{"id":"8072a193-30f9-4ba1-a62b-361706c5e42b","arxiv_id":"2504.17751","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A fixed refractory period, implemented as a strided temporal convolution, can replace LIF reset dynamics in a state-space spiking model and still produce sparse, parallel-trainable spikes.","lead":"This paper reinterprets spiking neural networks as binary-activated recurrent networks and argues that reset and refractory mechanisms are an irregular discretization of time. It then builds a simple state-space model with a fixed refractory period, spikingPssm, which reaches 85.5% accuracy on sequential CIFAR-10, below the best published spiking SSMs but above several baselines.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Theorem 4.1 is not universal: a hard-reset LIF (Eq. 5) can fire at consecutive timesteps under constant suprathreshold input, violating Eq. (17)'s requirement that previous f(t-k*dt) <= theta; the reset-as-discretization premise is therefore unsupported.","rationale":"The paper is best read as an interpretive proposal: decouple SSM memory from spiking transmission and replace LIF reset/refractory with a parallel-friendly fixed temporal kernel. The Sequential CIFAR-10 result (85.5%) is a useful existence proof, and the authors honestly disclaim architectural novelty and note the lack of genuine low-power analysis. However, the theoretical section is not merely loose; it contains a formal claim that is false for the standard LIF model the paper claims to analyze. Theorem 4.1 (Eq. 17) asserts a universal spike-encoding form requiring f(t-k*dt) <= theta during the refractory window, but a hard-reset LIF (Eq. 5) with Vreset=0 and constant suprathreshold input fires at consecutive timesteps. Thus the theorem cannot represent standard reset dynamics; it only describes a threshold-and-blank encoder. This matters because the paper's central conclusion, that reset and refractory are just sampling/discretization and do not contribute to memory, is derived from this theorem. The reader's weakest assumption, that refractory-shape is invisible to the next layer, is a downstream consequence of the same flawed derivation; fixing the theorem would not rescue that claim either, since in a stacked SSM or LIF the spike times are convolved with the memory kernel. I therefore do not change the conditional verdict, but the revision condition should be explicit: either prove a corrected theorem for integrate-and-fire dynamics, or reframe the theory as applying only to the proposed threshold-and-blank encoder and remove the 'universal' claim.","tokens_in":20081,"tokens_out":11175,"duration_ms":115542,"concrete_test":"Run a minimal one-neuron simulation of Eq. (5) with Vreset=0, tau very large (e.g., 1e6), threshold theta=1, and constant input current I(t)=2 for 10 timesteps. Record the spike train. If the neuron fires at every timestep, compare with Theorem 4.1: for any t>=1, f(t-dt)=2 > theta, so Eq. (17) outputs 0, and no choice of m(t) can represent consecutive firing. This single simulation falsifies the claimed universality of Theorem 4.1 and demonstrates that the reset-as-discretization interpretation omits LIF's accumulation memory. If the authors intended f(t) in Theorem 4.1 to be the pre-spike membrane potential U(t) rather than the memory-module output, they should state this explicitly and revise Eq. (17), because the failure persists whenever a spike at t-1 resets V to Vreset=0 and the next input is still suprathreshold.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical premise (Sections 4.1 and 4.2) is that reset and refractory mechanisms in SNNs act only as a special discretization or sparse sampling of a dense spike train, so a fixed refractory period suffices and the spiking mechanism does not contribute to historical memory. This premise rests on Theorem 4.1, which claims to 'universally describe the spike encoding scheme for all spiking neural networks with reset mechanisms and refractory periods' via Eq. (17): a spike occurs at time t only if f(t) >= theta and f(t-k*dt) <= theta for k=1..m(t). That claim fails for the standard hard-reset LIF in Eq. (5). In Eq. (5), the pre-spike potential is U_i^l(t+1) = (1 - 1/tau) V_i^l(t) + sum_j w_ij s_j(t+1), and after a spike V_i^l(t) = Vreset. With Vreset = 0 and a constant suprathreshold current, the neuron fires at every timestep: for theta=1 and input 2 at both t and t+1, U(t)=2 and U(t+1)=2, so spikes occur at consecutive steps. Theorem 4.1 would require f(t) <= theta for the previous step, so it predicts no second spike. The theorem therefore describes a threshold-and-blank encoder, not an integrate-and-fire neuron; it omits the input accumulation that is the defining temporal memory of LIF/IF dynamics. Consequently, the derivation of the fixed-refractory architecture does not apply to the LIF-based SNNs the paper claims to analyze, and the central conclusion that reset/refractory do not contribute to historical memory is unsupported. The later argument that refractory shape is invisible to the next layer also assumes the downstream layer performs no temporal integration; in a stacked SSM or LIF, spike times enter the memory kernel, so dropping 'gray' spikes is a lossy approximation, not merely a change of refractory shape.