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.

Neural burst codes disguised as rate codes.

The burst coding hypothesis posits that the occurrence of sudden high-frequency patterns of action potentials constitutes a salient syllable of the neural code. Many neurons, however, do not produce clearly demarcated bursts, an observation invoked to rule out the pervasiveness of this coding scheme across brain areas and cell types. Here we ask how detrimental ambiguous spike patterns, those that are neither clearly bursts nor isolated spikes, are for neuronal information transfer. We addressed this question using information theory and computational simulations. By quantifying how information transmission depends on firing statistics, we found that the information transmitted is not strongly influenced by the presence of clearly demarcated modes in the interspike interval distribution, a feature often used to identify the presence of burst coding. Instead, we found that neurons having unimodal interval distributions were still able to ascribe different meanings to bursts and isolated spikes. In this regime, information transmission depends on dynamical properties of the synapses as well as the length and relative frequency of bursts. Furthermore, we found that common metrics used to quantify burstiness were unable to predict the degree with which bursts could be used to carry information. Our results provide guiding principles for the implementation of coding strategies based on spike-timing patterns, and show that even unimodal firing statistics can be consistent with a bivariate neural code.