{"id":"e56be9ad-f1c9-4f40-b385-0bbc7fc93af7","arxiv_id":"2411.16061","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A spike-driven Transformer trained with integer activations reaches 86.2% top-1 on ImageNet, the highest reported accuracy for a directly trained spiking network at this scale.","lead":"The authors train spiking neural networks with integer activations and then convert those integers to bursts of spikes for inference, reporting ImageNet top-1 accuracy up to 86.2 percent with a 173M parameter spike-driven Transformer. The work claims this closes most of the accuracy gap to conventional neural networks while keeping the low-power, event-driven advantage of spiking hardware.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Integer-to-spike equivalence is proven only for a single IF-SR neuron; the E-SDSA attention layer is nonlinear, so D-step spike inference does not obviously compute the same function as one-step integer training.","rationale":"The reader's weakest assumption is that the layer-wise equivalence does not compose in deep networks. I agree this is the central risk, but the sharper form is not merely depth: E-SDSA is nonlinear in spike counts. For linear layers, timing-invariance of IF-SR total spike count may allow the composition to go through, but the attention product necessarily contains cross-timestep terms that a per-timestep event-driven implementation cannot reproduce. Since the central SOTA-accuracy claim concerns the deployed spike-driven model, this needs direct verification. The paper has real strengths: the efficient architecture redesign, the Masked Image Modeling adaptation with spike sparse convolution, large-scale experiments, and promised code. The concern is not fabrication; it is that the training-to-inference mapping is asserted beyond the scope of Proposition 1. The correct posture remains conditional pending an end-to-end equivalence check, so the reader's verdict does not need to change.","tokens_in":28284,"tokens_out":8093,"duration_ms":84732,"concrete_test":"Using the released code and pretrained checkpoints, run the 10M and 173M models on ImageNet validation in two modes: (i) the one-step integer forward of Eq. (5), and (ii) the D-step spike-driven inference with IF-SR neurons and per-timestep E-SDSA. Compare top-1 accuracy and final logits. Additionally, isolate one E-SDSA block and compare sum_d Q[d] K[d]^T V[d] against (sum_d Q[d])(sum_d K[d])^T (sum_d V[d]) on the same inputs. If validation accuracy differs by more than 0.5% or the attention expressions differ materially, the claimed training-to-inference equivalence fails and the reported inference numbers must be presented separately from training objective results.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The weakest link is the claimed equivalence in Section 4.1. Proposition 1 proves S_D^l = sum_d \\hat S^l[d] for one IF-SR neuron only under the assumption that nonzero input arrives at d=1 and input is zero for d=2,...,D (Eq. 16). In a deep network this premise fails at every layer after the first: layer l+1 receives spikes from layer l across all D timesteps. For purely linear/conv layers the issue might be salvageable, because an IF-SR neuron's total spike count over D steps is floor(total input) and is timing-invariant. But E-SpikeFormer contains E-SDSA (Section 3.3), a quadratic operation: U' = Linear_{1/gamma}(SN(Q_S K_S^T V_S * scale)). Integer training computes (sum_d Q[d]) (sum_d K[d])^T (sum_d V[d]) at one timestep, while per-timestep spike-driven inference accumulates sum_d Q[d] K[d]^T V[d]. These are not equal: the cross-timestep products with d != e are present in the trained objective but absent in the event-driven computation (or vice versa). No argument in the paper shows that these cross terms vanish or are negligible for D=4 or D=8. The same unaddressed issue affects bias terms, BatchNorm folding, and residual connections across expanded timesteps. Therefore, the reported '1 x 4' and '1 x 8' inference accuracies are not derivable from the trained integer model unless full-network equivalence is verified end-to-end.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Spike Firing Approximation (SFA), a training method that replaces binary spike activations with integer-valued activations (Fire_D) during training and converts them to spike trains during inference via IF-SR neurons with threshold 1. The authors also introduce an efficient spike-driven Transformer architecture (E-SpikeFormer) and a masked image modeling pre-training strategy with spike sparse convolution. They report state-of-the-art top-1 accuracies on ImageNet-1k at scales from 10M to 173M parameters (78.5% to 86.2%), with large improvements in training time and inference energy over prior SNNs, and validate the method on object detection, semantic segmentation, and neuromorphic action recognition. The central