Related papers: Proportoids

Related papers

Proportional Analogies on Probability Distributions via Bayesian Updating [13.360204757207262]
We introduce a notion of proportional analogy for probability distributions based on Bayesian updating.<n>Our approach builds upon the idea that two distributions are related whenever one can be transformed into the other.<n>We discuss how it naturally extends to arbitrary probability distributions through Gaussian mixture approximations.
arXiv Detail & Related papers (2026-08-12T07:02:43Z)
From numerical proportions to analogical proportions between probabilities [2.9649783577150832]
Analogical proportions link four items a, b, c, d by a relation stating that a is to b as c is to d"<n>In this paper, we consider another representation setting, which is the probabilistic one.
arXiv Detail & Related papers (2026-06-22T08:39:28Z)
A homotopy-type-theoretic generalization of neurosymbolic inference [46.36639624013224]
neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $$-structures.<n>We develop the framework from scratch for NeSy systems, prove a conservativity theorem that recovers the classical functional when symmetries are trivial, and show that the symmetry our framework exposes is exactly the one behind reasoning shortcuts.
arXiv Detail & Related papers (2026-06-16T12:22:12Z)
Simple Convergence Proof of Adam From a Sign-like Descent Perspective [58.89890024903816]
We show that Adam achieves the optimal rate of $cal O(frac1Ts14)$ rather than the previous $cal O(fracln TTs14)$.<n>Our theoretical analysis provides new insights into the role of momentum as a key factor ensuring convergence.
arXiv Detail & Related papers (2025-07-08T13:19:26Z)
$\mathbb{Z}_2$ gauging and self-dualities of the $XX$ model and its cousins [0.6073572808831218]
We investigate the one-dimensional $XX$ lattice model and its cousins through the lens of momentum and winding $U(1)$ symmetries.<n>We distinguish two closely related $mathbbZ$ symmetries based on their relation to the $U(1)$ symmetries, and establish a web of $mathbbZulo$-gauging relations.
arXiv Detail & Related papers (2025-03-03T18:55:01Z)
Analogical Proportions and Creativity: A Preliminary Study [4.005483185111992]
Analogical proportions are statements of the form "$a$ is to $b$ as $c$ is to $d$" We try to "create" new animals from existing ones, retrieving rare animals such as platypus.
arXiv Detail & Related papers (2023-10-20T13:46:04Z)
StoryAnalogy: Deriving Story-level Analogies from Large Language Models to Unlock Analogical Understanding [72.38872974837462]
We evaluate the ability to identify and generate analogies by constructing a first-of-its-kind large-scale story-level analogy corpus. textscStory Analogy contains 24K story pairs from diverse domains with human annotations on two similarities from the extended Structure-Mapping Theory. We observe that the data in textscStory Analogy can improve the quality of analogy generation in large language models.
arXiv Detail & Related papers (2023-10-19T16:29:23Z)
ANALOGYKB: Unlocking Analogical Reasoning of Language Models with A Million-scale Knowledge Base [51.777618249271725]
ANALOGYKB is a million-scale analogy knowledge base derived from existing knowledge graphs (KGs) It identifies two types of analogies from the KGs: 1) analogies of the same relations, which can be directly extracted from the KGs, and 2) analogies of analogous relations, which are identified with a selection and filtering pipeline enabled by large language models (LLMs)
arXiv Detail & Related papers (2023-05-10T09:03:01Z)
Bilingual analogical proportions via hedges [0.0]
Analogical proportions are expressions of the form $a$ is to $b$ what $c$ is to $d$'' at the core of analogical reasoning. The purpose of this paper is to generalize his unilingual framework to a bilingual one where the underlying languages may differ.
arXiv Detail & Related papers (2023-05-02T08:27:36Z)
Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
arXiv Detail & Related papers (2023-01-13T16:25:25Z)
Some recent advances in reasoning based on analogical proportions [9.861775841965386]
Analogical proportions play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference in terms of accuracy and in terms of computational cost.
arXiv Detail & Related papers (2022-12-22T14:10:14Z)
Galois theory for analogical classifiers [1.7132914341329848]
Analogical proportions are 4-ary relations that read "A is to B as C is to D" Recent works have highlighted the fact that such relations can support a specific form of inference, called analogical inference.
arXiv Detail & Related papers (2022-05-09T23:03:56Z)
q-Paths: Generalizing the Geometric Annealing Path using Power Means [51.73925445218366]
We introduce $q$-paths, a family of paths which includes the geometric and arithmetic mixtures as special cases. We show that small deviations away from the geometric path yield empirical gains for Bayesian inference.
arXiv Detail & Related papers (2021-07-01T21:09:06Z)
On the Generative Utility of Cyclic Conditionals [103.1624347008042]
We study whether and how can we model a joint distribution $p(x,z)$ using two conditional models $p(x|z)$ that form a cycle. We propose the CyGen framework for cyclic-conditional generative modeling, including methods to enforce compatibility and use the determined distribution to fit and generate data.
arXiv Detail & Related papers (2021-06-30T10:23:45Z)
On Exploiting Hitting Sets for Model Reconciliation [53.81101846598925]
In human-aware planning, a planning agent may need to provide an explanation to a human user on why its plan is optimal. A popular approach to do this is called model reconciliation, where the agent tries to reconcile the differences in its model and the human's model. We present a logic-based framework for model reconciliation that extends beyond the realm of planning.
arXiv Detail & Related papers (2020-12-16T21:25:53Z)
Analogical Proportions [0.0]
This paper introduces an abstract framework of analogical proportions of the form $a$ is to $b$ what $c$ is to $d$' in the general setting of universal algebra. It turns out that our notion of analogical proportions has appealing mathematical properties. This paper is a first step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems.
arXiv Detail & Related papers (2020-06-04T13:44:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.