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Numerous statistical and machine learning", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 604 + ], + "score": 1.0, + "content": "methods have been developed for time series analysis in the past. Inspired by its great success", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 602, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 506, + 615 + ], + "score": 1.0, + "content": "in natural language processing and computer vision Vaswani et al. (2017); Devlin et al. (2019);", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 613, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 506, + 626 + ], + "score": 1.0, + "content": "Dosovitskiy et al. (2021); Rao et al. (2021), transformer has been introduced to various time series", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 624, + 506, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 506, + 637 + ], + "score": 1.0, + "content": "tasks with promising results Wen et al. (2023), especially for time series forecasting Lim et al. (2021);", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 635, + 348, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 348, + 647 + ], + "score": 1.0, + "content": "Zhou et al. (2022, 2021); Wu et al. (2021); Nie et al. (2022).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30.5, + "bbox_fs": [ + 104, + 536, + 506, + 647 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 651, + 505, + 684 + ], + "lines": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "We have recently witnessed the rapid development of foundation models in NLP. The key idea is to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 662, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 505, + 675 + ], + "score": 1.0, + "content": "pre-train a large language model from billions of tokens to facilitate model training for downstream", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 673, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 106, + 673, + 505, + 685 + ], + "score": 1.0, + "content": "tasks, particularly when we have a few, sometimes even zero, labeled instances. Another advantage of", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 331, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 506, + 343 + ], + "score": 1.0, + "content": "foundation models is that they provide a unified framework for handling diverse tasks, which contrasts", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 342, + 506, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 506, + 355 + ], + "score": 1.0, + "content": "conventional wisdom where each task requires a specially designed algorithm. However, so far, little", + "type": "text", + "cross_page": true + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 353, + 506, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 365 + ], + "score": 1.0, + "content": "progress has been made to exploit pre-trained or foundation models for time series analysis. One main", + "type": "text", + "cross_page": true + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 364, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 106, + 364, + 506, + 376 + ], + "score": 1.0, + "content": "challenge is the lack of the large amount of data to train a foundation model for time series analysis.", + "type": "text", + "cross_page": true + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "score": 1.0, + "content": "The largest data sets for time series analysis is less than 10GB Godahewa et al. (2021), which is much", + "type": "text", + "cross_page": true + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "score": 1.0, + "content": "smaller than that for NLP. To address this challenge, we propose to leverage pre-trained language", + "type": "text", + "cross_page": true + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 397, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 506, + 409 + ], + "score": 1.0, + "content": "models for general time series analysis. Our approach provides a unified framework for diverse time", + "type": "text", + "cross_page": true + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 406, + 507, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 406, + 507, + 422 + ], + "score": 1.0, + "content": "series tasks, such as classification, anomaly detection, forecasting, and few-shot or zero-shot learning.", + "type": "text", + "cross_page": true + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "score": 1.0, + "content": "As shown in Figure 1, using the same backbone, our approach performs either on-par or better than", + "type": "text", + "cross_page": true + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 429, + 506, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 506, + 442 + ], + "score": 1.0, + "content": "the state-of-the-art methods for all main time series analysis tasks. Besides extensive empirical", + "type": "text", + "cross_page": true + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 440, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 506, + 453 + ], + "score": 1.0, + "content": "studies, we also investigate why a transformer model pre-trained from the language domain can be", + "type": "text", + "cross_page": true + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 451, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 505, + 462 + ], + "score": 1.0, + "content": "adapted to time series analysis with almost no change. Our analysis indicates that the self-attention", + "type": "text", + "cross_page": true + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "modules in the pre-trained transformer acquire the ability to perform certain non-data-dependent", + "type": "text", + "cross_page": true + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 473, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 485 + ], + "score": 1.0, + "content": "operations through training. These operations are closely linked to principal component analysis", + "type": "text", + "cross_page": true + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "over the input patterns. We believe it is this generic function performed by the self-attention module", + "type": "text", + "cross_page": true + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "that allows trained transformer models to be so-called universal compute engine Lu et al. (2022)", + "type": "text", + "cross_page": true + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 104, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "or general computation calculator Giannou et al. (2023). 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However, so far, little", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 353, + 506, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 365 + ], + "score": 1.0, + "content": "progress has been made to exploit pre-trained or foundation models for time series analysis. One main", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 364, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 106, + 364, + 506, + 376 + ], + "score": 1.0, + "content": "challenge is the lack of the large amount of data to train a foundation model for time series analysis.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 506, + 387 + ], + "score": 1.0, + "content": "The largest data sets for time series analysis is less than 10GB Godahewa et al. (2021), which is much", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "score": 1.0, + "content": "smaller than that for NLP. To address this challenge, we propose to leverage pre-trained language", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 397, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 506, + 409 + ], + "score": 1.0, + "content": "models for general time series analysis. Our approach provides a unified framework for diverse time", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 406, + 507, + 422 + ], + "spans": [ + { + "bbox": [ + 104, + 406, + 507, + 422 + ], + "score": 1.0, + "content": "series tasks, such as classification, anomaly detection, forecasting, and few-shot or zero-shot learning.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 431 + ], + "score": 1.0, + "content": "As shown in Figure 1, using the same backbone, our approach performs either on-par or better than", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 429, + 506, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 506, + 442 + ], + "score": 1.0, + "content": "the state-of-the-art methods for all main time series analysis tasks. Besides extensive empirical", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 440, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 440, + 506, + 453 + ], + "score": 1.0, + "content": "studies, we also investigate why a transformer model pre-trained from the language domain can be", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 451, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 505, + 462 + ], + "score": 1.0, + "content": "adapted to time series analysis with almost no change. Our analysis indicates that the self-attention", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "modules in the pre-trained transformer acquire the ability to perform certain non-data-dependent", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 473, + 506, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 485 + ], + "score": 1.0, + "content": "operations through training. These operations are closely linked to principal component analysis", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 496 + ], + "score": 1.0, + "content": "over the input patterns. We believe it is this generic function performed by the self-attention module", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 506, + 507 + ], + "score": 1.0, + "content": "that allows trained transformer models to be so-called universal compute engine Lu et al. (2022)", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 104, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "or general computation calculator Giannou et al. (2023). We support our claims by conducting an", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 506, + 529 + ], + "score": 1.0, + "content": "empirical investigation of the resemblance in model behaviors when self-attention is substituted with", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 528, + 366, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 366, + 540 + ], + "score": 1.0, + "content": "PCA, and by providing a theoretical analysis of their correlation.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 543, + 321, + 555 + ], + "lines": [ + { + "bbox": [ + 106, + 543, + 322, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 322, + 556 + ], + "score": 1.0, + "content": "Here we summarize our key contributions as follows:", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 129, + 563, + 505, + 670 + ], + "lines": [ + { + "bbox": [ + 129, + 564, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 129, + 564, + 505, + 576 + ], + "score": 1.0, + "content": "1. We propose a unified framework that uses a frozen pre-trained language model to achieve a", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 141, + 573, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 141, + 573, + 506, + 588 + ], + "score": 1.0, + "content": "SOTA or comparable performance in all major types of time series analysis tasks supported", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 142, + 586, + 505, + 598 + ], + "spans": [ + { + "bbox": [ + 142, + 586, + 505, + 598 + ], + "score": 1.0, + "content": "by thorough and extensive experiments, including time series classification, short/long-term", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 141, + 596, + 472, + 609 + ], + "spans": [ + { + "bbox": [ + 141, + 596, + 472, + 609 + ], + "score": 1.0, + "content": "forecasting, imputation, anomaly detection, few-shot and zero-sample forecasting.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 129, + 611, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 129, + 611, + 505, + 623 + ], + "score": 1.0, + "content": "2. 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Due to space limit, more extensive discussion", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 474, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 474, + 129 + ], + "score": 1.0, + "content": "of related work, experimental results, and theoretical analysis are provided in the Appendix.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "title", + "bbox": [ + 107, + 143, + 197, + 156 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 198, + 158 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 198, + 158 + ], + "score": 1.0, + "content": "2 Related Work", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 167, + 505, + 200 + ], + "lines": [ + { + "bbox": [ + 105, + 167, + 505, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 505, + 180 + ], + "score": 1.0, + "content": "In this section, we provide short reviews of literature in the areas of time series analysis, in-modality", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 179, + 505, + 191 + ], + "spans": [ + { + "bbox": [ + 106, + 179, + 505, + 191 + ], + "score": 1.0, + "content": "transfer learning, and cross-modality knowledge transfer learning. We postpone the discussion of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 189, + 436, + 203 + ], + "spans": [ + { + "bbox": [ + 105, + 189, + 436, + 203 + ], + "score": 1.0, + "content": "works for end-to-end time series analysis to Appendix B, due to the limited space.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 212, + 506, + 387 + ], + "lines": [ + { + "bbox": [ + 106, + 212, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 506, + 225 + ], + "score": 1.0, + "content": "In-modality Transfer Learning through pre-trained models In recent years, a large number of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 224, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 506, + 235 + ], + "score": 1.0, + "content": "research works have verified the effectiveness of the pre-trained model from NLP, CV to Vision-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 235, + 505, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 505, + 246 + ], + "score": 1.0, + "content": "and-Language (VL). Latest studies for NLP focus on learning contextual word embeddings for", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "score": 1.0, + "content": "downstream tasks. With the increase of computing power, the very deep transformer models have", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 256, + 507, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 507, + 269 + ], + "score": 1.0, + "content": "shown powerful representation ability in various language tasks. Among them, BERT Devlin et al.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "score": 1.0, + "content": "(2019) uses transformer encoders and employs masked language modeling task that aims to recover", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "score": 1.0, + "content": "the random masked tokens within a text. OpenAI proposed GPT Radford & Narasimhan (2018)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 288, + 506, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 506, + 301 + ], + "score": 1.0, + "content": "that trains transformer decoders on a large language corpus and then fine-tunes on task-specific data.