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[2602.18450] Asymptotic Semantic Collapse in Hierarchical Optimization
Summary
The paper explores 'Asymptotic Semantic Collapse' in multi-agent language systems, where agents converge to a uniform behavior due to a dominant context, impacting semantic representation and information content.
Why It Matters
Understanding semantic collapse is crucial for improving multi-agent systems and ensuring diverse semantic representations. This research connects information theory with optimization, offering insights into agent behavior and potential applications in AI and machine learning.
Key Takeaways
- Semantic collapse leads to uniform behavior among agents in multi-agent systems.
- The limiting semantic configuration is independent of the optimization history.
- Context dependence affects the information content of semantic representations.
- The study connects information theory with differential geometry.
- A dataset-free benchmark demonstrates the practical implications of the findings.
Computer Science > Computation and Language arXiv:2602.18450 (cs) [Submitted on 1 Feb 2026] Title:Asymptotic Semantic Collapse in Hierarchical Optimization Authors:Faruk Alpay, Bugra Kilictas View a PDF of the paper titled Asymptotic Semantic Collapse in Hierarchical Optimization, by Faruk Alpay and 1 other authors View PDF HTML (experimental) 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 lim...