theoretical claim is that one-timestep integer training is losslessly equivalent to multi-timestep spike-driven inference via Proposition 1.","tokens_in":1653,"tokens_out":1927,"duration_ms":111702,"significance":"If the claimed training-inference equivalence and the reported results hold, this work would be a significant step toward scaling SNNs to practical vision backbones while retaining the low-power advantages of event-driven computation. The paper's strengths include extensive experiments across multiple tasks and model scales, concrete efficiency gains (e.g., 4.5x training acceleration, 3.9x inference energy improvement at the 10M scale), and a stated public code release. The analysis of spike firing patterns (asynchronous versus synchronous) and the discussion of neuromorphic chip implementation are also valuable. However, the central equivalence proof is limited to a single neuron under an unrealistic assumption, and the extension to whole deep networks, especially the nonlinear attention module, is not established. This gap undermines the claim that the reported inference accuracies follow from the training objective, so the theoretical foundation needs substantial strengthening before the results can be fully credited.","major_comments":[{"comment":"The proof of the integer-to-spike equivalence assumes that for each neuron 'the input is zero at timesteps d = 2, ..., D' (after Eq. (16)). In a deep network this premise is violated for every layer after the first: each layer receives spikes from the previous layer across all D timesteps. The paper asserts, rather than proves, that one-timestep integer training equals D-timestep spike-driven inference for the whole network. For purely linear layers with nonnegative inputs the total spike count of an IF-SR neuron may be timing-invariant, but negative weights (which can occur) break this, and the E-SDSA module (Section 3.3) is quadratic: integer training computes a function of (sum_d Q[d], sum_d K[d], sum_d V[d]), while spike-driven inference accumulates sum_d (Q[d] K[d]^T V[d]); the cross-timestep products with d != e are not present in the inference computation, and the paper provides no argument that they vanish or are negligible. Please provide an end-to-end equivalence proof for linear layers with arbitrary weights and for the attention module, or, failing that, an experimental comparison of the one-step integer-trained model's accuracy versus the implemented D-step spike-driven inference accuracy for each model scale in Table 1.","section":"Section 4.1, Proposition 1 and Fig. 6"},{"comment":"The gradient-error derivation is dimensionally inconsistent. Eq. (27) defines Err^l as the integral over U of (Rect[0,D](U) - (1/D) round(clip(U,0,D))); the result of this integral is a constant (or divergent), but Eq. (28) reports a piecewise function of U, which is the integrand, not the integral. Consequently, the formal conclusion that larger D reduces the gradient error is not supported by the equations as written. Please correct the derivation or clarify what quantity is actually being computed; the empirical trend in the experiments may still hold, but the theoretical analysis needs repair.","section":"Section 4.2, Eqs. (26)-(28)"},{"comment":"The step from Eq. (19) to Eq. (20), where the 0.5 bias introduced by the round function is said to be 'incorporated into the weight,' is not formalized for a deep network. If every neuron's activation function is changed from round(clip(U,0,D)) to floor(clip(U,0,D)) by adding a constant 0.5 to the neuron's input, the network function changes unless the biases of the preceding layers are adjusted consistently. For the equivalence to be claimed, either the reparameterization must be specified explicitly for all layers, or the Fire_D function should be defined with floor from the outset.","section":"Section 4.1, Eqs. (18)-(20)"}],"minor_comments":[{"comment":"The notation in Eq. (16) appears to use {S^l[d]}_D for the spike train generated by IF-SR, but the output of IF-SR is the spike train {hat S^l[d]}_D; please correct the notation for consistency.","section":"Section 4.1, Eq. (16)"},{"comment":"The label 'al D = 0.3' in Fig. 3 seems to be a typo; it should likely read 'a^l_D = 0.3'.","section":"Fig. 3"},{"comment":"The row 'Spike-dirven Transformer' contains a typo; it should be 'Spike-driven Transformer'.","section":"Table 1"},{"comment":"The phrase 'K d=32' appears to be a formatting error; please clarify whether this is intended to denote the kernel size K^d = 32.","section":"Section 3.4"},{"comment":"Definitions 1 and 2 both use the symbol Err^l for different quantities (forward approximation error and backward gradient error); please use distinct symbols such as Err_fwd and Err_bwd to avoid ambiguity.","section":"Section 4.2"},{"comment":"Reference [24] is a closely related prior work on integer-valued training and spike-driven