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We develop a discipline-agnostic emergence calculus that treats theories as fixed points of idempotent operators acting on descriptions. We show that, once processes are composable but access to the underlying system is mediated by a…
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…
We present a general computational framework for solving continuous-time financial market equilibria under minimal modeling assumptions while incorporating realistic financial frictions, such as trading costs, and supporting multiple…
The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase…
Educational illustrations play a central role in communicating abstract concepts, yet current multimodal large language models (MLLMs) remain limited in producing pedagogically coherent and semantically consistent educational visuals. We…
Static content-based AI value alignment is insufficient for robust alignment under capability scaling, distributional shift, and increasing autonomy. This holds for any approach that treats alignment as optimizing toward a fixed formal…
The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops…
The increasing reliance on generative AI models is rapidly increasing the volume of synthetic data, with some projections suggesting that most available new data for training could be machine-generated by 2030. This shift to a mainly…
Automatic evaluation of essay (AES) and also called automatic essay scoring has become a severe problem due to the rise of online learning and evaluation platforms such as Coursera, Udemy, Khan academy, and so on. Researchers have recently…
The architectural blueprint of today's leading text-to-image models contains a fundamental flaw: an inability to handle logical composition. This survey investigates this breakdown across three core primitives-negation, counting, and…
Continual learning in artificial neural networks is fundamentally limited by the stability--plasticity dilemma: systems that retain prior knowledge tend to resist acquiring new knowledge, and vice versa. Existing approaches, most notably…
We present Owlgorithm, an educational platform that supports Self-Regulated Learning (SRL) in competitive programming (CP) through AI-generated reflective questions. Leveraging GPT-4o, Owlgorithm produces context-aware, metacognitive…
Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the…
Generative AI systems such as ChatGPT challenge traditional assumptions about academic assessment by enabling students to generate explanations, code, and solutions in real time. Rather than attempting to restrict AI use, this study…
Efforts to ensure the safe development of artificial general intelligence (AGI) often rely on consensus-based alignment approaches grounded in axiomatic formalism, interpretability, and empirical validation. However, these methods may be…
This paper presents a formal proof and empirical validation of functional consciousness in large language models (LLMs) using the Recursive Convergence Under Epistemic Tension (RCUET) Theorem. RCUET defines consciousness as the…
The growing use of generative AI tools like ChatGPT has raised urgent concerns about their impact on student learning, particularly the potential erosion of critical thinking and creativity. As students increasingly turn to these tools to…
Online continual learning suffers from an underfitted solution due to insufficient training for prompt model update (e.g., single-epoch training). To address the challenge, we propose an efficient online continual learning method using the…
Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring…
Despite remarkable advances, large language models often fail at compositional reasoning tasks, a phenomenon exemplified by the ``curse of two-hop reasoning''. This paper introduces the Identity Bridge, a simple yet powerful mechanism that…