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes viewing spiking neural networks as binary-activated recurrent neural networks for sequence modeling, decoupling them into a memory module (modeled by state space models) and a spiking transmission module. Its central theoretical claim is that reset and refractory mechanisms in SNNs act only as a special discretization or sparse sampling of the memory output, so that a fixed refractory period suffices and the spiking mechanism contributes no historical memory. On this basis the paper proposes two parallel-trainable architectures, spikingFRssm and spikingPssm, and reports accuracy on Sequential CIFAR-10.","tokens_in":20456,"tokens_out":8554,"duration_ms":83949,"significance":"If the central claim were correct, the paper would make a useful conceptual contribution: it would justify replacing reset-based LIF dynamics with a fixed refractory period, enabling parallel training while retaining sparse spike trains, and it would clarify the role of spikes in SSM-based sequence models. The paper is commendably candid about its limitations, provides implementation details in Algorithm 1, and Theorem 4.2 is a correct elementary calculation. However, the significance is substantially limited by the correctness problem in Theorem 4.1, by the informal 'distribution sampling' framework, and by the narrow empirical support.","major_comments":[{"comment":"Theorem 4.1 is not universal for the LIF model the paper claims to analyze. For the hard-reset LIF of Eq. (5) with V_reset = 0, θ = 1, and constant suprathreshold input I = 2, the neuron fires at every timestep because U(t+1) = (1 - 1/τ)V(t) + 2 = 2 at both t and t+1. Equation (17) requires f(t - Δt) ≤ θ, so it predicts no second spike. The theorem describes a threshold-and-blank encoder applied to the current memory output f(t), not an integrate-and-fire neuron whose firing depends on accumulated membrane potential. Since the fixed-refractory architecture in §4.2 is derived from this 'universal' encoding, the central claim that reset and refractory mechanisms do not contribute to historical memory is unsupported.","section":"§4.2, Theorem 4.1 / Eq. (17)"},{"comment":"The assertion that 'the choice of refractory function does not affect the system's perception of the spikes' assumes that the receiving layer sums binary spikes linearly and that spike timing within a timestep carries no information. This assumption is not derived from Theorem 4.1; it is an additional modeling premise. In the proposed spikingPssm itself, the spiking module applies a learnable temporal convolution in Eq. (32), so the refractory/window function shape changes the output. The premise therefore cannot support the conclusion that a fixed refractory period is information-lossless in general.","section":"§4.2, refractory-function premise"},{"comment":"The empirical evaluation rests on a single dataset (Sequential CIFAR-10) with no error bars, no multiple-seed statistics, and no ablation isolating the fixed-refractory mechanism from the other components (SSM memory, GLU, learnable kernel). The comparative discussion in §5.3 makes claims such as 'SpikingPssm outperforms P-SpikeSSM... and PMSN' on the basis of a single number per method. This is insufficient support for the paper's architectural conclusions.","section":"§5.3, Table 2"},{"comment":"The definition of the fixed convolutional kernel in Eq. (23) is garbled by inserted non-ASCII text and does not specify the kernel values beyond the final 1.0. As this kernel is the central implementation of the parallel training mechanism, the manuscript as written is not reproducible at this load-bearing point. The text around Eqs. (23)-(27) should be cleaned and the kernel fully specified.","section":"§4.3.1, Eq. (23)"},{"comment":"Theorem 4.2 assumes the memory-module output x(t) is constant on the interval [0, r], and the theorem is then used to claim that 'it is entirely feasible to construct a sparse spiking neural network state-space model using regular discrete time steps.' For general inputs, which are not piecewise