Related papers: Analogical Proportions and Creativity: A Prelimina…
Scientific idea generation is central to discovery, requiring the joint satisfaction of novelty and scientific soundness. Unlike standard reasoning or general creative generation, scientific ideation is inherently open-ended and…
This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…
We present a model to measure the similarity in appearance between different materials, which correlates with human similarity judgments. We first create a database of 9,000 rendered images depicting objects with varying materials, shape…
Post-hoc explanations for black box models have been studied extensively in classification and regression settings. However, explanations for models that output similarity between two inputs have received comparatively lesser attention. In…
Compatibility between items, such as clothes and shoes, is a major factor among customer's purchasing decisions. However, learning "compatibility" is challenging due to (1) broader notions of compatibility than those of similarity, (2) the…
Analogical reasoning is at the core of human cognition, serving as an important foundation for a variety of intellectual activities. While prior work has shown that LLMs can represent task patterns and surface-level concepts, it remains…
The automatic ranking of word pairs as per their semantic relatedness and ability to mimic human notions of semantic relatedness has widespread applications. Measures that rely on raw data (distributional measures) and those that use…
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions.…
Creativity, defined as the tendency to generate or recognize new ideas or alternatives and to make connections between seemingly unrelated phenomena, is too vast a horizon to be summed up in such a simple sentence. The extreme abstractness…
Analogical reasoning is an essential aspect of human cognition. In this paper, we summarize key theory about the processes underlying analogical reasoning from the cognitive science literature and relate it to current research in natural…
A superdiagonal composition is one in which the $i$-th part or summand is of size greater than or equal to $i$. In this paper, we study the number of palindromic superdiagonal compositions and colored superdiagonal compositions. In…
Many applications, e.g., Web service composition, complex system design, team formation, etc., rely on methods for identifying collections of objects or entities satisfying some functional requirement. Among the collections that satisfy the…
In the conference paper we construct analouge to Pascal's triangle that characterize primes with additional fascinating properties.
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
Recent work (Ross et al., 2025, 2024) has argued that the ability of humans and LLMs respectively to generalize to novel adjective-noun combinations shows that they each have access to a compositional mechanism to determine the phrase's…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
The field of computational linguistics constantly presents new challenges and topics for research. Whether it be analyzing word usage changes over time or identifying relationships between pairs of seemingly unrelated words. To this point,…
The theory of quasirandomness has greatly expanded from its inaugural graph theoretical setting to several different combinatorial objects such as hypergraphs, tournaments, permutations, etc. However, these quasirandomness variants have…
Several authors have proposed that a large number of unusual combinations of cited references in a paper point to its high creative potential (or novelty). However, it is still not clear whether the number of unusual combinations can really…