Equation 45 · Part 1 · The Economics and Physical Limits of Running AI Agents at Scale
Symbol m
What this part means
the number of steps.
Its job in the formula
m is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Full expression→Symbol m→Article meaning
Where the article explains it
Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed segment length m , not quadratic.
The passage around this formula
Compaction and editing are not free, and the model above shows why they earn their keep anyway. Reset the accumulated history to a small fixed-size summary of s tokens every m steps, and the trajectory becomes a sequence of n/m short quadratic segments instead of one long one: each segment’s own retransmission cost scales with , but the number of segments scales with n/m , so the total across the whole trajectory scales with m n — linear in n for a fixed…
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.