PYTHON · NUMPY

What a landscape holds

Build an energy over the action space and show it represents every valid action simultaneously.

01Challenge

Define an energy with one well per valid route and a barrier at the obstacle, then recover the routes by scanning for minima.

Predict firstYou scan the landscape and count local minima. How many do you expect for two routes?

02Model

Instead of asking a model for the action, ask it for a score over all actions, and agree that low means good. That object is an energy. It does not have to choose, so it can be low in two places at once, and the set of valid actions is simply the set of local minima. Nothing about this is exotic. It is the same move statistical physics makes when it describes a system by its energy rather than by its trajectory, and it is why the 2024 Nobel Prize in Physics went to the Hopfield network and the Boltzmann machine. The cost of the move is that you no longer get an answer by evaluating the model. You get an answer by searching the landscape, and that search is what the rest of this course is about.

03Guided practice

Scan the action axis, evaluate the energy, and collect the local minima.

04Feedback

PASS WHEN You recovered both routes as separate minima of a single function.

If your run fails, check:

One function, two answers. That is the property a point-valued model cannot have.
The squared-error answer sits at high energy, which is the landscape telling you it is bad. The regression model had no way to say so.
Adding a third route means adding a third well. The representation scales with the size of the answer set, not with a choice among them.

05Retrieve & space

What is the set of valid actions, expressed in terms of the energy?
Why does the energy at a equals zero come out high?
What did you give up by moving from a point-valued model to a landscape?

06Mastery & project

Given a set of valid actions, construct an energy whose minima are exactly that set, and verify by scanning.

Write an energy for a decision in your own domain with more than one right answer. Scan it and check the minima are the answers you intended.

GO FURTHER · THE LIVE PLAYGROUND

Open the lottery bench ↗ · One energy landscape, two substrates, and the crossover between them.

← The average of two good answers The policy you already run →

PYTHON · NUMPY

What a landscape holds

One energy function, one scan, and the set falls out.

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