BioOSS: A Bio-Inspired Oscillatory State System with Spatio-Temporal Dynamics

TL;DR

BioOSS introduces a bio-inspired oscillatory state system that models spatio-temporal wave propagation using two interacting neuron populations on a 2D grid. By incorporating trainable damping and wave speed and leveraging a PDE-based discretization with an efficient scan operator, the approach yields interpretable, frequency-selective dynamics and strong performance on time-series classification and forecasting tasks. The paper provides stability analyses, eigenfrequency interpretations, and empirical results across diverse datasets, highlighting the method's brain-inspired grounding and computational tractability. Potential impact includes more interpretable, wave-based architectures for time-series modeling that can better capture long-range dependencies and spatial structure in neural-inspired computation.

Abstract

Today's deep learning architectures are primarily based on perceptron models, which do not capture the oscillatory dynamics characteristic of biological neurons. Although oscillatory systems have recently gained attention for their closer resemblance to neural behavior, they still fall short of modeling the intricate spatio-temporal interactions observed in natural neural circuits. In this paper, we propose a bio-inspired oscillatory state system (BioOSS) designed to emulate the wave-like propagation dynamics critical to neural processing, particularly in the prefrontal cortex (PFC), where complex activity patterns emerge. BioOSS comprises two interacting populations of neurons: p neurons, which represent simplified membrane-potential-like units inspired by pyramidal cells in cortical columns, and o neurons, which govern propagation velocities and modulate the lateral spread of activity. Through local interactions, these neurons produce wave-like propagation patterns. The model incorporates trainable parameters for damping and propagation speed, enabling flexible adaptation to task-specific spatio-temporal structures. We evaluate BioOSS on both synthetic and real-world tasks, demonstrating superior performance and enhanced interpretability compared to alternative architectures.

Figures (17)

• Figure 1: (a) The Overview of the proposed BioOSS framework. (b) Structure of the 2D neural network composed of interacting $p$ (pressure-like) and $o$ (oscillation-like) neurons arranged on a spatial grid. (c) Distribution of the natural frequencies across the grid, illustrating local frequency heterogeneity. (d) Dynamic behavior of $p$ neurons in the proposed model with local interactions. The left panel shows the input signal to a left $p$ neuron; the right panel shows the enriched oscillatory pattern of a neighboring right $p$ neuron. (e) Behavior in the absence of local spatial interactions, where the right $p$ neuron exhibits only amplitude modulation without generating richer oscillatory dynamics.
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