Deep learning has achieved great success in recent years thanks to the availability of high-quality, well-annotated training data. However, this requirement is often not met in real-world applications. Weakly supervised learning aims to train an accurate model with incomplete, inexact, or inaccurate supervision. In this chapter, we will discuss recent advances in this field, including new supervision paradigms, relaxed assumptions, and practical solutions. First, we introduce a new weakly supervised binary classification problem called confidence-difference classification and propose consistent approaches to solve it. Next, we investigate complementary-label learning, a weakly supervised multi-class classification problem. Our proposed approaches are based on more relaxed assumptions about the data generation process than existing consistent approaches. Lastly, we present an evaluation framework for partial-label learning, another popular multi-class weakly supervised learning problem, in order to promote fair and realistic evaluation of algorithms in this field.

Tunnel entrances and exits are widely recognized as safety-critical zones due to abrupt environmental transitions. However, most prior work examines single domains (e.g., spatial or lighting) and often assumes linear, additive effects, leaving mixed, non-linear and interactive association patterns insufficiently understood. To address this gap, this study proposes a comprehensive framework that couples a continuous Driving Safety Margin Index (DSMI) with mixed-exposure modelling. A naturalistic driving experiment with 35 drivers collected synchronized spatial proximity to the portal (distance-to-entrance/exit, DTE), driver-view relative luminance proxy, visual fixation intensity, and physiological load. DSMI was derived via fuzzy clustering of multi-channel vehicle control behaviors, yielding a continuous measure of instantaneous safety margin. Bayesian Kernel Machine Regression (BKMR) was applied to quantify joint, nonlinear and interactive effects of mixed exposures on DSMI, separately for entrances and exits. The results reveal pronounced entrance-exit asymmetry in model-estimated risk-related association patterns at tunnel portals. At entrances, the joint effect increases monotonically, suggesting a cumulative association pattern in which DTE and physiological load show stronger relevance. At exits, the joint effect follows a nonlinear inverted-U pattern: safety margin is highest under moderate exposure but decreases under both low and high stimulation. Exposure-response results suggest a role reversal of illuminance: excessive brightness is associated with lower DSMI at exits, whereas stronger fixation intensity is associated with larger safety margins. Model-estimated interaction patterns are largely additive or compensatory at entrances, whereas they appear more synergistic and potentially vulnerability-amplifying at exits. Overall, this study suggests that driving risk at tunnel portals is associated with complex, nonlinear, and asymmetric mixed-exposure patterns rather than single-factor associations. The framework advances tunnel safety research by linking a continuous safety margin to mixed exposures, informing differentiated entrance-exit design and traffic management.

Positive-Unlabeled (PU) learning aims to train a binary classifier (positive vs. negative) where only limited positive data and abundant unlabeled data are available. While widely applicable, state-of-the-art PU learning methods substantially underperform their supervised counterparts on complex datasets, especially without auxiliary negatives or pre-estimated parameters (e.g., a 14.26% gap on CIFAR-100 dataset). We identify the primary bottleneck as the challenge of learning discriminative representations under unreliable supervision. To tackle this challenge, we propose NcPU, a non-contrastive PU learning framework that requires no auxiliary information. NcPU combines a noisy-pair robust supervised non-contrastive loss (NoiSNCL), which aligns intra-class representations despite unreliable supervision, with a phantom label disambiguation (PLD) scheme that supplies conservative negative supervision via regret-based label updates. Theoretically, NoiSNCL and PLD can iteratively benefit each other from the perspective of the Expectation-Maximization framework. Empirically, extensive experiments demonstrate that: (1) NoiSNCL enables simple PU methods to achieve competitive performance; and (2) NcPU achieves substantial improvements over state-of-the-art PU methods across diverse datasets, including challenging datasets on post-disaster building damage mapping, highlighting its promise for real-world applications. Code: https://github.com/ICLR2026-285/NcPU.git.

