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Signatures of criticality in efficient coding networks
The critical brain hypothesis states that the brain can benefit from operating close to a second-order phase transition. While it has been shown that several computational aspects of sensory information processing (e.g., sensitivity to input) are optimal in this regime, it is still unclear whether these computational benefits of criticality can be leveraged by neural systems performing behaviorally relevant computations. To address this question, we investigate signatures of criticality in networks optimized to perform efficient encoding. We consider a network of leaky integrate-and-fire neurons with synaptic transmission delays and input noise. Previously, it was shown that the performance of such networks varies non-monotonically with the noise amplitude. Interestingly, we find that in the vicinity of the optimal noise level for efficient coding, the network dynamics exhibits signatures of criticality, namely, the distribution of avalanche sizes follows a power law. When the noise amplitude is too low or too high for efficient coding, the network appears either super-critical or sub-critical, respectively. This result suggests that two influential, and previously disparate theories of neural processing optimization—efficient coding, and criticality—may be intimately related
Event-based Backpropagation for Exact Gradients in Spiking Neural Networks
Gradient-based optimization powered by the backpropagation algorithm proved to be the pivotal method in the training of non-spiking artificial neural networks. At the same time, spiking neural networks hold the promise for efficient processing of real-world sensory data by communicating using discrete events in continuous time. We derive the backpropagation algorithm for a recurrent network of spiking (leaky integrate-and-fire) neurons with hard thresholds and show that the backward dynamics amount to an event-based backpropagation of errors through time. Our derivation uses the jump conditions for partial derivatives at state discontinuities found by applying the implicit function theorem, allowing us to avoid approximations or substitutions. We find that the gradient exists and is finite almost everywhere in weight space, up to the null set where a membrane potential is precisely tangent to the threshold. Our presented algorithm, EventProp, computes the exact gradient with respect to a general loss function based on spike times and membrane potentials. Crucially, the algorithm allows for an event-based communication scheme in the backward phase, retaining the potential advantages of temporal sparsity afforded by spiking neural networks. We demonstrate the optimization of spiking networks using gradients computed via EventProp and the Yin-Yang and MNIST datasets with either a spike time-based or voltage-based loss function and report competitive performance. Our work supports the rigorous study of gradient-based optimization in spiking neural networks as well as the development of event-based neuromorphic architectures for the efficient training of spiking neural networks. While we consider the leaky integrate-and-fire model in this work, our methodology generalises to any neuron model defined as a hybrid dynamical system.