A Fast Inversion-Free Approach for Training Spiking Neural Networks via ADMM

Amid the remarkable growth of deep learning, Spiking Neural Networks (SNNs) stand out as an energy-efficient alternative, questioning established assumptions of how learning systems may be built when energy is a defining constraint. They rely on sparse, event-driven signals that model the dynamics of biological neurons. The discontinuous structure of spiking networks makes training challenging and existing methods struggle to extend reliably and scalably. This has given rise to a new line of research in which SNN learning is treated as an optimization problem. The Alternating Direction Method of Multipliers (ADMM) provides a gradient-free framework that fundamentally reconsiders how these networks can be trained. However, ADMM-based SNN training relies on repeated matrix inversions that significantly increase computational cost and create numerical instability when matrices are ill-conditioned. This work deepens and extends the recently proposed ADMM-based training framework for SNNs by reformulating its update rules and introducing two new configuration families that address computational bottlenecks while preserving its learning performance. One configuration removes all inversion steps, offering a fully surrogate alternative that remains lightweight and matches baseline performance. A second, hybrid configuration preserves exactness where it contributes most while replacing other components with surrogate updates. The hybrid method achieves accuracy of 98–97% across 1–3 hidden layers, compared to baseline performance of 90–55% on the Neuromorphic MNIST dataset, with improvements increasing for deeper networks. Finally, an Anderson-accelerated (AA) variant of the surrogate formulation is introduced to address the slow convergence typically associated with ADMM, and the results show that this acceleration further strengthens the surrogate method and points out a direction for potential developments. These improvements open new possibilities for SNNs deployment in energy-constrained systems such as federated learning, neuromorphic hardware, edge computing and other distributed or low-power platforms. More generally they support a broader move toward sustainable, parallel, and low-energy solutions that align more closely with the efficiency of biologically inspired neural computation.