INFERRING NEURAL NETWORK CONNECTIVITY ACROSS MULTIPLE TIMESCALES USING KINETIC ISING MODELS

The brain’s computational capabilities emerge from complex interactions between neurons within circuits, making accurate knowledge of network connectivity from neural activity recordings essential for understanding how neurons process and transmit information. Kinetic Ising models provide a minimal framework for inferring neural dynamics: they treat neurons as binary units (spiking or silent) with directed interactions, making them the simplest theoretical model capable of capturing observed spike dynamics. Additionally, they provide a generative probabilistic model of the dynamics that can be used to predict and reproduce network activity.
We present a temporally extended kinetic Ising inference framework that incorporates dependencies over multiple preceding time steps. We estimate the lag-resolved couplings using a free energy minimisation approach. This yields a self-consistent steady-state model of the observed dynamics, allowing the inferred parameters can be meaningfully related to underlying biological connectivity. Further, this formulation captures synaptic and network effects across multiple timescales and enables finer temporal binning than single time lag methods without sacrificing the ability to recover network structure.
We tested our approach on simulated spiking neural networks with known connectivity, showing accurate reconstruction of network structure across different temporal regimes. We further applied the method to biological in-vitro engineered neural networks grown on microelectrode arrays and confined through polydimethylsiloxane (PDMS) microstructures. The framework’s generative nature allows us to reproduce observed activity patterns and validate the inferred connectivity even when ground truth is not available, providing a powerful tool for understanding neural dynamics.