Using Quantum Computing to Infer Dynamic Behaviors of Biological and Artificial Neural Networks

The exploration of new problem classes for quantum computation is an active area of research. An essentially completely unexplored topic is the use of quantum algorithms and computing to explore and ask questions \textit{about} the functional dynamics of neural networks. This is a component of the still-nascent topic of applying quantum computing to the modeling and simulations of biological and artificial neural networks. In this work, we show how a carefully constructed set of conditions can use two foundational quantum algorithms, Grover and Deutsch-Josza, in such a way that the output measurements admit an interpretation that guarantees we can infer if a simple representation of a neural network (which applies to both biological and artificial networks) after some period of time has the potential to continue sustaining dynamic activity. Or whether the dynamics are guaranteed to stop either through 'epileptic' dynamics or quiescence.

Learning without gradient descent encoded by the dynamics of a neurobiological model

The success of state-of-the-art machine learning is essentially all based on different variations of gradient descent algorithms that minimize some version of a cost or loss function. A fundamental limitation, however, is the need to train these systems in either supervised or unsupervised ways by exposing them to typically large numbers of training examples. Here, we introduce a fundamentally novel conceptual approach to machine learning that takes advantage of a neurobiologically derived model of dynamic signaling, constrained by the geometric structure of a network. We show that MNIST images can be uniquely encoded and classified by the dynamics of geometric networks with nearly state-of-the-art accuracy in an unsupervised way, and without the need for any training.

Generalizable Machine Learning in Neuroscience using Graph Neural Networks

Although a number of studies have explored deep learning in neuroscience, the application of these algorithms to neural systems on a microscopic scale, i.e. parameters relevant to lower scales of organization, remains relatively novel. Motivated by advances in whole-brain imaging, we examined the performance of deep learning models on microscopic neural dynamics and resulting emergent behaviors using calcium imaging data from the nematode C. elegans. We show that neural networks perform remarkably well on both neuron-level dynamics prediction, and behavioral state classification. In addition, we compared the performance of structure agnostic neural networks and graph neural networks to investigate if graph structure can be exploited as a favorable inductive bias. To perform this experiment, we designed a graph neural network which explicitly infers relations between neurons from neural activity and leverages the inferred graph structure during computations. In our experiments, we found that graph neural networks generally outperformed structure agnostic models and excel in generalization on unseen organisms, implying a potential path to generalizable machine learning in neuroscience.

Mapping the spatiotemporal dynamics of calcium signaling in cellular neural networks using optical flow

An optical flow gradient algorithm was applied to spontaneously forming net- works of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution. Optical flow estimates the direction and speed of motion of objects in an image between subsequent frames in a recorded digital sequence of images (i.e. a movie). Computed vector field outputs by the algorithm were able to track the spatiotemporal dynamics of calcium signaling pat- terns. We begin by briefly reviewing the mathematics of the optical flow algorithm, and then describe how to solve for the displacement vectors and how to measure their reliability. We then compare computed flow vectors with manually estimated vectors for the progression of a calcium signal recorded from representative astrocyte cultures. Finally, we applied the algorithm to preparations of primary astrocytes and hippocampal neurons and to the rMC-1 Muller glial cell line in order to illustrate the capability of the algorithm for capturing different types of spatiotemporal calcium activity. We discuss the imaging requirements, parameter selection and threshold selection for reliable measurements, and offer perspectives on uses of the vector data.