ICML 2026 Tutorial · 2.5-hour overview

Unifying Attention and Diffusion with Kan Extension Transformers

Structured Deep Learning with Diagrammatic Backpropagation

A tutorial on building trustworthy foundation-model systems using Diagrammatic Backpropagation (DB), Kan Extension Transformers (KET), Infinitesimal Causality (IC), Universal Decision Learning (UDL), and Topos World Models.

Abstract

Modern foundation models are powerful, but their representations, training dynamics, and agentic workflows remain difficult to audit, compose, and trust. This tutorial presents a categorical and geometric framework for trustworthy foundation-model systems, unifying Diagrammatic Backpropagation (DB), Kan Extension Transformers (KET), Infinitesimal Causality (IC) , Universal Decision Learning (UDL) , and Topos World Models for structured foundry construction.

We interpret KET broadly: not only as a model architecture for attention-like computation, but as a principle for extending local evidence, skills, representations, and behaviors across contexts while preserving compatibility constraints. In this view, trustworthy foundation models are admitted artifacts: systems whose claims, skills, latent causal structures, and outputs are checked against typed evidence, restriction maps, obstruction signals, and promotion gates.

The tutorial is designed as a conceptual overview. Technical details are deferred to associated arXiv papers and the Categories for AGI book, while the demos provide an accessible path into the framework.

Tutorial Plan

Part	Theme	Focus
1	Why categorical structure?	Local truth, gluing, obstruction, and accountable foundation-model artifacts.
2	DB and Geometric Transformers	Diagrammatic learning signals, relational representations, and structured credit assignment.
3	Kan Extension Transformers	Attention, diffusion, representation transport, and cautious transfer across contexts.
4	Foundry construction	Democritus, Prometheus, Odyssey, TICKET admission, SkillOpt, BRIDGE, and SKFM.

Slides and Artifacts

Tutorial slides (updated June 29)

Static demo console
Date/Time: July 6, 9:00 - 11:30 a.m. Location: Hall C, Seoul, South Korea.

Demo Track

Causal claims

Democritus and Odyssey

Extract causal PSR cells, preserve uncertainty, and admit only claims that pass TICKET-style guardrails.

Skill learning

SkillOpt

Optimize a Markdown admission skill using rollout, reflection, validation gates, and held-out diagnostics.

Latent refinement

BRIDGE / SKFM

Use latent causal transport and spectral refinement to expose obstructions and guide trustworthy transfer.

The static demo console is designed to be uploaded as a self-contained tutorial artifact. If this page is hosted on the UMass site, place the console at icml-2026-ket-demo-console/index.html or update the link above.

Technical Resources

Contact

Instructor: Sridhar Mahadevan · Email: mahadeva@cs.umass.edu