Geometric Dyson Brownian Motions and the Free Log-Normal Limit for a Non-Square Gaussian Matrix Product
Mufan Li, Jaume de Dios Pont, Mihai Nica, Daniel M. Roy
math.PR, stat.ML
Submitted: 2026-06-29
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent
- Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation
- Polylogarithmic width suffices for gradient descent to achieve arbitrarily small test error with shallow ReLU networks
- Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks
- Non-asymptotic approximations of Gaussian neural networks via second-order Poincar'e inequalities
- Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processes
- Normal approximation of Random Gaussian Neural Networks
- Quantitative CLTs in Deep Neural Networks
- Entropic bounds for conditionally Gaussian vectors and applications to neural networks
- Gaussian random field approximation via Stein's method with applications to wide random neural networks
- Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights
- Wide neural networks with general weights: convergence rate and explicit dependence on the hyper-parameters
- Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle
- Trainability and Accuracy of Neural Networks: An Interacting Particle System Approach
- On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport
- Mean Field Analysis of Neural Networks: A Law of Large Numbers
- Feature Learning in Infinite-Width Neural Networks
- Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer
- Bayesian Inference with Deep Weakly Nonlinear Networks
- Proportional infinite-width infinite-depth limit for deep linear neural networks
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