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.
Most of modern machine learning was found by trial and error rather than worked out from theory. ENKAIDU is trying to supply the missing theory, so that the design of a learning system can be calculated from physics and mathematics instead of guessed at.
The research program says 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.
A model family is a guess that might be right, not a starting assumption. 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 treat it as a step along the way, not as an output.
We are not aiming at a run of papers or a product cycle. The plan is to build theory, models, software, and infrastructure in one place over many years, and to keep what is built.
Four things we do not acceptThat an architecture is right because it is popular. That a benchmark score explains anything. That an abstraction is sound because everyone uses it. That a result can be announced before anyone outside the lab can check it.
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 were found by experiment and then made bigger, and they work well enough that the question of why rarely gets asked. Nothing tells us they are the right design. Existing theory can analyze parts of their behavior once they exist, but it did not predict or produce any of them.
Our starting position is that computation and learning are physical processes, subject to laws about entropy and energy like anything else, and that the right designs can be calculated from those laws rather than found by trial. If that works, what comes out will not be a faster transformer. It will be a different sort of system, doing the job a different way.
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 of them 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. The research program says which description we work from and where it gives out.
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 research program 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. Treated as a way of computing in its own right rather than as something to simulate.
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.
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, not as a design to copy.
Open question. Which features of neural computation are forced by physical constraint, and which are accidents of how biology got there.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 rather than on a schedule.
| Date | Note | Kind |
|---|---|---|
| 2026-08-26 | One intelligence, two examples of it | Position |
| 2026-06-02 | Choosing the first falsification target | Decision |
| 2026-04-26 | Why waves | Position |
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.