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Efficient spiking neural

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Open problems in Efficient spiking neural

  • Efficient quantization for spiking neural networks1 paper raises it · 1 addresses it

    Low-bit weights and membrane potentials are needed for neuromorphic hardware but existing PTQ methods ignore spike-specific errors.

    • SpikeQ: Spike-Guided Post-Training Quantization for Spiking Neural Networksraises · addresses
  • Redundant subthreshold computation in SNNs1 paper raises it · 1 addresses it

    Postsynaptic neurons in subthreshold states waste computation despite low firing probability.

    • The Dormant Spiking Neuron: A State-Driven Mechanism for Efficient Spiking Neural Networksraises · addresses
  • Catastrophic forgetting in continual learning for SNNs1 paper raises it · 1 addresses it

    SNNs lose prior knowledge when learning new tasks sequentially under memory constraints.

    • Saliency-Guided Replay for Continual Learning in Deep Spiking Neural Networksraises · addresses
  • Hardware-aware training and inference for SNNs1 paper raises it · 2 address it

    Efficient on-device SNN deployment requires specialized hardware and memory-aware training.

    • An FPGA-Based Spiking Neural Network for Spatiotemporal Pattern Learning and Classificationraises · addresses
    • Removing the Compute Bottleneck for Event-based Visual Place Recognition with Spiking Neural Networksaddresses
  • Accuracy gap in spiking language models1 paper raises it · 1 addresses it

    Spiking language models suffer a persistent loss gap compared to dense baselines, limiting their practical use.

    • Compute-Optimal Scaling Laws for Spiking Language Modelsraises · addresses

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Papers

  • arXiv cs.LGOct 20

    Model- and Layer-Level Closed-Loop Forecasting with SSM-Based Spiking Neural Networks

    Erik Stolt, Sanja Karilanova, Ayca Ozcelikkale

    Deep State-Space Models (Deep SSMs) have shown promising performance and computational benefits in processing of time-series data with complex temporal dependencies. Spiking neural networks (SNNs) constitute a biologically inspired class of deep SSMs, where computing blocks communicate through spikes, discrete single-bit events rather than continuous activation functions. A particularly important task in time-series processing is forecasting, i.e. predicting future values of a sequence from past observations alone. However, how to best perform forecasting with SNNs is an open question, where the standard autoregressive nature of the data processing with SNNs requires values that are not available during the forecasting phase. In this article, we address this challenge. We explore two closed-loop forecasting strategies, in which the network's own generated values are fed back into the network as if they were observed past values: (i) model-level and (ii) layer-level closed-loop forecasting. We evaluate these approaches on the ETT-small datasets, a standard benchmark for time-series forecasting, under both spike-based and continuous activation functions. We compare the proposed…

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  • arXiv cs.AIOct 20

    Robust Representation Learning for Spiking Neural Networks based on Conditional Information Bottleneck

    Yuli Zha, Wang Fan, Yixiao Dai, Lingjie Wang, Bang Hu +3

    Spiking Neural Networks (SNNs) have shown great potential for low-power neuromorphic computing due to their event-driven processing and spatiotemporal sparsity, but they remain vulnerable to input perturbations, hardware-intrinsic noise, and adversarial attacks in real-world deployment. We attribute this vulnerability partly to input-specific hidden representations learned by standard SNNs trained with conventional cross-entropy loss, as our information-plane analysis empirically shows that substantial input-related information can still be retained after label-predictive information becomes stable. To address this issue, we propose SCIB, a simple yet effective robust learning objective for SNNs based on the Conditional Information Bottleneck. Different from conventional variational IB methods, SCIB replaces the mutual information compression term $I(X;S)$ with the conditional mutual information $I(X;S|Y)$ and derives a tractable variational upper bound. Moreover, it introduces a learnable class-conditional prior instead of a label-agnostic isotropic Gaussian prior, improving the expressiveness of variational compression and encouraging class-structured representations when…

