Mathematical Foundations · Est. 2025

Foundations for signals and intelligence

We work on the structure inside the data, not on top of it. Two areas, one mathematical foundation.

"Sparsity isn't just a property of data. It's a design principle for intelligence."

The SparseTech Research Team

What We Do

Two areas, one foundation

Most real-world signals contain a lot of structure under the noise. We apply that idea in two places: the radio frequencies that carry information, and the neural networks that interpret it.

Area OneSignal Processing

Deterministic signal processing

Efficient algorithms for next-generation wireless infrastructure such as 6G beamforming, massive MIMO, real-time spectrum analysis, and industrial sensing, with reproducible behavior we can test and verify.

6G beamforming & massive MIMO
Real-time spectrum analysis
Industrial sensing & biosignals

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Area TwoAI Frameworks

Principled AI frameworks

Frameworks for building intelligent systems on mathematical foundations: edge LLM deployment, principled compression, compositional reasoning, and deterministic inference.

Edge LLM & on-device inference
Principled model compression
Compositional reasoning

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Shared foundation

The same
mathematics
in both areas.

In signals

Most frequency bins are noise. Sparse methods identify and process only the components that carry information.

In models

Most parameters are redundant. Sparse methods discover and preserve the weights that matter.

Same math

Compressed sensing, sparse linear algebra, and deterministic optimization underlie both.

Selected Research

Published work

All publications

Certificate-Governed CRT Sparse FFT: Verified Global-Label Candidate Construction under Explicit Decoding Models

Aaron R. Flouro, Shawn P. Chadwick

Published: September 28, 2026

eess.SPcs.DS

We present a deterministic CRT-based sparse Fourier architecture for exact recovery of noiseless, on-grid, at-most-$k$-sparse spectra with an engineered transform length. The transform length $N$ is selected as an exact product of small pairwise-coprime stage primes, allowing each stage to use transforms whose size…

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Deterministic Sparse FFT via Keyed Multi-View Gating with $O(\sqrt{N} \log k)$ Expected Time

Aaron R. Flouro, Shawn P. Chadwick

Published: May 5, 2026

eess.SPcs.DScs.IT

We introduce a deterministic sparse Fourier transform framework based on a keyed multi-view gating mechanism that leverages 2-of-3 Chinese Remainder Theorem (CRT) agreement to reduce candidate frequency pairs from $O(k^2)$ to $Θ(k)$ under sparse-regime assumptions. Unlike prior approaches that rely on randomized…

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Safety-Certified CRT Sparse FFT: $Ω(k^2)$ Lower Bound and $O(N \log N)$ Worst-Case

Aaron R. Flouro, Shawn P. Chadwick

Published: April 20, 2026

eess.SPcs.DScs.IT

Computing Fourier transforms of k-sparse signals, where only k of N frequencies are non-zero, is fundamental in compressed sensing, radar, and medical imaging. While the Fast Fourier Transform (FFT) evaluates all N frequencies in $O(N \log N)$ time, sufficiently sparse signals should admit sub-linear complexity in N.…

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