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T2FSNN: Deep Spiking Neural Networks with Time-to-first-spike Coding

Seongsik Park, Seijoon Kim, Byunggook Na, Sungroh Yoon

arXiv:2003.11741v1cs.NEcs.LGstat.ML

TL;DR

Deep SNNs offer energy efficiency but remain constrained by limited scalable training and inefficient use of temporal coding. T2FSNN introduces TTFS coding with a kernel-based dynamic threshold and dendrite, together with gradient-based optimization and early firing, and reports substantial reductions in latency and spike count.

  • Problem

    Deep SNNs lack scalable training methods, while existing approaches do not fully exploit temporal coding and therefore remain inefficient in spike count and inference latency.

  • Method

    T2FSNN implements TTFS coding with a kernel-based dynamic threshold and dendrite, enhanced by gradient-based optimization and early firing.

  • Results

    The proposed methods improve deep-SNN inference efficiency in both latency and number of spikes across experiments on multiple tasks.

  • Takeaways & Limitations

    The results support T2FSNN as an approach for more energy-efficient deep-SNN inference using temporal coding.

Abstract

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Spiking neural networks (SNNs) have gained considerable interest due to their energy-efficient characteristics, yet lack of a scalable training algorithm has restricted their applicability in practical machine learning problems. The deep neural network-to-SNN conversion approach has been widely studied to broaden the applicability of SNNs. Most previous studies, however, have not fully utilized spatio-temporal aspects of SNNs, which has led to inefficiency in terms of number of spikes and inference latency. In this paper, we present T2FSNN, which introduces the concept of time-to-first-spike coding into deep SNNs using the kernel-based dynamic threshold and dendrite to overcome the aforementioned drawback. In addition, we propose gradient-based optimization and early firing methods to further increase the efficiency of the T2FSNN. According to our results, the proposed methods can reduce inference latency and number of spikes to 22% and less than 1%, compared to those of burst coding, which is the state-of-the-art result on the CIFAR-100.

I. INTRODUCTION

T2FSNN addresses the limited scalability and efficiency of deep SNNs by introducing TTFS coding with dynamic thresholds and dendrites, then adding optimization and early firing methods. The proposed approach targets lower latency and fewer spikes while maintaining competitive accuracy.

  • I. INTRODUCTION: Deep SNNs remain difficult to apply broadly because scalable training algorithms are lacking and approximate-SGD approaches have produced unsatisfactory results.SNNs offer energy efficiency through integrate-and-fire and event-based operations, but their performance has limited wider adoption.
  • I. INTRODUCTION: Rate, phase, and burst coding improve aspects of SNN inference, but existing schemes still fall short in latency and spike-count efficiency.Rate coding is robust and simple but generates many spikes and transmits information slowly; phase and burst coding improve efficiency without fully resolving these limitations.
  • I. INTRODUCTION: Earlier TTFS approaches reduced spikes or improved accuracy, but reported limitations included unsatisfactory results, missing latency and spike-count measurements, and auxiliary-spike overhead.The TDSNN used reverse coding and achieved competitive accuracy, yet did not report key efficiency measures and incurred additional spikes from auxiliary neurons.
  • I. INTRODUCTION: T2FSNN uses a kernel-based dynamic threshold and dendrite to implement TTFS coding, where earlier spikes represent more critical information.The model is designed to reduce inference spikes and latency through temporal information transmission.
  • I. INTRODUCTION: The evaluation measures accuracy, spike count, and latency on MNIST, CIFAR-10, and CIFAR-100 to assess the proposed efficiency improvements.The reported experiments apply the proposed methods to T2FSNN and compare their efficiency across multiple datasets.
  • I. INTRODUCTION: Gradient-based optimization improves T2FSNN efficiency by optimizing its kernels, while early firing further reduces inference latency.These methods are presented as complementary additions to the TTFS-based T2FSNN model.

II. BACKGROUND AND RELATED WORK

SNNs transmit information through discrete spike trains and exploit event-driven operation for energy efficiency. Their neuron dynamics integrate synaptic inputs and generate spikes only when a firing condition is satisfied.

