Expressivity of Neural Networks with Random Weights and Learned Biases

Landmark universal function approximation results for neural networks with trained weights and biases provided impetus for the ubiquitous use of neural networks as learning models in Artificial Intelligence (AI) and neuroscience. Recent work has pushed the bounds of universal approximation by showing that arbitrary functions can similarly be learned by tuning smaller subsets of parameters, for example the output weights, within randomly initialized networks. Motivated by the fact that biases can be interpreted as biologically plausible mechanisms for adjusting unit outputs in neural networks, such as tonic inputs or activation thresholds, we investigate the expressivity of neural networks with random weights where only biases are optimized. We provide theoretical and numerical evidence demonstrating that feedforward neural networks with fixed random weights can be trained to perform multiple tasks by learning biases only. We further show that an equivalent result holds for recurrent neural networks predicting dynamical system trajectories. Our results are relevant to neuroscience, where they demonstrate the potential for behaviourally relevant changes in dynamics without modifying synaptic weights, as well as for AI, where they shed light on multi-task methods such as bias fine-tuning and unit masking.

Flexible Phase Dynamics for Bio-Plausible Contrastive Learning

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.