Exploring Biological Neuronal Correlations with Quantum Generative Models

TL;DR

This work introduces a quantum generative model framework for generating synthetic data that captures the spatial and temporal correlations of biological neuronal activity and demonstrates the ability to achieve reliable outcomes with fewer trainable parameters compared to classical methods.

Abstract

Understanding of how biological neural networks process information is one of the biggest open scientific questions of our time. Advances in machine learning and artificial neural networks have enabled the modeling of neuronal behavior, but classical models often require a large number of parameters, complicating interpretability. Quantum computing offers an alternative approach through quantum machine learning, which can achieve efficient training with fewer parameters. In this work, we introduce a quantum generative model framework for generating synthetic data that captures the spatial and temporal correlations of biological neuronal activity. Our model demonstrates the ability to achieve reliable outcomes with fewer trainable parameters compared to classical methods. These findings highlight the potential of quantum generative models to provide new tools for modeling and understanding neuronal behavior, offering a promising avenue for future research in neuroscience.

Figures (14)

• Figure 1: Illustration of the model architecture. (A) Architecture of the model, with generator G producing generated samples, and dataset D producing biological samples, which are both used as input for critic C. (B) Architecture of generator. In the upper left corner, the generator composed of several sub-generators is shown. The bottom part shows that each sub-generator is a quantum circuit following a re-uploading scheme. Here a noise-encoding layer and a parametrized layer are repeated for $l$ layers, with the parametrized layer ansatz of each parametrized layer shown in the top right side. After trained, the generator can be used to produce samples (D) similar to samples obtained from the biological dataset (C).
• Figure 2: Comparison between distribution of states and JS divergence calculated using generated and real data. Each panel show the distribution of spiking states for generated data obtained after training with the K-loss (in red) and with the standard loss (in blue), and the real distribution of the spiking states (black), for (A) 2, (B) 4, (C) 6, and (D) 8 neurons, all for the case of 1 timestep. The bottom inset shows a zoom of the first four activation states. The upper inset shows the JS divergence for all training steps, for K (red) and standard (blue) loss.
• Figure 3: Statistics and generated data for 2 and 10 neurons. (A-H) Statistics for the case of 2 and 10 neurons, with 1, 5, 10, and 30 timesteps represented with different colors in each image. Specifically, (A,E) pairwise covariance, (B,F) k-probability, (C,G) firing rate, and (D,H) autocorrelogram are shown. (I-P) Spike traces for 2 and 10 neurons, for the case of generated data with 1 (I,M), 10 (J,N), and 30 timesteps (K,O), and for real data (L,P).
• Figure S1: Mean-Square Error of k-probability and firing for models using K-loss and standard loss. (A) Error of k-probability value for K (orange) and standard (blue) loss as a function of the number of neurons. (B) Error of k-probability value for K and standard loss as a function of the number of timesteps. (C) Difference between the mean-square error of k-probability obtained using the K-loss and the standard loss, for all combinations of (neurons, timesteps). (D) Error of firing rate value for K (orange) and standard (blue) loss as a function of the number of neurons. (E) Error of firing rate value for K and standard loss as a function of the number of timesteps. (F) Difference between the mean-square error of firing rate obtained using the K-loss and the standard loss, for all combinations of (neurons, timesteps).
• Figure S2: Statistics for 2 neurons. From left to right: pairwise covariance, k-probability, firing rate, and autocorrelogram. The first row shows the results for the model that uses standard loss, for the case of 1, 2, and 5 timesteps. The second row shows the results for the model that uses K-loss, for the case of 1, 2, and 5 timesteps. Third and fourth rows show the results for 10, 20, and 30 timesteps, for models using standard loss (third) and K-loss (fourth).