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arxiv: 2505.13741 · v2 · submitted 2025-05-19 · 💻 cs.CV · cs.NE

Frozen Backpropagation: Relaxing Weight Symmetry in Deep Spiking Neural Networks

Gaspard Goupy , Pierre Tirilly , Ioan Marius Bilasco This is my paper

Pith reviewed 2026-05-22 13:48 UTC · model grok-4.3

classification 💻 cs.CV cs.NE
keywords spiking neural networksbackpropagationweight symmetryweight transportneuromorphic hardwarefrozen backpropagationon-chip learningenergy efficiency
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The pith

Frozen Backpropagation relaxes weight symmetry in deep spiking neural networks by periodically freezing feedback weights.

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

The paper addresses the difficulty of running backpropagation directly on neuromorphic hardware for spiking neural networks. Separate forward and feedback networks normally require continuous weight transport to keep weights symmetric for correct gradient calculation, adding energy overhead. Frozen Backpropagation instead computes gradients using feedback weights that are held fixed for multiple steps before any update, cutting the number of transports needed. This keeps accuracy close to standard backpropagation across rate-coded and temporally coded SNNs on image tasks while lowering transport costs. Adding partial transport schemes, which move only subsets of weights at a time, reduces those costs by up to 10,000 times with only moderate accuracy trade-offs.

Core claim

fBP updates forward weights by computing gradients with periodically frozen feedback weights in a setting with distinct forward and feedback networks. This reduces the frequency of weight transports and synchronization overhead during training. When combined with three partial weight transport schemes of varying complexity, transport costs drop by up to 10,000x relative to full transport, at the expense of moderate accuracy loss on image recognition benchmarks.

What carries the argument

Periodically frozen feedback weights that supply gradients for forward-weight updates in separate forward and feedback networks.

Load-bearing premise

Periodically freezing feedback weights for multiple steps still produces usable gradients for forward-weight updates without extra compensation mechanisms or major hyperparameter retuning.

What would settle it

Train an SNN with fBP on a standard image classification benchmark while increasing the number of steps between feedback-weight updates and check whether accuracy stays within a few percent of full backpropagation.

Figures

Figures reproduced from arXiv: 2505.13741 by Gaspard Goupy, Ioan Marius Bilasco, Pierre Tirilly.

Figure 1
Figure 1. Figure 1: BP-based training in a dual-network configuration, consisting of a forward and a feedback [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Accuracy drop versus weight transport reduction factor of [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Cosine similarity between true and actual weight changes during training on CIFAR-100. Best seen in color. FBP aims to minimize the gradient bias introduced by the magnitude mismatch between forward and feed￾back weights. In this section, we quantify this bias by measuring the cosine similarity between true weight updates, computed using gradients based solely on forward weights (i.e., by replacing B with … view at source ↗
read the original abstract

Direct training of Spiking Neural Networks (SNNs) on neuromorphic hardware can greatly reduce energy costs compared to GPU-based training. However, implementing Backpropagation (BP) on such hardware is challenging because forward and backward passes are typically performed by separate networks with distinct weights. To compute correct gradients, forward and feedback weights must remain symmetric during training, necessitating weight transport between the two networks. This symmetry requirement imposes hardware overhead and increases energy costs. To address this issue, we introduce Frozen Backpropagation (\textsc{fBP}), a BP-based training algorithm relaxing weight symmetry in settings with separate networks. fBP updates forward weights by computing gradients with periodically frozen feedback weights, reducing weight transports during training and minimizing synchronization overhead. To further improve transport efficiency, we propose three partial weight transport schemes of varying computational complexity, where only a subset of weights is transported at a time. We evaluate our methods on image recognition tasks using both temporally and rate-coded SNNs, and compare them to existing approaches addressing the weight symmetry requirement. Our results show that fBP outperforms these methods and achieves accuracy comparable to BP while significantly lowering transport costs. With partial weight transport, fBP can further lower those costs by up to 10,000x at the expense of moderate accuracy loss. This work provides insights for guiding the design of neuromorphic hardware incorporating BP-based on-chip learning.

