On Space Folds of ReLU Neural Networks
This work is significant for researchers and developers of neural networks, as it provides a new perspective on how ReLU neural networks process input information, which can be useful for improving model design and interpretability.
The authors tackled the problem of understanding the geometric transformations in ReLU neural networks, and found that consecutive layers can be seen as space folding transformations, with a loss of convexity in the activation space. Their quantitative analysis provided new insights into how these models process input information, with empirical results on CantorNet and MNIST benchmarks.
Recent findings suggest that the consecutive layers of ReLU neural networks can be understood geometrically as space folding transformations of the input space, revealing patterns of self-similarity. In this paper, we present the first quantitative analysis of this space folding phenomenon in ReLU neural networks. Our approach focuses on examining how straight paths in the Euclidean input space are mapped to their counterparts in the Hamming activation space. In this process, the convexity of straight lines is generally lost, giving rise to non-convex folding behavior. To quantify this effect, we introduce a novel measure based on range metrics, similar to those used in the study of random walks, and provide the proof for the equivalence of convexity notions between the input and activation spaces. Furthermore, we provide empirical analysis on a geometrical analysis benchmark (CantorNet) as well as an image classification benchmark (MNIST). Our work advances the understanding of the activation space in ReLU neural networks by leveraging the phenomena of geometric folding, providing valuable insights on how these models process input information.