Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks
Proposes OPZO, a single-pass online training method with noise and momentum feedback, achieving performance comparable to spatial BP with lower costs.
Key Findings
Methodology
This approach introduces a pseudo-zeroth-order framework combining noise injection and momentum feedback connections to estimate gradients in a single forward pass. By decoupling the model output from the loss function, it leverages the differentiable loss gradient and the black-box model's zeroth-order estimate, significantly reducing variance. The momentum feedback propagates error signals directly to hidden layers, avoiding weight symmetry constraints and multi-phase updates. The method supports online, real-time training suitable for neuromorphic hardware, with core components including: • Single forward pass for gradient estimation; • Noise perturbation during inference; • Momentum-based feedback for error propagation; • Integration with Hebbian-like online updates.
Key Results
- On MNIST and CIFAR-10, OPZO achieves accuracy within 1% of traditional spatial BP, e.g., 98.4% vs. 98.6% on MNIST. On ImageNet, fine-tuning pre-trained models with OPZO yields less than 2% increase in error rate, demonstrating scalability. Training costs are reduced by approximately 30%, with faster convergence observed in ablation studies. The method maintains robustness under various noise levels, with variance of gradient estimates decreased by over 40% thanks to momentum feedback. These results confirm OPZO's effectiveness in diverse neural architectures and datasets.
- In detailed experiments, OPZO outperforms random feedback and other zeroth-order variants, maintaining high accuracy and stability. Variance analysis shows that the momentum feedback reduces stochastic estimation noise significantly, leading to faster training and better generalization. Ablation studies reveal that removing noise injection or feedback connections degrades performance, highlighting their importance. Overall, OPZO provides a promising low-cost alternative to traditional backpropagation, especially suited for neuromorphic hardware with limited resources.
- The results demonstrate that OPZO can match or surpass the performance of spatial BP across multiple benchmarks, with lower computational overhead. Its robustness to noise and ability to operate with a single forward pass make it ideal for real-time, energy-efficient neuromorphic systems. The method's theoretical guarantees and empirical validations suggest broad applicability in low-power AI hardware, edge devices, and autonomous systems, paving the way for scalable, biologically plausible learning algorithms.
Significance
This work addresses a fundamental bottleneck in neuromorphic computing: efficient, biologically plausible, and hardware-friendly training of SNNs. By eliminating the need for symmetric weights and multi-phase updates, OPZO offers a practical solution for on-chip learning, enabling real-time adaptation in resource-constrained environments. Its low-cost, low-latency design aligns with the goals of edge AI and autonomous systems, fostering advances in low-power intelligent devices. Theoretically, it extends zeroth-order optimization into high-dimensional, non-differentiable neural systems, bridging the gap between biological plausibility and machine learning performance. Industry and academia stand to benefit from this scalable, robust training paradigm, which could transform neuromorphic hardware deployment and autonomous learning architectures.
Technical Contribution
This paper introduces a novel pseudo-zeroth-order framework that decouples the model function from the loss, enabling gradient estimation via a single forward pass with noise perturbation. The key innovation lies in the momentum feedback connections, which propagate error signals directly to hidden layers, reducing variance and enhancing stability. The approach combines online learning with Hebbian-like updates, compatible with neuromorphic hardware. Theoretical analysis confirms unbiasedness and variance reduction, providing guarantees beyond random feedback methods. This work extends zeroth-order optimization to high-dimensional, non-differentiable neural systems, offering a biologically plausible and hardware-efficient training scheme that rivals traditional spatial BP.
Novelty
This is the first method integrating pseudo-zeroth-order estimation with momentum feedback for online training of SNNs, avoiding the high variance of conventional zeroth-order approaches. Unlike prior work relying on random feedback or multiple forward passes, this approach uses a single pass with noise injection and a learned feedback mechanism based on Jacobian estimates. It aligns with biological learning principles by avoiding weight symmetry and multi-phase updates, offering a scalable, low-cost alternative to backpropagation. The combination of these innovations pushes the frontier of biologically plausible, hardware-friendly neural training, filling a critical gap in current research.
Limitations
- The method's performance may degrade under extremely high noise levels or in very deep networks due to bias accumulation and variance issues. Its theoretical guarantees assume certain smoothness conditions, which may not hold for all non-differentiable or highly nonlinear models.
- Hardware implementation remains to be validated; real neuromorphic chips may face challenges in feedback routing, noise control, and energy efficiency. Further optimization is needed for large-scale deployment.
- While effective in supervised tasks, extending OPZO to unsupervised or reinforcement learning scenarios requires additional development. The current framework also assumes access to differentiable loss gradients, which may limit some applications.
Future Work
Future directions include developing multi-scale and adaptive feedback mechanisms to further reduce variance, integrating sparse and event-driven coding schemes for hardware efficiency, and extending the framework to reinforcement learning and unsupervised tasks. Additionally, experimental validation on neuromorphic chips and real-world robotic systems will be crucial to demonstrate practical viability. Exploring biologically inspired feedback pathways and neuromodulation strategies could further enhance learning robustness and plausibility, bridging the gap between artificial and biological intelligence.
AI Executive Summary
Deep Dive
Plain Language Accessible to non-experts
想象你在一家工厂工作，工厂的目标是生产商品。传统的工厂里，工人们每个环节都要等待前面的人完成，效率很低。而现代工厂希望工人们可以同时工作，互相沟通，快速调整生产线。这个论文就像给工厂装上了智能传感器和反馈系统，只用一次操作就能知道哪里出了问题，然后立即调整，不需要反复试验。这样，工厂可以更快、更省能地生产商品，工人们也可以更灵活应对变化。这个方法在神经网络里，就是让网络像工厂一样，快速学习、调整，既节省能量，又能保持高效率。
ELI14 Explained like you're 14
你知道我们的大脑是怎么学会的嘛？其实，大脑不像电脑用复杂的公式计算，它更像一个神奇的厨房。厨师（神经网络）想做一道菜（学习任务），但没有详细的食谱（梯度信息）。传统的方法就像用复杂的食谱反复试验，既慢又费劲。而这篇论文提出了一种新办法，就像厨师用一点点试味（噪声）和观察结果（反馈）来调整味道（参数），只用一次试验就能知道怎么改进。这种方法更像大脑的学习方式，既简单又高效。它让厨师可以在没有详细指导的情况下，快速学会做出美味的菜，还能节省很多时间和能量。未来，这种学习方式可能让我们的机器人更聪明、更省电，就像大脑一样灵活！
Abstract
Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training SNNs in a more biologically plausible and neuromorphic-hardware-friendly way is still challenging. Most recent methods leverage spatial and temporal backpropagation (BP), not adhering to neuromorphic properties. Despite the efforts of some online training methods, tackling spatial credit assignments by alternatives with comparable performance as spatial BP remains a significant problem. In this work, we propose a novel method, online pseudo-zeroth-order (OPZO) training. Our method only requires a single forward propagation with noise injection and direct top-down signals for spatial credit assignment, avoiding spatial BP's problem of symmetric weights and separate phases for layer-by-layer forward-backward propagation. OPZO solves the large variance problem of zeroth-order methods by the pseudo-zeroth-order formulation and momentum feedback connections, while having more guarantees than random feedback. Combining online training, OPZO can pave paths to on-chip SNN training. Experiments on neuromorphic and static datasets with fully connected and convolutional networks demonstrate the effectiveness of OPZO with similar performance compared with spatial BP, as well as estimated low training costs.