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  • arXiv cs.NEOct 16

    SpikeQ: Spike-Guided Post-Training Quantization for Spiking Neural Networks

    Kai Sun, Peibo Duan, Zhanglu Yan, Guowei Zhang, Yongsheng Huang +1

    On neuromorphic chips, spiking neural networks (SNNs) consume far less energy than artificial neural networks (ANNs), but the limited memory of these chips requires low-bit synaptic weights and membrane potentials. Existing post-training quantization (PTQ) methods provide them without retraining and, like those for ANNs, minimize numerical errors such as the mean squared error (MSE). In an SNN, however, a quantization error reaches later layers only through the spikes it flips. We find that errors of equal MSE can cause very different accuracy losses, whereas errors that flip the same fraction of spikes cause the same loss. We therefore propose SpikeQ, a spike-guided PTQ framework. For weights, we select the level of each weight by simulating the downstream neurons and minimizing their spike errors. For membrane potentials, most existing methods quantize the state after the reset, whereas neuromorphic chips compare the threshold with the membrane potential stored at a fixed bit width. We target this pre-fire quantization and build a reset-aware grid that places the threshold on a rounding boundary, so rounding never flips the spike at the current time step. We evaluate SpikeQ on…

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  • arXiv cs.CVOct 15

    The Dormant Spiking Neuron: A State-Driven Mechanism for Efficient Spiking Neural Networks

    Ruichen Ma, Yicai Chen, Pujun Zhou, Yue Zuo, Chongyang Li +3

    Spiking neural networks (SNNs) offer a compelling pathway toward energy-efficient artificial intelligence, fundamentally anchored in presynaptic input-driven sparsity. However, a substantial yet chronically overlooked source of computational overhead persists: the continuous subthreshold dynamics of postsynaptic neurons. Quantitative analysis reveals that up to 44% of neurons in an ImageNet-trained ResNet-18 model reside in a deeply inhibited state, imposing a persistent computational burden despite having a negligible probability of firing. To address this inefficiency, the Dormant Spiking Neuron (DSN) model is introduced. By incorporating a state-driven dynamic gate, the DSN allows a neuron to enter a dormant state when its membrane potential falls below a predefined negative threshold, dynamically pruning redundant computations at the instance level. Crucially, this dormancy mechanism is directly integrated into the neuronal dynamics and trained end-to-end via backpropagation through time using surrogate gradients, enabling the network to actively learn a robust dormancy policy that adaptively preserves critical information flow. Extensive experiments across static and…

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  • arXiv cs.LGOct 13

    Saliency-Guided Replay for Continual Learning in Deep Spiking Neural Networks

    Francesco Panetta, Federico Di Valerio, Michela Proietti

    Spiking Neural Networks (SNNs) are promising for energy-efficient neuromorphic computing, but they still suffer from catastrophic forgetting when learning tasks sequentially. This work investigates the integration of Experience Packing and Replay (EPR) as a memory-efficient continual learning strategy for deep SNNs under low-latency constraints. The proposed framework combines Batch Normalization Through Time stabilized VGG9 SNNs with Spike Activation Maps (SAM), which provide forward-only explanations based on spike activity. These explanations are temporally aggregated into spatial attention maps and used to select the most informative image patches for replay, instead of storing full images. Experiments on Split CIFAR10 and Split CIFAR100 show that SAM-guided EPR improves the accuracy-memory trade-off under tight memory budgets, and remains competitive while requiring substantially less storage.

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  • arXiv cs.LGOct 13

    Sea-Net: A Small and Inherently Interpretable Neural Network for Time Series Classification

    Ubaid Ur Rehman, Tanmoy Mondal

    Traditional time-series classification methods often operate as black boxes, providing a class prediction without indicating which time point or time interval within the series led to that prediction. To improve temporal interpretability, MILLET (Multiple Instance Learning with Temporal Explanation), which combines an InceptionTime encoder with Conjunctive Pooling, provides both classification and temporal explanations. However, MILLET contains approximately 424 K parameters, making it unsuitable for deployment on resource-constrained micro-controllers, and it achieves an overall time-series accuracy of 0.888 and an explanation score of 0.681 NDCG@n. We therefore propose SEA-Net, a lightweight architecture using small multi-scale depthwise-separable convolutional TSC encoders and improved Multiple Instance Learning (MIL) pooling heads. Our SEA-Net bottleneck encoder with Top-k pooling achieves 0.931 accuracy and 0.765 NDCG@n with only 41 K parameters. Another variant, using a gated encoder with Top-k pooling, achieves 0.955 accuracy and 0.750 NDCG@n with 62 K parameters. These results demonstrate that lightweight architectures can maintain strong classification performance and…

