arXiv AI
6d ago
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 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
Jun 30
An Information-Geometric Justification for Composite Coherence in Event-Based Narrative Extraction
arXiv:2606. 29118v1 Announce Type: cross Abstract: Graph-based narrative extraction relies on a coherence function to score transitions between events, but the coherence metrics in current use are defined operationally and lack an information-theoretic foundation.
arXiv Machine Learning
Jun 24
Does My Embedding Reflect That $A = B$? Evaluating Mathematical Equivalence in Embedding Models
arXiv:2606. 23959v1 Announce Type: cross Abstract: Because mathematics is highly abstract, a single statement can take very different forms depending on what subfield it is framed in.
arXiv Machine Learning
Jul 1
Symmetry in language statistics shapes the geometry of model representations
arXiv:2602. 15029v3 Announce Type: replace Abstract: The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe.
arXiv AI
Jun 9
Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.