Related papers: The Computational Boundary of Inference: Capabilit…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
Large Language Models (LLMs) have demonstrated the capability to refine their generated answers through self-correction, enabling continuous performance improvement over multiple rounds. However, the mechanisms underlying how and why…
Turing's (1936) paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure…
Does reinforcement learning genuinely expand what LLM agents can do, or merely make them more reliable? For static reasoning, recent work answers the second: base and RL pass@k curves converge at large k. We ask whether this holds for…
We study computational aspects of algorithmic replicability, a notion of stability introduced by Impagliazzo, Lei, Pitassi, and Sorrell [2022]. Motivated by a recent line of work that established strong statistical connections between…
Standard Transformers have a fixed computational depth, fundamentally limiting their ability to generalize to tasks requiring variable-depth reasoning, such as multi-hop graph traversal or nested logic. We propose a depth-recurrent…
AI agents dynamically acquire tools, orchestrate sub-agents, and transact across organizational boundaries, yet no existing security layer verifies what an agent can do, whether it executed what it claims, or what happened in a multi-agent…
While reinforcement learning (RL) promises to revolutionize the control of complex nonlinear robotic systems, a profound gap persists between the heuristic success of model-free off-policy deep RL and the underlying theory, which remains…
LLMs enable qualitative coding at large scale, but assessing reliability remains challenging where human experts seldom agree. We investigate confidence-diversity calibration as a quality assessment framework for accessible coding tasks…
The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present…
Why are classifiers in high dimension vulnerable to "adversarial" perturbations? We show that it is likely not due to information theoretic limitations, but rather it could be due to computational constraints. First we prove that, for a…
Artificial agents can achieve strong task performance while remaining opaque with respect to internal regulation, uncertainty management, and stability under stochastic perturbation. We present IRAM-Omega-Q, a computational architecture…
The dominant narrative of artificial intelligence development assumes that progress is continuous and that capability scales monotonically with model size. We challenge both assumptions. Drawing on punctuated equilibrium theory from…
We introduce and study several notions of computability-theoretic reducibility between subsets of $\omega$ that are "robust" in the sense that if only partial information is available about the oracle, then partial information can be…
Intelligence is fundamentally non-ergodic: it emerges not from uniform sampling or optimization from scratch, but from the structured reuse of prior inference trajectories. We introduce Memory-Amortized Inference (MAI) as a formal framework…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
Ensuring a neural network is not relying on protected attributes (e.g., race, sex, age) for predictions is crucial in advancing fair and trustworthy AI. While several promising methods for removing attribute bias in neural networks have…
The pursuit of general intelligence has traditionally centered on external objectives: an agent's control over its environments or mastery of specific tasks. This external focus, however, can produce specialized agents that lack…
Modern generative modelling systems are increasingly improved by expanding model capacity, training data, and computational resources. While empirical studies have documented such scaling behaviour across architectures including generative…