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 paper introduces Frozen Backpropagation (fBP), a training algorithm for deep spiking neural networks that periodically freezes feedback weights to relax the strict symmetry requirement between forward and feedback networks during backpropagation. This reduces weight transport overhead in neuromorphic hardware settings. The authors further propose three partial weight transport variants and evaluate fBP against existing symmetry-relaxation methods on image classification tasks using both temporally coded and rate-coded SNNs, claiming comparable accuracy to standard BP with substantially lower transport costs (up to 10,000x reduction via partial transport at moderate accuracy cost).

Significance. If the empirical results prove robust, the work has moderate significance for neuromorphic hardware design: it offers a practical heuristic to lower synchronization energy costs while retaining BP-based training for SNNs. The partial-transport schemes provide tunable trade-offs that could inform on-chip learning architectures. However, the absence of statistical controls and sensitivity analysis on the core freezing mechanism limits the strength of the contribution.

major comments (2)
  1. [Experimental Results] Experimental Results section: the central empirical claims (outperformance over baselines and accuracy comparable to BP) are reported without error bars, number of independent runs, dataset sizes, or statistical significance tests. This directly affects assessment of whether the reported gains are reliable or sensitive to the choice of freeze interval K.
  2. [Method] Method section (fBP description): no analysis, bound, or ablation is provided on gradient alignment or error accumulation as forward weights continue to update while feedback weights remain frozen. The assumption that usable gradients persist over multiple steps without compensation or retuning is load-bearing for the claim that fBP requires no additional mechanisms, yet remains unverified beyond the reported experiments.
minor comments (2)
  1. [Abstract] The 10,000x transport-cost reduction figure in the abstract lacks a precise baseline comparison and conditions under which it is achieved.
  2. [Figures] Figure captions and diagrams illustrating the freeze schedule would benefit from explicit labeling of the forward-update steps versus transport events.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their thoughtful and constructive comments on our manuscript introducing Frozen Backpropagation (fBP). We have addressed each of the major comments below and outline the revisions we intend to make to enhance the empirical robustness and methodological analysis of the work.

read point-by-point responses

  1. Referee: [Experimental Results] Experimental Results section: the central empirical claims (outperformance over baselines and accuracy comparable to BP) are reported without error bars, number of independent runs, dataset sizes, or statistical significance tests. This directly affects assessment of whether the reported gains are reliable or sensitive to the choice of freeze interval K.

    Authors: We agree that the reported results would be strengthened by including measures of variability and statistical analysis. In the revised manuscript we will report accuracies over multiple independent runs with error bars, explicitly state the number of runs and dataset sizes, and include statistical significance tests comparing fBP against baselines and standard BP. We will also add an ablation varying the freeze interval K to demonstrate sensitivity of accuracy and transport cost to this hyperparameter. revision: yes

  2. Referee: [Method] Method section (fBP description): no analysis, bound, or ablation is provided on gradient alignment or error accumulation as forward weights continue to update while feedback weights remain frozen. The assumption that usable gradients persist over multiple steps without compensation or retuning is load-bearing for the claim that fBP requires no additional mechanisms, yet remains unverified beyond the reported experiments.

    Authors: Our experiments across temporally and rate-coded SNNs on image classification tasks show that fBP achieves accuracy comparable to BP, indicating that gradients remain sufficiently aligned during frozen periods in practice. We acknowledge the value of additional verification. In the revision we will include an ablation measuring gradient alignment (e.g., cosine similarity) and error accumulation over varying freeze intervals, together with a discussion of these empirical observations. A formal theoretical bound on alignment is not provided in the current work. revision: partial

standing simulated objections not resolved
  • Providing a rigorous theoretical bound on gradient alignment and error accumulation during frozen periods

Circularity Check

0 steps flagged

No circularity: empirical heuristic validated externally

full rationale

The paper introduces Frozen Backpropagation as a practical training heuristic for SNNs that periodically freezes feedback weights to reduce transport overhead. Performance is demonstrated via direct experiments on image tasks against external baselines (standard BP and prior symmetry-relaxation methods), with no equations, derivations, or self-citations that reduce accuracy/efficiency claims to quantities defined by the method's own fitted parameters or internal assumptions. The central results rest on empirical measurement rather than any self-definitional or fitted-input reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that backpropagation gradients remain sufficiently accurate when feedback weights are held constant for multiple steps, plus the empirical observation that partial transport preserves enough information for learning.

axioms (1)
  • domain assumption Correct gradients in BP require symmetric forward and feedback weights when networks are separate.
    Invoked in the opening problem statement to motivate the need for weight transport.

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