Hyperspherical Semantic Trajectory Analysis: Mapping Technological Diffusion across Academic Preprints, Patent Signals, and Compute Scaling

Hyperspherical Semantic Trajectory Analysis. Mapping Technological Diffusion across Academic Preprints, Patent Signals, and Compute Scaling. By Muhammad Sukri Bin Ramli, from the Asia School of Business. Published on the twenty-fifth of September. No code repository is linked to it.

Macroeconomic productivity measures, Total Factor Productivity among them, notice a technological breakthrough only years after it happens. The lag is built into how they are produced: administrative surveys run at fixed intervals, and national accounts follow their own conventions. By the time a new technology shows up in those numbers, it has long since spread. Anyone who wants to see diffusion as it unfolds needs a faster signal.

Hyperspherical Semantic Trajectory Analysis, HSTA, looks for that signal in text. It is an unsupervised, quantitative method that tracks the diffusion of technology directly from unstructured scientific and commercial writing, rather than waiting for economic statistics to catch up. The premise is that the language of research and of patents moves as a technology moves.

The corpus is thirty thousand filtered document records: academic preprints from arXiv and patent applications from the USPTO. Sentence embeddings from a Transformer are projected onto unit hyperspheres, grouped with Spherical K-Means into eight primary sub-topics, and reduced with UMAP manifold reductions. On that geometry HSTA defines two metrics. The first, Semantic Centroid Vector Drift, follows how vocabulary shifts between sub-corpora from different periods, to spot structural changes of paradigm. The second, Commercialization Offset, compares where density peaks across the two corpora, lining up scientific discovery against intellectual property filings.

The method also connects text to hardware. Quarterly topic volume velocity is linked to physical compute metrics from the Epoch AI database, and Vector Autoregressive F-tests ask whether one series helps predict the other.

That test comes back negative in an informative way. Quarterly paper volume velocity alone does not Granger-cause surges in frontier compute allocation at conventional significance levels. The author reads this as a reason to condition textual signals on physical capital constraints rather than use them alone. On drift, the sub-topics covering Large Language Models and Artificial Intelligence Systems show the highest rate of semantic evolution, with drift metrics of zero point three three two and zero point two three four.

Text moves faster than national accounts, and HSTA is a way of reading that movement with geometry. The negative Granger result is part of the design lesson: talk in papers is a signal, but not one that predicts compute on its own. The author offers the method as an objective, real-time complement to traditional economic statistics, not a replacement for them.