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There is an interest in finding energy efficient alternatives to current state of the art neural network training algorithms. Spiking neural network are a promising approach, because they can be simulated energy efficiently on neuromorphic hardware platforms. However, these platforms come with limitations on the design of the training algorithm. Most importantly, backpropagation cannot be implemented on those. We propose a novel neuromorphic algorithm, the \textit{Spiking Forward Direct Feedback Alignment} (SFDFA) algorithm, an adaption of \textit{Forward Direct Feedback Alignment} to train SNNs. SFDFA estimates the weights between output and hidden neurons as feedback connections. The main contribution of this paper is to describe how exact local gradients of spikes can be computed in an online manner while taking into account the intra-neuron dependencies between post-synaptic spikes and derive a dynamical system for neuromorphic hardware compatibility. We compare the SFDFA algorithm with a number of competitor algorithms and show that the proposed algorithm achieves higher performance and convergence rates.

Feedback alignment algorithms are an alternative to backpropagation to train neural networks, whereby some of the partial derivatives that are required to compute the gradient are replaced by random terms. This essentially transforms the update rule into a random walk in weight space. Surprisingly, learning still works with those algorithms, including training of deep neural networks. This is generally attributed to an alignment of the update of the random walker with the true gradient - the eponymous gradient alignment -- which drives an approximate gradient descend. The mechanism that leads to this alignment remains unclear, however. In this paper, we use mathematical reasoning and simulations to investigate gradient alignment. We observe that the feedback alignment update rule has fixed points, which correspond to extrema of the loss function. We show that gradient alignment is a stability criterion for those fixed points. It is only a necessary criterion for algorithm performance. Experimentally, we demonstrate that high levels of gradient alignment can lead to poor algorithm performance and that the alignment is not always driving the gradient descend.

Spiking Neural Networks (SNNs) have emerged as a promising alternative to traditional Deep Neural Networks for low-power computing. However, the effectiveness of SNNs is not solely determined by their performance but also by their energy consumption, prediction speed, and robustness to noise. The recent method Fast \& Deep, along with others, achieves fast and energy-efficient computation by constraining neurons to fire at most once. Known as Time-To-First-Spike (TTFS), this constraint however restricts the capabilities of SNNs in many aspects. In this work, we explore the relationships between performance, energy consumption, speed and stability when using this constraint. More precisely, we highlight the existence of tradeoffs where performance and robustness are gained at the cost of sparsity and prediction latency. To improve these tradeoffs, we propose a relaxed version of Fast \& Deep that allows for multiple spikes per neuron. Our experiments show that relaxing the spike constraint provides higher performance while also benefiting from faster convergence, similar sparsity, comparable prediction latency, and better robustness to noise compared to TTFS SNNs. By highlighting the limitations of TTFS and demonstrating the advantages of unconstrained SNNs we provide valuable insight for the development of effective learning strategies for neuromorphic computing.

Supervised learning in deep neural networks is commonly performed using error backpropagation. However, the sequential propagation of errors during the backward pass limits its scalability and applicability to low-powered neuromorphic hardware. Therefore, there is growing interest in finding local alternatives to backpropagation. Recently proposed methods based on forward-mode automatic differentiation suffer from high variance in large deep neural networks, which affects convergence. In this paper, we propose the Forward Direct Feedback Alignment algorithm that combines Activity-Perturbed Forward Gradients with Direct Feedback Alignment and momentum. We provide both theoretical proofs and empirical evidence that our proposed method achieves lower variance than forward gradient techniques. In this way, our approach enables faster convergence and better performance when compared to other local alternatives to backpropagation and opens a new perspective for the development of online learning algorithms compatible with neuromorphic systems.