inference by the same group; the paper cites it but does not discuss its relationship to the proposed SFA method. Please clarify the differences and the specific novelties introduced here.","section":"References, [24]"}],"recommendation":"major_revision","confidential_remarks":"The main risk is the unproven end-to-end equivalence between integer training and spike-driven inference, especially for the E-SDSA attention module. I would ask the authors to provide either a rigorous proof for nonlinear layers or a direct empirical verification (integer-model accuracy vs. spike-inference accuracy at each scale). The gradient-error derivation also needs correction. The reported accuracies are impressive, but the theoretical gap is central to the paper's claim that the deployed spike model is what was trained. Also, the relationship to reference [24] should be clarified to avoid novelty ambiguity."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper reports the best directly trained SNN accuracies I've seen at scale (78.5% to 86.2% ImageNet at 10M to 173M params), and the architecture work is real. But the core equivalence between one-timestep integer training and D-timestep spike inference is proven only for a single IF-SR neuron under a very restrictive assumption. The paper then asserts that this holds for whole networks, including the quadratic spike-driven attention. That gap is the main thing to know.\n\nWhat's genuinely good: the E-SpikeFormer design (replacing RepConv with linear layers, adding SpikeSepConv, channel expansion in V) is a careful efficiency study, and the MIM-SNN pretraining with spike sparse convolution addresses a real information leakage problem. The training-time reduction from one-timestep training for static tasks is practical. The ablations and the spike firing rate/effective rank analyses are useful. If the reported numbers are correct—and I have no reason to doubt them beyond the usual—this is a milestone for the SNN scaling literature.\n\nWhere it gets soft: the equivalence proof in Section 4.1 assumes nonzero input only at d=1 and zero at d=2..D. In a deep network, every layer receives spikes across all D steps. For linear operations, total spike count is timing-invariant and the equivalence might be salvageable. But E-SDSA is quadratic: integer training computes attention on summed Q,K,V, while spike-driven inference accumulates per-timestep attention outputs. The cross-timestep products d≠e are simply not accounted for. No argument in the paper shows these terms vanish or are negligible. So the reported 1x4 and 1x8 inference accuracies are not derivative from the trained integer model without an additional empirical check. This is the paper's load-bearing weakness, and it needs to be addressed either by a proof for the actual network or by direct verification that the deployed spike model's outputs match the integer model (e.g., comparing logits or feature maps on a subset).\n\nTwo smaller things: the SFA idea appears to overlap with the group's earlier arXiv:2407.20708, which is in the references but not cited in the body—the novelty boundary should be clearer. And the energy numbers are model-based estimates, which is standard for this community but worth stating plainly as estimates rather than chip measurements.\n\nBottom line: this deserves a serious referee. It's not a desk reject—the empirical scaling results and architecture contributions are too important. I'd send it out with a request for a full-network equivalence check (or a convincing proof) and clearer disclosure. Conditional accept in my view, not a reject.","headline":"Big empirical gains for scaled SNNs, but the integer-to-spike equivalence is proven only for a single neuron and is not shown to compose through the attention layers.","tokens_in":29185,"tokens_out":5009,"would_cite":true,"duration_ms":48469,"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":"Training spiking networks with integers instead of binary spikes lets them match ANN accuracy at 86.2% top-1 on ImageNet.","keywords":["Spiking neural network","Spike-driven","Spiking Transformer","Neuromorphic computing","Efficient architecture and training","Spike Firing Approximation","Masked image modeling"],"falsifier":"Take a trained E-SpikeFormer and run the same ImageNet image through both the one-timestep integer forward pass used in training and the $D$-timestep spike deployment; if the equivalence composes, the two forward passes must give identical activations and the same prediction, and any systematic mismatch would show that the reported spike-deployed accuracy is not what the training objective optimized.","tokens_in":27933,"feed_emoji":"⚡","tokens_out":9435,"duration_ms":85782,"temperature":0.7,"pith_summary":"This paper tries to close the accuracy gap between spiking neural networks (SNNs) and ordinary artificial neural networks (ANNs) without giving up the