Learning from Label Proportions (LLP) aims to use bags of instances associated with the proportions of each label within the bag to learn an instance-level classifier. Proportion matching is a widely used strategy that aligns the average model outputs of all instances in a bag with the label proportions in order to induce the classifier. However, simply fitting the label proportion may cause over-smoothing problems and does not guarantee correct label prediction of individual instances, resulting in poor classification performance. In this paper, we propose a novel LLP approach that can mitigate the over-smoothing problems with theoretical guarantees. Rather than fitting the label proportions directly, we treat them as targets for an auxiliary proportional value classification task to induce the target classifier. Our approach only requires the incorporation of an aggregation function after the classification layer. We also introduce an efficient computational approach with a divide-and-conquer strategy. Extensive experiments on various image and text benchmark datasets demonstrate that our approach achieves superior performance against state-of-the-art LLP methods.

Positive-unlabeled (PU) learning is a weakly supervised binary classification problem, in which the goal is to learn a binary classifier from only positive and unlabeled data, without access to negative data. In recent years, many PU learning algorithms have been developed to improve model performance. However, experimental settings are highly inconsistent, making it difficult to identify which algorithm performs better. In this paper, we propose the first PU learning benchmark to systematically compare PU learning algorithms. During our implementation, we identify subtle yet critical factors that affect the realistic and fair evaluation of PU learning algorithms. On the one hand, many PU learning algorithms rely on a validation set that includes negative data for model selection. This is unrealistic in traditional PU learning settings, where no negative data are available. To handle this problem, we systematically investigate model selection criteria for PU learning. On the other hand, the problem settings and solutions of PU learning have different families, i.e., the one-sample and two-sample settings. However, existing evaluation protocols are heavily biased towards the one-sample setting and neglect the significant difference between them. We identify the internal label shift problem of unlabeled training data for the one-sample setting and propose a simple yet effective calibration approach to ensure fair comparisons within and across families. We hope our framework will provide an accessible, realistic, and fair environment for evaluating PU learning algorithms in the future.

Positive-Unlabeled (PU) learning is a weakly-supervised paradigm that trains a binary classifier from labeled positive and unlabeled instances. In PU risk estimation, the empirical risk consists of an unlabeled term and a positive term. In this paper, we observe that when labeled positives are scarce, the risk deviation is dominated by the generalization bound of the positive term, which is composed of a complexity term governed by Rademacher complexity and a concentration term governed by the uniform range bound, leading to estimator instability. Based on this observation, we theoretically derive the minimal sufficient learning threshold, defined as the smallest number of labeled positives required to achieve a target excess risk with high probability, and reveal its explicit dependence on both components. Inspired by this insight, we propose ScalePU, which incorporates variance regularization to induce a restricted sub-hypothesis space with reduced Rademacher complexity, and geometric regularization to encourage compact clustering of positive samples with a tighter effective range. Theoretical analysis demonstrates that both mechanisms effectively lower the threshold through improvements to different components of the bound. Experiments on eight benchmark datasets validate the effectiveness of ScalePU, with significant improvements under extreme label scarcity.

Partial multi-label learning and complementary multi-label learning are two popular weakly supervised multi-label classification paradigms that aim to alleviate the high annotation costs of collecting precisely annotated multi-label data. In partial multi-label learning, each instance is annotated with a candidate label set, among which only some labels are relevant; in complementary multi-label learning, each instance is annotated with complementary labels indicating the classes to which the instance does not belong. Existing consistent approaches for the two paradigms either require accurate estimation of the generation process of candidate or complementary labels or assume a uniform distribution to eliminate the estimation problem. However, both conditions are usually difficult to satisfy in real-world scenarios. In this paper, we propose consistent approaches that do not rely on the aforementioned conditions to handle both problems in a unified way. Specifically, we propose two risk estimators based on first- and second-order strategies. Theoretically, we prove consistency w.r.t. two widely used multi-label classification evaluation metrics and derive convergence rates for the estimation errors of the proposed risk estimators. Empirically, extensive experimental results validate the effectiveness of our proposed approaches against state-of-the-art methods.

