Two-argument activation functions learn soft XOR operations like cortical neurons

TL;DR

This paper introduces two-argument activation functions modeled after biological neurons, which learn soft XOR operations, improving learning speed, performance, and robustness in neural networks.

Contribution

It proposes biologically inspired two-input activation functions that emulate cortical neuron interactions, leading to enhanced neural network capabilities.

Findings

Learned nonlinearities produce soft XOR functions.

Networks with these nonlinearities outperform ReLU-based networks.

Enhanced robustness to natural and adversarial perturbations.

Abstract

Neurons in the brain are complex machines with distinct functional compartments that interact nonlinearly. In contrast, neurons in artificial neural networks abstract away this complexity, typically down to a scalar activation function of a weighted sum of inputs. Here we emulate more biologically realistic neurons by learning canonical activation functions with two input arguments, analogous to basal and apical dendrites. We use a network-in-network architecture where each neuron is modeled as a multilayer perceptron with two inputs and a single output. This inner perceptron is shared by all units in the outer network. Remarkably, the resultant nonlinearities often produce soft XOR functions, consistent with recent experimental observations about interactions between inputs in human cortical neurons. When hyperparameters are optimized, networks with these nonlinearities learn faster and perform better than conventional ReLU nonlinearities with matched parameter counts, and they are more robust to natural and adversarial perturbations.