Related papers: AlephZero and Mathematical Experience
Grammatical error detection and automated essay scoring are two tasks in the area of automated assessment. Traditionally these tasks have been treated independently with different machine learning models and features used for each task. In…
This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in…
In this short review, I will summarize my research experience in three fields in applied mathematics: mathematical biology, applied probability, and applied discrete mathematics. Specifically, I will show how each project was initiated, and…
Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
The recent progress in large language models (LLMs), especially the invention of chain-of-thought prompting, has made it possible to automatically answer questions by stepwise reasoning. However, when faced with more complicated problems…
How to design automated procedures which (i) accurately assess the knowledge of a student, and (ii) efficiently provide advices for further study? To produce well-founded answers, Knowledge Space Theory relies on a combinatorial viewpoint…
Despite the recent progress in automatic theorem provers, proof engineers are still suffering from the lack of powerful proof automation. In this position paper we first report our proof strategy language based on a meta-tool approach.…
This paper surveys and organizes research works in an under-studied area, which we call automated evaluation for student argumentative writing. Unlike traditional automated writing evaluation that focuses on holistic essay scoring, this…
This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…
Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of…
I present a formal connection between algebraic effects and game semantics, two important lines of work in programming languages semantics with applications in compositional software verification. Specifically, the algebraic signature…
The first automated essay scoring system was developed 50 years ago. Automated essay scoring systems are developing into systems with richer functions than the previous simple scoring systems. Its purpose is not only to score essays but…
There is an apparent similarity between the descriptions of small-step operational semantics of imperative programs and the semantics of finite automata, so defining an abstraction mapping from semantics to automata and proving a simulation…
$L$-functions typically encode interesting information about mathematical objects. This paper reports 29 identities between such functions that hitherto never appeared in the literature. Of these we have a complete proof for 9; all others…
Kant's Critique of Pure Reason, a major contribution to the history of epistemology, proposes a table of categories to elucidate the structure of the a priori principles underlying human judgment. Artificial intelligence (AI) technology,…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
The Turing test may or may not be a valid test of machine intelligence. But in an age of generative AI, the test describes the positions we humans occupy. Judging whether or not something is human or machine produced is an everyday…
Abstract reasoning ability reflects the intelligence and generalization capacity of LLMs to extract and apply abstract rules. However, accurately measuring this ability remains challenging: existing benchmarks either rely on expensive…
Artificial general intelligence (AGI) is an established field of research. Yet some have questioned if the term still has meaning. AGI has been subject to so much hype and speculation it has become something of a Rorschach test. Melanie…