# Quantifying analogy of concepts via ologs and wiring diagrams

arXiv: https://arxiv.org/abs/2402.01020 · HTML: https://mlsanity.com/paper/2402.01020/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 1 Feb 2024.

## Builds on (most cited first, 3 of 3)

- [The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits](https://mlsanity.com/paper/1305.0297/) (2013)
- [Can language models learn analogical reasoning? Investigating training objectives and comparisons to human performance](https://mlsanity.com/paper/2310.05597/) (2023)
- [The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes](https://mlsanity.com/paper/1307.6894/) (2013)

## Built on by (most cited first, 2 of 2)

- [From data to concepts via wiring diagrams](https://mlsanity.com/paper/2511.20138/) (2025)
- [Wiring diagram extraction and gluing: a case study in classifying figure skating jumps using 3D dataset](https://mlsanity.com/paper/2607.27598/) (2026)

## Abstract (arXiv)

We build on the theory of ontology logs (ologs) created by Spivak and Kent, and define a notion of wiring diagrams. In this article, a wiring diagram is a finite directed labelled graph. The labels correspond to types in an olog; they can also be interpreted as readings of sensors in an autonomous system. As such, wiring diagrams can be used as a framework for an autonomous system to form abstract concepts. We show that the graphs underlying skeleton wiring diagrams form a category. This allows skeleton wiring diagrams to be compared and manipulated using techniques from both graph theory and category theory. We also extend the usual definition of graph edit distance to the case of wiring diagrams by using operations only available to wiring diagrams, leading to a metric on the set of all skeleton wiring diagrams. In the end, we give an extended example on calculating the distance between two concepts represented by wiring diagrams, and explain how to apply our framework to any application domain.