Dynamic Weight Adaptation in Spiking Neural Networks Inspired by Biological Homeostasis

TL;DR

DWAM introduces a BCM-inspired, dynamic weight adaptation mechanism for spiking neural networks to achieve homeostasis during inference. It comprises a Synaptic Adjustment Mechanism, which updates weights via $ \frac{d w_{ij}}{dt} = \cdot \cdot \cdot $ and $ \phi_{ij}(t) = c_i^{l}(t) ( c_i^{l}(t) - \theta_i^{l}(t) ) $, and a Stability Maintenance Mechanism that modulates the sliding threshold with a CV-based term $ \theta_i^{l}(t) = \theta_{M,i}^{l}(t) \zeta \frac{\sigma}{\mu} + c_i^{l}(t) (1 - \zeta \frac{\sigma}{\mu}) $. The model is designed to be plug-and-play, applicable to pre-trained SNNs during inference, and is shown to improve performance and reduce firing-rate fluctuations in dynamic obstacle avoidance and continuous control tasks under degraded conditions, while coexisting with existing homeostatic mechanisms. The work demonstrates that BCM-inspired inter-neuronal regulation can enhance robustness and generalization in neuromorphic controllers without retraining. These results suggest DWAM as a practical, biologically grounded approach to stabilizing SNNs in real-world, noisy environments.

Abstract

Homeostatic mechanisms play a crucial role in maintaining optimal functionality within the neural circuits of the brain. By regulating physiological and biochemical processes, these mechanisms ensure the stability of an organism's internal environment, enabling it to better adapt to external changes. Among these mechanisms, the Bienenstock, Cooper, and Munro (BCM) theory has been extensively studied as a key principle for maintaining the balance of synaptic strengths in biological systems. Despite the extensive development of spiking neural networks (SNNs) as a model for bionic neural networks, no prior work in the machine learning community has integrated biologically plausible BCM formulations into SNNs to provide homeostasis. In this study, we propose a Dynamic Weight Adaptation Mechanism (DWAM) for SNNs, inspired by the BCM theory. DWAM can be integrated into the host SNN, dynamically adjusting network weights in real time to regulate neuronal activity, providing homeostasis to the host SNN without any fine-tuning. We validated our method through dynamic obstacle avoidance and continuous control tasks under both normal and specifically designed degraded conditions. Experimental results demonstrate that DWAM not only enhances the performance of SNNs without existing homeostatic mechanisms under various degraded conditions but also further improves the performance of SNNs that already incorporate homeostatic mechanisms.

Figures (4)

• Figure 1: Comparison between biological BCM theory and the proposed DWAM in SNNs. a. Illustration of the BCM theory in biological neural systems. The synaptic modification function ($\phi$) is governed by the postsynaptic neuron’s activity ($x$) and a modification threshold ($\theta_M$). The depression zone ($x < \theta_M$) leads to synaptic weakening (e.g., $x_1$), while the potentiation zone ($x > \theta_M$) results in synaptic strengthening (e.g., $x_2$). b. The dynamic adjustment of the modification threshold ($\theta_M$) based on the historical activity level of the postsynaptic neuron. A higher historical activity level shifts $\theta_M$ to the right, reducing potentiation likelihood, whereas lower historical activity shifts $\theta_M$ to the left, increasing potentiation likelihood.(illustrated as a shift from the solid line to the dashed line in the figure) c. Proposed DWAM for SNNs, inspired by the BCM theory. The synaptic modification function ($\phi$) in DWAM operates on a similar principle, where the postsynaptic neuron’s firing rate ($c$) interacts with a modification threshold ($\theta_M$) to determine weight weakening ($c_1$) or strengthening ($c_2$). d. As with BCM, a higher historical firing rate shifts $\theta_M$ to the right, whereas a lower firing rate shifts it to the left, enabling balanced and stable weight updates in the SNNs.
• Figure 2: Behavioral comparison between BioDWAM and DWAM in the toy example. All subplots show simulation steps (x-axis) versus value (y-axis), with green and pink curves indicating firing rate and modification threshold, respectively. a & b. Zoomed-in views of the initial phase in d and e, showing early threshold adaptation. c. Firing rate stabilizes at 1 without synaptic adjustment. d. BioDWAM induces oscillatory instability at high firing rates. e. DWAM maintains stability by modulating threshold according to firing variability.
• Figure 3: Illustrations of the training, static testing and dynamic testing environments. a. The training environments of the obstacle avoidance tasks. The training processes of all competing SNNs start from Env1 and end with Env4. b. Static testing environment. c. Dynamic testing environment. In addition to static obstacles, $11$ dynamic obstacles are inserted.
• Figure 4: PCA comparison of SAN and SAN-DWAM under noise.Each plot shows PCA projections of hidden-layer neuronal activity during a randomly selected trajectory. Green and blue points denote normal and noisy conditions, respectively.