Lab notes

Choosing the first falsification target

The first serious test of the framework will be recovery: established model families have to drop out of the substrate definition as limiting cases. The two targets are associative memories, which should appear when the field dynamics are driven to relaxation, and diffusion processes, which should appear when entropy production dominates transport.

The reasoning is economic. Recovery is the cheapest test that can kill the framework outright. If the definitions cannot reproduce what already works, they are wrong, and it is better to learn that from a month of derivation than from a year of building on top of it.

Both targets are tracked against the test sequence in the research program. Neither is claimed.

Why waves

A field is an unusual candidate for a learning substrate, so the reasons belong on the record. Superposition lets one medium carry many signals at once. Interference computes correlations passively, inside the propagation itself, at no cost beyond it. Conservation laws and locality act as built-in regularizers: the dynamics cannot invent energy and cannot act at a distance, which excludes whole classes of pathological solutions before training begins.

The honest gap is the learning rule. Gradient descent does not obviously survive translation into a physical process. Equilibrium propagation shows that relaxation dynamics can carry correct gradients in energy-based settings; whether anything comparable holds for wave dynamics is an open question of this program, not an assumption behind it.

The fragments already exist

A reading pass through the lineage confirms a pattern: the field keeps touching the same foundation without picking it up. Landauer made computation physical in 1961. Hopfield made inference relaxation in 1982. Sohl-Dickstein and colleagues built generative modeling on nonequilibrium thermodynamics in 2015. Hughes and colleagues trained a physical medium to classify signals as waves pass through it in 2019. Ramsauer and colleagues showed in 2020 that transformer attention coincides with a modern Hopfield update, which means the dominant architecture has been an energy method all along, unrecognized.

Each result is treated as a curiosity inside its own subfield. Read together, they are entries in one ledger. The program's bet is that the ledger closes: one framework in which all of them are consequences. The full list, with references, is in the research program.

What counts as a derivation

The word carries the whole program, so it gets a definition before anything else does. A derivation must satisfy four conditions. The assumptions are stated and countable. Every step can be checked by someone who is not its author. Established systems appear as special cases when the general structure is restricted. And the result disagrees with current practice somewhere a numerical experiment can settle.

Anything that fails one of these conditions is an analogy. Analogies are good for finding directions and useless for holding weight, and this distinction is where the program intends to be hardest on itself.