# Efficient Computation of Hessian Matrices in TensorFlow

arXiv: https://arxiv.org/abs/1905.05559 · HTML: https://mlsanity.com/paper/1905.05559/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2019.

## Built on by (most cited first, 2 of 2)

- [Unleashing the Power of Data Tsunami: A Comprehensive Survey on Data Assessment and Selection for Instruction Tuning of Language Models](https://mlsanity.com/paper/2408.02085/) (2024)
- [Differentiable and Scalable Generative Adversarial Models for Data Imputation](https://mlsanity.com/paper/2201.03202/) (2022)

## Abstract (arXiv)

The Hessian matrix has a number of important applications in a variety of different fields, such as optimzation, image processing and statistics. In this paper we focus on the practical aspects of efficiently computing Hessian matrices in the context of deep learning using the Python scripting language and the TensorFlow library. We define a general feed-forward neural network model and show how to efficiently compute two quantities: the cost function's exact Hessian matrix, and the cost function's approximate Hessian matrix, known as the Outer Product of Gradients (OPG) matrix. Furthermore, as the number of parameters (weights and biases) in deep learning usually is very large, we show how to reduce the quadratic space complexity by an efficient implementation based on approximate eigendecompositions.