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Published equation contexts

Hverify  =  ∑i=1mhiH_{\mathrm{verify}} \;=\; \sum_{i=1}^{m} h_i

Why this formula appears here

A simple model makes the scaling problem legible. Let a verified circuit claim require passing m distinct checks — faithfulness under intervention, completeness against the behavior it is meant to fully explain, minimality against components that turn out not to matter — and let each check take hih_i researcher-hours, including the false starts a competent skeptic would force. Total verification cost per claim is Hverify  =  ∑i=1mhiH_{\mathrm{verify}} \;=\; \sum_{i=1}^{m} h_i . and the field’s own most careful examples put each hih_i measured not in minutes but in dedicated researcher-days once ambiguity has to be resolved rather than merely observed. If a frontier model implements even a low four-figure count of distinguishable,…

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HverifyH_{\mathrm{verify}}

Symbol H_verify

HvH_verify is part of the quantity the equation computes from the expression on the right.

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ii

Symbol i

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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mm

Symbol m

m appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

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i=1i=1

Starting index or lower bound: i=1

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

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mm

Ending index or upper bound: m

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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How to interpret it

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Research cited beside this formula

Published contexts (1)

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Hverify  =  ∑i=1mhi,H_{\mathrm{verify}} \;=\; \sum_{i=1}^{m} h_i ,

Equation 23 · AI Research

What Interpretability Actually Costs to Do at Scale

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A simple model makes the scaling problem legible. Let a verified circuit claim require passing m distinct checks — faithfulness under intervention, completeness against the behavior it is meant to fully explain, minimality against components that turn out not to matter — and let each check take hih_i researcher-hours, including the false starts a competent skeptic would force. Total verification cost per claim is Hverify  =  ∑i=1mhiH_{\mathrm{verify}} \;=\; \sum_{i=1}^{m} h_i . and the field’s own most careful examples put each hih_i measured not in minutes but in dedicated researcher-days once ambiguity has to be resolved rather than merely observed. If a frontier model implements even a low four-figure count of distinguishable,…

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