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  • arXiv cs.AIOct 12

    An FPGA-Based Spiking Neural Network for Spatiotemporal Pattern Learning and Classification

    Jingang Jin, Yue Ma, Zhenhang Zhang, Qinru Qiu

    Spiking Neural Networks (SNNs) are promising for energy-efficient spatiotemporal pattern recognition at the edge, but efficient deployment and on-device adaptation require specialized hardware. In this work, we present an FPGA implementation of multilayer SNNs for spatiotemporal pattern classification, in which both inference and training take place on the same hardware. Our design adopts a temporal-forward-only training algorithm that avoids the memory and latency overhead associated with traditional Backpropagation Through Time (BPTT). A mixed-precision scheme balances training stability with resource efficiency, and architectural optimization maximizes hardware and memory utilization. We further identify and resolve hazards that arise when inference and learning share the same memory, including port conflicts between the forward and backward access patterns and read-after-write dependencies in floating-point potential accumulation. Experimental evaluations on MNIST and five multivariate time-series classification datasets demonstrate that, with fully on-chip training, our SNN model achieves accuracy comparable to SNN or LSTM trained with BPTT. Compared to CPU and GPU based…

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  • arXiv cs.ETOct 12

    Neuromorphic Decoding and Dynamical Image Reconstruction from Populations of Spiking Retinal Ganglion Cells

    Ning Zhang, Arto Nurmikko

    Decoding visual stimuli from the spiking activity of retinal ganglion cells (RGCs) informs both our understanding of the retinal code and the design of visual prostheses. Natural vision is dynamic, yet state-of-the-art decoders mostly reconstruct single frames with artificial neural networks that process dense, continuous-valued signals rather than the retina's sparse, asynchronous spikes. We asked whether dynamic scenes can be reconstructed and tracked entirely within the spike domain, and at what computational cost. We built an end-to-end spiking neural network (SNN) whose neurons integrate the recorded RGC spikes over time. Populations of up to 1836 RGCs were recorded ex vivo from mouse retina on high-density microelectrode arrays while flashed images, moving bars, drifting gratings and randomly moving handwritten digits were presented. For moving digits, one shared spiking encoder fed two readouts, one reconstructing the image and one decoding the digit's position. Compute energy was estimated from counted synaptic operations. The SNN decoded what and where at once. It reconstructed the stimuli with a structural similarity (SSIM) of up to 0.93, refining the reconstruction as…

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  • arXiv cs.CVOct 12

    Removing the Compute Bottleneck for Event-based Visual Place Recognition with Spiking Neural Networks

    Somayeh Hussaini, Tobias Fischer, Michael Milford

    Neuromorphic sensing and computing promise low latency and high energy efficiency for robotics, yet most event-based visual place recognition (VPR) pipelines reintroduce dense, frame-like computation downstream of an inherently sparse sensor, forfeiting the sensor's latency advantage. In this paper, we address the problem of resolving an event-based VPR query in tens of microseconds on a commodity CPU. We train a two-layer spiking neural network (SNN) with additive spike-timing-dependent plasticity (STDP), which drives the learned weight matrix towards a strongly bimodal distribution, amenable to aggressive magnitude pruning. At inference, our pipeline exploits this sparsity by reading only the pruned weights corresponding to the query's active pixels. As surviving weights share a near-uniform magnitude, each neuron's score reduces to an integer count of matching synapses instead of a weighted sum, lowering per-query latency. This computation is small enough to remain resident in a CPU's fast on-chip cache. On three event-based VPR benchmarks, our sparse SNN exceeds the recall of LENS, an existing event-based SNN, while reducing per-query latency by 5.5-6.2x to tens of…

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  • arXiv cs.CVOct 11

    SpikeOcc: Towards Resilient Multimodal 3D Occupancy Perception via Spiking Experts

    Yiding Sun, Zijie Xu, Hongqiang Lin, Jiajun Cao, Dongxu Zhang +5

    Multimodal 3D occupancy prediction underpins safe autonomous driving through comprehensive scene understanding. However, existing methods have largely pursued higher accuracy through sophisticated fusion, leaving resilience to missing sensors underexplored. In this paper, we investigate spiking neural networks (SNNs) as a means of building more resilient multimodal perception. Still, the discrete nature of spiking neurons makes optimization challenging. To overcome this difficulty, SpikeOcc is introduced with two complementary components, a Spiking Mixture-of-Experts (SMoE) and Sensor Availability Learning (SAL). Specifically, SMoE organizes RGB, LiDAR, and joint fusion into specialized pathways, enabling full-width unimodal representations while retaining the original multimodal features via a bounded residual. Beyond sensor dropout, SAL employs a staged curriculum with explicit routing supervision, progressively improving robustness under severe sensing conditions. Remarkably, SAL also yields notable gains for conventional models, highlighting its broader potential for resilient multimodal learning. Extensive experiments demonstrate that SpikeOcc maintains competitive…

