Machine learning & physics
Where, and what.
The calculations physicists most want — neutron-star interiors, collisions as they unfold — are throttled by one step: producing the sample configurations everything else is measured on. They are blocked by algorithms, not by missing physics, and the long-run aim here is a network cheap enough to stand in for the expensive part of that, most of the time. This paper is an early step toward it. Should a network treat a point of the grid and the value the field carries there as one kind of node, or two? That sounds like housekeeping. The measured cost of skipping it is the sharpest result in the paper.
The bottleneck is making the samples
The samples are field configurations on a grid of chopped-up spacetime, drawn in proportion to how likely the theory says they are. Near a tipping point each new one nearly repeats the last, a slowdown this toy can cure and the theories with quarks and gluons cannot. There the costly step is the arithmetic that decides whether to keep each proposal, and it can be arranged so a cheap scorer costs speed, never correctness.
Hand it one configuration and out comes one number: the action, which fixes how likely that configuration is. It does not create configurations or replace the simulation that made them. For this toy theory the action is also a one-line formula — deliberately: with the exact answer in hand, a flawed description of the physics shows up as a number, not an argument.
Two kinds of node
A field is not an object sitting somewhere: it has a value at every point, and one full set of those values is one configuration. As far as the literature goes, published approaches use one kind of node — a grid point with the field value stapled on.
- Latticewhich point is where, and which points touch
- Fieldthe value carried at that point
- A field value links only upward, to the point it belongs to — never sideways to another field value.
Each round of information spreading averages a node with its neighbours. The grid is identical everywhere and in every configuration, so everything that tells one configuration from another sits in the field values point by point — exactly the detail averaging destroys. QFT-Graph gives the field value a node of its own, linked to its grid point but never to another field node, so it reaches the answer intact rather than through a wire bolted past the network.
A new kind of field would be a new kind of node, not a redesign. That is motivation, not yet a result.
The strongest result is a negative one
The single-node version has a structural failure. Each round of information spreading washes out more of the field signal: on a scale where 1 is perfect agreement, predictions fall from 0.9995 after one round to 0.009 after six, unless a shortcut is bolted on. The two-node design holds above 0.999 at every depth without one.
Trained at 16-by-16 on a two-dimensional toy theory, the model predicts the action to within 0.05%. A model trained at that one size and never retrained holds to within 0.10% from 8-by-8 up to 64-by-64, a 64-fold change in volume. The edges are rough. One of five runs at 64-by-64 stalled at 0.910 inside the fixed budget. And where the action passes near zero the relative error blows up — 10.3% at a held-out setting inside the range it trained on, 19.5% past its edge — even though the ranking of configurations stays near-perfect there.
Where it stands
The paper is under peer review at Machine Learning: Science and Technology — submitted, past editorial screening, now with referees. No decision yet, nothing published, and it is not on any preprint server. Quarks are planned, not built. One independent researcher, no funding, data generated on a laptop CPU and training measured in minutes on a single free-tier cloud GPU; the manuscript discloses Claude assistance with the code, analysis, figures, and drafting.
Find the hidden structure in something that looks like noise and make it legible: that is how we like to build at Mentalis. This is that habit pointed at physics.