Kan Extension Transformers

KET is structured transport across contexts.

A Kan Extension Transformer has two tutorial roles. It can extend local information into a broader context, and it can pull proposed extensions back against constraints. That left/right pattern is the common thread connecting language modeling, Odyssey foundries, TICKET admission, and UDL.

View Kan-extension diagram Open language-modeling experiment Back to tutorial demo track KET arXiv paper

The Background Story

Before looking at perplexity curves, the audience needs the categorical picture. KET is not just another attention variant; it is a way of moving information through diagrams of contexts while preserving the maps that make those contexts meaningful.

Diagram explaining KET through left Kan extension as rollout and right Kan extension as pullback diagnostics.
Left Kan extension supplies the constructive move: extend local context into candidate global behavior. Right Kan extension supplies the checking move: pull the candidate back through constraints, diagnostics, and obstruction surfaces.

What The Two Moves Mean

1. Local Diagram

Start with partial information: token windows, evidence slices, claims, skills, or policy states.

2. Left Kan Extension

Extend local information into a target context: prediction, rollout, completion, synthesis, or foundry construction.

3. Right Kan Extension

Pull the proposed extension back through constraints: validation gates, evidence maps, and obstruction checks.

Next Layer: Language Modeling

The next drilldown makes the idea concrete with language modeling. There, local contexts are token neighborhoods and the experiment asks whether KET-style transport improves predictive behavior.

Open the language-modeling experiment.

Where KET Reappears

Odyssey Foundries

KET becomes structured completion from local artifacts into durable foundry state.

TICKET Admission

Kan-extension checks certify that admitted artifacts preserve evidence, scope, and obstruction signals.

UDL Semantics

Rollout acts like left Kan extension; pullback diagnostics act like right Kan consistency.