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "score": 1.0, + "content": "GPT2 Radford et al. (2019) is trained on larger datasets with much more parameters and can be", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 311, + 504, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 311, + 504, + 322 + ], + "score": 1.0, + "content": "transferred to various downstream tasks. Since transformer models can adapt to various inputs, the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 322, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 506, + 334 + ], + "score": 1.0, + "content": "idea of pre-training can also be well adapted to visual tasks. DEiT Touvron et al. (2021) proposed a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 332, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 505, + 345 + ], + "score": 1.0, + "content": "teacher-student strategy for transformers with convolution neural networks (CNNs) as the teacher", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "model and achieves competitive performance. BEiT Bao et al. (2022) converts images as visual", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 352, + 506, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 506, + 368 + ], + "score": 1.0, + "content": "tokens and successfully uses the BERT model in CV. However, because of the insufficient training", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 367, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 505, + 378 + ], + "score": 1.0, + "content": "sample, there is little research on pre-trained models on general time series analysis that cover all", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 377, + 255, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 377, + 255, + 389 + ], + "score": 1.0, + "content": "major tasks like CV or NLP domain.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 106, + 399, + 505, + 530 + ], + "lines": [ + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "Cross-modality knowledge transfer Since transformers can handle different modal tasks through", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 411, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 505, + 422 + ], + "score": 1.0, + "content": "tokenizing the inputs to embeddings, it is also an interesting topic whether the transformers have", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 422, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 422, + 505, + 433 + ], + "score": 1.0, + "content": "universal representation ability and can be used for transferring between various domains. The VL", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 432, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 506, + 446 + ], + "score": 1.0, + "content": "pre-trained model VLMo Bao et al. (2021) proposed a stagewise pre-training strategy that utilizes", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 442, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 505, + 456 + ], + "score": 1.0, + "content": "frozen attention blocks pre-trained by image-only data to train the language expert. One of the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 454, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 505, + 466 + ], + "score": 1.0, + "content": "most related works which transfer knowledge from a pre-trained language model to other domains", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "score": 1.0, + "content": "is Lu et al. (2022), which studies the strong performance of a frozen pre-trained language model", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "score": 1.0, + "content": "(LM) compared to an end-to-end transformer alternative learned from other domains’ data. Another", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "relative work for knowledge transfer to the time series is the Voice2series Yang et al. (2021), which", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 497, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 497, + 506, + 510 + ], + "score": 1.0, + "content": "leverages a pre-trained speech processing model for time series classification and achieves superior", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 509, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 505, + 521 + ], + "score": 1.0, + "content": "performance. To the best of our knowledge, no previous research has investigated cross-modality", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 519, + 478, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 478, + 533 + ], + "score": 1.0, + "content": "knowledge transfer for the time series forecasting task, let alone general time series analysis.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30.5 + }, + { + "type": "title", + "bbox": [ + 107, + 545, + 192, + 559 + ], + "lines": [ + { + "bbox": [ + 104, + 542, + 194, + 564 + ], + "spans": [ + { + "bbox": [ + 104, + 542, + 194, + 564 + ], + "score": 1.0, + "content": "3 Methodology", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "title", + "bbox": [ + 107, + 570, + 201, + 582 + ], + "lines": [ + { + "bbox": [ + 105, + 569, + 202, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 202, + 583 + ], + "score": 1.0, + "content": "3.1 Model Structure", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 591, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 589, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 506, + 603 + ], + "score": 1.0, + "content": "The architecture we employ is depicted in Figure 2. We utilize parameters from NLP pretrained", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 601, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 506, + 613 + ], + "score": 1.0, + "content": "transformer models for time series analysis, with a focus on the GPT2 model Radford et al. (2019).", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "score": 1.0, + "content": "We also experiment with other models, such as BERT Devlin et al. (2019) and BEiT Bao et al. (2022),", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 622, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 506, + 636 + ], + "score": 1.0, + "content": "to further demonstrate that the universal performance of cross-domain knowledge transfer exists in a", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 634, + 243, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 243, + 647 + ], + "score": 1.0, + "content": "wide range of pre-trained models.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 650, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 105, + 650, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 650, + 505, + 663 + ], + "score": 1.0, + "content": "Frozen Pretrained Block Our architecture retains the positional embedding layers and self-attention", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 662, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 505, + 674 + ], + "score": 1.0, + "content": "blocks from the pre-trained models. As self-attention layers and FFN (Feedforward Neural Networks)", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 672, + 506, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 506, + 686 + ], + "score": 1.0, + "content": "contain the majority of learned knowledge from pre-trained language models, we opt to freeze the", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 682, + 263, + 697 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 263, + 697 + ], + "score": 1.0, + "content": "self-attention blocks while fine-tuning.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5 + }, + { + "type": "text", + "bbox": [ + 106, + 700, + 502, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "Positional Embeddings and Layer Normalization To enhance downstream tasks with minimal", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "effort, we fine-tune the positional embeddings and layer normalization layer, which is considered a", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48.5 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 303, + 742, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 741, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 741, + 310, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 11, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 128 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 105, + 72, + 506, + 129 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 143, + 197, + 156 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 198, + 158 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 198, + 158 + ], + "score": 1.0, + "content": "2 Related Work", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 167, + 505, + 200 + ], + "lines": [ + { + "bbox": [ + 105, + 167, + 505, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 505, + 180 + ], + "score": 1.0, + "content": "In this section, we provide short reviews of literature in the areas of time series analysis, in-modality", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 179, + 505, + 191 + ], + "spans": [ + { + "bbox": [ + 106, + 179, + 505, + 191 + ], + "score": 1.0, + "content": "transfer learning, and cross-modality knowledge transfer learning. We postpone the discussion of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 189, + 436, + 203 + ], + "spans": [ + { + "bbox": [ + 105, + 189, + 436, + 203 + ], + "score": 1.0, + "content": "works for end-to-end time series analysis to Appendix B, due to the limited space.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 167, + 505, + 203 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 212, + 506, + 387 + ], + "lines": [ + { + "bbox": [ + 106, + 212, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 506, + 225 + ], + "score": 1.0, + "content": "In-modality Transfer Learning through pre-trained models In recent years, a large number of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 224, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 506, + 235 + ], + "score": 1.0, + "content": "research works have verified the effectiveness of the pre-trained model from NLP, CV to Vision-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 235, + 505, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 505, + 246 + ], + "score": 1.0, + "content": "and-Language (VL). Latest studies for NLP focus on learning contextual word embeddings for", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "score": 1.0, + "content": "downstream tasks. With the increase of computing power, the very deep transformer models have", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 256, + 507, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 256, + 507, + 269 + ], + "score": 1.0, + "content": "shown powerful representation ability in various language tasks. Among them, BERT Devlin et al.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "spans": [ + { + "bbox": [ + 105, + 267, + 506, + 280 + ], + "score": 1.0, + "content": "(2019) uses transformer encoders and employs masked language modeling task that aims to recover", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 506, + 290 + ], + "score": 1.0, + "content": "the random masked tokens within a text. OpenAI proposed GPT Radford & Narasimhan (2018)", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 288, + 506, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 506, + 301 + ], + "score": 1.0, + "content": "that trains transformer decoders on a large language corpus and then fine-tunes on task-specific data.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 505, + 312 + ], + "score": 1.0, + "content": "GPT2 Radford et al. (2019) is trained on larger datasets with much more parameters and can be", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 311, + 504, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 311, + 504, + 322 + ], + "score": 1.0, + "content": "transferred to various downstream tasks. Since transformer models can adapt to various inputs, the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 322, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 506, + 334 + ], + "score": 1.0, + "content": "idea of pre-training can also be well adapted to visual tasks. DEiT Touvron et al. (2021) proposed a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 332, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 332, + 505, + 345 + ], + "score": 1.0, + "content": "teacher-student strategy for transformers with convolution neural networks (CNNs) as the teacher", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "model and achieves competitive performance. BEiT Bao et al. (2022) converts images as visual", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 352, + 506, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 506, + 368 + ], + "score": 1.0, + "content": "tokens and successfully uses the BERT model in CV. However, because of the insufficient training", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 367, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 106, + 367, + 505, + 378 + ], + "score": 1.0, + "content": "sample, there is little research on pre-trained models on general time series analysis that cover all", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 377, + 255, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 377, + 255, + 389 + ], + "score": 1.0, + "content": "major tasks like CV or NLP domain.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 212, + 507, + 389 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 399, + 505, + 530 + ], + "lines": [ + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 412 + ], + "score": 1.0, + "content": "Cross-modality knowledge transfer Since transformers can handle different modal tasks through", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 411, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 505, + 422 + ], + "score": 1.0, + "content": "tokenizing the inputs to embeddings, it is also an interesting topic whether the transformers have", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 422, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 422, + 505, + 433 + ], + "score": 1.0, + "content": "universal representation ability and can be used for transferring between various domains. The VL", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 432, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 506, + 446 + ], + "score": 1.0, + "content": "pre-trained model VLMo Bao et al. (2021) proposed a stagewise pre-training strategy that utilizes", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 442, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 505, + 456 + ], + "score": 1.0, + "content": "frozen attention blocks pre-trained by image-only data to train the language expert. One of the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 454, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 505, + 466 + ], + "score": 1.0, + "content": "most related works which transfer knowledge from a pre-trained language model to other domains", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "score": 1.0, + "content": "is Lu et al. (2022), which studies the strong performance of a frozen pre-trained language model", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "score": 1.0, + "content": "(LM) compared to an end-to-end transformer alternative learned from other domains’ data. Another", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "relative work for knowledge transfer to the time series is the Voice2series Yang et al. (2021), which", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 497, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 497, + 506, + 510 + ], + "score": 1.0, + "content": "leverages a pre-trained speech processing model for time series classification and achieves superior", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 509, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 505, + 521 + ], + "score": 1.0, + "content": "performance. To the best of our knowledge, no previous research has investigated cross-modality", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 519, + 478, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 478, + 533 + ], + "score": 1.0, + "content": "knowledge transfer for the time series forecasting task, let alone general time series analysis.