{"id":"1885ab8c-6fd6-43b8-96eb-19cce120edbf","arxiv_id":"1908.06378","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"ST-RSBP trains deep recurrent spiking neural networks via spike-train-level backpropagation, reaching state-of-the-art accuracy on TI46, N-TIDIGITS, Fashion-MNIST, and MNIST benchmarks.","lead":"This paper presents a new backpropagation-style algorithm for training recurrent spiking neural networks, which communicate with discrete pulses. It reports top accuracies on speech and image benchmarks without unrolling the network in time.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fitted S-PSP derivative in Supp. Sec. 2.3 is load-bearing: every backpropagated error uses it, but no evidence shows it holds under recurrent spike statistics; the claimed SOTA accuracy depends on this unvalidated approximation.","rationale":"The reader's weakest_assumption identifies the same root cause I would flag: the S-PSP derivatives are obtained from an offline, random-spike-train fit and then used in every backpropagated error. I considered alternative concerns, such as the unquantified first-order Taylor expansion of (Ω−Θ)^−1 and the fairness of non-spiking baselines, but they are secondary. The Taylor expansion only affects the cost of solving the linear system, whereas the fitted derivative is the entry point for all gradient information. The non-spiking comparisons are architecture-specific and do not undermine the main SNN-BP comparisons. The released code is a genuine strength and makes the proposed test feasible, but it does not establish that the gradient surrogate matches the true sensitivity of S-PSPs under recurrent dynamics. My proposed test directly compares the offline polynomial to in-situ derivative estimates and retrains the headline model; if the accuracy gap is small, the concern is resolved, and if not, the paper's theoretical and empirical claims need to be conditioned on the approximation. Since the reader already reached CONDITIONAL and my analysis does not move that verdict, I recommend UNCHANGED.","tokens_in":18587,"tokens_out":6581,"duration_ms":70584,"concrete_test":"Retrain the 400-R400-400 TI46-Alpha model exactly as in Table 2, but replace the offline polynomial derivatives of Supp. Sec. 2.3 with derivatives estimated from the spike-train statistics of the actual network during a forward pass: collect (o_i,o_j,e_ij) samples from the live network, fit the same functional form in situ, and use those derivatives in Eqs. (20), (25), and (26). If the mean accuracy moves by more than about 1 percentage point from 93.06%, or if the in-situ derivative surface differs systematically from the offline fit, then the fitted approximation is confirmed as load-bearing. A secondary sanity check is to train with ∂e_ij/∂o_i forced to the linear HM2-BP surrogate; if accuracy is unchanged, the third-order polynomial is not actually responsible for the reported gains.","verdict_should_be":"UNCHANGED","load_bearing_attack":"ST-RSBP's central claim—state-of-the-art training of deep RSNNs—rests on the gradient formulas in Eqs. (20), (23), (25), and (26), all of which multiply errors by ∂e_ij/∂o_i and ∂e_ij/∂o_j. Supplementary Sec. 2.3 derives these derivatives empirically: ∂e_ij/∂o_j is taken as e_ij/o_j, and ∂e_ij/∂o_i is a third-order polynomial fit to 500 random spike-train simulations per (o_i,o_j) pair with uniformly random spike times. The supplement even notes that the linear-in-o_i assumption used by HM2-BP is inaccurate, but it does not show that the polynomial fit remains accurate when recurrent dynamics create correlated, non-uniform spike trains. Because the fitted derivative enters every backpropagated error through Φ, Θ, and the denominators of F, any systematic mismatch biases the entire gradient. The fit coefficients are not published, so the approximation is not independently checkable. The derivation also treats e_ij as a function of firing counts only: the chain rule in Eqs. (9)–(10) does not propagate through firing times, although e_ij is defined from those times. Thus the paper's 'rigorously derived' claim overstates the status of this empirically fitted component. The released code is real evidence for reproducibility, but it cannot by itself validate the gradient approximation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes ST-RSBP, a spike-train level backpropagation algorithm for training deep recurrent spiking neural networks (RSNNs) without unfolding the network through time. The method defines spike-train level post-synaptic potentials (S-PSPs) and total PSPs (T-PSPs), and derives error backpropagation through recurrent layers by solving a linear system of partial derivatives. The S-PSP derivatives with respect to pre- and post-synaptic firing counts are