Maximum Class Separation as Inductive Bias in One Matrix
This provides a simple, plug-and-play solution for enhancing deep learning performance in various recognition tasks, though it is incremental as it builds on existing separation principles.
The paper tackles the problem of deep networks lacking the inductive bias of maximum class separation by proposing a fixed matrix multiplication before softmax to encode this bias without optimization. The method improves classification, long-tailed recognition, out-of-distribution detection, and open-set recognition across datasets like CIFAR and ImageNet, with negligible computational overhead.
Maximizing the separation between classes constitutes a well-known inductive bias in machine learning and a pillar of many traditional algorithms. By default, deep networks are not equipped with this inductive bias and therefore many alternative solutions have been proposed through differential optimization. Current approaches tend to optimize classification and separation jointly: aligning inputs with class vectors and separating class vectors angularly. This paper proposes a simple alternative: encoding maximum separation as an inductive bias in the network by adding one fixed matrix multiplication before computing the softmax activations. The main observation behind our approach is that separation does not require optimization but can be solved in closed-form prior to training and plugged into a network. We outline a recursive approach to obtain the matrix consisting of maximally separable vectors for any number of classes, which can be added with negligible engineering effort and computational overhead. Despite its simple nature, this one matrix multiplication provides real impact. We show that our proposal directly boosts classification, long-tailed recognition, out-of-distribution detection, and open-set recognition, from CIFAR to ImageNet. We find empirically that maximum separation works best as a fixed bias; making the matrix learnable adds nothing to the performance. The closed-form implementation and code to reproduce the experiments are available on github.