Asymptotic Semantic Collapse in Hierarchical Optimization

• URL: http://arxiv.org/abs/2602.18450v1
• Date: Sun, 01 Feb 2026 00:02:01 GMT
• Title: Asymptotic Semantic Collapse in Hierarchical Optimization
• Abstract summary: Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics.<n>We study this effect under the name Asymptotic Semantic Collapse in Hierarchical Optimization.<n>We show that repeated interactions with Peripheral Agent Nodes drive an alignment that minimizes a global loss.
• Score: 0.5729426778193398
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Multi-agent language systems can exhibit a failure mode where a shared dominant context progressively absorbs individual semantics, yielding near-uniform behavior across agents. We study this effect under the name Asymptotic Semantic Collapse in Hierarchical Optimization. In a closed linguistic setting with a Dominant Anchor Node whose semantic state has effectively infinite inertia, we show that repeated interactions with Peripheral Agent Nodes drive an asymptotic alignment that minimizes a global loss. We model semantic states as points on a Riemannian manifold and analyze the induced projection dynamics. Two consequences follow. First, the limiting semantic configuration is insensitive to the optimization history: both smooth gradient-style updates and stochastic noisy updates converge to the same topological endpoint, establishing path independence at convergence. Second, the degree of context dependence controls information content: moving from atomic (independent) representations to fully entangled (context-bound) representations forces the node entropy, interpreted as available degrees of freedom, to vanish in the limit. The theory connects information-theoretic quantities with differential-geometric structure and suggests an interpretation as an immutable consensus rule that constrains agents to a shared semantic grammar. A lightweight dataset-free benchmark on an RWKV-7 13B GGUF checkpoint complements the analysis, reporting zero hash collisions, mean compliance of 0.50 under greedy decoding and 0.531 under stochastic decoding, and final Jaccard-to-anchor similarity values of 0.295 and 0.224, respectively.

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