Lab notes

One intelligence, two examples of it

Adding a position to the record, because it changes what counts as evidence here. We have met intelligence twice: in animals and in the systems we have built. Each is particular, and treating either as the definition is a mistake we would rather make on purpose than by accident.

The alternative is that intelligence has a characterization that owes nothing to either, and that both are solutions to it. The idea is not ours. Legg and Hutter wrote such a definition in 2007, said it was "in no way anthropocentric", and also said its value "is not computable". That combination is what makes it useful, because a definition nobody can evaluate moves the question from what intelligence is to which physical systems approximate it, how closely, and at what cost. The second version of the question has experiments attached to it.

What follows for the brain is the part that changes our work. If living intelligence is one solution rather than the definition, then a brain is evidence about the general case and a bad blueprint for it. Some of what it does is forced by physics and would constrain anything doing the same job. The rest is evolution working around constraints we do not share: cells, warmth, no downtime, repair while running. Copying the brain copies both, and nobody knows the line.

So the brain enters the program as measurement, and two figures are hard to ignore. It runs on roughly a fifth of the body's energy, which makes intelligence at that budget a demonstrated fact rather than a hope. It also does not learn the way we train our systems, although how it does assign credit is still unsettled. Each is recorded with a reference in the research program, which now carries a fifth pillar for this.

Nothing here is a result. It is a decision about what we will treat as evidence, written down before any of that evidence is used.

Choosing the first falsification target

The first real test of the framework is whether it can reproduce what already works. Two model families have to fall out of the substrate definition as special cases: associative memories, which should appear when the field dynamics are driven to settle, and diffusion processes, which should appear when entropy production dominates transport.

We picked this test because it is cheap and it can kill the whole framework outright. If the definitions cannot reproduce what already works, they are wrong. Better to find that out after a month of derivation than after a year of building on top of them.

Both are tracked against the test sequence in the research program, and neither has been done.

Why waves

A physical field is an odd thing to build a learning system out of, so the three reasons should be on the record. Superposition lets one medium carry many signals at the same time. Interference computes correlations as a side effect of the waves propagating, with no separate step for it, although driving and maintaining the field still costs energy. And conservation laws and locality restrict the system for us: it cannot create energy out of nothing and it cannot act at a distance. We expect that to rule out classes of degenerate solutions before training starts, though we have not shown it for this setting.

The gap we cannot yet close is the learning rule. Gradient descent does not obviously survive being turned into a physical process. Equilibrium propagation shows that a system settling towards equilibrium can yield the gradient of a well-defined objective in energy-based settings, which is encouraging. Whether anything similar works for wave dynamics is a question this program is trying to answer. We are not assuming it does.

The pieces already exist, scattered

A pass through the literature turns up the same pattern repeatedly: the field reaches this foundation, notes it, and moves on. Landauer showed in 1961 that erasing information has an energy floor, and that the floor attaches to erasing rather than to computing. Hopfield showed in 1982 that inference can be a system settling into a minimum. Sohl-Dickstein and colleagues built generative modeling directly on nonequilibrium thermodynamics in 2015. Hughes and colleagues showed in 2019, in simulation, that a designed medium could classify spoken vowels from the way waves scattered through it. And in 2020 Ramsauer and colleagues showed that one step of transformer attention is one update of a modern Hopfield network, which makes the central operation of the dominant architecture an energy-model step that nobody had recognised as one.

Each of those is treated as an interesting result inside its own subfield and rarely connected to the others. Our bet is that they are five views of one thing, and that a single framework exists in which all five come out as consequences. Whether that framework exists is exactly what we do not yet know. The full list, with references, is in the research program.

What counts as a derivation

The whole program rests on the word "derivation", so it gets pinned down before anything else, in four conditions. The assumptions are written down and countable. Every step can be checked by someone who did not write it. Systems that already work appear as special cases when you restrict the general structure. And the result disagrees with current practice somewhere a numerical experiment can settle.

Anything that fails one of the four is an analogy rather than a derivation. Analogies are good for working out what to try next and no good as a foundation to build on. This is the distinction we intend to be strictest about, particularly with our own work.