12 papers
A Version Space Approach for Digital Circuit Analysis
Mitchell A. Thornton
Many questions about a digital circuit take the same form. A hidden object is consistent with a set of observations, and one wants to know how many remain consistent and which obse…
Kernel Density Estimation by Spectral Decomposition: Data-Driven Tapering and Superposition
Mitchell A. Thornton
Kernel density estimation depends largely on one choice, the smoothing bandwidth. We treat bandwidth selection and density estimation in the characteristic-function domain, where t…
Matched Generators for the Karhunen--Loève Transform: A Double-Commutator Eigenvalue Theory
Mitchell A. Thornton
The Karhunen--Loève transform (KLT) diagonalizes the covariance of a second-order process and is optimal for mean-square truncation. Which classical transform it reduces to is gove…
Blind Symmetry Matching in Quantum States with Application to Shot-Count Reduction
Mitchell A. Thornton
Measuring a quantum computation in a basis adapted to a symmetry it carries reduces the repeated measurements, commonly referred to as ``shots'', needed to read a statistical answe…
Symmetry-Aware Convex Shrinkage for High-Dimensional Covariance Estimation
Mitchell A. Thornton
We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance…
Polynomial-Time Optimal Group Selection via the Double-Commutator Eigenvalue Problem
Mitchell A. Thornton
The algebraic diversity framework generalizes temporal averaging over multiple observations to algebraic group action on a single observation for second-order statistical estimatio…
Unification of Signal Transform Theory
Mitchell A. Thornton
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Loève transform (KLT), and several others along with their co…
Continuous Algebraic Diversity: Unifying Spectral, Wavelet, and Time-Frequency Analysis via Lie Group Actions
Mitchell A. Thornton
We provide a computable criterion for selecting among Fourier, wavelet, and time-frequency analysis by extending the algebraic diversity (AD) framework to Lie groups acting on $L^2…
Algebraic Diversity: Principles of a Group-Theoretic Approach to Signal Processing
Mitchell A. Thornton
We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complemen…
Quantum Algebraic Diversity: Single-Copy Density Matrix Estimation via Group-Structured Measurements
Mitchell A. Thornton
We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a gr…
Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations
Mitchell A. Thornton
We establish that temporal averaging over multiple observations is the degenerate case of algebraic group action with the trivial group . A General Replacement Theorem pro…
Programming Quantum Computers with Large Language Models
Elena R. Henderson, Jessie M. Henderson, Joshua Ange +1
Large language models (LLMs) promise transformative change to fields as diverse as medical diagnosis, legal services, and software development. One reason for such an impact is LLM…