream tasks like retrieval-augmented generation (RAG). To address this fundamental limitation, we introduce the MW loss, a new training objective that maximizes the Mann-Whitney U statistic, which is mathematically equivalent to the Area under the ROC Curve (AUC). MW loss encourages each positive-negative pair to be correctly ranked by minimizing binary cross entropy over score differences. We provide theoretical guarantees that MW loss directly upper-bounds the AoC, better aligning optimization with retrieval goals. We further promote ROC curves and AUC as natural threshold free diagnostics for evaluating retriever calibration and ranking quality. Empirically, retrievers trained with MW loss consistently outperform contrastive counterparts in AUC and standard retrieval metrics. Our experiments show that MW loss is an empirically superior alternative to Contrastive Loss, yielding better-calibrated and more discriminative retrievers for high-stakes applications like RAG.

Recently, self-supervised learning has attracted great attention, since it only requires unlabeled data for model training. Contrastive learning is one popular method for self-supervised learning and has achieved promising empirical performance. However, the theoretical understanding of its generalization ability is still limited. To this end, we define a kind of (sigma,delta)-measure to mathematically quantify the data augmentation, and then provide an upper bound of the downstream classification error rate based on the measure. It reveals that the generalization ability of contrastive self-supervised learning is related to three key factors: alignment of positive samples, divergence of class centers, and concentration of augmented data. The first two factors are properties of learned representations, while the third one is determined by pre-defined data augmentation. We further investigate two canonical contrastive losses, InfoNCE and cross-correlation, to show how they provably achieve the first two factors. Moreover, we conduct experiments to study the third factor, and observe a strong correlation between downstream performance and the concentration of augmented data.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)-the setting of the "conditional mutual information" framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

Loss functions serve as the foundation of supervised learning and are often chosen prior to model development. To avoid potentially ad hoc choices of losses, statistical decision theory describes a desirable property for losses known as properness, which asserts that Bayes' rule is optimal. Recent works have sought to learn losses and models jointly. Existing methods do this by fitting an inverse canonical link function which monotonically maps R to [0,1] to estimate probabilities for binary problems. In this paper, we extend monotonicity to maps between R^{C-1} and the projected probability simplex Delta^{C-1} by using monotonicity of gradients of convex functions. We present {\sc LegendreTron} as a novel and practical method that jointly learns proper canonical losses and probabilities for multiclass problems. Tested on a benchmark of domains with up to 1,000 classes, our experimental results show that our method consistently outperforms the natural multiclass baseline under a t-test at 99% significance on all datasets with greater than 10 classes.

We investigate imbalanced regression with tabular data that have an imbalance ratio larger than 1,000 ("highly imbalanced"). Accurately estimating the target values of rare instances is important in applications such as forecasting the intensity of rare harmful Solar Energetic Particle (SEP) events. For regression, the MSE loss does not consider the correlation between predicted and actual values. Typical inverse importance functions allow only convex functions. Uniform sampling might yield mini-batches that do not have rare instances. We propose CISIR that incorporates correlation, Monotonically Decreasing Involution (MDI) importance, and stratified sampling. Based on five datasets, our experimental results indicate that CISIR can achieve lower error and higher correlation than some recent methods. Also, adding our correlation component to other recent methods can improve their performance. Lastly, MDI importance can outperform other importance functions. Our code can be found in https://github.com/Machine-Earning/CISIR.

Deep learning models achieve state-of-the-art performance across domains but face scalability challenges in real-time or resource-constrained scenarios. To address this, we propose Correlation of Loss Differences (CLD), a simple and scalable metric for coreset selection that identifies the most impactful training samples by measuring their alignment with the loss trajectories of a held-out validation set. CLD is highly efficient, requiring only per-sample loss values computed at training checkpoints, and avoiding the costly gradient and curvature computations used in many existing subset selection methods. We develop a general theoretical framework that establishes convergence guarantees for CLD-based coresets, demonstrating that the convergence error is upper-bounded by the alignment of the selected samples and the representativeness of the validation set. On CIFAR-100 and ImageNet-1k, CLD-based coresets typically outperform or closely match state-of-the-art methods across subset sizes, and remain within 1% of more computationally expensive baselines even when not leading. CLD transfers effectively across architectures (ResNet, VGG, DenseNet), enabling proxy-to-target selection with <1% degradation. Moreover, CLD is stable when using only early checkpoints, incurring negligible accuracy loss. Finally, CLD exhibits inherent bias reduction via per-class validation alignment, obviating the need for additional stratified sampling. Together, these properties make CLD a principled, efficient, stable, and transferable tool for scalable dataset optimization.

Scaling laws in language modeling traditionally quantify training loss as a function of dataset size and model parameters, providing compute-optimal estimates but often neglecting the impact of data quality on model generalization. In this paper, we extend the conventional understanding of scaling law by offering a microscopic view of data quality within the original formulation -- effective training tokens -- which we posit to be a critical determinant of performance for parameter-constrained language models. Specifically, we formulate the proposed term of effective training tokens to be a combination of two readily-computed indicators of text: (i) text diversity and (ii) syntheticity as measured by a teacher model. We pretrained over 200 models of 25M to 1.5B parameters on a diverse set of sampled, synthetic data, and estimated the constants that relate text quality, model size, training tokens, and eight reasoning task accuracy scores. We demonstrated the estimated constants yield +0.83 Pearson correlation with true accuracies, and analyzed it in scenarios involving widely-used data techniques such as data sampling and synthesis which aim to improve data quality.

Cross-entropy is a widely used loss function in applications. It coincides with the logistic loss applied to the outputs of a neural network, when the softmax is used. But, what guarantees can we rely on when using cross-entropy as a surrogate loss? We present a theoretical analysis of a broad family of loss functions, comp-sum losses, that includes cross-entropy (or logistic loss), generalized cross-entropy, the mean absolute error and other cross-entropy-like loss functions. We give the first H-consistency bounds for these loss functions. These are non-asymptotic guarantees that upper bound the zero-one loss estimation error in terms of the estimation error of a surrogate loss, for the specific hypothesis set H used. We further show that our bounds are tight. These bounds depend on quantities called minimizability gaps. To make them more explicit, we give a specific analysis of these gaps for comp-sum losses. We also introduce a new family of loss functions, smooth adversarial comp-sum losses, that are derived from their comp-sum counterparts by adding in a related smooth term. We show that these loss functions are beneficial in the adversarial setting by proving that they admit H-consistency bounds. This leads to new adversarial robustness algorithms that consist of minimizing a regularized smooth adversarial comp-sum loss. While our main purpose is a theoretical analysis, we also present an extensive empirical analysis comparing comp-sum losses. We further report the results of a series of experiments demonstrating that our adversarial robustness algorithms outperform the current state-of-the-art, while also achieving a superior non-adversarial accuracy.

We consider learning representations (features) in the setting in which we have access to multiple unlabeled views of the data for learning while only one view is available for downstream tasks. Previous work on this problem has proposed several techniques based on deep neural networks, typically involving either autoencoder-like networks with a reconstruction objective or paired feedforward networks with a batch-style correlation-based objective. We analyze several techniques based on prior work, as well as new variants, and compare them empirically on image, speech, and text tasks. We find an advantage for correlation-based representation learning, while the best results on most tasks are obtained with our new variant, deep canonically correlated autoencoders (DCCAE). We also explore a stochastic optimization procedure for minibatch correlation-based objectives and discuss the time/performance trade-offs for kernel-based and neural network-based implementations.

While scaling laws provide a reliable methodology for predicting train loss across compute scales for a single data distribution, less is known about how these predictions should change as we change the distribution. In this paper, we derive a strategy for predicting one loss from another and apply it to predict across different pre-training datasets and from pre-training data to downstream task data. Our predictions extrapolate well even at 20x the largest FLOP budget used to fit the curves. More precisely, we find that there are simple shifted power law relationships between (1) the train losses of two models trained on two separate datasets when the models are paired by training compute (train-to-train), (2) the train loss and the test loss on any downstream distribution for a single model (train-to-test), and (3) the test losses of two models trained on two separate train datasets (test-to-test). The results hold up for pre-training datasets that differ substantially (some are entirely code and others have no code at all) and across a variety of downstream tasks. Finally, we find that in some settings these shifted power law relationships can yield more accurate predictions than extrapolating single-dataset scaling laws.

Much research in machine learning involves finding appropriate inductive biases (e.g. convolutional neural networks, momentum-based optimizers, transformers) to promote generalization on tasks. However, quantification of the amount of inductive bias associated with these architectures and hyperparameters has been limited. We propose a novel method for efficiently computing the inductive bias required for generalization on a task with a fixed training data budget; formally, this corresponds to the amount of information required to specify well-generalizing models within a specific hypothesis space of models. Our approach involves modeling the loss distribution of random hypotheses drawn from a hypothesis space to estimate the required inductive bias for a task relative to these hypotheses. Unlike prior work, our method provides a direct estimate of inductive bias without using bounds and is applicable to diverse hypothesis spaces. Moreover, we derive approximation error bounds for our estimation approach in terms of the number of sampled hypotheses. Consistent with prior results, our empirical results demonstrate that higher dimensional tasks require greater inductive bias. We show that relative to other expressive model classes, neural networks as a model class encode large amounts of inductive bias. Furthermore, our measure quantifies the relative difference in inductive bias between different neural network architectures. Our proposed inductive bias metric provides an information-theoretic interpretation of the benefits of specific model architectures for certain tasks and provides a quantitative guide to developing tasks requiring greater inductive bias, thereby encouraging the development of more powerful inductive biases.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

Few-shot learning is a challenging area of research that aims to learn new concepts with only a few labeled samples of data. Recent works based on metric-learning approaches leverage the meta-learning approach, which is encompassed by episodic tasks that make use a support (training) and query set (test) with the objective of learning a similarity comparison metric between those sets. Due to the lack of data, the learning process of the embedding network becomes an important part of the few-shot task. Previous works have addressed this problem using metric learning approaches, but the properties of the underlying latent space and the separability of the difference classes on it was not entirely enforced. In this work, we propose two different loss functions which consider the importance of the embedding vectors by looking at the intra-class and inter-class distance between the few data. The first loss function is the Proto-Triplet Loss, which is based on the original triplet loss with the modifications needed to better work on few-shot scenarios. The second loss function, which we dub ICNN loss is based on an inter and intra class nearest neighbors score, which help us to assess the quality of embeddings obtained from the trained network. Our results, obtained from a extensive experimental setup show a significant improvement in accuracy in the miniImagenNet benchmark compared to other metric-based few-shot learning methods by a margin of 2%, demonstrating the capability of these loss functions to allow the network to generalize better to previously unseen classes. In our experiments, we demonstrate competitive generalization capabilities to other domains, such as the Caltech CUB, Dogs and Cars datasets compared with the state of the art.

