arXiv subjects

Phillip Stanley-Marbell

Publications and source records attributed to Phillip Stanley-Marbell.

At least 19 recordsLinked to original sources

arXiv2026

Theoretical Analysis of Thermodynamic Matrix Inversion: First-order Equivalence to Preconditioned Gradient Descent and Implications for Analog Computing

Recent research has demonstrated the possibility of exploiting the thermodynamics of coupled electrical oscillators to implement computational tasks such as matrix inversion. While physical implementations rely on thermal noise to drive equilibration, we show that the underlying dynamics reduce to a deterministic iterative algorithm. Building on the framework of Aifer et al., we analyze the moment evolution of the Ornstein-Uhlenbeck process governing thermodynamic symmetric positive definite (SPD) matrix inversion. We prove that to a first-order approximation, the covariance dynamics are mathematically identical to preconditioned gradient descent on the Frobenius norm of the residual $\tilde{A}^{-1}A-I$. This equivalence demonstrates that thermal fluctuations, while essential for physical thermodynamic hardware, are algorithmically redundant for convex problems with a single global minimum. We validate the resulting algorithm against Thermox (Duffield et al.), a stochastic thermodynamic simulator, achieving speedups exceeding 100,000-fold while remaining competitive with the Newton-Schulz iteration. We also demonstrate acceleration through Schur complement techniques. These results establish a rigorous link between analog thermodynamic computing, statistical physics, and deterministic optimization methods.

math.NA↗

arXiv2026

Approximating Analytically-Intractable Likelihood Densities with Deterministic Arithmetic for Optimal Particle Filtering

Particle filtering algorithms have enabled practical solutions to problems in autonomous robotics (self-driving cars, UAVs, warehouse robots), target tracking, and econometrics, with further applications in speech processing and medicine (patient monitoring). Yet, their inherent weakness at representing the likelihood of the observation (which often leads to particle degeneracy) remains unaddressed for real-time resource-constrained systems. Improvements such as the optimal proposal and auxiliary particle filter mitigate this issue under specific circumstances and with increased computational cost. This work presents a new particle filtering method and its implementation, which enables tunably-approximative representation of arbitrary likelihood densities as program transformations of parametric distributions. Our method leverages a recent computing platform thatcan perform deterministic computation on probability distributionrepresentations (UxHw) without relying on stochastic methods. For non-Gaussian non-linear systems and with an optimal-auxiliary particle filter, we benchmark the likelihood evaluation error and speed for a total of 294840 evaluation points. For such models, the results show that the UxHw method leads to as much as 37.7x speedup compared to the Monte Carlo alternative. For narrow uniform measurement uncertainty, the particle filter falsely assigns zero likelihood as much as 81.89% of the time whereas UxHw achieves 1.52% false-zero rate. The UxHw approach achieves filter RMSE improvement of as much as 18.9% (average 3.3%) over the Monte Carlo alternative.

eess.SY↗

arXiv2026

Quantization of Probability Distributions via Divide-and-Conquer: Convergence and Error Propagation under Distributional Arithmetic Operations

This article studies a general divide-and-conquer algorithm for approximating continuous one-dimensional probability distributions with finite mean. The article presents a numerical study that compares pre-existing approximation schemes with a special focus on the stability of the discrete approximations when they undergo arithmetic operations. The main results are a simple upper bound of the approximation error in terms of the Wasserstein-1 distance that is valid for all continuous distributions with finite mean. In many use-cases, the studied method achieve optimal rate of convergence, and numerical experiments show that the algorithm is more stable than pre-existing approximation schemes in the context of arithmetic operations.

