Related papers: The Computational Boundary of Inference: Capabilit…

Reinforcement learning (RL) is a fundamental framework for sequential decision-making, in which an agent learns an optimal policy through interactions with an unknown environment. In settings with function approximation, many existing RL…

It is important for Large Language Models (LLMs) to be aware of the boundary of their knowledge, distinguishing queries they can confidently answer from those that lie beyond their capabilities. Such awareness enables models to perform…

Causal discovery is a cornerstone of scientific reasoning, yet whether large language models can perform it reliably remains an open question. Recent benchmarks show that even fine-tuned models plateau on simple causal graphs and degrade as…

All artificial Intelligence (AI) systems make errors. These errors are unexpected, and differ often from the typical human mistakes ("non-human" errors). The AI errors should be corrected without damage of existing skills and, hopefully,…

Large language models (LLMs) often exhibit a puzzling disconnect between their asserted confidence and actual problem-solving competence. We offer a mechanistic account of this decoupling by analyzing the geometry of internal states across…

Artificial general intelligence (AGI) may herald our extinction, according to AI safety research. Yet claims regarding AGI must rely upon mathematical formalisms -- theoretical agents we may analyse or attempt to build. AIXI appears to be…

The study of automorphisms of computable and other structures connects computability theory with classical group theory. Among the noncomputable countable structures, computably enumerable structures are one of the most important objects of…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

Safe reinforcement learning (RL) is still very challenging since it requires the agent to consider both return maximization and safe exploration. In this paper, we propose CUP, a Conservative Update Policy algorithm with a theoretical…

Replay in the brain has been viewed as rehearsal, or, more recently, as sampling from a transition model. Here, we propose a new hypothesis: that replay is able to implement a form of compositional computation where entities are assembled…

This study empirically validates automated logical specification methods for behavioural models, focusing on their robustness, scalability, and reproducibility. By the systematic reproduction and extension of prior results, we confirm key…

In the rapidly evolving fields of Artificial Intelligence (AI) and Machine Learning (ML), the reproducibility crisis underscores the urgent need for clear validation methodologies to maintain scientific integrity and encourage advancement.…

Inner Interpretability is a promising emerging field tasked with uncovering the inner mechanisms of AI systems, though how to develop these mechanistic theories is still much debated. Moreover, recent critiques raise issues that question…

The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing…

Recent advances in Transformer-based large language models (LLMs) have led to significant performance improvements across many tasks. These gains come with a drastic increase in the models' size, potentially leading to slow and costly use…

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…

While large language models (LLMs) have demonstrated remarkable reasoning capabilities, they often struggle with complex tasks that require specific thinking paradigms, such as divide-and-conquer and procedural deduction, \etc Previous…

Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…

We propose a new type of self-aware systems inspired by ideas from higher-order theories of consciousness. First, we discussed the crucial distinction between introspection and reflexion. Then, we focus on computational reflexion as a…

Undoing computations of a concurrent system is beneficial in many situations, e.g., in reversible debugging of multi-threaded programs and in recovery from errors due to optimistic execution in parallel discrete event simulation. A number…