Related papers: The Computational Boundary of Inference: Capabilit…
We consider quantum formalism limited by the classical simulating computer with the fixed memory. The memory is redistributed in the course of modeling by the variation of the set of classical states and the accuracy of the representation…
With the success of self-supervised representations, researchers seek a better understanding of the information encapsulated within a representation. Among various interpretability methods, we focus on classification-based linear probing.…
A hallmark of human intelligence is Introspection-the ability to assess and reason about one's own cognitive processes. Introspection has emerged as a promising but contested capability in large language models (LLMs). However, current…
The recent work by Shojaee et al. (2025), titled The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity, presents a compelling empirical finding, a reasoning cliff, where…
Throughout the modern era, when new technologies displaced workers, societies adapted through the same mechanism: education raised the cognitive ceiling, producing workers capable of tasks machines could not yet reach. Generative AI may be…
Recent breakthroughs in AI capability have been attributed to increasingly sophisticated architectures and alignment techniques, but a simpler principle may explain these advances: memory makes computation universal. Memory enables…
Computational models of human learning can play a significant role in enhancing our knowledge about nuances in theoretical and qualitative learning theories and frameworks. There are many existing frameworks in educational settings that…
The concept of intelligent software is flawed. The behaviour of software is determined by the hardware that "interprets" it. This undermines claims regarding the behaviour of theorised, software superintelligence. Here we characterise this…
We formalize two independent computational limitations that constrain algorithmic intelligence: formal incompleteness and dynamical unpredictability. The former limits the deductive power of consistent reasoning systems while the latter…
Artificial intelligence is increasingly embedded in human decision making. In some cases, it enhances human reasoning. In others, it fosters excessive cognitive dependence. This paper introduces a conceptual and mathematical framework to…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
This paper establishes a theoretical foundation for understanding the fundamental limits of AI explainability through algorithmic information theory. We formalize explainability as the approximation of complex models by simpler ones,…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
The notion of weak truth-table reducibility plays an important role in recursion theory. In this paper, we introduce an elaboration of this notion, where a computable bound on the use function is explicitly specified. This elaboration…
Large language models handle single-turn generation well, but multi-turn interactions still require the model to reconstruct user intent and task state from an expanding token history because internal representations do not persist across…
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
Can language models (LMs) learn to faithfully describe their internal computations? Are they better able to describe themselves than other models? We study the extent to which LMs' privileged access to their own internals can be leveraged…
The article contains an outline of a possible new direction for Computability Logic (see www.csc.villanova.edu/~japaridz/CL/ ), focused on computability without infinite memory or other impossible-to-possess computational resources. The new…