math.PR↗

arXiv2026

Digital Methods to Quantify Sensor Output Uncertainty in Real Time

Modern data-driven applications that make real-time decisions increasingly depend on advanced sensors which use pre-stored calibration data. In such applications, accurate characterization of sensor output uncertainty is important for reliable data interpretation. Here, we present a method for real-time on-device dynamic uncertainty quantification for sensor outputs which depend on pre-stored calibration data. We show how sensor calibration compensation equations (essential in advanced sensing systems) propagate uncertainties resulting from the quantization of calibration parameters to the sensor output. We use a low-cost thermal sensor as a motivating example and show these ideas are practical and possible on actual embedded sensor systems by prototyping them on two commercially-available uncertainty tracking hardware platforms. One has average power dissipation 16.7 mW and achieves 42.9x speedup compared to the equal-accuracy Monte Carlo computation (the status quo), and the other 147.15 mW and achieves 94.4x speedup. We present a proof-of-usefulness application using the quantified uncertainty in edge detection over ten test scenes where we show accuracy and precision average improvement by 4.97 and 40.25 percentage points, respectively, trading off sensitivity. Another application example examines uncertainty quantification for four different calibration-data storage scenarios and compute that a 48% increase in memory yields 75% smaller uncertainty metrics over the baseline.

eess.SP↗

arXiv2026

Distributional Computational Graphs: Error Bounds

We study a general framework of distributional computational graphs: computational graphs whose inputs are probability distributions rather than point values. We analyze the discretization error that arises when these graphs are evaluated using finite approximations of continuous probability distributions. Such an approximation might be the result of representing a continuous real-valued distribution using a discrete representation or from constructing an empirical distribution from samples (or might be the output of another distributional computational graph). We establish non-asymptotic error bounds in terms of the Wasserstein-1 distance, without imposing structural assumptions on the computational graph.

stat.ML↗

arXiv2025

Uncertainty Propagation in Finite Impulse Response Filters: Evaluating the Gaussian Assumption

A common assumption in signal processing is that underlying data numerically conforms to a Gaussian distribution. It is commonly utilized in signal processing to describe unknown additive noise in a system and is often justified by citing the central limit theorem for sums of random variables, although the central limit theorem applies only to sums of independent identically distributed random variables. However, many linear operations in signal processing take the form of weighted sums, which transforms the random variables such that their distributions are no longer identical. One such operation is a finite impulse response (FIR) filter. FIR filters are commonly used in signal processing applications as a pre-processing step. FIR output noise is generally assumed to be Gaussian. This article examines the FIR output response in the presence of uniformly distributed quantization noise. We express the FIR output uncertainty in terms of the input quantization uncertainty and filter coefficients. We show that the output uncertainty cannot be assumed to be Gaussian, but depending on the application a Gaussian estimation may still be useful. Then, we show through detailed numerical simulations that the output uncertainty distribution of the filter can be estimated through its most dominant coefficients.

eess.SP↗

arXiv2025

A Tensor Train Approach for Deterministic Arithmetic Operations on Discrete Representations of Probability Distributions

Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers from the curse of dimensionality, as memory and computational costs grow exponentially with dimension. Monte Carlo methods require thousands to billions of samples, incurring high computational costs and producing inconsistent results due to stochasticity. We present an efficient tensor train method for performing exact arithmetic operations on discretizations of continuous probability distributions while avoiding exponential growth. Our approach leverages low-rank tensor train decomposition to represent latent random variables compactly using Dirac deltas, enabling deterministic addition, subtraction and multiplication operations directly in the compressed format. We develop an efficient implementation using sparse matrices and specialized data structures that further enhances performance. Theoretical analysis demonstrates polynomial scaling of memory and computational complexity under rank assumptions, and shows how statistics of latent variables can be computed with polynomial complexity. Numerical experiments spanning randomized linear algebra to stochastic differential equations demonstrate orders-of-magnitude improvements in memory usage and computational time compared to conventional approaches, enabling tractable deterministic computations on discretized random variables in previously intractable dimensions.

math.NA↗

arXiv2025

The Monte Carlo Method and New Device and Architectural Techniques for Accelerating It

Computing systems interacting with real-world processes must safely and reliably process uncertain data. The Monte Carlo method is a popular approach for computing with such uncertain values. This article introduces a framework for describing the Monte Carlo method and highlights two advances in the domain of physics-based non-uniform random variate generators (PPRVGs) to overcome common limitations of traditional Monte Carlo sampling. This article also highlights recent advances in architectural techniques that eliminate the need to use the Monte Carlo method by leveraging distributional microarchitectural state to natively compute on probability distributions. Unlike Monte Carlo methods, uncertainty-tracking processor architectures can be said to be convergence-oblivious.