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30.5, + "bbox_fs": [ + 104, + 399, + 506, + 533 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 545, + 192, + 559 + ], + "lines": [ + { + "bbox": [ + 104, + 542, + 194, + 564 + ], + "spans": [ + { + "bbox": [ + 104, + 542, + 194, + 564 + ], + "score": 1.0, + "content": "3 Methodology", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "title", + "bbox": [ + 107, + 570, + 201, + 582 + ], + "lines": [ + { + "bbox": [ + 105, + 569, + 202, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 202, + 583 + ], + "score": 1.0, + "content": "3.1 Model Structure", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 591, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 589, + 506, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 506, + 603 + ], + "score": 1.0, + "content": "The architecture we employ is depicted in Figure 2. We utilize parameters from NLP pretrained", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 601, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 506, + 613 + ], + "score": 1.0, + "content": "transformer models for time series analysis, with a focus on the GPT2 model Radford et al. (2019).", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 506, + 626 + ], + "score": 1.0, + "content": "We also experiment with other models, such as BERT Devlin et al. (2019) and BEiT Bao et al. (2022),", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 622, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 506, + 636 + ], + "score": 1.0, + "content": "to further demonstrate that the universal performance of cross-domain knowledge transfer exists in a", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 634, + 243, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 243, + 647 + ], + "score": 1.0, + "content": "wide range of pre-trained models.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 589, + 506, + 647 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 650, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 105, + 650, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 650, + 505, + 663 + ], + "score": 1.0, + "content": "Frozen Pretrained Block Our architecture retains the positional embedding layers and self-attention", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 662, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 505, + 674 + ], + "score": 1.0, + "content": "blocks from the pre-trained models. As self-attention layers and FFN (Feedforward Neural Networks)", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 672, + 506, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 506, + 686 + ], + "score": 1.0, + "content": "contain the majority of learned knowledge from pre-trained language models, we opt to freeze the", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 682, + 263, + 697 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 263, + 697 + ], + "score": 1.0, + "content": "self-attention blocks while fine-tuning.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 650, + 506, + 697 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 700, + 502, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "Positional Embeddings and Layer Normalization To enhance downstream tasks with minimal", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "effort, we fine-tune the positional embeddings and layer normalization layer, which is considered a", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 298, + 505, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 313 + ], + "score": 1.0, + "content": "standard practiceLu et al. (2022); Houlsby et al. (2019). 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As a result, we retrain these components", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 309, + 184, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 184, + 324 + ], + "score": 1.0, + "content": "during fine-tuning.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5 + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 382 + ], + "lines": [ + { + "bbox": [ + 106, + 326, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 506, + 340 + ], + "score": 1.0, + "content": "Input Embedding Given our goal of applying the NLP pre-trained model to various tasks and a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 338, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 505, + 350 + ], + "score": 1.0, + "content": "new modality, we must redesign and train the input embedding layer. 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This", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "score": 1.0, + "content": "normalization block simply normalizes the input time series using mean and variance, and then adds", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 430, + 205, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 205, + 443 + ], + "score": 1.0, + "content": "them back to the output.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 446, + 505, + 501 + ], + "lines": [ + { + "bbox": [ + 105, + 445, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 460 + ], + "score": 1.0, + "content": "Patching To extract local semantic information, we utilize patching Nie et al. 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To ensure a fair comparison, we use GPT2-backbone", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "score": 1.0, + "content": "FPT and adhere to the experimental settings of TimesNet Wu et al. (2023). Due to the space limit,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 585, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 506, + 597 + ], + "score": 1.0, + "content": "only the summarized results are presented below except zero-shot forecasting. 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To ensure a fair comparison, we use GPT2-backbone", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 587 + ], + "score": 1.0, + "content": "FPT and adhere to the experimental settings of TimesNet Wu et al. (2023). Due to the space limit,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 585, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 506, + 597 + ], + "score": 1.0, + "content": "only the summarized results are presented below except zero-shot forecasting. Full experimental", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 609 + ], + "score": 1.0, + "content": "results of the other six downstream tasks can be found in Appendix D.3, D.2, D.7, H.6, H.7, H.8, H.9", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 607, + 159, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 159, + 621 + ], + "score": 1.0, + "content": "respectively.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 530, + 506, + 621 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 623, + 506, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 622, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 506, + 636 + ], + "score": 1.0, + "content": "Baselines We select representative baselines and cite their results from Wu et al. (2023), which", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 635, + 506, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 635, + 506, + 646 + ], + "score": 1.0, + "content": "includes the most recent and quite extensive empirical studies of time series. The baselines in-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 644, + 507, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 507, + 658 + ], + "score": 1.0, + "content": "clude CNN-based models: TimesNet Wu et al. (2023); MLP-based models: LightTS Zhang et al.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 655, + 507, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 507, + 669 + ], + "score": 1.0, + "content": "(2022) and DLinear Zeng et al. (2023); Transformer-based models: Reformer Kitaev et al. (2020),", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 667, + 507, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 507, + 680 + ], + "score": 1.0, + "content": "Informer Zhou et al. (2021), Autoformer Wu et al. (2021), FEDformer Zhou et al. (2022), Non-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 677, + 507, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 507, + 691 + ], + "score": 1.0, + "content": "stationary Transformer Liu et al. (2022), ETSformer Woo et al. (2022), PatchTST Nie et al. (2022).", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 688, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 505, + 701 + ], + "score": 1.0, + "content": "Besides, N-HiTS Challu et al. (2022) and N-BEATS Oreshkin et al. (2019) are used for short-term", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "forecasting. Anomaly Transformer Xu et al. (2021) is used for anomaly detection. XGBoost Chen &", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 507, + 723 + ], + "score": 1.0, + "content": "Guestrin (2016), Rocket Dempster et al. (2020), LSTNet Lai et al. (2018), LSSL Gu et al. (2021),", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 622, + 507, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 72, + 504, + 95 + ], + "lines": [ + { + "bbox": [ + 105, + 71, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 71, + 506, + 86 + ], + "score": 1.0, + "content": "Pyraformer Liu et al. (2021), TCN Franceschi et al. (2019) and Flowformer Huang et al. (2022) are", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 199, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 199, + 96 + ], + "score": 1.0, + "content": "used for classification.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "title", + "bbox": [ + 107, + 107, + 187, + 119 + ], + "lines": [ + { + "bbox": [ + 105, + 106, + 188, + 120 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 188, + 120 + ], + "score": 1.0, + "content": "4.1 Main Results", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 107, + 127, + 505, + 172 + ], + "lines": [ + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "score": 1.0, + "content": "Overall, as shown in Figure 1, GPT2-backbone FPT outperforms other models in most tasks, including", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "score": 1.0, + "content": "long/short-term forecasting, classification, anomaly detection, imputation, and fow-shot/zero-short", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 150, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 505, + 163 + ], + "score": 1.0, + "content": "forecasting. This confirms that time series tasks can also take advantage of cross-modality transferred", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 160, + 491, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 491, + 174 + ], + "score": 1.0, + "content": "knowledge. In the following, we use GPT2(K) to represent GPT2-backbone with first K Layers.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + }, + { + "type": "title", + "bbox": [ + 107, + 184, + 178, + 196 + ], + "lines": [ + { + "bbox": [ + 105, + 183, + 180, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 180, + 198 + ], + "score": 1.0, + "content": "4.2 Imputation", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 205, + 505, + 249 + ], + "lines": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "Setups We conduct experiments on six popular real-world datasets, including 4 ETT datasets Zhou", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 215, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 506, + 228 + ], + "score": 1.0, + "content": "et al. (2021) (ETTh1, ETTh2, ETTm1, ETTm2), Electricity and Weather, where the data-missing is", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 227, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 416, + 238 + ], + "score": 1.0, + "content": "common. Following the settings of TimesNet, different random mask ratios (", + "type": "text" + }, + { + "bbox": [ + 416, + 227, + 502, + 238 + ], + "score": 0.26, + "content": "\\{ 1 2 . 5 \\% , 2 5 \\% , 3 7 . 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 227, + 506, + 238 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 237, + 474, + 250 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 129, + 249 + ], + "score": 0.77, + "content": "5 0 \\% \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 130, + 237, + 474, + 250 + ], + "score": 1.0, + "content": ") of time points are selected for the evaluation on various proportions of missing data.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 106, + 253, + 505, + 308 + ], + "lines": [ + { + "bbox": [ + 106, + 253, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 506, + 266 + ], + "score": 1.0, + "content": "Results The results are shown in Table 1 that GPT2(3) FPT achieves the best performance on most", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 264, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 506, + 277 + ], + "score": 1.0, + "content": "datasets. Particularly, compared to the previous SOTA TimesNet, GPT2(3) FPT yields a relative", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 275, + 506, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 134, + 286 + ], + "score": 0.85, + "content": "1 1 . 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 275, + 264, + 289 + ], + "score": 1.0, + "content": "MSE reduction on ETTh1,and a", + "type": "text" + }, + { + "bbox": [ + 265, + 276, + 288, + 286 + ], + "score": 0.86, + "content": "4 . 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 275, + 506, + 289 + ], + "score": 1.0, + "content": "MSE reduction on average on six benchmark datasets.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "It verifies that the proposed method can also effectively mine temporal patterns of incomplete time", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 298, + 135, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 135, + 310 + ], + "score": 1.0, + "content": "series.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 109, + 360, + 540, + 435 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 323, + 505, + 354 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 323, + 506, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 275, + 335 + ], + "score": 1.0, + "content": "Table 1: Imputation task. We randomly mask {", + "type": "text" + }, + { + "bbox": [ + 275, + 324, + 299, + 334 + ], + "score": 0.72, + "content": "12 . 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 323, + 302, + 335 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 303, + 324, + 320, + 334 + ], + "score": 0.8, + "content": "2 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 323, + 323, + 335 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 324, + 324, + 348, + 334 + ], + "score": 0.82, + "content": "3 7 . 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 323, + 351, + 335 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 351, + 324, + 370, + 334 + ], + "score": 0.76, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 370, + 323, + 506, + 335 + ], + "score": 1.0, + "content": "} time points of 96-length time series.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 334, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 106, + 334, + 505, + 345 + ], + "score": 1.0, + "content": "The results are averaged from 4 different mask ratios. Black: best, Red: second best. Appendix H.8 shows the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 343, + 150, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 150, + 355 + ], + "score": 1.0, + "content": "full results.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18 + }, + { + "type": "table_body", + "bbox": [ + 109, + 360, + 540, + 435 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 360, + 540, + 435 + ], + "spans": [ + { + "bbox": [ + 109, + 360, + 540, + 435 + ], + "score": 0.981, + "html": "
