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Computational Mathematics

Computational Mathematics

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

4 papers in this specialization

Paperzilla Papers in Computational Mathematics

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.

Sep 14, 01:40 PM

Matrix Calculus (for Machine Learning and Beyond)

These lecture notes cover matrix calculus, explaining how to find derivatives of functions with matrix inputs and outputs. The notes discuss applications in machine learning and other fields, focusing on linear operators, Jacobians, and computational methods like automatic differentiation.

Aug 22, 01:28 PM

MATHEMATICAL THEORY OF DEEP LEARNING

This book presents a rigorous mathematical introduction to the theory of deep learning, focusing on approximation, optimization, and generalization. It explains how neural networks represent functions, how their training works, and why they can generalize to unseen data. The book primarily considers feedforward networks and omits certain advanced architectures or practical aspects.

Aug 19, 05:56 AM

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.

s41586-022-05172-4.pdf

Jul 14, 11:29 AM

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