{"id":"f75e2b0f-5b8c-4123-975a-ecf15477946d","arxiv_id":"2506.21324","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A stochastic quantum spiking neuron with internal quantum memory and a local perturbation-based learning rule improves classification accuracy over prior quantum spiking networks without global backpropagation.","lead":"This paper introduces a stochastic quantum spiking neuron that uses multi-qubit circuits with memory qubits to generate output spikes in a single measurement shot, and trains networks of these neurons with a local, perturbation-based learning rule.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline accuracy comparisons on MNIST, FMNIST, KMNIST, MNIST-DVS, and N-ISAC are produced with a classical surrogate-gradient simulator, not the proposed hardware-compatible local learning rule; without a direct equivalence check, those comparisons do not validate the paper's main algorithmic…","rationale":"The reader's weakest assumption identifies exactly the load-bearing concern: the large-scale accuracy comparisons are run with a classical surrogate-gradient simulator rather than with the proposed local zero-th order learning rule. My independent reading of Sections V-D and Appendix A confirms that the surrogate is not a minor implementation detail. The local rule in Algorithm 1 estimates gradients via local SPSA perturbations of synaptic weights and parameter-shift perturbations of PQC angles, using global scalar feedback signals; the surrogate instead computes a deterministic sigmoid-smoothed loss and propagates gradients globally with backpropagation. These are different optimization procedures, and the only evidence connecting them is the small USPS experiment in Fig. 7(b), which lacks error bars and covers a regime far from the large-network experiments. The paper is honest about this substitution, and the modeling contribution of the SQS neuron is clearly presented, but the headline accuracy claims for SQSNN on the larger datasets are conditional on an unproven surrogate/local equivalence. The correct response is therefore to require a direct validation of that equivalence, or to re-frame the large-scale results as applying to the surrogate-trained model. This does not change the reader's conditional verdict: the concern is real, addressable, and should be resolved before the central claim is accepted as established.","tokens_in":22363,"tokens_out":4186,"duration_ms":51929,"concrete_test":"Train the SQSNN on the USPS task and on a scaled version of MNIST or FMNIST using Algorithm 1 with exact classical evaluation of the probabilities in Eq. (15) (i.e., the noise-free ideal local rule), and compare final test accuracy and convergence against the surrogate-gradient training of Appendix A under identical architecture, initialization, and hyperparameters. If the ideal local rule matches the surrogate within a small margin (e.g., 2 percentage points) on the larger task, the equivalence assumption is supported; if not, the Figs. 8-11 superiority claims cannot be attributed to the proposed hardware-compatible training rule, and the surrogate-trained network should be reported as a separate model.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that an SQSNN trained with the proposed local zero-th order rule outperforms QLIF-SNN and classical SNN baselines at matched parameter counts—depends on an unvalidated equivalence between two training procedures. Section V-D states that after the small USPS hardware study, 'we henceforth employ classical simulations using a surrogate gradient-based approach to approximate the learning dynamics of the proposed rule.' The surrogate described in Appendix A does not implement Algorithm 1: Eq. (37) replaces the likelihood-bound objective of Eq. (26) with a cross-entropy loss over smoothed spike rates, Eq. (39) replaces stochastic spikes with sigmoid activations in the backward pass, and training uses global backpropagation rather than the local SPSA and parameter-shift estimates of Eqs. (34)-(35). Fig. 7(b) shows that the surrogate tracks the ideal local rule on the binary USPS task with two output neurons and T=10, but that single small task does not establish equivalence for 1000-hidden-neuron networks, rate-coded T=5 image tasks, or T=20 neuromorphic event streams. The likelihood bound in Eq. (25) is an upper bound whose tightness is never quantified, and Eq. (37) is a further, unanalyzed replacement of that bound. Consequently, Figs. 8-11 demonstrate the performance of a classically trained surrogate SQSNN, not of the local hardware-compatible rule that is the paper's main contribution; the observed improvement over baselines could reflect the surrogate's training objective rather than quantum memory or local learning.