{"id":"bb159f51-a02e-4158-add5-2a88fd63e95f","arxiv_id":"2601.00668","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A three-factor eligibility-trace rule lets LIF spiking networks learn synaptic and axonal delays online, matching offline backpropagation accuracy on SHD while cutting model size.","lead":"This paper introduces a training rule that lets spiking neural networks learn how much to delay spikes as well as how to weight them, working online rather than after the whole input has been seen. It reports accuracy close to offline training on speech datasets while using smaller models, which matters for low-power neuromorphic chips.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (12) misstates the delay gradient: the printed derivative is w.r.t. time and has the opposite sign, so a reader implementing the published rule would obtain an anti-correlated delay update.","rationale":"I selected the sign/notation error in Eq. (12) as the most load-bearing concern because it directly affects the exact update rule that constitutes the paper's central contribution. The paper reports empirical success, but the equation as written cannot be the gradient used in a correct gradient-descent scheme; it is the time derivative with an inverted sign. This is not a stylistic issue: it changes the direction of delay updates. The non-causal kernel is less concerning because online computation only needs past spikes and a finite buffer, as the authors explain. The unspecified Gaussian width σ is also a gap but is secondary to the explicit mathematical error. My suggested test would settle whether the published equation is actually what was run. If the printed equation is wrong, the paper's description is unreliable, and the conditional verdict is appropriate: the authors should correct Eq. (12) and provide the correct derivation. I therefore agree with the reader's overall verdict and recommend no change, though I focus on the sign issue rather than the causality issue, hence partial agreement.","tokens_in":11496,"tokens_out":9429,"duration_ms":92134,"concrete_test":"Re-implement the method from the paper without inspecting the authors' code. In the definition of the delay eligibility, replace Eq. (12) with (a) the printed time derivative and (b) the analytically correct derivative wrt D_ji. Run the SHD FC-128 SNN configuration (Table I, row 4) for both. If version (a) fails to approach 92% test accuracy or diverges, while version (b) reproduces the paper's result, then Eq. (12) is not the implemented rule. If both versions perform similarly, the sign is not load-bearing, but the equation still needs correction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central derivation rests on Eq. (12), which is supposed to give the gradient of the Gaussian surrogate spike kernel (Eq. 11) with respect to the delay parameter D_ji. As printed, the left-hand side is d x_t-D_ji / dt (a time derivative), not d x_t-D_ji / dD_ji, and the right-hand side is negative. The correct derivative with respect to D_ji is + (t - t_k - D_ji)/(sqrt(2π) σ^3) exp(-(t - t_k - D_ji)^2/(2σ^2)). Thus Eq. (12) has both a notational error and a sign error. Because the eligibility trace in Eq. (9) uses ∂v_t_j/∂D_ji, which is computed from this derivative, the published learning rule updates delays in the opposite direction of the intended gradient. A practitioner implementing the rule exactly as written would not obtain the accuracy gains reported in Table I; if the reported results are real, the implemented code must use a different (corrected) derivative. This makes the paper's central claim non-reproducible from the text alone. The non-causal (Gaussian) kernel is, by contrast, a manageable concern: a ring buffer of length proportional to max delay plus kernel width suffices for online operation, as Section VI indicates.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes three-factor learning rules for simultaneously learning synaptic and axonal delays in single-hidden-layer LIF-based SNNs and SRNNs. Delays are treated as parameters of a Gaussian surrogate spike kernel; the eligibility trace is computed recursively from the derivative of this kernel with respect to the delay, and a top-down error signal from the readout layer provides the third factor. The method is evaluated on the SHD and SSC keyword-spotting datasets, with comparisons to a DCLS/BPTT offline baseline, weights-only baselines, fixed-delay controls, and sparse-network variants. The paper reports that delays improve accuracy by up to 20%, that joint weight-delay learning yields up to 14% higher accuracy at comparable parameter counts, and that the online method matches offline BPTT to within 0.15% on SHD.","tokens_in":11885,"tokens_out":5612,"duration_ms":61304,"significance":"If the central derivation is correct and reproducible, this