cs.AR↗

arXiv2025

Sensitivity Analysis of the Laser Power Control System to Measurement Noise in SLS 3D Printers

Uniform temperature distribution in Selective Laser Sintering (SLS) is essential for producing durable 3D prints. Achieving uniformity requires a laser power control system that minimises deviation of the printing temperatures from the target temperature. Because the estimate of the actual process temperature is an input to the laser power control, uncertainty in the estimate of the actual temperature can lead to fluctuations in laser power that affect the thermal performance of the SLS. This article investigates the sensitivity of a laser power control system to temperature measurement uncertainty. This article evaluates the effectiveness of two methods for quantifying the effect of input uncertainty on a SLS laser power control system: a recent innovation in uncertainty-tracked architecture and traditional Monte Carlo simulation. We show that recent advances in computer architecture for arithmatic on probability distributions make it possible for the first time, to perform control system uncertainty analysis with latencies under 30 ms, while achieving the same level of uncertainty analysis as Monte Carlo methods with latencies that are two orders of magnitude slower.

eess.SY↗

arXiv2024

Simulated Eyeblink Artifact Removal with ICA: Effect of Measurement Uncertainty

Independent Component Analysis (ICA) is commonly-used in electroencephalogram (EEG) signal processing to remove non-cerebral artifacts from cerebral data. Despite the ubiquity of ICA, the effect of measurement uncertainty on the artifact removal process has not been thoroughly investigated. We first characterize the measurement uncertainty distribution of a common ADC and show that it quantitatively conforms to a Gaussian distribution. We then evaluate the effect of measurement uncertainty on the artifact identification process through several computer simulations. These computer simulations evaluate the performance of two different ICA algorithms, FastICA and Infomax, in removing eyeblink artifacts from five different electrode configurations with varying levels of measurement uncertainty. FastICA and Infomax show similar performance in identifying the eyeblink artifacts for a given uncertainty level and electrode configuration. We quantify the correlation performance degradation with respect to SNR and show that in general, an SNR of greater than 15 dB results in less than a 5% degradation in performance. The biggest difference in performance between the two algorithms is in their execution time. FastICA's execution time is dependent on the amount of measurement uncertainty, with a 50% to 85% reduction in execution time over an SNR range of 20 dB. This contrasts with Infomax's execution time, which is unaffected by measurement uncertainty.

eess.SY↗

arXiv2024

Electron-Tunnelling-Noise Programmable Random Variate Accelerator for Monte Carlo Sampling

This article presents an electron tunneling noise programmable random variate accelerator for accelerating the sampling stage of Monte Carlo simulations. We used the LiteX framework to generate a FemtoRV imfc RISC-V instruction set soft processor and deploy it on a Digilent Arty-100T FPGA development board. The RISC-V soft processor augmented with our programmable random variate accelerator achieves an average speedup of 8.70 times and a median speedup of 8.68 times for a suite of twelve different benchmark applications when compared to GNU Scientific Library software random number generation. These speedups are achievable because the benchmarks spend an average of 90.0 % of their execution time generating random samples. The results of the Monte Carlo benchmark programs run over the programmable random variate accelerator have an average Wasserstein distance of 1.48 times and a median Wasserstein distance of 1.41 times that of the results produced by the GNU Scientific Library random number generators. The soft processor samples the electron tunneling noise source using the hardened XADC block in the FPGA. The flexibility of the LiteX framework allows for the deployment of any LiteX-supported soft processor with an electron tunneling noise programmable random variate accelerator on any LiteX-supported development board that contains an FPGA with an XADC.

