Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks

ICLR 2026 Conference SubmissionAnonymous Authors
neuromorphic computingspiking neural networksnon-backpropagation trainingbiological plausibilitypseudo-zeroth-order
Abstract:

Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training deep 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 competitive 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 both fully connected and convolutional networks demonstrate the effectiveness of OPZO with competitive performance compared with spatial BP, as well as estimated low training costs.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper proposes OPZO, a training method for spiking neural networks that uses noise injection and direct top-down signals for spatial credit assignment, avoiding symmetric weight transport and separate forward-backward phases. It sits in the 'Zeroth-Order and Feedback-Based Approximations' leaf, which contains only three papers total, indicating a relatively sparse research direction within the broader field of biologically plausible SNN training. This leaf focuses specifically on methods that replace explicit gradient backpropagation with noise-based or feedback mechanisms, distinguishing it from the more populated gradient-adjustment approaches in the sibling leaf.

The taxonomy reveals that OPZO's parent branch, 'Gradient-Based and Backpropagation Alternatives', contains two main directions: spatiotemporal gradient adjustment methods and zeroth-order/feedback approaches. The sibling leaf on gradient adjustment includes techniques that still compute explicit gradients but modify their flow, whereas OPZO's leaf emphasizes avoiding gradient computation entirely. Neighboring branches in 'Learning Rule Design' include local Hebbian mechanisms and reinforcement learning methods, which differ fundamentally by relying on unsupervised correlation-based rules or reward signals rather than supervised error-driven updates. The taxonomy's scope notes clarify that OPZO belongs here because it uses feedback signals without explicit gradient backpropagation, not in the Hebbian category.

Among the three contributions analyzed across twenty-eight candidate papers, the pseudo-zeroth-order formulation examined eight candidates with none providing clear refutation, while the OPZO training method with momentum feedback examined ten candidates, also without refutation. The biologically plausible on-chip training framework examined ten candidates and found one that appears to provide overlapping prior work. This suggests that the core algorithmic innovations appear relatively novel within the limited search scope, while the on-chip training framing may have more substantial precedent. The analysis explicitly covers top-K semantic matches and citation expansion, not an exhaustive literature review.

Based on the limited search of twenty-eight candidates, the work appears to occupy a sparsely populated research direction with modest prior overlap. The core pseudo-zeroth-order formulation and momentum feedback mechanisms show no clear refutation among examined candidates, though the on-chip training motivation has at least one overlapping prior work. The taxonomy structure suggests this is an emerging area within biologically plausible SNN training, though definitive novelty claims would require broader literature coverage beyond the semantic search scope employed here.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
28
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: biologically plausible training of spiking neural networks. The field organizes around several complementary perspectives. Learning Rule Design and Theoretical Foundations explores how to derive training algorithms that respect biological constraints, including gradient-based alternatives and feedback mechanisms that avoid the implausibilities of standard backpropagation. Network Architecture and Structural Design examines neuron models, dendritic computation, and connectivity patterns inspired by cortical circuits. Training Efficiency and Optimization Techniques addresses practical concerns such as convergence speed, memory usage, and online learning regimes. Domain-Specific Applications and Implementations demonstrate these methods on tasks ranging from vision and speech recognition to robotics control, while Theoretical Analysis and Comparative Studies provide rigorous benchmarks and performance guarantees. Interdisciplinary Perspectives and Emerging Paradigms bring insights from neuroscience, evolutionary algorithms, and novel hardware substrates, creating a rich landscape that balances biological fidelity with computational performance. Within the gradient-based alternatives, a particularly active line of work focuses on zeroth-order and feedback-based approximations that sidestep the need for precise error backpropagation. Online Pseudo Zeroth Order[0] exemplifies this direction by proposing efficient pseudo-gradient estimates suitable for online learning scenarios. Nearby efforts such as BioGrad[12] and Approximating Backpropagation Local[22] similarly seek local update rules that approximate global objectives without violating biological constraints like weight transport or symmetric connectivity. These methods contrast with approaches in other branches that rely on more structured architectural priors or hybrid training schemes. A central tension across the field is whether to prioritize strict biological realism—potentially sacrificing some performance—or to adopt pragmatic approximations that retain key neuromorphic properties while achieving competitive accuracy. Online Pseudo Zeroth Order[0] navigates this trade-off by maintaining local computations and online adaptability, positioning itself among works that emphasize scalability and real-time learning over exact gradient fidelity.

Claimed Contributions

Pseudo-zeroth-order formulation for neural network training

The authors introduce a formulation that separates the model function from the loss function, maintaining a zeroth-order approach for the model while leveraging first-order gradients of the loss. This decoupling enables more informative error signals compared to standard zeroth-order methods, reducing variance while preserving the black-box property of the model.

8 retrieved papers
OPZO training method with momentum feedback connections

The authors develop the online pseudo-zeroth-order (OPZO) training method that uses only one forward pass with noise injection and direct top-down feedback via momentum-based connections. These connections are updated using one-point zeroth-order estimation of the Jacobian expectation, addressing the high variance problem of traditional zeroth-order approaches while maintaining computational efficiency.

10 retrieved papers
Biologically plausible on-chip training framework for SNNs

By combining the pseudo-zeroth-order approach with online training methods, OPZO achieves a form similar to three-factor Hebbian learning with direct top-down modulations. This framework avoids the biological implausibility of spatial backpropagation (symmetric weights, separate forward-backward phases) and is designed to be compatible with neuromorphic hardware for on-chip SNN training.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Pseudo-zeroth-order formulation for neural network training

The authors introduce a formulation that separates the model function from the loss function, maintaining a zeroth-order approach for the model while leveraging first-order gradients of the loss. This decoupling enables more informative error signals compared to standard zeroth-order methods, reducing variance while preserving the black-box property of the model.

Contribution

OPZO training method with momentum feedback connections

The authors develop the online pseudo-zeroth-order (OPZO) training method that uses only one forward pass with noise injection and direct top-down feedback via momentum-based connections. These connections are updated using one-point zeroth-order estimation of the Jacobian expectation, addressing the high variance problem of traditional zeroth-order approaches while maintaining computational efficiency.

Contribution

Biologically plausible on-chip training framework for SNNs

By combining the pseudo-zeroth-order approach with online training methods, OPZO achieves a form similar to three-factor Hebbian learning with direct top-down modulations. This framework avoids the biological implausibility of spatial backpropagation (symmetric weights, separate forward-backward phases) and is designed to be compatible with neuromorphic hardware for on-chip SNN training.