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Artificial Intelligence (AI) is one of today's most relevant emergent technologies. In view thereof, this paper proposes that more attention should be paid to the philosophical aspects of AI technology and its use. It is argued that this…

Recent years have witnessed the rapid progression of deep learning, pushing us closer to the realization of AGI (Artificial General Intelligence). Probabilistic modeling is critical to many of these advancements, which provides a…

A good theory of mathematical beauty is more practical than any current observation, as new predictions of physical reality can be verified self-consistently. This belief applies to the current status of understanding deep neural networks…

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…

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and…

The aim of these notes is to demonstrate the potential for ideas in machine learning to impact on the fields of inverse problems and data assimilation. The perspective is one that is primarily aimed at researchers from inverse problems…

Stock market prediction has been a classical yet challenging problem, with the attention from both economists and computer scientists. With the purpose of building an effective prediction model, both linear and machine learning tools have…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…

While deep learning has achieved remarkable success, there is no clear explanation about why it works so well. In order to discuss this question quantitatively, we need a mathematical framework that explains what learning is in the first…

In recent years, deep learning using neural network architecture, i.e. deep neural networks, has been on the frontier of computer science research. It has even lead to superhuman performance in some problems, e.g., in computer vision, games…

Creating learning models that can exhibit sophisticated reasoning skills is one of the greatest challenges in deep learning research, and mathematics is rapidly becoming one of the target domains for assessing scientific progress in this…

A major challenge in both neuroscience and machine learning is the development of useful tools for understanding complex information processing systems. One such tool is probes, i.e., supervised models that relate features of interest to…

Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…

The rapid evolution of artificial intelligence has led to expectations of transformative impact on science, yet current systems remain fundamentally limited in enabling genuine scientific discovery. This perspective contends that progress…

I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and…

Neural algorithmic reasoning is an emerging area of machine learning focusing on building models that can imitate the execution of classic algorithms, such as sorting, shortest paths, etc. One of the main challenges is to learn algorithms…

Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…

As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g., rising costs, declining survey response rates), researchers increasingly use predictions from…

Great endeavors have been made to study AI's ability in abstract reasoning, along with which different versions of RAVEN's progressive matrices (RPM) are proposed as benchmarks. Previous works give inkling that without sophisticated design…

Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of…