DODR: Deterministic Operator-Driven Reasoning in Latent Space

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.

arXiv:2609.04782v1 Announce Type: new Abstract: 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.