In this paper we introduce the SCoRe (Submodular Combinatorial Representation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the Total Information and Total Correlation, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6\% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.

High-precision modeling of systems is one of the main areas of industrial data analysis. Models of systems, their digital twins, are used to predict their behavior under various conditions. We have developed several models of a storage system using machine learning-based generative models. The system consists of several components: hard disk drive (HDD) and solid-state drive (SSD) storage pools with different RAID schemes and cache. Each storage component is represented by a probabilistic model that describes the probability distribution of the component performance in terms of IOPS and latency, depending on their configuration and external data load parameters. The results of the experiments demonstrate the errors of 4-10 % for IOPS and 3-16 % for latency predictions depending on the components and models of the system. The predictions show up to 0.99 Pearson correlation with Little's law, which can be used for unsupervised reliability checks of the models. In addition, we present novel data sets that can be used for benchmarking regression algorithms, conditional generative models, and uncertainty estimation methods in machine learning.

Deep neural networks have achieved remarkable performance on a range of classification tasks, with softmax cross-entropy (CE) loss emerging as the de-facto objective function. The CE loss encourages features of a class to have a higher projection score on the true class-vector compared to the negative classes. However, this is a relative constraint and does not explicitly force different class features to be well-separated. Motivated by the observation that ground-truth class representations in CE loss are orthogonal (one-hot encoded vectors), we develop a novel loss function termed `Orthogonal Projection Loss' (OPL) which imposes orthogonality in the feature space. OPL augments the properties of CE loss and directly enforces inter-class separation alongside intra-class clustering in the feature space through orthogonality constraints on the mini-batch level. As compared to other alternatives of CE, OPL offers unique advantages e.g., no additional learnable parameters, does not require careful negative mining and is not sensitive to the batch size. Given the plug-and-play nature of OPL, we evaluate it on a diverse range of tasks including image recognition (CIFAR-100), large-scale classification (ImageNet), domain generalization (PACS) and few-shot learning (miniImageNet, CIFAR-FS, tiered-ImageNet and Meta-dataset) and demonstrate its effectiveness across the board. Furthermore, OPL offers better robustness against practical nuisances such as adversarial attacks and label noise. Code is available at: https://github.com/kahnchana/opl.

Collaborative filtering (CF) is a widely studied research topic in recommender systems. The learning of a CF model generally depends on three major components, namely interaction encoder, loss function, and negative sampling. While many existing studies focus on the design of more powerful interaction encoders, the impacts of loss functions and negative sampling ratios have not yet been well explored. In this work, we show that the choice of loss function as well as negative sampling ratio is equivalently important. More specifically, we propose the cosine contrastive loss (CCL) and further incorporate it to a simple unified CF model, dubbed SimpleX. Extensive experiments have been conducted on 11 benchmark datasets and compared with 29 existing CF models in total. Surprisingly, the results show that, under our CCL loss and a large negative sampling ratio, SimpleX can surpass most sophisticated state-of-the-art models by a large margin (e.g., max 48.5% improvement in NDCG@20 over LightGCN). We believe that SimpleX could not only serve as a simple strong baseline to foster future research on CF, but also shed light on the potential research direction towards improving loss function and negative sampling. Our source code will be available at https://reczoo.github.io/SimpleX.

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

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

We used a dataset of daily Bloomberg Financial Market Summaries from 2010 to 2023, reposted on large financial media, to determine how global news headlines may affect stock market movements using ChatGPT and a two-stage prompt approach. We document a statistically significant positive correlation between the sentiment score and future equity market returns over short to medium term, which reverts to a negative correlation over longer horizons. Validation of this correlation pattern across multiple equity markets indicates its robustness across equity regions and resilience to non-linearity, evidenced by comparison of Pearson and Spearman correlations. Finally, we provide an estimate of the optimal horizon that strikes a balance between reactivity to new information and correlation.

Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Renyi entropy based on nearest neighbour distances. We prove the L2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods.

We study the problem of classification with a reject option for a fixed predictor, applicable in natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss function. We provide a complete theoretical analysis of the surrogate loss function with a strong H-consistency guarantee. For evaluation, we choose the decontextualization task, and provide a manually-labelled dataset of 2mathord,000 examples. Our algorithm significantly outperforms the baselines considered, with a sim!!25% improvement in coverage when halving the error rate, which is only sim!! 3 % away from the theoretical limit.

In this report, we present our champion solution for EPIC-KITCHENS-100 Multi-Instance Retrieval Challenge in CVPR 2024. Essentially, this challenge differs from traditional visual-text retrieval tasks by providing a correlation matrix that acts as a set of soft labels for video-text clip combinations. However, existing loss functions have not fully exploited this information. Motivated by this, we propose a novel loss function, Symmetric Multi-Similarity Loss, which offers a more precise learning objective. Together with tricks and ensemble learning, the model achieves 63.76% average mAP and 74.25% average nDCG on the public leaderboard, demonstrating the effectiveness of our approach. Our code will be released at: https://github.com/xqwang14/SMS-Loss/tree/main

Graph Neural Networks (GNNs) show promising results for graph tasks. However, existing GNNs' generalization ability will degrade when there exist distribution shifts between testing and training graph data. The cardinal impetus underlying the severe degeneration is that the GNNs are architected predicated upon the I.I.D assumptions. In such a setting, GNNs are inclined to leverage imperceptible statistical correlations subsisting in the training set to predict, albeit it is a spurious correlation. In this paper, we study the problem of the generalization ability of GNNs in Out-Of-Distribution (OOD) settings. To solve this problem, we propose the Learning to Reweight for Generalizable Graph Neural Network (L2R-GNN) to enhance the generalization ability for achieving satisfactory performance on unseen testing graphs that have different distributions with training graphs. We propose a novel nonlinear graph decorrelation method, which can substantially improve the out-of-distribution generalization ability and compares favorably to previous methods in restraining the over-reduced sample size. The variables of the graph representation are clustered based on the stability of the correlation, and the graph decorrelation method learns weights to remove correlations between the variables of different clusters rather than any two variables. Besides, we interpose an efficacious stochastic algorithm upon bi-level optimization for the L2R-GNN framework, which facilitates simultaneously learning the optimal weights and GNN parameters, and avoids the overfitting problem. Experimental results show that L2R-GNN greatly outperforms baselines on various graph prediction benchmarks under distribution shifts.

Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are largely heuristic and depend heavily on empirical results, lacking theoretical explanation. Furthermore, existing methods overlook the decision loss, which characterizes different costs associated with tailed classes. This paper presents a general and principled framework from a Bayesian-decision-theory perspective, which unifies existing techniques including re-balancing and ensemble methods, and provides theoretical justifications for their effectiveness. From this perspective, we derive a novel objective based on the integrated risk and a Bayesian deep-ensemble approach to improve the accuracy of all classes, especially the "tail". Besides, our framework allows for task-adaptive decision loss which provides provably optimal decisions in varying task scenarios, along with the capability to quantify uncertainty. Finally, We conduct comprehensive experiments, including standard classification, tail-sensitive classification with a new False Head Rate metric, calibration, and ablation studies. Our framework significantly improves the current SOTA even on large-scale real-world datasets like ImageNet.

While language models have exceptional capabilities at text generation, they lack a natural inductive bias for emitting numbers and thus struggle in tasks involving reasoning over quantities, especially arithmetics. This has particular relevance in scientific datasets where combinations of text and numerical data are abundant. One fundamental limitation is the nature of the CE loss, which assumes a nominal (categorical) scale and thus cannot convey proximity between generated number tokens. As a remedy, we here present two versions of a number token loss. The first is based on an L_p loss between the ground truth token value and the weighted sum of the predicted class probabilities. The second loss minimizes the Wasserstein-1 distance between the distribution of the predicted output probabilities and the ground truth distribution. These regression-like losses can easily be added to any language model and extend the CE objective during training. We compare the proposed schemes on a mathematics dataset against existing tokenization, encoding, and decoding schemes for improving number representation in language models. Our results reveal a significant improvement in numerical accuracy when equipping a standard T5 model with the proposed loss schemes.

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

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

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.

Coordinate-based neural representations have shown significant promise as an alternative to discrete, array-based representations for complex low dimensional signals. However, optimizing a coordinate-based network from randomly initialized weights for each new signal is inefficient. We propose applying standard meta-learning algorithms to learn the initial weight parameters for these fully-connected networks based on the underlying class of signals being represented (e.g., images of faces or 3D models of chairs). Despite requiring only a minor change in implementation, using these learned initial weights enables faster convergence during optimization and can serve as a strong prior over the signal class being modeled, resulting in better generalization when only partial observations of a given signal are available. We explore these benefits across a variety of tasks, including representing 2D images, reconstructing CT scans, and recovering 3D shapes and scenes from 2D image observations.

The Fisher information is a fundamental concept for characterizing the sensitivity of parameters in neural networks. However, leveraging the full observed Fisher information is too expensive for large models, so most methods rely on simple diagonal approximations. While efficient, this approach ignores parameter correlations, often resulting in reduced performance on downstream tasks. In this work, we mitigate these limitations and propose Generalized Fisher-Weighted SVD (GFWSVD), a post-training LLM compression technique that accounts for both diagonal and off-diagonal elements of the Fisher information matrix, providing a more accurate reflection of parameter importance. To make the method tractable, we introduce a scalable adaptation of the Kronecker-factored approximation algorithm for the observed Fisher information. We demonstrate the effectiveness of our method on LLM compression, showing improvements over existing compression baselines. For example, at a 20 compression rate on the MMLU benchmark, our method outperforms FWSVD, which is based on a diagonal approximation of the Fisher information, by 5 percent, SVD-LLM by 3 percent, and ASVD by 6 percent compression rate.

