Why can genetic algorithms work in high-dimensional search spaces?

We show that the effective dynamics of the elitist $(1+M)$ genetic algorithm is, in the limit of small mutations, clipped gradient descent on the loss in the presence of anisotropic Gaussian white noise. In expectation, therefore, a simple mutation-selection genetic algorithm follows the gradient of the loss, without explicit calculation of gradients and without averaging over loss evaluations. The genetic algorithm is slower than gradient descent because of the noise that acts in directions transverse to the gradient. However, this slowdown is controlled not by the number of parameters of the search space but by the effective rank of the Hessian of the loss function. For the concentrated Hessian spectra observed in neural-network loss functions the effective rank can be far smaller than the number of parameters, which may explain why genetic algorithms can scale to large search spaces.

Evolutionary design of thermodynamic logic gates and their heat emission

Landauer's principle bounds the heat generated by logical operations, but in practice the thermodynamic cost of computation is dominated by the control systems that implement logic. CMOS gates dissipate energy far above the Landauer bound, while laboratory demonstrations of near-Landauer erasure rely on external measurement or feedback systems whose energy costs exceed that of the logic operation by many orders of magnitude. Here we use simulations to show that a genetic algorithm can program a thermodynamic computer to implement logic operations in which the total heat emitted by the control system is of a similar order of magnitude to that of the information-bearing degrees of freedom. Moreover, the computer can be programmed so that heat is drawn away from the information-bearing degrees of freedom and dissipated within the control unit, suggesting the possibility of computing architectures in which heat management is an integral part of the program design.

Training thermodynamic computers by gradient descent

We show how to adjust the parameters of a thermodynamic computer by gradient descent in order to perform a desired computation at a specified observation time. Within a digital simulation of a thermodynamic computer, training proceeds by maximizing the probability with which the computer would generate an idealized dynamical trajectory. The idealized trajectory is designed to reproduce the activations of a neural network trained to perform the desired computation. This teacher-student scheme results in a thermodynamic computer whose finite-time dynamics enacts a computation analogous to that of the neural network. The parameters identified in this way can be implemented in the hardware realization of the thermodynamic computer, which will perform the desired computation automatically, driven by thermal noise. We demonstrate the method on a standard image-classification task, and estimate the thermodynamic advantage -- the ratio of energy costs of the digital and thermodynamic implementations -- to exceed seven orders of magnitude. Our results establish gradient descent as a viable training method for thermodynamic computing, enabling application of the core methodology of machine learning to this emerging field.

Generative thermodynamic computing

We introduce a generative modeling framework for thermodynamic computing, in which structured data is synthesized from noise by the natural time evolution of a physical system governed by Langevin dynamics. While conventional diffusion models use neural networks to perform denoising, here the information needed to generate structure from noise is encoded by the dynamics of a thermodynamic system. Training proceeds by maximizing the probability with which the computer generates the reverse of a noising trajectory, which ensures that the computer generates data with minimal heat emission. We demonstrate this framework within a digital simulation of a thermodynamic computer. If realized in analog hardware, such a system would function as a generative model that produces structured samples without the need for artificially-injected noise or active control of denoising.

Thermodynamic computing out of equilibrium

We present the design for a thermodynamic computer that can perform arbitrary nonlinear calculations in or out of equilibrium. Simple thermodynamic circuits, fluctuating degrees of freedom in contact with a thermal bath and confined by a quartic potential, display an activity that is a nonlinear function of their input. Such circuits can therefore be regarded as thermodynamic neurons, and can serve as the building blocks of networked structures that act as thermodynamic neural networks, universal function approximators whose operation is powered by thermal fluctuations. We simulate a digital model of a thermodynamic neural network, and show that its parameters can be adjusted by genetic algorithm to perform nonlinear calculations at specified observation times, regardless of whether the system has attained thermal equilibrium. This work expands the field of thermodynamic computing beyond the regime of thermal equilibrium, enabling fully nonlinear computations, analogous to those performed by classical neural networks, at specified observation times.

