The Mathematics Behind Artificial Neural Networks

Abstract

The workshop "The Mathematics Behind Artificial Neural Networks" aims to demystify the mathematical foundations that support the functioning of artificial neural networks, allowing participants to develop a solid understanding of the theoretical and applied processes that permeate this technology. With a duration of up to 2 hours and 30 minutes, the activity seeks to present, in a clear and didactic way, the main mathematical concepts involved in the training, use, and performance of neural networks, in addition to offering practical examples that connect theory to application. Sixty spots will be available, ensuring an interactive environment conducive to learning. The central objectives of the workshop include: understanding the fundamentals of linear algebra and calculus applied to neural networks, such as the use of matrices and vectors to represent input data, weights, and bias; exploring the role of differential calculus in adjusting weights during training, focusing on the backpropagation algorithm and gradient descents; discussing the use of probability and statistics in activation functions and performance metrics; and introducing optimization concepts for adjusting hyperparameters and preventing problems such as overfitting. Another fundamental mathematical concept involves optimization theory, which helps in adjusting hyperparameters to ensure that the network reaches an ideal balance between accuracy and efficiency. In addition, studies on network topologies, such as convolutional networks (CNNs) and recurrent networks (RNNs), delve into specific mathematical transformations that make ANNs suitable for tasks such as image processing or time series. The methodology used will be based on a practical and interactive approach, structured in three main stages. In the first stage, a theoretical introduction will be carried out to present the fundamental mathematical concepts, using applied examples to facilitate participants' understanding. In the second stage, guided practical activities will be developed, in which participants will be able to simulate some aspects of the functioning of neural networks in accessible computational tools, such as Python notebooks prepared for the minicourse. Finally, the last part will be dedicated to the application of the content through exercises and discussion on the challenges and limitations of artificial intelligence models, promoting the active participation of those present. The workshop does not require advanced prior knowledge, being suitable for students and professionals from different areas who are interested in artificial intelligence and artificial neural networks. The main focus is to provide comprehensive and accessible learning, emphasizing the mathematical elements that allow the development of sophisticated models capable of solving complex problems. With this activity, it is expected to provide participants with the intellectual and technical tools necessary to understand and apply artificial neural networks in different contexts.