# Language Is an Insufficient Substrate for Quantitative Reasoning, and Consequential Domains Need Large Quantitative Models

arXiv: https://arxiv.org/abs/2609.12105 · HTML: https://mlsanity.com/paper/2609.12105/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

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

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [SENTINEL-RL: Offloading Topological Reasoning from LLM Agents in the Security Operations Center](https://mlsanity.com/paper/2609.04159/) (2026)

## Abstract (arXiv)

The prevailing assumption in applied machine learning is that progress on consequential quantitative decisions such as pricing risk, allocating capital, triaging patients, or containing a network intrusion will follow from progress in large language models (LLMs). A language model is trained on a representation of the world that was produced by human description; description is a lossy encoding of the quantitative record, and the loss is irreversible: no downstream model, at any scale, can recover from a description what the description did not encode. We formalize this as a property of the representation on which a model is trained rather than of the model capacity, and we identify three further properties that consequential settings demand of a model and that a language substrate cannot supply by construction: reproducibility, lineage from every output back to the source records that produced. it, and calibrated uncertainty. We argue that these properties define a distinct model class, which we call the Large Quantitative Model (LQM).