Among many mysteries behind the success of deep networks lies the exceptional discriminative power of their learned representations as manifested by the intriguing Neural Collapse (NC) phenomenon, where simple feature structures emerge at the last layer of a trained neural network. Prior works on the theoretical understandings of NC have focused on analyzing the optimization landscape of matrix-factorization-like problems by considering the last-layer features as unconstrained free optimization variables and showing that their global minima exhibit NC. In this paper, we show that gradient flow on a two-layer ReLU network for classifying orthogonally separable data provably exhibits NC, thereby advancing prior results in two ways: First, we relax the assumption of unconstrained features, showing the effect of data structure and nonlinear activations on NC characterizations. Second, we reveal the role of the implicit bias of the training dynamics in facilitating the emergence of NC.

We consider the problem of estimating the correlation of two random variables $X$ and $Y$, where the pairs $(X,Y)$ are not observed together, but are instead separated co-ordinate-wise at two servers: server 1 contains all the $X$ observations, and server 2 contains the corresponding $Y$ observations. In this vertically distributed setting, we assume that each server has its own privacy constraints, owing to which they can only share suitably privatized statistics of their own component observations. We consider differing privacy budgets $(\varepsilon_1,\delta_1)$ and $(\varepsilon_2,\delta_2)$ for the two servers and determine the minimax optimal rates for correlation estimation allowing for both non-interactive and interactive mechanisms. We also provide correlation estimators that achieve these rates and further develop inference procedures, namely, confidence intervals, for the estimated correlations. Our results are characterized by an interesting rate in terms of the sample size $n$, $\varepsilon_1$, $\varepsilon_2$, which is strictly slower than the usual central privacy estimation rates. More interestingly, we find that the interactive mechanism is always better than its non-interactive counterpart whenever the two privacy budgets are different. Results from extensive numerical experiments support our theoretical findings.

These limitations hinder their ability to capture the sharp, high-frequency signals that often define tabular structure, especially under limited labeled samples. While self-supervised learning (SSL) offers promise in such settings, it remains challenging in tabular domains due to the lack of effective data augmentations. We propose a hybrid autoencoder that combines a neural encoder with an oblivious soft decision tree (OSDT) encoder, each guided by its own stochastic gating network that performs sample-specific feature selection. Together, these structurally different encoders and model-specific gating networks implement model-based augmentation, producing complementary input views tailored to each architecture. The two encoders, trained with a shared decoder and cross-reconstruction loss, learn distinct yet aligned representations that reflect their respective inductive biases. During training, the OSDT encoder (robust to noise and effective at modeling localized, high-frequency structure) guides the neural encoder toward representations more aligned with tabular data. At inference, only the neural encoder is used, preserving flexibility and SSL compatibility. Spectral analysis highlights the distinct inductive biases of each encoder. Our method achieves consistent gains in low-label classification and regression across diverse tabular datasets, outperforming deep and tree-based supervised baselines.

Text-to-image diffusion models rely on text embeddings from a pre-trained text encoder, but these embeddings remain fixed across all diffusion timesteps, limiting their adaptability to the generative process. We propose Diffusion Adaptive Text Embedding (DATE), which dynamically updates text embeddings at each diffusion timestep based on intermediate perturbed data. We formulate an optimization problem and derive an update rule that refines the text embeddings at each sampling step to improve alignment and preference between the mean predicted image and the text. This allows DATE to dynamically adapts the text conditions to the reverse-diffused images throughout diffusion sampling without requiring additional model training. Through theoretical analysis and empirical results, we show that DATE maintains the generative capability of the model while providing superior text-image alignment over fixed text embeddings across various tasks, including multi-concept generation and text-guided image editing.

It's to ensure compliance with a government directive citing national security concerns. Anthroic has disabled all of its customers' access to Fable 5 and Mythos 5 in order to ensure compliance with an order it received from the government on Friday, June 12. All its other models and its Claude chatbot are not affected. The company said in its announcement that the US government wanted it to suspend all foreign nationals' access to its newly launched AI models, whether they're inside or outside the US and even if they're Anthropic employees, citing national security concerns. While the US government didn't specify those concerns, Anthropic believes that it's because the government heard about a method of jailbreaking Fable 5.

