Related papers: LeanBET: Formally-verified surface area calculatio…
The physics community relies on index notation to effectively manipulate types of tensors. This paper introduces the first formally verified implementation of index notation in the interactive theorem prover Lean 4. By integrating index…
We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…
Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…
Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…
The conceptual design of Blended Wing Body (BWB) aircraft is often constrained by the high computational cost of resolving complex aerodynamics over a high-dimensional design space. While deep learning offers a pathway to rapid aerodynamic…
This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set…
In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…
In this paper, we present ELEET, a novel execution engine that allows one to seamlessly query and process text as a first-class citizen along with tables. To enable such a seamless integration of text and tables, ELEET leverages learned…
Large-scale transformer-based models like the Bidirectional Encoder Representations from Transformers (BERT) are widely used for Natural Language Processing (NLP) applications, wherein these models are initially pre-trained with a large…
In this paper, we describe the approach that we employed to address the task of Entity Recognition over Wet Lab Protocols -- a shared task in EMNLP WNUT-2020 Workshop. Our approach is composed of two phases. In the first phase, we…
We present a formally verified framework for patent analysis as a hybrid AI + Lean 4 pipeline. The DAG-coverage core (Algorithm 1b) is fully machine-verified once bounded match scores are fixed. Freedom-to-operate, claim-construction…
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic…
This is the first work to investigate the effectiveness of BERT-based contextual embeddings in active learning (AL) tasks on cold-start scenarios, where traditional fine-tuning is infeasible due to the absence of labeled data. Our primary…
We explore advanced fine-tuning techniques to boost BERT's performance in sentiment analysis, paraphrase detection, and semantic textual similarity. Our approach leverages SMART regularization to combat overfitting, improves hyperparameter…
Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees a good…
Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…
Recent advances in large language models (LLMs) have shown promise in formal theorem proving, yet evaluating semantic correctness remains challenging. Existing evaluations rely on indirect proxies such as lexical overlap with…
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…
Purpose: Transcatheter edge-to-edge repair (TEER) and annuloplasty devices are increasingly used to treat mitral valve regurgitation, yet their mechanical effects and interactions remain poorly understood. This study aimed to establish an…
Verification is a critical process in the development of engineered systems. Through verification, engineers gain confidence in the correct functionality of the system before it is deployed into operation. Traditionally, verification…