Abeliuk Institute

A system can be fully specified and still not be understood. We know every weight in a trained network and every rule of an evolving population, and we still cannot say from the specification alone what either will do — where the behaviour changes character, which part of it is necessary and which is an accident of how it was built. That gap between having the rules and knowing the behaviour is not a gap in our record-keeping. It is the subject.

The Institute exists because the tools for closing it already exist in physics, and have not yet been pointed at the systems that now matter most. We are a small group doing that work, and we fund undergraduate research grants for people who want to do it with us.

computed at load

Fig. I — One line of arithmetic, x ↦ r x(1 − x), iterated for 1,024 values of r. Nothing in the rule names the doubling, and no amount of reading it tells you where the order ends. We are a small research group working on systems of this kind — where the behaviour cannot be recovered from the specification — at the point where they turn up in learning theory, statistical physics and the theory of computation.

Scope

Modern machine learning produced a class of objects that behave like physical systems and are studied like them: they have phases, thresholds, order parameters and collective behaviour that no line of their code mentions. We think the useful theory of these objects is closer to statistical mechanics and dynamical systems than to software engineering, and that is the bet the Institute is set up to test.

The work is theoretical, with simulation used as the experiment. The output is proofs, models and small reproducible numerical studies — not products.

RK4 · 26,000 steps

Fig. II — Two integrations of the same three equations, started 10⁻⁵ apart. Every constant is shared; the histories are not. Determinism is not predictability, and the gap between them is measurable — it has a rate, a horizon and a cost in bits. Much of what is called unreliability in learned systems is this, and asking a model to be more careful will not close it.

seeded · BFS labelling

Fig. III — A lattice occupied at p ≈ p_c, its clusters labelled by exhaustive search; the largest is inked dark. Just below this density the picture is dust, just above it is a single sheet, and the change is not gradual. Capability arriving suddenly with scale is the ordinary behaviour of systems near a threshold — the interesting question is never whether it happens, but which parameter the threshold is in.

marching squares · 17 levels

Fig. IV — A non-convex surface, contoured, with two descents begun 0.15 apart. They end in different valleys at different depths — and in a real network the choice of valley, not the depth reached, is most of what decides whether the thing generalises. Why a procedure this blind works as well as it does is, we think, the central open problem in the subject.

How we work

MethodSmall problems stated precisely, carried to a theorem or to a simulation whose code is short enough to read. A result that cannot be reproduced on one machine is treated as a conjecture.
FormPreprints and correspondence. We collaborate with university groups and with people working inside industrial labs who have questions their roadmap will not let them chase.
FundingPrivately funded, which is why the register is short and the topics are chosen for interest rather than fundability.
GrantsWe fund small research grants for undergraduates with a question of their own — open call, read as they arrive.
EnquiriesSerious enquiries, including from students looking for a problem, are welcome — use the form below.

Correspondence

Notes, counterexamples, objections and enquiries reach the Institute here. We read everything that arrives and answer what we can.