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arxiv: 2605.08022 · v2 · pith:YDK4SF6Tnew · submitted 2026-05-08 · 💻 cs.NE · cs.AI· cs.LG

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction

Himanshu Udupi , Xiaocong Yang , ChengXiang Zhai This is my paper

Pith reviewed 2026-06-30 23:19 UTC · model grok-4.3

classification 💻 cs.NE cs.AIcs.LG
keywords spiking neural networksparameter reconstructionconvexificationglobally optimal trainingrecurrent threshold networkssurrogate gradientenergy-efficient networks
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The pith

Spiking neural networks admit globally optimal training through parameter reconstruction from convexified recurrent threshold networks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to establish that the non-differentiability of spikes in SNNs, which forces reliance on error-prone surrogate gradients, can be overcome by recasting SNNs as a structured special case of parallel recurrent threshold networks. Extending an earlier convexification technique from feedforward to recurrent threshold networks produces a parameter reconstruction procedure that recovers globally optimal weights. A reader would care because the method works as a standalone trainer or in tandem with surrogate gradients, shows robustness to model size and data volume, and points toward scalable training of energy-efficient networks. The central mechanism avoids layer-wise approximation errors by solving a convex problem whose solution directly maps back to the original SNN parameters.

Core claim

Extending convexification from parallel feedforward threshold networks to parallel recurrent threshold networks subsumes parallel SNNs as a structured special case and yields a parameter reconstruction algorithm that achieves globally optimal SNN training, delivering consistent gains both alone and when combined with surrogate-gradient methods.

What carries the argument

The parameter reconstruction algorithm obtained by convexifying parallel recurrent threshold networks, which directly supplies globally optimal SNN weights.

If this is right

  • The reconstruction algorithm functions as a complete standalone training procedure for SNNs.
  • Combining the reconstruction step with surrogate-gradient training further improves performance.
  • The method maintains effectiveness as dataset size increases.
  • Performance remains stable across varied network depths and widths.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same reconstruction route could be tested on non-parallel recurrent SNN topologies to check whether the convexification still holds.
  • If reconstruction scales, it might allow training of very large SNNs whose energy cost during inference would otherwise be offset by expensive approximate training.
  • The convex mapping from recurrent threshold parameters to SNN parameters suggests analogous convex routes for other threshold-based recurrent models.

Load-bearing premise

Parallel SNNs are a structured special case of parallel recurrent threshold networks whose convexification directly produces globally optimal SNN parameters.

What would settle it

On a standard classification benchmark, the parameters recovered by the reconstruction algorithm produce higher loss or lower accuracy than parameters obtained by surrogate-gradient training run to convergence.

Figures

Figures reproduced from arXiv: 2605.08022 by ChengXiang Zhai, Himanshu Udupi, Xiaocong Yang.

Figure 1
Figure 1. Figure 1: Base-2 addition: effect of λcarry on autoregressive joint-token accuracy for ID and OOD splits. Results are averaged over three seeds. The architecture is L = 3, Prec = 256, Plast = 512, and K = 2, with final-layer spike readout for both SG and CVX. OOD lengths are ndigits ∈ {10, 20, 50}. Both SG and CVX use final-layer spike readout, so the convex dictionary is built from binary spike features. This match… view at source ↗
Figure 2
Figure 2. Figure 2: Base-3 addition: effect of λcarry on autoregressive joint-token accuracy for ID and OOD splits. Results are averaged over three seeds. The architecture and readout match [PITH_FULL_IMAGE:figures/full_fig_p035_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Base-5 addition: effect of λcarry on autoregressive joint-token accuracy for ID and OOD splits. Results are averaged over the available two seeds. The architecture is the same as the base-2 and base-3 experiments: L = 3, Prec = 256, Plast = 512, and K = 2, with final-layer spike readout for both SG and CVX. OOD lengths are ndigits ∈ {10, 25, 50}. 35 [PITH_FULL_IMAGE:figures/full_fig_p035_3.png] view at source ↗
read the original abstract

Spiking Neural Networks (SNNs) have been proposed as biologically plausible and energy-efficient alternatives to conventional Artificial Neural Networks (ANNs). However, the training of SNN usually relies on surrogate gradients due to the non-differentiability of the spike function, introducing approximation errors that accumulate across layers. To address this challenge, we extend the work on convexification of parallel feedforward threshold networks to parallel recurrent threshold networks, which subsume parallel SNNs as a structured special case. Building on this theoretical framework, we propose a parameter reconstruction algorithm for SNN training that demonstrates consistent and significant advantages across various tasks, both as a standalone method and in combination with surrogate-gradient training. The ablations further demonstrate the data scalability and robustness to model configurations of our training algorithm, pointing toward its potential in large-scale SNN training.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript extends convexification results from parallel feedforward threshold networks to parallel recurrent threshold networks, asserts that parallel SNNs are a structured special case of the latter, and introduces a parameter-reconstruction algorithm claimed to achieve globally optimal SNN training. It reports consistent performance gains both standalone and when combined with surrogate-gradient methods, together with ablations on data scalability and robustness.

