Surrogategradient

Surrogate gradient refers to a family of techniques used to train neural networks that include non-differentiable components, most notably spiking neurons. The core idea is to replace the true derivative of a non-differentiable activation (such as a Heaviside spike function) with a differentiable surrogate during backpropagation, allowing gradient-based optimization to proceed with standard methods.

In spiking neural networks, neurons emit discrete spikes when their membrane potential crosses a threshold. Because the spike function is non-differentiable, conventional backpropagation cannot flow gradients through spike events. Surrogate gradients provide a smooth, differentiable approximation of the spike derivative around the threshold, enabling end-to-end training with backpropagation through time or across layers.

Common surrogate choices include piecewise-linear functions, sigmoid derivatives, Gaussian or fast-tanh shapes, and other smooth approximations. These surrogates are applied only in the backward pass; the forward pass still uses the actual spiking nonlinearity. Surrogate gradients are typically scaled and shaped to control gradient magnitude and temporal spread, with hyperparameters tuned for stability and learning efficiency.

Advantages of the approach include enabling effective training of spiking neural networks within standard deep learning frameworks and leveraging established optimization methods. Limitations include the bias introduced by replacing the true gradient, sensitivity to surrogate choice and hyperparameters, and potential issues with convergence and stability.

Surrogate gradient methods have become a common tool in research on spiking models and neuromorphic-inspired learning, offering a practical path to train networks with discrete events using conventional gradient-based algorithms.