Figure: a logarithmic time axis running from 10 microseconds to 100 milliseconds, comparing movement against regeneration for a single 5.00 mebibyte KV block, which is 16 tokens of Llama-3 70B under GQA at 320 kibibytes per token. The movement bar spans 43 microseconds at 121 gigabytes per second, through 82 microseconds at 64 gigabytes per second, to 164 microseconds at 32 gigabytes per second. The regeneration bar spans 9 milliseconds at 50 per cent MFU, through 11 milliseconds at 40 per cent MFU, to 18 milliseconds at 25 per cent MFU, for 16 tokens of forward compute. A labelled span between the two reads two to three orders of magnitude. A third, open-ended hatched bar shows that regenerating an arbitrary interior block costs at least 18 milliseconds and potentially far higher, because interior KV is not independently reproducible: hidden states depend recursively on all preceding context. No precise multiple is claimed, because the two quantities do not measure the same operation; 218 times, from 17.9 milliseconds divided by 82 microseconds, is one point inside the range and must always be quoted with those inputs. This is an analytical model. No CXL hardware was measured.
Figure 5.1 · Analytical model
Moving a KV block against regenerating it — per 5.00 MiB block, log scale
Both sides are ranges, because both rest on assumptions rather than measurements. The gap between them is the structural argument for tiering KV state rather than discarding and recomputing it.
Table view
| Operation | Assumption | Cost |
|---|---|---|
| Tier fetch, 5.00 MiB | 121 GB/s (CXL 3.0 ×16 theoretical, one direction) | 43 µs |
| Tier fetch, 5.00 MiB | 64 GB/s (mid-range — unmeasured) | 82 µs |
| Tier fetch, 5.00 MiB | 32 GB/s (pessimistic) | 164 µs |
| Forward compute, 16 tokens | 50% MFU | 9 ms |
| Forward compute, 16 tokens | 40% MFU | 11 ms |
| Forward compute, 16 tokens | 25% MFU | 18 ms |
| Regeneration, arbitrary interior block | recursive dependency on all preceding context | ≥ the above, potentially far higher |
Claim the order of magnitude, not the digit.Pick the optimistic ends of both ranges and the ratio is nearer two orders of magnitude; pick the pessimistic ends and it is nearer three. Any single multiple is an artifact of which two assumptions were chosen. And the regeneration side is a floor: an arbitrary interior block may cost far more, because interior KV is not independently reproducible — a hidden state at position i depends recursively on every token from 0 through i, through every attention layer.
Analytical model — CANONICAL-NUMBERS.md §4. No CXL hardware was measured.