The Transformer as a Polar State Estimator

arXiv:2605.11007 · cs.LG, cs.AI · Submitted 2026-05-10 · Read on arXiv

cs.LG, cs.AI

Submitted: 2026-05-10

Updated: 2026-09-07

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Transformer — 93× in this paper · explained in 2 episodes
• Covariance Propagation — 12× in this paper · explained in 2 episodes
• Embeddings — 9× in this paper · explained in 2 episodes
• Attention Mechanism — 5× in this paper · explained in 2 episodes
• Robust Filter Attention — 5× in this paper
• Aggregation — 4× in this paper · explained in 1 episode
• Decoupling — 4× in this paper · explained in 2 episodes
• Robustness — 4× in this paper · explained in 5 episodes
• Latent Space — 3× in this paper · explained in 7 episodes
• Transformer Architecture — 3× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Associative Memory — 1× in this paper · explained in 2 episodes
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Cosine Similarity — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Iteratively Reweighted Least Squares — 1× in this paper
• Latent Dynamics — 1× in this paper · explained in 2 episodes
• Positional Bias — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Stochastic Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Kalman Filters on Differentiable Manifolds
• RiemannFormer: A Framework for Attention in Curved Spaces
• Traveling Words: A Geometric Interpretation of Transformers
• Retentive Network: A Successor to Transformer for Large Language Models
• Exclusive Self Attention
• GeoNorm: Unify Pre-Norm and Post-Norm with Geodesic Optimization

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