Related papers: ZFLean: a framework for set-level mathematics in L…
We present two logical systems based on dependent types that are comparable to ZFC, both in terms of simplicity and having natural set theoretic interpretations. Our perspective is that of a mathematician trained in classical logic, but…
Federeated Learning (FL) offers a privacy-preserving solution for Semantic Segmentation (SS) tasks to adapt to new domains, but faces significant challenges from these domain shifts, particularly when client data is unlabeled. However, most…
Typeclasses provide an elegant and effective way of managing ad-hoc polymorphism in both programming languages and interactive proof assistants. However, the increasingly sophisticated uses of typeclasses within proof assistants, especially…
The Lean mathematical library mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean's mechanism of instance parameters. Related mechanisms for typeclasses are available in other…
Building Information Modeling (BIM) is widely used in the Architecture, Engineering, and Construction (AEC) industry, but the complexity of Industry Foundation Classes (IFC) limits accessibility for non-expert users. To address this, we…
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…
This paper introduces \textsc{FuzzyLogic.jl}, a Julia library to perform fuzzy inference. The library is fully open-source and released under a permissive license. The core design principles of the library are: user-friendliness,…
We will discuss our experiences and design decisions obtained from building a formal library for the convolution of two functions. Convolution is a fundamental concept with applications throughout mathematics. We will focus on the design…
Organizations and enterprises across domains such as healthcare, finance, and scientific research are increasingly required to extract collective intelligence from distributed, siloed datasets while adhering to strict privacy, regulatory,…
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…
Modern federated networks, such as those comprised of wearable devices, mobile phones, or autonomous vehicles, generate massive amounts of data each day. This wealth of data can help to learn models that can improve the user experience on…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Federated Learning (FL) is a method of training machine learning models on private data distributed over a large number of possibly heterogeneous clients such as mobile phones and IoT devices. In this work, we propose a new federated…
Federated learning (FL) is a distributed machine learning technique in which multiple clients cooperate to train a shared model without exchanging their raw data. However, heterogeneity of data distribution among clients usually leads to…
Federated learning (FL), aimed at leveraging vast distributed datasets, confronts a crucial challenge: the heterogeneity of data across different silos. While previous studies have explored discrete representations to enhance model…
Federated learning (FL) is a machine learning paradigm, which enables multiple and decentralized clients to collaboratively train a model under the orchestration of a central aggregator. FL can be a scalable machine learning solution in big…
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…
Federated learning is a distributed learning framework that allows a set of clients to collaboratively train a model under the orchestration of a central server, without sharing raw data samples. Although in many practical scenarios the…
We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and…