arXiv AI
Jul 16
CAS I: A Geometric Coding Theorem
arXiv:2607. 13796v1 Announce Type: cross Abstract: This paper establishes a direct analogue of the classical Coding Theorem in the setting of symmetry groups.
CAS II: Symmetric Partitions as Kolmogorov Models
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arXiv Statistics ML
Sep 25
Transitional Conditional Independence
arXiv:2104. 11547v5 Announce Type: replace-cross Abstract: Statistical models contain variables that are not random: parameters, treatments, environments, design points.
arXiv Machine Learning
Jul 14
Generalized and Unified Equivalences between Hardness and Pseudoentropy
arXiv:2507. 05972v3 Announce Type: replace-cross Abstract: Pseudoentropy characterizations give quantitatively precise formulations of the relationship between computational hardness and computational randomness.
arXiv Machine Learning
Aug 4
Polyatomic Complexes: A topologically-informed learning representation for atomistic systems
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 Machine Learning
Jul 30
Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules
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 AI
Aug 12
Reasoning Shortcuts and Value Symmetries: What Symmetry Permits, Architecture Realizes, and Optimization Selects
arXiv:2608. 10420v1 Announce Type: new Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.
arXiv AI
Aug 11
Neurosymbolic Discovery of Algebraic Graph Constructions
arXiv:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
arXiv AI
Jul 14
Instruction Set and Language for Hypergraphs
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv AI
Jun 17
A homotopy-type-theoretic generalization of neurosymbolic inference
arXiv:2606. 17851v1 Announce Type: new Abstract: A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $\sigma$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases.
arXiv Machine Learning
Jul 30
Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks
arXiv:2607. 26344v1 Announce Type: new Abstract: A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit.
arXiv Machine Learning
Sep 22
Counting and Covering in Nearest-Neighbour Representations of Boolean Functions
arXiv:2609.23094v1 Announce Type: cross Abstract: We study the number of prototypes needed to represent Boolean functions by nearest-neighbour classification. There are two distinct settings: the pro...
arXiv Machine Learning
Sep 15
$\mathbb{SL}(n)$ Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition
arXiv:2609.15083v1 Announce Type: new Abstract: Mixed-curvature representation learning seeks to capture rich geometric structures that cannot be adequately modeled by a single curvature regime. Exis...