DODR：隐空间中确定性算子驱动推理

中文摘要 AI 辅助

自回归（AR）大语言模型将推理表述为 token 级概率采样，这在复杂逻辑推理中会引发三个根本缺陷：误差累积、概率替代必然性、以及线性链信息瓶颈。本文提出隐空间中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。推理状态表示为快照向量，其基元是语义单元（短语或句子）而非 token，每一步推理都是无 token 采样的确定性矩阵运算。皮尔士的三类推理被形式化为三个可训练矩阵算子：秩亏的演绎算子（信息坍缩）、满秩的归纳算子（信息扩展）、以及定义为演绎算子摩尔-彭罗斯伪逆的溯因算子（信息假设）。我们证明，基于皮尔士三分法，该算子集是极小且完备的；不存在单一“超级算子”能实现所有三类推理（存在秩障碍）；且推理图具有图灵完备性，其收缩回流通过巴拿赫不动点定理收敛。在专用设置与端到端设置的 503 条样本记录（420 条去重样本）上的实验显示：演绎损失收敛至 1.40e-05；归纳在反例上实现 0.9996 的泛化覆盖率与 20/20 硬否决；溯因解决方案较随机基线高出 28 倍，判断准确率分别为 72.5%（58/80，Wilson 95%置信区间[61.9%, 81.1%]）和 81.7%（49/60，置信区间[70.1%, 89.4%]）；冻结算子在未见跨域演绎上达到 100%（60/60）准确率。该架构提供结构零幻觉保证与三层持续学习机制，所有数据与代码均已公开。

英文摘要

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.

发表机构

• Beijing MQPat Technologies, Co., Ltd.（北京MQ帕特科技有限公司）

机构由 AI 辅助整理，请以论文原文为准。