cs.AR↗

arXiv2023

The Data Conversion Bottleneck in Analog Computing Accelerators

Most modern computing tasks have digital electronic input and output data. Due to these constraints imposed by real-world use cases of computer systems, any analog computing accelerator, whether analog electronic or optical, must perform an analog-to-digital conversion on its input data and a subsequent digital-to-analog conversion on its output data. The energy and latency costs incurred by data conversion place performance limits on analog computing accelerators. To avoid this overhead, analog hardware must replace the full functionality of traditional digital electronic computer hardware. This is not currently possible for optical computing accelerators due to limitations in gain, input-output isolation, and information storage in optical hardware. This article presents a case study that profiles 27 benchmarks for an analog optical Fourier transform and convolution accelerator which we designed and built. The case study shows that an ideal optical Fourier transform and convolution accelerator can produce an average speedup of 9.4 times and a median speedup of 1.9 times for the set of benchmarks. The optical Fourier transform and convolution accelerator only produces significant speedup for pure Fourier transform (45.3 times) and convolution (159.4 times) applications.

cs.AR↗

arXiv2022

GFET Lab: A Graphene Field-Effect Transistor TCAD Tool

Graphene field-effect transistors (GFETs) are experimental devices which are increasingly seeing commercial and research applications. Simulation and modelling forms an important stage in facilitating this transition, however the majority of GFET modelling relies on user implementation. To this end, we present GFET Lab, a user-friendly, open-source software tool for simulating GFETs. We first provide an overview of approaches to device modelling and a brief survey of GFET compact models and limitations. From this survey, we identify three key criteria for a suitable predictive model for circuit design: it must be a compact model; it must be SPICE-compatible; it must have a minimal number of fitting parameters. We selected Jimenez's drain-current model as it best matched these criteria, and we introduce some modifications to improve the predictive properties, namely accounting for saturation velocity and the asymmetry in n- and p-type carrier mobilities. We then validate the model by comparing GFETs simulated in our tool against experimentally-obtained GFET characteristics with the same materials and geometries and find good agreement between GFET Lab and experiment. We demonstrate the ability to export SPICE models for use in higher level circuit simulations and compare SPICE simulations of GFETs against GFETs simulated in GFET Lab, again showing good agreement. Lastly, we provide a brief tutorial of GFET Lab to demonstrate and encourage its use as a community-developed piece of software with both research and educational applications.

cond-mat.mes-hall↗

arXiv2021

An Algorithm for Sensor Data Uncertainty Quantification

This article presents an algorithm for reducing measurement uncertainty of one physical quantity when given oversampled measurements of two physical quantities with correlated noise. The algorithm assumes that the aleatoric measurement uncertainty in both physical quantities follows a Gaussian distribution and relies on sampling faster than it is possible for the measurand (the true value of the physical quantity that we are trying to measure) to change (due to the system thermal time constant) to calculate the parameters of the noise distribution. In contrast to the Kalman and particle filters, which respectively require state update equations and a map of one physical quality, our algorithm requires only the oversampled sensor measurements. When applied to temperature-compensated humidity sensors, it provides reduced uncertainty in humidity estimates from correlated temperature and humidity measurements. In an experimental evaluation, the algorithm achieves average uncertainty reduction of 10.3 %. The algorithm incurs an execution time overhead of 5.3 % when compared to the minimum algorithm required to measure and calculate the uncertainty. Detailed instruction-level emulation of a C-language implementation compiled to the RISC-V architecture shows that the uncertainty reduction program required 0.05 % more instructions per iteration than the minimum operations required to calculate the uncertainty.

eess.SP↗

arXiv2021

Machine Learning for Sensor Transducer Conversion Routines

Sensors with digital outputs require software conversion routines to transform the unitless analogue-to-digital converter samples to physical quantities with correct units. These conversion routines are computationally complex given the limited computational resources of low-power embedded systems. This article presents a set of machine learning methods to learn new, less-complex conversion routines that do not sacrifice accuracy for the BME680 environmental sensor. We present a Pareto analysis of the tradeoff between accuracy and computational overhead for the models and models that reduce the computational overhead of the existing industry-standard conversion routines for temperature, pressure, and humidity by 62%, 71 %, and 18 % respectively. The corresponding RMS errors are 0.0114 degrees C, 0.0280 KPa, and 0.0337 %. These results show that machine learning methods for learning conversion routines can produce conversion routines with reduced computational overhead which maintain good accuracy.

