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Published equation contexts

I=∑i=1nwi si,∑i=1nwi=1I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1

Why this formula appears here

This is also where a composite measure earns its own paragraph, because a composite index is not a repeat measurement of a single-benchmark headline claim — it is a different object. Artificial Analysis, an independent evaluation firm that runs every model it tracks through one fixed harness, reports an “Intelligence Index” built from nine separate evaluations, including Humanity’s Last Exam and GPQA Diamond among others [ 8 ] . A composite index of this kind is, formally, a weighted sum I=∑i=1nwi si,∑i=1nwi=1I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1. where each sis_i is a model’s normalized score on component benchmark i and each wiw_i is a weight chosen by whoever maintains the index. That weight vector is an editorial decision, not a…

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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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nn

Symbol n

n 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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sis_i

Symbol s_i

a model’s normalized score on component benchmark i and each wiw_i is a weight chosen by whoever maintains the index.

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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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nn

Ending index or upper bound: n

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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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.

Read this term in its guide →
nn

Ending index or upper bound: n

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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Research cited beside this formula

Published contexts (1)

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I=∑i=1nwi si,∑i=1nwi=1,I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1,

Equation 1 · AI Industry

What Independent Evidence Actually Supports About Grok's Capabilities

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

This is also where a composite measure earns its own paragraph, because a composite index is not a repeat measurement of a single-benchmark headline claim — it is a different object. Artificial Analysis, an independent evaluation firm that runs every model it tracks through one fixed harness, reports an “Intelligence Index” built from nine separate evaluations, including Humanity’s Last Exam and GPQA Diamond among others [ 8 ] . A composite index of this kind is, formally, a weighted sum I=∑i=1nwi si,∑i=1nwi=1I = \sum_{i=1}^{n} w_i \, s_i, \qquad \sum_{i=1}^{n} w_i = 1. where each sis_i is a model’s normalized score on component benchmark i and each wiw_i is a weight chosen by whoever maintains the index. That weight vector is an editorial decision, not a…

Meanings in this article

  • wiw_i: a weight chosen by whoever maintains the index.
  • sis_i: a model’s normalized score on component benchmark i and each wiw_i is a weight chosen by whoever maintains the index.
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