Here we summarize all our model assumptions and highlight what are learned from data.

Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper describes a framework particularly useful for semi-supervised learning based on Fredholm kernels. The classical supervised learning optimization problem solved in kernel-based methods is extended to incorporate unlabeled information leading to discretized version of the Fredholm integral equation. Quality The paper has high technical quality with well-supported claims by theoretical analysis and convincing experimental results. The proposed formulation leads to a new data-dependent kernel that incorporates unlabeled information.

First of all, we would like to thank all the reviewers' valuable comments and their recognition (mainly from R #3 and R We will improve the writing and release the source code. The clustering accuracy dropped from 0.849 to 0.772.

Reinforcement learning with human-annotated data has boosted chain-of-thought reasoning in large reasoning models, but these gains come at high costs in labeled data while faltering on harder tasks. A natural next step is experience-driven learning, where models improve without curated labels by adapting to unlabeled data. We introduce RESTRAIN (REinforcement learning with Self-restraint), a self-penalizing RL framework that converts the absence of gold labels into a useful learning signal. Instead of overcommitting to spurious majority votes, RESTRAIN exploits signals from the model's entire answer distribution: penalizing overconfident rollouts and low-consistency examples while preserving promising reasoning chains. The self-penalization mechanism integrates seamlessly into policy optimization methods such as GRPO, enabling continual self-improvement without supervision. On challenging reasoning benchmarks, RESTRAIN delivers large gains using only unlabeled data. With Qwen3-4B-Base and OctoThinker Hybrid-8B-Base, it improves Pass@1 by up to +140.7 percent on AIME25, +36.2 percent on MMLU_STEM, and +19.6 percent on GPQA-Diamond, nearly matching gold-label training while using no gold labels. These results demonstrate that RESTRAIN establishes a scalable path toward stronger reasoning without gold labels.

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: Code will be open-sourced after review.

Representation learning from unlabeled data has been extensively studied in statistics, data science and signal processing with a rich literature on techniques for dimension reduction, compression, multi-dimensional scaling among others. However, current deep learning models use new principles for unsupervised representation learning that cannot be easily analyzed using classical theories. For example, visual foundation models have found tremendous success using self-supervision or denoising/masked autoencoders, which effectively learn representations from massive amounts of unlabeled data. However, it remains difficult to characterize the representations learned by these models and to explain why they perform well for diverse prediction tasks or show emergent behavior. To answer these questions, one needs to combine mathematical tools from statistics and optimization. This paper provides an overview of recent theoretical advances in representation learning from unlabeled data and mentions our contributions in this direction.

Long-tailed learning has garnered increasing attention due to its wide applicability in real-world scenarios. Among existing approaches, Long-Tailed Semi-Supervised Learning (L TSSL) has emerged as an effective solution by incorporating a large amount of unlabeled data into the imbalanced labeled dataset. However, most prior L TSSL methods are designed to train models from scratch, which often leads to issues such as overconfidence and low-quality pseudo-labels. To address these challenges, we extend L TSSL into the foundation model fine-tuning paradigm and propose a novel framework: LoFT (Long-tailed semi-supervised learning via parameter-efficient Fine-Tuning). We demonstrate that fine-tuned foundation models can generate more reliable pseudolabels, thereby benefiting imbalanced learning. Furthermore, we explore a more practical setting by investigating semi-supervised learning under open-world conditions, where the unlabeled data may include out-of-distribution (OOD) samples. To handle this problem, we propose LoFT - OW (LoFT under Open-World scenarios) to improve the discriminative ability. Experimental results on multiple benchmarks demonstrate that our method achieves superior performance compared to previous approaches, even when utilizing only 1% of the unlabeled data compared with previous works.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/