obtained empirically: the pre-synaptic derivative is approximated linearly, and the post-synaptic derivative is fit with a third-order polynomial from random spike-train simulations (Supplementary Section 2.3). Experiments on TI46-Alpha, TI46-Digits, N-TIDIGITS, Fashion-MNIST, and MNIST spiking CNN report state-of-the-art accuracies, with the CUDA implementation released on GitHub.","tokens_in":19040,"tokens_out":3513,"duration_ms":35555,"significance":"If the empirical derivative approximations are valid under the spike statistics encountered during training, ST-RSBP is a substantial contribution: it provides a tractable supervised training rule for deep RSNNs that avoids BPTT, demonstrates strong results across speech and image benchmarks, and ships reproducible GPU code. The paper explicitly identifies a weakness in the HM2-BP linearity assumption and improves on it with a polynomial fit, which is a genuine step forward. However, the fitted derivative is the linchpin of the entire gradient computation, and its validation is currently incomplete; the manuscript's claim that ST-RSBP is 'rigorously derived' overstates the status of this empirically fitted component. The release of source code is a clear strength, but it does not substitute for an analysis of the approximation's range of validity.","major_comments":[{"comment":"The derivative ∂e_ij/∂o_i is obtained by fitting a third-order polynomial to 500 random spike-train simulations per (o_i, o_j) pair with uniformly random spike times. This fitted derivative enters every backpropagated error and every differentiation-of-activation matrix in the algorithm. The manuscript provides no evidence that the fit remains accurate when recurrent layers produce correlated, non-uniform spike trains, nor does it report the polynomial coefficients, so the approximation is not independently checkable or reproducible from the text alone. This is a load-bearing component: if the fit is systematically biased during training, the claimed accuracy gains are not guaranteed. Please either derive this derivative analytically, validate the fit on spike statistics actually encountered during training, or release the fitted coefficients along with a sensitivity analysis.","section":"Supplementary Section 2.3; Eqs. (19), (23), (25), (26)"},{"comment":"The approximation o_i ≈ a_i/ν replaces an integer firing count with a continuous value and is used throughout the chain rule in Eqs. (9), (10), (23), (25), and (26). The error of this substitution is never quantified, and it is applied uniformly to all layers, including those with low firing counts where discreteness effects are largest. Since the loss function is defined on firing counts, the accuracy of this approximation directly affects the correctness of the gradient. Please provide a bound or empirical characterization of the approximation error, or demonstrate that training is insensitive to it.","section":"Eq. (1) and Supplementary Eq. (7)"},{"comment":"The S-PSP e_ij is defined in Supplementary Eq. (6) as an explicit function of both pre- and post-synaptic firing times, yet the chain rule in Eqs. (9) and (10) differentiates only with respect to firing counts, completely discarding the dependence on spike timing. The main text states that temporal effects are captured in the backward pass, but the derivation as written does not propagate errors through firing times. This is an inconsistency between the definition of S-PSP and the derivative computation, and it should be either resolved by including time-dependent derivatives or explicitly acknowledged as a modeling approximation.","section":"Eqs. (7)-(10) and Supplementary Eq. (12)"},{"comment":"The matrix inversion (Ω − Θ)^{-1} is approximated by a first-order Taylor expansion to avoid matrix factorization, but no condition is given for when this expansion is valid (e.g., a spectral radius or norm bound on ΘΩ^{-1}), nor is any error analysis provided. Since this approximation affects the backpropagated error in recurrent layers, the paper should state the validity condition and report how it was checked in the experiments.","section":"After Eq. (13)"}],"minor_comments":[{"comment":"The heading 'TI46-Digits Speech Datasest' contains a typo; it should read 'Dataset'.","section":"Section 4.3 heading"},{"comment":"The word 'spatio-temproally' should be 'spatio-temporally'.","section":"Section 2, paragraph 2"},{"comment":"The phrase 'state-of-art' should be 'state-of-the-art'.","section":"Abstract"},{"comment":"Beyond the coefficients, please specify the exact functional form of the fitted polynomial, the range of o_i and o_j over which it was fit, and how the derivative is extrapolated outside that range.","section":"Supplementary Section 2.3"},{"comment":"The comparison with SLAYER