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Equation 17 · AI Memory Systems and the Bandwidth Wall in 2035: Scenarios, Signals, and Falsifiable Predictions

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Hkv⋅dhH_{\mathrm{kv}} \cdot d_h

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HkvH_{\mathrm{kv}}

Symbol H_kv

HkH_kv is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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dhd_h

Symbol d_h

the head dimension.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

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.

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Peer-reviewed evidence, three different levers. DeepSeek-V2 replaces full multi-head keys and values with a low-rank latent projection — reducing HkvH_{\mathrm{kv}} ⋅\cdot dhd_h to a much smaller compressed dimension — and reports a 93.3 percent reduction in KV-cache size relative to the company’s own prior 67-billion-parameter dense model, while extending supported context to 128,000 tokens [ 15 ] . That shrinks the per-token cost of the equation above. StreamingLLM instead shrinks effective S : it keeps only a small window of recent tokens plus a handful of initial “attention sink” tokens, and reports enabling stable generation over sequences up to four million tokens with up to a 22.2-times…
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Peer-reviewed evidence, three different levers. DeepSeek-V2 replaces full multi-head keys and values with a low-rank latent projection — reducing HkvH_{\mathrm{kv}} ⋅\cdot dhd_h to a much smaller compressed dimension — and reports a 93.3 percent reduction in KV-cache size relative to the company’s own prior 67-billion-parameter dense model, while extending supported context to 128,000 tokens [ 15 ] . That shrinks the per-token cost of the equation above. StreamingLLM instead shrinks effective S : it keeps only a small window of recent tokens plus a handful of initial “attention sink” tokens, and reports enabling stable generation over sequences up to four million tokens with up to a 22.2-times speedup over recomputing a sliding window from scratch [ 14 ] . H2O shrinks S adaptively rather than with a fixed window, formulating cache eviction as a submodular optimization that keeps a mix of recent tokens and empirically important “heavy hitter” tokens, and reports throughput improvements of up to 29 times over baseline serving systems when retaining only 20 percent of tokens as heavy hitters [ 16 ] . Three different research groups, three different terms in the same equation, converging on the same conclusion: the cache is too large to leave alone.

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