arXiv:2510.05497v4 Announce Type: replace-cross Abstract: Large-scale Mixture of Experts (MoE) Large Language Models (LLMs) have recently become the frontier open weight models, achieving remarkable model capability similar to proprietary ones. But their random expert selection mechanism introduces significant data movement…
arXiv:2604.02450v1 Announce Type: new Abstract: Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural…
arXiv:2603.02417v2 Announce Type: replace-cross Abstract: Classical stochastic-approximation analyses treat the covariance of stochastic gradients as an exogenous modeling input. We show that under exchangeable mini-batch sampling this covariance is identified by the sampling mechanism itself: to leading order it is…
arXiv:2604.02459v1 Announce Type: new Abstract: We study the geometric structure of layer updates in deep language models. Rather than analyzing what information is encoded in intermediate representations, we ask how representations change from one layer to the next. We show…
arXiv:2604.02889v1 Announce Type: cross Abstract: Data assimilation is the process of estimating the time-evolving state of a dynamical system by integrating model predictions and noisy observations. It is commonly formulated as Bayesian filtering, but classical filters often struggle with accuracy…
arXiv:2604.03086v1 Announce Type: cross Abstract: This work establishes a rigorous bridge between infinite-dimensional delay dynamics and finite-dimensional Koopman learning, with explicit and interpretable error guarantees. While Koopman analysis is well-developed for ordinary differential equations (ODEs) and partially for partial differential…
arXiv:2511.14617v3 Announce Type: replace-cross Abstract: Reinforcement Learning (RL) has emerged as a critical technique for advancing modern Large Language Models (LLMs), yet existing synchronous RL systems face severe performance bottlenecks. The rollout phase, which dominates end-to-end iteration time, suffers from…
arXiv:2604.02337v1 Announce Type: new Abstract: Counterfactual simulation – exploring hypothetical consequences under alternative clinical scenarios – holds promise for transformative applications such as personalized medicine and in silico trials. However, it remains challenging due to methodological limitations. Here, we show…
arXiv:2602.18523v3 Announce Type: replace Abstract: Grokking — the abrupt transition from memorization to generalization long after near-zero training loss — has been studied mainly in single-task settings. We extend geometric analysis to multi-task modular arithmetic, training shared-trunk Transformers on dual-task…
arXiv:2503.02178v2 Announce Type: replace-cross Abstract: This paper develops asymptotic theory for quantile estimation via stochastic gradient descent (SGD) with a constant learning rate. The quantile loss function is neither smooth nor strongly convex. Beyond conventional perspectives and techniques, we view…
