# Formalizing the presumption of independence

arXiv: https://arxiv.org/abs/2211.06738 · HTML: https://mlsanity.com/paper/2211.06738/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 16 references that are in the map.
- First posted on arXiv 12 Nov 2022.

## Builds on (most cited first, 1 of 1)

- [Simply Exponential Approximation of the Permanent of Positive Semidefinite Matrices](https://mlsanity.com/paper/1704.03486/) (2017)

## Built on by (most cited first, 8 of 8)

- [Compact Proofs of Model Performance via Mechanistic Interpretability](https://mlsanity.com/paper/2406.11779/) (2024)
- [Using Degeneracy in the Loss Landscape for Mechanistic Interpretability](https://mlsanity.com/paper/2405.10927/) (2024)
- [Benchmarks for Detecting Measurement Tampering](https://mlsanity.com/paper/2308.15605/) (2023)
- [Towards Worst-Case Guarantees with Scale-Aware Interpretability](https://mlsanity.com/paper/2602.05184/) (2026)
- [Research Superalignment Should Advance Now with Alternating Competence and Conformity Optimization](https://mlsanity.com/paper/2503.07660/) (2025)
- [Estimating the expected output of wide random MLPs more efficiently than sampling](https://mlsanity.com/paper/2605.05179/) (2026)
- [Polynomial Precision Dependence Solutions to Alignment Research Center Matrix Completion Problems](https://mlsanity.com/paper/2401.03999/) (2024)
- [Towards a Law of Iterated Expectations for Heuristic Estimators](https://mlsanity.com/paper/2410.01290/) (2024)

## Abstract (arXiv)

Mathematical proof aims to deliver confident conclusions, but a very similar process of deduction can be used to make uncertain estimates that are open to revision. A key ingredient in such reasoning is the use of a "default" estimate of mathbbE[XY] = mathbbE[X] mathbbE[Y] in the absence of any specific information about the correlation between X and Y, which we call *the presumption of independence*. Reasoning based on this heuristic is commonplace, intuitively compelling, and often quite successful -- but completely informal. In this paper we introduce the concept of a heuristic estimator as a potential formalization of this type of defeasible reasoning. We introduce a set of intuitively desirable coherence properties for heuristic estimators that are not satisfied by any existing candidates. Then we present our main open problem: is there a heuristic estimator that formalizes intuitively valid applications of the presumption of independence without also accepting spurious arguments?