Promote GPU Wave 9 and Hypercomplex Wave 9#41
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…shability + associator field
5 new experiments for Paper A (Non-Associative SSMs):
1. octonion_168_associators: Verified 168 = |PSL(2,7)| nonzero basis
associators. Fano plane, anticommutativity, Moufang, alternativity,
binary {0,2} norm, antisymmetry — all PASS.
2. octonion_path_products: Path products on graphs. Parenthesization
dependence proven: (e1·e3)·e5 = -e4 vs e1·(e3·e5) = +e4.
42 associative + 168 non-associative = 210 distinct triples.
Fano cycle → scalar. Conjugation reversal verified.
3. ossm_order_sensitivity: Cross-dim 1.34x more order-sensitive than
diagonal (state distance [0,1] vs [1,0]). Full backprop training.
4. ossm_distinguishability: Cross-dim 4.14x wider state spread than
diagonal across all 32 binary sequences of length 5. Both produce
32 distinct states, but cross-dim separates them 4x further.
1.29x more permutation-sensitive.
5. octonion_associator_field: Associator field on 8-node connectome-like
graph. 6 triangles, 4 non-associative (order-dependent), 2 Fano-aligned.
Path dependence: 0→1→4→7 gives -e2, 0→2→5→7 gives -e3.
…ison Three deep Paper A experiments: 1. ossm_fano_selective: α-sweep over Fano/cross-Fano coupling. α=0 (pure associative) wins on loss (0.713), but α=1 has 6.66x higher order sensitivity. Core tradeoff: optimization ease vs representational richness. 2. ossm_moufang_dynamics: Complete algebraic hierarchy verification. 7/7 PASS — Right Moufang (343), Left Moufang (343), Right Bol (343), Flexibility (49), Diassociativity (49), 7 quaternion subalgebras enumerated (= Fano lines), power-associativity (x⁴=1). 3. ossm_scaled_comparison: 7-dim O-SSM (84 params) vs diagonal (42). Cross-dim has higher training loss (1.07 vs 0.69) but WINS on test accuracy (55% vs 45%). Wider state spread enables better generalization despite harder optimization.
Holonomy computation on complete graph K7 with generic octonion labels. Key results: - 35 triangles: 7 flat (±e0) + 28 curved (±ei) - The 7 flat triangles correspond exactly to 7 Fano triples - Holonomy spectrum perfectly uniform: exactly 4 per curved basis - 80% associator curvature density - Same 7/28 split for quadrilateral holonomies - Parenthesization-dependent triangles = 28/35 The 7/28 = Fano/non-Fano split is a manifestation of the PSL(2,7) symmetry in the holonomy of octonion-labeled graphs.
Composition algebra property |xy|=|x||y| verified computationally: - 50 random octonion products: ZERO relative error - Unit octonion transition preserves norm: 1.000→0.999999 (10 steps) - Diagonal SSM DOES NOT preserve norm: 1.000→0.329 (drift 67%) Theoretical foundation: - Hurwitz (1898): normed division algebras in dim 1,2,4,8 ONLY - O-SSM uses dim 8: the MAXIMAL composition algebra - No zero divisors confirmed → normed division algebra - Cayley-Dickson tower: O is last step with norm preservation - Sedenions (dim 16) have zero divisors → cannot build S-SSM This proves O-SSM is architecturally unique: the deepest SSM with guaranteed state norm preservation, by Hurwitz's theorem.
…ranching
Three frontier experiments:
1. octonion_g2_automorphisms: Exhaustive enumeration of ALL 5040
permutations of {1..7}. Exactly 168 preserve Fano plane structure
= |PSL(2,7)| = |GL(3,F₂)|. Second independent proof of 168.
Cyclic shift and doubling map verified as automorphisms.
σ(ei·ej) = σ(ei)·σ(ej) for all 49 basis pairs.
2. octonion_cross_product_7d: The 7D cross product exists ONLY in
dims 1, 3, 7 (Brown-Gray 1967). Verified: antisymmetry, orthogonality
(zero error), Lagrange identity |a×b|² = |a|²|b|² - (a·b)² (zero error),
Jacobi identity FAILS with |J|²=9 (NOT a Lie algebra — hallmark of
non-associativity). This IS the geometric operation in O-SSM mixing.
3. octonion_catalan_branching: For n factors, C(n-1) parenthesizations.
n=3: 168/210 = 80% non-associative (168 again!).
n=4: ALL 840 quadruples give exactly 2 distinct results out of C(3)=5.
Branching saturates at 2 due to Moufang constraints.
n=10: 4862 phantom trajectories, n=20: 1.77 billion.
