Equation 19 · Cognitive Bias Was the Label; Attention Sink Is the Suspect
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol phi_sink
phink is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
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.
Denominator: SPEM_softmax
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Everything above is a case for treating the architectural account as at least as well supported as the psychological framing. It is not, on its own, a decisive discriminator, and this article’s one genuine contribution is naming and specifying the measurement that would be. Call it the sink-attributable fraction, , defined as . where is Guo and Vosoughi’s own Jensen–Shannon-divergence effect magnitude, measured by their own published protocol, on an ordinary sink-forming model, and is the identical measurement on an architecture- and data-matched twin trained with sigmoid attention…
Read the full surrounding passage
Everything above is a case for treating the architectural account as at least as well supported as the psychological framing. It is not, on its own, a decisive discriminator, and this article’s one genuine contribution is naming and specifying the measurement that would be. Call it the sink-attributable fraction, , defined as . where is Guo and Vosoughi’s own Jensen–Shannon-divergence effect magnitude, measured by their own published protocol, on an ordinary sink-forming model, and is the identical measurement on an architecture- and data-matched twin trained with sigmoid attention instead of softmax — the exact contrast Gu and colleagues’ released training pipeline was built to produce [ 3 ] . The quantity is dimensionless, bounded in the neighborhood of zero to one for any model pair where the sink-free twin is not somehow more position-sensitive than its sink-forming counterpart, and it answers a single, sharp question: of the effect magnitude the original paper measured, how much of it disappears when the one specific architectural mechanism this article names is removed and nothing else changes?
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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