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Equation 1 · Part 9 · Evaluating Trajectories, Not Answers

subscript

τ=(s0, (a1,o1), …, (an,on), sn)\tau = \big(s_0,\ (a_1, o_1),\ \dots,\ (a_n, o_n),\ s_n\big)
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

A language model evaluation is, structurally, a function from a prompt to a string. Grading the string may be very hard, but the object being graded is small, static, and fully observed. An agent produces something categorically larger. The natural unit of observation is a trajectory: τ=(s0, (a1,o1), …, (an,on), sn)\tau = \big(s_0,\ (a_1, o_1),\ \dots,\ (a_n, o_n),\ s_n\big). an initial environment state, an ordered sequence of actions with the observations they returned, and a terminal state. Everything that separates a competent run from a lucky one lives in the middle terms. A conventional success indicator reads only the last one.

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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.