# Quantitative Gaussian-Process limits of Tensor Programs

arXiv: https://arxiv.org/abs/2607.06290 · HTML: https://mlsanity.com/paper/2607.06290/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [Gaussian Process Behaviour in Wide Deep Neural Networks](https://mlsanity.com/paper/1804.11271/) (2018)
- [Tensor Programs I: Wide Feedforward or Recurrent Neural Networks of Any Architecture are Gaussian Processes](https://mlsanity.com/paper/1910.12478/) (2019)
- [Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation](https://mlsanity.com/paper/1902.04760/) (2019)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Infinite attention: NNGP and NTK for deep attention networks](https://mlsanity.com/paper/2006.10540/) (2020)
- [Tensor Programs III: Neural Matrix Laws](https://mlsanity.com/paper/2009.10685/) (2020)
- [Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks](https://mlsanity.com/paper/2203.07379/) (2022)
- [Quantitative CLTs in Deep Neural Networks](https://mlsanity.com/paper/2307.06092/) (2023)
- [Non-asymptotic approximations of neural networks by Gaussian processes](https://mlsanity.com/paper/2102.08668/) (2021)
- [Wide Deep Neural Networks with Gaussian Weights are Very Close to Gaussian Processes](https://mlsanity.com/paper/2312.11737/) (2023)
- [Non-asymptotic approximations of Gaussian neural networks via second-order Poincar'e inequalities](https://mlsanity.com/paper/2304.04010/) (2023)
- [A Quantitative Functional Central Limit Theorem for Shallow Neural Networks](https://mlsanity.com/paper/2306.16932/) (2023)
- [Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models](https://mlsanity.com/paper/2604.26898/) (2026)
- [Trained quantum neural networks are Gaussian processes](https://mlsanity.com/paper/2402.08726/) (2024)
- [Infinite-Width Limit of a Single Attention Layer: Analysis via Tensor Programs](https://mlsanity.com/paper/2506.00846/) (2025)
- [Universality in Deep Neural Networks: An approach via the Lindeberg exchange principle](https://mlsanity.com/paper/2605.02771/) (2026)
- [Quantitative convergence of trained single layer neural networks to Gaussian processes](https://mlsanity.com/paper/2509.24544/) (2025)

## Built on by (most cited first, 1 of 1)

- [Lifting Finite-Sample Gaussian Approximation of Wide Neural Networks to Functional Convergence](https://mlsanity.com/paper/2610.18166/) (2026)

## 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.