In deep metric learning, the Triplet Loss has emerged as a popular method to learn many computer vision and natural language processing tasks such as facial recognition, object detection, and visual-semantic embeddings. One issue that plagues the Triplet Loss is network collapse, an undesirable phenomenon where the network projects the embeddings of all data onto a single point. Researchers predominately solve this problem by using triplet mining strategies. While hard negative mining is the most effective of these strategies, existing formulations lack strong theoretical justification for their empirical success. In this paper, we utilize the mathematical theory of isometric approximation to show an equivalence between the Triplet Loss sampled by hard negative mining and an optimization problem that minimizes a Hausdorff-like distance between the neural network and its ideal counterpart function. This provides the theoretical justifications for hard negative mining's empirical efficacy. In addition, our novel application of the isometric approximation theorem provides the groundwork for future forms of hard negative mining that avoid network collapse. Our theory can also be extended to analyze other Euclidean space-based metric learning methods like Ladder Loss or Contrastive Learning.

Learning compact discrete representations of data is a key task on its own or for facilitating subsequent processing of data. In this paper we present a model that produces Discrete InfoMax Codes (DIMCO); we learn a probabilistic encoder that yields k-way d-dimensional codes associated with input data. Our model's learning objective is to maximize the mutual information between codes and labels with a regularization, which enforces entries of a codeword to be as independent as possible. We show that the infomax principle also justifies previous loss functions (e.g., cross-entropy) as its special cases. Our analysis also shows that using shorter codes, as DIMCO does, reduces overfitting in the context of few-shot classification. Through experiments in various domains, we observe this implicit meta-regularization effect of DIMCO. Furthermore, we show that the codes learned by DIMCO are efficient in terms of both memory and retrieval time compared to previous methods.

Discriminative approaches to classification often learn shortcuts that hold in-distribution but fail even under minor distribution shift. This failure mode stems from an overreliance on features that are spuriously correlated with the label. We show that generative classifiers, which use class-conditional generative models, can avoid this issue by modeling all features, both core and spurious, instead of mainly spurious ones. These generative classifiers are simple to train, avoiding the need for specialized augmentations, strong regularization, extra hyperparameters, or knowledge of the specific spurious correlations to avoid. We find that diffusion-based and autoregressive generative classifiers achieve state-of-the-art performance on five standard image and text distribution shift benchmarks and reduce the impact of spurious correlations in realistic applications, such as medical or satellite datasets. Finally, we carefully analyze a Gaussian toy setting to understand the inductive biases of generative classifiers, as well as the data properties that determine when generative classifiers outperform discriminative ones.

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in the high-dimensional, undersampled regimes typical of modern experiments. Recent machine learning-based estimators show promise, but their accuracy depends sensitively on dataset size, structure, and hyperparameters, with no accepted tests to detect failures. We close these gaps through a systematic evaluation of classical and neural MI estimators across standard benchmarks and new synthetic datasets tailored to challenging high-dimensional, undersampled regimes. We contribute: (i) a practical protocol for reliable MI estimation with explicit checks for statistical consistency; (ii) confidence intervals (error bars around estimates) that existing neural MI estimator do not provide; and (iii) a new class of probabilistic critics designed for high-dimensional, high-information settings. We demonstrate the effectiveness of our protocol with computational experiments, showing that it consistently matches or surpasses existing methods while uniquely quantifying its own reliability. We show that reliable MI estimation is sometimes achievable even in severely undersampled, high-dimensional datasets, provided they admit accurate low-dimensional representations. This broadens the scope of applicability of neural MI estimators and clarifies when such estimators can be trusted.

Perceptual similarity scores that align with human vision are critical for both training and evaluating computer vision models. Deep perceptual losses, such as LPIPS, achieve good alignment but rely on complex, highly non-linear discriminative features with unknown invariances, while hand-crafted measures like SSIM are interpretable but miss key perceptual properties. We introduce the Structured Uncertainty Similarity Score (SUSS); it models each image through a set of perceptual components, each represented by a structured multivariate Normal distribution. These are trained in a generative, self-supervised manner to assign high likelihood to human-imperceptible augmentations. The final score is a weighted sum of component log-probabilities with weights learned from human perceptual datasets. Unlike feature-based methods, SUSS learns image-specific linear transformations of residuals in pixel space, enabling transparent inspection through decorrelated residuals and sampling. SUSS aligns closely with human perceptual judgments, shows strong perceptual calibration across diverse distortion types, and provides localized, interpretable explanations of its similarity assessments. We further demonstrate stable optimization behavior and competitive performance when using SUSS as a perceptual loss for downstream imaging tasks.

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

In a typical multi-label setting, a picture contains on average few positive labels, and many negative ones. This positive-negative imbalance dominates the optimization process, and can lead to under-emphasizing gradients from positive labels during training, resulting in poor accuracy. In this paper, we introduce a novel asymmetric loss ("ASL"), which operates differently on positive and negative samples. The loss enables to dynamically down-weights and hard-thresholds easy negative samples, while also discarding possibly mislabeled samples. We demonstrate how ASL can balance the probabilities of different samples, and how this balancing is translated to better mAP scores. With ASL, we reach state-of-the-art results on multiple popular multi-label datasets: MS-COCO, Pascal-VOC, NUS-WIDE and Open Images. We also demonstrate ASL applicability for other tasks, such as single-label classification and object detection. ASL is effective, easy to implement, and does not increase the training time or complexity. Implementation is available at: https://github.com/Alibaba-MIIL/ASL.

Self-Supervised Learning (SSL) frameworks became the standard for learning robust class representations by benefiting from large unlabeled datasets. For Speaker Verification (SV), most SSL systems rely on contrastive-based loss functions. We explore different ways to improve the performance of these techniques by revisiting the NT-Xent contrastive loss. Our main contribution is the definition of the NT-Xent-AM loss and the study of the importance of Additive Margin (AM) in SimCLR and MoCo SSL methods to further separate positive from negative pairs. Despite class collisions, we show that AM enhances the compactness of same-speaker embeddings and reduces the number of false negatives and false positives on SV. Additionally, we demonstrate the effectiveness of the symmetric contrastive loss, which provides more supervision for the SSL task. Implementing these two modifications to SimCLR improves performance and results in 7.85% EER on VoxCeleb1-O, outperforming other equivalent methods.

In this paper, we propose KaLM-Embedding-V2, a versatile and compact embedding model, which achieves impressive performance in general-purpose text embedding tasks by leveraging superior training techniques and data. Our key innovations include: (1) To better align the architecture with representation learning, we remove the causal attention mask and adopt a fully bidirectional transformer with simple yet effective mean-pooling to produce fixed-length embeddings; (2) We employ a multi-stage training pipeline: (i) pre-training on large-scale weakly supervised open-source corpora; (ii) fine-tuning on high-quality retrieval and non-retrieval datasets; and (iii) model-soup parameter averaging for robust generalization. Besides, we introduce a focal-style reweighting mechanism that concentrates learning on difficult samples and an online hard-negative mixing strategy to continuously enrich hard negatives without expensive offline mining; (3) We collect over 20 categories of data for pre-training and 100 categories of data for fine-tuning, to boost both the performance and generalization of the embedding model. Extensive evaluations on the Massive Text Embedding Benchmark (MTEB) Chinese and English show that our model significantly outperforms others of comparable size, and competes with 3x, 14x, 18x, and 26x larger embedding models, setting a new standard for a versatile and compact embedding model with less than 1B parameters.

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

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class H that makes use only of a standard squared error regression oracle for H. We give a weak learning assumption on H that ensures convergence to Bayes optimality without the need to make any realizability assumptions -- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on H is both necessary and sufficient for multicalibration with respect to H to imply Bayes optimality. We also show that if H satisfies our weak learning condition relative to another class C then multicalibration with respect to H implies multicalibration with respect to C. Finally we investigate the empirical performance of our algorithm experimentally using an open source implementation that we make available. Our code repository can be found at https://github.com/Declancharrison/Level-Set-Boosting.

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

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the well-known Pearson correlation coefficient, the most important is that distance correlation equals zero if and only if the random vectors are independent. There are two different estimators of the distance correlation available in the literature. The first one, proposed by Székely et al. (2007), is based on an asymptotically unbiased estimator of the distance covariance which turns out to be a V-statistic. The second one builds on an unbiased estimator of the distance covariance proposed in Székely et al. (2014), proved to be an U-statistic by Székely and Huo (2016). This study evaluates their efficiency (mean squared error) and compares computational times for both methods under different dependence structures. Under conditions of independence or near-independence, the V-estimates are biased, while the U-estimator frequently cannot be computed due to negative values. To address this challenge, a convex linear combination of the former estimators is proposed and studied, yielding good results regardless of the level of dependence.

Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w.r.t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: the label-wise class imbalance. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.

Contrastive learning -- a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones -- has driven significant progress in foundation models. In this work, we develop a new theoretical framework for analyzing data augmentation-based contrastive learning, with a focus on SimCLR as a representative example. Our approach is based on the concept of approximate sufficient statistics, which we extend beyond its original definition in oko2025statistical for contrastive language-image pretraining (CLIP) using KL-divergence. We generalize it to equivalent forms and general f-divergences, and show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient. Furthermore, we demonstrate that these near-sufficient encoders can be effectively adapted to downstream regression and classification tasks, with performance depending on their sufficiency and the error induced by data augmentation in contrastive learning. Concrete examples in linear regression and topic classification are provided to illustrate the broad applicability of our results.

A family of loss functions built on pair-based computation have been proposed in the literature which provide a myriad of solutions for deep metric learning. In this paper, we provide a general weighting framework for understanding recent pair-based loss functions. Our contributions are three-fold: (1) we establish a General Pair Weighting (GPW) framework, which casts the sampling problem of deep metric learning into a unified view of pair weighting through gradient analysis, providing a powerful tool for understanding recent pair-based loss functions; (2) we show that with GPW, various existing pair-based methods can be compared and discussed comprehensively, with clear differences and key limitations identified; (3) we propose a new loss called multi-similarity loss (MS loss) under the GPW, which is implemented in two iterative steps (i.e., mining and weighting). This allows it to fully consider three similarities for pair weighting, providing a more principled approach for collecting and weighting informative pairs. Finally, the proposed MS loss obtains new state-of-the-art performance on four image retrieval benchmarks, where it outperforms the most recent approaches, such as ABEKim_2018_ECCV and HTL by a large margin: 60.6% to 65.7% on CUB200, and 80.9% to 88.0% on In-Shop Clothes Retrieval dataset at Recall@1. Code is available at https://github.com/MalongTech/research-ms-loss.

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

We study the problem of learning mixtures of Gaussians with censored data. Statistical learning with censored data is a classical problem, with numerous practical applications, however, finite-sample guarantees for even simple latent variable models such as Gaussian mixtures are missing. Formally, we are given censored data from a mixture of univariate Gaussians $sum_{i=1}^k w_i N(mu_i,sigma^2), i.e. the sample is observed only if it lies inside a set S. The goal is to learn the weights w_i and the means \mu_i. We propose an algorithm that takes only 1{\varepsilon^{O(k)}} samples to estimate the weights w_i and the means \mu_i within \varepsilon$ error.