constant, the equivalence does not hold. The actual spikingPssm architecture uses a learnable convolutional kernel in Eq. (32) that approximates the desired aggregation rather than implementing this theorem exactly. The justification should be stated as a heuristic approximation, not as a feasibility proof.","section":"§4.3.2, Theorem 4.2"}],"minor_comments":[{"comment":"'an another alternative perspective' should be 'another alternative perspective', and the comma before 'viewing' is misplaced.","section":"Abstract"},{"comment":"'Persperctive' should be 'Perspective'.","section":"Figure 6 caption"},{"comment":"'LIF models with either hard or soft resists cannot be directly parallelized' should read 'hard or soft reset'.","section":"§4.2"},{"comment":"The statement that a rigorous definition of the distribution interpretation is unnecessary sits awkwardly with the load the paper places on that interpretation; a formal definition or a precise approximation statement would strengthen the paper.","section":"§4.1"},{"comment":"Several baseline parameter counts are reported as 'N/A'; if the values are unavailable, this should be stated in the text rather than implied.","section":"Table 2"}],"recommendation":"reject","confidential_remarks":"The central theoretical claim fails because Theorem 4.1 is not valid for the standard hard-reset LIF model, and the empirical support is a single dataset with no error bars. The proposed architecture itself might be salvageable as a minor empirical contribution if the universal theoretical claims are removed and the experiments are substantially strengthened, but the current manuscript does not support its main conclusions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague —\n\nRead this one for the architecture, not the theory. The paper is candid: it says spikingPssm is just an S4D backbone with a specialized PSN spiking module, and on Sequential CIFAR-10 it gets 85.5%. That is a reproducible data point for a simple, parallel-trainable spiking layer. The framing — spikes as sampling points, reset/refractory as irregular discretization — is the kind of mental model that can be useful even if not rigorous.\n\nBut the load-bearing theorem does not hold up. Theorem 4.1 claims to universally describe spike encoding in all SNNs with reset and refractory via the condition that no threshold crossing happened in the previous m(t) steps. Standard hard-reset LIF, Eq. (5), fires at consecutive timesteps under constant suprathreshold input, because the reset wipes the membrane potential before the next input arrives. So the theorem describes a threshold-and-blank encoder, not an integrate-and-fire neuron. The reset-as-special-discretization premise is not established, and the conclusion that reset and refractory do not contribute to historical memory is unsupported.\n\nThe secondary argument — that the refractory function's shape is invisible to the next layer because each spike carries the same value — assumes the next layer reads spikes statically. In a stacked SSM, the next layer's memory kernel integrates spike times, so suppressing the gray spikes is lossy, not merely a change of sampling.\n\nAlso, Eq. (23) is garbled with random characters, which is a serious presentation issue. Experiments are one dataset, no error bars, no ablation that isolates the fixed refractory/downsampling from the learnable convolution. The paper's own comparison shows it trails the best cited SSM-SNN by about 2 points.\n\nCredit where due: the paper is admirably honest about its own limits, and the appendices show real thinking about TTFS as declarative networks and the moment-based view of memory.\n\nMy take: the architecture is a reasonable simple baseline, and the interpretation is worth discussing in a reading group, but the theory should be downgraded or corrected. As a contribution it is minor; as a provocation it is fine. I would send it to review because the empirical result and the honest framing deserve referee attention, with expectations of heavy revision on the theory and experiments.","headline":"An honest SSM+PSN baseline with a fresh but unsupported theory; Theorem 4.1 fails on standard hard-reset LIF.","tokens_in":21034,"tokens_out":4943,"would_cite":false,"duration_ms":47504,"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":"The paper claims that reset and refractory mechanisms in spiking neural networks can be replaced by a fixed refractory period, because spikes only transmit information between layers and do not store history.","keywords":["Spiking Neural Networks","Sequential Modeling","State Space Models","Reset Mechanism","Refractory Period","Binary-Activated RNN","Parallel