Notes
A collection of technical notes, mathematical derivations, and research insights, particularly focused on computer architecture and deep learning. These notes serve as a personal knowledge base and may be useful for others working in similar areas.
A beleza da convolución - The beauty of convolution
This document analyzes the mathematical connection between classical convolution operations from signal theory and convolutional neural networks. The author demonstrates that convolutional layers are mathematically equivalent to standard perceptrons with constrained weight matrices—specifically, weights that are shared across spatial locations with many connections set to zero. By representing images as discrete functions and showing how convolution kernels correspond to these weight-sharing patterns, the document explains why convolutional networks, while not more expressive than multilayer perceptrons, are dramatically more efficient to train due to significant parameter reduction. The work bridges theoretical signal processing with practical deep learning implementations, providing mathematical insight into why convolutional architectures excel in computer vision tasks.