DODR: Deterministic Operator-Driven Reasoning in Latent Space

The researchers proposed a deterministic operator-driven latent space reasoning architecture called DODR (Deterministic Operator-Driven Reasoning). This architecture reconstructs the reasoning process as reasoning graph calculations in high-dimensional linear algebra spaces, using semantic units rather than word elements as snapshot vector primitives, and implementing reasoning steps through sampling-free matrix operations. Its core includes three trainable operators: rank-deficiency deduction based on Peirce’s triple classification, full-rank induction, and abduction operator based on Moore-Penrose pseudo-inverse. Experiments verified the effectiveness of this architecture using 503 sample records; the results showed that the deductive loss converged to 1.40e-05, the induction generalization coverage reached 99.96%, and the abduction solution was 28 times better than the random baseline. Additionally, the frozen resolver maintained 100% accuracy in unseen cross-domain deduction tasks.