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a stochastic quantum spiking neuron (SQS) with multiple input-output qubits and unmeasured memory qubits, yielding an autoregressive spiking model with single-shot, event-driven spike generation. The authors derive a local zero-th order learning rule from an upper bound on the negative log-likelihood, using SPSA for synaptic weights and parameter-shift rules for PQC angles, with global scalar feedback to hidden neurons. They report a hardware demonstration on IBM Brisbane for binary USPS classification, and then use a classical surrogate-gradient simulator (Appendix A) to evaluate the model on MNIST, FMNIST, KMNIST, MNIST-DVS, and a neuromorphic integrated sensing and communications task, claiming that SQSNN outperforms QLIF-SNN, a classical SNN, and a QNN baseline at matched parameter counts.","tokens_in":22619,"tokens_out":7716,"duration_ms":85882,"significance":"The SQS neuron architecture and the local learning rule are novel, and the derivation of the local rule from a maximum-likelihood objective is principled. If the surrogate-to-local transfer were established, this would be a meaningful step toward trainable quantum neuromorphic systems with quantum memory, single-shot readout, and local training. The paper is commendably explicit about using a surrogate for the large-scale experiments and about the exact hardware configuration used. However, the current evidence does not yet establish the central claim, because the headline accuracy comparisons come from a different training algorithm than the proposed local rule.","major_comments":[{"comment":"The headline accuracy results on MNIST, FMNIST, KMNIST, MNIST-DVS, and N-ISAC are obtained with the surrogate-gradient classical simulator described in Appendix A, not with the proposed local zero-th order learning rule (Algorithm 1). The paper states this directly: 'we henceforth employ classical simulations using a surrogate gradient-based approach to approximate the learning dynamics of the proposed rule.' The surrogate differs from Algorithm 1 in the objective (Eq. (37) replaces the likelihood-bound objective of Eq. (26) with a cross-entropy loss over spike rates), in the backward pass (Eq. (39) replaces stochastic spike sampling with a sigmoid surrogate), and in the use of global backpropagation instead of the local SPSA/PSR estimates of Eqs. (34)-(35). The only evidence that the surrogate tracks the local rule is Fig. 7(b), which uses a binary USPS task with two output neurons and no hidden layer. That small-scale comparison does not establish equivalence for the 1000-hidden-neuron rate-coded tasks or for the T=20 neuromorphic event-stream task. Consequently, Figs. 8-11 demonstrate the performance of a classically trained surrogate model, and the paper's central claim that the proposed hardware-compatible local rule yields state-of-the-art accuracy is not established.","section":"V-D, Appendix A, Figs. 8-11"},{"comment":"The hardware demonstration on IBM Brisbane only exercises a network with a single output layer of two neurons (Section V-C states 'For the USPS dataset, we use fully connected models with a single, output, layer of two neurons'). This means the hidden-neuron part of the local rule—the REINFORCE-style gradient in Eq. (33), the global feedback signals ℓ(m), and the local hidden-neuron updates—is never tested on quantum hardware. The hardware experiment therefore validates only output-neuron SPSA and parameter-shift estimates, not the 'local learning' mechanism that is the paper's main algorithmic contribution. To support the claim that SQSNNs can be trained on hardware with hidden layers, an experiment or a realistic noise-model simulation with at least one hidden SQS neuron is needed.","section":"V-D and V-C, Fig. 7"},{"comment":"The local rule minimizes an upper bound on the negative log-likelihood obtained by Jensen's inequality in Eq. (25). The tightness of this bound is never quantified, and the surrogate in Appendix A replaces the bound with yet another objective (cross-entropy on smoothed spike rates). The paper does not analyze whether the bound gap or the surrogate replacement changes the ordering of models or the qualitative conclusions. This compounds the transfer problem in the first comment: even a perfect match between the surrogate and the ideal local rule would not automatically validate the original likelihood-based objective as the quantity being optimized. At minimum, the authors should report bound tightness on a small task and justify why optimizing the bound is expected to yield the same model ranking as optimizing the true likelihood.","section":"IV-D and Eq. (25), Appendix A Eq. (37)"},{"comment":"The parameter-shift estimator in Eq. (35) is not fully specified for hardware implementation. It divides by Tr(ρI_{i,t} S_{i,t}) without saying how this denominator is estimated from local measurements; if