arXiv:2510.11942v1 Announce Type: new Abstract: We show that emph{efficient Turing computability} at any fixed input/output precision implies the existence of emph{compositionally sparse} (bounded-fan-in, polynomial-size) DAG representations and of corresponding neural approximants achieving the target precision. Concretely: if $f:[0,1]^dtoR^m$ is computable…
arXiv:2507.00546v2 Announce Type: replace-cross Abstract: Inverse design in nanophotonics, the computational discovery of structures achieving targeted electromagnetic (EM) responses, has become a key tool for recent optical advances. Traditional intuition-driven or iterative optimization methods struggle with the inherently high-dimensional, non-convex…
arXiv:2510.11953v1 Announce Type: new Abstract: Learning disentangled representations, where distinct factors of variation are captured by independent latent variables, is a central goal in machine learning. The dominant approach has been the Variational Autoencoder (VAE) framework, which uses a Kullback-Leibler…
arXiv:2510.04407v2 Announce Type: replace-cross Abstract: A considerable chasm has been looming for decades between theory and practice in zero-sum game solving through first-order methods. Although a convergence rate of $T^{-1}$ has long been established since Nemirovski’s mirror-prox algorithm and Nesterov’s…
arXiv:2510.11955v1 Announce Type: new Abstract: Modern continuous-time generative models often induce V-shaped transport: each sample travels independently along nearly straight trajectories from prior to data, overlooking shared structure. We introduce Y-shaped generative flows, which move probability mass together along shared…
arXiv:2510.12581v1 Announce Type: cross Abstract: We propose LayerSync, a domain-agnostic approach for improving the generation quality and the training efficiency of diffusion models. Prior studies have highlighted the connection between the quality of generation and the representations learned by diffusion…
arXiv:2510.11962v1 Announce Type: new Abstract: Diffusion models are renowned for their generative capabilities, yet their pretraining processes exhibit distinct phases of learning speed that have been entirely overlooked in prior post-training acceleration efforts in the community. In this study, we…
arXiv:2510.12744v1 Announce Type: cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic…
arXiv:2510.11963v1 Announce Type: new Abstract: In natural language processing, current methods for understanding Transformers are successful at identifying intermediate predictions during a model’s inference. However, these approaches function as limited diagnostic checkpoints, lacking a mathematical framework for mechanistically modeling how…
arXiv:2302.09904v4 Announce Type: replace Abstract: Federated learning (FL) is an efficient approach for large-scale distributed machine learning that promises data privacy by keeping training data on client devices. However, recent research has uncovered vulnerabilities in FL, impacting both security and…
