Exploiting Space Folding by Neural Networks

Recent findings suggest that consecutive layers of neural networks with the ReLU activation function fold the input space during the learning process. While many works hint at this phenomenon, an approach to quantify the folding was only recently proposed by means of a space folding measure based on the Hamming distance in the discrete activation space. We generalize the space folding measure to a wider class of activation functions through the introduction of equivalence classes of input data. We then analyze its mathematical and computational properties. Lastly, we link the folding to geometry of adversarial attacks. We underpin our claims with an experimental evaluation.