Local Learning Rules for Out-of-Equilibrium Physical Generative Models

We show that the out-of-equilibrium driving protocol of score-based generative models (SGMs) can be learned via a local learning rule. The gradient with respect to the parameters of the driving protocol are computed directly from force measurements or from observed system dynamics. As a demonstration, we implement an SGM in a network of driven, nonlinear, overdamped oscillators coupled to a thermal bath. We first apply it to the problem of sampling from a mixture of two Gaussians in 2D. Finally, we train a network of 10x10 oscillators to sample images of 0s and 1s from the MNIST dataset.

Learning in a Multifield Coherent Ising Machine

Physical information processors can learn from examples if they are modified according to an abstract parameter update equation, termed a learning rule. We introduce a physical model for self-learning that encodes the learning rule in the Hamiltonian of the system. The model consists of a network of multi-modal resonators. One of the modes is driven parametrically into a bi-stable regime, forming a coherent Ising machine (CIM) -- that provides the long-term memory that stores learned responses (weights). The CIM is augmented with an additional spinor field that acts as short-term (activation) memory. We numerically demonstrate that, in the presence of suitable nonlinear interactions between the long-term memory Ising machine and the short-term memory auxiliary field, the system autonomously learns from examples.

Personalized identification, prediction, and stimulation of neural oscillations via data-driven models of epileptic network dynamics

Neural oscillations are considered to be brain-specific signatures of information processing and communication in the brain. They also reflect pathological brain activity in neurological disorders, thus offering a basis for diagnoses and forecasting. Epilepsy is one of the most common neurological disorders, characterized by abnormal synchronization and desynchronization of the oscillations in the brain. About one third of epilepsy cases are pharmacoresistant, and as such emphasize the need for novel therapy approaches, where brain stimulation appears to be a promising therapeutic option. The development of brain stimulation paradigms, however, is often based on generalized assumptions about brain dynamics, although it is known that significant differences occur between patients and brain states. We developed a framework to extract individualized predictive models of epileptic network dynamics directly from EEG data. The models are based on the dominant coherent oscillations and their dynamical coupling, thus combining an established interpretation of dynamics through neural oscillations, with accurate patient-specific features. We show that it is possible to build a direct correspondence between the models of brain-network dynamics under periodic driving, and the mechanism of neural entrainment via periodic stimulation. When our framework is applied to EEG recordings of patients in status epilepticus (a brain state of perpetual seizure activity), it yields a model-driven predictive analysis of the therapeutic performance of periodic brain stimulation. This suggests that periodic brain stimulation can drive pathological states of epileptic network dynamics towards a healthy functional brain state.

Binary classification of spoken words with passive elastic metastructures

Many electronic devices spend most of their time waiting for a wake-up event: pacemakers waiting for an anomalous heartbeat, security systems on alert to detect an intruder, smartphones listening for the user to say a wake-up phrase. These devices continuously convert physical signals into electrical currents that are then analyzed on a digital computer -- leading to power consumption even when no event is taking place. Solving this problem requires the ability to passively distinguish relevant from irrelevant events (e.g. tell a wake-up phrase from a regular conversation). Here, we experimentally demonstrate an elastic metastructure, consisting of a network of coupled silicon resonators, that passively discriminates between pairs of spoken words -- solving the wake-up problem for scenarios where only two classes of events are possible. This passive speech recognition is demonstrated on a dataset from speakers with significant gender and accent diversity. The geometry of the metastructure is determined during the design process, in which the network of resonators ('mechanical neurones') learns to selectively respond to spoken words. Training is facilitated by a machine learning model that reduces the number of computationally expensive three-dimensional elastic wave simulations. By embedding event detection in the structural dynamics, mechanical neural networks thus enable novel classes of always-on smart devices with no standby power consumption.