Ex luto ad astra. From mud to the stars.
No dominant architecture in modern machine learning has been worked out end to end from a physical or mathematical starting point. Parts were reasoned, and the rest was found by experiment and then made bigger. ENKAIDU is building the theory that was skipped, starting from entropy, energy, and wave dynamics, so that the design of a learning system can be calculated rather than guessed.
The lab starts from the physical laws that limit any computer and works out on paper which designs for a learning system those laws allow. The designs that hold up in a small numerical test are the ones we then build.
Machine learning can build systems that nobody is able to explain, and closing that gap is what this lab works on.
Transformers, diffusion models, and the variants around them work well enough that the question of why rarely gets asked. Existing theory can analyze parts of their behavior once they exist, but it did not predict or produce any of them, and nothing tells us they are the right design.
Our starting position is that computation and learning are physical processes, subject to laws about entropy and energy like anything else. If the right designs can be calculated from those laws, what comes out would be a different sort of system from a transformer, built on different principles.
There is a larger question behind that one. We have seen intelligence in two forms, living brains and the models we have built, and both are particular. If intelligence can be described mathematically without reference to either, then each is one solution to that description rather than the thing itself. Descriptions like that already exist. The best known, published by Legg and Hutter in 2007, cannot actually be calculated, which sounds like a dead end and is not one. It means the useful question stops being what intelligence is, and becomes which physical systems get close to it, how close, and at what cost in energy and time. Those are questions you can run an experiment on. Note 005 sets out the position and what it changes about how we treat the brain.
Thermodynamics, statistical mechanics, and information theory put hard limits on any learning system, whatever it is made of. Those limits are narrow enough to be useful: they rule out large classes of design before anyone writes code, which is what makes them a place to start.
Energy landscapes, wave equations, and entropy functionals are used here as the actual mathematical objects a model is built out of. They are not illustrations of how a model behaves or analogies for explaining it afterwards.
Brains are the only systems everyone agrees are intelligent, which makes them easy to mistake for what intelligence is. We read them the other way round, as one implementation that physics arrived at under constraints no designer would have chosen. That makes a brain evidence about the general case and a poor blueprint for it.
A piece of theory is finished when it produces something that runs: a design, a procedure, or a prediction an experiment can check. Until it does, it stays on the list of things in progress.
The work splits into five areas: the thing that does the computing, the mathematics that describes it, the physical limits on it, what happens when a system has to model itself, and what the brain, the one working example any of us can measure, says about the other four. Each one below carries a question we currently cannot answer. The full research program, linked below, covers all five in detail, with the methods and the tests.
Using physical processes to compute: a wave spreading out, a system settling into its lowest-energy state, entropy increasing. Interference stores as well as computes, which is what a hologram does. We treat it as a way of computing in its own right.
Open question. Which useful computations a physical system can perform just by settling or by letting waves interfere, and what that costs in time and energy once the field has to be generated and maintained.What complexity theory, information geometry, and topology say about learning: what shape a set of models has, and what that shape makes easy or impossible.
Open question. Which of those structures make learning tractable, and which make it hopeless.What running a computation costs in energy and heat, how much of that is unavoidable, and how close real machines get to the floor physics sets.
Open question. How much more energy a real system uses than physics says it must, and what it would take to close that gap.What a system needs in order to represent its own workings without running into contradiction, and what that representation costs it in energy and time, counted the same way as any other computation.
Open question. Which mathematical structures let a system hold a model of itself without that model collapsing into contradiction.The brain is the one working example anyone can measure. It runs on about a fifth of the energy a body uses. It signals in spikes, it is noisy, and it never comes to rest. It does not learn the way our systems do, and how it does assign credit for a mistake is still unknown. We read all of this as measurement from a physical system that already solved the problem.
Open question. Which features of neural computation are forced by physical constraint, and which are accidents of how biology got there.The research areas say what we are trying to find out. These four rules say how we go about it: what we refuse to assume, what we count as evidence, and what has to happen to a result before we treat it as real.
We treat a model family as a guess that might be right. When theory or experiment stops supporting one, we drop it. That includes anything we come up with ourselves.
Scoring well on a benchmark does not mean anyone understands why. For any result we want to be able to say why it holds: from the mathematics, from a measurable physical limit, or from a mechanism someone can point at and check.
A theoretical result that cannot change how a system is designed or how it runs is unfinished. We count it as a step along the way.
The plan is to build theory, models, software, and infrastructure in one place over many years, and to keep what is built. That is a longer horizon than a run of papers or a product cycle.
Two more things we do not acceptThat an abstraction is sound because everyone uses it. That a result can be announced before anyone outside the lab can check it.
Working notes from the program, each one dated: positions we have taken, decisions about method, things we have read, and approaches that did not work. They go up when there is something to record.
| Date | Note | Kind |
|---|---|---|
| 2026-08-26 | One intelligence, two examples of itWhy a brain counts here as evidence about intelligence in general and as a poor blueprint for it. | Position |
| 2026-06-02 | Choosing the first falsification targetThe framework first has to reproduce associative memory and diffusion as special cases, and neither has been done. | Decision |
| 2026-04-26 | Why wavesThree reasons to build on physical fields, and the learning rule we cannot yet supply. | Position |
Founder. Lead researcher, Ising machines.
ML/AI researcher and engineer with a focus on neuromorphic and physics-inspired computing, especially Ising machines, wave-based computation, entropy-driven learning, and novel computational architectures.
That work sits directly in the first research area, computing with waves and energy, since a Hopfield network is an Ising model with couplings that were learned rather than fixed.
Researchers in mathematical physics, information theory, and computational science, and engineers who can build the systems this work needs.
Send finished work rather than a CV. A derivation, a proof, a simulation, or a system that runs.
The work runs from formal theory through numerical experiment to systems engineering, and a lot of it falls between those labels. What helps is either working across more than one of them or being deep enough in one to push it forward. When you write, include something you have actually finished. We will read that before anything else, and it counts for more than where you have worked or studied.