Significance. A correct transfer of the convexity guarantee to SNNs would remove the need for surrogate-gradient approximations and their accumulated errors, offering a principled route to globally optimal training; the reported empirical advantages and scalability ablations would then constitute a substantial practical contribution if the theoretical embedding holds.

major comments (2)
  1. [Introduction / Theoretical Framework] The load-bearing step is the assertion that SNN membrane integration, threshold crossing, and reset map exactly onto the parallel recurrent threshold-network formalism without extra non-convex constraints. No explicit embedding equations or proof sketch are supplied in the abstract or early sections to verify that temporal dynamics and reset nonlinearities remain inside the convexified regime; if the mapping introduces unaccounted constraints, the global-optimality claim does not transfer.
  2. [Algorithm Description] The parameter-reconstruction algorithm is presented as recovering a globally optimal parameter set, yet the manuscript does not show that the reconstruction procedure itself is free of non-convex optimization sub-problems once the SNN-to-threshold-network embedding is performed.
minor comments (2)
  1. [Experiments] Clarify whether the reported advantages are measured against the same number of epochs or the same computational budget when comparing standalone reconstruction, surrogate-gradient, and hybrid training.
  2. [Ablations] The abstract states that ablations demonstrate data scalability; the corresponding figures or tables should explicitly report the range of dataset sizes and model widths tested.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The two major comments identify areas where the presentation of the theoretical embedding and the convexity of the reconstruction procedure can be strengthened for clarity. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Introduction / Theoretical Framework] The load-bearing step is the assertion that SNN membrane integration, threshold crossing, and reset map exactly onto the parallel recurrent threshold-network formalism without extra non-convex constraints. No explicit embedding equations or proof sketch are supplied in the abstract or early sections to verify that temporal dynamics and reset nonlinearities remain inside the convexified regime; if the mapping introduces unaccounted constraints, the global-optimality claim does not transfer.

    Authors: We agree that the embedding requires clearer early exposition. Section 3 of the manuscript derives the exact mapping of SNN membrane integration, threshold crossing, and reset onto the parallel recurrent threshold-network model, demonstrating that the reset nonlinearity is absorbed into the threshold function without introducing additional non-convex constraints. However, we acknowledge that a concise proof sketch and the key embedding equations are not present in the introduction. We will add a short subsection (or expanded paragraph) in the introduction that states the embedding equations and notes why the temporal dynamics remain inside the convexified regime. revision: yes

  2. Referee: [Algorithm Description] The parameter-reconstruction algorithm is presented as recovering a globally optimal parameter set, yet the manuscript does not show that the reconstruction procedure itself is free of non-convex optimization sub-problems once the SNN-to-threshold-network embedding is performed.

    Authors: The reconstruction procedure is obtained by direct application of the convex parameter-reconstruction method for parallel recurrent threshold networks; after the embedding, every sub-problem solved by the algorithm is a convex program (linear or quadratic programs with convex constraints) whose global optimality is guaranteed by the framework. We will revise the algorithm section to list the sequence of sub-problems explicitly, state their convexity, and reference the relevant theorem from the recurrent-network convexification result. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation rests on claimed extension of convexification rather than self-referential definitions or fits.

full rationale

The paper's central step is an explicit extension of prior convexification results for feedforward threshold networks to the recurrent case, followed by the assertion that parallel SNNs form a structured special case inside that formalism. No equations are presented in the provided abstract that define a quantity in terms of itself or rename a fitted parameter as a prediction. The subsumption claim is presented as a modeling step whose validity would be established by the (unseen) embedding proof rather than by construction from the target optimality result. No self-citation is quoted as the sole justification for a uniqueness theorem or ansatz. The parameter-reconstruction algorithm is therefore treated as an independent algorithmic contribution whose global-optimality guarantee is conditional on the modeling claim, not tautological with it. This satisfies the criteria for a self-contained derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; all such elements remain unknown.

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    Proof.For each hidden nodev, define its incoming norm av =   X (u,v)∈E |w(u, v)|p   1/p

    equivalently, for each hidden-layer weight matrix, ¯Wl[:, i] = Wl[:, i] ∥Wl[:, i]∥p . Proof.For each hidden nodev, define its incoming norm av =   X (u,v)∈E |w(u, v)|p   1/p . By assumption,a v >0. Define the normalized incoming weights by ¯w(u, v) =w(u, v) av for all hidden nodesv. Output-layer weights are left unchanged. Then X (u,v)∈E |¯w(u, v)|p =...

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    14 Proof

    equivalently, ¯Wl,k[:, i] = Wl,k[:, i] ∥Wl,k[:, i]∥p . 14 Proof. The K subnetworks share the same input nodes but have disjoint hidden parameters. Therefore, the normalization from Theorem A.1 can be applied independently to each subnetworkG k. For eachk, Theorem A.1 gives f L,k,Θk(X) =f L,k, ¯Θk(X) and Φp( ¯Θk) =   X (uk,Vout)∈Ek |¯wk(uk, Vout)|p   1...