Pre-trained models have revolutionized natural language understanding. However, researchers have found they can encode artifacts undesired in many applications, such as professions correlating with one gender more than another. We explore such gendered correlations as a case study for how to address unintended correlations in pre-trained models. We define metrics and reveal that it is possible for models with similar accuracy to encode correlations at very different rates. We show how measured correlations can be reduced with general-purpose techniques, and highlight the trade offs different strategies have. With these results, we make recommendations for training robust models: (1) carefully evaluate unintended correlations, (2) be mindful of seemingly innocuous configuration differences, and (3) focus on general mitigations.

Model calibration aims to align confidence with prediction correctness. The Cross-Entropy (CE) loss is widely used for calibrator training, which enforces the model to increase confidence on the ground truth class. However, we find the CE loss has intrinsic limitations. For example, for a narrow misclassification, a calibrator trained by the CE loss often produces high confidence on the wrongly predicted class (e.g., a test sample is wrongly classified and its softmax score on the ground truth class is around 0.4), which is undesirable. In this paper, we propose a new post-hoc calibration objective derived from the aim of calibration. Intuitively, the proposed objective function asks that the calibrator decrease model confidence on wrongly predicted samples and increase confidence on correctly predicted samples. Because a sample itself has insufficient ability to indicate correctness, we use its transformed versions (e.g., rotated, greyscaled and color-jittered) during calibrator training. Trained on an in-distribution validation set and tested with isolated, individual test samples, our method achieves competitive calibration performance on both in-distribution and out-of-distribution test sets compared with the state of the art. Further, our analysis points out the difference between our method and commonly used objectives such as CE loss and mean square error loss, where the latters sometimes deviates from the calibration aim.

Vision-language models like CLIP excel at recognizing the single, prominent object in a scene. However, they struggle in complex scenes containing multiple objects. We identify a fundamental reason for this limitation: VLM feature space exhibits excessive mutual feature information (MFI), where the features of one class contain substantial information about other, unrelated classes. This high MFI becomes evident during class-specific queries, as unrelated objects are activated alongside the queried class. To address this limitation, we propose DCLIP, an efficient framework that learns an optimal level of mutual information while adding only minimal learnable parameters to a frozen VLM. DCLIP uses two complementary losses: a novel MFI Loss that regulates class feature similarity to prevent excessive overlap while preserving necessary shared information, and the Asymmetric Loss (ASL) that aligns image features with the disentangled text features. Through this disentanglement, DCLIP reduces excessive inter-class similarity by 30%. On multi-label recognition, DCLIP performs favorably over SOTA approaches on VOC2007 and COCO-14 while using 75% fewer training parameters. For zero-shot semantic segmentation, it shows improved performance across six benchmark datasets. These results highlight the importance of feature disentanglement for multi-object perception in VLMs.

Loss Given Default (LGD) modeling faces a fundamental data quality constraint: 90% of available training data consists of proxy estimates based on pre-distress balance sheets rather than actual recovery outcomes from completed bankruptcy proceedings. We demonstrate that this mixture-contaminated training structure causes systematic failure of recursive partitioning methods, with Random Forest achieving negative r-squared (-0.664, worse than predicting the mean) on held-out test data. Information-theoretic approaches based on Shannon entropy and mutual information provide superior generalization, achieving r-squared of 0.191 and RMSE of 0.284 on 1,218 corporate bankruptcies (1980-2023). Analysis reveals that leverage-based features contain 1.510 bits of mutual information while size effects contribute only 0.086 bits, contradicting regulatory assumptions about scale-dependent recovery. These results establish practical guidance for financial institutions deploying LGD models under Basel III requirements when representative outcome data is unavailable at sufficient scale. The findings generalize to medical outcomes research, climate forecasting, and technology reliability-domains where extended observation periods create unavoidable mixture structure in training data.

We study a family of loss functions named label-distributionally robust (LDR) losses for multi-class classification that are formulated from distributionally robust optimization (DRO) perspective, where the uncertainty in the given label information are modeled and captured by taking the worse case of distributional weights. The benefits of this perspective are several fold: (i) it provides a unified framework to explain the classical cross-entropy (CE) loss and SVM loss and their variants, (ii) it includes a special family corresponding to the temperature-scaled CE loss, which is widely adopted but poorly understood; (iii) it allows us to achieve adaptivity to the uncertainty degree of label information at an instance level. Our contributions include: (1) we study both consistency and robustness by establishing top-k (forall kgeq 1) consistency of LDR losses for multi-class classification, and a negative result that a top-1 consistent and symmetric robust loss cannot achieve top-k consistency simultaneously for all kgeq 2; (2) we propose a new adaptive LDR loss that automatically adapts the individualized temperature parameter to the noise degree of class label of each instance; (3) we demonstrate stable and competitive performance for the proposed adaptive LDR loss on 7 benchmark datasets under 6 noisy label and 1 clean settings against 13 loss functions, and on one real-world noisy dataset. The code is open-sourced at https://github.com/Optimization-AI/ICML2023_LDR.

Many NLP tasks such as tagging and machine reading comprehension are faced with the severe data imbalance issue: negative examples significantly outnumber positive examples, and the huge number of background examples (or easy-negative examples) overwhelms the training. The most commonly used cross entropy (CE) criteria is actually an accuracy-oriented objective, and thus creates a discrepancy between training and test: at training time, each training instance contributes equally to the objective function, while at test time F1 score concerns more about positive examples. In this paper, we propose to use dice loss in replacement of the standard cross-entropy objective for data-imbalanced NLP tasks. Dice loss is based on the Sorensen-Dice coefficient or Tversky index, which attaches similar importance to false positives and false negatives, and is more immune to the data-imbalance issue. To further alleviate the dominating influence from easy-negative examples in training, we propose to associate training examples with dynamically adjusted weights to deemphasize easy-negative examples.Theoretical analysis shows that this strategy narrows down the gap between the F1 score in evaluation and the dice loss in training. With the proposed training objective, we observe significant performance boost on a wide range of data imbalanced NLP tasks. Notably, we are able to achieve SOTA results on CTB5, CTB6 and UD1.4 for the part of speech tagging task; SOTA results on CoNLL03, OntoNotes5.0, MSRA and OntoNotes4.0 for the named entity recognition task; along with competitive results on the tasks of machine reading comprehension and paraphrase identification.

The goal of face recognition (FR) can be viewed as a pair similarity optimization problem, maximizing a similarity set S^p over positive pairs, while minimizing similarity set S^n over negative pairs. Ideally, it is expected that FR models form a well-discriminative feature space (WDFS) that satisfies mathcal{S^p} > mathcal{S^n}. With regard to WDFS, the existing deep feature learning paradigms (i.e., metric and classification losses) can be expressed as a unified perspective on different pair generation (PG) strategies. Unfortunately, in the metric loss (ML), it is infeasible to generate negative pairs taking all classes into account in each iteration because of the limited mini-batch size. In contrast, in classification loss (CL), it is difficult to generate extremely hard negative pairs owing to the convergence of the class weight vectors to their center. This leads to a mismatch between the two similarity distributions of the sampled pairs and all negative pairs. Thus, this paper proposes a unified negative pair generation (UNPG) by combining two PG strategies (i.e., MLPG and CLPG) from a unified perspective to alleviate the mismatch. UNPG introduces useful information about negative pairs using MLPG to overcome the CLPG deficiency. Moreover, it includes filtering the similarities of noisy negative pairs to guarantee reliable convergence and improved performance. Exhaustive experiments show the superiority of UNPG by achieving state-of-the-art performance across recent loss functions on public benchmark datasets. Our code and pretrained models are publicly available.

Learning discriminative shape representations is a crucial issue for large-scale 3D shape retrieval. In this paper, we propose the Collaborative Inner Product Loss (CIP Loss) to obtain ideal shape embedding that discriminative among different categories and clustered within the same class. Utilizing simple inner product operation, CIP loss explicitly enforces the features of the same class to be clustered in a linear subspace, while inter-class subspaces are constrained to be at least orthogonal. Compared to previous metric loss functions, CIP loss could provide more clear geometric interpretation for the embedding than Euclidean margin, and is easy to implement without normalization operation referring to cosine margin. Moreover, our proposed loss term can combine with other commonly used loss functions and can be easily plugged into existing off-the-shelf architectures. Extensive experiments conducted on the two public 3D object retrieval datasets, ModelNet and ShapeNetCore 55, demonstrate the effectiveness of our proposal, and our method has achieved state-of-the-art results on both datasets.

Machine learning systems are known to be sensitive to spurious correlations between biased features of the inputs (e.g., background, texture, and secondary objects) and the corresponding labels. These features and their correlations with the labels are known as "spurious" because they tend to change with shifts in real-world data distributions, which can negatively impact the model's generalization and robustness. In this survey, we provide a comprehensive review of this issue, along with a taxonomy of current state-of-the-art methods for addressing spurious correlations in machine learning models. Additionally, we summarize existing datasets, benchmarks, and metrics to aid future research. The paper concludes with a discussion of the recent advancements and future research challenges in this field, aiming to provide valuable insights for researchers in the related domains.

Many evaluation metrics can be used to assess the performance of models in binary classification tasks. However, most of them are derived from a confusion matrix in a non-differentiable form, making it very difficult to generate a differentiable loss function that could directly optimize them. The lack of solutions to bridge this challenge not only hinders our ability to solve difficult tasks, such as imbalanced learning, but also requires the deployment of computationally expensive hyperparameter search processes in model selection. In this paper, we propose a general-purpose approach that transforms any confusion matrix-based metric into a loss function, AnyLoss, that is available in optimization processes. To this end, we use an approximation function to make a confusion matrix represented in a differentiable form, and this approach enables any confusion matrix-based metric to be directly used as a loss function. The mechanism of the approximation function is provided to ensure its operability and the differentiability of our loss functions is proved by suggesting their derivatives. We conduct extensive experiments under diverse neural networks with many datasets, and we demonstrate their general availability to target any confusion matrix-based metrics. Our method, especially, shows outstanding achievements in dealing with imbalanced datasets, and its competitive learning speed, compared to multiple baseline models, underscores its efficiency.