Weakly supervised classification (WSC) is a popular machine learning paradigm that aims to train a classifier using incomplete, inexact, or inaccurate supervision. Recently, it has become common practice to use a general-purpose, large, pre-trained model as a foundation model that is fine-tuned to solve complex, challenging downstream classification problems. However, collecting fully supervised downstream data can be costly in certain domains. Thus, it makes sense to apply the WSC paradigm to the fine-tuning scenario. In this paper, we attempt to fine-tune a pre-trained vision transformer using the WSC approach. Our experiments show that naive use of existing WSC losses degrades performance due to severe overfitting exacerbation and feature degeneration problems. To address these problems, we propose a novel robust fine-tuning approach using dual classification heads that are trained synergistically by alternately distilling reliable supervision and performing efficient model fine-tuning. Theoretically, we prove the consistency and convergence rate for the proposed risk estimator. Empirically, extensive experimental results on diverse benchmark datasets validate the effectiveness of our proposed approach against state-of-the-art approaches.

The effectiveness of contrastive learning in sequential recommendation hinges on the construction of contrastive views, which ideally should be both semantically consistent and diverse. However, most existing CL-based methods rely on heuristic augmentations that are prone to removing crucial items or disrupting transition patterns, leading to semantic drift. While a few studies have explored learnable augmentations to improve view quality, they often suffer from limited diversity and still necessitate heuristic aids. Furthermore, the quality differences across views are rarely modeled explicitly and adaptively, aggravating the false-positive issue. To address these issues, we propose Quality-aware Collaborative Multi-Positive Contrastive Learning for sequential recommendation. First, we introduce a learnable collaborative sequence augmentation module that generates two augmented views under two complementary collaborative contexts, one based on same-target sequences and the other on similar sequences, thereby enhancing view diversity while preserving intent consistency.Second, we design a quality-aware mechanism, tightly integrated into the model representations, which estimates each view' s quality from the confidence of its augmentation operations and assigns adaptive weights to ensure that high-confidence views contribute more supervision while low-confidence ones contribute less.Extensive experiments on three real-world datasets demonstrate that QCMP-CL outperforms state-of-the-art CL-based sequential recommendation baselines.

Partial-label learning (PLL) is a weakly supervised learning problem in whicheach example is associated with multiple candidate labels and only one is thetrue label. In recent years, many deep PLL algorithms have been developed toimprove model performance. However, we find that some early developedalgorithms are often underestimated and can outperform many later algorithmswith complicated designs. In this paper, we delve into the empiricalperspective of PLL and identify several critical but previously overlookedissues. First, model selection for PLL is non-trivial, but has never beensystematically studied. Second, the experimental settings are highlyinconsistent, making it difficult to evaluate the effectiveness of thealgorithms. Third, there is a lack of real-world image datasets that can becompatible with modern network architectures. Based on these findings, wepropose PLENCH, the first Partial-Label learning bENCHmark to systematicallycompare state-of-the-art deep PLL algorithms. We investigate the modelselection problem for PLL for the first time, and propose novel model selectioncriteria with theoretical guarantees. We also create Partial-Label CIFAR-10(PLCIFAR10), an image dataset of human-annotated partial labels collected fromAmazon Mechanical Turk, to provide a testbed for evaluating the performance ofPLL algorithms in more realistic scenarios. Researchers can quickly andconveniently perform a comprehensive and fair evaluation and verify theeffectiveness of newly developed algorithms based on PLENCH. We hope thatPLENCH will facilitate standardized, fair, and practical evaluation of PLLalgorithms in the future.

Conditional diffusion models have achieved remarkable success in various generative tasks recently, but their training typically relies on large-scale datasets that inevitably contain imprecise information in conditional inputs. Such supervision, often stemming from noisy, ambiguous, or incomplete labels, will cause condition mismatch and degrade generation quality. To address this challenge, we propose DMIS, a unified framework for training robust Diffusion Models from Imprecise Supervision, which is the first systematic study within diffusion models. Our framework is derived from likelihood maximization and decomposes the objective into generative and classification components: the generative component models imprecise-label distributions, while the classification component leverages a diffusion classifier to infer class-posterior probabilities, with its efficiency further improved by an optimized timestep sampling strategy. Extensive experiments on diverse forms of imprecise supervision, covering tasks of image generation, weakly supervised learning, and noisy dataset condensation demonstrate that DMIS consistently produces high-quality and class-discriminative samples.

