Recent insights have revealed that rate-coding is a primary form of information representation captured by surrogate-gradient-based Backpropagation Through Time (BPTT) in training deep Spiking Neural Networks (SNNs). Motivated by these findings, we propose rate-based backpropagation, a training strategy specifically designed to exploit rate-based representations to reduce the complexity of BPTT. Our method minimizes reliance on detailed temporal derivatives by focusing on averaged dynamics, streamlining the computational graph to reduce memory and computational demands of SNNs training. We substantiate the rationality of the gradient approximation between BPTT and the proposed method through both theoretical analysis and empirical observations. Comprehensive experiments on CIFAR-10, CIFAR-100, ImageNet, and CIFAR10-DVS validate that our method achieves comparable performance to BPTT counterparts, and surpasses state-of-the-art efficient training techniques. By leveraging the inherent benefits of rate-coding, this work sets the stage for more scalable and efficient SNNs training within resource-constrained environments.

Learning long-term dependencies in extended temporal sequences requires credit assignment to events far back in the past. The most common method for training recurrent neural networks, back-propagation through time (BPTT), requires credit information to be propagated backwards through every single step of the forward computation, potentially over thousands or millions of time steps. This becomes computationally expensive or even infeasible when used with long sequences. Importantly, biological brains are unlikely to perform such detailed reverse replay over very long sequences of internal states (consider days, months, or years.) However, humans are often reminded of past memories or mental states which are associated with the current mental state. We consider the hypothesis that such memory associations between past and present could be used for credit assignment through arbitrarily long sequences, propagating the credit assigned to the current state to the associated past state. Based on this principle, we study a novel algorithm which only back-propagates through a few of these temporal skip connections, realized by a learned attention mechanism that associates current states with relevant past states. We demonstrate in experiments that our method matches or outperforms regular BPTT and truncated BPTT in tasks involving particularly long-term dependencies, but without requiring the biologically implausible backward replay through the whole history of states. Additionally, we demonstrate that the proposed method transfers to longer sequences significantly better than LSTMs trained with BPTT and LSTMs trained with full self-attention.

Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with ANNs. We address two possible reasons for that. One is that RSNNs in the brain are not randomly connected or designed according to simple rules, and they do not start learning as a tabula rasa network. Rather, RSNNs in the brain were optimized for their tasks through evolution, development, and prior experience. Details of these optimization processes are largely unknown. But their functional contribution can be approximated through powerful optimization methods, such as backpropagation through time (BPTT). A second major mismatch between RSNNs in the brain and models is that the latter only show a small fraction of the dynamics of neurons and synapses in the brain. We include neurons in our RSNN model that reproduce one prominent dynamical process of biological neurons that takes place at the behaviourally relevant time scale of seconds: neuronal adaptation.

Equilibrium Propagation (EP) is a biologically inspired learning algorithm for convergent recurrent neural networks, i.e. RNNs that are fed by a static input x and settle to a steady state. Training convergent RNNs consists in adjusting the weights until the steady state of output neurons coincides with a target y. Convergent RNNs can also be trained with the more conventional Backpropagation Through Time (BPTT) algorithm. In its original formulation EP was described in the case of real-time neuronal dynamics, which is computationally costly.

Graph neural networks (GNNs) have become the dominant solution for learning on graphs, the typical non-Euclidean structures. Conventional GNNs, constructed with the Artificial Neuron Network (ANN), have achieved impressive performance at the cost of high computation and energy consumption. In parallel, spiking GNNs with brain-like spiking neurons are drawing increasing research attention owing to the energy efficiency. So far, existing spiking GNNs consider graphs in Euclidean space, ignoring the structural geometry, and suffer from the high latency issue due to Back-Propagation-Through-Time (BPTT) with the surrogate gradient. In light of the aforementioned issues, we are devoted to exploring spiking GNN on Riemannian manifolds, and present a Manifold-valued Spiking GNN (MSG). In particular, we design a new spiking neuron on geodesically complete manifolds with the diffeomorphism, so that BPTT regarding the spikes is replaced by the proposed differentiation via manifold. Theoretically, we show that MSG approximates a solver of the manifold ordinary differential equation. Extensive experiments on common graphs show the proposed MSG achieves superior performance to previous spiking GNNs and energy efficiency to conventional GNNs.

Spiking neural networks (SNNs) are promising brain-inspired energy-efficient models. Recent progress in training methods has enabled successful deep SNNs on large-scale tasks with low latency. Particularly, backpropagation through time (BPTT) with surrogate gradients (SG) is popularly used to enable models to achieve high performance in a very small number of time steps. However, it is at the cost of large memory consumption for training, lack of theoretical clarity for optimization, and inconsistency with the online property of biological learning rules and rules on neuromorphic hardware. Other works connect the spike representations of SNNs with equivalent artificial neural network formulation and train SNNs by gradients from equivalent mappings to ensure descent directions. But they fail to achieve low latency and are also not online.

We propose a novel approach to reduce memory consumption of the backpropagation through time (BPTT) algorithm when training recurrent neural networks (RNNs). Our approach uses dynamic programming to balance a trade-off between caching of intermediate results and recomputation. The algorithm is capable of tightly fitting within almost any user-set memory budget while finding an optimal execution policy minimizing the computational cost. Computational devices have limited memory capacity and maximizing a computational performance given a fixed memory budget is a practical use-case. We provide asymptotic computational upper bounds for various regimes. The algorithm is particularly effective for long sequences. For sequences of length 1000, our algorithm saves 95\% of memory usage while using only one third more time per iteration than the standard BPTT.

Learning long-term dependencies in extended temporal sequences requires credit assignment to events far back in the past. The most common method for training recurrent neural networks, back-propagation through time (BPTT), requires credit information to be propagated backwards through every single step of the forward computation, potentially over thousands or millions of time steps. This becomes computationally expensive or even infeasible when used with long sequences. Importantly, biological brains are unlikely to perform such detailed reverse replay over very long sequences of internal states (consider days, months, or years.) However, humans are often reminded of past memories or mental states which are associated with the current mental state. We consider the hypothesis that such memory associations between past and present could be used for credit assignment through arbitrarily long sequences, propagating the credit assigned to the current state to the associated past state. Based on this principle, we study a novel algorithm which only back-propagates through a few of these temporal skip connections, realized by a learned attention mechanism that associates current states with relevant past states. We demonstrate in experiments that our method matches or outperforms regular BPTT and truncated BPTT in tasks involving particularly long-term dependencies, but without requiring the biologically implausible backward replay through the whole history of states. Additionally, we demonstrate that the proposed method transfers to longer sequences significantly better than LSTMs trained with BPTT and LSTMs trained with full self-attention.

Recurrent networks of spiking neurons (RSNNs) underlie the astounding computing and learning capabilities of the brain. But computing and learning capabilities of RSNN models have remained poor, at least in comparison with ANNs. We address two possible reasons for that. One is that RSNNs in the brain are not randomly connected or designed according to simple rules, and they do not start learning as a tabula rasa network. Rather, RSNNs in the brain were optimized for their tasks through evolution, development, and prior experience. Details of these optimization processes are largely unknown. But their functional contribution can be approximated through powerful optimization methods, such as backpropagation through time (BPTT). A second major mismatch between RSNNs in the brain and models is that the latter only show a small fraction of the dynamics of neurons and synapses in the brain. We include neurons in our RSNN model that reproduce one prominent dynamical process of biological neurons that takes place at the behaviourally relevant time scale of seconds: neuronal adaptation.