Didactic Visualization of Convergence Dynamics in Neural Networks: A Geometric Approach to Teaching Machine Learning

The teaching of Artificial Neural Networks (ANNs) in engineering courses often comes up against the mathematical abstraction of their hyperparameters, resulting in a 'black box' perception on the part of students. This work presents the development of a didactic tool in Python aimed at the geometric visualization of convergence and the Universal Approximation Theorem. The methodology employed a Multilayer Perceptron (MLP) network with 50 neurons in the hidden layer to approximate a noisy sinusoidal function. The Sigmoid, Hyperbolic Tangent (Tanh) and ReLU activation functions were compared over 1000 training epochs. The qualitative and quantitative results show the particularities of each function: Tanh demonstrated superiority in the modeling of oscillatory signals, while ReLU stood out for its piecewise nature and sensitivity to noise. The integrated analysis of predictions and loss curves consolidates the tool as an effective pedagogical resource for practical Machine Learning laboratories.