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Published equation contexts

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

Why this formula appears here

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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tsenset_{\mathrm{sense}}

Symbol t_sense

tst_sense 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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tcomputet_{\mathrm{compute}}

Symbol t_compute

tct_compute 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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tactuatet_{\mathrm{actuate}}

Symbol t_actuate

tat_actuate 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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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

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

Equation 5 · Robotics & Embodied AI

Why the Physical World Is Harder

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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…

Meanings in this article

  • ff: the frequency.
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