[Paper Review] Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks

Wei Fang, Zhaofei Yu+4 more|arXiv (Cornell University)|Jul 11, 2020

Advanced Memory and Neural Computing4 citations

TL;DR

This paper proposes a backpropagation-based training method for Spiking Neural Networks (SNNs) that learns both synaptic weights and membrane time constants using Parametric Leaky Integrate-and-Fire (PLIF) neurons. By making membrane time constants learnable, the method enhances network expressiveness, improves robustness to initialization, accelerates learning, and achieves state-of-the-art accuracy on MNIST, Fashion-MNIST, CIFAR-10, N-MNIST, CIFAR10-DVS, and DVS128 Gesture datasets with fewer time-steps.

ABSTRACT

Spiking Neural Networks (SNNs) have attracted enormous research interest due to temporal information processing capability, low power consumption, and high biological plausibility. However, the formulation of efficient and high-performance learning algorithms for SNNs is still challenging. Most existing learning methods learn weights only, and require manual tuning of the membrane-related parameters that determine the dynamics of a single spiking neuron. These parameters are typically chosen to be the same for all neurons, which limits the diversity of neurons and thus the expressiveness of the resulting SNNs. In this paper, we take inspiration from the observation that membrane-related parameters are different across brain regions, and propose a training algorithm that is capable of learning not only the synaptic weights but also the membrane time constants of SNNs. We show that incorporating learnable membrane time constants can make the network less sensitive to initial values and can speed up learning. In addition, we reevaluate the pooling methods in SNNs and find that max-pooling will not lead to significant information loss and have the advantage of low computation cost and binary compatibility. We evaluate the proposed method for image classification tasks on both traditional static MNIST, Fashion-MNIST, CIFAR-10 datasets, and neuromorphic N-MNIST, CIFAR10-DVS, DVS128 Gesture datasets. The experiment results show that the proposed method outperforms the state-of-the-art accuracy on nearly all datasets, using fewer time-steps. Our codes are available at https://github.com/fangwei123456/Parametric-Leaky-Integrate-and-Fire-Spiking-Neuron.

Motivation & Objective

• To address the limitation of fixed membrane time constants in SNNs, which restricts neuronal heterogeneity and network expressiveness.
• To develop a backpropagation-based training algorithm that jointly optimizes synaptic weights and membrane time constants.
• To re-evaluate pooling strategies in SNNs and challenge the assumption that max-pooling causes significant information loss.
• To demonstrate improved performance and efficiency on both static and neuromorphic spiking datasets.

Proposed method

• Introduces Parametric Leaky Integrate-and-Fire (PLIF) neurons where the membrane time constant τ is a learnable parameter per neuron, enabling dynamic adaptation of neuronal integration time.
• Extends backpropagation through time (BPTT) to include gradients w.r.t. τ, allowing end-to-end training of both weights and time constants.
• Uses a learnable input encoder (Conv2d + Spiking Neurons) that maps input pixels directly to spike patterns, replacing fixed encoders like Poisson or latency encoding.
• Employs max-pooling in SNNs, demonstrating it preserves temporal sparsity and asynchronous firing patterns while reducing computational cost.
• Applies the PLIF-based SNN to image classification tasks using both static datasets (e.g., MNIST) and neuromorphic datasets (e.g., N-MNIST, DVS128 Gesture).
• Treats τ as a per-neuron parameter initialized with a distribution, allowing diversity in neuronal dynamics during training.

Experimental results

Research questions

• RQ1 Can learning membrane time constants improve the expressiveness and performance of SNNs compared to fixed τ?
• RQ2 Does joint optimization of weights and τ enhance training stability and convergence speed?
• RQ3 Is max-pooling in SNNs truly detrimental to performance, or can it preserve critical temporal information?
• RQ4 Can a learnable encoder outperform standard rate or latency encoding in SNNs?
• RQ5 Does the proposed method achieve state-of-the-art accuracy on both static and neuromorphic datasets with fewer time-steps?

Key findings

• The proposed PLIF-SNN achieves state-of-the-art accuracy on static MNIST, Fashion-MNIST, and CIFAR-10 datasets, outperforming prior SOTA methods.
• On neuromorphic datasets (N-MNIST, CIFAR10-DVS, DVS128 Gesture), the model achieves higher accuracy than existing SNNs while using fewer time-steps.
• The network with learnable τ is less sensitive to weight initialization and converges faster than SNNs with fixed τ.
• Max-pooling in SNNs preserves asynchronous firing patterns and reduces computation cost without significant performance degradation, outperforming average-pooling in some cases.
• The learnable encoder (Conv2d + Spiking Neurons) effectively extracts semantic features, such as edges and gestures, and can filter out irrelevant information like the player in DVS128 Gesture.
• The model demonstrates robustness and efficiency by achieving high accuracy with reduced temporal integration windows, indicating effective temporal coding.