相关论文: Mathematical Foundations of Consciousness

Knowledge graph reasoning is the fundamental component to support machine learning applications such as information extraction, information retrieval, and recommendation. Since knowledge graphs can be viewed as the discrete symbolic…

We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…

Large language models (LLMs) solve complex problems yet fail on simpler variants, suggesting they achieve correct outputs through mechanisms fundamentally different from human reasoning. To understand this gap, we synthesize cognitive…

A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered…

Skeleton-based human activity recognition has achieved strong empirical performance, yet most existing models remain black boxes and difficult to interpret. In this work, we introduce a neurosymbolic formulation of skeleton-based HAR that…

Foundation models excel at language, where sentences become tokens, and vision, where images become pixels, because both reduce to discrete symbols on a shared, fixed grid. Knowledge Graphs share the discreteness, but not the geometry.…

In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving…

Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of…

We propose a set theory strong enough to interpret powerful type theories underlying proof assistants such as LEGO and also possibly Coq, which at the same time enables program extraction from its constructive proofs. For this purpose, we…

This paper proposes an approach to framing and answering fundamental questions about consciousness. It argues that many of the more theoretical debates about consciousness, such as debates about "when does it begin?", are misplaced and…

We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's…

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined…

Even though classic theories and models of discrete choice pose man as a rational being, it has been shown extensively that people persistently violate rationality in their actual choices. Recent models of decision-making take these…

The hypothesis considered here is that cognition is based on a small set of systems-level computational primitives that are defined at a level higher than single neurons. It is pointed out that for one such set of primitives, whose…

A variety of methods exist to explain image classification models. However, whether they provide any benefit to users over simply comparing various inputs and the model's respective predictions remains unclear. We conducted a user study…

Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be…

We have analysed the many facets of Consciousness into two distinct categories. First: the organisational state of the neural networks at any one time, which determines whether a person is conscious - awake, or unconscious - asleep. Second:…

Human vision is able to compensate imperfections in sensory inputs from the real world by reasoning based on prior knowledge about the world. Machine learning has had a significant impact on computer vision due to its inherent ability in…

We seek general principles of the structure of the cellular collective activity associated with conscious awareness. Can we obtain evidence for features of the optimal brain organization that allows for adequate processing of stimuli and…

In psychology and neuroscience it is common to describe cognitive systems as input/output devices where perceptual and motor functions are implemented in a purely feedforward, open-loop fashion. On this view, perception and action are often…