Empirical risk minimization (ERM) with a computationally feasible surrogate loss is a widely accepted approach for classification. Notably, the convexity and calibration (CC) properties of a loss function ensure consistency of ERM in maximizing accuracy, thereby offering a wide range of options for surrogate losses. In this article, we propose a novel ensemble method, namely EnsLoss, which extends the ensemble learning concept to combine loss functions within the ERM framework. A key feature of our method is the consideration on preserving the "legitimacy" of the combined losses, i.e., ensuring the CC properties. Specifically, we first transform the CC conditions of losses into loss-derivatives, thereby bypassing the need for explicit loss functions and directly generating calibrated loss-derivatives. Therefore, inspired by Dropout, EnsLoss enables loss ensembles through one training process with doubly stochastic gradient descent (i.e., random batch samples and random calibrated loss-derivatives). We theoretically establish the statistical consistency of our approach and provide insights into its benefits. The numerical effectiveness of EnsLoss compared to fixed loss methods is demonstrated through experiments on a broad range of 14 OpenML tabular datasets and 46 image datasets with various deep learning architectures. Python repository and source code are available on GitHub at https://github.com/statmlben/ensloss.

Semi-supervised learning based methods are current SOTA solutions to the noisy-label learning problem, which rely on learning an unsupervised label cleaner first to divide the training samples into a labeled set for clean data and an unlabeled set for noise data. Typically, the cleaner is obtained via fitting a mixture model to the distribution of per-sample training losses. However, the modeling procedure is class agnostic and assumes the loss distributions of clean and noise samples are the same across different classes. Unfortunately, in practice, such an assumption does not always hold due to the varying learning difficulty of different classes, thus leading to sub-optimal label noise partition criteria. In this work, we reveal this long-ignored problem and propose a simple yet effective solution, named Class Prototype-based label noise Cleaner (CPC). Unlike previous works treating all the classes equally, CPC fully considers loss distribution heterogeneity and applies class-aware modulation to partition the clean and noise data. CPC takes advantage of loss distribution modeling and intra-class consistency regularization in feature space simultaneously and thus can better distinguish clean and noise labels. We theoretically justify the effectiveness of our method by explaining it from the Expectation-Maximization (EM) framework. Extensive experiments are conducted on the noisy-label benchmarks CIFAR-10, CIFAR-100, Clothing1M and WebVision. The results show that CPC consistently brings about performance improvement across all benchmarks. Codes and pre-trained models will be released at https://github.com/hjjpku/CPC.git.

We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.

In this study, we dive deep into the inconsistency of pseudo targets in semi-supervised object detection (SSOD). Our core observation is that the oscillating pseudo-targets undermine the training of an accurate detector. It injects noise into the student's training, leading to severe overfitting problems. Therefore, we propose a systematic solution, termed ConsistentTeacher, to reduce the inconsistency. First, adaptive anchor assignment~(ASA) substitutes the static IoU-based strategy, which enables the student network to be resistant to noisy pseudo-bounding boxes. Then we calibrate the subtask predictions by designing a 3D feature alignment module~(FAM-3D). It allows each classification feature to adaptively query the optimal feature vector for the regression task at arbitrary scales and locations. Lastly, a Gaussian Mixture Model (GMM) dynamically revises the score threshold of pseudo-bboxes, which stabilizes the number of ground truths at an early stage and remedies the unreliable supervision signal during training. ConsistentTeacher provides strong results on a large range of SSOD evaluations. It achieves 40.0 mAP with ResNet-50 backbone given only 10% of annotated MS-COCO data, which surpasses previous baselines using pseudo labels by around 3 mAP. When trained on fully annotated MS-COCO with additional unlabeled data, the performance further increases to 47.7 mAP. Our code is available at https://github.com/Adamdad/ConsistentTeacher.

Face recognition technology has become an integral part of modern security systems and user authentication processes. However, these systems are vulnerable to spoofing attacks and can easily be circumvented. Most prior research in face anti-spoofing (FAS) approaches it as a two-class classification task where models are trained on real samples and known spoof attacks and tested for detection performance on unknown spoof attacks. However, in practice, FAS should be treated as a one-class classification task where, while training, one cannot assume any knowledge regarding the spoof samples a priori. In this paper, we reformulate the face anti-spoofing task from a one-class perspective and propose a novel hyperbolic one-class classification framework. To train our network, we use a pseudo-negative class sampled from the Gaussian distribution with a weighted running mean and propose two novel loss functions: (1) Hyp-PC: Hyperbolic Pairwise Confusion loss, and (2) Hyp-CE: Hyperbolic Cross Entropy loss, which operate in the hyperbolic space. Additionally, we employ Euclidean feature clipping and gradient clipping to stabilize the training in the hyperbolic space. To the best of our knowledge, this is the first work extending hyperbolic embeddings for face anti-spoofing in a one-class manner. With extensive experiments on five benchmark datasets: Rose-Youtu, MSU-MFSD, CASIA-MFSD, Idiap Replay-Attack, and OULU-NPU, we demonstrate that our method significantly outperforms the state-of-the-art, achieving better spoof detection performance.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

Conditional contrastive learning frameworks consider the conditional sampling procedure that constructs positive or negative data pairs conditioned on specific variables. Fair contrastive learning constructs negative pairs, for example, from the same gender (conditioning on sensitive information), which in turn reduces undesirable information from the learned representations; weakly supervised contrastive learning constructs positive pairs with similar annotative attributes (conditioning on auxiliary information), which in turn are incorporated into the representations. Although conditional contrastive learning enables many applications, the conditional sampling procedure can be challenging if we cannot obtain sufficient data pairs for some values of the conditioning variable. This paper presents Conditional Contrastive Learning with Kernel (CCL-K) that converts existing conditional contrastive objectives into alternative forms that mitigate the insufficient data problem. Instead of sampling data according to the value of the conditioning variable, CCL-K uses the Kernel Conditional Embedding Operator that samples data from all available data and assigns weights to each sampled data given the kernel similarity between the values of the conditioning variable. We conduct experiments using weakly supervised, fair, and hard negatives contrastive learning, showing CCL-K outperforms state-of-the-art baselines.

With the rapid advancement of Multi-modal Large Language Models (MLLMs), MLLM-based Image Quality Assessment (IQA) methods have shown promising performance in linguistic quality description. However, current methods still fall short in accurately scoring image quality. In this work, we aim to leverage MLLMs to regress accurate quality scores. A key challenge is that the quality score is inherently continuous, typically modeled as a Gaussian distribution, whereas MLLMs generate discrete token outputs. This mismatch necessitates score discretization. Previous approaches discretize the mean score into a one-hot label, resulting in information loss and failing to capture inter-image relationships. We propose a distribution-based approach that discretizes the score distribution into a soft label. This method preserves the characteristics of the score distribution, achieving high accuracy and maintaining inter-image relationships. Moreover, to address dataset variation, where different IQA datasets exhibit various distributions, we introduce a fidelity loss based on Thurstone's model. This loss captures intra-dataset relationships, facilitating co-training across multiple IQA datasets. With these designs, we develop the distribution-based Depicted image Quality Assessment model for Score regression (DeQA-Score). Experiments across multiple benchmarks show that DeQA-Score stably outperforms baselines in score regression. Also, DeQA-Score can predict the score distribution that closely aligns with human annotations. Codes and model weights have been released in https://depictqa.github.io/deqa-score/.

Training vision-language models (VLMs) for medical report generation is often hindered by the scarcity of high-quality annotated data. This work evaluates the use of a weighted loss function to improve data efficiency. Compared to standard cross-entropy loss, which treats all token prediction errors equally, the reweighted loss shifts the focus to semantically salient tokens with outsized clinical importance. In experiments on ophthalmological report generation, we show that this simple method improves efficiency across multiple data scales, achieving similar report quality with up to ten times less training data.

In this paper, we introduce fastHDMI, a Python package designed for efficient variable screening in high-dimensional datasets, particularly neuroimaging data. This work pioneers the application of three mutual information estimation methods for neuroimaging variable selection, a novel approach implemented via fastHDMI. These advancements enhance our ability to analyze the complex structures of neuroimaging datasets, providing improved tools for variable selection in high-dimensional spaces. Using the preprocessed ABIDE dataset, we evaluate the performance of these methods through extensive simulations. The tests cover a range of conditions, including linear and nonlinear associations, as well as continuous and binary outcomes. Our results highlight the superiority of the FFTKDE-based mutual information estimation for feature screening in continuous nonlinear outcomes, while binning-based methods outperform others for binary outcomes with nonlinear probability preimages. For linear simulations, both Pearson correlation and FFTKDE-based methods show comparable performance for continuous outcomes, while Pearson excels in binary outcomes with linear probability preimages. A comprehensive case study using the ABIDE dataset further demonstrates fastHDMI's practical utility, showcasing the predictive power of models built from variables selected using our screening techniques. This research affirms the computational efficiency and methodological strength of fastHDMI, significantly enriching the toolkit available for neuroimaging analysis.

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying commercial image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Extensive experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

The recent success of SimCSE has greatly advanced state-of-the-art sentence representations. However, the original formulation of SimCSE does not fully exploit the potential of hard negative samples in contrastive learning. This study introduces an unsupervised contrastive learning framework that combines SimCSE with hard negative mining, aiming to enhance the quality of sentence embeddings. The proposed focal-InfoNCE function introduces self-paced modulation terms in the contrastive objective, downweighting the loss associated with easy negatives and encouraging the model focusing on hard negatives. Experimentation on various STS benchmarks shows that our method improves sentence embeddings in terms of Spearman's correlation and representation alignment and uniformity.

This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with different labels are negatively correlated. Our analysis shows that, during the early phase of training, neurons in the first layer try to align with either the positive data or the negative data, depending on its corresponding weight on the second layer. A careful analysis of the neurons' directional dynamics allows us to provide an O(log n{mu}) upper bound on the time it takes for all neurons to achieve good alignment with the input data, where n is the number of data points and mu measures how well the data are separated. After the early alignment phase, the loss converges to zero at a O(1{t}) rate, and the weight matrix on the first layer is approximately low-rank. Numerical experiments on the MNIST dataset illustrate our theoretical findings.

