Audio note: this article contains 629 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

Last week, ARC released a paper called Towards a Law of Iterated Expectations for Heuristic Estimators, which follows up on previous work on formalizing the presumption of independence. Most of the work described here was done in 2023.

A brief table of contents for this post:

What is a heuristic estimator? (One example and three analogies.)
How might heuristic estimators help with understanding neural networks? (Three potential applications.)
Formalizing the principle of unpredictable errors for heuristic estimation (the technical meat of the paper).

In "Formalizing the Presumption of Independence", we defined a heuristic estimator to be a hypothetical algorithm that estimates the values of mathematical expression based on arguments. That is, a heuristic estimator is [...]

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Outline:

(04:56) What is a heuristic estimator?

(05:31) Example: Sum of sixth digits of square roots

(07:11) Analogy #1: Proof verification

(08:36) Analogy #2: Conditional expectation

(09:38) Analogy #3: Subjective probabilities and estimates

(11:43) How can heuristic estimation help us understand neural networks?

(14:16) Mechanistic anomaly detection

(16:33) Safe distillation

(19:28) Low probability estimation

(21:37) Formalizing the principle of unpredictable errors

(22:50) The subjective approach: Iterated estimation and error orthogonality

(26:37) Challenges with the subjective approach

(28:43) The objective approach: Accuracy

(35:28) Challenges with the objective approach

(36:14) Estimating the product of jointly normal random variables

(41:07) Estimating the permanent of a matrix

(44:21) Conclusion

The original text contained 19 footnotes which were omitted from this narration.

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First published:
October 7th, 2024

Source:
https://www.lesswrong.com/posts/QA3cmgNtNriMpxQgo/research-update-towards-a-law-of-iterated-expectations-for

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“Research update: Towards a Law of Iterated Expectations for Heuristic Estimators” by Eric Neyman

LessWrong (30+ Karma)