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Computational Mathematics

Numerical algorithms and computational techniques, including numerical analysis, scientific computing, high-performance computing, computational algebra, and mathematical software development

4 papers

Papers

Mathematics of Neural Networks

This document provides a comprehensive overview of the mathematics behind neural networks, starting with the basics of supervised learning and progressing to advanced topics like deep learning, convolutional neural networks, and the novel concept of equivariant tropical operators. It explains key concepts like activation functions, gradient descent, and backpropagation, offering detailed examples and mathematical formulations. The document also explores how geometric transformations can be integrated into neural network design for tasks requiring specific symmetries.

Computational Mathematics Sep 14, 01:40 PM

Discovering faster matrix multiplication algorithms with reinforcement learning

This paper introduces AlphaTensor, a deep reinforcement learning agent that discovers novel algorithms for matrix multiplication, outperforming human-designed algorithms in certain cases. AlphaTensor finds a faster algorithm for 4x4 matrix multiplication in a finite field and also discovers algorithms tailored to specific hardware, achieving speed-ups compared to existing methods.

Computational Mathematics Jul 14, 11:29 AM