PYTHON · NUMPY

Computation as relaxation

Solve the same problem twice — once by executing a fixed sequence, once by letting a system settle into a low-energy state — and compare what each one costs.

01Challenge

Pose a small constrained decision as an energy landscape and let it settle. Count the operations each approach needs.

Predict firstGreedy settling on 16 coupled variables — how close to brute force will its operation count be?

02Model

An energy-based model does not execute a recipe. It defines a landscape and falls into a good answer. That distinction matters for energy because settling can be done by physics itself: a circuit that relaxes, a spin system that anneals, a memory array that sums currents. The arithmetic becomes a side effect of the material rather than a sequence of fetches. This is why Toshiba's settling machines already hold a real record — microsecond constrained decisions in production — while the efficiency prize remains open.

03Guided practice

1. Pose the landscape. Define an energy function over a small binary decision problem.

2. Settle it. Descend the energy greedily and watch it fall.

3. Count. Compare the operation count against brute-force enumeration, and note that a physical settling machine pays for the descent with physics rather than with fetches.

04Feedback

PASS WHEN PASS when the settled energy is clearly below the starting energy and your operation count is far below 2^16.

If your run fails, check:

If the energy does not fall, check the flip condition: flip variable i when s[i] and its local field disagree in sign.
The point is not that greedy descent is optimal. It is that a good answer is reachable by falling downhill rather than by enumerating.

05Retrieve & space

What does an energy-based model do instead of executing a fixed sequence?
Why is settling attractive for energy specifically, not just for speed?
Which capability record does physical settling already hold?

06Mastery & project

You can pose a constrained decision as an energy landscape, settle it, and explain why relaxation maps onto physical substrates in a way a matrix multiply does not.

Find a decision problem in your own work and write its energy function. If you can pose it, a settling substrate can in principle run it.

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PYTHON · NUMPY

Computation as relaxation

Solve a constrained decision two ways and compare the cost.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you