Reinforcement Learning with Verifiable Rewards (RLVR) trains policies against automated verifiers to avoid costly human labeling. To reduce vulnerability to verifier hacking, many RLVR systems collapse rewards to binary {0,1} during training. This choice carries a cost: it introduces false negatives (rejecting correct answers, FNs) and false positives (accepting incorrect ones, FPs). For instance, a rule-based checker may mark the correct fraction 12/36 as wrong when compared against the canonical 1/3 due to brittle parsing/equivalence rules (FN), while a large language model (LLM) judges can be gamed by superficial cues or even a single adversarial token, yielding inflated correctness for wrong solutions (FP). We formalize verifier unreliability by modeling the verifier as a stochastic reward channel with asymmetric noise rates. From this abstraction, we derive two correction algorithms for verifier errors. The first is a backward correction that de-biases the observed binary reward to recover an unbiased estimator of the clean policy gradient. The second is a forward correction that reweights score-function terms so that the expected update direction aligns with the clean gradient; notably, it requires only the FN rate. We implement both as lightweight hooks in a group relative policy optimization (GRPO)-based RLVR pipeline and evaluate them on math-reasoning models and benchmarks. Across models and datasets, both corrections improve over uncorrected training; the forward variant converges faster and remains stable under heavier noise. Finally, we show a practical appeal mechanism in which a lightweight LLM verifier estimates the FN rate online by rechecking rule-based negatives, obtaining outperformance compared with other state-of-the-art contenders.

Obtaining a high-quality frontal facial image from a low-resolution (LR) non-frontal facial image is crucial for many facial analysis tasks. Recently, diffusion models (DMs) have made impressive progress in near-frontal face super-resolution. However, when faced with non-frontal LR faces, the existing DMs exhibit poor identity preservation and facial detail fidelity. In this paper, we present a novel high-fidelity DM named HifiDiff for simultaneously super-resolving and frontalizing tiny non-frontal facial images. It consists of a two-stage pipeline: facial preview and facial refinement. In the first stage, we pretrain a coarse restoration module to obtain a coarse high-resolution (HR) frontal face, which serves as a superior constraint condition to enhance the ability to solve complex inverse transform issues. In the second stage, we leverage the strong generation capabilities of the latent DM to refine the facial details. Specifically, we design a two-pathway control structure that consists of a facial prior guidance (FPG) module and an identity consistency (IDC) module to control the denoising process. FPG encodes multilevel features derived from latent coarse HR frontal faces and employs hybrid cross-attention to capture their intrinsic correlations with the denoiser features, thereby improving the fidelity of the facial details. IDC utilizes contrastive learning to extract high-level semantic identity-representing features to constrain the denoiser, thereby maintaining the fidelity of facial identities. Extensive experiments demonstrate that our HifiDiff produces both high-fidelity and realistic HR frontal facial images, surpassing other state-of-the-art methods in qualitative and quantitative analyses, as well as in downstream facial recognition tasks.

In dynamic and complex environments, particularly when rare but realistic emergent traffic events occur, enabling existing Traffic Signal Control (TSC) systems to respond flexibly and maintain reliability remains a substantial challenge. Given the ability of Large Language Models (LLMs) to exhibit human-level reasoning through chain-of-thought (CoT) processes, they show great potential in solving complex tasks. To this end, this study proposes a multi-agent proximal policy optimization (MAPPO) framework integrated with the LLM, where the LLM evaluates and refines the initial decisions made by MAPPO agents. This approach addresses the inherent limitation of conventional Multi-Agent Reinforcement Learning (MARL)-based TSC systems, which optimize solely for reward functions and often neglect anomalous environmental states. Experiments are conducted in a 2x2 grid network, where three types of emergent traffic events: emergency vehicles, sensor failure, and roadblock are respectively designed and investigated. Experimental results demonstrate that, compared to standalone MAPPO method, the proposed MAPPO-LLM collaborative framework achieves remarkable reductions in both average travel time and average waiting time across various emergent traffic scenarios. These findings highlight the effectiveness of incorporating LLMs in enhancing the adaptability and robustness of MARL-based TSC systems in the presence of real-world traffic emergencies.