MethodsGPT2(3) MSEMAETimesNet MSE MAEPatchTST MSE MAEETSformer MSE MAELightTS MSEMAEDLinear MSE MAEFEDformer MSEMAEStationary MSE MAEAutoformer MSE MAEInformer MSE MAEMSE MAEReformer
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Weather Average0.031 0.056 ：|0.0470.1270.0300.054 0.0490.132|0.0340.0760.1710.1170.0520.1100.099 0.2030.032 [0.060 0.144|0.1970.309|0.1230.228|0.1190.224|0.1120.229|0.0560.142|0.0610.151|0.1650.273|0.134 0.2400.059 0.0310.0570.0450.1040.0380.087
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MethodsGPT2(3) MSEMAETimesNet MSE MAEPatchTST MSE MAEETSformer MSE MAELightTS MSEMAEDLinear MSE MAEFEDformer MSEMAEStationary MSE MAEAutoformer MSE MAEInformer MSE MAEMSE MAEReformer
ETTm1 ETTm2 ETTh1 ETTh2 ECL0.028 0.105 0.021 0.084 0.069 0.173 0.048 0.141 0.0900.2070.0270.107 0.0220.088 0.078 0.187 0.049 0.146 0.092 0.2100.0470.140 0.029 0.102 0.115 0.065 0.072 0.1830.224 0.202 0.163 0.367 0.214 0.0550.1200.253 0.208 0.327 0.329 0.436 0.3390.1040.218 0.046 0.151 0.284 0.373 0.119 0.250 0.131 0.262 0.0550.201 0.142 0.1320.0930.206 0.0960.208 0.306 0.259 0.2600.0620.177 0.101 0.215 0.117 0.246 0.163 0.279 0.1300.2590.0360.126 0.0260.099 0.094 0.053 0.100 0.2180.201 0.152 0.1010.0510.150 0.029 0.105 0.103 0.214 0.055 0.156 0.2250.071 0.188 0.156 0.292 0.161 0.337 0.2220.279 0.452 0.3280.055 0.166 0.157 0.280 0.1220.245 0.2340.352 0.2000.313
Weather Average0.031 0.056 ：|0.0470.1270.0300.054 0.0490.132|0.0340.0760.1710.1170.0520.1100.099 0.2030.032 [0.060 0.144|0.1970.309|0.1230.228|0.1190.224|0.1120.229|0.0560.142|0.0610.151|0.1650.273|0.134 0.2400.059 0.0310.0570.0450.1040.0380.087
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MethodsGPT2(6) OursTimesNet PatchTS.ETS.FED.LightTS DLinear StationaryAuto.In.Re.LogTrans.Trans.
SMD86.8984.6184.6283.1385.0882.5377.1084.7285.1183.0485.4981.6575.3276.2179.56
MSL82.4581.8478.7085.0378.5778.9584.8877.5079.0584.8683.3184.0684.4079.5778.68
SMAP72.8869.3968.8269.5070.7669.2169.2671.0971.12 71.0971.1869.92 70.4069.9769.70
SWaT94.2393.0285.7284.9193.1993.3387.5279.8892.7491.7883.1081.43 82.8080.5280.37
PSM97.1397.3496.0891.7697.2397.1593.5597.2993.2982.0879.4077.10 73.6176.7476.07
Average86.7285.2482.7982.87 84.9784.2382.4682.0884.26 82.5780.5078.8377.3176.6076.88
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MethodsGPT2(6) MSE MAETimesNet MSEMAEETSformer MSE MAELightTS MSEMAEDLinear MSEMAEFEDformer MSEMAEPatchTST MSE MAEStationary MSEMAEAutoformer MSEMAEInformer MSE MAEReformer MSE MAE
Weather ETTh1 ETTh2 ETTm10.2370.270 0.427 0.426 0.3460.394 0.352 0.3830.2590.287 0.4580.450 0.4140.427 0.400 0.406 0.2910.439 0.4290.271 0.334 0.5420.510 0.452 0.425[0.261 0.312 0.491 0.479 0.602 0.543 0.435 0.4370.2490.300 0.4230.437 0.431 0.3570.447 0.378 0.3340.3090.360 0.4400.460 0.437 0.449 0.448 0.4520.2250.264 0.413 0.430 0.330 0.379 0.351 0.3870.288 0.314 0.5700.537 0.5260.516 0.4810.4560.3380.382 0.4960.487 0.450 0.459 0.588 0.51710.6340.548 1.040 0.795 4.431 0.9611.729 0.734 0.7990.8030.656 1.0290.915 6.7362.191 0.671
ETTm2 ILI ECL Traffic0.2660.326 1.9250.903 0.1670.263 0.414 0.2940.333 2.139 0.931 0.1920.295 0.620 0.336 |0.5960.433|0.293 2.497 0.621 |0.662 0.473|1.303 0.616|0.562 0.436|0.701 0.489|0.342 1.004 0.2080.323 0.3960.409 0.436 7.382 2.003 0.229 0.329 0.622 0.3920.267 2.169 0.166 0.4340.305 1.041 2.847 50.263 0.295 0.6100.349 1.144 0.214 0.327 0.3760.255 0.315 1.4430.798 0.161 0.253 0.390 0.264 |0.4460.386|0.6330.465|0.757 0.511|0.306 2.077 0.1930.296 0.6240.347 0.327 0.914 3.006 0.227 0.340 0.6280.371 1.161 0.338 0.3791.410 5.137 1.544 0.311 0.397 0.764 0.4160.810 1.479 4.724 0.7410.915 1.445 0.3380.422 0.422
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MethodsGPT2(6) OursTimesNet PatchTS.ETS.FED.LightTS DLinear StationaryAuto.In.Re.LogTrans.Trans.
SMD86.8984.6184.6283.1385.0882.5377.1084.7285.1183.0485.4981.6575.3276.2179.56
MSL82.4581.8478.7085.0378.5778.9584.8877.5079.0584.8683.3184.0684.4079.5778.68
SMAP72.8869.3968.8269.5070.7669.2169.2671.0971.12 71.0971.1869.92 70.4069.9769.70
SWaT94.2393.0285.7284.9193.1993.3387.5279.8892.7491.7883.1081.43 82.8080.5280.37
PSM97.1397.3496.0891.7697.2397.1593.5597.2993.2982.0879.4077.10 73.6176.7476.07
Average86.7285.2482.7982.87 84.9784.2382.4682.0884.26 82.5780.5078.8377.3176.6076.88
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MethodsGPT2(6) MSE MAETimesNet MSEMAEETSformer MSE MAELightTS MSEMAEDLinear MSEMAEFEDformer MSEMAEPatchTST MSE MAEStationary MSEMAEAutoformer MSEMAEInformer MSE MAEReformer MSE MAE
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(2018),", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 599, + 297, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 599, + 297, + 611 + ], + "score": 1.0, + "content": "contains marketing data of various frequencies.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30, + "bbox_fs": [ + 106, + 577, + 506, + 611 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 615, + 504, + 637 + ], + "lines": [ + { + "bbox": [ + 105, + 614, + 506, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 506, + 628 + ], + "score": 1.0, + "content": "Results The results in Table 4 show that the performance of GPT2-backbone (6) FPT is superior to", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 626, + 504, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 626, + 504, + 637 + ], + "score": 1.0, + "content": "advanced Transformer-based and MLP-based models, and comparable to TimesNet and N-BEATS.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5, + "bbox_fs": [ + 105, + 614, + 506, + 637 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 651, + 221, + 663 + ], + "lines": [ + { + "bbox": [ + 105, + 649, + 222, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 222, + 666 + ], + "score": 1.0, + "content": "4.7 Few-shot Forecasting", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 108, + 671, + 505, + 694 + ], + "lines": [ + { + "bbox": [ + 106, + 671, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 505, + 684 + ], + "score": 1.0, + "content": "The large language model (LLM) has demonstrated remarkable performance in both few-shot and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 682, + 505, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 505, + 695 + ], + "score": 1.0, + "content": "zero-shot learning settings Brown et al. (2020); OpenAI (2023). It can be argued that few-shot and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 163, + 505, + 174 + ], + "spans": [ + { + "bbox": [ + 106, + 163, + 505, + 174 + ], + "score": 1.0, + "content": "zero-shot learning also represent the ultimate tasks for a universal time series forecasting model. To", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 173, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 106, + 173, + 505, + 186 + ], + "score": 1.0, + "content": "extensively evaluate the representation power of the GPT2(6) for time series analysis, we conduct", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 184, + 347, + 198 + ], + "spans": [ + { + "bbox": [ + 106, + 184, + 347, + 198 + ], + "score": 1.0, + "content": "experiments under few-shot and zero-shot learning settings.", + "type": "text", + "cross_page": true + } + ], + "index": 8 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 671, + 505, + 695 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 109, + 106, + 509, + 144 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 63, + 504, + 93 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 63, + 505, + 74 + ], + "spans": [ + { + "bbox": [ + 105, + 63, + 505, + 74 + ], + "score": 1.0, + "content": "Table 4: Short-term forecasting task on M4. The prediction lengths are in [6, 48] and results are weighted", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "score": 1.0, + "content": "averaged from several datasets under different sample intervals. Black: best, Red: second best. Appendix H.9", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 82, + 187, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 187, + 94 + ], + "score": 1.0, + "content": "shows the full results.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 109, + 106, + 509, + 144 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 106, + 509, + 144 + ], + "spans": [ + { + "bbox": [ + 109, + 106, + 509, + 144 + ], + "score": 0.974, + "html": "
Methods ||GPT2(6)TimesNetPatchTSTN-HiTS N-BEATSETSformerLightTSDLinearFEDformer StationaryAutoformer InformerReformer
SMAPE11.99111.82912.05911.92711.85114.71813.52513.63912.84012.78012.90914.08618.200
MASE1.6001.5851.6231.6131.5992.4082.1112.0951.7011.7561.7712.7184.223
OWA0.8610.8510.8690.8610.8551.1721.0511.0510.9180.9300.9391.2301.775
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MethodsGPT2(6) MSE MAETimesNet MSE MAEDLinear MSE MAEFEDformer MSEMAEPatchTST MSEMAEAutoformer MSE MAEStationary MSE MAEETSformer MSE MAELightTS MSE MAEInformer MSE MAEReformer MSE MAE
Weather ETTh1 ETTh20.238 0.275 0.5900.524 0.3970.4210.279 0.301 0.869 0.628 0.479 0.4650.301 0.283 0.691 0.599 0.608 0.5380.2840.324 0.638 0.561 0.4660.4750.241 0.6330.542 0.415 0.4310.27910.3000.342 0.701 0.596 0.4880.4990.318 0.322 0.9140.639 0.4610.4540.317 0.359 1.179 0.833 0.8930.7130.289 0.322 1.375 0.877 2.6550.597 1.199 0.8080.4940.545 0.469 1.249 0.833
ETTm1 ETTm20.4640.441 0.2930.3350.676 0.537 0.319 0.3530.4110.429 0.3160.3680.721 0.605 0.463 0.4880.501 0.296 0.3430.466 0.8020.628 0.9300.797 0.3320.577 0.979 0.714 0.4470.4871.159 0.970 0.7043.871 1.192 3.3691.512 3.485 0.820 1.4251.485 0.856
ECL0.1760.2690.323 0.3920.2800.3460.4280.180 0.2691.3410.4780.366 0.4430.987 0.4410.755 0.4881.439 1.194 0.8903.9771.586 50.768
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The GPT2(6) FPT model consistently outperforms all recent", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "score": 1.0, + "content": "state-of-the-art transformer and MLP-based time series forecasting methods. 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We attribute", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 587, + 355, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 355, + 599 + ], + "score": 1.0, + "content": "this to the knowledge transfer capability from the FPT model.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 107, + 614, + 175, + 627 + ], + "lines": [ + { + "bbox": [ + 104, + 613, + 177, + 630 + ], + "spans": [ + { + "bbox": [ + 104, + 613, + 177, + 630 + ], + "score": 1.0, + "content": "5 Ablations", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 640, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 105, + 639, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 652 + ], + "score": 1.0, + "content": "In this section, we conduct several ablations on model selection and effectiveness of pre-training. The", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 649, + 506, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 506, + 663 + ], + "score": 1.0, + "content": "detailed results are shown in Appendix H. We introduce several variants, GPT2(0) FPT, GPT2(6)", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 660, + 314, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 314, + 675 + ], + "score": 1.0, + "content": "without freezing and GPT2(6) without pre-training.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "Model Selection We separately analyze the number of GPT2 layers and the fine-tuning parameters", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "selection. 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Methods ||GPT2(6)TimesNetPatchTSTN-HiTS N-BEATSETSformerLightTSDLinearFEDformer StationaryAutoformer InformerReformer
SMAPE11.99111.82912.05911.92711.85114.71813.52513.63912.84012.78012.90914.08618.200
MASE1.6001.5851.6231.6131.5992.4082.1112.0951.7011.7561.7712.7184.223
OWA0.8610.8510.8690.8610.8551.1721.0511.0510.9180.9300.9391.2301.775
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MethodsGPT2(6) MSE MAETimesNet MSE MAEDLinear MSE MAEFEDformer MSEMAEPatchTST MSEMAEAutoformer MSE MAEStationary MSE MAEETSformer MSE MAELightTS MSE MAEInformer MSE MAEReformer MSE MAE
Weather ETTh1 ETTh20.238 0.275 0.5900.524 0.3970.4210.279 0.301 0.869 0.628 0.479 0.4650.301 0.283 0.691 0.599 0.608 0.5380.2840.324 0.638 0.561 0.4660.4750.241 0.6330.542 0.415 0.4310.27910.3000.342 0.701 0.596 0.4880.4990.318 0.322 0.9140.639 0.4610.4540.317 0.359 1.179 0.833 0.8930.7130.289 0.322 1.375 0.877 2.6550.597 1.199 0.8080.4940.545 0.469 1.249 0.833
ETTm1 ETTm20.4640.441 0.2930.3350.676 0.537 0.319 0.3530.4110.429 0.3160.3680.721 0.605 0.463 0.4880.501 0.296 0.3430.466 0.8020.628 0.9300.797 0.3320.577 0.979 0.714 0.4470.4871.159 0.970 0.7043.871 1.192 3.3691.512 3.485 0.820 1.4251.485 0.856
ECL0.1760.2690.323 0.3920.2800.3460.4280.180 0.2691.3410.4780.366 0.4430.987 0.4410.755 0.4881.439 1.194 0.8903.9771.586 50.768
