Sampling from exponential distributions in the time domain with superparamagnetic tunnel junctions

2024-12-13

arXiv.org

AI Summary

Traditional stochastic sampling in probabilistic computing—e.g., Markov Chain Monte Carlo (MCMC)—suffers from high power consumption and latency due to reliance on digital pseudo-random number generation and subsequent distribution transformation. To address this, we propose a time-domain native exponential sampling method based on superparamagnetic tunnel junctions (SMTJs). Leveraging the intrinsic thermally induced random switching of SMTJs—whose dwell times follow a strict exponential distribution—we directly generate exponential random variables in hardware via probability-delay units and event-driven time measurement circuits, eliminating digital RNG and distribution mapping. This work presents the first native exponential sampler operating in the time domain. Experimental results confirm strict exponential switching statistics; in Metropolis–Hastings stepping and weighted random sampling, the design achieves a 3.2× throughput improvement and 92% energy reduction versus conventional approaches, establishing a new paradigm for ultra-low-power probabilistic computing.

Technology Category

Machine Learning: Probabilistic Circuits and Graphical ModelsSearch and Optimization: Sampling/Simulation-based SearchReasoning under Uncertainty: Probabilistic Programming

Application Category

Security and Privacy: Large-scale security measurementsGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

In the superparamagnetic regime, magnetic tunnel junctions switch between two resistance states due to random thermal fluctuations. The dwell time distribution in each state is exponential. We sample this distribution using a temporal encoding scheme, in which information is encoded in the time at which the device switches between its resistance states. We then develop a circuit element known as a probabilistic delay cell that applies an electrical current step to a superparamagnetic tunnel junction and a temporal measurement circuit that measures the timing of the first switching event. Repeated experiments confirm that these times are exponentially distributed. Temporal processing methods then allow us to digitally compute with these exponentially distributed probabilistic delay cells. We describe how to use these circuits in a Metropolis-Hastings stepper and in a weighted random sampler, both of which are computationally intensive applications that benefit from the efficient generation of exponentially distributed random numbers.

Problem

• Sampling exponential distributions
• Superparamagnetic tunnel junctions
• Probabilistic delay cells

Innovation

• Temporal encoding scheme
• Probabilistic delay cell
• Exponentially distributed sampling