event-driven, addition-only inference that makes SNNs low-power. It identifies binary spike firing as the root flaw, and replaces it during training with integer-valued activations: a neuron outputs an integer in $[0,D]$ rather than a single bit, and at inference that integer is re-expanded into a train of $D$ spikes. On ImageNet-1k the resulting E-SpikeFormer family reaches 78.5%, 79.8%, 84.0%, and 86.2% top-1 accuracy at 10M, 19M, 83M, and 173M parameters, which the paper reports as the best results for directly trained spiking networks at these scales and comparable to classic ANN vision Transformer backbones. Training for static tasks is reduced to one timestep, giving about 4.5x faster ImageNet training and 3.9x lower inference energy at the 10M scale, and a spike-masked autoencoder with spike sparse convolution is added to keep accuracy from degrading as models scale. If the claim holds, SNNs become a practical low-power visual backbone rather than a research curiosity.","feed_headline":"Integer spike training scales spiking Transformers to 86.2% ImageNet","feed_subtitle":"Switching from binary spikes to integer training closes the SNN accuracy gap while keeping event-driven, low-power inference.","key_machinery":"The load-bearing object is the integer fire function $\\operatorname{Fire}_D(U)=\\lfloor\\operatorname{clip}(U,0,D)\\rceil$ together with the identity in Proposition 1: feeding the membrane potential $U$ to an integrate-and-fire neuron with soft reset and threshold 1, with nonzero input only at the first of $D$ timesteps, produces a spike train whose sum equals $\\operatorname{Fire}_D(U)$. This is what lets the network be trained as a one-timestep integer network and then expanded into $D$ timesteps of spike-driven inference, so the energy advantage comes from sparse additions triggered only when spikes arrive. The second mechanism is the changed firing pattern it induces: SFA firing is asynchronous and concentrated at early timesteps, whereas ANN-to-SNN conversion and vanilla direct training fire randomly and need all timesteps to compute a rate. Supporting machinery includes the E-SpikeFormer block, built from SpikeSepConv and efficient spike-driven self-attention with a widened value branch, and the Spike Sparse Convolution used in masked autoencoding, which restricts convolution to unmasked positions to prevent information leakage.","core_discovery":"The central claim is that binary firing is not just a quantization nuisance but a mechanistic defect in spiking neurons, harming both spatial representation (a spike cannot encode how strong the input was) and temporal dynamics (reset can only forget a fixed amount). The proposed cure, Spike Firing Approximation (SFA), trains with the integer fire function $\\operatorname{Fire}_D(U)=\\lfloor\\operatorname{clip}(U,0,D)\\rceil$ and deploys at inference by replacing each integer with $D$ binary spikes from an integrate-and-fire neuron with soft reset and threshold 1. Proposition 1 gives the per-neuron identity $S^l_D=\\sum_{d=1}^{D}\\hat{S}^l[d]$, and the paper argues that this makes a one-timestep integer forward pass equivalent to a $D$-timestep spike-driven forward pass for the network. On top of this the paper builds E-SpikeFormer, an efficient spike-driven Transformer that removes energy-hungry reparameterized convolutions, and a masked-image-modeling pretraining scheme with Spike Sparse Convolution that prevents the feature collapse, measured by effective rank, that scaling induces in binary-spike networks. The result, as the paper states, is that directly trained SNNs reach ANN-level accuracy while preserving the low-power, sparse-addition inference path.","pith_inferences":["Extension: Because $\\operatorname{Fire}_D$ is uniform $D$-level quantization, SFA suggests a broader recipe: any ANN trained with $D$-level integer activations and threshold-normalized weights could be deployed as a spike-driven network, putting spike-driven efficiency within reach of standard quantization-aware training.","Extension: The paper's firing-pattern analysis implies $D$ can be treated as a tunable accuracy-latency dial, so an adaptive version that spends fewer timesteps on easy inputs or early layers could extend the reported $1\\times4$ versus $1\\times8$ trade-off beyond the fixed settings tested.","Extension: The effective-rank view of why binary networks fail to scale points to a practical diagnostic: monitor the encoder's effective rank during masked pretraining as an early indicator of downstream fine-tuning quality, potentially guiding architecture or mask-ratio choices without full fine-tuning."],"forward_implications":["Directly trained spiking networks can now reach 86.2% top-1 on ImageNet at 173M parameters, a higher accuracy than prior directly trained SNNs at this scale and comparable to several classical ANN backbones.","Static-image training collapses to one