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  • arXiv cs.LGOct 10

    Compute-Optimal Scaling Laws for Spiking Language Models

    Dan Saunders, Benjamin Ren, Catherine He

    Spiking neural networks target energy-efficient language modeling through sparse, binary activations, but the efficiency-accuracy tradeoff of spiking language models is uncharacterized at scale. We present the first Chinchilla-style IsoFLOP scaling study of a spiking language model, sweeping SpikeGPT-family models (RWKV backbone) from width 384 to 1536 across compute budgets from $3\times10^{17}$ to $10^{19}$ FLOPs on FineWeb-EDU. We report two findings. First, the compute-optimal frontier is $N_{opt} \propto C^{0.56}$, close to the 0.50 that Hoffmann et al. report for dense Transformers, so spiking does not change how parameters and data should be traded off under a compute budget. Second, against non-spiking RWKV and Transformer baselines trained the same way, the loss gap splits into a backbone cost of about 0.16 nats that does not change with compute and a spiking cost that falls from 0.34 to about 0.23 nats and then levels off. These results give the first compute-optimal recipe for spiking language models and quantify the accuracy cost of their sparsity.

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  • arXiv cs.ROOct 8

    SDPAD: A Fully Spike-Driven Pipeline for End-to-End Autonomous Driving

    Chengjun Zhang, Yuhao Zhang, Jie Yang, Mohamad Sawan

    End-to-end autonomous driving demands trajectory planners that are both highly accurate and cheap enough for edge deployment. State-of-the-art artificial neural network (ANN) planners meet the accuracy requirement at the cost of heavy dense computation, while spiking neural networks (SNNs)---though promising orders-of-magnitude energy savings through sparse, event-driven arithmetic---still lag far behind in planning accuracy. We present \textbf{SDPAD}, a fully spike-driven end-to-end planning pipeline that closes this gap. SDPAD converts a pre-trained ANN perception stack into integer-spike form via quantized ANN2SNN conversion, lifts multi-view images into the bird's-eye-view (BEV) space with a spike-driven-max (SDM) depth distribution (Spike-3D-Lift), and plans through the Spike-QFormer, a spiking query transformer in which ego, agent, and map queries distilled from the BEV scene are fused by learnable waypoint queries via cross-attention, followed by deformable spike-cross-attention refinement. Every operation is gated by integer spikes and inference is a single feed-forward pass without temporal simulation loops. On the nuScenes open-loop benchmark, SDPAD achieves an average…

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  • arXiv cs.CVOct 8

    MSGAT: Multi-Head Spiking Graph Attention with Similarity-Space Fusion for Image-Text Retrieval

    Xintao Zong, Wenxuan Liu, Jianhao Ding, Zhaofei Yu, Tiejun Huang

    Spiking neural networks (SNNs) offer an energy-efficient computing paradigm through sparse event-driven computation, showing great potential for efficient multimodal learning. However, applying SNNs to high-level multimodal tasks, such as image-text retrieval (ITR), remains challenging, since sparse spike representations make it difficult to capture semantic structures required for cross-modal alignment. Existing spiking ITR methods rely on local alignment and additional soft-label supervision during training, while lacking awareness of structural and multi-granularity relationships. To address these issues, we propose a Multi-head Spiking Graph Attention Network (\textbf{MSGAT}) for structural modeling and equip it with dynamic attention heads to capture complementary relational patterns and enable spike-driven graph reasoning and aggregation. However, within a two-branch multi-granularity fusion framework, the fine-grained spike representations generated by MSGAT are sparse and discrete, whereas the global representations are continuous, making conventional feature-level fusion susceptible to interference across heterogeneous representations. Therefore, we introduce…

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  • arXiv cs.AIOct 8

    SpikeSSL: A Universal Spike Inference Framework with Dynamics-Informed State-Space Layers