Online learning algorithms for designing optimal bilateral trade mechanisms have recently received significant attention. This paper addresses a key inefficiency in prior two-bit feedback models, which synchronously query both the buyer and the seller for their willingness to trade. This approach is inherently inefficient as it offers a trade to the seller even if the buyer rejects the offer. We propose an asynchronous mechanism that queries the seller only if the buyer has already accepted the offer. Consequently, the mechanism receives one bit of feedback from the buyer and a censored bit from the seller---a signal richer than the standard one-bit (trade/no-trade) feedback, but less informative than the two-bit model. Assuming independent valuations with bounded densities---the same distributional conditions underlying the two-bit results of Cesa-Bianchi et al. [2024a]---we design an algorithm that achieves $\tilde{O}(T^{2/3})$ regret against the best fixed price in hindsight. This matches the lower bound for the strictly richer two-bit model, showing that our mechanism elicits the minimal feedback necessary to attain optimal rates.

Geometric diffusion models have shown remarkable success in molecular dynamics and structure generation. However, efficiently fine-tuning them for downstream tasks with varying geometric controls remains underexplored. In this work, we propose an SE(3)-equivariant adapter framework (GeoAda) that enables flexible and parameter-efficient fine-tuning for controlled generative tasks without modifying the original model architecture. GeoAda introduces a structured adapter design: control signals are first encoded through coupling operators, then processed by a trainable copy of selected base model layers, and finally projected back via decoupling operators followed by an equivariant zero-initialized convolution. By fine-tuning only these lightweight adapter modules, GeoAda preserves the model's geometric consistency while mitigating overfitting and catastrophic forgetting. We theoretically prove that the proposed adapters maintain SE(3)-equivariance, ensuring that the geometric inductive biases of the pretrained diffusion model remain intact during adaptation. We demonstrate the wide applicability of \method across diverse geometric control types, including frame control, global control, subgraph control, and a broad range of application domains such as particle dynamics, molecular dynamics, human motion prediction, and molecule generation. Empirical results show that GeoAda achieves state-of-the-art fine-tuning performance while preserving original task accuracy, whereas other baselines experience significant performance degradation due to overfitting and catastrophic forgetting.

Stochastic Gradient Descent (SGD) and its Ruppert-Polyak averaged variant (ASGD) lie at the heart of modern large-scale learning, yet their theoretical properties in high-dimensional settings are rarely understood. In this paper, we provide rigorous statistical guarantees for constant learning-rate SGD and ASGD in high-dimensional regimes. Our key innovation is to transfer powerful tools from high-dimensional time series to online learning. Specifically, by viewing SGD as a nonlinear autoregressive process and adapting existing coupling techniques, we prove the geometric-moment contraction of high-dimensional SGD for constant learning rates, thereby establishing asymptotic stationarity of the iterates. Building on this, we derive the $q$-th moment convergence of SGD and ASGD for any $q\ge2$ in general $\ell^s$-norms, and, in particular, the $\ell^{\infty}$-norm that is frequently adopted in high-dimensional sparse or structured models. Furthermore, we provide sharp high-probability concentration analysis which entails the probabilistic bound of high-dimensional ASGD. Beyond closing a critical gap in SGD theory, our proposed framework offers a novel toolkit for analyzing a broad class of high-dimensional learning algorithms.

Inspired by the success of DeepSeek-R1, we explore the potential of rule-based reinforcement learning (RL) in MLLM post-training for perception policy learning. While promising, our initial experiments reveal that incorporating a thinking process through RL does not consistently lead to performance gains across all visual perception tasks. This leads us to delve into the essential role of RL in the context of visual perception. In this work, we return to the fundamentals and explore the effects of RL on different perception tasks. We observe that the perceptual perplexity is a major factor in determining the effectiveness of RL. We also observe that reward design plays a crucial role in further approaching the upper limit of model perception. To leverage these findings, we propose Perception-R1, a scalable RL framework using GRPO during MLLM post-training.

The reasoning capabilities of large language models (LLMs) have advanced rapidly, particularly following the release of DeepSeek-R1, which has inspired a surge of research into data quality and reinforcement learning (RL) algorithms. Despite the pivotal role diversity plays in RL, its influence on LLM reasoning remains largely underexplored. To bridge this gap, this work presents a systematic investigation into the impact of diversity in RL-based training for LLM reasoning, and proposes a novel diversity-aware policy optimization method. Across evaluations on 12 LLMs, we observe a strong positive correlation between the solution diversity and potential@k (a novel metric quantifying an LLM's reasoning potential) in high-performing models. This finding motivates our method to explicitly promote diversity during RL training. Specifically, we design a token-level diversity and reformulate it into a practical objective, then we selectively apply it to positive samples. Integrated into the R1-zero training framework, our method achieves a 3.5\% average improvement across four mathematical reasoning benchmarks, while generating more diverse and robust solutions.