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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.20364393 |
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Table of Contents:
- <p>We apply the matrix Amari-Schwarzian trace invariants</p> <p>f_{2k} = tr([U,Q]^{2k}) from Paper 7 (Maino, 2026) to the</p> <p>hidden-state geometry of a transformer language model during</p> <p>autoregressive generation. Three diagnostic findings emerge:</p> <p>(1) a symplectic gauge transition where the odd-trace ratio</p> <p>drops from 0.017 to 0.002 at mid-depth; (2) multi-genus</p> <p>persistence with corr(f_2, f_4) = 0.21–0.39; (3) a damped</p> <p>velocity-Verlet corrector achieving 66% commutator norm</p> <p>reduction.</p> <p>Version 2 extends the framework from diagnostics to control.</p> <p>A GF(2) hybrid engine (direct Gauss-Jordan for n ≤ 256,</p> <p>Method of Four Russians for n > 256, supporting up to 2048</p> <p>variables) validates the logical satisfiability of parsed</p> <p>CFL modules in under 2 µs (AES S-box) to 544 µs (1024-var</p> <p>UNSAT detection). The engine's free-variable count k feeds</p> <p>back into the generation manifold via α_eff = α_base ×</p> <p>(1 + λ·k/n), providing proportional compression of the logit</p> <p>repulsion boundary under high logical entropy. The complete</p> <p>detection–validation–correction loop operates at < 0.01%</p> <p>latency overhead relative to the token forward pass.</p> <p>A correctness contribution is documented: the M4RI intra-block</p> <p>RREF requires a backward elimination pass after forward</p> <p>pivoting to prevent cross-contamination of the lookup table.</p> <p>Without this pass, block pivot rows retain entries from earlier</p> <p>columns, corrupting the 2^k XOR table and producing incorrect</p> <p>solutions. All results verified across 8–2048 variables on</p> <p>sparse random, NTT butterfly, and UNSAT systems.</p>