Modular Neural Networks Learn Three-Valued Logic Without Symbolic Solvers
THEIA demonstrates that dedicated domain engines enable neural networks to master Kleene three-valued logic and generalize compositionally to sequences 100x longer than training.
THEIA, a modular neural system, learns complete three-valued logic end-to-end and generalizes to sequences far longer than training data.
- — Four specialized engines (arithmetic, order, set, propositional) feed into a final logic module for Kleene K3 coverage.
- — Trained on 2M samples; achieves all 12 K3 rules in ~8 minutes across five independent runs.
- — Generalizes from 5-step sequences to 500-step evaluation at 99.97% accuracy via modular structure.
- — Flat MLPs collapse to chance-level performance by 50 steps; modularity is causally necessary.
- — Mechanistic probing shows upstream engines delay truth-value commitment until the logic boundary.
- — Transformer baseline reaches similar accuracy through different representational dynamics (contraction-then-expansion).
- — Activation patching confirms 100% causal control over OR and AND outputs via logic engine.
Astrobobo tool mapping
- Knowledge Capture Record the paper's core claim (modularity enables compositional generalization) and the three architectural patterns it compares (modular, flat MLP, Transformer). Tag with your domain to surface when similar trade-offs arise in your own system design.
- Focus Brief Summarize the mechanistic finding (delayed verdict at logic boundary) in one paragraph. Use this as a reference when designing multi-stage inference pipelines to decide whether to commit to intermediate conclusions or defer them.
- Reading Queue Queue the paper's appendices (especially F and G) for deeper study of Transformer vs. modular performance curves. This informs capacity planning for your next architecture experiment.
Frequently asked
- Kleene three-valued logic (K3) extends classical true/false reasoning to include a third state: unknown or undefined. This models real-world scenarios where information is incomplete or contradictory. THEIA learns K3 to demonstrate that neural networks can handle uncertainty without external symbolic solvers, using four domain-specific engines that converge on a final logic module.
cite ▸
APA
Augustus Haoyang Li. (2026, April 17). Modular Neural Networks Learn Three-Valued Logic Without Symbolic Solvers. Astrobobo Content Engine (rewrite of arxiv/cs.AI). https://astrobobo-content-engine.vercel.app/article/modular-neural-networks-learn-three-valued-logic-without-symbolic-solvers-f0027a
MLA
Augustus Haoyang Li. "Modular Neural Networks Learn Three-Valued Logic Without Symbolic Solvers." Astrobobo Content Engine, 17 Apr 2026, https://astrobobo-content-engine.vercel.app/article/modular-neural-networks-learn-three-valued-logic-without-symbolic-solvers-f0027a. Based on "arxiv/cs.AI", https://arxiv.org/abs/2604.11284.
BibTeX
@misc{astrobobo_modular-neural-networks-learn-three-valued-logic-without-symbolic-solvers-f0027a_2026,
author = {Augustus Haoyang Li},
title = {Modular Neural Networks Learn Three-Valued Logic Without Symbolic Solvers},
year = {2026},
url = {https://astrobobo-content-engine.vercel.app/article/modular-neural-networks-learn-three-valued-logic-without-symbolic-solvers-f0027a},
note = {Astrobobo rewrite of arxiv/cs.AI, https://arxiv.org/abs/2604.11284},
}