The Matrix Calculus You Need For Deep Learning
This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. We assume no math knowledge beyond what you learned in calculus 1, and provide links to help you refresh the necessary math where needed. Note that you do not need to understand this material before you start learning to train and use deep learning in practice; rather, this material is for those who are already familiar with the basics of neural networks, and wish to deepen their understanding of the underlying math. Don't worry if you get stuck at some point along the way---just go back and reread the previous section, and try writing down and working through some examples. And if you're still stuck, we're happy to answer your questions in the Theory category at theory category at fast ai forums. Note: There is a reference section at the end of the paper summarizing all the key matrix calculus rules and terminology discussed here. See related articles at explained.ai - Deep explanations of machine learning and related topics
Frugal Machine Learning for Energy-efficient, and Resource-aware Artificial Intelligence
Frugal Machine Learning (FML) refers to the practice of designing Machine Learning (ML) models that are efficient, cost-effective, and mindful of resource constraints. This field aims to achieve acceptable performance while minimizing the use of computational resources, time, energy, and data for both training and inference. FML strategies can be broadly categorized into input frugality, learning process frugality, and model frugality, each focusing on reducing resource consumption at different stages of the ML pipeline. This chapter explores recent advancements, applications, and open challenges in FML, emphasizing its importance for smart environments that incorporate edge computing and IoT devices, which often face strict limitations in bandwidth, energy, or latency. Technological enablers such as model compression, energy-efficient hardware, and data-efficient learning techniques are discussed, along with adaptive methods including parameter regularization, knowledge distillation, and dynamic architecture design that enable incremental model updates without full retraining. Furthermore, it provides a comprehensive taxonomy of frugal methods, discusses case studies across diverse domains, and identifies future research directions to drive innovation in this evolving field.
An Introduction to Discrete Variational Autoencoders
Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from which we can sample and pass realizations to a decoder network. This model is trained to reconstruct its inputs and is optimized through the evidence lower bound. In recent years, discrete latent spaces have grown in popularity, suggesting that they may be a natural choice for many data modalities (e.g. text). In this tutorial, we provide a rigorous, yet practical, introduction to discrete variational autoencoders -- specifically, VAEs in which the latent space is made up of latent variables that follow a categorical distribution. We assume only a basic mathematical background with which we carefully derive each step from first principles. From there, we develop a concrete training recipe and provide an example implementation, hosted at https://github.com/alanjeffares/discreteVAE.
A Practical Introduction to Deep Reinforcement Learning
Deep reinforcement learning (DRL) has emerged as a powerful framework for solving sequential decision-making problems, achieving remarkable success in a wide range of applications, including game AI, autonomous driving, biomedicine, and large language models. However, the diversity of algorithms and the complexity of theoretical foundations often pose significant challenges for beginners seeking to enter the field. This tutorial aims to provide a concise, intuitive, and practical introduction to DRL, with a particular focus on the Proximal Policy Optimization (PPO) algorithm, which is one of the most widely used and effective DRL methods. To facilitate learning, we organize all algorithms under the Generalized Policy Iteration (GPI) framework, offering readers a unified and systematic perspective. Instead of lengthy theoretical proofs, we emphasize intuitive explanations, illustrative examples, and practical engineering techniques. This work serves as an efficient and accessible guide, helping readers rapidly progress from basic concepts to the implementation of advanced DRL algorithms.