uses different network sizes (12C5-p2-64C5-p2 versus 15C5-P2-40C5-P2-300); please clarify whether the comparison is intended to be at similar model complexity or simply to report the best published result on MNIST.","section":"Table 6"}],"recommendation":"major_revision","confidential_remarks":"The main risk is the unpublished, empirically fitted S-PSP derivative, which is the core of the gradient computation. If the authors can validate it under training conditions or provide the coefficients and sensitivity experiments, the contribution would be much stronger. The released code is a positive sign, but the paper's 'rigorously derived' phrasing should be tempered. I see this as a major-revision issue rather than rejection because the overall approach is plausible and the empirical results are strong."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"ST-RSBP is a real extension of the authors' HM2-BP method to recurrent spiking networks, and it delivers strong results. The coupled linear system for recurrent S-PSP derivatives and the third-order polynomial derivative model are genuine technical advances over prior feedforward-only SNN backprop. The reported accuracies on TI46, N-TIDIGITS, Fashion-MNIST, and the MNIST spiking CNN are plausible and often beat earlier SNN training algorithms, and the released CUDA code is concrete evidence that the method works.\n\nThe soft spot is exactly the one the stress-test flags: the derivative ∂e_ij/∂o_i, which appears in every backpropagated error, is not derived analytically but fitted to random spike-train simulations in Supp. Sec. 2.3. That fit is load-bearing, and the paper does not show that it remains accurate under recurrent spike statistics, where spike trains become correlated and non-uniform. The fit coefficients are not published, so the approximation is not independently checkable. The chain rule also treats S-PSPs as functions of firing counts only, ignoring firing times, even though the S-PSP definition depends on them. And the first-order Taylor expansion for the matrix inverse in Eq. 13 is an unquantified approximation. These are real limitations, but they are not fatal—the empirical results and code show that the method works despite them. The paper's phrase 'rigorously derived' overstates the case; it would be more accurate to call it 'derived with a fitted surrogate derivative.'\n\nWho is this for? People working on SNN training, especially recurrent and deep hybrid spiking networks for speech and neuromorphic audio. It deserves a serious referee. I would send it to review and ask the authors to publish the fit coefficients, validate the derivative approximation under recurrent spiking conditions, and report sensitivity to the Taylor expansion.","headline":"A genuine extension of HM2-BP to recurrent spiking networks with strong empirical wins, but the load-bearing fitted derivative is under-validated.","tokens_in":19502,"tokens_out":3041,"would_cite":true,"duration_ms":30169,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"By treating spike trains as differentiable aggregate signals, ST-RSBP trains deep recurrent spiking networks without unrolling them in time, surpassing prior spiking and non-spiking baselines on speech and image benchmarks.","keywords":["spiking neural networks","recurrent spiking neural networks","backpropagation","spike-train level post-synaptic potential","rate-coded loss","LIF neuron model","neuromorphic speech recognition","gradient computation"],"falsifier":"Record the actual spike trains during ST-RSBP training and numerically perturb a single weight to estimate the true gradient of the rate-coded loss; compare with ST-RSBP's analytic gradient for the same sample. A systematic mismatch that grows as firing rates leave the ranges covered by the offline random simulations would show the fitted derivative is the load-bearing approximation.","tokens_in":18376,"feed_emoji":"⚡","tokens_out":5002,"duration_ms":49826,"temperature":0.7,"pith_summary":"ST-RSBP is a supervised learning rule that trains recurrent spiking neural networks by treating each neuron's total post-synaptic potential as a differentiable function of firing counts, so gradients of a rate-coded loss can be backpropagated through both feedforward and recurrent layers without unfolding the network in time. A sympathetic reader would care because recurrent spiking networks have attractive temporal dynamics but previously lacked a general supervised training method: existing approaches either train only the readout, smooth away spike discontinuities, or unroll the network time step by time step. The paper reports that ST-RSBP trains deep hybrid feedforward/recurrent networks to accuracies above prior spiking backpropagation rules and above conventional non-spiking