Bookmarks
Logic and linear algebra: an introduction
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit by showing how to represent proofs in linear logic as linear maps between vector spaces. The interesting part of this vector space semantics is based on the cofree cocommutative coalgebra of Sweedler.
immersivemath: Immersive Linear Algebra
This text introduces a book on linear algebra with chapters covering vectors, dot products, matrix operations, and more. It aims to help readers understand fundamental concepts and tools in linear algebra through clear explanations and examples. The book includes topics such as Gaussian elimination, determinants, rank, and eigenvalues.
LADW_2017-09-04
This text discusses properties of vector spaces and matrices, particularly focusing on bases and eigenvalues. It establishes that any linearly independent system of vectors can be completed to form a basis in a finite-dimensional vector space. Additionally, it explains that operators in inner product spaces have an upper triangular matrix representation under certain conditions.
Deep Learning Course
This document provides resources for François Fleuret's deep-learning course at the University of Geneva. The course offers a thorough introduction to deep learning, with examples using the PyTorch framework. The materials include slides, recordings, and a virtual machine. The course covers topics such as machine learning objectives, tensor operations, automatic differentiation, gradient descent, and deep-learning techniques. The document also includes prerequisites for the course, such as knowledge of linear algebra, differential calculus, Python programming, and probability and statistics.
Pen and Paper Exercises in Machine Learning
This is a collection of (mostly) pen-and-paper exercises in machine learning.
The exercises are on the following topics: linear algebra, optimisation,
directed graphical models, undirected graphical models, expressive power of
graphical models, factor graphs and message passing, inference for hidden
Markov models, model-based learning (including ICA and unnormalised models),
sampling and Monte-Carlo integration, and variational inference.
Linear Algebra Review and Reference
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Linear Algebra
Linear algebra is a fundamental topic in understanding and working with machine learning algorithms, especially deep learning algorithms. This chapter provides an introduction to scalars, vectors, matrices, and tensors, which are the key mathematical objects in linear algebra. It explains the concepts and notation used in linear algebra, such as matrix multiplication, transpose, identity and inverse matrices, and norms. The chapter also introduces special kinds of matrices and vectors, such as diagonal matrices, orthogonal matrices, and eigenvalues and eigenvectors. These concepts are important for analyzing and solving equations in machine learning.
The Random Transformer
This blog post provides an end-to-end example of the math within a transformer model, with a focus on the encoder part. The goal is to understand how the model works, and to make it more manageable, simplifications are made and the dimensions of the model are reduced. The post recommends reading "The Illustrated Transformer" blog for a more intuitive explanation of the transformer model. The prerequisites for understanding the content include basic knowledge of linear algebra, machine learning, and deep learning. The post covers the math within a transformer model during inference, attention mechanisms, residual connections and layer normalization, and provides some code to scale it up.
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