it is estimated from the same finite shot counts as the numerator, the estimator is biased and can be undefined when the estimated probability is zero. Similarly, the SPSA gradient in Eq. (34) applies logarithms to estimated probabilities, which are problematic for zero-count estimates with few shots. These details are relevant to the claim that the rule is 'hardware-friendly', and they should be addressed by specifying shot allocations or regularized estimators.","section":"IV-F, Eq. (35)"}],"minor_comments":[{"comment":"The pseudocode in Algorithm 1 lists the local gradient estimation inside a loop over t, but Eqs. (30) and (33) sum over t after collecting M global trajectories; the ordering should be clarified to avoid the impression that gradients are computed sequentially in time before feedback is available.","section":"Algorithm 1"},{"comment":"In Eq. (37), the spike rate r_i is defined as a full-sequence average, while the loss sums over time steps with per-step targets o^n_{i,t}; please clarify whether the target is constant across t (as in rate encoding) or whether a time-dependent rate should be used.","section":"Appendix A, Eq. (37)"},{"comment":"The box plots in Figs. 8 and 9 do not state the number of independent runs or seeds; please report these, and indicate whether the 'consistently highest' accuracy claims are supported by non-overlapping intervals or a statistical test.","section":"V-E and V-F, Figs. 8-9"},{"comment":"The average spike count per time step is an aggregate over the whole network, but the models have different neuron counts (e.g., 1000 hidden SQS neurons vs adjusted SNN/QLIF neuron counts). The comparison would be easier to interpret if per-neuron spike rates were reported alongside the aggregate counts.","section":"V-E, Fig. 8(b)"},{"comment":"There are minor typos, e.g., 'pertubation-based' in the conclusions, and inconsistent capitalization such as 'ibm brisbane'.","section":"VI"}],"recommendation":"major_revision","confidential_remarks":"The paper's core derivation is sound, and the research direction is promising. The main risk is overclaiming: the abstract and conclusions present the surrogate-gradient results as evidence for the proposed local hardware-compatible rule, even though the paper itself clearly discloses the substitution. In revision, the authors should either provide transfer experiments (surrogate vs local rule on a task with hidden neurons, or a noise-model simulation of Algorithm 1 on a larger network) or substantially soften the claims in the abstract and conclusions. The paper's fit to the journal is good if the transfer issue is addressed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's my take on arXiv:2506.21324. The genuinely new piece is the SQS neuron: a multi-qubit QRNN-style unit with unmeasured memory qubits and single-shot Born-rule spike generation. That removes the multi-shot measurement overhead of QLIF and is a real architectural step. The local learning rule is also new: it uses M global forward passes independent of parameter count, then local SPSA/parameter-shift estimates per neuron. The derivation from a Jensen bound on the log-likelihood is standard and coherent. The small hardware experiment on ibm_brisbane with QEM, reaching ~98% on binary USPS and matching the ideal local rule, is genuinely useful evidence that the rule can run on current NISQ devices.\n\nThe soft spot is exactly what the reader's report flags. After the USPS study, the paper switches to a surrogate-gradient classical simulator for all large-scale benchmarks. Equation (39) replaces stochastic spikes with sigmoid probabilities in the backward pass, and training uses global backprop, not Algorithm 1. The paper says this plainly; there is no deception. But the only evidence that the surrogate tracks the local rule is Fig. 7(b) on a two-output-neuron, T=10 task. That is a thin bridge to the 1000-hidden-neuron, T=5 and T=20 results in Figs. 8-11. The bound in Eq. (25) is an upper bound whose tightness is never quantified, and Eq. (37) is a further heuristic replacement of that bound. So the headline comparisons demonstrate the performance of a classically trained surrogate SQSNN, not of the proposed local rule.\n\nTwo smaller issues: the hardware curves in Fig. 7 lack error bars or seed counts, and the paper reports box plots without explicit numbers for Figs. 8-10. Both are easy to fix.