Learning Internal Biological Neuron Parameters and Complexity-Based Encoding for Improved Spiking Neural Networks Performance

TL;DR

A novel learning paradigm for spiking neural networks (SNNs) is proposed that replaces the perceptron-inspired abstraction with biologically grounded neuron models, jointly optimizing synaptic weights and intrinsic neuronal parameters, enabling efficient and interpretable classification of spatiotemporal spike data.

Abstract

This study proposes a novel learning paradigm for spiking neural networks (SNNs) that replaces the perceptron-inspired abstraction with biologically grounded neuron models, jointly optimizing synaptic weights and intrinsic neuronal parameters. We evaluate two architectures, leaky integrate-and-fire (LIF) and a meta-neuron model, under fixed and learnable intrinsic dynamics. Additionally, we introduce a biologically inspired classification framework that combines SNN dynamics with Lempel-Ziv complexity (LZC), enabling efficient and interpretable classification of spatiotemporal spike data. Training is conducted using surrogate-gradient backpropagation, spike-timing-dependent plasticity (STDP), and the Tempotron rule on spike trains generated from Poisson processes, widely adopted in computational neuroscience as a standard stochastic model of neuronal spike generation due to their analytical tractability and empirical relevance. Learning intrinsic parameters improves classification accuracy by up to 13.50 percentage points for LIF networks and 8.50 for meta-neuron models compared to baselines tuning only network size and learning rate. The proposed SNN-LZC classifier achieves up to 99.50% accuracy with sub-millisecond inference latency and competitive energy consumption. We further provide theoretical justification by formalizing how optimizing intrinsic dynamics enlarges the hypothesis class and proving descent guarantees for intrinsic-parameter updates under standard smoothness assumptions, linking intrinsic optimization to provable improvements in the surrogate objective.

Figures (5)

• Figure 1: Comparison of the standard Leaky Integrate-and-Fire (LIF) neuron model and the extended meta-neuron architecture. The LIF neuron integrates the input current $I(t)$ over time according to the leaky membrane equation $\tau \frac{dV}{dt} = -V + RI(t)$, where $\tau$ is the membrane time constant and $R$ is the membrane resistance. A spike is emitted when the membrane potential $V(t)$ exceeds a fixed threshold $V_{\mathrm{th}}$, followed by a reset to $V_{\mathrm{reset}}$. The meta-neuron preserves this core structure but incorporates dynamic, adaptive components. Specifically, the membrane time constant $\tau(t)$ and threshold $V_{\mathrm{th}}(t)$ can vary over time, enabling richer and more flexible temporal dynamics. More generally, the meta-neuron can be interpreted as computing a parameterized function $y=f(\mathbf{x};\boldsymbol{\theta})$, where the input vector $\mathbf{x}$ is mapped to an output $y$ through parameters $\boldsymbol{\theta}$, which may be adapted online through feedback mechanisms or learning algorithms.
• Figure 2: Schematic of the spiking neural network and its post-processing through Lempel–Ziv Complexity. The architecture includes an input layer $X = \{x^{(i)}\}$, hidden layer $H = \{h^{(i)}\}$, and output layer $Z = \{z^{(i)}\}$, each consisting of $n$ neurons. Binary input sequences of length 1024 are encoded into $n$-bit spike trains and propagated through the network. The output activity of each neuron $z^{(i)}$ is converted into a binary sequence $\mathbf{x}_n = [x_1, x_2, \dots, x_n]$, which is parsed into substrings to build a dictionary $\mathcal{D}$ of unique patterns. The LZC is computed as $c_{\alpha}(\mathbf{x}_n) = \frac{C_{\alpha}(\mathbf{x}_n)}{{n}} \log_{\alpha} n$, where $C_{\alpha}(\cdot)$ counts the number of distinct substrings that appear consecutively along the sequence. This measure quantifies the spatiotemporal complexity of the spike output.
• Figure 3: SNN trained with backpropagation learning. Output spike trains $\mathbf{z}^{(i)}$ are analyzed by LZC for classification. Error signals (red) propagate globally from output to input.
• Figure 4: SNN trained using STDP. Local spike timing between pre- and post-synaptic neurons adjusts weights.
• Figure 5: SNN trained using Tempotron rule. Local error signals flow from the output to hidden layer.