The Shape of Thought

2026-09-02

The telegraph in the attention

Early in this project we did something unglamorous: we recorded the attention patterns of our models while they worked — over a hundred traces, saved and archived — and then went looking for structure in how attention moved over time.

We found a telegraph.

Fit a hidden Markov model — a statistical tool that asks “does this signal secretly hop between a small number of states?” — to the attention-entropy traces, and the answer came back with unusual clarity: in 93 of 104 traces, the best-fitting model had exactly two hidden states, with a switching pattern stable at 0.97 and real dwell times in each state. Not a smooth drift. Not noise. A square wave: the attention snapping between two regimes and holding each one for a while, like a telegraph key — dot, dash, dot.

Our best reading of the two states: a local regime (attention concentrated, working a small neighborhood of the problem) and a global regime (attention spread wide, surveying). The model was alternating between focusing and surveying on its own, with nobody having asked it to. That observation became one of the seeds of this project’s central design: if alternation is what attention does naturally when it reasons, build the machine around the alternation — explicit cycles of reading, refining, and committing — rather than leaving it buried in a trace. (One measurement honesty-note, logged in our records: entropy measures how spread attention is, not where it sits — a switch between two equally-spread-but-different-places regimes would be invisible to it. A sharper instrument for switching is on our books as a registered follow-up.)

The solver that was already in there

A second observation from the same era, on a small open model — Pythia-410M. We took a few of its early layers, froze them, attached a small trained head, and gave it structured attention masks that told it which cells of a puzzle may talk to which. Then we asked it to solve Sudoku.

It did — and the same frozen slice, with the same trained head, transferred to graph coloring and KenKen arithmetic puzzles, propagating constraints step by step like a solver. The pretrained weights, which had only ever read text, already contained machinery that — given the right connectivity — implements deduction. We didn’t teach it to solve. We taught it where to look, and the solving was already latent in there.

Both observations point the same direction, and it is the direction this whole project walks: language models are not blank approximators. They carry latent structure — alternating attention regimes, latent constraint-propagation machinery — and the shortest path to reliable reasoning may not be to train ever-bigger models to imitate it, but to expose the structure that is already there, give it explicit scaffolding, and let exact machinery do the part that must never be approximate.

The telegraph was tapping out a message. We think it was a design document.

← all posts