F·01
Geometric Information Theory
Curvature, topology, and the geometry of data structure.
Independent research in geometric information theory,
applied topology & edge intelligence
Villines Research is an independent practice applying geometric and topological methods to data structure, machine learning, and economic systems — backed by a granted U.S. patent and a body of SSRN research.
Villines Research is an independent research practice founded by Gregory Villines. It works at the intersection of geometric information theory, topological data analysis, compression, and machine intelligence — developing both the foundational methods and the applied systems that put them to work.
The practice is built around a single conviction: that the structure of data, treated as a geometric and topological object, carries signal that conventional tools routinely discard.
The research program spans more than a dozen working papers published through SSRN, covering topological data analysis, labor-market econometrics, and behavioral economics. Representative lines of work apply topological data analysis to unemployment-insurance and reemployment data — surfacing structure that fixed-threshold policy models miss — and the Industrial Curvature Index, which uses Fisher–Rao geometry and Ollivier–Ricci curvature on county adjacency graphs to characterize regional economic structure. The unifying thread is geometric: shape, curvature, and topology as primary instruments of measurement.
Gregory Villines brings a background in pattern recognition and signals analysis to that work. He served as a signals intelligence specialist in the U.S. Air Force, and later as a network analyst at the National Security Agency.
There, multi-hop link analysis, anomaly detection, and the disciplined study of structure in noisy, high-dimensional data became core craft. That lineage runs through everything Villines Research produces — from econometric studies to encryption architecture.
Curvature, topology, and the geometry of data structure.
Applied to labor markets, economic systems, and time-series signals.
Behavioral economics and the structure of regional economies.
Novel encoders and embeddings for machine learning.
KV-cache quantization and compression at scale.
Compact models, learned compression, and anomaly detection.
Applied cryptographic systems and secure design.
Foundational research moves along a full arc — from geometric theory, through peer-circulated papers, to patented and deployable systems.
A learned tokenization system that compresses text far past conventional byte-pair encoders, benchmarked against established baselines.
A high-dimensional embedding architecture developed alongside Glyph, mapping tokens into a geometry tuned for compression and downstream learning.
A benchmark harness and KV-cache quantization toolkit. Norm–direction decomposition quantizes magnitude and unit direction separately; a per-head minimum-cosine diagnostic exposes worst-case collapse hidden by averaged metrics.
A working edge-AI and IoT prototype built on compact models, learned compression, and residual anomaly detection.
An experimental cognitive architecture for persistent memory and autonomous research.
The granted patent anchoring the Villines Helix Encryption system, and the cornerstone of an applied cryptographic line of work — alongside a portfolio of provisional filings covering tokenization and edge-intelligence architecture.
More than a dozen working papers spanning topological data analysis, labor-market econometrics, and behavioral economics. See the catalogue ↗
An Apache-2.0 benchmark harness and norm-direction quantization toolkit for LLM KV-caches — benchmarked across the Qwen, Llama, and Mistral model families.
U.S. Air Force signals intelligence specialist; National Security Agency network analyst — pattern recognition, link analysis, and anomaly detection.
An independent practice applying geometric and topological methods to data structure, machine learning, and economic systems — theory carried through research into patented, deployable work.