THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913050370506752 |
|---|---|
| author | Li, Augustus Haoyang |
| author_facet | Li, Augustus Haoyang |
| contents | We present THEIA, a 2.75M modular neural architecture that learns the complete Kleene three-valued logic (K3) truth table from task data without external symbolic inference or hand-encoded K3 gate primitives. Across 5 seeds, THEIA achieves all 39 K3 rules at >99% per-rule accuracy. K3 learnability is not the central finding: Transformer baselines also reach >99% on all 39 rules, and flat MLPs match THEIA on Phase-1 accuracy within 0.04pp. The central findings are two properties of the learned system.
(1) Uncertainty-verdict asymmetric propagation. The network preserves Has-Unknown at every upstream boundary (80.0/91.1/90.8/99.7% across Arith/Order/Set/Logic vs. ~52% majority) while final-verdict decodability stays at or below a 73.4% U-vs-non-U oracle reference under linear and nonlinear MLP probes. Activation patching on non-absorbent T->U configurations flips 4,898/4,898 OR pairs (4,719/4,719 AND) across 5 seeds, ruling out residual shortcuts.
(2) Reliability spectrum under discretized end-to-end training, on task structures decomposable along the engine boundaries. A mod-3 sequential composition task generalizes from 5- to 500-step eval at 99.96+-0.04% (5 seeds). Under identical Gumbel-softmax training, flat MLPs collapse to chance by 50 steps; a 2x2 ResMLP depth x expansion grid reaches >=99% on only 3/20 (config, seed) trials; a pre-LN Transformer reaches 99.24+-0.34%. The 500-step figure is dominated by straight-through discretization preventing 0.999^500 compounding; the architectural separator is sustaining Phase-1 accuracy under Phase-3 end-to-end Gumbel training, where flat MLPs fail.
Auxiliary: under matched optimizer settings THEIA reaches 12/12 Kleene coverage 6.5x faster than a parameter-comparable 8L Transformer; the ratio narrows to ~3.6x under Transformer-standard tuning. We did not perform a THEIA-optimal sweep; ratios are specific-config, not asymptotic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11284 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture Li, Augustus Haoyang Machine Learning Artificial Intelligence Logic in Computer Science We present THEIA, a 2.75M modular neural architecture that learns the complete Kleene three-valued logic (K3) truth table from task data without external symbolic inference or hand-encoded K3 gate primitives. Across 5 seeds, THEIA achieves all 39 K3 rules at >99% per-rule accuracy. K3 learnability is not the central finding: Transformer baselines also reach >99% on all 39 rules, and flat MLPs match THEIA on Phase-1 accuracy within 0.04pp. The central findings are two properties of the learned system. (1) Uncertainty-verdict asymmetric propagation. The network preserves Has-Unknown at every upstream boundary (80.0/91.1/90.8/99.7% across Arith/Order/Set/Logic vs. ~52% majority) while final-verdict decodability stays at or below a 73.4% U-vs-non-U oracle reference under linear and nonlinear MLP probes. Activation patching on non-absorbent T->U configurations flips 4,898/4,898 OR pairs (4,719/4,719 AND) across 5 seeds, ruling out residual shortcuts. (2) Reliability spectrum under discretized end-to-end training, on task structures decomposable along the engine boundaries. A mod-3 sequential composition task generalizes from 5- to 500-step eval at 99.96+-0.04% (5 seeds). Under identical Gumbel-softmax training, flat MLPs collapse to chance by 50 steps; a 2x2 ResMLP depth x expansion grid reaches >=99% on only 3/20 (config, seed) trials; a pre-LN Transformer reaches 99.24+-0.34%. The 500-step figure is dominated by straight-through discretization preventing 0.999^500 compounding; the architectural separator is sustaining Phase-1 accuracy under Phase-3 end-to-end Gumbel training, where flat MLPs fail. Auxiliary: under matched optimizer settings THEIA reaches 12/12 Kleene coverage 6.5x faster than a parameter-comparable 8L Transformer; the ratio narrows to ~3.6x under Transformer-standard tuning. We did not perform a THEIA-optimal sweep; ratios are specific-config, not asymptotic. |
| title | THEIA: Learning Complete Kleene Three-Valued Logic in a Pure-Neural Modular Architecture |
| topic | Machine Learning Artificial Intelligence Logic in Computer Science |
| url | https://arxiv.org/abs/2604.11284 |