Equation 13 · Part 4 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions
Symbol d_h
What this part means
the head dimension.
Its job in the formula
is an input to the expression that computes the quantity on the left.
Full expression→Symbol d_h→Article meaning
Where the article explains it
For a model with L layers, key-value heads, head dimension , sequence length S , batch size B , and p bytes stored per element, the cache occupies approximately .
The passage around this formula
…in-flight generation — its key-value cache — grows linearly in exactly the variables that make serving expensive: sequence length and batch size. For a model with L layers, key-value heads, head dimension , sequence length S , batch size B , and p bytes stored per element, the cache occupies approximately . bytes, the leading factor of two accounting for keys and values together. That equation is worth writing out because it exposes the one real lever every mitigation below…
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 →
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Sources cited in the article section
- [15] DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model ↗
- [14] Efficient Streaming Language Models with Attention Sinks ↗
- [16] H2O: Heavy-Hitter Oracle for Efficient Generative Inference of Large Language Models ↗
These citations provide research context; check each source for the exact claim it supports.