arXiv AI
Aug 13
Proportional Analogies on Probability Distributions via Bayesian Updating
arXiv:2608. 11724v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "A is to B as C is to D".
A Generalized Parallelogram Rule for Proportional Analogies on Riemannian Manifolds
arXiv:2608. 14220v1 Announce Type: new Abstract: Analogies are quaternary relations of the form "a is to b as c is to d", usually denoted a : b :: c : d.
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Hugging Face Trending Papers
Aug 12
Proportional Analogies on Probability Distributions via Bayesian Updating
Analogies are quaternary relations of the form "A is to B as C is to D". Among the various formalizations of analogical reasoning, proportional analogies provide an important axiomatic framework by characterizing valid analogies through a set of postulates.
arXiv AI
Aug 5
Large Language Models provide support for the parallelogram theory of analogy
arXiv:2603. 19066v2 Announce Type: replace-cross Abstract: Four-term word analogies (A:B::C:D) are classically modeled geometrically as parallelograms: adding the vector B-A+C produces D.
Hugging Face Trending Papers
Jun 22
From numerical proportions to analogical proportions between probabilities
Analogical proportions link four items a, b, c, d by a relation stating that ``a is to b as c is to d", a, b, c, d being the formal representation of real world entities, ranging from simple numerical values to more complex structures such as profiles. Accordingly, $a, b, c, d$ could be atomic values like Boolean, nominal or numerical values, more generally vectors of such values, or even families of items represented by logical formulas.
arXiv Computation and Language
Sep 22
A vector logic for intensional formal semantics
arXiv:2602.02940v2 Announce Type: replace-cross Abstract: Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model...
arXiv AI
4d ago
When Models Don't Manipulate Manifolds: The Geometry of a Comparison Task
arXiv:2609.37680v1 Announce Type: cross Abstract: One of the current premises of mechanistic interpretability research is that detailed accounts of the geometry of neural network representations can...
arXiv Machine Learning
Sep 18
Embedding Models Measure in Peculiar Ways
The paper investigates whether embedding spaces capture objective physical measurements such as mass, distance, time, and volume. It finds that these embeddings only weakly model such measurements and instead exhibit peculiar patterns. Further analysis shows that superficial string similarity heavily influences the representation of physical measurements, and recalibrating similarity does not significantly improve alignment.
arXiv AI
Jul 9
Riemannian Geometry for Pre-trained Language Model Embeddings
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
arXiv AI
Jul 24
Inducing Comparability of Factorised Probability Distributions
arXiv:2607. 20502v1 Announce Type: new Abstract: To allow for principled comparison between two probabilistic graphical models defined over non-identical variable sets, they have to be lifted to a common measurable space.
arXiv Machine Learning
Jun 9
Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
arXiv:2606. 07926v1 Announce Type: cross Abstract: Optimal transport couplings are probabilistic objects, while many learning pipelines require deterministic maps.
arXiv Machine Learning
Aug 4
Riemannian Attention Mechanisms for Transformers: A Theoretical Framework and Architecture Design
arXiv:2608. 01283v1 Announce Type: new Abstract: All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al.
arXiv Machine Learning
Sep 17
Symmetrizing Bregman Divergence on the Cone of Positive Definite Matrices: Which Mean to Use and Why
arXiv:2603.28917v3 Announce Type: replace-cross Abstract: This work uncovers variational principles behind symmetrizing the Bregman divergences induced by generic mirror maps over the cone of positiv...