models such as LSTM and GRN on the same benchmarks: 93.35% on TI46-Alpha, 99.39% on TI46-Digits, 93.90% on N-TIDIGITS, 90.13% on Fashion-MNIST, and 99.62% on a spiking CNN for MNIST. The central move is to keep the spiking behavior intact at the spike-train level rather than smoothing microscopic membrane waveforms.","feed_headline":"Spike-train backprop trains recurrent spiking networks","feed_subtitle":"Rate-coded gradients beat LSTM and prior SNN rules on speech and image benchmarks.","key_machinery":"The key object is the S-PSP, the spike-train-level post-synaptic potential: the accumulated normalized contribution of a presynaptic neuron's spike train to a postsynaptic neuron's membrane potential right before each postsynaptic spike. It converts spike trains into quantities $a_i$ and $o_i$ that obey ANN-like relations, letting the rate-coded loss be differentiated through hidden recurrent layers. Recurrent backpropagation solves the linear system in Eq. (20), while the spike-level derivative $\\partial e_{ij}/\\partial o_j$ is taken as $e_{ij}/o_j$ and $\\partial e_{ij}/\\partial o_i$ is read from a third-order polynomial fitted offline to random spike-train simulations of LIF neurons.","core_discovery":"The paper's central claim is that the non-differentiability of spikes can be handled without temporal unrolling or waveform smoothing. Each synapse's aggregate effect is summarized by the spike-train-level post-synaptic potential $e_{ij}$, the accumulated contribution of the presynaptic spike train to the postsynaptic neuron's membrane potential just before each of its firings. Because the firing count satisfies $o_i \\approx a_i/\\nu$, the total post-synaptic potential $a_i = \\sum_j w_{ij} e_{ij}$ behaves like a conventional ANN pre-activation, so the chain rule applies at the level of whole spike trains. For recurrent layers, the needed cross-layer derivatives form a coupled linear system $\\Omega P = \\Phi + \\Theta P$, whose solution $P = (\\Omega - \\Theta)^{-1}\\Phi$ propagates errors without unrolling time; for feedforward layers the formula simplifies to a diagonal form. The paper argues that this computes gradients of the true rate-coded loss more faithfully than smoothing-based methods and avoids vanishing or exploding gradients because no temporal unrolling occurs.","pith_inferences":["If the fitted derivative $\\partial e_{ij}/\\partial o_i$ is the main approximation, then refitting that polynomial online during training, as firing statistics drift, could improve robustness and possibly accuracy; the paper fixes it offline before training.","Because the S-PSP is defined for any all-or-none spiking neuron model, the same spike-train-level linear-system backpropagation could extend beyond LIF neurons to adaptive or conductance-based models, though the paper only demonstrates LIF.","The reported gains are on accuracy at matched parameter counts; whether the advantage persists at matched inference energy or latency on event-driven hardware remains untested and would be a natural next check.","The avoidance of vanishing gradients concerns the backward-pass structure, but long temporal dependencies in the hidden state are not directly probed by the four datasets, so tasks requiring very long memory remain an open question."],"forward_implications":["Deep RSNNs with multiple feedforward and recurrent layers can be trained end-to-end under a rate-coded loss, making recurrent spiking models a practical option for temporal tasks such as speech recognition.","Because the backward pass does not unroll the network in time, training avoids the exploding and vanishing gradient failure mode and the computational cost of point-by-point backpropagation through time.","On feedforward spiking CNNs, ST-RSBP improves over HM2-BP with the same model complexity, indicating that the more accurate spike-train derivative treatment also benefits standard feedforward training.","The reported results imply that spike-based recurrent networks can match or exceed conventional recurrent models such as LSTM and GRN on neuromorphic speech benchmarks, narrowing the accuracy gap that previously favored non-spiking networks."],"supporting_citations":[{"why":"Introduces HM2-BP, the hybrid macro/micro-level backpropagation and S-PSP formulation that ST-RSBP extends, corrects, and uses as its primary feedforward baseline.","marker":"[19]"},{"why":"Provides STBP, a spatio-temporal backpropagation baseline for spiking CNNs and BPTT-style recurrent training that ST-RSBP compares against.","marker":"[39]"},{"why":"Provides SLAYER, a spike-layer error reassignment baseline that approximates spike discontinuities probabilistically and is used as a comparison on MNIST.","marker":"[33]"},{"why":"Supplies an earlier rate-coded backpropagation