Loss reweighting has shown significant benefits for machine unlearning with large language models (LLMs). However, their exact functionalities are left unclear and the optimal strategy remains an open question, thus impeding the understanding and improvement of existing methodologies. In this paper, we identify two distinct goals of loss reweighting, namely, Saturation and Importance -- the former indicates that those insufficiently optimized data should be emphasized, while the latter stresses some critical data that are most influential for loss minimization. To study their usefulness, we design specific reweighting strategies for each goal and evaluate their respective effects on unlearning. We conduct extensive empirical analyses on well-established benchmarks, and summarize some important observations as follows: (i) Saturation enhances efficacy more than importance-based reweighting, and their combination can yield additional improvements. (ii) Saturation typically allocates lower weights to data with lower likelihoods, whereas importance-based reweighting does the opposite. (iii) The efficacy of unlearning is also largely influenced by the smoothness and granularity of the weight distributions. Based on these findings, we propose SatImp, a simple reweighting method that combines the advantages of both saturation and importance. Empirical results on extensive datasets validate the efficacy of our method, potentially bridging existing research gaps and indicating directions for future research. Our code is available at https://github.com/tmlr-group/SatImp.

We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods.

Recent advances in diffusion models bring state-of-the-art performance on image generation tasks. However, empirical results from previous research in diffusion models imply an inverse correlation between density estimation and sample generation performances. This paper investigates with sufficient empirical evidence that such inverse correlation happens because density estimation is significantly contributed by small diffusion time, whereas sample generation mainly depends on large diffusion time. However, training a score network well across the entire diffusion time is demanding because the loss scale is significantly imbalanced at each diffusion time. For successful training, therefore, we introduce Soft Truncation, a universally applicable training technique for diffusion models, that softens the fixed and static truncation hyperparameter into a random variable. In experiments, Soft Truncation achieves state-of-the-art performance on CIFAR-10, CelebA, CelebA-HQ 256x256, and STL-10 datasets.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

Deep neural networks have demonstrated remarkable performance across numerous learning tasks but often suffer from miscalibration, resulting in unreliable probability outputs. This has inspired many recent works on mitigating miscalibration, particularly through post-hoc recalibration methods that aim to obtain calibrated probabilities without sacrificing the classification performance of pre-trained models. In this study, we summarize and categorize previous works into three general strategies: intuitively designed methods, binning-based methods, and methods based on formulations of ideal calibration. Through theoretical and practical analysis, we highlight ten common limitations in previous approaches. To address these limitations, we propose a probabilistic learning framework for calibration called h-calibration, which theoretically constructs an equivalent learning formulation for canonical calibration with boundedness. On this basis, we design a simple yet effective post-hoc calibration algorithm. Our method not only overcomes the ten identified limitations but also achieves markedly better performance than traditional methods, as validated by extensive experiments. We further analyze, both theoretically and experimentally, the relationship and advantages of our learning objective compared to traditional proper scoring rule. In summary, our probabilistic framework derives an approximately equivalent differentiable objective for learning error-bounded calibrated probabilities, elucidating the correspondence and convergence properties of computational statistics with respect to theoretical bounds in canonical calibration. The theoretical effectiveness is verified on standard post-hoc calibration benchmarks by achieving state-of-the-art performance. This research offers valuable reference for learning reliable likelihood in related fields.

Exemplar-free class-incremental learning (EFCIL) presents a significant challenge as the old class samples are absent for new task learning. Due to the severe imbalance between old and new class samples, the learned classifiers can be easily biased toward the new ones. Moreover, continually updating the feature extractor under EFCIL can compromise the discriminative power of old class features, e.g., leading to less compact and more overlapping distributions across classes. Existing methods mainly focus on handling biased classifier learning. In this work, both cases are considered using the proposed method. Specifically, we first introduce a Distribution-Based Global Classifier (DBGC) to avoid bias factors in existing methods, such as data imbalance and sampling. More importantly, the compromised distributions of old classes are simulated via a simple operation, variance enlarging (VE). Incorporating VE based on DBGC results in a novel classification loss for EFCIL. This loss is proven equivalent to an Adaptive Margin Softmax Cross Entropy (AMarX). The proposed method is thus called Adaptive Margin Global Classifier (AMGC). AMGC is simple yet effective. Extensive experiments show that AMGC achieves superior image classification results on its own under a challenging EFCIL setting. Detailed analysis is also provided for further demonstration.

We introduce a novel and general loss function, called Symmetric Contrastive (Sy-CON) loss, for effective continual self-supervised learning (CSSL). We first argue that the conventional loss form of continual learning which consists of single task-specific loss (for plasticity) and a regularizer (for stability) may not be ideal for contrastive loss based CSSL that focus on representation learning. Our reasoning is that, in contrastive learning based methods, the task-specific loss would suffer from decreasing diversity of negative samples and the regularizer may hinder learning new distinctive representations. To that end, we propose Sy-CON that consists of two losses (one for plasticity and the other for stability) with symmetric dependence on current and past models' negative sample embeddings. We argue our model can naturally find good trade-off between the plasticity and stability without any explicit hyperparameter tuning. We validate the effectiveness of our approach through extensive experiments, demonstrating that MoCo-based implementation of Sy-CON loss achieves superior performance compared to other state-of-the-art CSSL methods.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

The task of abductive natural language inference (nli), to decide which hypothesis is the more likely explanation for a set of observations, is a particularly difficult type of NLI. Instead of just determining a causal relationship, it requires common sense to also evaluate how reasonable an explanation is. All recent competitive systems build on top of contextualized representations and make use of transformer architectures for learning an NLI model. When somebody is faced with a particular NLI task, they need to select the best model that is available. This is a time-consuming and resource-intense endeavour. To solve this practical problem, we propose a simple method for predicting the performance without actually fine-tuning the model. We do this by testing how well the pre-trained models perform on the nli task when just comparing sentence embeddings with cosine similarity to what the performance that is achieved when training a classifier on top of these embeddings. We show that the accuracy of the cosine similarity approach correlates strongly with the accuracy of the classification approach with a Pearson correlation coefficient of 0.65. Since the similarity computation is orders of magnitude faster to compute on a given dataset (less than a minute vs. hours), our method can lead to significant time savings in the process of model selection.

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering -- i.e., deep constrained clustering (DCC) -- has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under unknown annotation confusions, the data membership can still be provably identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.

In semantic segmentation, the accuracy of models heavily depends on the high-quality annotations. However, in many practical scenarios such as medical imaging and remote sensing, obtaining true annotations is not straightforward and usually requires significant human labor. Relying on human labor often introduces annotation errors, including mislabeling, omissions, and inconsistency between annotators. In the case of remote sensing, differences in procurement time can lead to misaligned ground truth annotations. These label errors are not independently distributed, and instead usually appear in spatially connected regions where adjacent pixels are more likely to share the same errors. To address these issues, we propose an approximate Bayesian estimation based on a probabilistic model that assumes training data includes label errors, incorporating the tendency for these errors to occur with spatial correlations between adjacent pixels. Bayesian inference requires computing the posterior distribution of label errors, which becomes intractable when spatial correlations are present. We represent the correlation of label errors between adjacent pixels through a Gaussian distribution whose covariance is structured by a Kac-Murdock-Szeg\"{o} (KMS) matrix, solving the computational challenges. Through experiments on multiple segmentation tasks, we confirm that leveraging the spatial correlation of label errors significantly improves performance. Notably, in specific tasks such as lung segmentation, the proposed method achieves performance comparable to training with clean labels under moderate noise levels. Code is available at https://github.com/pfnet-research/Bayesian_SpatialCorr.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

Most of the current self-supervised representation learning (SSL) methods are based on the contrastive loss and the instance-discrimination task, where augmented versions of the same image instance ("positives") are contrasted with instances extracted from other images ("negatives"). For the learning to be effective, many negatives should be compared with a positive pair, which is computationally demanding. In this paper, we propose a different direction and a new loss function for SSL, which is based on the whitening of the latent-space features. The whitening operation has a "scattering" effect on the batch samples, avoiding degenerate solutions where all the sample representations collapse to a single point. Our solution does not require asymmetric networks and it is conceptually simple. Moreover, since negatives are not needed, we can extract multiple positive pairs from the same image instance. The source code of the method and of all the experiments is available at: https://github.com/htdt/self-supervised.

State-of-the-art natural language processing (NLP) models often learn to model dataset biases and surface form correlations instead of features that target the intended underlying task. Previous work has demonstrated effective methods to circumvent these issues when knowledge of the bias is available. We consider cases where the bias issues may not be explicitly identified, and show a method for training models that learn to ignore these problematic correlations. Our approach relies on the observation that models with limited capacity primarily learn to exploit biases in the dataset. We can leverage the errors of such limited capacity models to train a more robust model in a product of experts, thus bypassing the need to hand-craft a biased model. We show the effectiveness of this method to retain improvements in out-of-distribution settings even if no particular bias is targeted by the biased model.

Due to the difficulty of collecting exhaustive multi-label annotations, multi-label datasets often contain partial labels. We consider an extreme of this weakly supervised learning problem, called single positive multi-label learning (SPML), where each multi-label training image has only one positive label. Traditionally, all unannotated labels are assumed as negative labels in SPML, which introduces false negative labels and causes model training to be dominated by assumed negative labels. In this work, we choose to treat all unannotated labels from an alternative perspective, i.e. acknowledging they are unknown. Hence, we propose entropy-maximization (EM) loss to attain a special gradient regime for providing proper supervision signals. Moreover, we propose asymmetric pseudo-labeling (APL), which adopts asymmetric-tolerance strategies and a self-paced procedure, to cooperate with EM loss and then provide more precise supervision. Experiments show that our method significantly improves performance and achieves state-of-the-art results on all four benchmarks. Code is available at https://github.com/Correr-Zhou/SPML-AckTheUnknown.

We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules.

In self-supervised learning, a system is tasked with achieving a surrogate objective by defining alternative targets on a set of unlabeled data. The aim is to build useful representations that can be used in downstream tasks, without costly manual annotation. In this work, we propose a novel self-supervised formulation of relational reasoning that allows a learner to bootstrap a signal from information implicit in unlabeled data. Training a relation head to discriminate how entities relate to themselves (intra-reasoning) and other entities (inter-reasoning), results in rich and descriptive representations in the underlying neural network backbone, which can be used in downstream tasks such as classification and image retrieval. We evaluate the proposed method following a rigorous experimental procedure, using standard datasets, protocols, and backbones. Self-supervised relational reasoning outperforms the best competitor in all conditions by an average 14% in accuracy, and the most recent state-of-the-art model by 3%. We link the effectiveness of the method to the maximization of a Bernoulli log-likelihood, which can be considered as a proxy for maximizing the mutual information, resulting in a more efficient objective with respect to the commonly used contrastive losses.

