Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks

TL;DR

This work develops a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks.

Abstract

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Figures (8)

• Figure 1: Illustration of the proposed Hebbian learning based orthogonal projection (HLOP). (a) Overview of HLOP for continual learning. Hebbian learning extracts the principal subspace of neuronal activities to support orthogonal projection. For successive tasks, orthogonal projection is based on the consolidated subspace, and a new subspace is constructed by Hebbian learning, which is merged for consolidation after learning. (b) Illustration of lateral circuits with skew-symmetric connection weights. (c) Hebbian learning in lateral circuits for construction of new subspaces for new tasks. (d) Orthogonal projection based on recurrent lateral connections. The presynaptic activity traces $\mathbf{x}$, whose definition depends on training algorithms, are modified by signals from lateral connections. Synaptic weights $\mathbf{W}$ are updated based on the projected traces.
• Figure 2: Illustration of combining HLOP with SNN training. (a) Illustration of spiking neural networks with temporal spike trains. (b) SNN training methods based on eligibility traces and online calculation through time bellec2020solutionxiao2022online. (c) Applying HLOP by modifying traces with lateral circuits. The eligibility traces correspond to activity traces in the illustration of HLOP and are modified for synaptic weight update. Neuronal traces will consider both spike responses for feedforward inputs and responses for recurrent lateral circuits. (d) Illustration of HLOP with lateral spiking neurons based on the rate coding of high-frequency bursts.
• Figure 3: Continual learning results under different settings. "Multitask" does not adhere to continual learning and can be viewed as an upper bound. "BP" (backpropagation), "FA" (feedback alignment), "SS" (sign symmetric) denote different error propagation methods. "MR" denotes memory replay. (a) Average accuracy and backward transfer (BWT) results on PMNIST under the online setting. (b) Average accuracy and BWT results on 10-split CIFAR-100. (c) Average accuracy and BWT results on 5-Datasets (CIFAR-10, MNIST, SVHN, FashionMNIST, and notMNIST).
• Figure 4: Continual learning results of HLOP with lateral spiking neurons. "Multitask" does not adhere to continual learning and can be viewed as an upper bound. "(spiking, $T_l$)" denotes lateral spiking neurons with $T_l$ time steps for discrete simulation of bursts. (a) Average accuracy and backward transfer (BWT) results on PMNIST under different time steps for HLOP (spiking). (b) Average accuracy and BWT results on 10-split CIFAR-100 under different time steps for HLOP (spiking).
• Figure 5: Continual learning results of different methods on 5-Datasets for each task after learning successive ones.