    Chenghao Yue, Siming Xing, Shuran Liu, Angran Li, Yuanlong Zhang

    Two-photon calcium imaging is a standard tool for recording large neural populations in vivo, yet inferring spikes accurately across the growing diversity of calcium indicators remains an open problem. Existing supervised methods achieve reasonable in-domain accuracy but generalize poorly to unseen indicators, because different indicators induce distinct fluorescence kinetics and signal statistics while existing architectures remain relatively simple generic temporal regressors without dynamics-matched inductive bias. We propose SpikeSSL, a universal spike inference framework whose temporal backbone is a bank of bidirectional IIR state-space layers broadly motivated by calcium dynamics. A multi-modal conditioning encoder maps indicator identity, sampling rate, and trace-level signal statistics into a global conditioning vector that modulates the backbone via Adaptive Layer Normalization, while a heteroscedastic variance head provides calibrated per-frame uncertainty. On a benchmark with five fixed evaluation splits built from 33 public ground-truth datasets, SpikeSSL achieves state-of-the-art performance in both in-domain and zero-shot leave-one-indicator-out settings. We also…

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  • arXiv cs.LGOct 7

    Rethinking the Tradeoff Between Temporal Encoding and Nonlinear Computation in Spiking Language Models

    Hanfei Liu, Shuchang Feng, Yanxia Chen, Changzeng Fu, Shiqi Zhao

    Spiking language models face a tradeoff between representing continuous semantic features over short temporal windows and retaining costly nonlinear attention operations. We introduce Spora, which jointly designs spike encodings and attention operators. Binary temporal weights let $T$ spikes represent compositional values with up to $T$ bits of capacity, compared with $O(\log_2 T)$ bits for spike-count readout. Unipolar Binary Spiking (UBS) uses thresholds and spike-triggered residual decay to produce non-negative integer codes; Bipolar Binary Spiking (BBS) separates sign and magnitude and learns a scale for signed activations. These representations support accumulation-and-shift dot products and integer-exponent mappings in attention. With four time steps, Spora achieves 76.6 average GLUE score and 44.1 CoLA MCC, improving over SpikeLM by 1.2 and 6.2 points, respectively. Extending BBS to six steps raises these scores to 78.2 and 47.4. Conditional-decay analysis, matched-budget activation-quantization comparisons, event-workload statistics, and fixed-point evaluation further characterize the connection between encoding fidelity and computational cost.

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  • arXiv q-bio.NCOct 7

    Structure alone supports efficient visual computation in the Drosophila visual system

    Eudald Correig-Fraga, Roger Guimerà, Marta Sales-Pardo

    Understanding the extent to which measured synaptic wiring determines computation remains a central challenge. Here, we couple the proofread adult Drosophila melanogaster connectome to an anatomically faithful model of its eye. Visual information is inputted in the eye model, then passed to the connectome, and finally read from a Kenyon-cell-centered linear decoder. This creates a connectome-only model in which the anatomical graph and eye geometry are fixed and only scalar synaptic gains and neuronal thresholds may be learned. The model supports multitask vision, including color discrimination, shape classification, and numerical discrimination that follows a ratio-dependent scaling characteristic of approximate number perception. To test whether precise connectivity is consequential under wiring economy, we compare the biological graph to randomized ensembles that increasingly preserve biological synaptic constraints. At matched wiring cost, the biological network consistently yields higher accuracy, whereas less constrained rewiring surpasses it at the cost of inflated wiring. These findings indicate that the measured connectivity and eye geometry jointly set efficient…

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  • arXiv cs.CLOct 7

    SpikingVLA: Asynchronous Spiking Vision-Language-Action Models

    Jingya Wang, Dehao Zhang, Shuai Wang, Malu Zhang, Yang Yang +1

    ANN-to-SNN conversion offers a practical route toward energy-efficient spiking Vision-Language-Action (VLA) models by bypassing the substantial cost of training large-scale SNNs from scratch. However, existing methods often require many timesteps to maintain competitive performance, resulting in substantial inference latency for real-time VLA deployment. To address this challenge, we introduce SpikingVLA, an ANN-to-SNN conversion framework that enables accurate and low-latency spiking VLA inference. Specifically, we propose a Dendritic Integrate-and-Fire (DIF) neuron that alleviates channel-wise activation outliers through dendritic mixing and adaptive somatic firing, enabling accurate ANN-to-SNN conversion with fewer timesteps. Building on DIF neurons, we further introduce an asynchronous execution mechanism that overlaps temporal computation across VLA components, reducing synchronization overhead and latency. Extensive experiments demonstrate that SpikingVLA achieves competitive navigation performance with substantially improved inference efficiency. Compared with existing spiking VLA methods, SpikingVLA improves SR and SPL by 11.9\% and 12.6\%, respectively, while reducing…

