SearchEyes unifies multimodal search-agent training via Perception-Knowledge Chains on Wikidata5M and Hop-Anchored Policy Optimization, claiming a 6.2-point average gain over the strongest open-source baseline on six benchmarks.
A Study of Directional Entropy Arising from \(\mathbb{Z} \times \mathbb{Z}_+\) Semigroup Actions
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abstract
In this chapter, we investigate directional entropy for semigroup actions generated by one-dimensional linear cellular automata (LCAs) and the shift transformation on the compact metric space $\mathbb{Z}_m^{\mathbb{N}}$. This work provides a systematic study of both \emph{topological directional entropy} (TDE) within Milnor's geometric framework and \emph{measure-theoretic directional entropy} via the Kolmogorov--Sinai formalism.
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2026 1verdicts
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SearchEyes: Towards Frontier Multimodal Deep Search Intelligence via Search World Simulation
SearchEyes unifies multimodal search-agent training via Perception-Knowledge Chains on Wikidata5M and Hop-Anchored Policy Optimization, claiming a 6.2-point average gain over the strongest open-source baseline on six benchmarks.