# A Quantitative Definition of Intelligence

arXiv: https://arxiv.org/abs/2604.10873 · HTML: https://mlsanity.com/paper/2604.10873/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 57 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Analogies Explained: Towards Understanding Word Embeddings](https://mlsanity.com/paper/1901.09813/) (2019)

## Abstract (arXiv)

We propose an operational, quantitative definition of intelligence for arbitrary physical systems. The intelligence density of a system is the ratio of the logarithm of its independent outputs to its total description length. A system memorizes if its description length grows with its output count; it knows if its description length remains fixed while its output count diverges. The criterion for knowing is generalization. A system knows its domain if a single finite mechanism can produce correct outputs across an unbounded range of inputs, rather than storing each answer individually. The definition places intelligence on a substrate-independent continuum from logic gates to brains. We then argue that meaning over a domain is a selection and ordering of functions that produces correct outputs where correctness is specifiable. We also define a measure of contextuality of an output as the inverse of its conditional Kolmogorov complexity given the context of prior outputs, which unifies correctness and independence into a single condition. Together, these refute Searle's third premise, that syntax is insufficient for semantics, over any domain where correctness is specifiable.