Diffusion models have achieved impressive performance in generating high-quality and diverse synthetic data. However, their success typically assumes a classbalanced training distribution. In real-world settings, multi-class data often follow a long-tailed distribution, where standard diffusion models struggleproducing lowdiversity and lower-quality samples for tail classes. While this degradation is well-documented, its underlying cause remains poorly understood. In this work, we investigate the behavior of diffusion models trained on long-tailed datasets and identify a key issue: the latent representations (from the bottleneck layer of the U-Net) for tail class subspaces exhibit significant overlap with those of head classes, leading to feature borrowing and poor generation quality. Importantly, we show that this is not merely due to limited data per class, but that the relative class imbalance significantly contributes to this phenomenon. To address this, we propose COntrastive Regularization for Aligning Latents (CORAL), a contrastive latent alignment framework that leverages supervised contrastive losses to encourage well-separated latent class representations. Experiments demonstrate that CORAL significantly improves both the diversity and visual quality of samples generated for tail classes relative to state-of-the-art methods.

We propose a generalized score-based diffusion framework for learning multivariate Gaussian mixture models with homoscedastic or heteroscedastic noise. Our goal is to nonparametrically estimate the latent location distribution and denoise the observations.

Scaling language models to handle longer input sequences typically necessitates large key-value (KV) caches, resulting in substantial memory overhead during inference. In this paper, we propose Tensor Product Attention (TPA), a novel attention mechanism that uses tensor decompositions to represent queries, keys, and values compactly, substantially shrinking the KV cache size at inference time. By factorizing these representations into contextual low-rank components and seamlessly integrating with RoPE and any possible position encoding mechanisms, TPA achieves improved model quality alongside memory efficiency. Based on TPA, we introduce the Tensor ProducTATTenTion Transformer (T6), a new model architecture for sequence modeling. Through extensive empirical evaluation on language modeling tasks, we demonstrate that T6 surpasses or matches the performance of standard Transformer baselines, including Multi-Head Attention (MHA), Multi-Query Attention (MQA), Grouped-Query Attention (GQA), and Multi-Head Latent Attention (MLA) across various metrics, including perplexity and a range of established evaluation benchmarks. Notably, TPA's memory efficiency and computational efficiency at the decoding stage enable processing longer sequences under fixed resource constraints, addressing a critical scalability challenge in modern language models.

We consider random instances of non-convex perceptron problems in the highdimensional limit of a large number of examples M and weights N, with finite load α = M/N. We develop a formalism based on replica theory to predict the fundamental limits of efficiently sampling the solution space using generative diffusion algorithms, conjectured to be saturated when the score function is provided by Approximate Message Passing. For the spherical perceptron with negative margin κ, we find that the uniform distribution over solutions can be efficiently sampled in most of the Replica Symmetric region of the α-κplane. In contrast, for binary weights, sampling from the uniform distribution remains intractable. A theoretical analysis of this obstruction leads us to identify a potential U(s)= log(s), under which the corresponding tilted distribution becomes efficiently samplable via diffusion. Moreover, we show numerically that an annealing procedure over the shape of this potential yields a fast and robust Markov Chain Monte Carlo algorithm for sampling the solution space of the binary perceptron.

Machine learning is a vital part of many real-world systems, but concerns remain about the lack of interpretability, explainability and robustness of black-box AI systems. Concept Bottleneck Models (CBM) address some of these challenges by learning interpretable concepts from high-dimensional data, e.g.

Generalized Category Discovery (GCD) aims to leverage labeled samples from known categories to cluster unlabeled data that may include both known and unknown categories. While existing methods have achieved impressive results under standard conditions, their performance often deteriorates in the presence of distribution shifts. In this paper, we explore a more realistic task: DomainShifted Generalized Category Discovery (DS_GCD), where the unlabeled data includes not only unknown categories but also samples from unknown domains. To tackle this challenge, we propose a Frequency-guided Generalized Category Discovery framework (FREE) that enhances the model's ability to discover categories under distributional shift by leveraging frequency-domain information. Specifically, we first propose a frequency-based domain separation strategy that partitions samples into known and unknown domains by measuring their amplitude differences. We then propose two types of frequency-domain perturbation strategies: a cross-domain strategy, which adapts to new distributions by exchanging amplitude components across domains, and an intra-domain strategy, which enhances robustness to intra-domain variations within the unknown domain. Furthermore, we extend the self-supervised contrastive objective and semantic clustering loss to better guide the training process. Finally, we introduce a clustering-difficultyaware resampling technique to adaptively focus on harder-to-cluster categories, further enhancing model performance. Extensive experiments demonstrate that our method effectively mitigates the impact of distributional shifts across various benchmark datasets and achieves superior performance in discovering both known and unknown categories.

Density estimation is essential for generative modeling, particularly with the rise of modern neural networks. While existing methods capture complex data distributions, they often lack interpretability and uncertainty quantification.

Large Vision-Language Models (LVLMs) with discrete image tokenizers unify multimodal representations by encoding visual inputs into a finite set of tokens. Despite their effectiveness, we find that these models still hallucinate non-existent objects. We hypothesize that this may be due to visual priors induced during training: When certain image tokens frequently co-occur in the same spatial regions and represent shared objects, they become strongly associated with the verbalizations of those objects.

Contrastive learning involves learning representations via a loss function that encourages each (unlabeled) sample to be far from other samples, but close to its own augmentation. In this paper, we aim to understand why this simple idea performs remarkably well, by theoretically analyzing it for a simple, natural problem setting: dimensionality reduction in Gaussian Mixture Models (GMMs). Note that the standard GMM setup lacks the concept of augmentations. We study an intuitive extension: we define the pair of data sample and its augmentation as a coupled random draw from the GMM such that the marginal over the "noisy" augmentation is biased towards the component of the data sample. For this setup, we show that vanilla contrastive loss, e.g., InfoNCE, is able to find the optimal lower-dimensional subspace even when the Gaussian components are non-isotropic. In particular, we show that InfoNCE can match the performance of a fully supervised algorithm, e.g., LDA, (where each data point is labeled with the mixture component it comes from) even when the augmentations are "noisy". We further extend our setup to the multi-modal case, and develop a GMM-like setting to study the contrastive CLIP loss. We corroborate our theory with experiments on CIFAR100; representations learned by InfoNCE loss match the performance of LDA on clustering metrics.

Large Language Models (LLMs) have demonstrated remarkable capabilities but typically require extensive computational resources and memory for inference. Post-training quantization (PTQ) can effectively reduce these demands by storing weights in lower bit-width formats. However, standard uniform quantization often leads to notable performance degradation, particularly in low-bit scenarios. In this work, we introduce a Grouped Lattice Vector Quantization (GLVQ) framework that assigns each group of weights a customized lattice codebook, defined by a learnable generation matrix. To address the non-differentiability of the quantization process, we adopt Babai rounding to approximate nearest-lattice-point search during training, which enables stable optimization of the generation matrices. Once trained, decoding reduces to a simple matrix-vector multiplication, yielding an efficient and practical quantization pipeline. Experiments on multiple benchmarks show that our approach achieves a better trade-off between model size and accuracy compared to existing post-training quantization baselines, highlighting its effectiveness in deploying large models under stringent resource constraints. Our source code is available on GitHub repository: https://github.com/xzhang9308/GLVQ.