is a timely and practically relevant contribution to online, on-device learning in neuromorphic systems. The experimental design has several strengths: results are reported with 95% confidence intervals from repeated runs; the online method is compared directly to an offline DCLS/BPTT baseline; fixed-delay controls isolate the contribution of delay learning; and the memory-footprint analysis for on-chip implementation is useful. However, the central delay-gradient equation contains a sign/notation error, and a key kernel hyperparameter is not reported. These issues must be resolved before the claimed results can be independently reproduced from the text.","major_comments":[{"comment":"Equation (12) is stated as the derivative of the Gaussian surrogate with respect to the delay parameters, but as printed the left-hand side is d x(t-D_ji)/dt and the right-hand side is negative of the time derivative of the Gaussian. Since x(t-D_ji) = G(t - t_k - D_ji), the correct derivative with respect to D_ji is + (t - t_k - D_ji)/(sqrt(2 pi) sigma^3) * exp(-(t - t_k - D_ji)^2/(2 sigma^2)), which is the negative of the printed right-hand side. This derivative enters the eligibility trace in Eq. (9) and hence the update rule in Eq. (8). A reader implementing Eq. (12) exactly as written would update delays in the opposite direction of the intended gradient. The reported experimental results must therefore have been obtained with a corrected derivative. This is a load-bearing reproducibility defect in the central learning rule; please correct Eq. (12) and explicitly confirm the sign use","section":"Eq. (12), Sec. III-D"},{"comment":"The Gaussian width sigma in Eq. (11) is never specified. The magnitude and direction of all delay gradients depend directly on sigma, and the paper reports that causal kernels 'did not support effective learning', so the choice of sigma is not a neutral detail. Without a reported value for sigma (or a sigma schedule, if used), the experiments in Table I cannot be reproduced from the text. Please add the sigma value used for each experiment and, ideally, a short sensitivity analysis.","section":"Sec. III-D / IV-B"},{"comment":"The paper claims a 6.6x model size reduction and 67% lower inference latency relative to the DCLS baseline, but Table I shows the same FC-128 configuration with 32.3k parameters for both the BP baseline (row 1) and the online method (row 4) in the synaptic-delay condition. The basis for the 6.6x reduction is therefore unclear from the reported data. Please specify the exact baseline architecture and parameter count used for this claim, or revise the claim so that it is directly supported by Table I or a companion table.","section":"Sec. VI / Table I"}],"minor_comments":[{"comment":"The notation in Eq. (9) is inconsistent: the eligibility trace is written as e_t_ji = partial z_t_j / partial v_t'_j, but the prime on t' is not defined and the subsequent bracket includes partial v_t_j / partial D_ji. Please rewrite with consistent time indices, e.g., partial z_t_j / partial v_t_j times the recursive trace.","section":"Eq. (9)"},{"comment":"Equation (10) writes x^{t-D_ji}_i as a sum of Dirac deltas, but in the discrete-time dynamics of Eq. (3) the input is a sequence indexed by time. Please clarify the relationship between the continuous-time kernel notation and the discrete-time update used in the implementation.","section":"Eq. (10)-(11)"},{"comment":"The text states that the weights-only SRNN baseline is 85.72%, while Table I row 9 reports 85.77% +/- 0.94%. Please correct the inconsistency.","section":"Table I / Sec. V"},{"comment":"There is a typo, 'Section Section VI', and the discussion of ring-buffer sizes would benefit from a more precise explanation of when the buffer depth is 'kernel length' versus 'maximum delay'.","section":"Sec. VI-A"},{"comment":"The paper attributes the large weights-only performance gap between online and DCLS/BPTT to analytical LIF dynamics versus Euler integration, but no direct comparison or citation is given for that claim in this context. Please add a reference or a small control experiment to support this attribution.","section":"Sec. IV-B"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision rather than rejection because the sign/notation error in Eq. (12) is a local, correctable defect and the experimental protocol is otherwise credible. The key question for the revision is whether the implemented code actually uses the corrected derivative; if so, reporting sigma and the corrected equation should be straightforward. The 6.6x model-size claim also needs to be reconciled with Table I."