Blind Image Quality Assessment (BIQA) has advanced significantly through deep learning, but the scarcity of large-scale labeled datasets remains a challenge. While synthetic data offers a promising solution, models trained on existing synthetic datasets often show limited generalization ability. In this work, we make a key observation that representations learned from synthetic datasets often exhibit a discrete and clustered pattern that hinders regression performance: features of high-quality images cluster around reference images, while those of low-quality images cluster based on distortion types. Our analysis reveals that this issue stems from the distribution of synthetic data rather than model architecture. Consequently, we introduce a novel framework SynDR-IQA, which reshapes synthetic data distribution to enhance BIQA generalization. Based on theoretical derivations of sample diversity and redundancy's impact on generalization error, SynDR-IQA employs two strategies: distribution-aware diverse content upsampling, which enhances visual diversity while preserving content distribution, and density-aware redundant cluster downsampling, which balances samples by reducing the density of densely clustered areas. Extensive experiments across three cross-dataset settings (synthetic-to-authentic, synthetic-to-algorithmic, and synthetic-to-synthetic) demonstrate the effectiveness of our method.

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 Oko et al. [28] for contrastive languageimage 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.

Multi-view multi-label learning typically suffers from dual data incompleteness due to limitations in feature storage and annotation costs.

We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over high-dimensional embeddings. Unlike prior tractable attention models, AIM allows full-width key and query matrices, aligning more closely with practical transformers. Using tools from statistical mechanics and random matrix theory, we derive closed-form predictions for Bayes-optimal generalization error and identify sharp phase transitions as a function of sample complexity, model width, and sequence length. We propose a matching approximate message passing algorithm and show that gradient descent can reach optimal performance. AIM offers a solvable playground for understanding learning in self-attention layers, that are key components of modern architectures.

Decentralized training removes the centralized server, making it a communicationefficient approach that can significantly improve training efficiency, but it often suffers from degraded performance compared to centralized training. Multi-Gossip Steps (MGS) serve as a simple yet effective bridge between decentralized and centralized training, significantly reducing experiment performance gaps. However, the theoretical reasons for its effectiveness and whether this gap can be fully eliminated by MGS remain open questions. In this paper, we derive upper bounds on the generalization error and excess error of MGS using stability analysis, systematically answering these two key questions.

Unfolding networks are interpretable networks emerging from iterative algorithms, incorporate prior knowledge of data structure, and are designed to solve inverse problems like compressed sensing, which deals with recovering data from noisy, missing observations. Compressed sensing finds applications in critical domains, from medical imaging to cryptography, where adversarial robustness is crucial to prevent catastrophic failures. However, a solid theoretical understanding of the performance of unfolding networks in the presence of adversarial attacks is still in its infancy. In this paper, we study the adversarial generalization of unfolding networks when perturbed with l2-norm constrained attacks, generated by the fast gradient sign method. Particularly, we choose a family of state-ofthe-art overaparameterized unfolding networks and deploy a new framework to estimate their adversarial Rademacher complexity. Given this estimate, we provide adversarial generalization error bounds for the networks under study, which are tight with respect to the attack level. To our knowledge, this is the first theoretical analysis on the adversarial generalization of unfolding networks. We further present a series of experiments on real-world data, with results corroborating our derived theory, consistently for all data. Finally, we observe that the family's overparameterization can be exploited to promote adversarial robustness, shedding light on how to efficiently robustify neural networks.

Neural networks are powered by an implicit bias: a tendency of gradient descent to fit training data in a way that generalizes to unseen data. A recent class of neural network models gaining increasing popularity is structured state space models (SSMs). Prior work argued that the implicit bias of SSMs leads to generalization in a setting where data is generated by a low dimensional teacher. In this paper, we revisit the latter setting, and formally establish a phenomenon entirely undetected by prior work on the implicit bias of SSMs. Namely, we prove that while implicit bias leads to generalization under many choices of training data, there exist special examples whose inclusion in training completely distorts the implicit bias, to a point where generalization fails. This failure occurs despite the special training examples being labeled by the teacher, i.e., having clean labels! We empirically demonstrate the phenomenon, with SSMs trained independently and as part of non-linear neural networks. In the area of adversarial machine learning, disrupting generalization with cleanly labeled training examples is known as clean-label poisoning. Given the proliferation of SSMs, we believe that delineating their susceptibility to clean-label poisoning, and developing methods for overcoming this susceptibility, are critical research directions to pursue.

Latent variables (LVs) play a crucial role in encoder-decoder models by enabling effective data compression, prediction, and generation. Although their theoretical properties, such as generalization, have been extensively studied in supervised learning, similar analyses for unsupervised models such as variational autoencoders (VAEs) remain insufficiently explored. In this work, we extend informationtheoretic generalization analysis to vector-quantized (VQ) VAEs with discrete latent spaces, introducing a novel data-dependent prior to rigorously analyze the relationship among LVs, generalization, and data generation. We derive a novel generalization error bound of the reconstruction loss of VQ-VAEs, which depends solely on the complexity of LVs and the encoder, independent of the decoder. Additionally, we provide the upper bound of the 2-Wasserstein distance between the distributions of the true data and the generated data, explaining how the regularization of the LVs contributes to the data generation performance.

Large language models (LLMs) have demonstrated remarkable capabilities but often struggle to align with human preferences, leading to harmful or undesirable outputs. Preference learning, which trains models to distinguish between preferred and non-preferred responses based on human feedback, has become a crucial component for ensuring that LLMs align with human values. An essential part of ensuring that LLMs are aligned for all people is accounting for a diverse set of values. This paper introduces a new theoretical framework to analyze how generalization scales with value diversity and sample quantity in models trained with direct preference optimization. Our framework rigorously assesses how well models generalize after a finite number of gradient steps, reflecting realworld LLM training practices. By analyzing the reward margin associated with each sample and its trajectory throughout training, we provide a bound on the generalization error that demonstrates the challenges of effectively learning a wide set of concepts or values. These insights are empirically validated on contemporary LLMs, underscoring the practical relevance of our theory.

We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our bounds are time-independent and decay to zero as the sample size increases, regardless of the number of iterations and whether the step size is fixed. Unlike previous studies, we derive the generalization error bounds by focusing on the time evolution of the Kullback-Leibler divergence, which is related to the stability of datasets and is the upper bound of the mutual information between output parameters and an input dataset. Additionally, we establish the first information-theoretic generalization bound when the training and test loss are the same by showing that a loss function of SGLD is sub-exponential. This bound is also time-independent and removes the problematic step size dependence in existing work, leading to an improved excess risk bound by combining our analysis with the existing non-convex optimization error bounds.