[Paper] Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction

Source: arXiv - 2605.08022v1

Overview

The paper introduces a globally optimal training algorithm for Spiking Neural Networks (SNNs) that sidesteps the usual reliance on surrogate gradients. By reformulating the SNN learning problem as a parameter reconstruction task, the authors achieve provably optimal solutions for a broad class of SNN architectures, delivering more stable and accurate models across a variety of benchmarks.

Key Contributions

• Convexification of Parallel Recurrent Threshold Networks: Extends prior convex‑analysis work from feed‑forward to recurrent structures, covering the full spectrum of parallel SNNs.
• Parameter Reconstruction Algorithm: A novel training pipeline that directly recovers optimal weight parameters without approximating the non‑differentiable spike function.
• Hybrid Training Mode: Demonstrates that the reconstruction step can be combined with traditional surrogate‑gradient updates for even better performance.
• Extensive Empirical Validation: Shows consistent gains on image classification (e.g., CIFAR‑10/100), neuromorphic event‑based datasets (e.g., DVS‑Gesture), and reinforcement learning tasks.
• Scalability & Robustness Analyses: Ablation studies confirm that the method scales with dataset size and remains stable across different network depths, neuron thresholds, and time‑step settings.

Methodology

1. Problem Reformulation – The authors treat an SNN as a parallel recurrent threshold network where each neuron’s output is a binary threshold of a linear combination of past spikes. By exploiting this structure, they prove that the loss surface becomes convex when expressed in terms of a lifted set of auxiliary variables.
2. Parameter Reconstruction – Instead of back‑propagating through the non‑differentiable spike, the algorithm solves a series of convex optimization problems that reconstruct the weight matrices from the auxiliary variables. This yields a closed‑form (or efficiently solvable) solution that is globally optimal for the given auxiliary state.
3. Training Loop
   • Forward Pass: Simulate spikes using the standard leaky‑integrate‑and‑fire dynamics to collect auxiliary variables.
   • Reconstruction Step: Solve the convex sub‑problem to update weights.
   • Optional Surrogate‑Gradient Step: Fine‑tune the network with a few surrogate‑gradient epochs to capture any residual non‑convexities.
4. Implementation Details – The convex sub‑problems are solved with off‑the‑shelf solvers (e.g., projected gradient descent) that scale linearly with the number of neurons and time steps, making the approach practical for modern GPU/TPU pipelines.

Results & Findings

• Consistent Accuracy Boost: Across all benchmarks, the reconstruction method outperforms pure surrogate‑gradient training, often by 5–7 % absolute accuracy.
• Faster Convergence: Training curves reach near‑optimal performance in roughly half the epochs required by surrogate methods.
• Stability: Gradient explosion/vanishing issues disappear because the weight update is solved analytically rather than approximated.
• Compatibility: Adding a short surrogate‑gradient fine‑tuning phase yields the best of both worlds, pushing the state‑of‑the‑art on several neuromorphic benchmarks.

Practical Implications

• Energy‑Efficient Edge Deployment: More accurate SNNs mean fewer spikes are needed to achieve a target performance, directly translating to lower power consumption on neuromorphic hardware (e.g., Intel Loihi, IBM TrueNorth).
• Simplified Training Pipelines: Developers can replace the delicate surrogate‑gradient hyper‑parameter tuning with a deterministic reconstruction step, reducing engineering overhead.
• Rapid Prototyping for Event‑Based Sensors: The method’s robustness to different time‑step resolutions makes it attractive for applications like autonomous drones, wearable health monitors, and real‑time video analytics that rely on event cameras.
• Hybrid Learning Strategies: Existing SNN libraries (e.g., BindsNET, Norse) can integrate the reconstruction module as a plug‑in, allowing teams to experiment with the hybrid approach without rewriting their entire codebase.
• Potential for Large‑Scale SNNs: The demonstrated scalability hints that future large‑scale neuromorphic models (e.g., for speech or language processing) could be trained more reliably, opening doors to SNN‑based alternatives to massive transformer models.

Limitations & Future Work

• Convexity Assumptions: The global optimality guarantee holds under the specific parallel recurrent threshold formulation; extensions to more exotic neuron models (e.g., adaptive thresholds, dendritic processing) remain open.
• Solver Overhead: While the convex sub‑problems are linear‑time in theory, solving them on very deep networks (hundreds of layers) can introduce non‑trivial runtime compared to pure back‑propagation.
• Hardware Compatibility: The current implementation assumes full‑precision floating‑point solvers; adapting the reconstruction step to low‑precision or on‑chip neuromorphic solvers will require additional engineering.
• Broader Benchmarks: Experiments focus on image classification and simple RL tasks; evaluating the method on large‑scale vision (e.g., ImageNet) or natural language benchmarks would further validate its generality.

The authors suggest exploring adaptive reconstruction strategies that dynamically choose between convex updates and surrogate gradients, and extending the theory to spiking transformer architectures as promising avenues for future research.

Authors

• Himanshu Udupi
• Xiaocong Yang
• ChengXiang Zhai

Paper Information

• arXiv ID: 2605.08022v1
• Categories: cs.NE, cs.AI, cs.LG
• Published: May 8, 2026
• PDF: Download PDF