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper. It is the first online three-factor rule I know of that learns both synaptic and axonal delays in LIF networks, and the experimental work is honest: repeated runs, confidence intervals, a direct DCLS baseline, and ablations that separate fixed from learned delays. But the printed central derivative in Eq. (12) is wrong as written—it is the time derivative of the Gaussian kernel with a negative sign, not the derivative with respect to the delay, which has the opposite sign. That matters because the eligibility trace in Eq. (9) feeds on it. A reader implementing exactly what is printed would update delays in the wrong direction. The reported results presumably come from a corrected derivative in code, but the paper is not reproducible from the text until this is fixed.\n\nWhat is new: e-prop eligibility traces were for weights; this paper extends the same machinery to delay parameters using a Gaussian surrogate. That combination is new, and the results are plausible: online delay learning roughly matches offline DCLS-BPTT on SHD, and the parameter-efficiency gains in sparse configurations are real. The authors also show sense in their ablations—fixed delays buy most of the accuracy, and learning delays matters most under sparsity.\n\nSoft spots, in order of importance. The Eq. (12) error is the main one; it is a one-line fix but it is load-bearing. Second, the Gaussian width σ is never given, so the surrogate is not fully specified. Third, the kernel is anti-causal; the authors acknowledge this and propose a ring buffer, which is a reasonable engineering answer, but it does soften the 'real-time' claim. Minor: the 15% weights-only gain over DCLS is attributed to analytical LIF dynamics rather than surrogate differences; that claim would be nice to see supported by an ablated baseline.\n\nOverall: this is a solid, useful paper for the SNN and neuromorphic community, provided the derivation is corrected. The contribution is real even if the published math has a typo-level flaw that is not actually typo-level in consequence. It deserves serious peer review—an editor should send it out, and the reviewers should insist on the corrected derivative and fully specified hyperparameters.","headline":"A genuinely useful online delay-learning rule for SNNs, but the printed delay gradient has a sign/notation error that must be corrected.","tokens_in":12321,"tokens_out":2925,"would_cite":true,"duration_ms":26757,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper proposes three-factor learning rules that let LIF spiking networks learn synaptic and axonal delays online, achieving accuracy close to offline backpropagation on speech recognition tasks.","keywords":["spiking neural networks","delay learning","three-factor learning rules","online learning","eligibility traces","Gaussian surrogate","keyword spotting","LIF neurons"],"falsifier":"Run the same training pipeline with a causal exponential or truncated causal Gaussian kernel of matched width replacing Eq. 11; if delays still learn and accuracy gains survive, the method does not depend on non-causal smoothing as the paper argues. Conversely, verify Eq. 12 by finite differences on Eq. 11; if the sign or normalization is wrong, the reported gradient is not the one being implemented.","tokens_in":11412,"feed_emoji":"🧠","tokens_out":4365,"duration_ms":44418,"temperature":0.7,"pith_summary":"The paper tries to show that temporal delays in spiking neural networks can be treated as learnable parameters and trained online, without backpropagation through time. It derives three-factor learning rules — an eligibility trace capturing how a delay shift changes a neuron's spike, multiplied by a top-down error signal — and uses a smooth Gaussian surrogate to make the non-differentiable spike-delay relationship differentiable. On speech keyword-spotting tasks, this online method reaches accuracy within 0.15% of an offline backpropagation baseline on the SHD dataset, improves accuracy by up to 20% over weights-only networks, and yields up to 14% higher accuracy at comparable parameter counts. If correct, it lets neuromorphic chips learn temporal features on-device with far less memory and latency than offline training.","feed_headline":"Online spike-delay learning matches offline backprop on speech","feed_subtitle":"Three-factor rules add learnable synaptic and axonal delays to LIF spiking networks, enabling on-device training with up to 20% accuracy gai","key_machinery":"The load-bearing object is the three-factor update in Equation 8: the delay gradient for a synapse decomposes into a top-down error signal and a local eligibility trace that recursively tracks the sensitivity of the neuron's output to the delay. Because the delayed spike is not differentiable, the paper replaces the Dirac spike train in Equation 10 with a Gaussian kernel in Equation 11 and uses its derivative in Equation 12; this surrogate supplies the missing gradient and is only used during learning, not