A novel gradient boosting framework is proposed where shallow neural networks are employed as ``weak learners''. General loss functions are considered under this unified framework with specific examples presented for classification, regression, and learning to rank. A fully corrective step is incorporated to remedy the pitfall of greedy function approximation of classic gradient boosting decision tree. The proposed model rendered outperforming results against state-of-the-art boosting methods in all three tasks on multiple datasets. An ablation study is performed to shed light on the effect of each model components and model hyperparameters.

In dense retrieval, effective training hinges on selecting high quality hard negatives while avoiding false negatives. Recent methods apply heuristics based on positive document scores to identify hard negatives, improving both performance and interpretability. However, these global, example agnostic strategies often miss instance specific false negatives. To address this, we propose a learnable adapter module that monitors Bi-Encoder representations to estimate the likelihood that a hard negative is actually a false negative. This probability is modeled dynamically and contextually, enabling fine-grained, query specific judgments. The predicted scores are used in two downstream components: (1) resampling, where negatives are reweighted during training, and (2) reranking, where top-k retrieved documents are reordered at inference. Empirical results on standard benchmarks show that our adapter-enhanced framework consistently outperforms strong Bi-Encoder baselines, underscoring the benefit of explicit false negative modeling in dense retrieval.

The generalization performance of a machine learning algorithm such as a neural network depends in a non-trivial way on the structure of the data distribution. To analyze the influence of data structure on test loss dynamics, we study an exactly solveable model of stochastic gradient descent (SGD) on mean square loss which predicts test loss when training on features with arbitrary covariance structure. We solve the theory exactly for both Gaussian features and arbitrary features and we show that the simpler Gaussian model accurately predicts test loss of nonlinear random-feature models and deep neural networks trained with SGD on real datasets such as MNIST and CIFAR-10. We show that the optimal batch size at a fixed compute budget is typically small and depends on the feature correlation structure, demonstrating the computational benefits of SGD with small batch sizes. Lastly, we extend our theory to the more usual setting of stochastic gradient descent on a fixed subsampled training set, showing that both training and test error can be accurately predicted in our framework on real data.

Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder varphi^* that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder Phi^*_tau. We prove that non-commutativity steers the optimization towards Phi^*_tau instead of varphi^*, bringing the H-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning Phi^*_tau, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over 2%, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.

A large-scale image-text pair dataset has greatly contributed to the development of vision-language pre-training (VLP) models, which enable zero-shot or few-shot classification without costly annotation. However, in the medical domain, the scarcity of data remains a significant challenge for developing a powerful VLP model. In this paper, we tackle the lack of image-text data in chest X-ray by expanding image-label pair as image-text pair via general prompt and utilizing multiple images and multiple sections in a radiologic report. We also design two contrastive losses, named ICL and TCL, for learning study-level characteristics of medical images and reports, respectively. Our model outperforms the state-of-the-art models trained under the same conditions. Also, enlarged dataset improve the discriminative power of our pre-trained model for classification, while sacrificing marginal retrieval performance. Code is available at https://github.com/kakaobrain/cxr-clip.

Learning with few samples is a major challenge for parameter-rich models like deep networks. In contrast, people learn complex new concepts even from very few examples, suggesting that the sample complexity of learning can often be reduced. Many approaches to few-shot learning build on transferring a representation from well-sampled classes, or using meta learning to favor architectures that can learn with few samples. Unfortunately, such approaches often struggle when learning in an online way or with non-stationary data streams. Here we describe a new approach to learn with fewer samples, by using additional information that is provided per sample. Specifically, we show how the sample complexity can be reduced by providing semantic information about the relevance of features per sample, like information about the presence of objects in a scene or confidence of detecting attributes in an image. We provide an improved generalization error bound for this case. We cast the problem of using per-sample feature relevance by using a new ellipsoid-margin loss, and develop an online algorithm that minimizes this loss effectively. Empirical evaluation on two machine vision benchmarks for scene classification and fine-grain bird classification demonstrate the benefits of this approach for few-shot learning.

Learning representations that are useful for unknown downstream tasks is a fundamental challenge in representation learning. Prominent approaches in this domain include contrastive learning, self-supervised masking, and denoising auto-encoders. In this paper, we introduce a novel method, termed contrastive Mutual Information Machine (cMIM), which aims to enhance the utility of learned representations for downstream tasks. cMIM integrates a new contrastive learning loss with the Mutual Information Machine (MIM) learning framework, a probabilistic auto-encoder that maximizes the mutual information between inputs and latent representations while clustering the latent codes. Despite MIM's potential, initial experiments indicated that the representations learned by MIM were less effective for discriminative downstream tasks compared to state-of-the-art (SOTA) models. The proposed cMIM method directly addresses this limitation. The main contributions of this work are twofold: (1) We propose a novel contrastive extension to MIM for learning discriminative representations which eliminates the need for data augmentation and is robust to variations in the number of negative examples (i.e., batch size). (2) We introduce a generic method for extracting informative embeddings from encoder-decoder models, which significantly improves performance in discriminative downstream tasks without requiring additional training. This method is applicable to any pre-trained encoder-decoder model. By presenting cMIM, we aim to offer a unified generative model that is effective for both generative and discriminative tasks. Our results demonstrate that the learned representations are valuable for downstream tasks while maintaining the generative capabilities of MIM.

Humans recognize anomalies through two aspects: larger patch-wise representation discrepancies and weaker patch-to-normal-patch correlations. However, the previous AD methods didn't sufficiently combine the two complementary aspects to design AD models. To this end, we find that Transformer can ideally satisfy the two aspects as its great power in the unified modeling of patch-wise representations and patch-to-patch correlations. In this paper, we propose a novel AD framework: FOcus-the-Discrepancy (FOD), which can simultaneously spot the patch-wise, intra- and inter-discrepancies of anomalies. The major characteristic of our method is that we renovate the self-attention maps in transformers to Intra-Inter-Correlation (I2Correlation). The I2Correlation contains a two-branch structure to first explicitly establish intra- and inter-image correlations, and then fuses the features of two-branch to spotlight the abnormal patterns. To learn the intra- and inter-correlations adaptively, we propose the RBF-kernel-based target-correlations as learning targets for self-supervised learning. Besides, we introduce an entropy constraint strategy to solve the mode collapse issue in optimization and further amplify the normal-abnormal distinguishability. Extensive experiments on three unsupervised real-world AD benchmarks show the superior performance of our approach. Code will be available at https://github.com/xcyao00/FOD.

We propose that the grokking phenomenon, where the train loss of a neural network decreases much earlier than its test loss, can arise due to a neural network transitioning from lazy training dynamics to a rich, feature learning regime. To illustrate this mechanism, we study the simple setting of vanilla gradient descent on a polynomial regression problem with a two layer neural network which exhibits grokking without regularization in a way that cannot be explained by existing theories. We identify sufficient statistics for the test loss of such a network, and tracking these over training reveals that grokking arises in this setting when the network first attempts to fit a kernel regression solution with its initial features, followed by late-time feature learning where a generalizing solution is identified after train loss is already low. We provide an asymptotic theoretical description of the grokking dynamics in this model using dynamical mean field theory (DMFT) for high dimensional data. We find that the key determinants of grokking are the rate of feature learning -- which can be controlled precisely by parameters that scale the network output -- and the alignment of the initial features with the target function y(x). We argue this delayed generalization arises when (1) the top eigenvectors of the initial neural tangent kernel and the task labels y(x) are misaligned, but (2) the dataset size is large enough so that it is possible for the network to generalize eventually, but not so large that train loss perfectly tracks test loss at all epochs, and (3) the network begins training in the lazy regime so does not learn features immediately. We conclude with evidence that this transition from lazy (linear model) to rich training (feature learning) can control grokking in more general settings, like on MNIST, one-layer Transformers, and student-teacher networks.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

We propose sparsemax, a new activation function similar to the traditional softmax, but able to output sparse probabilities. After deriving its properties, we show how its Jacobian can be efficiently computed, enabling its use in a network trained with backpropagation. Then, we propose a new smooth and convex loss function which is the sparsemax analogue of the logistic loss. We reveal an unexpected connection between this new loss and the Huber classification loss. We obtain promising empirical results in multi-label classification problems and in attention-based neural networks for natural language inference. For the latter, we achieve a similar performance as the traditional softmax, but with a selective, more compact, attention focus.

Learning from label proportions (LLP) is a promising weakly supervised learning problem. In LLP, a set of instances (bag) has label proportions, but no instance-level labels are given. LLP aims to train an instance-level classifier by using the label proportions of the bag. In this paper, we propose a bag-level data augmentation method for LLP called MixBag, based on the key observation from our preliminary experiments; that the instance-level classification accuracy improves as the number of labeled bags increases even though the total number of instances is fixed. We also propose a confidence interval loss designed based on statistical theory to use the augmented bags effectively. To the best of our knowledge, this is the first attempt to propose bag-level data augmentation for LLP. The advantage of MixBag is that it can be applied to instance-level data augmentation techniques and any LLP method that uses the proportion loss. Experimental results demonstrate this advantage and the effectiveness of our method.

Language models have recently been shown capable of performing regression tasks wherein numeric predictions are represented as decoded strings. In this work, we provide theoretical grounds for this capability and furthermore investigate the utility of causal auto-regressive sequence models when they are applied to any feature representation. We find that, despite being trained in the usual way - for next-token prediction via cross-entropy loss - decoding-based regression is as performant as traditional approaches for tabular regression tasks, while being flexible enough to capture arbitrary distributions, such as in the task of density estimation.

Models driven by spurious correlations often yield poor generalization performance. We propose the counterfactual (CF) alignment method to detect and quantify spurious correlations of black box classifiers. Our methodology is based on counterfactual images generated with respect to one classifier being input into other classifiers to see if they also induce changes in the outputs of these classifiers. The relationship between these responses can be quantified and used to identify specific instances where a spurious correlation exists. This is validated by observing intuitive trends in face-attribute and waterbird classifiers, as well as by fabricating spurious correlations and detecting their presence, both visually and quantitatively. Furthermore, utilizing the CF alignment method, we demonstrate that we can evaluate robust optimization methods (GroupDRO, JTT, and FLAC) by detecting a reduction in spurious correlations.

