Today’s frontier models need more resources than exist. meu needs a fraction of the data, and runs on the computers you already have.
1 · puzzles to learn from
Learning the rule, not the pattern
Traditional architectures, unless very large, struggle with abstract reasoning.
meu is a new foundational model, based on topos theory. We use it to let machines learn abstraction from first principles.
As a toy example, let’s compare two small instances of meu and a transformer respectively. We’ll test them on something akin to an IQ test: Raven matrices. We will use these matrices as a comparative litmus test for the meu architecture, since solving them requires at least some degree of abstract reasoning ability.
meu goes about it in its own way: it first builds a language for the problem (a DSL), then learns in it.
The answer, in place.
The ninth cell is the mystery cell. Its contents are determined by the contents of prior cells in the grid. One of the eight pictures below belongs there.
The goal: choose the right picture and, for extra credit, state the actual rule all cells follow.
2 · learning
Live: a minimal, but still realistic transformer
We’ve been getting a lot of attention recently, so there might be a queue to our server.
transformer waiting…
For it to have a fighting chance at success, let’s give it 3,000 finished examples to work with.
≈ J of energy
starting…
A minimal meu, on the same task and the same server
meu waiting…
Let’s give 30 examples to meu (as opposed to 3,000).
≈ J of energy
starting…
In meu’s own language, a row of the thirty reads:
3 · new puzzles
Both side by side, on twenty-four new puzzles
To test whether either model has mastered abstraction, we’ll throw them a curve ball. In the training matrices, sizes, shades and positions changed in patterns, but the shapes never did. This exam also switches up the shapes, so solving it takes actual abstraction.
transformer
puzzles to learn from
processor time to learn
energy to learn
new puzzles solved
what it keeps
meu AB · demo
meu
puzzles to learn from
processor time to learn
energy to learn
new puzzles solved
what it keeps
4 · the extra credit
The actual rule
For the purposes of both demonstration and protecting the meu core IP, we will omit some mathematical detail pertaining to how the underlying topos-theoretic structures are being generated. Rather, let’s focus on the resultant artifacts: meu generates a vocabulary of functions over the sorts of the task at hand. These are subsequently used to learn the internal logic of the problem, its rules.
Crucially, the transformer is not able to articulate the actual rule of the puzzle. With a fraction of the resources at its disposal, meu has correctly identified the rules which govern the puzzle in first order logic (FOL):
Puzzles and pictures: A-I-RAVEN (M. Małkiński and J. Mańdziuk, IJCAI 2025; data), Creative Commons licence, panels rearranged. Built on RAVEN and I-RAVEN.