A Maze With Many Right Answers · Sasini Wickramatunga

Ask a mouse to press a lever for a treat and there is one right answer. Drop a mouse into a big, complicated world and let it look for food, and there are hundreds. The Koay Lab, where I work, is interested in the second kind of problem.

Free-form behaviour

The lab calls these free-form cognitive behaviors: “behaviors that do not have strongly constrained task structures, but where many different ‘solutions’ can be found by animals to satisfy their internal drives.”

Spatial exploration is the classic example. In a rich environment there are many possible places to go next, “and each decision modifies the set of feasible choices in the future”. The lab studies it with free-form spatial exploration tasks for mice in virtual reality, which turns the world itself into something that can be designed.

Why random isn’t good enough

The catch, in the lab’s words: “In environments with more complex obstructed geometries, a blindly random strategy can be highly inefficient in covering space.”

That’s easy to see with a toy. Put a simulated explorer on a grid, let it step to a random neighbouring square each turn, and count how much of the space it has visited. Do it once in an open arena and once in a maze of sixteen rooms joined by narrow doorways:

Two square maps and a chart. Left, an open arena criss-crossed by a random path that already reaches most corners. Middle, a maze of sixteen rooms where the same number of steps leaves whole rooms untouched. Right, percent of space visited against steps taken: the open-arena curve climbs to nearly 100 percent, the maze curve stalls around two-thirds. — A random walker in an open arena and in a maze of rooms. Toy simulation made for this page (40 walks each), not lab data.

Coverage is just a fraction:

C(t) = \frac{\text{squares visited by step } t}{\text{all open squares}}

After this many random steps	Open arena	Maze of rooms
2,000	32%	18%
5,000	64%	34%
20,000	97%	66%

So the interesting question isn’t whether animals explore, but how. The lab wants to know “how animals can use knowledge gathered via exploration to modify the statistical distributions of their future exploration patterns”: in other words, how the walk stops being blind.

Three things a good explorer does

A small four-room maze criss-crossed by a meandering trail, with a question mark in the one room it hasn’t reached — Explore: map the world

The same maze with several nearly identical paths running straight from the start to a gold diamond — Exploit: go straight back

Two identical rooms side by side labelled today and tomorrow, with the gold diamond in a different place in each — Infer: same room, different answer

These are the three core functions the lab names: exploration to form knowledge of world structure, strategic exploitation of located resources, and inference of hidden contexts that may differentiate outwardly similar environmental conditions. The third is the subtle one: two situations can look identical from the outside, and the right move still depends on something you can’t see.