arXiv subjects

Janith Petangoda

Publications and source records attributed to Janith Petangoda.

7 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↗

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↗

arXiv2021

Learning to Transfer: A Foliated Theory

Learning to transfer considers learning solutions to tasks in a such way that relevant knowledge can be transferred from known task solutions to new, related tasks. This is important for general learning, as well as for improving the efficiency of the learning process. While techniques for learning to transfer have been studied experimentally, we still lack a foundational description of the problem that exposes what related tasks are, and how relationships between tasks can be exploited constructively. In this work, we introduce a framework using the differential geometric theory of foliations that provides such a foundation.

cs.LG↗

arXiv2020

GENNI: Visualising the Geometry of Equivalences for Neural Network Identifiability

We propose an efficient algorithm to visualise symmetries in neural networks. Typically, models are defined with respect to a parameter space, where non-equal parameters can produce the same input-output map. Our proposed method, GENNI, allows us to efficiently identify parameters that are functionally equivalent and then visualise the subspace of the resulting equivalence class. By doing so, we are now able to better explore questions surrounding identifiability, with applications to optimisation and generalizability, for commonly used or newly developed neural network architectures.

cs.LG↗

arXiv2020

A Foliated View of Transfer Learning

Transfer learning considers a learning process where a new task is solved by transferring relevant knowledge from known solutions to related tasks. While this has been studied experimentally, there lacks a foundational description of the transfer learning problem that exposes what related tasks are, and how they can be exploited. In this work, we present a definition for relatedness between tasks and identify foliations as a mathematical framework to represent such relationships.

cs.LG↗