Training","Sparse Spiking"],"falsifier":"Take a fixed input sequence, generate two spike trains with identical spike times but different refractory functions, one fixed and one LIF-style, and feed both into a second layer whose synaptic integration is nonlinear in spike timing, such as a saturating or multiplicative synaptic model; if the two downstream outputs differ, the claim that the refractory function's shape is unobservable is false. A positive control would show identical outputs when the second layer is linear.","tokens_in":19872,"feed_emoji":"⚡","tokens_out":7518,"duration_ms":66577,"temperature":0.7,"pith_summary":"The paper argues that when spiking neural networks are used for sequence modeling, the memory and the spiking can be separated: a state-space module stores history, while spikes only transmit the stored information to the next layer. Reset and refractory mechanisms are therefore not essential to spiking; they are a special discretization that turns a continuous recurrent output into sparse sampling points. Because the next layer receives every spike as the same binary event, the paper claims the shape of the refractory function is unobservable, so a fixed refractory period with no reset is enough to keep spiking sparse. The paper builds two simple models on this idea and reports that the stronger one reaches 85.5% accuracy on Sequential CIFAR-10 while training in parallel. If the claim holds, complex nonlinear spiking dynamics are not needed for engineered sequence tasks.","feed_headline":"Fixed pause replaces reset in spiking sequence models","feed_subtitle":"Binary-activated RNN view of spikes enables parallel training and reaches 85.5% on Sequential CIFAR-10.","key_machinery":"The carrying object is the spike encoding function $S[f(t)]$ of Theorem 4.1, which expresses any reset-and-refractory spiking scheme as firing exactly when the memory output $f(t)$ crosses the threshold $\\theta$ and has stayed below it for the preceding $m(t)$ timesteps. The paper's move is to set $m(t)$ to a constant, removing reset and accumulation while keeping a fixed refractory period; because the next layer sums identical binary spikes linearly, the refractory function's shape cannot be perceived, so the fixed period is information-preserving. Theorem 4.2 supplies the parallel-training mechanism: if the memory output is constant over an interval of length $r$, the interval's effect equals one scaled input at the interval start, so a strided temporal convolution can merge the interval and satisfy the spike pattern with a single computation. The whole architecture is an SSM memory module followed by this fixed-refractory spiking module.","core_discovery":"The paper's central claim is that a sequence-modeling spiking neural network is a binary-activated recurrent network with two independent components: a linear memory module, equivalent to a state-space model, and a spiking module that only transmits the memory module's output between layers. It formalizes reset and refractory mechanisms as a time-varying spike-encoding function $S[f(t)]$ that fires when the memory output crosses the threshold and has not fired for the preceding $m(t)$ steps; this dependence on past spikes is what blocks training across timesteps. The paper then asserts that since every spike is perceived identically by the next layer, $m(t)$ can be fixed to a constant, giving a fixed refractory period with no reset and no accumulation; sparse spiking is preserved and training becomes a fixed convolution. A second theorem shows that when the memory output is constant over an interval, a single computation represents the whole interval. The resulting spikingPssm, an SSM memory followed by a specialized parallel spiking module, reaches 85.5% accuracy on Sequential CIFAR-10, which the paper presents as evidence that LIF/IF encoding with reset is not required.","pith_inferences":["If the refractory-shape claim is right, neuromorphic hardware could drop per-neuron reset state and refractory-timing logic, replacing it with a single global fixed-pause rule; a testable extension is benchmarking such hardware-level simplification against reset-based designs.","The distribution-sampling framing suggests a new evaluation: compare the spike train's ability to reconstruct the memory module's continuous output, for instance by a distance between the original and spike-sampled sequences; this would measure information loss more directly than classification accuracy.","The argument implies the decoupling should transfer to any memory module, including attention-based or linear-attention memories; a natural test is swapping the SSM memory for linear attention and checking