相关论文: Similarity Field Theory: A Mathematical Framework …

The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…

This paper highlights distinctive features of the "SP theory of intelligence" and its apparent advantages compared with some AI-related alternatives. Distinctive features and advantages are: simplification and integration of observations…

In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field…

We present a flexible framework for learning predictive models that approximately satisfy the equalized odds notion of fairness. This is achieved by introducing a general discrepancy functional that rigorously quantifies violations of this…

For decades, neuroscientists and computer scientists have pursued a shared ambition: to understand intelligence and build it. Modern artificial neural networks now rival humans in language, perception, and reasoning, yet it is still largely…

This study aims to reinforce the theoretical foundation for diverse systems--including the axiomatic definition of intelligence--by introducing a mathematically rigorous and unified formal structure for the concept of 'state,' which has…

Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we…

Machine learning systems exhibit diverse failure modes: unfairness toward protected groups, brittleness to spurious correlations, poor performance on minority sub-populations, which are typically studied in isolation by distinct research…

A symmetry is a `change without change'. As simple as it sounds, this concept is the fundamental cornerstone that unifies all branches of theoretical physics. Virtually all physical laws -- ranging from classical mechanics and…

Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space…

What is intelligence? We argue for a structural-dynamical account rooted in a topological closure law: \emph{the boundary of a boundary vanishes} ($\partial^2=0$). This principle forces transient fragments to cancel while closed cycles…

Parametricity is a key metatheoretic property of type systems, which implies strong uniformity & modularity properties of the structure of types within systems possessing it. In recent years, various systems of dependent type theory have…

We consider the problem of classification using similarity/distance functions over data. Specifically, we propose a framework for defining the goodness of a (dis)similarity function with respect to a given learning task and propose…

Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…

The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…

Recent interest in codifying fairness in Automated Decision Systems (ADS) has resulted in a wide range of formulations of what it means for an algorithmic system to be fair. Most of these propositions are inspired by, but inadequately…

This paper introduces the Theory of the Unique Latent Pattern (ULP), a formal epistemic framework that redefines the origin of apparent complexity in dynamic systems. Rather than attributing unpredictability to intrinsic randomness or…

We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive. Typically, we can represent constraints on allowed…

Joint representation learning over multi-sourced knowledge graphs (KGs) yields transferable and expressive embeddings that improve downstream tasks. Entity alignment (EA) is a critical step in this process. Despite recent considerable…

We establish uniform bounds on the multiplicities of irreducible admissible representations appearing in spaces of functions on symmetric spaces over $p$-adic fields. These multiplicities can exceed one and depend intricately on the group,…