Denis Melanson

Patrick J. Coles, Collin Szczepanski, Denis Melanson et al.

Many Artificial Intelligence (AI) algorithms are inspired by physics and employ stochastic fluctuations. We connect these physics-inspired AI algorithms by unifying them under a single mathematical framework that we call Thermodynamic AI. Seemingly disparate algorithmic classes can be described by this framework, for example, (1) Generative diffusion models, (2) Bayesian neural networks, (3) Monte Carlo sampling and (4) Simulated annealing. Such Thermodynamic AI algorithms are currently run on digital hardware, ultimately limiting their scalability and overall potential. Stochastic fluctuations naturally occur in physical thermodynamic systems, and such fluctuations can be viewed as a computational resource. Hence, we propose a novel computing paradigm, where software and hardware become inseparable. Our algorithmic unification allows us to identify a single full-stack paradigm, involving Thermodynamic AI hardware, that could accelerate such algorithms. We contrast Thermodynamic AI hardware with quantum computing where noise is a roadblock rather than a resource. Thermodynamic AI hardware can be viewed as a novel form of computing, since it uses a novel fundamental building block. We identify stochastic bits (s-bits) and stochastic modes (s-modes) as the respective building blocks for discrete and continuous Thermodynamic AI hardware. In addition to these stochastic units, Thermodynamic AI hardware employs a Maxwell's demon device that guides the system to produce non-trivial states. We provide a few simple physical architectures for building these devices and we develop a formalism for programming the hardware via gate sequences. We hope to stimulate discussion around this new computing paradigm. Beyond acceleration, we believe it will impact the design of both hardware and algorithms, while also deepening our understanding of the connection between physics and intelligence.

Denis Melanson, Mohammad Abu Khater, Maxwell Aifer et al.

Recent breakthroughs in artificial intelligence (AI) algorithms have highlighted the need for novel computing hardware in order to truly unlock the potential for AI. Physics-based hardware, such as thermodynamic computing, has the potential to provide a fast, low-power means to accelerate AI primitives, especially generative AI and probabilistic AI. In this work, we present the first continuous-variable thermodynamic computer, which we call the stochastic processing unit (SPU). Our SPU is composed of RLC circuits, as unit cells, on a printed circuit board, with 8 unit cells that are all-to-all coupled via switched capacitances. It can be used for either sampling or linear algebra primitives, and we demonstrate Gaussian sampling and matrix inversion on our hardware. The latter represents the first thermodynamic linear algebra experiment. We also illustrate the applicability of the SPU to uncertainty quantification for neural network classification. We envision that this hardware, when scaled up in size, will have significant impact on accelerating various probabilistic AI applications.

Kaelan Donatella, Samuel Duffield, Maxwell Aifer et al.

Second-order training methods have better convergence properties than gradient descent but are rarely used in practice for large-scale training due to their computational overhead. This can be viewed as a hardware limitation (imposed by digital computers). Here we show that natural gradient descent (NGD), a second-order method, can have a similar computational complexity per iteration to a first-order method, when employing appropriate hardware. We present a new hybrid digital-analog algorithm for training neural networks that is equivalent to NGD in a certain parameter regime but avoids prohibitively costly linear system solves. Our algorithm exploits the thermodynamic properties of an analog system at equilibrium, and hence requires an analog thermodynamic computer. The training occurs in a hybrid digital-analog loop, where the gradient and Fisher information matrix (or any other positive semi-definite curvature matrix) are calculated at given time intervals while the analog dynamics take place. We numerically demonstrate the superiority of this approach over state-of-the-art digital first- and second-order training methods on classification tasks and language model fine-tuning tasks.

Kaelan Donatella, Samuel Duffield, Denis Melanson et al.

Many hardware proposals have aimed to accelerate inference in AI workloads. Less attention has been paid to hardware acceleration of training, despite the enormous societal impact of rapid training of AI models. Physics-based computers, such as thermodynamic computers, offer an efficient means to solve key primitives in AI training algorithms. Optimizers that normally would be computationally out-of-reach (e.g., due to expensive matrix inversions) on digital hardware could be unlocked with physics-based hardware. In this work, we propose a scalable algorithm for employing thermodynamic computers to accelerate a popular second-order optimizer called Kronecker-factored approximate curvature (K-FAC). Our asymptotic complexity analysis predicts increasing advantage with our algorithm as $n$, the number of neurons per layer, increases. Numerical experiments show that even under significant quantization noise, the benefits of second-order optimization can be preserved. Finally, we predict substantial speedups for large-scale vision and graph problems based on realistic hardware characteristics.