  • A. Spiking Neural Networks: SNNs transmit information through binary spike trains rather than continuous real values, enabling event-driven computation.This representation is central to the energy-efficiency characteristics of SNNs.
  • A. Spiking Neural Networks: The threshold is time-dependent, and TTFS coding assumes each neuron generates only one spike, so spike timing carries the encoded information.The paper uses a simplified notation based on this one-spike-per-neuron assumption.
  • A. Spiking Neural Networks: An SNN neuron receives synaptic input, integrates it into a membrane potential, and uses a threshold to determine spike generation.The background describes synaptic input and postsynaptic potentials as components of this integration process.
  • A. Spiking Neural Networks: Only neurons satisfying the firing condition generate spikes, increasing spike sparsity.The firing condition determines which neurons emit spikes during operation.

B. Neural Coding

Neural coding determines how SNNs represent information in spike trains, with TTFS using spike timing to reduce spikes while preserving temporal information.

  • B. Neural Coding: Rate coding is robust and simple but cannot exploit temporal information, producing many spikes and increasing energy consumption and inference latency.
  • B. Neural Coding: Phase coding reduces spikes but may be inefficient when hidden-layer inputs change dynamically and unpredictably.
  • B. Neural Coding: TTFS neurons generate one spike per inference, encoding information through spike timing rather than firing rate.Earlier spikes represent larger integrated membrane potentials, and postsynaptic neurons decode them through induced postsynaptic potentials.
  • B. Neural Coding: Reverse coding in TDSNN reduces spikes, but later delivery of larger values and auxiliary-neuron activity limit latency improvements.

III. PROPOSED METHODS

T2FSNN implements TTFS coding through kernel-based dynamic thresholds and dendrites, using layer-wise integration and firing to encode and decode information.

  • III. PROPOSED METHODS: Each layer sequentially integrates presynaptic spike trains into membrane potentials, then encodes the integrated values as spike times.Integration and firing occur in separate phases within each layer.
  • III. PROPOSED METHODS: T2FSNN combines kernel-based dynamic-threshold encoding with dendritic decoding to implement TTFS coding without auxiliary neurons.The method uses a fire kernel in the threshold and an integration kernel in the dendrite.
  • III. PROPOSED METHODS: The dynamic threshold makes neurons with larger integrated information fire earlier during the fire phase.The threshold uses trainable layer-specific time constants and delays.
  • III. PROPOSED METHODS: During decoding, dendritic integration restores information from spike timing by accumulating postsynaptic-potential contributions.

B. Gradient-Based Optimization Method

T2FSNN optimizes kernel parameters with supervised loss terms that balance representation accuracy and latency, addressing the kernel’s precision–latency trade-off.

  • B. Gradient-Based Optimization Method: Information below the kernel’s minimum representable value cannot be transmitted within the time window.This lower bound is exp(-(T-t_d)/τ).
  • B. Gradient-Based Optimization Method: The proposed precision and representation losses optimize kernel parameters against DNN values while considering both accuracy and inference latency.Gradient-based optimization minimizes these losses layer by layer using supervised learning targets from the converted DNN.
  • B. Gradient-Based Optimization Method: The representation loss uses minimum and maximum representable values so kernels learn the distribution of DNN ground-truth values.

C. Early Firing Method

The baseline pipeline separates integration and firing across layers, increasing latency, while early firing overlaps them to reduce inference time at the cost of non-guaranteed integration.

  • C. Early Firing Method: The baseline executes integration and firing sequentially across layers, guaranteeing complete prior-layer information before encoding.This dependency increases latency as network depth grows.
  • C. Early Firing Method: Early firing starts each layer’s firing phase before integration is complete, overlapping the two phases to reduce inference latency.The method must start late enough to preserve integration of critical information.
  • C. Early Firing Method: Non-guaranteed integration can discard information accumulated after a neuron has already fired because each neuron emits at most one spike.Early-firing timing therefore balances latency reduction against information loss.

