# A Modern Analysis of Hutchinson's Trace Estimator

arXiv: https://arxiv.org/abs/2012.12895 · HTML: https://mlsanity.com/paper/2012.12895/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2020.

## Built on by (most cited first, 11 of 11)

- [FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation](https://mlsanity.com/paper/2210.04296/) (2022)
- [Preconditioning for Scalable Gaussian Process Hyperparameter Optimization](https://mlsanity.com/paper/2107.00243/) (2021)
- [Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks](https://mlsanity.com/paper/2312.14499/) (2023)
- [Stochastic Taylor Derivative Estimator: Efficient amortization for arbitrary differential operators](https://mlsanity.com/paper/2412.00088/) (2024)
- [Understanding Hessian Alignment for Domain Generalization](https://mlsanity.com/paper/2308.11778/) (2023)
- [Efficiently Access Diffusion Fisher: Within the Outer Product Span Space](https://mlsanity.com/paper/2505.23264/) (2025)
- [Tensorizing flows: a tool for variational inference](https://mlsanity.com/paper/2305.02460/) (2023)
- [Covariance-aware sampling for Diffusion Models](https://mlsanity.com/paper/2605.13910/) (2026)
- [A Novel Approach for Intrinsic Dimension Estimation](https://mlsanity.com/paper/2503.09485/) (2025)
- [Deterministic Bounds and Random Estimates of Metric Tensors on Neuromanifolds](https://mlsanity.com/paper/2505.13614/) (2025)
- [Discrete Double-Bracket Flows for Isotropic-Noise Invariant Eigendecomposition](https://mlsanity.com/paper/2602.13759/) (2026)

## Abstract (arXiv)

The paper establishes the new state-of-art in the accuracy analysis of Hutchinson's trace estimator. Leveraging tools that have not been previously used in this context, particularly hypercontractive inequalities and concentration properties of sub-gamma distributions, we offer an elegant and modular analysis, as well as numerically superior bounds. Besides these improvements, this work aims to better popularize the aforementioned techniques within the CS community.