inference. The recursive eligibility trace allows the computation to happen online with a ring buffer, despite the kernel being nominally non-causal.","core_discovery":"The central discovery is that delay parameters — both synaptic delays at individual connections and axonal delays at virtual input neurons — can be updated online using a three-factor rule whose eligibility trace is computed with a Gaussian surrogate for the spike train. Although shifting a spike by a delay is discontinuous in the delay parameter, representing the delayed spike as a Gaussian kernel makes the derivative well-defined; the product of this derivative with the surrogate spiking nonlinearity and the error signal gives a gradient-equivalent update. In experiments, this local online rule closely matches offline backpropagation for fully connected feedforward and recurrent networks,","pith_inferences":["The consistent failure of causal kernels reported in the paper suggests a testable design principle: non-causal smoothing may be what makes delay gradients informative, so hardware that wants causal operation would need to approximate or accept a learning-accuracy penalty.","If axonal delay updates accumulate error because each axonal parameter pools contributions from many postsynaptic neurons, then switching to time-to-first-spike coding, where delays attach to hidden neurons rather than input neurons, could make those updates local and more accurate — a natural extension.","Across setups, accuracy on SHD saturates around 92.5% even when SRNNs double parameters; this hints that delay learning is supplying the temporal feature extraction that additional recurrent capacity would otherwise provide, and that scaling to harder tasks would likely need more layers rather than more parameters per layer.","The memory-overhead figures imply a concrete design rule: delay learning is memory-favorable only in sparse regimes; testing at which sparsity each delay type breaks even (43% for axonal, 74% for synaptic per the paper) turns the result into an engineering guideline."],"forward_implications":["On the SHD speech dataset, online delay learning reaches 92.64% test accuracy, within 0.15 percentage points of the 92.79% offline backpropagation baseline under the same network.","Adding learnable delays improves accuracy by up to 20% over weights-only networks; jointly learning weights and delays adds up to 14% at comparable parameter counts, with the largest gains in small and sparse models.","Because delay updates are computed from recursively maintained eligibility traces rather than unrolled sequences, learning can proceed sample-by-sample in real time, removing update locking.","A sparse model with learnable delays can match a denser weights-only model's accuracy with a 6.6x smaller model and 67% lower inference latency in the comparison reported.","On-chip memory planning changes: axonal delays add about 8.3% memory overhead, synaptic delays about 57.7%, but the delays' accuracy gains pay off once the network is sparse enough."],"fun_headline_variants":["Up to 20% accuracy boost from learned spike delays","Learnable delays shrink SNNs 6.6x, speed inference 67%","Online delay learning rivals offline backprop in SNNs","Three-factor rule tunes delays for real-time SNN learning"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The Gaussian surrogate in Eq. 11 and its derivative in Eq. 12 correctly capture the sensitivity of a postsynaptic neuron to a shift in spike timing, even though the true spike-delay relationship is a discontinuous shift and the surrogate kernel is non-causal; causal exponential kernels did not support learning.","fun_headline_variants_meta":{"raw":{"variants":["Up to 20% accuracy boost from learned spike delays","Learnable delays shrink SNNs 6.6x, speed inference 67%","Online delay learning rivals offline backprop in SNNs","Three-factor rule tunes delays for real-time SNN learning"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000503,"raw_usage":{"total_tokens":2299,"prompt_tokens":756,"completion_tokens":1543,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":500,"completion_tokens_details":{"reasoning_tokens":1480}},"tokens_in":500,"tokens_out":1543,"duration_ms":15317,"temperature":1.0,"reasoning_tokens":1480,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T13:00:31.900747+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same training pipeline with a causal exponential or truncated causal Gaussian kernel of matched width replacing Eq. 11; if delays still learn and accuracy gains survive, the method does not depend on non-causal smoothing as the paper argues. Conversely, verify Eq. 12 by finite differences on Eq. 11; if the sign or normalization is wrong, the reported gradient is not the one being implemented.","supporting_citations":[],"review_version":1}