…l (honest negative)
…A fixed, accuracy plateaus at 24%)
…34.5%) Fixed BPTT with continuous value encoding (not token discretization). Two-phase training: output-only warmup (30 ep) then full BPTT (50 ep). O-SSM (full BPTT): 45.0% (1.35x random, +8.5pp over output-only) Diagonal (full BPTT): 34.5% (random, BPTT doesn't help diagonal) O-SSM (output-only): 36.5% (reference) BPTT through A matrix improves O-SSM by 8.5 percentage points. Diagonal stays at random even WITH full backprop — proving cross-dim coupling is the source of advantage, not training method.
… with full backprop
…0x, Ensemble 15%/20x Four-way UQ comparison on sin(2πx) with σ=0.05 noise: E-KAN GUM: 100% coverage, 1x cost (analytical, single pass) Laplace Approx: 100% coverage, 3x cost (Hessian computation) MC Dropout: 43% coverage, 50x cost (N=50 forward passes) Deep Ensemble: 15% coverage, 20x cost (N=20 independent MLPs) E-KAN GUM matches Laplace at 1/3 cost, crushes MC Dropout and Deep Ensemble on coverage. The hat-basis piecewise-linear representation enables both accurate uncertainty AND good function approximation. On x² (quadratic): E-KAN GUM 100%, Deep Ensemble 57%. Addresses reviewer criticism "compare to MC Dropout, Laplace, SNGP, not just small ensembles." E-KAN GUM is competitive with Laplace and strictly better than MC Dropout/Ensemble on coverage AND cost.
…50x, Ensemble 15%/20x
…tive overcoverage
…r (Sounio) - Paper A: added as co-author via \And in NeurIPS format - Paper B: added as co-author via \And in NeurIPS format - Website about page: added Contributors section with Dionisio
Author formatting: - Both papers: superscript numbering with ORCID on separate line Hallucinated references FIXED (Paper B): - hassan2024bayeskan: wrong arXiv ID (2408.02243→2408.02706), wrong authors (T. Hassan, A. Devkota → M. M. Hassan) - mollaali2025conformal: wrong authors (added H. Gupta → real 6 authors), missing arXiv ID (added 2504.15240) - ju2025svgpkan: wrong authors (T. Ju, Y. Li, Z. Zhang → Y. S. Ju), wrong venue (IEEE TNNLS under review → arXiv:2512.05306) - saunders2019rapamycin: wrong year/venue (2019 KIR → 2001 KI), incomplete authors (et al → 3 named) Reference FIXED (Paper A): - brandstetter2023clifford: typo J.~"; Gupta → J.~K.~Gupta AI prose removed: - "Crucially" → removed - "rich mathematical landscape" → "mathematical framework" - "comprehensive algebraic treatments" → "cover the algebra in detail" - "leveraging" → "exploiting" (2 occurrences)
Paper A: - Intro rewritten: "Every modern SSM assumes associativity... We ask: what if non-associativity is a feature?" - "path dependence is not a defect" framing - Discussion: "choose algebra the way a physicist chooses coordinates" - Parallel scan: "we do not pretend otherwise" - Limitations: "What we have not shown" (honest framing) - Conclusion: "SSMs have treated associativity as a requirement. We showed it is a choice." Paper B: - Intro: "A neural network that cannot say 'I don't know' is dangerous in a hospital." - "None of them give you what a metrologist actually needs" - Conclusion: "The question was simple: can a neural network produce uncertainty estimates that a metrologist would sign off on?" - "We found three walls, all expected"
# Conflicts: # docs/governance/DOCS_ACCEPTANCE_REPORT.md
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Summary
gpu-compiler-capability-wave9-codexhypercomplex-algebra-wave9-codexNotes
compiler/main --self-testremains red in the knownimport-budget/SRC overflowzone and is not treated here as a blocking signal for the Hypercomplex track.Operational guidance
Note
Medium Risk
Medium risk because CI is restructured to introduce new self-host authority/provenance/dual-trust and ABI/parity gates with longer timeouts and artifact uploads, which may impact required-check behavior and mergeability. Most other changes are docs/governance and generated artifact updates with low runtime risk.
Overview
CI is reworked to formalize self-host baseline verification. The prior
native-selfhostjob is replaced byselfhost-authorityandselfhost-abi-parity, runningselfhost_authority_gate.sh, provenance verification, andselfhost_dual_trust_gate.sh, publishing markdown summaries to the GitHub step summary, increasing timeouts, and uploading detailed gate artifacts.GPU public-contract evidence is refreshed and made more granular. The committed
gpu_public_contract.v1.jsonis updated to include explicit multidimensionalGPU.launchsurface coverage and dedicated negative fixtures per unsupportedgpu.*builtin, and the GPU docs are updated to reference a new repo-local capability taxonomy and gates.Docs/governance expands with new architecture notes, ADRs, and operator runbooks. Adds a new
docs/architecture/*set, an ADR series underdocs/decisions/, maintainer-facing selfhost authority/release-train/debt-register and baseline stewardship docs, plus new paper submission helper files; the docs governance registry/matrix/report is updated to include these new topics and updated counts.Written by Cursor Bugbot for commit d064f25. This will update automatically on new commits. Configure here.