Related papers: Towards Machine Learning Induction
Automated reasoning and theorem proving have recently become major challenges for machine learning. In other domains, representations that are able to abstract over unimportant transformations, such as abstraction over translations and…
A main driver behind the digitization of industry and society is the belief that data-driven model building and decision making can contribute to higher degrees of automation and more informed decisions. Building such models from data often…
Automated machine learning (AutoML) was formed around the fundamental objectives of automatically and efficiently configuring machine learning (ML) workflows, aiding the research of new ML algorithms, and contributing to the democratization…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
Informed machine learning methods allow the integration of prior knowledge into learning systems. This can increase accuracy and robustness or reduce data needs. However, existing methods often assume hard constraining knowledge, that does…
Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…
This paper introduces a new algorithm for the induction if complex finite state automata from samples of behavior. The algorithm is based on information theoretic principles. The algorithm reduces the search space by many orders of…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
We present a novel approach for teaching logic and the metatheory of logic to students who have some experience with functional programming. We define concepts in logic as a series of functional programs in the language of the proof…
Can a physicist make only a finite number of errors in the eternal quest to uncover the law of nature? This millennium-old philosophical problem, known as inductive inference, lies at the heart of epistemology. Despite its significance to…
Today, intelligent systems that offer artificial intelligence capabilities often rely on machine learning. Machine learning describes the capacity of systems to learn from problem-specific training data to automate the process of analytical…
A fascinating hypothesis is that human and animal intelligence could be explained by a few principles (rather than an encyclopedic list of heuristics). If that hypothesis was correct, we could more easily both understand our own…
The ability to derive underlying principles from a handful of observations and then generalize to novel situations -- known as inductive reasoning -- is central to human intelligence. Prior work suggests that language models (LMs) often…
Machine Learning (ML) is applicable to scientific problems, i.e. to those which have a well defined answer, only if this answer can be brought to a peculiar form ${\cal G}: X\longrightarrow Z$ with ${\cal G}(\vec x)$ expressed as a…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
In this position paper, we argue that application-driven research has been systemically under-valued in the machine learning community. As applications of machine learning proliferate, innovative algorithms inspired by specific real-world…
Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
Numerous theorems, such as those in geometry, are often presented in multimodal forms (e.g., diagrams). Humans benefit from visual reasoning in such settings, using diagrams to gain intuition and guide the proof process. Modern Multimodal…