Equation 16 · Part 2 · Comparing the Main Approaches to AI Memory Systems and the Bandwidth Wall
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
with L layers, H key/value heads, head dimension, b bytes per stored element and T tokens of context — a quantity that scales linearly with context length and batch size, and has to be both stored somewhere and streamed through the arithmetic units on every generated token. Pope and colleagues showed that partitioning strategies which shrink the key/value representation, such as multi-query attention, can extend the usable context length by up to 32 times for a fixed memory budget, precisely because they attack the capacity term of that formula without touching the bandwidth term [ 11 ] . Kwon and colleagues showed the complementary move on the software side: treating the KV cache as…
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
- [11] Efficiently Scaling Transformer Inference ↗
- [12] Efficient Memory Management for Large Language Model Serving with PagedAttention ↗
These citations provide research context; check each source for the exact claim it supports.