We systematically study antithetic initial noise in diffusion models, discovering that pairing each noise sample with its negation consistently produces strong negative correlation. This universal phenomenon holds across datasets, model architectures, conditional and unconditional sampling, and even other generative models such as VAEs and Normalizing Flows. To explain it, we combine experiments and theory and propose a symmetry conjecture that the learned score function is approximately affine antisymmetric (odd symmetry up to a constant shift), supported by empirical evidence. This negative correlation leads to substantially more reliable uncertainty quantification with up to 90% narrower confidence intervals. We demonstrate these gains on tasks including estimating pixel-wise statistics and evaluating diffusion inverse solvers. We also provide extensions with randomized quasi-Monte Carlo noise designs for uncertainty quantification, and explore additional applications of the antithetic noise design to improve image editing and generation diversity. Our framework is training-free, model-agnostic, and adds no runtime overhead. Code is available at https://github.com/jjia131/Antithetic-Noise-in-Diffusion-Models-page.

Addressing imbalanced or long-tailed data is a major challenge in visual recognition tasks due to disparities between training and testing distributions and issues with data noise. We propose the Wrapped Cauchy Distributed Angular Softmax (WCDAS), a novel softmax function that incorporates data-wise Gaussian-based kernels into the angular correlation between feature representations and classifier weights, effectively mitigating noise and sparse sampling concerns. The class-wise distribution of angular representation becomes a sum of these kernels. Our theoretical analysis reveals that the wrapped Cauchy distribution excels the Gaussian distribution in approximating mixed distributions. Additionally, WCDAS uses trainable concentration parameters to dynamically adjust the compactness and margin of each class. Empirical results confirm label-aware behavior in these parameters and demonstrate WCDAS's superiority over other state-of-the-art softmax-based methods in handling long-tailed visual recognition across multiple benchmark datasets. The code is public available.

Aiming to generalize the label knowledge from a source domain with continuous outputs to an unlabeled target domain, Domain Adaptation Regression (DAR) is developed for complex practical learning problems. However, due to the continuity problem in regression, existing conditional distribution alignment theory and methods with discrete prior, which are proven to be effective in classification settings, are no longer applicable. In this work, focusing on the feasibility problems in DAR, we establish the sufficiency theory for the regression model, which shows the generalization error can be sufficiently dominated by the cross-domain conditional discrepancy. Further, to characterize conditional discrepancy with continuous conditioning variable, a novel Conditional Operator Discrepancy (COD) is proposed, which admits the metric property on conditional distributions via the kernel embedding theory. Finally, to minimize the discrepancy, a COD-based conditional invariant representation learning model is proposed, and the reformulation is derived to show that reasonable modifications on moment statistics can further improve the discriminability of the adaptation model. Extensive experiments on standard DAR datasets verify the validity of theoretical results and the superiority over SOTA DAR methods.

In this paper, we consider a problem of self-supervised learning for small-scale datasets based on contrastive loss between multiple views of the data, which demonstrates the state-of-the-art performance in classification task. Despite the reported results, such factors as the complexity of training requiring complex architectures, the needed number of views produced by data augmentation, and their impact on the classification accuracy are understudied problems. To establish the role of these factors, we consider an architecture of contrastive loss system such as SimCLR, where baseline model is replaced by geometrically invariant "hand-crafted" network ScatNet with small trainable adapter network and argue that the number of parameters of the whole system and the number of views can be considerably reduced while practically preserving the same classification accuracy. In addition, we investigate the impact of regularization strategies using pretext task learning based on an estimation of parameters of augmentation transform such as rotation and jigsaw permutation for both traditional baseline models and ScatNet based models. Finally, we demonstrate that the proposed architecture with pretext task learning regularization achieves the state-of-the-art classification performance with a smaller number of trainable parameters and with reduced number of views.

Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open issue. With a few exceptions, deep neural networks (DNNs) have seldom been applied to density estimation, mostly due to the unsupervised nature of the estimation task, and (especially) due to the need for constrained training algorithms that ended up realizing proper probabilistic models that satisfy Kolmogorov's axioms. Moreover, in spite of the well-known improvement in terms of modeling capabilities yielded by mixture models over plain single-density statistical estimators, no proper mixtures of multivariate DNN-based component densities have been investigated so far. The paper fills this gap by extending our previous work on Neural Mixture Densities (NMMs) to multivariate DNN mixtures. A maximum-likelihood (ML) algorithm for estimating Deep NMMs (DNMMs) is handed out, which satisfies numerically a combination of hard and soft constraints aimed at ensuring satisfaction of Kolmogorov's axioms. The class of probability density functions that can be modeled to any degree of precision via DNMMs is formally defined. A procedure for the automatic selection of the DNMM architecture, as well as of the hyperparameters for its ML training algorithm, is presented (exploiting the probabilistic nature of the DNMM). Experimental results on univariate and multivariate data are reported on, corroborating the effectiveness of the approach and its superiority to the most popular statistical estimation techniques.

When training or evaluating deep learning models, two essential parts are picking the proper loss function and deciding on performance metrics. In this paper, we provide a comprehensive overview of the most common loss functions and metrics used across many different types of deep learning tasks, from general tasks such as regression and classification to more specific tasks in Computer Vision and Natural Language Processing. We introduce the formula for each loss and metric, discuss their strengths and limitations, and describe how these methods can be applied to various problems within deep learning. This work can serve as a reference for researchers and practitioners in the field, helping them make informed decisions when selecting the most appropriate loss function and performance metrics for their deep learning projects.

Supervised learning of image classifiers distills human knowledge into a parametric model through pairs of images and corresponding labels (X,Y). We argue that this simple and widely used representation of human knowledge neglects rich auxiliary information from the annotation procedure, such as the time-series of mouse traces and clicks left after image selection. Our insight is that such annotation byproducts Z provide approximate human attention that weakly guides the model to focus on the foreground cues, reducing spurious correlations and discouraging shortcut learning. To verify this, we create ImageNet-AB and COCO-AB. They are ImageNet and COCO training sets enriched with sample-wise annotation byproducts, collected by replicating the respective original annotation tasks. We refer to the new paradigm of training models with annotation byproducts as learning using annotation byproducts (LUAB). We show that a simple multitask loss for regressing Z together with Y already improves the generalisability and robustness of the learned models. Compared to the original supervised learning, LUAB does not require extra annotation costs. ImageNet-AB and COCO-AB are at https://github.com/naver-ai/NeglectedFreeLunch.

Unsupervised contrastive learning has achieved outstanding success, while the mechanism of contrastive loss has been less studied. In this paper, we concentrate on the understanding of the behaviours of unsupervised contrastive loss. We will show that the contrastive loss is a hardness-aware loss function, and the temperature {\tau} controls the strength of penalties on hard negative samples. The previous study has shown that uniformity is a key property of contrastive learning. We build relations between the uniformity and the temperature {\tau} . We will show that uniformity helps the contrastive learning to learn separable features, however excessive pursuit to the uniformity makes the contrastive loss not tolerant to semantically similar samples, which may break the underlying semantic structure and be harmful to the formation of features useful for downstream tasks. This is caused by the inherent defect of the instance discrimination objective. Specifically, instance discrimination objective tries to push all different instances apart, ignoring the underlying relations between samples. Pushing semantically consistent samples apart has no positive effect for acquiring a prior informative to general downstream tasks. A well-designed contrastive loss should have some extents of tolerance to the closeness of semantically similar samples. Therefore, we find that the contrastive loss meets a uniformity-tolerance dilemma, and a good choice of temperature can compromise these two properties properly to both learn separable features and tolerant to semantically similar samples, improving the feature qualities and the downstream performances.

Fine-tuned vision-language models (VLMs) often capture spurious correlations between image features and textual attributes, resulting in degraded zero-shot performance at test time. Existing approaches for addressing spurious correlations (i) primarily operate at the global image-level rather than intervening directly on fine-grained image features and (ii) are predominantly designed for unimodal settings. In this work, we present RaVL, which takes a fine-grained perspective on VLM robustness by discovering and mitigating spurious correlations using local image features rather than operating at the global image level. Given a fine-tuned VLM, RaVL first discovers spurious correlations by leveraging a region-level clustering approach to identify precise image features contributing to zero-shot classification errors. Then, RaVL mitigates the identified spurious correlation with a novel region-aware loss function that enables the VLM to focus on relevant regions and ignore spurious relationships during fine-tuning. We evaluate RaVL on 654 VLMs with various model architectures, data domains, and learned spurious correlations. Our results show that RaVL accurately discovers (191% improvement over the closest baseline) and mitigates (8.2% improvement on worst-group image classification accuracy) spurious correlations. Qualitative evaluations on general-domain and medical-domain VLMs confirm our findings.

Modern knowledge-intensive systems, such as retrieval-augmented generation (RAG), rely on effective retrievers to establish the performance ceiling for downstream modules. However, retriever training has been bottlenecked by sparse, single-positive annotations, which lead to false-negative noise and suboptimal supervision. While the advent of large language models (LLMs) makes it feasible to collect comprehensive multi-positive relevance labels at scale, the optimal strategy for incorporating these dense signals into training remains poorly understood. In this paper, we present a systematic study of multi-positive optimization objectives for retriever training. We unify representative objectives, including Joint Likelihood (JointLH), Summed Marginal Likelihood (SumMargLH), and Log-Sum-Exp Pairwise (LSEPair) loss, under a shared contrastive learning framework. Our theoretical analysis characterizes their distinct gradient behaviors, revealing how each allocates probability mass across positive document sets. Empirically, we conduct extensive evaluations on Natural Questions, MS MARCO, and the BEIR benchmark across two realistic regimes: homogeneous LLM-annotated data and heterogeneous mixtures of human and LLM labels. Our results show that LSEPair consistently achieves superior robustness and performance across settings, while JointLH and SumMargLH exhibit high sensitivity to the quality of positives. Furthermore, we find that the simple strategy of random sampling (Rand1LH) serves as a reliable baseline. By aligning theoretical insights with empirical findings, we provide practical design principles for leveraging dense, LLM-augmented supervision to enhance retriever effectiveness.

Model attributions are important in deep neural networks as they aid practitioners in understanding the models, but recent studies reveal that attributions can be easily perturbed by adding imperceptible noise to the input. The non-differentiable Kendall's rank correlation is a key performance index for attribution protection. In this paper, we first show that the expected Kendall's rank correlation is positively correlated to cosine similarity and then indicate that the direction of attribution is the key to attribution robustness. Based on these findings, we explore the vector space of attribution to explain the shortcomings of attribution defense methods using ell_p norm and propose integrated gradient regularizer (IGR), which maximizes the cosine similarity between natural and perturbed attributions. Our analysis further exposes that IGR encourages neurons with the same activation states for natural samples and the corresponding perturbed samples, which is shown to induce robustness to gradient-based attribution methods. Our experiments on different models and datasets confirm our analysis on attribution protection and demonstrate a decent improvement in adversarial robustness.