Related papers: Automated Discovery of New $L$-Function Relations
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
We give conditions for when two Euler products are the same given that they satisfy a functional equation and their coefficients are not too large and do not differ from each other by too much. Additionally, we prove a number of…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
Building machines that can understand text like humans is an AI-complete problem. A great deal of research has already gone into this, with astounding results, allowing everyday people to discuss with their telephones, or have their reading…
Reward function design and exploration time are arguably the biggest obstacles to the deployment of reinforcement learning (RL) agents in the real world. In many real-world tasks, designing a reward function takes considerable hand…
Terms in arithmetic of the form s in the formula s=t(< s >), with t a term with one free variable and < s > a numeral denoting the G\"odel number of s, are examined by writing the explicit definition of the encoding functions whose…
In this paper, we explore an approach to auxiliary task discovery in reinforcement learning based on ideas from representation learning. Auxiliary tasks tend to improve data efficiency by forcing the agent to learn auxiliary prediction and…
Online fraud often involves identity theft. Since most security measures are weak or can be spoofed, we investigate a more nuanced and less explored avenue: behavioral biometrics via handwriting movements. This kind of data can be used to…
We propose a symbolic generative task description language and a corresponding inference engine capable of representing arbitrary multimodal tasks as structured symbolic flows. Unlike conventional generative models that rely on large-scale…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
We present an algorithmic approach to the verification of identities on multiple theta functions in the form of products of theta functions $[(-1)^{\delta}a_1^{\alpha_1}a_2^{\alpha_2}\cdots a_r^{\alpha_r}q^{s}; q^{t}]_\infty$, where…
Multi-round incomplete information tasks are crucial for evaluating the lateral thinking capabilities of large language models (LLMs). Currently, research primarily relies on multiple benchmarks and automated evaluation metrics to assess…
Artificial intelligence (AI) has acquired notorious relevance in modern computing as it effectively solves complex tasks traditionally done by humans. AI provides methods to represent and infer knowledge, efficiently manipulate texts and…
In this paper, we compare different existing approaches employed in data mining of big proof libraries in automated and interactive theorem proving.
The field of Automatic Machine Learning (AutoML) has recently attained impressive results, including the discovery of state-of-the-art machine learning solutions, such as neural image classifiers. This is often done by applying an…
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Self-preference is a fundamental feature of biological organisms. Since large language models (LLMs) lack sentience, they might be expected to avoid such distortions. Yet, across 72 experiments and ~41,000 queries, we discovered massive…