Supervised learning based on temporal coding in spiking neural networks (1606.08165v2)

Abstract: Gradient descent training techniques are remarkably successful in training analog-valued artificial neural networks (ANNs). Such training techniques, however, do not transfer easily to spiking networks due to the spike generation hard non-linearity and the discrete nature of spike communication. We show that in a feedforward spiking network that uses a temporal coding scheme where information is encoded in spike times instead of spike rates, the network input-output relation is differentiable almost everywhere. Moreover, this relation is piece-wise linear after a transformation of variables. Methods for training ANNs thus carry directly to the training of such spiking networks as we show when training on the permutation invariant MNIST task. In contrast to rate-based spiking networks that are often used to approximate the behavior of ANNs, the networks we present spike much more sparsely and their behavior can not be directly approximated by conventional ANNs. Our results highlight a new approach for controlling the behavior of spiking networks with realistic temporal dynamics, opening up the potential for using these networks to process spike patterns with complex temporal information.

• The paper introduces a novel temporal coding method that transforms spike times into an exponential z-domain, enabling gradient descent learning in spiking neural networks.
• It demonstrates efficient nonlinear representation by successfully solving the XOR task and achieving a 2.45% test error on the MNIST classification benchmark.
• The approach offers sparse, rapid classification by processing only a small fraction of spikes, paving the way for power-efficient, real-time neuromorphic applications.

Supervised Learning Using Temporal Coding in Spiking Neural Networks

The paper "Supervised learning based on temporal coding in spiking neural networks" by Hesham Mostafa proposes an innovative approach to training spiking neural networks (SNNs) using supervised learning techniques. This work addresses a significant challenge in the field of neuromorphic computing: the difficulty of applying gradient descent training methods, which are successful in analog-valued artificial neural networks (ANNs), to SNNs. This is due to the all-or-nothing nature of spikes and the discrete spike communication which presents a non-differentiable nature traditionally.

Key Contributions

The paper introduces a novel method of encoding information through the timing of spikes rather than conventional spike rates. By demonstrating that, in a feedforward SNN using temporal coding, the input-output relationship is differentiable almost everywhere and is piece-wise linear after variable transformation, this work enables the direct application of ANN training methods to SNNs. This approach diverges from typical rate-based spiking networks, offering a sparse spiking alternative that realistically models temporal dynamics without simplifying them to ANN behaviors.

A significant assertion in the paper is that by using spike timing for information encoding, the resulting SNNs can process complex temporal information efficiently, a capability not feasible with prior rate-coding mechanisms.

Methodology

The network architecture employs a transformation where spike times are represented in an exponential form, creating a z-domain where the linear relations can be efficiently manipulated through standard gradient descent. A crucial aspect of the training method developed involves imposing a differentiable cost function directly on spike times, which enables the rigorous tuning of individual spike timings within the network.

The researchers employ non-leaky integrate-and-fire neuron models with exponentially decaying synaptic currents, a choice that allows them to derive mathematical expressions for membrane potentials and synaptic currents analytically. This approach leads to precise formulations for updating neuron states that are critical for training these models with gradient-based methods.

Experimental Evaluation

The paper presents two key experiments: an XOR task and the permutation invariant MNIST classification task. The XOR task demonstrates the network's capability to represent nonlinear functions, a fundamental requirement for universal computation, while the performance on the MNIST task highlights the network's capability to generalize in a classification setting.

Impressively, the network achieves a test error rate of 2.45% on MNIST after training with noise-input perturbed spike times, indicating a robust mechanism for avoiding overfitting. The networks are shown to make rapid classification decisions, with one network variant making decisions after processing only 3.0% of hidden neuron spikes on average.

Implications and Future Directions

The ability to utilize SNNs with temporal coding and gradient descent methods opens new avenues in efficient, power-reduced neuromorphic processing, beneficial in scenarios where rapid event-driven computation is critical. The sparse spike activity aligns well with the operational paradigms of neuromorphic hardware, promising reductions in power consumption and improvements in real-time responsiveness.

Further research could explore extending these methods to recurrent SNN architectures, potentially allowing for continuous input processing and enhancing the applicability of SNNs in complex sequential decision-making tasks. Additionally, addressing overfitting through advanced regularization methods remains a relevant challenge, one that could further enhance generalization performance.

In essence, this paper yields critical insights into the practical training of SNNs, paving the way for broader application in fields where temporal dynamics and efficiency are of paramount importance.