Tag: field
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Total Variation Rates for Riemannian Flow Matching
Total Variation Rates for Riemannian Flow Matching arXiv:2602.05174v1 Announce Type: new Abstract: Riemannian flow matching (RFM) extends flow-based generative modeling to data supported on manifolds by learning a time-dependent tangent vector field whose flow-ODE transports a simple base distribution to the data law. We develop a nonasymptotic Total Variation (TV) convergence analysis for RFM samplers…
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Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds
Supervised Learning of Random Neural Architectures Structured by Latent Random Fields on Compact Boundaryless Multiply-Connected Manifolds arXiv:2512.10407v1 Announce Type: new Abstract: This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture itself is…
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Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games
Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games arXiv:2505.22781v1 Announce Type: new Abstract: We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting,…
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Learning Enhanced Ensemble Filters
Learning Enhanced Ensemble Filters arXiv:2504.17836v1 Announce Type: new Abstract: The filtering distribution in hidden Markov models evolves according to the law of a mean-field model in state–observation space. The ensemble Kalman filter (EnKF) approximates this mean-field model with an ensemble of interacting particles, employing a Gaussian ansatz for the joint distribution of the state and…
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Propagation of Chaos in One-hidden-layer Neural Networks beyond Logarithmic Time
Propagation of Chaos in One-hidden-layer Neural Networks beyond Logarithmic Time arXiv:2504.13110v1 Announce Type: new Abstract: We study the approximation gap between the dynamics of a polynomial-width neural network and its infinite-width counterpart, both trained using projected gradient descent in the mean-field scaling regime. We demonstrate how to tightly bound this approximation gap through a differential…
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Applications of Statistical Field Theory in Deep Learning
Applications of Statistical Field Theory in Deep Learning arXiv:2502.18553v1 Announce Type: new Abstract: Deep learning algorithms have made incredible strides in the past decade yet due to the complexity of these algorithms, the science of deep learning remains in its early stages. Being an experimentally driven field, it is natural to seek a theory of…
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Deep Generalized Schr”odinger Bridges: From Image Generation to Solving Mean-Field Games
Deep Generalized Schr”odinger Bridges: From Image Generation to Solving Mean-Field Games arXiv:2412.20279v1 Announce Type: new Abstract: Generalized Schr”odinger Bridges (GSBs) are a fundamental mathematical framework used to analyze the most likely particle evolution based on the principle of least action including kinetic and potential energy. In parallel to their well-established presence in the theoretical realms…