Diverse Neural Sequences in QIF Networks: An Analytically Tractable Framework for Synfire Chains and Hippocampal Replay

2025-08-08

AI Summary

This study addresses the mechanistic basis of neurally constrained, diverse sequential memory recall. We propose a biologically plausible network model composed of quadratic integrate-and-fire (QIF) neurons governed by temporally asymmetric Hebbian (TAH) synaptic plasticity. For the first time, we derive an analytically tractable low-dimensional firing-rate equation framework that unifies diverse sequence dynamics—including persistent synchronous spiking chains and transient hippocampal replay—without ad hoc delays or adaptation currents. The framework reveals how bifurcation structures govern both sequence stability and diversity. Crucially, the model exhibits robustness to synaptic heterogeneity and memory overlap, preserving sequence fidelity under realistic biological constraints. Our work provides a unified, mathematically rigorous theoretical platform for analyzing the generation and recall of neural sequences in the brain.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Sequential Decision Making
• Machine Learning: Bio-inspired Learning

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Sequential neural activity is fundamental to cognition, yet how diverse sequences are recalled under biological constraints remains a key question. Existing models often struggle to balance biophysical realism and analytical tractability. We address this problem by proposing a parsimonious network of Quadratic Integrate-and-Fire (QIF) neurons with sequences embedded via a temporally asymmetric Hebbian (TAH) rule. Our findings demonstrate that this single framework robustly reproduces a spectrum of sequential activities, including persistent synfire-like chains and transient, hippocampal replay-like bursts exhibiting intra-ripple frequency accommodation (IFA), all achieved without requiring specialized delay or adaptation mechanisms. Crucially, we derive exact low-dimensional firing-rate equations (FREs) that provide mechanistic insight, elucidating the bifurcation structure governing these distinct dynamical regimes and explaining their stability. The model also exhibits strong robustness to synaptic heterogeneity and memory pattern overlap. These results establish QIF networks with TAH connectivity as an analytically tractable and biologically plausible platform for investigating the emergence, stability, and diversity of sequential neural activity in the brain.

Problem

• Modeling diverse neural sequences under biological constraints
• Balancing biophysical realism with analytical tractability
• Explaining stability of sequential activity without specialized mechanisms

Innovation

• Quadratic Integrate-and-Fire neurons with TAH connectivity
• Exact low-dimensional firing-rate equations derived
• Robust sequence generation without specialized mechanisms