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The GPT2(6) FPT model consistently outperforms all recent", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "score": 1.0, + "content": "state-of-the-art transformer and MLP-based time series forecasting methods. 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We attribute", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 587, + 355, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 355, + 599 + ], + "score": 1.0, + "content": "this to the knowledge transfer capability from the FPT model.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 522, + 505, + 599 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 614, + 175, + 627 + ], + "lines": [ + { + "bbox": [ + 104, + 613, + 177, + 630 + ], + "spans": [ + { + "bbox": [ + 104, + 613, + 177, + 630 + ], + "score": 1.0, + "content": "5 Ablations", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 640, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 105, + 639, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 505, + 652 + ], + "score": 1.0, + "content": "In this section, we conduct several ablations on model selection and effectiveness of pre-training. The", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 649, + 506, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 506, + 663 + ], + "score": 1.0, + "content": "detailed results are shown in Appendix H. We introduce several variants, GPT2(0) FPT, GPT2(6)", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 660, + 314, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 314, + 675 + ], + "score": 1.0, + "content": "without freezing and GPT2(6) without pre-training.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 639, + 506, + 675 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "Model Selection We separately analyze the number of GPT2 layers and the fine-tuning parameters", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "selection. The results in Appendix H show that GPT2 with 6-layers is a sound choice compared", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 713 + ], + "score": 1.0, + "content": "to full or few layers and partially freezing can avoid catastrophic forgetting, enabling fine-tuning", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 710, + 185, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 185, + 724 + ], + "score": 1.0, + "content": "without overfitting.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 677, + 505, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 190, + 114, + 418, + 245 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 63, + 504, + 103 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 62, + 505, + 74 + ], + "spans": [ + { + "bbox": [ + 106, + 62, + 505, + 74 + ], + "score": 1.0, + "content": "Table 6: Zero-shot learning results. Dataset-specific metrics aggregated over each dataset. A lower value", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "score": 1.0, + "content": "indicates better performance. The source dataset of M3, Tourism, Electricity are M4. For M4, the source data", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "for N-BEATS is FRED, and M3 for other models. Black: best, Red: second best, Violet: third best. Appendix", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 92, + 189, + 104 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 189, + 104 + ], + "score": 1.0, + "content": "D.7 shows full results.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "table_body", + "bbox": [ + 190, + 114, + 418, + 245 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 190, + 114, + 418, + 245 + ], + "spans": [ + { + "bbox": [ + 190, + 114, + 418, + 245 + ], + "score": 0.98, + "html": "
Methods MetricM4 sMAPEM3 sMAPETOURISM MAPEELECTR ND×100Average
N-BEATS11.7012.4418.8217.815.19
DLinear15.3314.0328.5117.618.86
TimesNet13.5514.1728.8419.318.96
PatchTST13.2213.0627.1017.317.67
ETSformer27.7416.03180.4044.267.09
LightTS13.6217.9066.9919.629.52
Stationary13.3215.2943.7522.023.59
FEDformer15.0413.5331.5518.419.63
Autoformer20.0215.8740.3933.927.54
Informer19.0415.8235.8221.222.97
Reformer14.0913.3725.4821.618.63
GPT2(6)13.1213.0622.1417.216.38
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MethodsGPT2(6)GPT2(0)No FreezeNo Pretrain
MSEMAEMSEMAEMSEMAEMSEMAE
Weather0.2370.2700.2630.2970.2730.3020.2770.305
ETTh10.4270.4260.8740.6470.7530.5961.3260.743
ETTh20.3460.3940.6660.5590.4470.4510.5020.479
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MethodsGPT2(6)BERT(6)BEiT(6)DLinearPatchTSTFEDformerAutoformer
MSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
ETTh20.4000.4330.4520.4510.4590.4540.8270.6150.4390.4480.4410.4570.4700.489
ETTm20.3080.3460.3180.3570.3150.3570.3990.4260.3140.3520.3810.4040.3880.433
", + "type": "table", + "image_path": "aca78e62e46454b40ef10750bc166ad4c3021943e9114ee884d894aedca6b005.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 108, + 601, + 554, + 616.6666666666666 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 108, + 616.6666666666666, + 554, + 632.3333333333333 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 108, + 632.3333333333333, + 554, + 647.9999999999999 + ], + "spans": [], + "index": 36 + } + ] + } + ], + "index": 33.75 + }, + { + "type": "title", + "bbox": [ + 107, + 675, + 259, + 689 + ], + "lines": [ + { + "bbox": [ + 104, + 673, + 261, + 692 + ], + "spans": [ + { + "bbox": [ + 104, + 673, + 261, + 692 + ], + "score": 1.0, + "content": "7 Training/Inferencing Cost", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 106, + 699, + 504, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "Analysis of computational cost is helpful for investigating the practicality of the LLM-based model.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 711, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 505, + 722 + ], + "score": 1.0, + "content": "The results can be found in table 9. Each baseline model comes in two variants, featuring model", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 38.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 300, + 740, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 300, + 740, + 309, + 752 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 190, + 114, + 418, + 245 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 63, + 504, + 103 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 62, + 505, + 74 + ], + "spans": [ + { + "bbox": [ + 106, + 62, + 505, + 74 + ], + "score": 1.0, + "content": "Table 6: Zero-shot learning results. Dataset-specific metrics aggregated over each dataset. A lower value", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 504, + 83 + ], + "score": 1.0, + "content": "indicates better performance. The source dataset of M3, Tourism, Electricity are M4. For M4, the source data", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "for N-BEATS is FRED, and M3 for other models. Black: best, Red: second best, Violet: third best. Appendix", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 92, + 189, + 104 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 189, + 104 + ], + "score": 1.0, + "content": "D.7 shows full results.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "table_body", + "bbox": [ + 190, + 114, + 418, + 245 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 190, + 114, + 418, + 245 + ], + "spans": [ + { + "bbox": [ + 190, + 114, + 418, + 245 + ], + "score": 0.98, + "html": "
Methods MetricM4 sMAPEM3 sMAPETOURISM MAPEELECTR ND×100Average
N-BEATS11.7012.4418.8217.815.19
DLinear15.3314.0328.5117.618.86
TimesNet13.5514.1728.8419.318.96
PatchTST13.2213.0627.1017.317.67
ETSformer27.7416.03180.4044.267.09
LightTS13.6217.9066.9919.629.52
Stationary13.3215.2943.7522.023.59
FEDformer15.0413.5331.5518.419.63
Autoformer20.0215.8740.3933.927.54
Informer19.0415.8235.8221.222.97
Reformer14.0913.3725.4821.618.63
GPT2(6)13.1213.0622.1417.216.38
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MethodsGPT2(6)GPT2(0)No FreezeNo Pretrain
MSEMAEMSEMAEMSEMAEMSEMAE
Weather0.2370.2700.2630.2970.2730.3020.2770.305
ETTh10.4270.4260.8740.6470.7530.5961.3260.743
ETTh20.3460.3940.6660.5590.4470.4510.5020.479
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MethodsGPT2(6)BERT(6)BEiT(6)DLinearPatchTSTFEDformerAutoformer
MSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
ETTh20.4000.4330.4520.4510.4590.4540.8270.6150.4390.4480.4410.4570.4700.489
ETTm20.3080.3460.3180.3570.3150.3570.3990.4260.3140.3520.3810.4040.3880.433
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ModelTraining Params Training Params Percentages Training Time for l step(s） Inference Time for 1 Batch(s)
FEDformer-3244k1000.8890.170
TimesNet-322M1000.7470.302
PatchTST-32543K1000.0430.022
FEDformer-76833M1000.2080.056
TimesNet-76842M1005.7232.162
PatchTST-76820M1000.4570.123
GPT-2(3)-7684M6.120.0930.032
GPT-2(6)-7684M4.60.1040.054
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Furthermore, the majority", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 212, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 212, + 505, + 225 + ], + "score": 1.0, + "content": "of the baseline models consist of three layers. We assessed the computational cost using a batch from", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 223, + 330, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 223, + 330, + 236 + ], + "score": 1.0, + "content": "ETTh2 (with a batch size of 128) on a 32G V100 GPU.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 240, + 505, + 306 + ], + "lines": [ + { + "bbox": [ + 105, + 239, + 506, + 253 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 506, + 253 + ], + "score": 1.0, + "content": "The results indicate that GPT-2(3) has substantially enhanced time efficiency and reduced parameter", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 250, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 105, + 250, + 505, + 264 + ], + "score": 1.0, + "content": "quantity compared to baselines with the same model dimension. This was a surprise since we initially", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 262, + 506, + 274 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 274 + ], + "score": 1.0, + "content": "anticipated that this large language model might be slower. However, we surmise that the efficient", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 273, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 506, + 286 + ], + "score": 1.0, + "content": "optimization of huggingface’s GPT model implementation primarily accounts for such a significant", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 284, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 459, + 295 + ], + "score": 1.0, + "content": "improvement in time costs. Furthermore, GPT-2(3) and GPT-2(6) demonstrate a mere", + "type": "text" + }, + { + "bbox": [ + 459, + 284, + 487, + 294 + ], + "score": 0.87, + "content": "6 . 1 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 284, + 505, + 295 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 294, + 464, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 133, + 306 + ], + "score": 0.86, + "content": "4 . 6 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 294, + 464, + 307 + ], + "score": 1.0, + "content": "proportion of learnable parameters among the overall parameter size, respectively.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9.5 + }, + { + "type": "title", + "bbox": [ + 107, + 330, + 481, + 357 + ], + "lines": [ + { + "bbox": [ + 103, + 328, + 482, + 345 + ], + "spans": [ + { + "bbox": [ + 103, + 328, + 482, + 345 + ], + "score": 1.0, + "content": "8 Towards Understanding the Universality of Transformer: Connecting", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 123, + 344, + 252, + 357 + ], + "spans": [ + { + "bbox": [ + 123, + 344, + 252, + 357 + ], + "score": 1.0, + "content": "Self-Attention with PCA", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 374, + 505, + 483 + ], + "lines": [ + { + "bbox": [ + 105, + 371, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 388 + ], + "score": 1.0, + "content": "The observation, i.e. we can directly use a trained LM for time series forecasting without having", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "score": 1.0, + "content": "to modify its model, makes us believe that the underlying model is doing something very generic", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "and independent from texts despite it being trained from text data. Our analysis aims to show that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "part of this generic function can be related to PCA, as minimizing the gradient with respect to the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "self-attention layer seems to do something similar to PCA. In this section, we take the first step", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "towards revealing the generality of self-attention by connecting the self-attention with principal", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "score": 1.0, + "content": "component analysis (PCA). Moreover, when coming the question of why fine-tuning is restricted to", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 450, + 504, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 504, + 463 + ], + "score": 1.0, + "content": "the embedding layer and layer norm, following our hypothesis that the pre-trained LM as a whole", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "performs something generic, partially fine-tuning any of its components may break the generic", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 471, + 398, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 398, + 485 + ], + "score": 1.0, + "content": "function and lead to relatively poor performance for time series analysis.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 488, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 488, + 507, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 507, + 501 + ], + "score": 1.0, + "content": "For each layer, we calculate and perform statistical analysis of the pairwise token similarity values.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 498, + 507, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 364, + 512 + ], + "score": 1.0, + "content": "Specifically, we denote each output feature map with shape of", + "type": "text" + }, + { + "bbox": [ + 364, + 500, + 396, + 511 + ], + "score": 0.93, + "content": "( b , n , d )", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 498, + 428, + 512 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 429, + 500, + 434, + 510 + ], + "score": 0.75, + "content": "b", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 498, + 507, + 512 + ], + "score": 1.0, + "content": "is the batch size,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 511, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 114, + 520 + ], + "score": 0.7, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 511, + 235, + 523 + ], + "score": 1.0, + "content": "is the number of tokens, and", + "type": "text" + }, + { + "bbox": [ + 235, + 511, + 242, + 520 + ], + "score": 0.78, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 511, + 505, + 523 + ], + "score": 1.0, + "content": "is the dimension of each token feature. We calculate the cosine", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 522, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 359, + 533 + ], + "score": 1.0, + "content": "similarity, and the resulting pairwise similarity matrix of shape", + "type": "text" + }, + { + "bbox": [ + 360, + 522, + 393, + 533 + ], + "score": 0.92, + "content": "( b , n , n )", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 522, + 505, + 533 + ], + "score": 1.0, + "content": ". Next we count the number", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 533, + 452, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 452, + 545 + ], + "score": 1.0, + "content": "of occurrences of similarity values within each interval as a simple statistical analysis.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 549, + 505, + 669 + ], + "lines": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "score": 1.0, + "content": "Our analysis is motivated by the observation that the within-layer token similarity increases with", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "score": 1.0, + "content": "deeper layers in transformer. We report the layer-wise average token cosine similarity on ETTh2", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "score": 1.0, + "content": "dataset in Figure 4 (a, c), where we mix weights from pre-trained LM with weights randomly sampled", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "from Gaussian distribution. Here we summarize our observations: a) in a randomly initialed GPT2", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 591, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 321, + 605 + ], + "score": 1.0, + "content": "(6) model, the token similarity is low among all layers", + "type": "text" + }, + { + "bbox": [ + 321, + 592, + 365, + 604 + ], + "score": 0.49, + "content": "( 0 . 