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  1. Textual analogies that make comparisons between two concepts are often used for explaining complex ideas, creative writing, and scientific discovery. In this paper, we propose and study a new task, called Analogy Detection and Extraction (AnaDE), which includes three synergistic sub-tasks: 1) detecting documents containing analogies, 2) extracting text segments that make up the analogy, and 3) identifying the (source and target) concepts being compared. To facilitate the study of this new task, we create a benchmark dataset by scraping Metamia.com and investigate the performances of state-of-the-art models on all sub-tasks to establish the first-generation benchmark results for this new task. We find that the Longformer model achieves the best performance on all the three sub-tasks demonstrating its effectiveness for handling long texts. Moreover, smaller models fine-tuned on our dataset perform better than non-finetuned ChatGPT, suggesting high task difficulty. Overall, the models achieve a high performance on documents detection suggesting that it could be used to develop applications like analogy search engines. Further, there is a large room for improvement on the segment and concept extraction tasks. 
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    Free, publicly-accessible full text available March 22, 2025
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    Abstract Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD-based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets. 
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