Toward a Unified Mathematics of Concepts
Read the original on arXiv Computation and Language →The Flow has not summarised this story yet — read it at arXiv Computation and Language.
The Flow has not summarised this story yet — read it at arXiv Computation and Language.
arXiv:2608. 06839v1 Announce Type: new Abstract: Artificial Neural networks (ANNs) are often treated as black-box models, making explainability a central challenge in deep learning.
arXiv:2512. 09831v2 Announce Type: replace Abstract: This paper develops a geometric framework for modeling concepts, motivation, and influence across cognitively heterogeneous agents.
arXiv:2608.29530v1 Announce Type: cross Abstract: Modern systems in artificial intelligence (AI) somehow excel in domains for which they seem poorly suited. Intelligence has traditionally been modele...
arXiv:2605. 22093v3 Announce Type: replace Abstract: Knowledge graphs have become the primary vehicle for data integration and are critical to the success of modern AI, but the diversity of KG modelling practices, from lightweight vocabularies to richly axiomatised ontologies, makes integration and reuse expensive and brittle.
The paper argues that human cognitive constraints, often seen as limits, actually drive mathematical progress by creating bottlenecks that force the development of new abstractions. It proposes a resource‑rational theory of mathematical abstraction, showing how these bottlenecks can lead to novel formalisms with broader applications. The authors illustrate this with historical examples and suggest that incorporating similar constraints into machine learning could aid in discovering useful mathematical abstractions.
The article discusses goals as cognitive states that combine with world knowledge to guide purposeful behavior, emphasizing their compositional nature and relation to rational action. It draws parallels between goal representations and the syntax‑semantics interface in linguistics and logic, highlighting questions about expressivity, design, and efficiency of different goal languages. The authors synthesize research on goal representation properties, propose a broader design space, and suggest that distinguishing form and meaning can clarify assumptions, inform cognition‑motivation interactions, and identify variation axes in goal conceptions.