{"slug": "dodr-deterministic-operator-driven-reasoning-in-latent-space", "title": "DODR: Deterministic Operator-Driven Reasoning in Latent Space", "summary": "A new arXiv paper (2609.04782v1) introduces DODR, a Deterministic Operator-Driven Reasoning architecture that replaces token-level probabilistic sampling in autoregressive LLMs with deterministic matrix operations in latent space, reporting deduction loss convergence to 1.40e-05, induction generalization coverage of 0.9996 with 20/20 hard vetoes, abduction solutions exceeding random baseline by 28x with judgment accuracies of 72.5% and 81.7%, and 100% accuracy on unseen cross-domain deduction with frozen operators. The authors claim a structural zero-hallucination guarantee and release all data and code.", "body_md": "arXiv:2609.04782v1 Announce Type: new \nAbstract: Autoregressive (AR) large language models formulate reasoning as token-level probabilistic sampling, which induces three fundamental defects in complex logical reasoning: error accumulation, probability substituting necessity, and the linear-chain information bottleneck. This paper proposes the Deterministic Operator-Driven Reasoning in Latent Space architecture (DODR), which reconstructs reasoning as reasoning-graph computation in a high-dimensional linear-algebraic space. Reasoning states are represented as snapshot vectors whose primitives are semantic units (phrases or sentences) rather than tokens, and each inference step is a deterministic matrix operation with no token sampling. Peirce's three inference types are formalized as three trainable matrix operators: a rank-deficient deduction operator (information collapse), a full-rank induction operator (information expansion), and an abduction operator defined as the Moore-Penrose pseudo-inverse of deduction (information hypothesizing). We prove that the operator set is minimal and complete given Peirce's trichotomy, that no single \"super-operator\" can realize all three types (a rank obstruction), and that reasoning graphs are Turing-complete with contractive backflow converging by Banach's fixed-point theorem. Experiments on 503 sample records (420 deduplicated samples) across dedicated and end-to-end settings show: deduction loss converges to 1.40e-05; induction achieves 0.9996 generalization coverage with 20/20 hard vetoes on counterexamples; abduction solutions exceed the random baseline by 28x with judgment accuracies of 72.5% (58/80, Wilson 95% CI [61.9%, 81.1%]) and 81.7% (49/60, CI [70.1%, 89.4%]); frozen operators attain 100% (60/60) on unseen cross-domain deduction. The architecture provides a structural zero-hallucination guarantee and a three-layer continual-learning mechanism. All data and code are released.", "url": "https://wpnews.pro/news/dodr-deterministic-operator-driven-reasoning-in-latent-space", "canonical_source": "https://www.machinebrief.com/news/dodr-deterministic-operator-driven-reasoning-in-latent-space-qxsg", "published_at": "2026-09-07 04:00:00+00:00", "updated_at": "2026-09-07 04:56:41.393329+00:00", "lang": "en", "topics": ["artificial-intelligence", "large-language-models", "ai-research"], "entities": ["arXiv", "DODR", "Peirce", "Moore-Penrose", "Banach"], "alternates": {"html": "https://wpnews.pro/news/dodr-deterministic-operator-driven-reasoning-in-latent-space", "markdown": "https://wpnews.pro/news/dodr-deterministic-operator-driven-reasoning-in-latent-space.md", "text": "https://wpnews.pro/news/dodr-deterministic-operator-driven-reasoning-in-latent-space.txt", "jsonld": "https://wpnews.pro/news/dodr-deterministic-operator-driven-reasoning-in-latent-space.jsonld"}}