  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.
