The Cost of the Loop: What a sense is worth, and how many runs before a difference is real
PAI-320 establishes what a body carries below its first transducer. This course prices it. You will put a joule figure against each of four sensor channels, separate the two halves of a robot's energy bill and find that only one of them scales with the world, settle a two-tier architecture question with arithmetic before building it, and write a disclosure that refuses every field your measurement cannot support.
▶ Start the course ← All coursesWhere this sits, and what moves it.
Binding constraint · What a machine spends looking. Task energy on a body is reported as compute against everything else, and sensing sits inside the second half undifferentiated even though it is measurable on the same meter. The size that bill has to be is set earlier still, by the pivot stiffness of the body, which is a mechanical quantity fixed before any perception exists.
Sensor suites were specified by capability and then a power budget was found for them. Cost of transport priced the motors and left compute out of its own numerator; the inference benchmarks priced the silicon and left the body out of their scope. Nothing put a joule figure against a single sensor channel.
This course prices four channels in joules against the region each buys, measures compute and actuation separately across a thirteenfold change in disturbance, and measures its own instrument: at sixteen seeds the bench cannot resolve the effects it reports, and two of its published results were withdrawn for exactly that. What this review did not locate is a curriculum in any language that teaches the energy of the loop rather than of a datacentre or an industrial trajectory.
A body whose compute draws through its own instrumented rail, so the three terms can be read apart rather than modelled apart. The precondition is not more sensors; it is a shunt and a named barrier, which is what a student leaves this course able to specify.
Every hard thing was impossible until the constraint that made it impossible was named. How we read a frontier →
What a sense is worth
Price each sensor channel in joules per unit of region, and establish whether a bench resolves its own effects.
- L3Which sense is the best buy?Attitude channels cost about a third of what the cart-position channels cost per read. Per unit of certified region bought, attitude is:Price every sensor set in joules per unit of region bought, and identify which vector is cheaper.→
- L4How many runs before a difference is real?A bench reports task error 1.078 against 0.973 from sixteen seeds, with a per-episode spread of 0.25. What is that result?Compute the standard error of a bench comparison and decide whether an effect the bench reports is resolved by its own sample.→
Constant power, moving focus
Separate the two halves of the energy bill, and show that cheapness follows from neither rate nor extent.
- L3Does a harder world cost more energy?Raise the disturbance on a balancing robot by a factor of thirteen. Compute energy does what?Measure compute and actuation separately across a thirteenfold change in disturbance and say which one scales.→
- L3How can a layer be vast and cheap at the same time?In this loop the cheap path runs more often AND uses more of the state than the expensive one. What does that tell you about cost?Separate rate, extent and cost for the two paths in this loop, and show that cheapness follows from neither of the other two.→
Allocation, and the arithmetic that settles it
Derive the break-even for a two-tier stack and establish whether deliberation earns its cost on a given body.
- L4When does a fast/slow split stop paying?A cascade's break-even hit rate depends on which of these?Derive the break-even hit rate from the cost ratio alone, then sweep the gate cost and check the formula against measured energy.→
- L4Does a longer horizon ever make deliberation worth it?A deliberative planner costs up to 1440 times a one-dot-product law. Sweeping its horizon from 0.12 s to 1.20 s on a cart that relocates in about a second, when does it track better?Sweep the rollout horizon on two bodies and establish whether deliberation ever beats a one-dot-product law.→
The receipt
Say what a measurement can honestly claim, and write a disclosure that refuses the rest.
- L3What can a single energy total honestly claim?Two allocation designs read within a few percent of each other on total joules. What can a wall meter conclude about their compute?Find two architectures with nearly the same total energy and different splits, and say what a wall meter can conclude about them.→
- L4What should a disclosure refuse to state?An energy claim reports compute measured at the mains, a region of 0.94 with no barrier named, an effect of 0.03 from sixteen seeds, and a twelve percent architectural difference on a part with an eighty percent idle floor. How many of its four fields are supportable?Implement the refusal rules for an energy disclosure and run them against two claims, one supportable and one not.→