← All parts of this equation

Equation 1 · Part 7 · Ten Failure Modes That Show Up Across Every Frontier Model, Not Just One

subscript

sobserved=scapability+Δcontamination+Δconfigurations_{\text{observed}} = s_{\text{capability}} + \Delta_{\text{contamination}} + \Delta_{\text{configuration}}
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

One assumption threads through everything that follows, and it is worth making explicit before the catalogue starts. A published benchmark score is not a direct read of capability; it is a sum of capability plus at least two other things that vary independently of it: sobserved=scapability+Δcontamination+Δconfigurations_{\text{observed}} = s_{\text{capability}} + \Delta_{\text{contamination}} + \Delta_{\text{configuration}}. Δcontamination\Delta_{\text{contamination}} is inflation from the model having seen the benchmark, or something close to it, during training. Δconfiguration\Delta_{\text{configuration}} is variance from everything about how the question was asked, formatted, and scored — prompt wording, decoding settings, which variant answered. Both terms are provider-specific and time-specific; neither is disclosed by the headline number. Three of…

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

The article lists its research sources here.