Complementary-label learning is a weakly supervised learning problem in which each training example is associated with one or multiple complementary labels indicating the classes to which it does not belong. Existing consistent approaches have relied on the uniform distribution assumption to model the generation of complementary labels, or on an ordinary-label training set to estimate the transition matrix. However, both conditions may not be satisfied in real-world scenarios. In this paper, we propose a novel complementary-label learning approach that does not rely on these conditions. We find that complementary-label learning can be expressed as a set of negative-unlabeled binary classification problems when using the one-versus-rest strategy. This observation allows us to propose a risk-consistent approach with theoretical guarantees. Furthermore, we introduce a risk correction approach to address overfitting problems when using complex models. We also prove the statistical consistency and convergence rate of the corrected risk estimator. Extensive experimental results on both synthetic and real-world benchmark datasets validate the superiority of our proposed approach over state-of-the-art methods.

Complementary-label learning is a weakly supervised learning problem in which each training example is associated with one or multiple complementary labels indicating the classes to which it does not belong. Existing consistent approaches have relied on the uniform distribution assumption to model the generation of complementary labels, or on an ordinary-label training set to estimate the transition matrix in non-uniform cases. However, either condition may not be satisfied in real-world scenarios. In this paper, we propose a novel consistent approach that does not rely on these conditions. Inspired by the positive-unlabeled (PU) learning literature, we propose an unbiased risk estimator based on the Selected-Completely-at-Random assumption for complementary-label learning. We then introduce a risk-correction approach to address overfitting problems. Furthermore, we find that complementary-label learning can be expressed as a set of negative-unlabeled binary classification problems when using the one-versus-rest strategy. Extensive experimental results on both synthetic and real-world benchmark datasets validate the superiority of our proposed approach over state-of-the-art methods.

Learning with confidence labels is an emerging weakly supervised learning paradigm, where training data are equipped with confidence labels instead of exact labels. Positive-confidence (Pconf) classification is a typical learning problem in this context, where we are given only positive data equipped with confidence. However, pointwise confidence may not be accessible in real-world scenarios. In this paper, we dive into a novel weakly supervised learning problem called confidence-difference (ConfDiff) classification. Instead of pointwise confidence, we are given only unlabeled data pairs equipped with confidence difference specifying the difference in the probabilities of being positive. An unbiased risk estimator is derived to tackle the problem, and we show that the estimation error bound achieves the optimal convergence rate. Extensive experiments on benchmark data sets validate the effectiveness of our proposed approaches in leveraging the supervision information of the confidence difference.

Recently, learning with soft labels has been shown to achieve better performance than learning with hard labels in terms of model generalization, calibration, and robustness. However, collecting pointwise labeling confidence for all training examples can be challenging and time-consuming in real-world scenarios. This paper delves into a novel weakly supervised binary classification problem called confidence-difference (ConfDiff) classification. Instead of pointwise labeling confidence, we are given only unlabeled data pairs with confidence difference that specifies the difference in the probabilities of being positive. We propose a risk-consistent approach to tackle this problem and show that the estimation error bound achieves the optimal convergence rate. We also introduce a risk correction approach to mitigate overfitting problems, whose consistency and convergence rate are also proven. Extensive experiments on benchmark data sets and a real-world recommender system data set validate the effectiveness of our proposed approaches in exploiting the supervision information of the confidence difference.

In multi-label classification, it is critical to capitalize on complicated data structures and semantic relationships. Metric learning serves as an effective strategy to provide a better measurement of distances between examples. Existing works on metric learning for multi-label classification mainly learn one single global metric that characterizes latent semantic similarity between multi-label instances. However, such single-semantics metric exploitation approaches can not capture the intrinsic properties of multi-label data possessed of rich semantics. In this paper, the first attempt towards multi-semantics metric learning for multi-label classification is investigated. Specifically, the proposed LIMIC approach simultaneously learns one global and multiple label-specific local metrics by exploiting label-specific side information. The global metric is learned to capture the commonality across all the labels and label-specific local metrics characterize the individuality of each semantic space. The combination of global metric and label-specific local metrics is utilized to construct latent semantic space for each label, in which similar intra-class instances are pushed closer and inter-class instances are pulled apart. Furthermore, metric-based label correlation regularization is constructed to maintain similarity between correlated label spaces. Extensive experiments on benchmark multi-label data sets validate the superiority of our proposed approach in learning effective distance metrics for multi-label classification.