IV. EXPERIMENTAL RESULTS

The experiments initialize T2FSNN parameters empirically, optimize with mini-batch SGD, and evaluate the proposed methods against other neural coding schemes across multiple datasets.

  • IV. EXPERIMENTAL RESULTS: Early firing begins halfway through the time window T, while τ, t_d, and T are empirically initialized.These settings are applied before gradient-based optimization and early firing evaluation.

A. Evaluation of the Proposed Methods

The proposed optimization improves T2FSNN’s representation dynamics and benchmark efficiency, while early firing and optimization together improve accuracy and reduce latency and spikes.

  • A. Evaluation of the Proposed Methods: When τ=18, optimization decreases τ to minimize Lmin, whereas τ=2 allows small kernel values but lower transmission precision.The experiment uses T=20 and tracks Lprec, Lmin, and Lmax.
  • A. Evaluation of the Proposed Methods: The optimized T2FSNN shifts layer spike-time distributions relative to T2FSNN, indicating faster inference with less computation.The cited evaluation connects gradient-based optimization with the spike-time distribution analysis.
  • A. Evaluation of the Proposed Methods: 46.9% lower inference latency accompanies accuracy gains of 0.07% on CIFAR-10 and 2.75% on CIFAR-100 for T2FSNN+GO+EF.The same variant reduces spike counts by 0.3% and 2.1%, respectively.
  • A. Evaluation of the Proposed Methods: Early firing improves accuracy despite fewer spikes, although its non-guaranteed integration changes whether accumulated information contributes to spike generation.The paper interprets this result as a possible generalization effect from stochastic integration.

B. Comparison with Other Methods

T2FSNN+GO+EF achieved the strongest overall efficiency results across MNIST, CIFAR-10, and CIFAR-100, combining highest accuracy with fewer spikes and lower latency than other coding methods. Its estimated energy consumption was also lower than rate and burst coding.

  • Inference speed on CIFAR-10 followed the order burst, phase, T2FSNN, and rate coding from fastest to slowest.Applying gradient-based optimization or early firing made T2FSNN inference as fast as phase coding.
  • The proposed T2FSNN+GO+EF achieved the best accuracy with the lowest number of spikes across MNIST, CIFAR-10, and CIFAR-100.Table II compares accuracy, latency, number of spikes, and estimated energy consumption across the three datasets.
  • In CIFAR-100, T2FSNN reduced inference latency to 22% and the number of spikes to less than 1% of burst coding.The method generates at most one spike per neuron.
  • The estimated energy consumption was about 6% and 16% of rate and burst coding, respectively, on average.Energy estimation incorporated measured latency and spike counts using TrueNorth and SpiNNaker parameters.

V. DISCUSSION

The discussion compares T2FSNN with TDSNN through estimated computational cost because TDSNN does not report spikes or latency. T2FSNN avoids auxiliary ticking neurons and repeated exponential operations required by TDSNN's reverse-coding implementation.

  • Direct comparison with TDSNN was unavailable because TDSNN did not report its number of spikes or latency, so the paper compared estimated computational cost instead.The comparison used VGG-16 on CIFAR-100, as specified in Table III.
  • TDSNN's ticking neurons generate frequent spikes, causing numerous accumulation operations proportional to time steps and neuron count.TDSNN also uses leaky integrate-and-fire neurons requiring an exponential operation at every time step.
  • T2FSNN avoids the ticking-neuron and per-time-step exponential-operation overhead described for TDSNN.The passage contrasts these TDSNN costs with the proposed T2FSNN implementation.

VI. CONCLUSION

The paper concludes that T2FSNN, gradient-based optimization, and early firing improve deep-SNN inference efficiency. The demonstrated gains concern both latency and number of spikes across various tasks.

  • Experiments across various tasks demonstrated improved deep-SNN inference efficiency in both latency and number of spikes.The authors position the methods as supporting energy-efficient inference with temporal coding.
  • The proposed T2FSNN combines gradient-based optimization and early firing to utilize TTFS coding in deep SNNs.
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