Equation 18 · Part 2 · OpenAI Model Systems from First Principles: Weights, Post-Training, and Inference Compute
subscript
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.
Full expression→subscript→Article meaning
The passage around this formula
Hoffmann and colleagues then showed that the allocation between N and D at fixed C had been wrong in practice: for compute-optimal training, parameters and tokens should scale in roughly equal proportion, and models of the era were substantially undertrained relative to their size [ 6 ] . That result changed industry practice, but it optimises the wrong objective for a served product. Compute-optimal training minimises loss for a fixed training budget. A commercial system minimises total cost over training and inference, and when Q is very large the third term in dominates. The rational response is to train smaller models for longer than the compute-optimal recipe…
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 →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.