[Paper Review] Event-based Backpropagation for Analog Neuromorphic Hardware

Christian Pehle, Luca Blessing+3 more|arXiv (Cornell University)|Feb 13, 2023

Advanced Memory and Neural Computing4 citations

TL;DR

This paper introduces EventProp, an event-based backpropagation algorithm for analog neuromorphic hardware that estimates gradients using only spike time observations, achieving a tenfold improvement in information efficiency over surrogate gradient methods. It enables scalable, energy-efficient, on-device learning in large-scale neuromorphic systems without requiring dense state measurements.

ABSTRACT

Neuromorphic computing aims to incorporate lessons from studying biological nervous systems in the design of computer architectures. While existing approaches have successfully implemented aspects of those computational principles, such as sparse spike-based computation, event-based scalable learning has remained an elusive goal in large-scale systems. However, only then the potential energy-efficiency advantages of neuromorphic systems relative to other hardware architectures can be realized during learning. We present our progress implementing the EventProp algorithm using the example of the BrainScaleS-2 analog neuromorphic hardware. Previous gradient-based approaches to learning used "surrogate gradients" and dense sampling of observables or were limited by assumptions on the underlying dynamics and loss functions. In contrast, our approach only needs spike time observations from the system while being able to incorporate other system observables, such as membrane voltage measurements, in a principled way. This leads to a one-order-of-magnitude improvement in the information efficiency of the gradient estimate, which would directly translate to corresponding energy efficiency improvements in an optimized hardware implementation. We present the theoretical framework for estimating gradients and results verifying the correctness of the estimation, as well as results on a low-dimensional classification task using the BrainScaleS-2 system. Building on this work has the potential to enable scalable gradient estimation in large-scale neuromorphic hardware as a continuous measurement of the system state would be prohibitive and energy-inefficient in such instances. It also suggests the feasibility of a full on-device implementation of the algorithm that would enable scalable, energy-efficient, event-based learning in large-scale analog neuromorphic hardware.

Motivation & Objective

• To enable scalable, energy-efficient, on-device gradient-based learning in large-scale analog neuromorphic hardware.
• To overcome limitations of prior gradient estimation methods that require dense sampling of neuron dynamics or rely on restrictive assumptions about network dynamics or topology.
• To demonstrate that spike time observations alone are sufficient for accurate gradient estimation in neuromorphic hardware.
• To validate the robustness of the method under hardware variability and non-idealities.
• To enable full in-the-loop training on physical neuromorphic chips using only event-based data.

Proposed method

• The EventProp algorithm estimates gradients using only spike time observations from the neuromorphic hardware, avoiding the need for continuous state monitoring.
• It employs a software-based adjoint dynamics model in PyTorch to compute parameter gradients from recorded spike events and optional membrane voltage traces.
• The method integrates forward and backward passes using discrete Euler integration of Leaky Integrate-and-Fire (LIF) neuron dynamics with spike-induced jumps.
• Gradients are computed via the adjoint method, with the loss function based on a max-over-time output voltage formulation for classification.
• The algorithm is designed to be compatible with arbitrary network topologies, dynamics, and loss functions, without requiring assumptions on time constants or spiking behavior.
• Hardware-in-the-loop training is performed on the BrainScaleS-2 platform, where input spikes are sent, output spikes and voltages are recorded, and gradients are estimated in software.

Experimental results

Research questions

• RQ1 Can gradient estimation in analog neuromorphic hardware be achieved using only spike time observations, without dense state measurements?
• RQ2 Does the EventProp algorithm achieve comparable learning performance to surrogate gradient methods while being significantly more information-efficient?
• RQ3 How robust is the gradient estimation to hardware variability and non-idealities in real neuromorphic substrates?
• RQ4 Can the algorithm be successfully applied to a physical neuromorphic chip for end-to-end in-the-loop training?
• RQ5 What is the information efficiency gain of EventProp over traditional surrogate gradient approaches in hardware settings?

Key findings

• The EventProp algorithm achieves equivalent classification performance on the Yin-Yang dataset compared to surrogate gradient methods, both in simulation and on the BrainScaleS-2 hardware.
• The method reduces the required data by a factor of ten, demonstrating a one-order-of-magnitude improvement in information efficiency.
• The mean gradient estimate from hardware spike time measurements closely matches the analytical solution, confirming robustness to substrate variability.
• The algorithm successfully enables in-the-loop training on physical analog neuromorphic hardware using only event-based observations.
• The gradient estimation remains accurate even when using only spike times, without requiring continuous membrane voltage recordings.
• The method is compatible with arbitrary network topologies, dynamics, and loss functions, overcoming prior limitations of existing approaches.