Fast reconstruction of degenerate populations of conductance-based neuron models from spike times

Inferring the biophysical parameters of conductance-based models (CBMs) from experimentally accessible recordings remains a central challenge in computational neuroscience. Spike times are the most widely available data, yet they reveal little about which combinations of ion channel conductances generate the observed activity. This inverse problem is further complicated by neuronal degeneracy, where multiple distinct conductance sets yield similar spiking patterns. We introduce a method that addresses this challenge by combining deep learning with Dynamic Input Conductances (DICs), a theoretical framework that reduces complex CBMs to three interpretable feedback components governing excitability and firing patterns. Our approach first maps spike times directly to DIC densities at threshold using a lightweight neural network that learns a low-dimensional representation of neuronal activity. The predicted DIC values are then used to generate degenerate CBM populations via an iterative compensation algorithm, ensuring compatibility with the intermediate target DICs, and thereby reproducing the corresponding firing patterns, even in high-dimensional models. Applied to two neuronal models, this algorithmic pipeline reconstructs spiking, bursting, and irregular regimes with high accuracy and robustness to variability, including spike trains generated under noisy current injection mimicking physiological stochasticity. It produces diverse degenerate populations within milliseconds on standard hardware, enabling scalable and efficient inference from spike recordings alone. Beyond methodological advances, we provide an open-source software package with a graphical interface that allows experimentalists to generate and explore CBM populations directly from spike trains without requiring programming expertise. Together, this work positions DICs as a practical and interpretable link between experimentally observed activity and mechanistic models. By enabling fast and scalable reconstruction of degenerate populations directly from spike times, our approach provides a powerful way to investigate how neurons exploit conductance variability to achieve reliable computation and provides the foundation for experimental applications that span from neuromodulation studies to real-time model-guided interventions.