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

arXiv: https://arxiv.org/abs/2509.12783 · HTML: https://mlsanity.com/paper/2509.12783/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 59 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Flexible statistical inference for mechanistic models of neural dynamics](https://mlsanity.com/paper/1711.01861/) (2017)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithful](https://mlsanity.com/paper/2110.06581/) (2021)
- [Sourcerer: Sample-based Maximum Entropy Source Distribution Estimation](https://mlsanity.com/paper/2402.07808/) (2024)
- [Distributed online estimation of biophysical neural networks](https://mlsanity.com/paper/2204.01472/) (2022)
- [Dimensionality reduction of neuronal degeneracy reveals two interfering physiological mechanisms](https://mlsanity.com/paper/2405.02038/) (2024)
- [Feedback Identification of conductance-based models](https://mlsanity.com/paper/2002.09626/) (2020)

## Abstract (arXiv)

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 to DIC densities at threshold using a 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 models, this algorithmic pipeline reconstructs spiking and bursting 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. 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.