arXiv:2607.01746v1 Announce Type: new Abstract: Recurrent representations are trajectories, but representation geometry is often measured from static snapshots. We develop finite-lag operator geometry for recurrent hidden states from observed source-successor pairs $(X_t,X_{t+\Delta})$. The primitive is the conditional transport law $Q_\Delta(dy\mid x)$, estimated by a dense Gaussian source-smoothing operator. From this directed finite-lag law we derive a source-centered transport tensor $G_\Delta$, which decomposes exactly into conditional spread and coherent displacement, and an antisymmetri
This paper represents continued academic inquiry into the underlying mechanics of recurrent neural networks, a fundamental component of various AI systems.
Understanding the geometry of recurrent representations is crucial for developing more robust, interpretable, and efficient AI models, impacting numerous downstream applications.
This research provides a new mathematical framework for analyzing how recurrent networks process sequences, potentially leading to advancements in model design and performance.
- · AI researchers
- · Machine learning engineers
- · Developers of sequential data models
Improved understanding and interpretability of recurrent neural networks.
Development of new recurrent architectures with enhanced learning capabilities and efficiency based on these geometric insights.
These advancements could lead to more effective AI agents, better natural language processing, and improved time series forecasting across various industries.
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