摘要 当代人工智能(artificial intelligence, AI)的深层困境不止于算力、数据或模型规模,而在于图灵范式机器把连续的互为因果结构压缩为符号、token、状态或向量之后,必然留下未被当前编码关系吸收的结构余项。 本文在配套元理论论文《自然界的双重宪法:论互为因果、热力学箭头与莫比乌斯本体论》的基础上,将互为因果引入机器智能问题,指出图灵范式 AI 具有两类不完备性:一是形式系统自我编码中的反身不完备性,表现为哥德尔式不完备、图灵式不可判定和停机问题;二是离散编码面对连续世界时的编码适配性不完备,表现为语境余项截断、关系失配和幻觉生成。 基于这一判断,本文以 U 型积分余项级数为数学原型,提出余项换轨机制。机器智能的关键不在于无限延长旧有部分和,而在于越过最优截断区后能够回读被遮蔽的连续余项,并据此重构通项、解释框架和生成关系。由此,幻觉可以被理解为余项处理失衡后的结构性显影;在确定性任务中应被抑制,在创造性任务中则可能被调适利用。 本文据此提出“机器智能源于余项”的核心命题:真正的机器理解来自系统对自身编码过程中必然产生的结构余项的读取、演化与换轨能力。 进一步地,本文将积分型余项延拓到复数域和希尔伯特空间,提出量子化余项的概念,并以经典图灵机和量子协处理器之间的闭环说明经典—量子融合计算的可能方向。在更一般的层面上,本文将这种以图灵式局部计算为内核、以余项读取为回返机制、以换轨重构为通项更新方式的计算形态称为“莫比乌斯环计算范式”,将承载该范式的抽象机器称为“莫比乌斯机”;莫比乌斯环型 AI 则是这一范式在机器智能领域中的具体表现。 由此,本文为大语言模型(large language model, LLM)幻觉治理、具身智能、对齐问题、存算一体、经典—量子融合计算以及通用计算中的无功算力问题提供一种统一的概念框架。 Abstract The deep predicament of contemporary artificial intelligence (AI) does not lie only in computing power, data, or model scale. It lies in the fact that, after Turing-paradigm machines compress continuous co-constitutive causal structures into symbols, tokens, states, or vectors, they necessarily leave behind structural remainders that have not been absorbed by the current encoding relation. Building on the companion metatheoretical paper The Dual Constitution of Nature: On Co-Constitutive Causality, the Thermodynamic Arrow, and Möbius Ontology, this paper introduces co-constitutive causality into the problem of machine intelligence and argues that Turing-paradigm AI has two forms of incompleteness. The first is reflexive incompleteness within the self-encoding of formal systems, manifested in Gödelian incompleteness, Turing undecidability, and the halting problem. The second is encoding-adaptive incompleteness at the application layer, which appears when discrete encoding confronts a continuous world, and which manifests as the truncation of contextual remainders, relational mismatch, and hallucination generation. On this basis, the paper takes a U-shaped integral-remainder series as its mathematical prototype and proposes a mechanism of remainder switching. The key to machine intelligence is not to extend an old partial sum without limit, but to be able, after crossing the region of optimal truncation, to read back the obscured continuous remainder and thereby reconstruct the general term, the interpretive framework, and the generative relation. From this perspective, hallucination can be understood as a structural manifestation of imbalance in remainder processing: it should be suppressed in deterministic tasks, while in creative tasks it may be regulated and used. The paper therefore advances the core thesis that “machine intelligence arises from remainders”: genuine machine understanding emerges from a system’s capacity to read, evolve, and switch tracks on the basis of the structural remainders that are inevitably produced in its own encoding process. Furthermore, this paper extends integral remainders into the complex domain and Hilbert space, proposes the concept of the quantized remainder, and uses the closed loop between a classical Turing machine and a quantum coprocessor to explain a possible direction for classical–quantum fusion computation. At a more general level, the paper calls this computational form—one that takes Turing-style local computation as its core, remainder reading as its return mechanism, and switching reconstruction as its method of updating the general term—the “Möbius-loop computing paradigm,” and calls the abstract machine that carries this paradigm the “Möbius Machine.” Möbius-loop AI is the concrete manifestation of this paradigm in the field of machine intelligence. In this way, the paper offers a unified conceptual framework for hallucination governance in large language models (LLMs), embodied intelligence, alignment problems, compute-in-memory, classical–quantum fusion computation, and the problem of ineffective computing power in general computation.
Wu et al. (Sun,) studied this question.