Quantitative Gaussian-Process limits of Tensor Programs
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Abstract (arXiv)
We study the infinite-width Gaussian-process limit of random neural networks through the lens of tensor programs, and we provide a quantitative convergence theory in Wasserstein distance. Our main result gives explicit finite-width error bounds, of order inverse square-root of the widths between finite-network executions and their Gaussian-process limits. The framework is architecture-agnostic and covers feed-forward models together with weight-sharing schemes relevant for recurrent and transformer-type architectures.
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References · 20
- 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
- 2019Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descentcited by 732
- 2019On Exact Computation with an Infinitely Wide Neural Netcited by 572
- 2018Gaussian Process Behaviour in Wide Deep Neural Networkscited by 314
- 2019Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processescited by 148
- 2019Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivationcited by 146
- 2020Tensor Programs II: Neural Tangent Kernel for Any Architecturecited by 139
- 2020Infinite attention: NNGP and NTK for deep attention networkscited by 117
- 2020Tensor Programs III: Neural Matrix Lawscited by 47
- 2022Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networkscited by 24
- 2023Quantitative CLTs in Deep Neural Networkscited by 19
- 2021Non-asymptotic approximations of neural networks by Gaussian processescited by 18
8 more
- 2023Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processescited by 11
- 2023Non-asymptotic approximations of Gaussian neural networks via second-order Poincar'e inequalitiescited by 10
- 2023A Quantitative Functional Central Limit Theorem for Shallow Neural Networkscited by 8
- 2024Trained quantum neural networks are Gaussian processescited by 5
- 2025Infinite-Width Limit of a Single Attention Layer: Analysis via Tensor Programscited by 5
- 2026Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Modelscited by 5
- 2026Universality in Deep Neural Networks: An approach via the Lindeberg exchange principlecited by 2
- 2025Quantitative convergence of trained single layer neural networks to Gaussian processescited by 1
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