Related papers: Learning Foundations Beneath the Stars

By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…

Many scientific fields, from medicine to seismology, rely on analyzing sequences of events over time to understand complex systems. Traditionally, machine learning models must be built and trained from scratch for each new dataset, which is…

This paper studies the viability of making a country a developmental state. In particular it studies the characteristics of a developmental state and how they are linked to technology. It then identifies technical education, as a vital…

I provide an introduction to quantum computers, describing how they might be realized using language accessible to a solid state physicist. A listing of the minimal requirements for creating a quantum computer is given. I also discuss…

Foundation models are premised on the idea that sequence prediction can uncover deeper domain understanding, much like how Kepler's predictions of planetary motion later led to the discovery of Newtonian mechanics. However, evaluating…

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment,…

Computational methods and associated software implementations are central to every field of scientific investigation. Modern biological research, particularly within systems biology, has relied heavily on the development of software tools…

This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.

Nowadays the Science progress depends on the numerical calculus, due to the possibility of obtention of solutions using simulations which would be impracticable, or even impossible, to be analitically obtained. In this aspect, it becomes…

In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis is first introduced by Diaconis and Sturmfels (1998) for…

We study a class of minimal geometric partial differential equations that serves as a framework to understand the evolution of boundaries between states in different pattern forming systems. The framework combines normal growth, curvature…

Proof competence, i.e. the ability to write and check (mathematical) proofs, is an important skill in Computer Science, but for many students it represents a difficult challenge. The main issues are the correct use of formal language and…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…

Process science is a highly interdisciplinary field of research. Despite numerous proposals, process science lacks an adequate understanding of the core concepts of the field, including notions such as process, event, and system. A more…

Foundation Models (FMs) display exceptional performance in tasks such as natural language processing and are being applied across a growing range of disciplines. Although typically trained on large public datasets, FMs are often fine-tuned…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…

"What Should be Hidden and Open in Computer Security: Lessons from Deception, the Art of War, Law, and Economic Theory" Peter P. Swire, George Washington University. Imagine a military base. It is defended against possible attack. Do we…

To make progress in learning the underlying fundamental theory, it will be necessary to combine bottom-up phenomenology and top-down analysis -- in particular, top-down is unlikely to succeed alone. Here I elaborate on the role of both, and…

Spatio-temporal deep learning models aims to utilize useful patterns in such data to support tasks like prediction. However, previous deep learning models designed for specific tasks typically require separate training for each use case,…