Spiking Neural Networks -- Part II: Detecting Spatio-Temporal Patterns

Abstract: Inspired by the operation of biological brains, Spiking Neural Networks (SNNs) have the unique ability to detect information encoded in spatio-temporal patterns of spiking signals. Examples of data types requiring spatio-temporal processing include logs of time stamps, e.g., of tweets, and outputs of neural prostheses and neuromorphic sensors. In this paper, the second of a series of three review papers on SNNs, we first review models and training algorithms for the dominant approach that considers SNNs as a Recurrent Neural Network (RNN) and adapt learning rules based on backpropagation through time to the requirements of SNNs. In order to tackle the non-differentiability of the spiking mechanism, state-of-the-art solutions use surrogate gradients that approximate the threshold activation function with a differentiable function. Then, we describe an alternative approach that relies on probabilistic models for spiking neurons, allowing the derivation of local learning rules via stochastic estimates of the gradient. Finally, experiments are provided for neuromorphic data sets, yielding insights on accuracy and convergence under different SNN models.

• The paper introduces deterministic (SRM) and probabilistic (GLM) SNN models designed for accurate spatio-temporal pattern recognition.
• It details surrogate gradient and ML-based learning algorithms that overcome non-differentiability in spiking functions.
• Experimental evaluation shows SRM-based networks achieving up to 99.4% accuracy on neuromorphic datasets, highlighting trade-offs in convergence and robustness.

Detecting Spatio-Temporal Patterns with Spiking Neural Networks

Background and Motivation

Spiking Neural Networks (SNNs) represent a biologically inspired paradigm distinct from classical Artificial Neural Networks (ANNs), characterized by their sparse binary event-driven computations and intrinsic capability to encode information in both spatial and temporal dimensions. SNNs are fundamentally suitable for processing time-stamped or event-based data (e.g., neuromorphic sensors), due to their energy-efficient implementations and high temporal resolution. However, the non-differentiability of the spiking mechanism—arising from threshold activation functions—renders traditional gradient-based training approaches ineffective, motivating dedicated learning algorithms that address both spatial and temporal credit assignment in SNNs.

Model Architectures for Spatio-Temporal Pattern Detection

The paper systematically reviews two modeling frameworks for SNNs as applied to the detection of spatio-temporal patterns:

Spike Response Model (SRM):

The deterministic SRM represents neuron dynamics in discrete time, where output spikes are triggered by the membrane potential crossing a fixed threshold. The membrane potential aggregates synaptic inputs filtered through autoregressive spike response functions. SRMs are typically implementable as recurrent neural networks with binary threshold activations, capturing both spatial and temporal dependencies.

Generalized Linear Model (GLM):

GLMs introduce a probabilistic extension to the SRM, modeling the probability of spike emission as a function of the membrane potential passed through a sigmoid activation. This allows for stochastic spike generation while maintaining explicit chains of causal dependencies, yielding differentiable loss functions amenable to principled optimization via Maximum Likelihood (ML) or related learning criteria.

Learning Algorithms and Credit Assignment

The paper delineates rigorous methods for supervised and unsupervised learning of SNNs:

Surrogate Gradient Methods for SRM:

To mitigate the issue of a zero derivative in threshold activations, surrogate gradient (SG) algorithms substitute the hard threshold function with smooth, differentiable surrogate functions (rectifier, sigmoid, exponential) during gradient computation. This enables gradient-based learning in SRM-based SNNs and facilitates the application of backpropagation through time (BPTT) or forward-mode differentiation. Updates typically manifest as three-factor rules: multiplicative interactions between pre-synaptic activity, post-synaptic sensitivity, and per-neuron error signals.

Gradient-Based Learning for GLM:

GLM-based SNNs optimize parameters using stochastic gradient descent driven by the negative log-likelihood (NLL) loss. Due to the exponential complexity associated with marginalizing over hidden neurons' spike sequences, Jensen’s inequality is used to upper bound the NLL, allowing empirical gradient estimates. Learning rules for visible neurons are formulated as two-factor updates (local pre-synaptic trace and post-synaptic error), while hidden neuron updates employ REINFORCE-type gradients incorporating a global error signal.

Experimental Evaluation on Neuromorphic Datasets

The paper empirically compares SRM and GLM-based SNNs using the MNIST-DVS and DVSGesture datasets. MNIST-DVS captures dynamic MNIST images using neuromorphic cameras, while DVSGesture records various hand gestures. Key experimental findings include:

• SRM-based SNNs with convolutional architectures yield maximal accuracy on MNIST-DVS (up to 99.4% test accuracy), outperforming GLM-based models when sufficient hidden neurons and high temporal resolution are available.
• GLM-based SNNs exhibit greater robustness in resource-constrained settings (lower sampling rates, fewer neurons), maintaining high performance when SRM-based models degrade.
• Convergence speed analyses reveal that SRM-based SNNs trained with DECOLLE (layered local error signals) often converge more rapidly than GLM-based counterparts, particularly when large mini-batch sizes are used.

These results suggest that per-neuron local error signals within SRM-based models can yield more informative weight updates than global random-projection error signals, at the cost of greater architectural complexity and resource consumption.

Theoretical and Practical Implications

The reviewed frameworks clarify the fundamental trade-offs between deterministic and probabilistic SNN formulations in terms of convergence, robustness, and hardware compatibility. The surrogate gradient methodology extends gradient-based optimization to highly non-smooth activations, broadening the applicability of SNNs in real-world, low-power applications. The use of differentiable probabilistic models (GLM) provides a pathway to scalable learning algorithms that are compatible with local rules and efficient sampling strategies, essential for neuromorphic hardware.

The paper's findings imply that future AI systems targeting spatio-temporal event-based data processing will benefit from hybrid approaches leveraging the strengths of both deterministic and probabilistic SNNs, guided by task-specific hardware constraints. Improvements in benchmark neuromorphic datasets and local learning rule derivations are anticipated to drive further progress.

Conclusion

This review provides an authoritative synthesis of SNN modeling and training strategies for spatio-temporal pattern recognition. It rigorously contrasts deterministic SRM and probabilistic GLM-based SNNs, offering detailed analyses of learning dynamics, numerical performance, and convergence characteristics across neuromorphic datasets. The implications for energy-efficient, temporally precise signal processing in future AI systems are substantial, highlighting key areas for continued methodological innovation and hardware integration.