\n\nFor whom is this paper? Researchers in quantum neuromorphic computing. The neuron model and local rule are worth knowing about and citing. Whether the performance claims hold up depends on a direct surrogate-vs-local equivalence check on at least a medium-scale task, or a larger hardware demo. I would send it to peer review with a request for that validation; it is not a desk reject. The ideas are clear, the authors are honest about the substitution, and the core derivation is sound.","headline":"Solid new neuron model and local learning rule, but the headline accuracy claims are produced by a surrogate classical simulator, not the hardware-compatible rule, so the paper needs a direct equivalence check before the main claim is credible.","tokens_in":23262,"tokens_out":2388,"would_cite":true,"duration_ms":23263,"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":"This paper claims that spiking neurons built on multi-qubit circuits with unmeasured memory qubits, trained by a local single-shot rule, beat classical and prior quantum spiking networks at matched parameter counts on standard and…","keywords":["quantum neuromorphic computing","spiking neural networks","stochastic quantum spiking neuron","quantum memory","local learning rules","zero-th order gradient estimation","single-shot measurement","event-driven computation"],"falsifier":"Compare the proposed local zero-th order rule — not the surrogate-gradient substitute — against the surrogate on the same SQSNN architecture for at least one of MNIST, FMNIST, or KMNIST at the paper's matched parameter counts, either on a noiseless classical simulation or on quantum hardware. If final test accuracy (or the distribution of output spike trains on held-out inputs) diverges by more than a few points, the claim that the local rule achieves the reported benchmark performance fails; a cheaper first screen is to compare the spike-train statistics produced by both rules on identical held-out inputs.","tokens_in":22053,"feed_emoji":"⚛️","tokens_out":14191,"duration_ms":143582,"temperature":0.7,"pith_summary":"This paper sets out to remove the two bottlenecks of existing quantum spiking neurons: classical memory on a single qubit, whose firing probability must be re-estimated through repeated measurements, and training by classical backpropagation. Its stochastic quantum spiking (SQS) neuron runs instead on $N$ input-output qubits plus $N_{\\mathrm{mem}}$ memory qubits, leaves the memory qubits unmeasured so quantum information persists across time steps, and emits spikes from a single measurement of the input-output qubits. The authors build networks of such neurons and derive a local learning rule that needs only a constant number $M$ of global forward passes, after which each neuron estimates its own gradient from local perturbations and a scalar feedback signal. They report about 98% test accuracy on USPS with this rule on current noisy quantum hardware under error mitigation, and report that SQSNNs consistently beat a classical spiking network, a variational quantum classifier, and the prior QLIF spiking network on MNIST, FMNIST, KMNIST, and the neuromorphic MNIST-DVS dataset at matched trainable parameters. If these results hold, quantum spiking networks become trainable directly on device for event-driven tasks rather than only on classical simulators.","feed_headline":"Quantum-memory spiking neurons outlearn classical SNNs","feed_subtitle":"Single-shot spikes and local updates let quantum spiking networks train on-device, hitting ~98% on USPS","key_machinery":"The load-bearing object is the SQS neuron: $N$ input-output qubits plus $N_{\\mathrm{mem}}$ memory qubits that jointly evolve through a trainable unitary each time step, after which only the input-output qubits are measured and the memory qubits' post-measurement state $\\sigma^{\\mathrm{mem}}_t$ is carried to the next step — effectively a dynamic parameterized quantum circuit with state space dimension $2^{N+N_{\\mathrm{mem}}}$ replacing the single-qubit membrane potential of the QLIF neuron. The second piece of machinery is the local zero-th order learning rule: $M$ global forward passes supply hidden spike samples and scalar feedback losses $\\ell_t(m)$; each neuron then estimates its own gradient locally, applying simultaneous perturbation stochastic approximation (SPSA) with Rademacher perturbations to its synaptic weights and the parameter-shift rule to its circuit angles. This moves the learning cost from one global forward pass per parameter to a constant $M$ global passes plus $2TM_p|S|(M_{\\mathrm{som}}G+M_{\\mathrm{syn}})$ local passes per iteration.","core_discovery":"The central claim is that a spiking neuron whose internal state lives on a multi-qubit Hilbert space, with a subset of qubits deliberately left unmeasured to carry quantum memory forward in time, is a strictly richer computational unit than the single-qubit QLIF neuron — and that networks of such neurons can be trained without global classical backpropagation. At each time step the SQS neuron encodes weighted presynaptic spikes as rotation angles $\\varphi_t^n$, applies a trainable unitary $U(z_t,\\theta)=V(\\theta)(\\bigotimes_n R_X(\\varphi_t^n)\\otimes I)$ to the whole register, and measures only the input-output