1 - 0 . 2 )", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 591, + 505, + 605 + ], + "score": 1.0, + "content": "; b) when gradually switched to the", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 104, + 602, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 104, + 602, + 505, + 617 + ], + "score": 1.0, + "content": "pretrained GPT2 model, the token similarity significantly increases in the deep layers and eventually", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 614, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 505, + 627 + ], + "score": 1.0, + "content": "reaches more than 0.9 in the last layer. One potential explanation for the increasing token similarity", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 624, + 506, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 506, + 638 + ], + "score": 1.0, + "content": "is that all the token vectors are projected into the low-dimensional top eigenvector space of input", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 636, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 506, + 648 + ], + "score": 1.0, + "content": "patterns. To verify this idea, we further conduct experiments where we replace the self-attention", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 646, + 506, + 659 + ], + "score": 1.0, + "content": "module with PCA and find token similarity patterns remain unchanged according to Figure 4 (b),", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 658, + 426, + 670 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 426, + 670 + ], + "score": 1.0, + "content": "which further justifies the potential connection between PCA and self-attention.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 674, + 505, + 721 + ], + "lines": [ + { + "bbox": [ + 105, + 672, + 507, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 507, + 686 + ], + "score": 1.0, + "content": "To build the theoretical connection between PCA and self-attention, we first analyze the gradi-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 103, + 682, + 507, + 699 + ], + "spans": [ + { + "bbox": [ + 103, + 682, + 258, + 699 + ], + "score": 1.0, + "content": "ent structure of self-attention. Let", + "type": "text" + }, + { + "bbox": [ + 258, + 684, + 394, + 696 + ], + "score": 0.89, + "content": "\\ b X \\ = \\ ( x _ { 1 } , \\dots , x _ { N } ) ^ { \\top } \\ \\in \\ \\mathbb { R } ^ { N \\times D }", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 682, + 507, + 699 + ], + "score": 1.0, + "content": "be the input pattern, and", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 693, + 509, + 711 + ], + "spans": [ + { + "bbox": [ + 104, + 693, + 120, + 711 + ], + "score": 1.0, + "content": "let", + "type": "text" + }, + { + "bbox": [ + 120, + 696, + 342, + 709 + ], + "score": 0.82, + "content": "f ( X ) \\ = \\ ( f _ { 1 } ( X ) , \\ldots , f _ { N } ( x ) ) ^ { \\top } \\ : \\ \\mathbb { R } ^ { N \\times D } \\ \\mapsto \\ \\mathbb { R } ^ { N \\times D }", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 693, + 509, + 711 + ], + "score": 1.0, + "content": "be the function for self-attention, i.e.,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 114, + 707, + 371, + 723 + ], + "spans": [ + { + "bbox": [ + 114, + 709, + 237, + 721 + ], + "score": 0.77, + "content": "f _ { i } ( X ) = \\operatorname { s o f t m a x } ( X A X ^ { \\top } ) X", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 707, + 270, + 723 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 271, + 708, + 365, + 721 + ], + "score": 0.91, + "content": "A = W _ { Q } W _ { K } ^ { \\top } \\in \\mathbb { R } ^ { D \\times D }", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 707, + 371, + 723 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 42.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 110, + 86, + 521, + 183 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 180, + 63, + 433, + 74 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 178, + 63, + 433, + 75 + ], + "spans": [ + { + "bbox": [ + 178, + 63, + 433, + 75 + ], + "score": 1.0, + "content": "Table 9: Training parameters and Training/Inference Cost Comparison", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 110, + 86, + 521, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 110, + 86, + 521, + 183 + ], + "spans": [ + { + "bbox": [ + 110, + 86, + 521, + 183 + ], + "score": 0.978, + "html": "
ModelTraining Params Training Params Percentages Training Time for l step(s） Inference Time for 1 Batch(s)
FEDformer-3244k1000.8890.170
TimesNet-322M1000.7470.302
PatchTST-32543K1000.0430.022
FEDformer-76833M1000.2080.056
TimesNet-76842M1005.7232.162
PatchTST-76820M1000.4570.123
GPT-2(3)-7684M6.120.0930.032
GPT-2(6)-7684M4.60.1040.054
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This was a surprise since we initially", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 262, + 506, + 274 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 274 + ], + "score": 1.0, + "content": "anticipated that this large language model might be slower. However, we surmise that the efficient", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 273, + 506, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 506, + 286 + ], + "score": 1.0, + "content": "optimization of huggingface’s GPT model implementation primarily accounts for such a significant", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 284, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 459, + 295 + ], + "score": 1.0, + "content": "improvement in time costs. Furthermore, GPT-2(3) and GPT-2(6) demonstrate a mere", + "type": "text" + }, + { + "bbox": [ + 459, + 284, + 487, + 294 + ], + "score": 0.87, + "content": "6 . 1 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 284, + 505, + 295 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 294, + 464, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 133, + 306 + ], + "score": 0.86, + "content": "4 . 6 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 294, + 464, + 307 + ], + "score": 1.0, + "content": "proportion of learnable parameters among the overall parameter size, respectively.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9.5, + "bbox_fs": [ + 105, + 239, + 506, + 307 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 330, + 481, + 357 + ], + "lines": [ + { + "bbox": [ + 103, + 328, + 482, + 345 + ], + "spans": [ + { + "bbox": [ + 103, + 328, + 482, + 345 + ], + "score": 1.0, + "content": "8 Towards Understanding the Universality of Transformer: Connecting", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 123, + 344, + 252, + 357 + ], + "spans": [ + { + "bbox": [ + 123, + 344, + 252, + 357 + ], + "score": 1.0, + "content": "Self-Attention with PCA", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 374, + 505, + 483 + ], + "lines": [ + { + "bbox": [ + 105, + 371, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 505, + 388 + ], + "score": 1.0, + "content": "The observation, i.e. we can directly use a trained LM for time series forecasting without having", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "score": 1.0, + "content": "to modify its model, makes us believe that the underlying model is doing something very generic", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 408 + ], + "score": 1.0, + "content": "and independent from texts despite it being trained from text data. Our analysis aims to show that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "part of this generic function can be related to PCA, as minimizing the gradient with respect to the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "self-attention layer seems to do something similar to PCA. In this section, we take the first step", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "towards revealing the generality of self-attention by connecting the self-attention with principal", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 506, + 453 + ], + "score": 1.0, + "content": "component analysis (PCA). Moreover, when coming the question of why fine-tuning is restricted to", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 450, + 504, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 504, + 463 + ], + "score": 1.0, + "content": "the embedding layer and layer norm, following our hypothesis that the pre-trained LM as a whole", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 474 + ], + "score": 1.0, + "content": "performs something generic, partially fine-tuning any of its components may break the generic", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 471, + 398, + 485 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 398, + 485 + ], + "score": 1.0, + "content": "function and lead to relatively poor performance for time series analysis.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 371, + 506, + 485 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 488, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 488, + 507, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 507, + 501 + ], + "score": 1.0, + "content": "For each layer, we calculate and perform statistical analysis of the pairwise token similarity values.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 498, + 507, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 364, + 512 + ], + "score": 1.0, + "content": "Specifically, we denote each output feature map with shape of", + "type": "text" + }, + { + "bbox": [ + 364, + 500, + 396, + 511 + ], + "score": 0.93, + "content": "( b , n , d )", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 498, + 428, + 512 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 429, + 500, + 434, + 510 + ], + "score": 0.75, + "content": "b", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 498, + 507, + 512 + ], + "score": 1.0, + "content": "is the batch size,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 107, + 511, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 107, + 513, + 114, + 520 + ], + "score": 0.7, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 511, + 235, + 523 + ], + "score": 1.0, + "content": "is the number of tokens, and", + "type": "text" + }, + { + "bbox": [ + 235, + 511, + 242, + 520 + ], + "score": 0.78, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 242, + 511, + 505, + 523 + ], + "score": 1.0, + "content": "is the dimension of each token feature. We calculate the cosine", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 522, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 522, + 359, + 533 + ], + "score": 1.0, + "content": "similarity, and the resulting pairwise similarity matrix of shape", + "type": "text" + }, + { + "bbox": [ + 360, + 522, + 393, + 533 + ], + "score": 0.92, + "content": "( b , n , n )", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 522, + 505, + 533 + ], + "score": 1.0, + "content": ". Next we count the number", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 533, + 452, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 452, + 545 + ], + "score": 1.0, + "content": "of occurrences of similarity values within each interval as a simple statistical analysis.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 488, + 507, + 545 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 549, + 505, + 669 + ], + "lines": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "score": 1.0, + "content": "Our analysis is motivated by the observation that the within-layer token similarity increases with", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "score": 1.0, + "content": "deeper layers in transformer. We report the layer-wise average token cosine similarity on ETTh2", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "score": 1.0, + "content": "dataset in Figure 4 (a, c), where we mix weights from pre-trained LM with weights randomly sampled", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "from Gaussian distribution. 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One potential explanation for the increasing token similarity", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 624, + 506, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 506, + 638 + ], + "score": 1.0, + "content": "is that all the token vectors are projected into the low-dimensional top eigenvector space of input", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 636, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 506, + 648 + ], + "score": 1.0, + "content": "patterns. To verify this idea, we further conduct experiments where we replace the self-attention", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 646, + 506, + 659 + ], + "spans": [ + { + "bbox": [ + 105, + 646, + 506, + 659 + ], + "score": 1.0, + "content": "module with PCA and find token similarity patterns remain unchanged according to Figure 4 (b),", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 658, + 426, + 670 + ], + "spans": [ + { + "bbox": [ + 106, + 658, + 426, + 670 + ], + "score": 1.0, + "content": "which further justifies the potential connection between PCA and self-attention.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 35, + "bbox_fs": [ + 104, + 549, + 506, + 670 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 674, + 505, + 721 + ], + "lines": [ + { + "bbox": [ + 105, + 672, + 507, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 507, + 686 + ], + "score": 1.0, + "content": "To build the theoretical connection between PCA and self-attention, we first analyze the gradi-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 103, + 682, + 507, + 699 + ], + "spans": [ + { + "bbox": [ + 103, + 682, + 258, + 699 + ], + "score": 1.0, + "content": "ent structure of self-attention. 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Let the Jacobian", + "type": "text" + }, + { + "bbox": [ + 244, + 276, + 334, + 299 + ], + "score": 0.9, + "content": "\\begin{array} { l l l } { \\boldsymbol { J } } & { = } & { \\left[ \\frac { \\partial f _ { i } ( \\boldsymbol { X } ) } { \\partial x _ { j } } \\right] _ { i , j = 1 } ^ { N } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 281, + 438, + 295 + ], + "score": 1.0, + "content": "represent the gradient", + "type": "text" + }, + { + "bbox": [ + 438, + 282, + 462, + 294 + ], + "score": 0.91, + "content": "f ( X )", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 281, + 504, + 295 + ], + "score": 1.0, + "content": "w.r.t the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 297, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 102, + 297, + 111, + 323 + ], + "score": 1.0, + "content": "i", + "type": "text" + }, + { + "bbox": [ + 112, + 300, + 501, + 344 + ], + "score": 0.82, + "content": "\\begin{array} { r l } & { \\mathrm { ~ \\mathrm { ~ \\ r p u t ~ } } \\mathrm { ~ \\ p a t t e r n , \\ t h e n ~ } \\mathrm { ~ w e ~ } \\mathrm { ~ \\ h a v e ~ } \\quad | J | _ { 2 } \\leq | A | _ { 2 } \\sum _ { i = 1 } ^ { N } \\left( P _ { i , i } + \\frac { 1 } { 2 } \\right) \\bigg | x _ { i } - \\sum _ { j = 1 } ^ { N } P _ { i , j } x _ { j } \\bigg | ^ { 2 } + \\Delta \\quad \\mathrm { w h e r e } } \\\\ & { \\Delta = | A | _ { 2 } \\sum _ { i \\neq j } ^ { N } P _ { i , j } \\left| x _ { j } - \\sum _ { k = 1 } ^ { N } P _ { i , k } x _ { k } \\right| ^ { 2 } + \\frac { | A | _ { 2 } } { 2 } \\sum _ { j = 1 } ^ { N } | x _ { i } | ^ { 2 } \\quad \\mathrm { a n d } \\quad P _ { i , j } = \\frac { \\exp ( x _ { i } ^ { \\top } A x _ { j } ) } { \\sum _ { k = 1 } ^ { N } \\exp ( x _ { i } ^ { \\top } A x _ { k } ) } \\ . } \\end{array}", + "type": "inline_equation", + "image_path": "a9b30c471c223a5444599eaebb6318b3230e6321dd6fbf52e6c3c04e366108b2.jpg" + }, + { + "bbox": [ + 502, + 302, + 505, + 317 + ], + "score": 0.752, + "content": "e", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5 + }, + { + "type": "text", + "bbox": [ + 107, + 347, + 504, + 370 + ], + "lines": [ + { + "bbox": [ + 106, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 318, + 360 + ], + "score": 1.0, + "content": "This lemma reveals an important gradient structure of", + "type": "text" + }, + { + "bbox": [ + 318, + 348, + 326, + 357 + ], + "score": 0.82, + "content": "J", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 347, + 505, + 360 + ], + "score": 1.0, + "content": ". 