Related papers: Alpay Algebra III: Observer-Coupled Collapse and t…
In this second installment of the Alpay Algebra framework, I formally define identity as a fixed point that emerges through categorical recursion. Building upon the transfinite operator $\varphi^\infty$, I characterize identity as the…
We present a theoretical framework in which a document and an AI model engage in a transfinite fixed-point interaction that leads to stable semantic alignment. Building on the foundations of Alpay Algebra, we introduce a functorial system…
Alpay Algebra is introduced as a universal, category-theoretic framework that unifies classical algebraic structures with modern needs in symbolic recursion and explainable AI. Starting from a minimal list of axioms, we model each algebra…
This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stages, is identical to the unique equilibrium of an unbounded…
We present a thermodynamic rendering model in which the traditional quantum observer is reframed as a special case of a coherence-constrained interface. Collapse is treated not as an interpretive postulate but as a structural threshold -…
In the pursuit of autonomous learning systems, the foundational assumption of stationarity, the premise that data distributions and model behaviors remain constant, is fundamentally untenable. Historically, the research community has…
Large language models (LLMs) are reshaping how knowledge is produced, with increasing reliance on AI systems for generation, summarization, and reasoning. While prior work has studied cognitive offloading in humans and model collapse in…
In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed…
Scientific theory shift in AI agents requires more than fitting equations to data. An artificial scientific agent must detect whether an existing representational framework remains transportable into a new regime, or whether its language…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
Hallucinations can be produced by conversational AI systems, particularly in multi-turn conversations where context changes and contradictions may eventually surface. By representing the entire conversation as a temporal graph, we present a…
While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent…
Advanced Persistent Threat (APT) have grown increasingly complex and concealed, posing formidable challenges to existing Intrusion Detection Systems in identifying and mitigating these attacks. Recent studies have incorporated graph…
In this paper we present a novel algorithm and efficient data structure for anomaly detection based on temporal data. Time-series data are represented by a sequence of symbolic time intervals, describing increasing and decreasing trends, in…
Large language models confidently produce outdated answers, and no existing method can detect them. We show this is not an engineering failure but a structural one: temporal drift, whether a stored fact has changed since training, is…
Backpropagation (BP) is the cornerstone of today's deep learning algorithms, but it is inefficient partially because of backward locking, which means updating the weights of one layer locks the weight updates in the other layers.…
As artificial intelligence (AI) is increasingly deployed in high-stakes public decision-making (from resource allocation to welfare distribution), public trust in these systems has become a critical determinant of their legitimacy and…
Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…
The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…
Classical algebraic structures require exact satisfaction of their defining axioms. We propose similarity algebra, a framework extending algebraic and Lie structures to settings where operations satisfy quantitative bounds up to a tolerance…