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  • arXiv cs.CVOct 7

    EM-SNN: Efficiently Modulated Spiking Neural Network for Remote Sensing Image Dehazing

    Jie Shao, Jiaqi Ma, Wenwen Min, Beihang Song, Ning Chen +2

    Although spiking neural networks (SNNs) provide an energy-efficient alternative to artificial neural networks (ANNs), their application to remote sensing image dehazing remains limited. A key challenge arises from the coupling between haze-induced high-frequency attenuation and discrete spike thresholding. This interaction suppresses weak responses and fundamentally limits the recovery of edges, textures, and fine details in spiking dehazing models. To address this challenge, we propose the Efficiently Modulated Spiking Neural Network (EM-SNN), a dedicated spiking framework tailored to remote sensing image dehazing. EM-SNN integrates a statistics-driven Threshold-Modulated Leaky Integrate-and-Fire (TM-LIF) neuron to adaptively compensate for haze-induced contrast compression, together with a Spike Sobel Modulation (SSM) module that enhances structural cues and reduces depth-wise attenuation during spiking feature propagation. By jointly modulating activation scales and structural representations, EM-SNN improves dehazing performance while preserving the inherent event-driven sparsity of SNNs. Experiments on HRSD, RICE, RRSHID, and SateHaze1K demonstrate that EM-SNN achieves…

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  • arXiv cs.NEOct 6

    Energy-Efficient Spiking Neural Networks for Sensing-Aided Beam Prediction

    Nhan Thanh Nguyen, Phuong Nam Tran, Mengyuan Ma, Huy T. Nguyen, Ahmed Alkhateeb +1

    Sensing-aided beam prediction can reduce the beam-training overhead of millimeter-wave (mmWave) systems by leveraging environmental information from complementary modalities such as vision and position. However, the resulting sensing and inference pipeline can be energy-intensive, motivating the use of energy-efficient spiking neural networks (SNNs) as an alternative to conventional artificial neural networks (ANNs). In this work, we develop SNN architectures for beam prediction and systematically compare them with ANNs using position-only, vision-only, and multimodal inputs. Our results show that compact ANNs consistently outperform SNNs for position-only sensing. In contrast, for vision and multimodal sensing, SNNs achieve higher accuracy than ANNs at similar energy costs and require up to an order of magnitude less energy at a comparable accuracy. For example, the multimodal SNN achieves 58.08% top-1 accuracy, outperforming the closest-energy ANN by 18.11 percentage points. We further show that SNN accuracy is limited by the binary communication between layers rather than by model size. These results demonstrate the potential of SNNs for energy-efficient sensing-aided beam…

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  • arXiv cs.NEOct 6

    Common-Mode Errors Limit Low-Timestep Deep Spiking Q-Networks

    Zijie Xu, Bingrui Guo, Yiding Sun, Yiting Dong, Zhile Yang +1

    Spiking neural networks (SNNs) offer sparse and event-driven computation, making them attractive for energy-constrained reinforcement learning (RL) on edge devices. In value-based RL, deep spiking Q-networks (DSQNs) combine such efficiency with action-value estimation for decision making. However, existing DSQNs often require multiple simulation timesteps for competitive performance, increasing computational and energy costs, whereas reducing the timesteps can cause substantial performance degradation. We investigate this degradation from the perspective of Q-value estimation errors. By decomposing errors across actions into common-mode and differential-mode components, we find that low-timestep DSQNs suffer disproportionately from common-mode errors shared across action values, which are particularly detrimental to temporal-difference learning through bootstrapped targets. Based on this finding, we propose Common-Mode Compensation Deep Spiking Q-Network (CMC-DSQN), which uses an auxiliary ANN to compensate for common-mode errors in the SNN outputs. At inference, greedy action selection can be performed directly from the SNN outputs, allowing the auxiliary ANN to be completely…

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