Modeling Retinal Ganglion Cells with Neural Differential Equations

TL;DR

The paper investigates modeling retinal ganglion cell responses in tiger salamanders using Neural Ordinary Differential Equation (NODE) variants, specifically Liquid Time-Constant (LTC) and Closed-form Continuous-time (CfC) networks, and compares them to a ConvNet baseline and an LSTM on three datasets with a shared encoder and a 40-frame input history. NODEs achieve lower MAE and substantially smaller parameter counts with rapid convergence and fast inference, though they exhibit slightly lower Pearson correlation than the ConvNet, indicating a trade-off between value prediction and timing precision. The study also analyzes robustness to noise, the effect of temporal representation, and hyperparameter tuning, finding that multi-scale temporal representations do not improve performance and that NODEs excel in data-scarce, retraining-heavy edge settings. Overall, the results support NODE-based temporal models as efficient and adaptable options for real-time neural decoding and potential vision-prosthetic applications, while highlighting domain-specific limits on temporal precision. The work emphasizes practical advantages for edge deployments due to quick convergence and smaller models, at the cost of some temporal fidelity in predictions.

Abstract

This work explores Liquid Time-Constant Networks (LTCs) and Closed-form Continuous-time Networks (CfCs) for modeling retinal ganglion cell activity in tiger salamanders across three datasets. Compared to a convolutional baseline and an LSTM, both architectures achieved lower MAE, faster convergence, smaller model sizes, and favorable query times, though with slightly lower Pearson correlation. Their efficiency and adaptability make them well suited for scenarios with limited data and frequent retraining, such as edge deployments in vision prosthetics.

Figures (19)

• Figure 1: Selected input frames from the dataset.
• Figure 2: Test-set predictions for a selected ganglion cell of rgc9 (top), and a comparison of test-set correlation between CfC, ConvNet, LSTM, and LTC.
• Figure 3: Tiger salamander (Ambystoma tigrinum). Image source: Ribeiro2009.
• Figure 4: A sample input and output sequence from rgc9, channel 1. Observe the frame at time step 0 (left), which has distinct visual characteristics as compared to the following frames. For time step 10, we can see a very high firing rate, suggesting a lag between the change of the stimuli and the RGC signal.
• Figure 5: Firing responses to natural stimuli recorded for three selected retinal ganglion cells -- rgc91, rgc94, and rgc99 from the test set of rgc9. The subscripts refer to the channel numbers (1-based).