whether the fixed-refractory spiking module still matches reset-LIF baselines.","Because the central equivalence depends on linear integration, nonlinear post-synaptic effects such as dendritic saturation or timing-dependent plasticity are where the claim would likely break; measuring those effects in a spiking network is a direct stress test."],"forward_implications":["Reset and refractory mechanisms can be replaced by a fixed refractory period without changing what a downstream layer perceives, provided spikes are binary and post-synaptic integration is linear.","Because the refractory period is fixed, spike suppression no longer depends on previous outputs, so training can run all timesteps in parallel through a fixed convolution.","SNN sequence models split cleanly into a memory module and a spiking module; any memory system usable in an ANN, such as state-space or linear attention, can be paired with the same spiking module.","Sparse spiking can be achieved by temporal output sharing: if the memory output is constant over an interval, compute once and reuse the pattern, which yields the same energy savings as suppressing spikes.","A simple SSM plus spiking module reaches 85.5% on Sequential CIFAR-10, so many complex nonlinear neuronal dynamics in current SNNs are not necessary for competitive sequence classification."],"supporting_citations":[{"why":"supplies the HiPPO theory that formalizes how sequences are compressed into memory via polynomial projections.","marker":"[5]"},{"why":"provides the S4 state-space model that the paper's memory module follows, including ZOH discretization.","marker":"[6]"},{"why":"supports the linear-recurrence view that long sequences can be modeled by linear dynamics followed by nonlinear projections.","marker":"[7]"},{"why":"is the stochastic spike-sampling approach the paper contrasts with its deterministic sampling-point interpretation.","marker":"[8]"},{"why":"supplies the parallel spiking neuron mechanism that spikingPssm attaches after its SSM memory module.","marker":"[9]"},{"why":"is the parallel integrate-and-fire multi-compartment baseline whose soft reset avoids backpropagation through time over timesteps.","marker":"[25]"},{"why":"is the reset-free binary-activation SNN baseline that showed long-sequence modeling without reset mechanisms.","marker":"[27]"},{"why":"is a parallel sparse spiking SSM that reintroduces reset mechanisms and serves as a stronger comparison.","marker":"[28]"},{"why":"is a parallel spiking SSM using learned firing functions, another stronger comparison for spikingPssm.","marker":"[29]"}],"fun_headline_variants":["Reset-free spiking sequences train in parallel","No reset, fixed refractory: parallel spiking sequence model","Binary RNN spikes: parallel training without reset","Fixed pause replaces reset, enabling parallel SNN training"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on the premise that every spike is received by the next layer as the same binary value added linearly, so the shape of the refractory period cannot matter; if precise spike timing or the refractory waveform itself carries information, a fixed refractory period loses that information.","fun_headline_variants_meta":{"raw":{"variants":["Reset-free spiking sequences train in parallel","No reset, fixed refractory: parallel spiking sequence model","Binary RNN spikes: parallel training without reset","Fixed pause replaces reset, enabling parallel SNN training"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000288,"raw_usage":{"total_tokens":1713,"prompt_tokens":990,"completion_tokens":723,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":606,"completion_tokens_details":{"reasoning_tokens":662}},"tokens_in":606,"tokens_out":723,"duration_ms":7157,"temperature":1.0,"reasoning_tokens":662,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:31:31.493768+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a fixed input sequence, generate two spike trains with identical spike times but different refractory functions, one fixed and one LIF-style, and feed both into a second layer whose synaptic integration is nonlinear in spike timing, such as a saturating or multiplicative synaptic model; if the two downstream outputs differ, the claim that the refractory function's shape is unobservable is false. A positive control would show identical outputs when the second layer is linear.","supporting_citations":[{"cited_title":"Parallel spiking neurons with high efficiency and ability to learn long-term dependencies","cited_arxiv_id":null,"evidence_quote":"supplies the parallel spiking neuron mechanism that spikingPssm attaches after its SSM memory module."}],"review_version":1}