Problem Statement

SBIR/STTR grants (221K records, 1983-2025) contain abstracts describing funded research. The challenge: how to classify this research in a way useful for venture capital analysis?

Existing scientific taxonomies (FoS, MeSH, PACS) speak the language of academia. A physicist understands “Quantum optics > Photon manipulation.” But a VC thinks in terms of “DeepTech > Photonics.”

Research question: Can we build a mapping between scientific and business classifications?

Approach

Tag each grant with two independent taxonomies:

1. Science taxonomy — what field of research
2. VC taxonomy — what investment sector

The result is a density matrix showing how scientific fields map to investment categories.

Taxonomy Selection

Science Layer

Evaluated five sources:

Source	Categories	Coverage	Decision
FoS (UNESCO)	2,232	Broad but outdated	No — lacks AI/ML/Quantum
ASJC (Scopus)	333	Journal-focused	No — not R&D relevant
MeSH (NIH)	2,065	Medical only	Partial — supplement
PACS (AIP)	2,200	Deep physics	Yes — excellent for hardware
arXiv	155	Modern CS/Physics	Yes — modern terminology
OpenAlex	65K	Comprehensive	Yes — Level 1 for gaps

Final composition (3,150 categories):

• PACS for physics/materials/engineering depth (2,147)
• arXiv for computer science and quantitative biology (104)
• OpenAlex Level 1 for general science (71)
• MeSH Level 1+2 for medicine and biology (828)

VC Layer

Custom taxonomy (238 categories) organized by investment thesis:

• 35 top-level sectors (FinTech, DeepTech, SpaceTech, HealthTech…)
• 5 subcategories per sector (uniform coverage)
• 2-level hierarchy with descriptions optimized for embedding quality

Intentional cross-listings exist where technologies span multiple sectors (e.g., “Renewable Energy” under both CleanTech and ClimateTech). These are kept as distinct categories — same technology, different investment thesis.

Cross-Source Validation

Combining multiple taxonomies risks semantic overlap. If PACS “Quantum computing” and arXiv “quant-ph” have near-identical embeddings, one is redundant.

Test: Compute pairwise cosine similarity between all categories from different sources. Flag pairs with similarity > 0.95 as potential duplicates.

Results (3,150 × 3,150 comparisons, cross-source only):

Comparison	Max similarity
PACS vs arXiv	0.71
PACS vs OpenAlex	0.77
PACS vs MeSH	0.84
arXiv vs OpenAlex	0.67
arXiv vs MeSH	0.57
OpenAlex vs MeSH	0.78

No pairs exceeded 0.85. The highest match (0.84) was:

• PACS: “Biological and medical physics > Muscles”
• MeSH: “Medicine > Tissues > Muscles”

These describe the same organ from different perspectives (biophysics vs anatomy) — complementary, not redundant.

Conclusion: The four sources partition scientific knowledge without significant overlap. No pruning required.

Embedding Space Quality

How well do our taxonomies utilize the embedding space? Four metrics characterize this:

Mean Pairwise Similarity — average cosine similarity across all category pairs. High values (~1.0) indicate vectors clustered in a narrow cone; low values (~0) suggest uniform distribution.

Isotropy — measures how uniformly vectors occupy the space. Defined as 1 - mean_similarity. Score of 1.0 means perfectly uniform; 0 means all vectors identical.

Singular Value Spectrum — decomposing the embedding matrix via SVD reveals how information distributes across dimensions. Fewer dimensions for 90% variance = more concentrated information.

Effective Dimensionality — quantifies how many dimensions carry meaningful variance:

$$d_{eff} = \frac{(\sum_i \lambda_i)^2}{\sum_i \lambda_i^2}$$

Comparative Results:

Metric	Science (3,150)	VC (238)	Interpretation
Mean similarity	0.43	0.38	VC better separated
Isotropy	0.57	0.62	VC more uniform
Dims for 90% var	355	108	VC more compact
Effective dims	52.8	54.6	Similar complexity

Both taxonomies show similar effective dimensionality (~53) despite different sizes. The VC taxonomy achieves better separation (lower similarity) and higher isotropy, likely due to more diverse semantic domains (FinTech to BioTech) vs. the more cohesive scientific vocabulary.

Implication: The 3,072-dimensional embeddings are overcomplete — both taxonomies effectively use only ~50 dimensions. Based on this analysis, final embeddings use 1,536 dimensions (text-embedding-3-large with dimensions=1536), reducing storage by 50% while preserving semantic quality.

Embedding Strategy

Text format for embedding preserves hierarchical context:

{level1} > {level2} > {level3} — {description}

Example: "Optics > Quantum optics > Photon manipulation — controlling individual photons for quantum information"

Storage: PostgreSQL with pgvector extension. HNSW indexes enable fast approximate nearest neighbor search (pgvector IVFFlat limited to 2000 dims; HNSW supports 1536).

Expected Output

A matrix where rows are science categories, columns are VC sectors, and values are grant counts:

	DeepTech	HealthTech	SpaceTech
Quantum	1,203	89	445
Genomics	156	4,521	23
Materials	892	234	1,102

This enables:

• Translation between scientific and business language
• Identification of emerging intersections
• Trend analysis over time

Status

• Science taxonomy merged (3,150 categories from PACS, arXiv, OpenAlex, MeSH)
• VC taxonomy prepared (238 categories, 35 sectors)
• Embeddings generated (text-embedding-3-large, 1536 dims)
• Cross-source duplicate validation (no overlaps in science layer)
• Embedding space quality analysis (both taxonomies)
• Taxonomies loaded to PostgreSQL (pgvector + HNSW indexes)
• Grant abstracts embedded (~30h serial, need batch approach)
• Matching pipeline
• Matrix visualization

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Work in progress