Related papers: Algorithmic Randomness as Foundation of Inductive …
The framework of algorithmic knowledge assumes that agents use algorithms to compute the facts they explicitly know. In many cases of interest, a deductive system, rather than a particular algorithm, captures the formal reasoning used by…
Exponentiation makes the difference between the bit-size of this line and the number (<< 2^{300}) of particles in the known Universe. The expulsion of exponential time algorithms from Computer Theory in the 60's broke its umbilical cord…
Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…
The concept of rationality is central to the field of artificial intelligence (AI). Whether we are seeking to simulate human reasoning, or trying to achieve bounded optimality, our goal is generally to make artificial agents as rational as…
We reminisce and discuss applications of algorithmic probability to a wide range of problems in artificial intelligence, philosophy and technological society. We propose that Solomonoff has effectively axiomatized the field of artificial…
As algorithms are increasingly used to make important decisions that affect human lives, ranging from social benefit assignment to predicting risk of criminal recidivism, concerns have been raised about the fairness of algorithmic decision…
Explainable artificial intelligence and interpretable machine learning are research domains growing in importance. Yet, the underlying concepts remain somewhat elusive and lack generally agreed definitions. While recent inspiration from…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
Recent advancements in machine learning have emphasized the need for transparency in model predictions, particularly as interpretability diminishes when using increasingly complex architectures. In this paper, we propose leveraging…
The term artificial implies an inherent dichotomy from the natural or organic. However, AI, as we know it, is a product of organic ingenuity: designed, implemented, and iteratively improved by human cognition. The very principles that…
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…
If quantum mechanics is taken for granted the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. "Random" quantum events are intimately related to the emergence of both space-time as…
In recent years, there has been an increasing awareness of both the public and scientific community that algorithmic systems can reproduce, amplify, or even introduce unfairness in our societies. These lecture notes provide an introduction…
Algorithmic decision-making (ADM) increasingly shapes people's daily lives. Given that such autonomous systems can cause severe harm to individuals and social groups, fairness concerns have arisen. A human-centric approach demanded by…
We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…
Algorithms learned from data are increasingly used for deciding many aspects in our life: from movies we see, to prices we pay, or medicine we get. Yet there is growing evidence that decision making by inappropriately trained algorithms may…
Current discrete randomness and information conservation inequalities are over total recursive functions, i.e. restricted to deterministic processing. This restriction implies that an algorithm can break algorithmic randomness conservation…
Artificial intelligence (AI) has a history of nearly a century from its inception to the present day. We have summarized the development trends and discovered universal rules, including both success and failure. We have analyzed the reasons…
I argue for an approach to the Foundations of Physics that puts the question in the title center stage, rather than asking "what is the case in the world?". This approach, algorithmic idealism, attempts to give a mathematically rigorous…