arXiv subjects

Edward Finkelstein

Publications and source records attributed to Edward Finkelstein.

4 recordsLinked to original sources

arXiv2026

Searching the Space of Feed-Forward Neural-Network Weight-Update Rules with Fixed Depth Symbolic Regression

We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks. Candidate update rules are represented as fixed-depth symbolic expressions over operands derived from common optimizers, including gradient, momentum, adaptive-gradient, and moment-estimate quantities. Across 30 benchmark/neural network combinations, the symbolic regression procedure found an update rule outperforming the best hyperparameter-tuned established optimizer in 25 cases, with an aggregate MSE reduction of 44.47\% over the improved cases. The discovered rules do not all share a single common symbolic form, but many combine adaptive normalization, momentum-like quantities, nonlinear transformations, and rational expressions. These results suggest that symbolic regression can serve as a lightweight mechanism for discovering compact optimizer variants, while also highlighting the need for larger-scale validation.

cs.LG↗

arXiv2025

Deducing Closed-Form Expressions for Bright-Solitons in Strongly Magnetized Plasmas with Physics Informed Symbolic Regression (PISR)

This paper presents a novel approach to finding analytical approximations for bright-soliton solutions in strongly magnetized plasmas. We leverage Physics-Informed Symbolic Regression (PISR) to discover closed-form expressions for the vector potential and number density profiles, governed by a reduced-order model derived from Maxwell-fluid equations. The PISR framework combines symbolic regression with physics-based constraints, boundary conditions, and available simulation data to guide the search for solutions. We demonstrate the effectiveness of the approach by rediscovering approximate solutions consistent with previously published numerical results, showcasing the potential of PISR for reducing simulation costs of reduced-order models in plasma physics.

cs.SC↗

arXiv2024

Solving the 2D Advection-Diffusion Equation using Fixed-Depth Symbolic Regression and Symbolic Differentiation without Expression Trees

This paper presents a novel method for solving the 2D advection-diffusion equation using fixed-depth symbolic regression and symbolic differentiation without expression trees. The method is applied to two cases with distinct initial and boundary conditions, demonstrating its accuracy and ability to find approximate solutions efficiently. This framework offers a promising, scalable solution for finding approximate solutions to differential equations, with the potential for future improvements in computational performance and applicability to more complex systems involving vector-valued objectives.

stat.CO↗

arXiv2024

Generalized Fixed-Depth Prefix and Postfix Symbolic Regression Grammars

We develop faultless, fixed-depth, string-based, prefix and postfix symbolic regression grammars, capable of producing \emph{any} expression from a set of operands, unary operators and/or binary operators. Using these grammars, we outline simplified forms of 5 popular heuristic search strategies: Brute Force Search, Monte Carlo Tree Search, Particle Swarm Optimization, Genetic Programming, and Simulated Annealing. For each algorithm, we compare the relative performance of prefix vs postfix for ten ground-truth expressions implemented entirely within a common C++/Eigen framework. Our experiments show a comparatively strong correlation between the average number of nodes per layer of the ground truth expression tree and the relative performance of prefix vs postfix. The fixed-depth grammars developed herein can enhance scientific discovery by increasing the efficiency of symbolic regression, enabling faster identification of accurate mathematical models across various disciplines.

cs.SC↗