Related papers: On the Computability of AIXI
Explainable Artificial Intelligence (XAI) has experienced a significant growth over the last few years. This is due to the widespread application of machine learning, particularly deep learning, that has led to the development of highly…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
Despite significant efforts towards extending the AGM paradigm of belief change beyond finitary logics, the computational aspects of AGM have remained almost untouched. We investigate the computability of AGM contraction on non-finitary…
Artificial intelligence now outperforms humans in several scientific and engineering tasks, yet its internal representations often remain opaque. In this Perspective, we argue that explainable artificial intelligence (XAI), combined with…
Our work serves as a framework for unifying the challenges of contemporary explainable AI (XAI). We demonstrate that while XAI methods provide supplementary and potentially useful output for machine learning models, researchers and…
We investigate the computability (in the sense of computable analysis) of the topological pressure $P_{\rm top}(\phi)$ on compact shift spaces $X$ for continuous potentials $\phi:X\to {\mathbb R}$. This question has recently been studied…
We present an alternative methodology for the analysis of algorithms, based on the concept of expected discounted reward. This methodology naturally handles algorithms that do not always terminate, so it can (theoretically) be used with…
Indecipherable black boxes are common in machine learning (ML), but applications increasingly require explainable artificial intelligence (XAI). The core of XAI is to establish transparent and interpretable data-driven algorithms. This work…
We introduce an increasing-complexity, open-ended, and human-agnostic metric to evaluate foundational and frontier AI models in the context of Artificial General Intelligence (AGI) and Artificial Super Intelligence (ASI) claims. Unlike…
Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the…
According to cognitive psychology and related disciplines, the development of complex problem-solving behaviour in biological agents depends on hierarchical cognitive mechanisms. Hierarchical reinforcement learning is a promising…
In this article we review Tononi's (2008) theory of consciousness as integrated information. We argue that previous formalizations of integrated information (e.g. Griffith, 2014) depend on information loss. Since lossy integration would…
There has recently been a surge of work in explanatory artificial intelligence (XAI). This research area tackles the important problem that complex machines and algorithms often cannot provide insights into their behavior and thought…
Solomonoff's uncomputable universal prediction scheme $\xi$ allows to predict the next symbol $x_k$ of a sequence $x_1...x_{k-1}$ for any Turing computable, but otherwise unknown, probabilistic environment $\mu$. This scheme will be…
The lack of explainability of a decision from an Artificial Intelligence (AI) based "black box" system/model, despite its superiority in many real-world applications, is a key stumbling block for adopting AI in many high stakes applications…
Artificial Intelligence (AI) increasingly shows its potential to outperform predicate logic algorithms and human control alike. In automatically deriving a system model, AI algorithms learn relations in data that are not detectable for…
This paper offers a new perspective on the limits of machine learning: the ceiling on progress is set not by model size or algorithm choice but by the information structure of the task itself. Code generation has progressed more reliably…
We present two new results on the computational limitations of affine automata. First, we show that the computation of bounded-error rational-values affine automata is simulated in logarithmic space. Second, we give an impossibility result…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a…