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Equation 5 · Part 1 · Why the Physical World Is Harder

Symbol t_sense

tsense+tcompute+tactuate<1f.t_{\mathrm{sense}} + t_{\mathrm{compute}} + t_{\mathrm{actuate}} < \frac{1}{f}.
tsenset_{\mathrm{sense}}

What this part means

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

Its job in the formula

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

The passage around this formula

Language models became substantially more capable by thinking for longer at inference time. That option is bounded on a robot, and the bound is not a matter of taste. A closed-loop controller running at frequency f must complete sensing, computation and actuation within one cycle: tsense+tcompute+tactuate<1ft_{\mathrm{sense}} + t_{\mathrm{compute}} + t_{\mathrm{actuate}} < \frac{1}{f}. The pi-zero model is documented as producing actions at up to 50 Hz for dexterous tasks [ 3 ] , which leaves a 20-millisecond budget for everything. No amount of chain-of-thought fits in 20 milliseconds. Worse, missing the deadline is not merely slow: a controller that arrives late in a contact-rich interaction is acting on a stale world model, and in a stiff contact the resulting force error…

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