Equation 15 · Part 2 · How AI Memory Systems and the Bandwidth Wall Actually Work
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
which grows linearly in both batch size and sequence length, with the leading factor of two accounting for storing both keys and values [ 9 ] . That single equation is the whole mechanism: nothing about it is a design choice an inference engineer can simply decline. Extend the conversation, and l grows; serve more requests at once, and b grows; either way grows with it, and Hooper and colleagues note that at sufficiently long context lengths the KV cache — not the model’s weights — becomes the dominant consumer of memory during inference [ 9 ] .
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.