用确定性矩阵运算替代概率采样，实现更可靠的逻辑推理。
DODR: Deterministic Operator-Driven Reasoning in Latent Space
- 将推理建模为潜空间中的确定性矩阵操作，避免逐词采样误差
- 在503个样本上实现99.96%归纳泛化率和72.5%的归因准确率
- 适合需要零幻觉、高可解释性的严谨逻辑任务
自回归大模型将推理视为基于词元的概率采样，导致复杂逻辑推理中存在错误累积、概率替代必然性及线性链信息瓶颈三大缺陷。本文提出潜空间中的确定性算子驱动推理架构（DODR），将推理重构为高维线性代数空间中的推理图计算。推理状态以语义单元（短语或句子）为基本单元的快照向量表示，每一步推理由无采样的确定性矩阵运算完成。皮尔士三类推理被形式化为三个可训练矩阵算子：秩亏演绎算子（信息坍缩）、满秩归纳算子（信息扩展）和基于摩尔-彭罗斯伪逆的溯因算子（信息假设）。证明了该算子集在皮尔士三分法下最小完备，且单个“超算子”无法实现三类推理（秩障碍），推理图具备图灵完备性，收缩反馈流由巴拿赫不动点定理保证收敛。在503个样本（420个去重）的专用与端到端设置中，演绎损失收敛至1.40e-05；归纳达到0.9996泛化覆盖率，20/20硬验证通过反例；溯因解优于随机基线28倍，判断准确率达72.5%（58/80，威尔逊95%置信区间[61.9%, 81.1%]）和81.7%（49/60，CI [70.1%, 89.4%]）；冻结算子在未见跨领域演绎任务上达100%（60/60）表现。该架构提供结构化零幻觉保障与三层持续学习机制。所有数据与代码已公开。
原文摘要 · Abstract (English)
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.
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