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Let", + "type": "text" + }, + { + "bbox": [ + 177, + 461, + 194, + 473 + ], + "score": 0.89, + "content": "W _ { Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 459, + 214, + 473 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 215, + 461, + 233, + 472 + ], + "score": 0.89, + "content": "W _ { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 233, + 459, + 318, + 473 + ], + "score": 1.0, + "content": "be matrices of size", + "type": "text" + }, + { + "bbox": [ + 319, + 461, + 351, + 471 + ], + "score": 0.91, + "content": "D \\times m", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 459, + 376, + 473 + ], + "score": 1.0, + "content": ". 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Following Theorem 1, through the training of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 529, + 471, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 471, + 541 + ], + "score": 1.0, + "content": "pushing gradient to zero, self-attention learns to perform a function closely related to PCA.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 19.5 + }, + { + "type": "title", + "bbox": [ + 106, + 555, + 188, + 569 + ], + "lines": [ + { + "bbox": [ + 104, + 554, + 190, + 571 + ], + "spans": [ + { + "bbox": [ + 104, + 554, + 190, + 571 + ], + "score": 1.0, + "content": "9 Conclusions", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 579, + 506, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 579, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 506, + 592 + ], + "score": 1.0, + "content": "In this paper, we developed a foundation model for time series analysis, based on pre-trained model", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "from NLP or CV, that can (a) facilitate the model training for downstream tasks, and (b) provide", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "score": 1.0, + "content": "unified framework for diverse time series analysis tasks. 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Following Theorem 1, through the training of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 529, + 471, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 471, + 541 + ], + "score": 1.0, + "content": "pushing gradient to zero, self-attention learns to perform a function closely related to PCA.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 518, + 505, + 541 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 555, + 188, + 569 + ], + "lines": [ + { + "bbox": [ + 104, + 554, + 190, + 571 + ], + "spans": [ + { + "bbox": [ + 104, + 554, + 190, + 571 + ], + "score": 1.0, + "content": "9 Conclusions", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 579, + 506, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 579, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 506, + 592 + ], + "score": 1.0, + "content": "In this paper, we developed a foundation model for time series analysis, based on pre-trained model", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "from NLP or CV, that can (a) facilitate the model training for downstream tasks, and (b) provide", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 506, + 615 + ], + "score": 1.0, + "content": "unified framework for diverse time series analysis tasks. 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On the other hand, we do", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 645, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 505, + 658 + ], + "score": 1.0, + "content": "recognize some limitations of our work: the zero-shot performance of our approach is still behind", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 654, + 507, + 671 + ], + "spans": [ + { + "bbox": [ + 104, + 654, + 507, + 671 + ], + "score": 1.0, + "content": "N-beat on several datasets, and our analysis of the generality of transformer is still in the early stage.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 666, + 506, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 681 + ], + "score": 1.0, + "content": "Moving forward, we plan to improve the performance of our approach by exploiting the parameter", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 506, + 691 + ], + "score": 1.0, + "content": "efficient fine-tuning approaches which usually introduce additional structures into the pre-trained", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "score": 1.0, + "content": "model for better adaption. To better understand the universality of transformer, we also plan to", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "examine it from the viewpoint of n-gram language model, an approach that is taken by Elhage et al.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 710, + 489, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 489, + 723 + ], + "score": 1.0, + "content": "(2021); Olsson et al. (2022). In Appendix F, we include our initial analysis along this direction.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 28, + "bbox_fs": [ + 104, + 579, + 507, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 71, + 202, + 84 + ], + "lines": [ + { + "bbox": [ + 106, + 70, + 204, + 87 + ], + "spans": [ + { + "bbox": [ + 106, + 70, + 204, + 87 + ], + "score": 1.0, + "content": "Acknowledgement", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 95, + 505, + 139 + ], + "lines": [ + { + "bbox": [ + 105, + 95, + 505, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 95, + 505, + 108 + ], + "score": 1.0, + "content": "We would like to express our sincere gratitude to Ziqing Ma, Qingsong Wen, Mengni Ye, and Tao", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 106, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 505, + 119 + ], + "score": 1.0, + "content": "Yao for their valuable suggestions and proofreading assistance throughout the development of this", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 117, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 104, + 117, + 506, + 131 + ], + "score": 1.0, + "content": "paper. 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(2021) contain electricity load of various resolutions (ETTh &", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 288, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 301 + ], + "score": 1.0, + "content": "ETTm) from two electricity stations. 2) Weather contains 21 meteorological indicators of Germany", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 312 + ], + "score": 1.0, + "content": "within 1 year; 3) Illness contains the influenza-like illness patients in the United States; 4) Electricity", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 309, + 506, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 506, + 324 + ], + "score": 1.0, + "content": "dataset contains the electricity consumption; 5) Traffic dataset contains the occupation rate of freeway", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 321, + 454, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 454, + 333 + ], + "score": 1.0, + "content": "system across the State of California. 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Also, ILI is not used for few-shot learning for the limited quantity that is hard to follow the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 370, + 198, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 198, + 381 + ], + "score": 1.0, + "content": "definition of few-shot.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21.5 + }, + { + "type": "table", + "bbox": [ + 204, + 417, + 406, + 501 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 212, + 396, + 397, + 408 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 211, + 394, + 399, + 410 + ], + "spans": [ + { + "bbox": [ + 211, + 394, + 399, + 410 + ], + "score": 1.0, + "content": "Table 10: Dataset details of few-shot learning.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "table_body", + "bbox": [ + 204, + 417, + 406, + 501 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 204, + 417, + 406, + 501 + ], + "spans": [ + { + "bbox": [ + 204, + 417, + 406, + 501 + ], + "score": 0.979, + "html": "
DatasetLengthDimensionFrequency
ETTh1742071 hour
ETTm69680715 min
Weather526962210 min
ILI96677 days
Electricity263043211 hour
Traffic175448621 hour
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DatasetLengthDimensionFrequency
ETTh1742071 hour
ETTm69680715 min
Weather526962210 min
ILI96677 days
Electricity263043211 hour
Traffic175448621 hour
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MethodsGPT2(6)GPT2(0)DLinearPatchTSTTimesNetFEDformerAutoformerStationaryETSformerLightTSInformerReformer
MetricMSEMAE|MSEMAE MSEMAE|MSEMAEMSEMAE|MSE MAEMSE MAEMSEMAEMSEMAE|MSEMAEMSEMAE|MSEMAE
96 0.1750.230 0.191 0.2760.243 0.2440.28910.184 0.242 0.2280.28310.171 0.224 0.2300.2770.207 0.253 0.272 0.307[0.2290.309 0.2650.3170.227 0.299 0.278 0.3330.215 0.2900.2520.218 0.2950.230 0.2850.4970.497[0.406 0.435
Waaeet192 0.227 336 0.2860.322 720 0.3660.379 0.3910.3030.332 0.3930.2790.322 0.364 40.3880.2940.326 0.384 0.3870.313 0.328 0.400 0.3850.3530.392 0.391 0.3940.351 0.393 0.387 0.3890.353 0.4520.307 0.348 0.4070.2940.331 0.3590.398 0.461 0.4610.2740.323 0.3180.355 0.4010.4180.620 0.545 0.6490.547 0.570 0.5220.4460.450 0.4650.459 0.471 0.468
Avg. 0.263 96 0.5430.5060.3010.2820.314 0.8250.6380.2630.308 0.5470.5030.2690.303 0.5570.5190.298 0.318 0.892 0.6250.3090.353 0.5930.5290.310 0.353 0.6810.5700.327 0.9520.6500.3280.333 0.371 1.169 0.8320.305 0.345 1.483 0.910.5840.527 1.2250.8120.4470.453 1.1980.795
LLI192 0.7480.580 336 0.7540.595 7201.2200.7781.852 0.9650.7200.604 0.9840.7270.711 0.570 0.8160.6190.940 0.665 0.9450.6530.652 0.563 0.7310.5940.7250.602 0.761 0.6240.9430.645 0.9350.6441.221 0.853 1.1790.8321.525 0.93 1.347 0.871.249 0.828 1.202 0.8111.2730.853 1.2540.857
Avg. 0.6810.5601.2990.793 0.551 0.5070.750 0.611 10.4420.4560.6940.569 0.4010.4210.9250.647 0.409 0.4200.658 0.562 |0.390 0.4240.722 0.5980.9430.6461.189 0.8391.451(0.903 1.2250.8171.241 0.835
LLI96 [0.376 0.421 192 0.418 0.4410.7650.610 0.6170.5420.452 0.4550.4830.4640.457 0.4650.4280.468 0.4960.5040.4080.423 0.4970.6780.619 0.6972.0221.006 3.837 3.9751.5083.7531.518 3.5161.473
336 0.4080.4390.7670.6141.424 0.8490.4640.4690.499 0.4790.477 0.4830.486 0.4960.507 0.4810.4680.845 0.9050.7273.5341.3481.933 3.9561.5203.3121.427
7204.0631.451
Avg. 0.4000.4330.6940.5770.8270.6150.4390.4480.4630.4540.4410.4570.47 0.4890.470 0.4573.527 1.472
0.5820.512 0.3320.3740.3990.4140.606 0.5180.6280.54450.5780.809 0.6813.2061.268 3.9221.653
96 0.386 0.405 0.4400.4380.6320.5360.3580.3900.4410.4360.681 0.5390.6660.5660.7260.8230.5871.031 0.7471.0480.7331.130 0.7751.2340.798
LL192 336 0.4850.4590.7670.5840.4020.4160.4990.4670.7860.5970.8070.6280.7500.591 0.8510.8440.591 0.8700.6031.0870.7661.0970.7561.150 0.7881.287 0.839
720 0.5770.499 1.3340.7420.5110.4890.767 0.5870.7960.5930.8220.6330.659 0.857 0.6550.8930.6111.1380.7871.1470.7751.198 0.8091.2880.842
Avg. 0.472 0.4500.828 0.5930.4000.4170.5260.4760.717 0.5610.730 0.5920.7960.6200.8571.2450.8311.200 0.7991.175 0.7941.2470.828
0.5981.1250.7821.1230.7651.1630.7911.2640.826
96 [0.1990.280[0.282 0.347 0.3460.3830.236 0.3260.2060.288[0.220 0.299|[0.229 0.3200.232 0.3220.2380.3160.4040.4851.1080.7723.5991.4783.883 1.545
192 0.2560.3160.4290.4270.3060.373 0.3800.4230.2640.3240.311 0.3610.3940.3610.291 0.3570.2980.3490.4790.5211.317 0.8503.5781.4753.5531.484
L336 0.3180.3530.751 0.5680.6740.5830.334 0.3670.338 0.3660.378 0.4270.478 30.5170.353 0.3800.552 0.5551.415 0.8793.5611.4733.4461.460
720 0.460 0.4360.4520.4310.4540.4320.5090.4650.523 0.5100.553 0.5380.4750.4450.7010.6271.8220.9843.8961.5333.4451.460
Avg. 0.3080.3460.3990.4260.314 0.3520.3440.3720.381 0.4040.388 30.4330.3410.3720.5340.5471.4150.8713.6581.4893.5811.487
96 [0.1430.241[0.1470.2460.1500.2510.1450.2440.315 0.389[0.235 0.3220.2970.3670.4840.518
GCI192 0.159 0.2550.1630.2600.1630.2630.163 0.2600.318 0.3960.2470.3410.3080.3750.501 0.5310.697 0.63810.639 0.6091.265 0.9191.4140.855
0.1820.2780.1750.2780.2810.3400.4150.267 0.3560.3540.4110.5740.7180.6480.772 0.6781.298 0.9391.2400.919
336 0.1790.2740.2190.3110.1830.4260.4660.9520.7860.5780.758 0.6670.9010.7451.3020.9421.2530.921
720 0.2330.3230.2390.3290.2330.3230.6350.6130.3180.3940.3460.4040.6271.0280.7881.2000.8711.2590.919 1.281 0.9291.2490.921 1.2890.904
mffoiAvg. 0.1780.2730.1820.278 0.419 0.2980.4680.354 10.4270.1760.275 0.3040.181 0.277 0.4040.2860.402 0.453 0.8540.4920.266 0.353 [0.6700.4210.7950.481 0.8370.5031.4680.8210.603 1.6430.8550.800 0.6850.878 0.725 1.1570.636
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MethodsGPT2(6)GPT2(0)DLinearPatchTSTTimesNetFEDformerAutoformerStationaryETSformerLightTSInformerReformer
MetricMSEMAE|MSEMAE MSEMAE|MSEMAEMSEMAE|MSE MAEMSE MAEMSEMAEMSEMAE|MSEMAEMSEMAE|MSEMAE
96 0.1750.230 0.191 0.2760.243 0.2440.28910.184 0.242 0.2280.28310.171 0.224 0.2300.2770.207 0.253 0.272 0.307[0.2290.309 0.2650.3170.227 0.299 0.278 0.3330.215 0.2900.2520.218 0.2950.230 0.2850.4970.497[0.406 0.435
Waaeet192 0.227 336 0.2860.322 720 0.3660.379 0.3910.3030.332 0.3930.2790.322 0.364 40.3880.2940.326 0.384 0.3870.313 0.328 0.400 0.3850.3530.392 0.391 0.3940.351 0.393 0.387 0.3890.353 0.4520.307 0.348 0.4070.2940.331 0.3590.398 0.461 0.4610.2740.323 0.3180.355 0.4010.4180.620 0.545 0.6490.547 0.570 0.5220.4460.450 0.4650.459 0.471 0.468
Avg. 0.263 96 0.5430.5060.3010.2820.314 0.8250.6380.2630.308 0.5470.5030.2690.303 0.5570.5190.298 0.318 0.892 0.6250.3090.353 0.5930.5290.310 0.353 0.6810.5700.327 0.9520.6500.3280.333 0.371 1.169 0.8320.305 0.345 1.483 0.910.5840.527 1.2250.8120.4470.453 1.1980.795
LLI192 0.7480.580 336 0.7540.595 7201.2200.7781.852 0.9650.7200.604 0.9840.7270.711 0.570 0.8160.6190.940 0.665 0.9450.6530.652 0.563 0.7310.5940.7250.602 0.761 0.6240.9430.645 0.9350.6441.221 0.853 1.1790.8321.525 0.93 1.347 0.871.249 0.828 1.202 0.8111.2730.853 1.2540.857
Avg. 0.6810.5601.2990.793 0.551 0.5070.750 0.611 10.4420.4560.6940.569 0.4010.4210.9250.647 0.409 0.4200.658 0.562 |0.390 0.4240.722 0.5980.9430.6461.189 0.8391.451(0.903 1.2250.8171.241 0.835
LLI96 [0.376 0.421 192 0.418 0.4410.7650.610 0.6170.5420.452 0.4550.4830.4640.457 0.4650.4280.468 0.4960.5040.4080.423 0.4970.6780.619 0.6972.0221.006 3.837 3.9751.5083.7531.518 3.5161.473
336 0.4080.4390.7670.6141.424 0.8490.4640.4690.499 0.4790.477 0.4830.486 0.4960.507 0.4810.4680.845 0.9050.7273.5341.3481.933 3.9561.5203.3121.427
7204.0631.451