qubits; the post-measurement state of the memory qubits becomes the input state of the next step. Because the joint spiking probability of the network factorizes over time and over neurons, the negative log-likelihood is bounded above by a Monte-Carlo-estimable objective, from which the authors derive a local zero-th order learning rule: hidden-neuron spike samples and scalar losses come from $M$ global forward passes, and each neuron then estimates its own gradient using simultaneous perturbation for synaptic weights and the parameter-shift rule for circuit angles. The experiments show the local rule matching an idealized exact rule (about 98% on USPS with error mitigation), and, switching to the classical surrogate-gradient simulator the paper introduces for larger tasks, the SQSNN is reported to achieve the highest accuracy among SNN, QNN, QLIF-SNN, and SQSNN on MNIST, FMNIST, and KMNIST, and to outperform both spiking baselines on MNIST-DVS at matched parameter counts while spiking less than the classical SNN.","pith_inferences":["The surrogate-to-local validation shown in Fig. 7(b) is limited to the small USPS task; matching the surrogate-trained SQSNN against the same architecture trained by the local rule on at least one large benchmark would settle whether the accuracy gap over baselines is a property of the learning rule or only of the architecture.","If the surrogate assumption holds, the reported gains stem from the multi-qubit quantum memory itself: the natural control is the same SQSNN architecture trained with both rules from identical initializations, which would isolate the contribution of the training algorithm.","The noisier-but-better operating point ($M=1$, $M_{\\mathrm{syn}}=5$, no error mitigation) suggests measurement noise rather than gradient variance was the binding constraint on the hardware run, so improvements in mid-circuit measurement or error mitigation could shift the optimal operating point and shrink the shot budget.","Because the network factorizes as a probabilistic autoregressive model with a three-factor local update, SQSNNs are structurally compatible with online and continual learning on streaming data — a direction the paper leaves for future work but that the derivation already supports."],"forward_implications":["Training can move onto the quantum device: the rule needs only a constant number $M$ of global forward passes, after which every neuron updates from local measurements and a scalar feedback signal, with no classical backpropagation through the network.","Inference cost stops scaling with measurement shots: single-shot Born-rule spike emission replaces the multi-shot probability estimation of QLIF neurons, matching the event-driven principle that computation happens only when spikes occur.","Multi-qubit memory buys accuracy without proportional spiking cost: on FMNIST, enlarging the register from $(N=1, N_{\\mathrm{mem}}=1)$ to $(N=2, N_{\\mathrm{mem}}=2)$ raises accuracy while keeping spike density nearly flat.","In streaming and data-scarce regimes the architecture is reported to win on both axes: on MNIST-DVS and in the neuromorphic integrated sensing and communications scenario, SQSNN keeps higher accuracy than a classical SNN while emitting fewer spikes.","The probabilistic autoregressive formulation with a Jensen-bound objective carries over as a template for training other dynamic quantum circuits with mid-circuit measurements."],"supporting_citations":[{"why":"Defines the single-qubit QLIF spiking neuron and network that the SQS neuron extends and that SQSNN is benchmarked against.","marker":"[11]"},{"why":"Supplies the quantum recurrent neural network approach whose unmeasured memory qubits give the SQS neuron its internal quantum memory.","marker":"[17]"},{"why":"Provides the probabilistic autoregressive spiking-model formalism, the Jensen-bound log-loss upper bound, and the REINFORCE and three-factor learning template used to derive the local rule.","marker":"[19]"},{"why":"Defines the conventional zeroth-order perturbation scheme that requires one global forward pass per parameter and serves as the per-iteration-cost baseline the local rule improves on.","marker":"[35]"},{"why":"Supplies the simultaneous perturbation stochastic approximation (SPSA) estimator used for synaptic-weight gradients in each neuron.","marker":"[37]"},{"why":"Provides the surrogate-gradient training method for classical SNNs that Appendix A adapts for the classical simulator producing the large-scale benchmark results.","marker":"[39]"},{"why":"Supplies the circuit ansatz (controlled-RX plus single-qubit RX rotations) used inside each SQS neuron and defines the variational QNN baseline.","marker":"[43]"},{"why":"Is the software implementation stack used for the NISQ-device experiments and for the zero-noise-extrapolation error