Thesis · 9 Jul 2026 · 2 min

Shared context is shared bias

Tree-of-thought widens the frontier and carries the same anchor down every branch. Isolation is not a prompt you write, it is a property you enforce.

Udit Akhouri · architecture · divergence

Every method that claims breadth eventually has to answer one question: are the branches actually independent, or do they merely look different?

Tree-of-thought expands a frontier, but each node is conditioned on the path that produced it. The tree gets wider without getting more independent. If the root commits to a framing, every leaf inherits it — you have paid for $N$ candidates and received one idea in $N$ costumes.

Independence, stated properly

Call each branch a sample $c_{i}$ drawn under a frame $f_{i}$ . What we want is not just variety in the outputs, but low correlation between them:

ρ (c_{i}, c_{j}) \to 0 for all i \neq = j

You cannot get there by asking for it. A prompt that says "consider several very different approaches" produces one distribution with wider variance, not several distributions. The context is still shared, so the anchor is still shared.

The only reliable lever is structural: give each branch its own context window and its own frame, and let none of them observe the others until they are done.

// Each branch gets a frame and an empty context. Nothing is shared until the
// critic pass, by which point every candidate is already committed to paper.
const branches = FRAMES.map((frame) =>
  generate({
    stimulus,
    frame,
    context: [],
  }),
);
 
const candidates = await Promise.all(branches);

That is the whole trick, and it is deliberately boring. context: [] is doing more work than any amount of prompt engineering above it.

Why the frames are strange on purpose

The fifteen frames are not fifteen personas. They are fifteen constraints — a regulator, a biologist, a speedrunner, a ten-year-old, a zero-budget build. A frame is useful in proportion to how much it forbids.

Frames that are merely flavourful — "be creative", "think differently" — do not change what the model can reach. Frames that are restrictive move the sample into a different region entirely, which is the only thing that lowers $ρ$ .

This is the failure mode the harness is built against.

Fig. B — one context, scanned repeatedly. Breadth without independence: the frontier widens but the anchor does not move.

The cost, stated plainly

Isolation is expensive. You run $N$ generations where a single-shot run does one, and most of them get pruned. On a problem with a known answer that spend buys nothing — see the eval note for the case we lost.

The argument for paying it is narrow: when there is no known answer, the first plausible direction is not evidence, and committing to it early is the most expensive mistake available. Everything downstream inherits it, and no amount of subsequent reasoning revisits the choice that framed the reasoning.

We publish the harness before we train the model, so this claim stays checkable.

[ ← All writing ]