cs.LG↗

arXiv2021

Bridging the Band Gap: What Device Physicists Need to Know About Machine Learning

This article surveys the landscape of semiconductor materials and devices research for the acceleration of machine learning (ML) algorithms. We observe a disconnect between the semiconductor and device physics and engineering communities, and the digital logic and computer hardware architecture communities. The article first provides an overview of the principles of computational complexity and fundamental physical limits to computing and their relation to physical systems. The article then provides an introduction to ML by presenting three key components of ML systems: representation, evaluation, and optimisation. The article then discusses and provides examples of the application of emerging technologies from the demiconductor and device physics domains as solutions to computational problems, alongside a brief overview of emerging devices for computing applications. The article then reviews the landscape of ML accelerators, comparing fixed-function and reprogrammable digital logic with novel devices such as memristors, resistive memories, magnetic memories, and probabilistic bits. We observe broadly lower performance of ML accelerators based on novel devices and materials when compared to those based on digital complimentary metal-oxide semiconductor (CMOS) technology, particularly in the MNIST optical character recognition task, a common ML benchmark, and also highlight the lack of a trend of progress in approaches based on novel materials and devices. Lastly, the article proposes figures of merit for meaningful evaluation and comparison of different ML implementations in the hope of fostering a dialogue between the materials science, device physics, digital logic, and computer architecture communities by providing a common frame of reference for their work.

cs.ET↗

arXiv2020

A System for Generating Non-Uniform Random Variates using Graphene Field-Effect Transistors

We introduce a new method for hardware non-uniform random number generation based on the transfer characteristics of graphene field-effect transistors (GFETs) which requires as few as two transistors and a resistor (or transimpedance amplifier). The method could be integrated into a custom computing system to provide samples from arbitrary univariate distributions. We also demonstrate the use of wavelet decomposition of the target distribution to determine GFET bias voltages in a multi-GFET array. We implement the method by fabricating multiple GFETs and experimentally validating that their transfer characteristics exhibit the nonlinearity on which our method depends. We use the characterization data in simulations of a proposed architecture for generating samples from dynamically-selectable non-uniform probability distributions. Using a combination of experimental measurements of GFETs under a range of biasing conditions and simulation of the GFET-based non-uniform random variate generator architecture, we demonstrate a speedup of Monte Carlo integration by a factor of up to 2$\times$. This speedup assumes the analog-to-digital converters reading the outputs from the circuit can produce samples in the same amount of time that it takes to perform memory accesses.

cs.ET↗

arXiv2020

Probabilistic Value-Deviation-Bounded Source-Dependent Bit-Level Channel Adaptation for Approximate Communication

Computing systems that can tolerate effects of errors in their communicated data values can trade this tolerance for improved resource efficiency. Many important applications of computing, such as embedded sensor systems, can tolerate errors that are bounded in their distribution of deviation from correctness (distortion). We present a channel adaptation technique which modulates properties of I/O channels typical in embedded sensor systems, to provide a tradeoff between I/O power dissipation and distortion of communicated data. We provide an efficient-to-compute formulation for the distribution of integer distortion accounting for the distribution of transmitted values. Using this formulation we implement our value-deviation-bounded (VDB) channel adaptation. We experimentally quantify the achieved reduction in power dissipation on a hardware prototype integrated with the required programmable channel modulation circuitry. We augment these experimental measurements with an analysis of the distributions of distortions. We show that our probabilistic VDB channel adaptation can provide up to a 2$\times$ reduction in I/O power dissipation. When synthesized for a miniature low-power FPGA intended for use in sensor interfaces, a register transfer level implementation of the channel adaptation control logic requires only 106 flip-flops and 224 4-input LUTs for implementing per-bit channel adaptation on serialized streams of 8-bit sensor data.

eess.SP↗