[Paper Review] Surrogate Gradient Learning in Spiking Neural Networks

Emre Neftci, Hesham Mostafa+1 more|arXiv (Cornell University)|Jan 28, 2019

Advanced Memory and Neural ComputingEngineering40 references149 citations

TL;DR

The paper reviews training spiking neural networks (SNNs) and advocates surrogate gradient methods to overcome non-differentiable spiking dynamics, detailing how SNNs map to RNNs and how SGs enable effective learning.

ABSTRACT

Spiking neural networks are nature's versatile solution to fault-tolerant and energy efficient signal processing. To translate these benefits into hardware, a growing number of neuromorphic spiking neural network processors attempt to emulate biological neural networks. These developments have created an imminent need for methods and tools to enable such systems to solve real-world signal processing problems. Like conventional neural networks, spiking neural networks can be trained on real, domain specific data. However, their training requires overcoming a number of challenges linked to their binary and dynamical nature. This article elucidates step-by-step the problems typically encountered when training spiking neural networks, and guides the reader through the key concepts of synaptic plasticity and data-driven learning in the spiking setting. To that end, it gives an overview of existing approaches and provides an introduction to surrogate gradient methods, specifically, as a particularly flexible and efficient method to overcome the aforementioned challenges.

Motivation & Objective

• Explain the challenges of training deep spiking neural networks with hidden layers.
• Introduce and categorize surrogate gradient methods as a flexible solution for non-differentiable spiking nonlinearity.
• Show how SNNs can be formulated as recurrent neural networks to transfer training techniques from RNNs.
• Discuss practical considerations for implementing training on neuromorphic or hardware-oriented platforms.

Proposed method

• Formulate spiking LIF neurons with current-based synapses as an equivalent RCNN/RNN to unify training perspectives.
• Describe discrete-time dynamics equations for synaptic currents and membrane potentials (Equations 2–5) and relate to RNN state updates.
• Review and categorize training methods for RNNs (BP/Backpropagation Through Time, forward methods, locality) and map them to SNNs.
• Introduce surrogate gradient (SG) approaches to address the non-differentiability of spiking nonlinearity, including how SGs are integrated with standard gradient-based methods.
• Differentiate smoothed approaches (soft/nonlinear models, probabilistic models, rate coding, single-spike timing) from SG-based approaches (gradients via surrogate derivatives).
• Summarize how SGs enable end-to-end training of SNNs with various coding schemes and hardware considerations.

Experimental results

Research questions

• RQ1 What are the main challenges in training deep SNNs with hidden layers?
• RQ2 How can surrogate gradient methods address the non-differentiable spiking nonlinearity to enable gradient-based learning in SNNs?
• RQ3 How can SNNs be effectively trained using RNN-based techniques like BPTT or forward methods?
• RQ4 What are the practical implications of SG methods for hardware implementations and local learning rules?

Key findings

• SNNs can be treated as a form of RNNs, enabling the transfer of gradient-based training techniques from RNNs to SNNs.
• Surrogate gradient methods provide continuous, differentiable approximations to the spiking nonlinearity, enabling effective gradient-based optimization.
• SGs can be paired with conventional backpropagation (BPTT) or forward methods, including eligibility traces, to train SNNs.
• Smoothing-based approaches and SG-based approaches are compared, highlighting that the exact choice of surrogate is less crucial than preserving a useful gradient signal.
• SG techniques accommodate various coding schemes (rate, timing) and can be adapted for hardware constraints where full BPTT is impractical.
• The literature survey covers a range of surrogate derivatives (piecewise linear, fast sigmoid, exponential) and their successful application to RCNNs and deep SNNs.