Unifying Attention and Diffusion with Kan Extension Transformers: Structured Deep Learning with Diagrammatic Backpropagation
The slides give the tutorial a linear spine; this console lets you walk the same structure nonlinearly, zig-zagging from categorical ideas to recipes, runs, dashboards, and audit artifacts.
Modern foundation models are powerful, but their representations, training dynamics, and agentic workflows remain difficult to audit, compose, and trust. The tutorial challenge is to build categorical and geometric foundations for trustworthy foundation-model systems, unifying Diagrammatic Backpropagation, Kan Extension Transformers, Infinitesimal Causality, and structured foundry construction using Topos World Models.
Start with the story, then decide how deep to go. Each lane begins with the high-level categorical idea, then opens into recipe-specific drilldowns, figures, metrics, JSON records, dashboards, and audit gates. You do not have to follow the slide order: the console is meant for random-access exploration across the tutorial structure.
Many agents have only local views, but global structure emerges through compatible local actions.
Ant colonies and beehives sustain nests, foraging, allocation, and repair without any single agent knowing the whole global state.
TICKET = Topos Integration using Causal Kan Extension Transformers.
Each demo lane is labeled by the categorical structure it instantiates. First-level pages tell the story; deeper drilldowns name the current computational recipe and expose the evidence trail.
The final ICML tutorial deck will be linked here after the slide refresh is complete and uploaded through the ICML portal.
TICKET: TICKET(icml_2026_tutorial_slides_run)
Target: tutorial_presentation
Categorical lens: restriction of the generic Result Communication foundry to the final ICML tutorial slide deck
Start with KET as left/right Kan-extension transport, then drill down into language modeling, foundry construction, and UDL semantics.
TICKET: TICKET(ket_language_modeling_run)
Target: representation_transport
Categorical lens: Kan extension as structured transport from local token contexts to reusable foundry behavior
scylla_interface.html, language_modeling_details.html, Kan diagram and KET comparison plotsTechnical framework linking Infinitesimal Causality to typed Markdown artifacts with tangent directions. SkillOpt and BASKET/ROCKET appear as two agentic workflow optimizers over this structure.
TICKET: TICKET(markdown_tangent_category_framework)
Target: markdown_tangent_categories
Categorical lens: tangent-category bridge from IC obstruction language to KET/UDL workflow transport
index.htmlFour demo lanes for Chain-of-Toulmin-Thought on sheaf foundries.
TICKET: TICKET(agentic_workflow_catalog_run)
Target: agentic_workflow_catalog
Categorical lens: a catalog-level left Kan extension from tutorial theme to demo lanes
Service-repair foundry from request intake to structurally admitted Odyssey guardrails.
TICKET: TICKET(guardrail_autowiring_run)
Target: operational_decision
Categorical lens: completion of a vague service-agent plan into structural guardrails
Scylla JSON spec to Homer/Athena/Prometheus scaffold benchmark.
TICKET: TICKET(foundry_automation_benchmark_run)
Target: evaluation_harness
Categorical lens: benchmarking whether the model can compute a useful foundry completion
Hand-built sheaf smoke test for local store truth and gluing.
TICKET: TICKET(storefront_static_baseline_run)
Target: operational_decision
Categorical lens: manual baseline for extending local store state into global operational guidance
Large-document filing workflow for section anchors and numeric qualification; useful as a scale vignette, not a live walkthrough of the complete sheaf.
TICKET: TICKET(ten_k_prometheus_run)
Target: institutional_financial
Categorical lens: completion from a corporate filing PDF into an admitted financial evidence slice
Local causal-variation workflow with scoped source-grounded claims; the drilldown shows the Democritus recipe currently used to compute it.
TICKET: TICKET(democritus_prometheus_run)
Target: causal_claims_foundry
Categorical lens: completion from literature manifest to scoped causal research foundry
Universal Decision Learning view of causal-claim admission; start with the abstraction layer, then drill down into the SkillOpt rollout-plus-pullback experiment.
TICKET: TICKET(skillopt_odyssey_causal_claim_run)
Target: causal_claims_foundry
Categorical lens: UDL combines rollout (left Kan) with pullback diagnostics (right Kan); SkillOpt is the current computational recipe
index.html, experiments.html, seed-42.html, seed-43.html, seed-44.html, demo.css, demo.jsProduct feedback workflow with overclaim gates and theme qualification.
TICKET: TICKET(brand_product_prometheus_run)
Target: market_meaning
Categorical lens: completion from customer feedback to qualified brand/product semantics