CAS II: Symmetric Partitions as Kolmogorov Models
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arXiv:2607. 13796v1 Announce Type: cross Abstract: This paper establishes a direct analogue of the classical Coding Theorem in the setting of symmetry groups.
arXiv:2104. 11547v5 Announce Type: replace-cross Abstract: Statistical models contain variables that are not random: parameters, treatments, environments, design points.
arXiv:2507. 05972v3 Announce Type: replace-cross Abstract: Pseudoentropy characterizations give quantitatively precise formulations of the relationship between computational hardness and computational randomness.
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
arXiv:2605. 20440v2 Announce Type: replace Abstract: Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude.
arXiv:2608. 10420v1 Announce Type: new Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.