mitigation.","marker":"[44]"},{"why":"Defines the neuromorphic integrated sensing and communications scenario used as the application study.","marker":"[46]"}],"fun_headline_variants":["Quantum spiking nets with memory beat classical benchmarks","Local learning quantum spiking networks edge out classical SNNs","Multiqubit memory spiking neurons train without backprop","Quantum spiking neurons with memory outperform on neuromorphic data","Stochastic quantum spiking nets use quantum memory for single-shot spikes"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is stated in the paper itself (Section V-D and Appendix A): after the small USPS hardware study, all larger benchmarks are run on a classical simulator that replaces stochastic spikes with sigmoid probabilities and trains by backpropagation, under the stated assumption that this surrogate-gradient scheme closely approximates the learning dynamics of the proposed local rule. If that surrogate dynamics diverges from what the local rule actually learns on hardware, the headline accuracy comparisons do not follow from the proposed training method.","fun_headline_variants_meta":{"raw":{"variants":["Quantum spiking nets with memory beat classical benchmarks","Local learning quantum spiking networks edge out classical SNNs","Multiqubit memory spiking neurons train without backprop","Quantum spiking neurons with memory outperform on neuromorphic data","Stochastic quantum spiking nets use quantum memory for single-shot spikes"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000406,"raw_usage":{"total_tokens":2228,"prompt_tokens":1180,"completion_tokens":1048,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":796,"completion_tokens_details":{"reasoning_tokens":967}},"tokens_in":796,"tokens_out":1048,"duration_ms":9432,"temperature":1.0,"reasoning_tokens":967,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:26:06.058367+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare the proposed local zero-th order rule — not the surrogate-gradient substitute — against the surrogate on the same SQSNN architecture for at least one of MNIST, FMNIST, or KMNIST at the paper's matched parameter counts, either on a noiseless classical simulation or on quantum hardware. If final test accuracy (or the distribution of output spike trains on held-out inputs) diverges by more than a few points, the claim that the local rule achieves the reported benchmark performance fails; a cheaper first screen is to compare the spike-train statistics produced by both rules on identical held-out inputs.","supporting_citations":[{"cited_title":"A quantum leaky integrate -and- fire spiking neuron and network,","cited_arxiv_id":null,"evidence_quote":"Defines the single-qubit QLIF spiking neuron and network that the SQS neuron extends and that SQSNN is benchmarked against."},{"cited_title":"Learning temporal data with a variational quantum recurre nt neural network,","cited_arxiv_id":null,"evidence_quote":"Supplies the quantum recurrent neural network approach whose unmeasured memory qubits give the SQS neuron its internal quantum memory."},{"cited_title":"An intr o- duction to probabilistic spiking neural networks: Probabi listic models, learning rules, and applications,","cited_arxiv_id":null,"evidence_quote":"Provides the probabilistic autoregressive spiking-model formalism, the Jensen-bound log-loss upper bound, and the REINFORCE and three-factor learning template used to derive the local rule."},{"cited_title":"Multivariate stochastic approximation u sing a simultaneous perturbation gradient approximation,","cited_arxiv_id":null,"evidence_quote":"Defines the conventional zeroth-order perturbation scheme that requires one global forward pass per parameter and serves as the per-iteration-cost baseline the local rule improves on."},{"cited_title":"An overview of the simultaneous perturbat ion method for efficient optimization,","cited_arxiv_id":null,"evidence_quote":"Supplies the simultaneous perturbation stochastic approximation (SPSA) estimator used for synaptic-weight gradients in each neuron."},{"cited_title":"Training spiking neural networks using lessons from deep learning,","cited_arxiv_id":null,"evidence_quote":"Provides the surrogate-gradient training method for classical SNNs that Appendix A adapts for the classical simulator producing the large-scale benchmark results."},{"cited_title":"Circu it- centric quantum classifiers,","cited_arxiv_id":null,"evidence_quote":"Supplies the circuit ansatz (controlled-RX plus single-qubit RX rotations) used inside each SQS neuron and defines the variational QNN baseline."},{"cited_title":"Neuromorphi c integrated sensing and communications,","cited_arxiv_id":null,"evidence_quote":"Defines the neuromorphic integrated sensing and communications scenario used as the application study."}],"review_version":1}