method for deep spiking networks and the baseline spiking CNN results on MNIST.","marker":"[23]"},{"why":"Provides the liquid-state-machine baseline that trains only the readout layer, demonstrating the limitation ST-RSBP addresses by training all layers.","marker":"[38]"},{"why":"Provides SpiLinCa, a recurrent liquid-ensemble method with STDP-trained input weights, used as a recurrent SNN baseline on TI46-Digits.","marker":"[35]"},{"why":"Supplies the N-TIDIGITS neuromorphic speech dataset and the non-spiking GRN and Phased-LSTM baselines that ST-RSBP outperforms.","marker":"[3]"},{"why":"Supplies the TI46 speech corpus used for the TI46-Alpha and TI46-Digits speech recognition experiments.","marker":"[25]"},{"why":"Supplies the Fashion-MNIST image dataset used to benchmark ST-RSBP against non-spiking and spiking backpropagation methods.","marker":"[40]"}],"fun_headline_variants":["Spike-train backprop without time unrolling","ST-RSBP: rate-coded gradients for recurrent SNNs","Spike-train gradients beat LSTM on benchmarks","Direct spike-train backprop for deep RSNNs","Training RSNNs via firing-rate loss gradients"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The gradient formulas rest on treating each synapse's aggregate spike-train effect as a differentiable function of firing counts, with one derivative measured offline from random spike-train simulations; if real training spike trains differ from those simulations, the backpropagated gradients are systematically biased.","fun_headline_variants_meta":{"raw":{"variants":["Spike-train backprop without time unrolling","ST-RSBP: rate-coded gradients for recurrent SNNs","Spike-train gradients beat LSTM on benchmarks","Direct spike-train backprop for deep RSNNs","Training RSNNs via firing-rate loss gradients"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000224,"raw_usage":{"total_tokens":1519,"prompt_tokens":1060,"completion_tokens":459,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":676,"completion_tokens_details":{"reasoning_tokens":380}},"tokens_in":676,"tokens_out":459,"duration_ms":5493,"temperature":1.0,"reasoning_tokens":380,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:47:32.205812+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Record the actual spike trains during ST-RSBP training and numerically perturb a single weight to estimate the true gradient of the rate-coded loss; compare with ST-RSBP's analytic gradient for the same sample. A systematic mismatch that grows as firing rates leave the ranges covered by the offline random simulations would show the fitted derivative is the load-bearing approximation.","supporting_citations":[{"cited_title":"Hybrid macro/micro level backpropagation for training deep spiking neural networks","cited_arxiv_id":null,"evidence_quote":"Introduces HM2-BP, the hybrid macro/micro-level backpropagation and S-PSP formulation that ST-RSBP extends, corrects, and uses as its primary feedforward baseline."},{"cited_title":"Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks","cited_arxiv_id":"1706.02609","evidence_quote":"Provides STBP, a spatio-temporal backpropagation baseline for spiking CNNs and BPTT-style recurrent training that ST-RSBP compares against."},{"cited_title":"Slayer: Spike layer error reassignment in time","cited_arxiv_id":null,"evidence_quote":"Provides SLAYER, a spike-layer error reassignment baseline that approximates spike discontinuities probabilistically and is used as a comparison on MNIST."},{"cited_title":"Training deep spiking neural networks using backpropagation","cited_arxiv_id":null,"evidence_quote":"Supplies an earlier rate-coded backpropagation method for deep spiking networks and the baseline spiking CNN results on MNIST."},{"cited_title":"Analysis of liquid ensembles for enhancing the performance and accuracy of liquid state machines","cited_arxiv_id":null,"evidence_quote":"Provides the liquid-state-machine baseline that trains only the readout layer, demonstrating the limitation ST-RSBP addresses by training all layers."},{"cited_title":"Spilinc: Spiking liquid-ensemble computing for unsupervised speech and image recognition","cited_arxiv_id":null,"evidence_quote":"Provides SpiLinCa, a recurrent liquid-ensemble method with STDP-trained input weights, used as a recurrent SNN baseline on TI46-Digits."},{"cited_title":"Feature representations for neuromorphic audio spike streams","cited_arxiv_id":null,"evidence_quote":"Supplies the N-TIDIGITS neuromorphic speech dataset and the non-spiking GRN and Phased-LSTM baselines that ST-RSBP outperforms."},{"cited_title":"TI 46-word LDC93S9 , 1991","cited_arxiv_id":null,"evidence_quote":"Supplies the TI46 speech corpus used for the TI46-Alpha and TI46-Digits speech recognition experiments."}],"review_version":1}