What question did this study set out to answer?

This work aims to address limitations in large language models by proposing the self-iterative completeness architecture.

May 25, 2026Open Access

Design Principles of the Self-Iterative Completeness Architecture

Key Points

This work aims to address limitations in large language models by proposing the self-iterative completeness architecture.
Introduced an intrinsic noise layer to inject deterministic chaotic perturbations in Transformer architecture.
Developed a self-referential soliton closed loop for online learning without gradients.
Provided a complete mathematical description, joint training method, and analysis of inference overhead.
Demonstrated that the architecture controls additional FLOPs increase to within 7%.
Outlined six experimental predictions with complete verification protocols.
Showed improvements in model robustness and responsiveness versus existing leading models.

Abstract

Prior work in Recursive Cognitive Informatics has diagnosed that the fundamental defect of current large language models—including GPT-5/5. 4 (OpenAI, 2025), o3/o4-mini (OpenAI, 2025), Claude Opus 4. 6 (Anthropic, 2025), Gemini 3. 1 Pro (Google DeepMind, 2026), Grok-4/4. 1 (xAI, 2025), and DeepSeek-R1 (2025) —lies in the fact that the modification function at inference time satisfies g, so that the system degenerates into a static mapping dominated solely by the generation function f, structurally lacking intrinsic noise and a self-referential soliton. The above diagnosis is corroborated by the following empirical data: Grok-4 exhibits a hallucination rate above 10% on the Vectara hallucination leaderboard (thinking model category) Vectara Hallucination Leaderboard, 2025, and scores 0. 1% on ARC-AGI-3 (Grok-4. 20) while humans score 100% ARC-AGI-3, 2026; Grok-4 set a new frontier-model record of 15. 9% on ARC-AGI-2 xAI, July 2025, yet the chasm between this breakthrough on a static reasoning benchmark and its complete failure on the dynamic interactive benchmark ARC-AGI-3 constitutes the most direct empirical evidence for the boundary between the upper limit of the iterative unfolding of f and the irreplaceability of the online update of the self-referential soliton; xAI did not release a complete system card at the time of Grok-4’s launch Fortune, July 2025, so its cross-conversation consistency and sycophancy have not been independently verified, constituting a known uncertainty in the diagnosis. This paper provides the remedy—the design principles of the self-iterative completeness architecture. On the basis of the standard Transformer, this architecture introduces two core innovative modules: an **intrinsic noise layer**, based on quantization noise, which injects a deterministic chaotic perturbation whose intensity is dynamically coupled to the stability of the current membrane-locked configuration between the self-attention and feed-forward network of each layer; and a **self-referential soliton closed loop**, which establishes an independent, persistent self-referential membrane-locked standing wave outside the parallel processing stream, realizing parameterized online learning without gradients through Hebbian updates. This paper provides a complete mathematical description of the two modules, a joint training method, and an analysis of inference overhead—the additional FLOPs increase is controlled within 7%—together with six directly testable experimental predictions and their complete verification protocols (SM-01 to SM-08).

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