Gradient-Free Training of Spiking Neural Networks via Low-Rank Evolution Strategies

Technical Summary: Gradient-Free Training of Spiking Neural Networks via Low-Rank Evolution Strategies

Problem Statement
Spiking Neural Networks (SNNs) offer significant energy efficiency advantages on neuromorphic hardware (e.g., Intel Loihi, IBM TrueNorth) by utilizing sparse, event-driven computation. However, training SNNs remains a major bottleneck. The core issue is the non-differentiable nature of the spike generation function (a Heaviside step function), which prevents the use of standard backpropagation. While surrogate-gradient methods approximate this derivative to enable backpropagation, they rely on autograd infrastructure that is incompatible with on-chip learning constraints. Evolution Strategies (ES) provide a gradient-free alternative by perturbing weights and evaluating fitness; however, standard ES scales poorly with model size, requiring $O(Pmn)$ memory per generation (where $P$ is population size and $m \times n$ are weight matrix dimensions), rendering it impractical for large networks.

Methodology
The authors propose integrating Eggroll, a low-rank factorization technique for Evolution Strategies, into the SNN training loop.

• Low-Rank Perturbation: Instead of sampling full-rank perturbation matrices $E \in \mathbb{R}^{m \times n}$, the method approximates perturbations as a low-rank product $E_i = \frac{1}{\sqrt{r}} A_i B_i^\top$, where $A_i \in \mathbb{R}^{m \times r}$ and $B_i \in \mathbb{R}^{n \times r}$. This reduces the per-generation memory complexity from $O(Pmn)$ to $O(r(m+n))$.
• Deterministic Reconstruction: To further optimize memory, the noise factors ($A, B$) are not stored but reconstructed on-demand from a stored seed using a counter-based deterministic random number generator (RNG).
• Training Loop: The method employs a Leaky Integrate-and-Fire (LIF) network. During each generation, $P$ perturbed network copies are evaluated simultaneously on a mini-batch of the N-MNIST dataset. The fitness signal is derived from negative cross-entropy (log-likelihood) rather than raw accuracy to provide a smoother landscape for the optimizer. The gradient estimate is reconstructed via a $(\text{diag}(f)A)^\top B$ formulation and used to update weights via the Adam optimizer.
• Dataset: The experiments utilize N-MNIST, a native neuromorphic dataset generated by moving an ATIS sensor over MNIST images. This dataset provides asynchronous event streams (ON/OFF polarities) without requiring rate-coding approximations.

Key Contributions

1. Characterization of Eggroll on SNNs: The paper demonstrates that Eggroll can effectively train SNNs with non-differentiable spike functions, enabling fully gradient-free training without surrogate approximations.
2. Rank Ablation Study: The authors show that accuracy remains relatively stable as the rank $r$ decreases, identifying a clear efficiency–accuracy Pareto frontier.
3. Principled Evaluation: The method is benchmarked on N-MNIST against vanilla ES and surrogate-gradient Backpropagation Through Time (BPTT), avoiding the rate-coding approximations often used in static MNIST evaluations.

Experimental Results
Experiments were conducted on an NVIDIA RTX 3070 Ti using a two-layer fully connected LIF network.

• Accuracy vs. Speed: The proposed method achieved a test accuracy of 79.21% with a rank of $r=4$. This represents a negligible drop compared to the 76.17% achieved by vanilla ES, but with a 2.23× speedup in per-generation wall-clock time.
• Comparison to BPTT: While surrogate-gradient BPTT achieved higher accuracy (94.03%), it was significantly slower (31.69s per generation vs. 5.82s for Eggroll $r=4$).
• Rank Sensitivity: The best accuracy-per-second tradeoff was observed at $r=4$. Lower ranks (e.g., $r=1$) offered the fastest execution (3.41s) with 78.75% accuracy, while higher ranks showed increased variance.
• Convergence: EGGROLL variants converged slightly faster in terms of wall-clock time than vanilla ES, despite similar generation-level convergence behaviors.

Significance and Claims
The paper claims that EGGROLL is a viable method for training SNNs without relying on surrogate gradients or backpropagation infrastructure. This is significant because it addresses the compatibility gap between modern training algorithms and the constraints of neuromorphic hardware, which cannot support the autograd mechanisms required by surrogate gradients.

The authors maintain a modest stance regarding the results:

• They acknowledge an accuracy gap between their method (79.21%) and surrogate BPTT (94.03%), attributing this to a limited compute budget (100 generations) and the use of a lightweight, two-layer network architecture.
• They note that the method has not yet been tested on real neuromorphic hardware or on more complex datasets like CIFAR10-DVS or N-Caltech101.
• The work establishes a proof-of-concept that low-rank evolution strategies can scale to SNNs, offering a clear tradeoff between computational efficiency and model accuracy, paving the way for future on-chip learning applications.