March 2026

The core of molecular dynamics simulation fundamentally lies in the interatomic potential. Traditional empirical potentials lack accuracy, while first-principles methods are computationally prohibitive. Machine learning interatomic potentials (MLIPs) promise near-quantum accuracy at linear cost, but existing models still face challenges in efficiency and stability. We presents Machine Learning Advances Neural Network (MLANet), an efficient and robust graph neural network framework. MLANet introduces a dual-path dynamic attention mechanism for geometry-aware message passing and a multi-perspective pooling strategy to construct […]

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I wrote about Dan Woods’ experiments with streaming experts the other day, the trick where you run larger Mixture-of-Experts models on hardware that doesn’t have enough RAM to fit the entire model by instead streaming the necessary expert weights from SSD for each token that you process. Five days ago Dan was running Qwen3.5-397B-A17B in 48GB of RAM. Today @seikixtc reported running the colossal Kimi K2.5 – a 1 trillion parameter model with 32B active weights at any […]

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Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile scenarios and tasks, we theoretically investigate utilizing transformers as students to learn from a class of teacher models. Specifically, the teacher models covered in our analysis include convolution layers with average pooling, graph convolution layers, and various classic statistical learning models, including a variant of sparse token […]

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arXiv:2603.15232v2 Announce Type: replace-cross Abstract: Calibration is a conditional property that depends on the information retained by a predictor. We develop decomposition identities for arbitrary proper losses that make this dependence explicit. At any information level $mathcal A$, the expected loss of an $mathcal A$-measurable predictor splits into a proper-regret (reliability) term and a conditional entropy (residual uncertainty) term. For nested levels $mathcal Asubseteqmathcal B$, a chain decomposition quantifies the information gain from $mathcal A$ to $mathcal B$. […]

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arXiv:2603.01162v3 Announce Type: replace-cross Abstract: Group relative policy optimization (GRPO), a core methodological component of DeepSeekMath and DeepSeek-R1, has emerged as a cornerstone for scaling reasoning capabilities of large language models. Despite its widespread adoption and the proliferation of follow-up works, the theoretical properties of GRPO remain less studied. This paper provides a unified framework to understand GRPO through the lens of classical U-statistics. We demonstrate that the GRPO policy gradient is inherently a U-statistic, allowing us to […]

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arXiv:2602.12683v2 Announce Type: replace-cross Abstract: We reformulate Optimal Transport Conditional Flow Matching (OT-CFM), a class of dynamical generative models, showing that it admits an exact proximal formulation via an extended Brenier potential, without assuming that the target distribution has a density. In particular, the mapping to recover the target point is exactly given by a proximal operator, which yields an explicit proximal expression of the vector field. We also discuss the convergence of minibatch OT-CFM to the population […]

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arXiv:2602.08998v4 Announce Type: replace-cross Abstract: We study homology of ample groupoids via the compactly supported Moore complex of the nerve. Let $A$ be a topological abelian group. For $nge 0$ set $C_n(mathcal G;A) := C_c(mathcal G_n,A)$ and define $partial_n^A=sum_{i=0}^n(-1)^i(d_i)_*$. This defines $H_n(mathcal G;A)$. The theory is functorial for continuous ‘etale homomorphisms. It is compatible with standard reductions, including restriction to saturated clopen subsets. In the ample setting it is invariant under Kakutani equivalence. We reprove Matui type long […]

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arXiv:2602.07098v2 Announce Type: replace-cross Abstract: Modern Bayesian inference involves a mixture of computational methods for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows. An overarching motif of many Bayesian methods is that they are relatively slow, which often becomes prohibitive when fitting complex models to large data sets. Amortized Bayesian inference (ABI) offers a path to solving the computational challenges of Bayes. ABI trains neural networks on model simulations, rewarding users with rapid […]

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arXiv:2601.22481v2 Announce Type: replace-cross Abstract: This dissertation presents a general framework for changepoint detection based on L0 model selection. The core method, Iteratively Reweighted Fused Lasso (IRFL), improves upon the generalized lasso by adaptively reweighting penalties to enhance support recovery and minimize criteria such as the Bayesian Information Criterion (BIC). The approach allows for flexible modeling of seasonal patterns, linear and quadratic trends, and autoregressive dependence in the presence of changepoints. Simulation studies demonstrate that IRFL achieves accurate […]

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