timestep, cutting ImageNet training time by about 4.5x at the 10M scale while inference still runs as a single image presentation followed by $D$ spike steps.","Inference power drops: the 10M E-SpikeFormer uses 3.0 mJ versus 11.9 mJ for the Meta-SpikeFormer baseline, and the spike firing rate decreases as timesteps advance, making later computation sparser.","SFA-trained models fit asynchronous neuromorphic chips, because the $D$ spikes can be emitted in a short window without a global clock, unlike vanilla multi-timestep direct training.","Combining SFA with masked-image-modeling pretraining and Spike Sparse Convolution avoids the performance degradation that still occurs when binary-spike networks are scaled with the same MIM strategy."],"supporting_citations":[{"why":"Defines the integrate-and-fire neuron dynamics that SFA's inference neuron instantiates.","marker":"[3]"},{"why":"Establishes spatio-temporal backpropagation and surrogate gradients, the direct-training paradigm SFA replaces with one-step integer training.","marker":"[16]"},{"why":"Provides the Meta-SpikeFormer baseline architecture and pretrain-finetune setup that E-SpikeFormer upgrades and ablates against.","marker":"[28]"},{"why":"Introduces spike-driven self-attention, the operator family E-SpikeFormer's efficient self-attention builds on.","marker":"[29]"},{"why":"Supplies masked autoencoding as the pretraining framework for scaling visual backbones.","marker":"[30]"},{"why":"Shows why masked image modeling fails on plain CNNs and introduces sparse convolution encoding, which the proposed Spike Sparse Convolution adapts to SNNs.","marker":"[31]"},{"why":"Documents the asynchronous sensing-computing neuromorphic chip used to argue SFA is compatible with asynchronous spike-driven deployment.","marker":"[10]"},{"why":"Provides ImageNet-1k, the benchmark for the paper's principal accuracy and scaling results.","marker":"[32]"}],"fun_headline_variants":["Integer firing closes SNN-ANN gap, scales to 86.2% ImageNet","Spike firing approximation trains spiking Transformers 4.5x faster","Scaling spiking Transformers with integer training beats binary spikes","Efficient spike-driven Transformer hits 86.2% ImageNet with low power","SFA method: integer training, spike-driven inference for SNN scaling"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that what holds for one neuron whose input arrives in a single moment also holds for a whole network whose layers receive spikes spread over many moments, but the proof only covers the single-neuron, single-moment case.","fun_headline_variants_meta":{"raw":{"variants":["Integer firing closes SNN-ANN gap, scales to 86.2% ImageNet","Spike firing approximation trains spiking Transformers 4.5x faster","Scaling spiking Transformers with integer training beats binary spikes","Efficient spike-driven Transformer hits 86.2% ImageNet with low power","SFA method: integer training, spike-driven inference for SNN scaling"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000443,"raw_usage":{"total_tokens":2338,"prompt_tokens":1135,"completion_tokens":1203,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":751,"completion_tokens_details":{"reasoning_tokens":1102}},"tokens_in":751,"tokens_out":1203,"duration_ms":8993,"temperature":1.0,"reasoning_tokens":1102,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T13:36:03.525157+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a trained E-SpikeFormer and run the same ImageNet image through both the one-timestep integer forward pass used in training and the $D$-timestep spike deployment; if the equivalence composes, the two forward passes must give identical activations and the same prediction, and any systematic mismatch would show that the reported spike-deployed accuracy is not what the training objective optimized.","supporting_citations":[{"cited_title":"Spike-driven transformer v2: Meta spiking neural network ar- chitecture inspiring the design of next-generation neuromorphic chips,","cited_arxiv_id":null,"evidence_quote":"Provides the Meta-SpikeFormer baseline architecture and pretrain-finetune setup that E-SpikeFormer upgrades and ablates against."},{"cited_title":"Spike- driven transformer,","cited_arxiv_id":null,"evidence_quote":"Introduces spike-driven self-attention, the operator family E-SpikeFormer's efficient self-attention builds on."},{"cited_title":"Designing bert for convolutional networks: Sparse and hierarchical masked FOR REVIEW 16 modeling,","cited_arxiv_id":null,"evidence_quote":"Shows why masked image modeling fails on plain CNNs and introduces sparse convolution encoding, which the proposed Spike Sparse Convolution adapts to SNNs."},{"cited_title":"Imagenet: A large-scale hierarchical image database,","cited_arxiv_id":null,"evidence_quote":"Provides ImageNet-1k, the benchmark for the paper's principal accuracy and scaling results."}],"review_version":1}