# Topological Void Analysis A Mathematical Framework for Systematic Technical Innovation Discovery in Knowledge Spaces

arXiv: https://arxiv.org/abs/2607.00005 · HTML: https://mlsanity.com/paper/2607.00005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 20 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)

## Abstract (arXiv)

Identifying where to innovate in a dense technical domain - such as operating systems or hardware/software co-design - is fundamentally a search problem in a high-dimensional knowledge space. Existing approaches rely on keyword search, citation proximity, or human intuition, none of which formalise the notion of an unexplored region that is simultaneously relevant to a target goal and absent from prior art. We present Topological Void Analysis (TVA), a mathematical framework that defines topological voids as triads (A, B, C) in a dense-sparse hybrid embedding space. A void requires three conditions: (i) both concepts A and B are semantically cohesive with domain anchor C; (ii) their pairwise similarity falls within a calibrated marginality band - avoiding both obvious combinations and unrelated noise; and (iii) they share a sparse lexical bridge while the geodesic midpoint on the embedding hypersphere is unoccupied. Applied to ~140k indexed documents, TVA generates 2,128 invention candidates across 96 targets; 90% survive automated quality filtering, yielding 191 REVISE and 1 APPROVE verdict from four-specialist adversarial review (0.05% end-to-end). Two case studies demonstrate the framework surfaces non-obvious connective tissue rather than merely obvious related pairs.