Increasing the clock speed of a thermodynamic computer by adding noise

We describe a proposal for increasing the effective clock speed of a thermodynamic computer, by altering the interaction scale of the units within the computer and introducing to the computer an additional source of noise. The resulting thermodynamic computer program is equivalent to the original computer program, but runs at a higher clock speed. This approach offers a way of increasing the speed of thermodynamic computing while preserving the fidelity of computation.

Adaptive AI-Driven Material Synthesis: Towards Autonomous 2D Materials Growth

Two-dimensional (2D) materials are poised to revolutionize current solid-state technology with their extraordinary properties. Yet, the primary challenge remains their scalable production. While there have been significant advancements, much of the scientific progress has depended on the exfoliation of materials, a method that poses severe challenges for large-scale applications. With the advent of artificial intelligence (AI) in materials science, innovative synthesis methodologies are now on the horizon. This study explores the forefront of autonomous materials synthesis using an artificial neural network (ANN) trained by evolutionary methods, focusing on the efficient production of graphene. Our approach demonstrates that a neural network can iteratively and autonomously learn a time-dependent protocol for the efficient growth of graphene, without requiring pretraining on what constitutes an effective recipe. Evaluation criteria are based on the proximity of the Raman signature to that of monolayer graphene: higher scores are granted to outcomes whose spectrum more closely resembles that of an ideal continuous monolayer structure. This feedback mechanism allows for iterative refinement of the ANN's time-dependent synthesis protocols, progressively improving sample quality. Through the advancement and application of AI methodologies, this work makes a substantial contribution to the field of materials engineering, fostering a new era of innovation and efficiency in the synthesis process.

Oscillatrons: neural units with time-dependent multifunctionality

Several branches of computing use a system's physical dynamics to do computation. We show that the dynamics of an underdamped harmonic oscillator can perform multifunctional computation, solving distinct problems at distinct times within a dynamical trajectory. Oscillator computing usually focuses on the oscillator's phase as the information-carrying component. Here we focus on the time-resolved amplitude of an oscillator whose inputs influence its frequency, which has a natural parallel as the activity of a time-dependent neural unit. We call this unit an oscillatron. The activity of an oscillatron at fixed time is a nonmonotonic function of the input, and so it can solve nonlinearly-separable problems such as XOR. The activity of the oscillatron at fixed input is a nonmonotonic function of time, and so it is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. Time-resolved computing of this nature can be done in or out of equilibrium, with the natural time evolution of the system giving us multiple computations for the price of one.

Springs and a stopwatch: neural units with time-dependent multifunctionality

Several branches of computing use a system's physical dynamics to do computation. We show that the dynamics of an underdamped harmonic oscillator can perform multifunctional computation, solving distinct problems at distinct times within a single dynamical trajectory. Oscillator computing usually focuses on the oscillator's phase as the information-carrying component. Here we focus on the time-resolved amplitude of an oscillator whose inputs influence its frequency, which has a natural parallel as the activity of a time-dependent neural unit. Because the activity of the unit at fixed time is a nonmonotonic function of the input, the unit can solve nonlinearly-separable problems such as XOR. Because the activity of the unit at fixed input is a nonmonotonic function of time, the unit is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. Time-resolved computing of this nature can be done in or out of equilibrium, with the natural time evolution of the system giving us multiple computations for the price of one.

How to train your demon to do fast information erasure without heat production

Time-dependent protocols that perform irreversible logical operations, such as memory erasure, cost work and produce heat, placing bounds on the efficiency of computers. Here we use a prototypical computer model of a physical memory to show that it is possible to learn feedback-control protocols to do fast memory erasure without input of work or production of heat. These protocols, which are enacted by a neural-network "demon", do not violate the second law of thermodynamics because the demon generates more heat than the memory absorbs. The result is a form of nonlocal heat exchange in which one computation is rendered energetically favorable while a compensating one produces heat elsewhere, a tactic that could be used to rationally design the flow of energy within a computer.