Avg. 0.4000.4330.6940.5770.8270.6150.4390.4480.4630.4540.4410.4570.47 0.4890.470 0.4573.527 1.472
0.5820.512 0.3320.3740.3990.4140.606 0.5180.6280.54450.5780.809 0.6813.2061.268 3.9221.653
96 0.386 0.405 0.4400.4380.6320.5360.3580.3900.4410.4360.681 0.5390.6660.5660.7260.8230.5871.031 0.7471.0480.7331.130 0.7751.2340.798
LL192 336 0.4850.4590.7670.5840.4020.4160.4990.4670.7860.5970.8070.6280.7500.591 0.8510.8440.591 0.8700.6031.0870.7661.0970.7561.150 0.7881.287 0.839
720 0.5770.499 1.3340.7420.5110.4890.767 0.5870.7960.5930.8220.6330.659 0.857 0.6550.8930.6111.1380.7871.1470.7751.198 0.8091.2880.842
Avg. 0.472 0.4500.828 0.5930.4000.4170.5260.4760.717 0.5610.730 0.5920.7960.6200.8571.2450.8311.200 0.7991.175 0.7941.2470.828
0.5981.1250.7821.1230.7651.1630.7911.2640.826
96 [0.1990.280[0.282 0.347 0.3460.3830.236 0.3260.2060.288[0.220 0.299|[0.229 0.3200.232 0.3220.2380.3160.4040.4851.1080.7723.5991.4783.883 1.545
192 0.2560.3160.4290.4270.3060.373 0.3800.4230.2640.3240.311 0.3610.3940.3610.291 0.3570.2980.3490.4790.5211.317 0.8503.5781.4753.5531.484
L336 0.3180.3530.751 0.5680.6740.5830.334 0.3670.338 0.3660.378 0.4270.478 30.5170.353 0.3800.552 0.5551.415 0.8793.5611.4733.4461.460
720 0.460 0.4360.4520.4310.4540.4320.5090.4650.523 0.5100.553 0.5380.4750.4450.7010.6271.8220.9843.8961.5333.4451.460
Avg. 0.3080.3460.3990.4260.314 0.3520.3440.3720.381 0.4040.388 30.4330.3410.3720.5340.5471.4150.8713.6581.4893.5811.487
96 [0.1430.241[0.1470.2460.1500.2510.1450.2440.315 0.389[0.235 0.3220.2970.3670.4840.518
GCI192 0.159 0.2550.1630.2600.1630.2630.163 0.2600.318 0.3960.2470.3410.3080.3750.501 0.5310.697 0.63810.639 0.6091.265 0.9191.4140.855
0.1820.2780.1750.2780.2810.3400.4150.267 0.3560.3540.4110.5740.7180.6480.772 0.6781.298 0.9391.2400.919
336 0.1790.2740.2190.3110.1830.4260.4660.9520.7860.5780.758 0.6670.9010.7451.3020.9421.2530.921
720 0.2330.3230.2390.3290.2330.3230.6350.6130.3180.3940.3460.4040.6271.0280.7881.2000.8711.2590.919 1.281 0.9291.2490.921 1.2890.904
mffoiAvg. 0.1780.2730.1820.278 0.419 0.2980.4680.354 10.4270.1760.275 0.3040.181 0.277 0.4040.2860.402 0.453 0.8540.4920.266 0.353 [0.6700.4210.7950.481 0.8370.5031.4680.8210.603 1.6430.8550.800 0.6850.878 0.725 1.1570.636
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MethodsGPT2(6)GPT2(0)DLinearPatchTSTTimesNetFEDformerAutoformerStationaryETSformerLightTSInformerReformer
MetricMSEMAEMSE MAEMSEMAE MSEMAE MSEMAE|MSEMAE|MSEMAEMSEMAE| MSEMAE|MSE MAE||MSE MAE|MSEMAE
96 0.163（0.215 0.1900.2400.171 0.2240.165 0.2150.184 0.2300.1880.2530.221 0.2970.192 0.2340.1990.272 10.2170.2690.3740.4010.3350.380
192 0.2100.2540.2430.2840.215 50.2630.2100.2570.245 0.2830.2500.3040.2700.3220.2690.295 0.2790.332 0.2590.3040.5520.4780.5220.462
Waaeet336 0.2560.2920.270 0.3050.258 0.2990.259 0.2970.305 0.3210.312 0.3460.320 0.3510.370 0.3570.356 0.3860.3030.3340.7240.5410.7150.535
720 0.321 0.3390.348 0.3590.320 0.3460.332 0.3460.381 0.3710.387 0.3930.390 0.3960.4410.405 0.4370.448 0.3770.3820.7390.5580.611 0.500
Avg. 0.238 0.2750.263 0.2970.241 0.2830.242 0.2790.279 0.3010.284 0.3240.3000.3420.318 0.3230.3180.3600.2890.3220.597 0.4950.5460.469
96 0.4580.4560.601 0.5360.4920.4950.5160.4850.861 0.6280.5120.4990.6130.5520.9180.6391.1120.8061.2980.8381.1790.7921.1840.790
LLI192 0.570 0.5160.7090.587 0.535 0.8010.565 0.5380.598 0.5240.797 0.5930.624 0.5550.722 0.5980.9150.629 1.1550.823 1.3220.8541.199 0.8061.2950.850
336 0.6081.3850.8310.635 0.721 0.6220.657 0.5500.941 0.6480.691 0.5740.750 0.6190.9390.644 1.1790.832 1.3470.8701.202 0.8111.2940.854
720 0.7250.591 0.5900.5250.8740.6470.986 0.7430.762 0.6100.877 0.6410.7280.6140.721 0.6160.8870.645 1.2730.874 1.5340.9471.2170.8251.2230.838
Avg.0.691 0.6000.633 0.5420.869 0.6280.6390.5610.702 0.5960.9150.639 1.180 0.8341.3750.8771.199 0.8091.2490.833
96 0.3310.374 0.5390.4950.357 0.4110.353 0.3890.378 0.409[0.382 0.4160.413 0.4510.3890.4110.6780.6192.0221.0063.837 1.5083.788 1.533
LLE192 0.4020.411 0.6750.5550.569 0.5190.4030.4140.490 0.4670.4780.4740.4740.4770.4730.455 0.7850.6662.3291.1043.856 1.5133.552 1.483
336 0.4060.4330.718 0.5800.671 0.5720.4260.4410.5370.4940.5040.5010.547 0.5430.5070.4800.8390.6942.4531.1223.952 1.5263.395 1.526
720 0.4490.464 Avg. 0.3970.4210.732 0.6050.824 0.6480.477 0.4800.5100.4910.4990.5090.5160.5230.4770.472 1.2730.8743.8161.4073.842 1.5033.205 1.401
0.6660.5590.605 0.5380.415 0.4310.4790.4650.4660.4750.4880.4990.4620.455 0.8940.713 2.6551.1603.872 1.5133.485 1.486
L96 0.390 0.404[0.610 0.5080.352 0.392[0.410 0.4190.583 0.5010.578 0.518[0.7740.6140.7610.568 0.9110.688 0.9210.6821.162 0.7851.4420.847
192 0.4290.423 336 0.4690.4390.6660.5400.3820.4120.437 0.4340.630 0.5280.6170.5460.7540.5920.7810.574 0.9550.703 0.9570.7011.1720.7931.4440.862
720 0.5690.4980.895 0.615 0.9160.6460.419 0.4340.476 0.4540.7250.5680.9980.7750.8690.6770.8030.587 0.9910.719 0.9980.7161.227 0.9081.450 0.866
Avg. 0.4640.4410.7720.5770.4900.4770.681 0.5560.769 0.5490.6930.579 0.722 0.6050.810 0.6300.844 0.5811.0620.747 1.0070.7191.207 0.7971.366 0.850
96 [0.1880.2690.411 0.4290.501 0.4660.677 0.5370.802 0.6280.797 0.5780.980 0.7140.9710.7051.192 0.8211.4260.856
L192 0.251 0.3090.2830.3440.2130.3030.191 0.2740.212 0.2850.291 0.39910.3520.4540.2290.3080.3310.430 0.8130.6883.2031.4074.1951.628
336 0.3070.3460.353 0.3840.278 0.3450.252 0.3170.270 0.3230.3070.3790.694 0.6910.291 0.3430.400 0.4641.0080.7683.112 1.3874.042 1.601
720 0.4260.4170.4200.4220.3380.3850.306 0.3530.323 0.3530.5430.5592.408 1.4070.348 0.3760.4690.498 1.0310.7753.255 1.4213.963 1.585
0.2930.3350.5530.4910.4360.4400.433 0.4270.4740.4490.7120.6141.913 1.1660.461 0.4380.5890.5571.0960.7913.9091.5433.7111 1.532
Avg.0.4020.4100.3160.3680.296 0.3430.320 0.3530.4630.4881.342 0.9300.332 0.3660.4470.4870.9870.7563.370 1.4403.978 1.587
96 [0.139 0.2370.142 0.2400.1500.2530.140 0.2380.2990.3730.231 0.3230.261 0.3480.420 0.4660.5990.5870.3500.425
ECE192 0.1560.2520.1580.2540.164 0.2640.160 0.2550.3050.3790.261 0.3560.338 0.4060.411 0.4590.620 0.5980.3760.4481.259 0.9190.9930.784
336 0.1750.2700.1750.2710.181 0.2820.180 0.2760.319 0.3910.360 0.4450.410 0.4740.4340.4730.6620.6190.4280.4851.1600.873 1.1570.8720.938 0.753 0.925 0.745
720 0.2330.3170.2300.3150.2230.321 0.180 0.2800.241 0.323 0.180 0.2730.369 0.426 0.323 0.3920.5300.585 0.3460.4270.7150.685 0.431 0.4780.510 0.521 0.4440.4800.7570.664 0.6600.6170.611 0.4410.597 0.489 1.1950.8911.2030.8981.0040.790
TffoosAvg. 0.1760.269 96 0.4140.2970.1760.270 0.478 0.368
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MethodsGPT2(6)GPT2(0)DLinearPatchTSTTimesNetFEDformerAutoformerStationaryETSformerLightTSInformerReformer
MetricMSEMAEMSE MAEMSEMAE MSEMAE MSEMAE|MSEMAE|MSEMAEMSEMAE| MSEMAE|MSE MAE||MSE MAE|MSEMAE
96 0.163（0.215 0.1900.2400.171 0.2240.165 0.2150.184 0.2300.1880.2530.221 0.2970.192 0.2340.1990.272 10.2170.2690.3740.4010.3350.380
192 0.2100.2540.2430.2840.215 50.2630.2100.2570.245 0.2830.2500.3040.2700.3220.2690.295 0.2790.332 0.2590.3040.5520.4780.5220.462
Waaeet336 0.2560.2920.270 0.3050.258 0.2990.259 0.2970.305 0.3210.312 0.3460.320 0.3510.370 0.3570.356 0.3860.3030.3340.7240.5410.7150.535
720 0.321 0.3390.348 0.3590.320 0.3460.332 0.3460.381 0.3710.387 0.3930.390 0.3960.4410.405 0.4370.448 0.3770.3820.7390.5580.611 0.500
Avg. 0.238 0.2750.263 0.2970.241 0.2830.242 0.2790.279 0.3010.284 0.3240.3000.3420.318 0.3230.3180.3600.2890.3220.597 0.4950.5460.469
96 0.4580.4560.601 0.5360.4920.4950.5160.4850.861 0.6280.5120.4990.6130.5520.9180.6391.1120.8061.2980.8381.1790.7921.1840.790
LLI192 0.570 0.5160.7090.587 0.535 0.8010.565 0.5380.598 0.5240.797 0.5930.624 0.5550.722 0.5980.9150.629 1.1550.823 1.3220.8541.199 0.8061.2950.850
336 0.6081.3850.8310.635 0.721 0.6220.657 0.5500.941 0.6480.691 0.5740.750 0.6190.9390.644 1.1790.832 1.3470.8701.202 0.8111.2940.854
720 0.7250.591 0.5900.5250.8740.6470.986 0.7430.762 0.6100.877 0.6410.7280.6140.721 0.6160.8870.645 1.2730.874 1.5340.9471.2170.8251.2230.838
Avg.0.691 0.6000.633 0.5420.869 0.6280.6390.5610.702 0.5960.9150.639 1.180 0.8341.3750.8771.199 0.8091.2490.833
96 0.3310.374 0.5390.4950.357 0.4110.353 0.3890.378 0.409[0.382 0.4160.413 0.4510.3890.4110.6780.6192.0221.0063.837 1.5083.788 1.533
LLE192 0.4020.411 0.6750.5550.569 0.5190.4030.4140.490 0.4670.4780.4740.4740.4770.4730.455 0.7850.6662.3291.1043.856 1.5133.552 1.483
336 0.4060.4330.718 0.5800.671 0.5720.4260.4410.5370.4940.5040.5010.547 0.5430.5070.4800.8390.6942.4531.1223.952 1.5263.395 1.526
720 0.4490.464 Avg. 0.3970.4210.732 0.6050.824 0.6480.477 0.4800.5100.4910.4990.5090.5160.5230.4770.472 1.2730.8743.8161.4073.842 1.5033.205 1.401
0.6660.5590.605 0.5380.415 0.4310.4790.4650.4660.4750.4880.4990.4620.455 0.8940.713 2.6551.1603.872 1.5133.485 1.486
L96 0.390 0.404[0.610 0.5080.352 0.392[0.410 0.4190.583 0.5010.578 0.518[0.7740.6140.7610.568 0.9110.688 0.9210.6821.162 0.7851.4420.847
192 0.4290.423 336 0.4690.4390.6660.5400.3820.4120.437 0.4340.630 0.5280.6170.5460.7540.5920.7810.574 0.9550.703 0.9570.7011.1720.7931.4440.862
720 0.5690.4980.895 0.615 0.9160.6460.419 0.4340.476 0.4540.7250.5680.9980.7750.8690.6770.8030.587 0.9910.719 0.9980.7161.227 0.9081.450 0.866
Avg. 0.4640.4410.7720.5770.4900.4770.681 0.5560.769 0.5490.6930.579 0.722 0.6050.810 0.6300.844 0.5811.0620.747 1.0070.7191.207 0.7971.366 0.850
96 [0.1880.2690.411 0.4290.501 0.4660.677 0.5370.802 0.6280.797 0.5780.980 0.7140.9710.7051.192 0.8211.4260.856
L192 0.251 0.3090.2830.3440.2130.3030.191 0.2740.212 0.2850.291 0.39910.3520.4540.2290.3080.3310.430 0.8130.6883.2031.4074.1951.628
336 0.3070.3460.353 0.3840.278 0.3450.252 0.3170.270 0.3230.3070.3790.694 0.6910.291 0.3430.400 0.4641.0080.7683.112 1.3874.042 1.601
720 0.4260.4170.4200.4220.3380.3850.306 0.3530.323 0.3530.5430.5592.408 1.4070.348 0.3760.4690.498 1.0310.7753.255 1.4213.963 1.585
0.2930.3350.5530.4910.4360.4400.433 0.4270.4740.4490.7120.6141.913 1.1660.461 0.4380.5890.5571.0960.7913.9091.5433.7111 1.532
Avg.0.4020.4100.3160.3680.296 0.3430.320 0.3530.4630.4881.342 0.9300.332 0.3660.4470.4870.9870.7563.370 1.4403.978 1.587
96 [0.139 0.2370.142 0.2400.1500.2530.140 0.2380.2990.3730.231 0.3230.261 0.3480.420 0.4660.5990.5870.3500.425
ECE192 0.1560.2520.1580.2540.164 0.2640.160 0.2550.3050.3790.261 0.3560.338 0.4060.411 0.4590.620 0.5980.3760.4481.259 0.9190.9930.784
336 0.1750.2700.1750.2710.181 0.2820.180 0.2760.319 0.3910.360 0.4450.410 0.4740.4340.4730.6620.6190.4280.4851.1600.873 1.1570.8720.938 0.753 0.925 0.745
720 0.2330.3170.2300.3150.2230.321 0.180 0.2800.241 0.323 0.180 0.2730.369 0.426 0.323 0.3920.5300.585 0.3460.4270.7150.685 0.431 0.4780.510 0.521 0.4440.4800.7570.664 0.6600.6170.611 0.4410.597 0.489 1.1950.8911.2030.8981.0040.790
TffoosAvg. 0.1760.269 96 0.4140.2970.1760.270 0.478 0.368
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(2022) and conduct experiments on full", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "data. The results are shown in Table 14. Overall, GPT2(6) FPT achieves comparable performance to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "score": 1.0, + "content": "PatchTST, Dlinear and outperforms other baselines by a large margin. Compared with the second", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 135, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 135, + 437, + 149 + ], + "score": 1.0, + "content": "best transformer-based baseline method FEDformer, GPT2(6) FPT yields an overall", + "type": "text" + }, + { + "bbox": [ + 437, + 136, + 465, + 147 + ], + "score": 0.87, + "content": "1 8 . 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 135, + 505, + 149 + ], + "score": 1.0, + "content": "relatively", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 146, + 506, + 161 + ], + "spans": [ + { + "bbox": [ + 104, + 146, + 506, + 161 + ], + "score": 1.0, + "content": "MSE reduction. It verifies the effectiveness of NLP pretrained model in time series forecasting, not", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 157, + 231, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 157, + 231, + 171 + ], + "score": 1.0, + "content": "limited to the few-shot setting.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4 + }, + { + "type": "title", + "bbox": [ + 106, + 174, + 428, + 186 + ], + "lines": [ + { + "bbox": [ + 106, + 173, + 429, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 173, + 429, + 188 + ], + "score": 1.0, + "content": "Detail Experiment Table for Long-term Time-Series Forecasting in table 14", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 196, + 506, + 229 + ], + "lines": [ + { + "bbox": [ + 105, + 195, + 505, + 209 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 354, + 209 + ], + "score": 1.0, + "content": "Table 14: Full results on full data. We use prediction length", + "type": "text" + }, + { + "bbox": [ + 355, + 196, + 456, + 208 + ], + "score": 0.9, + "content": "O \\in \\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 195, + 505, + 209 + ], + "score": 1.0, + "content": "for ILI and", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 107, + 206, + 507, + 219 + ], + "spans": [ + { + "bbox": [ + 107, + 207, + 194, + 219 + ], + "score": 0.91, + "content": "O \\in \\{ 2 4 , 3 6 , 4 8 , 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 206, + 507, + 219 + ], + "score": 1.0, + "content": "for others. A lower MSE indicates better performance. Black: best, Red:", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 218, + 159, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 159, + 229 + ], + "score": 1.0, + "content": "second best.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 109, + 248, + 581, + 588 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 109, + 248, + 581, + 588 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 248, + 581, + 588 + ], + "spans": [ + { + "bbox": [ + 109, + 248, + 581, + 588 + ], + "score": 0.982, + "html": "
Methods |GPT2(6)GPT2(0) DLinearPatchTSTTimesNetFEDformerAutoformer StationaryETSformerLightTSInformerReformer
MetricMSEMAE|MSEMAEMSE MAEMSEMAEMSEMAEMSEMAE|MSEMAEMSEMAE|MSEMAEMSEMAEMSEMAE
96 0.162 0.20420.212 0.181 0.248 0.2220.232 0.2660.176 0.2200.237 0.149 0.198 0.2820.1720.220 0.2190.2610.217 0.296 0.2760.3360.2660.336MSEMAE| 0.173 0.223[0.197 0.2810.1820.242 0.3000.3840.689 0.596
Wareet192 336 7200.2540.286 0.3260.3370.270 0.299 0.338 0.3450.2650.319 0.3330.3620.1940.241 0.2450.282 0.3140.3340.2800.306 0.3650.3590.403（0.3390.380 0.4280.307 0.3590.395 0.4190.4280.367 0.2450.285 0.321 0.338 0.4140.4100.237 0.312 0.2980.353 0.3520.2880.227 0.287 0.282 0.334 0.352 20.3860.5980.544 0.578 0.523 1.0590.7410.7520.638 0.639 0.5961.1300.792
Avg 960.2370.270 0.3760.397 0.4160.4180.252 0.422 0.4660.285 0.428 0.3750.248 0.300 0.3990.2250.264 0.3700.3990.3840.259 0.287 0.402 0.4360.4290.420（0.309 0.360 [0.376 0.4190.338 0.3820.4490.4590.288 0.314 0.513 0.4910.271 0.334 0.494 0.4790.261 0.312 10.424 40.4320.6340.548 0.8650.7130.8030.656 0.837 0.728
ULL192 336 720 Avg0.4420.433 0.4770.456 0.427 0.4260.450 0.488 0.464 0.485 0.478 0.465 0.4550.405 0.4220.416 0.4390.443 0.4720.490 0.4370.413 0.421 0.4220.436 0.4470.466 0.413 0.4300.5210.491 0.469 0.500 0.4580.4500.448 0.4590.465 0.506 0.507 0.4400.4600.5000.482 0.521 0.496 0.514 0.512 0.4960.4870.5340.504 0.5880.535 0.643 0.6160.5380.504 0.5740.521 0.562 0.5350.4750.462 0.518 30.488 0.547 0.5331.0080.792 1.107 0.809 1.181 0.8650.9230.766 1.0970.8351.257 0.889
TLL96 192 3360.2850.342 0.3540.389 0.3730.4070.318 0.368 0.383 0.407 0.4060.4270.2890.353 0.3830.418 0.4480.4650.274 0.336 0.3390.379 0.3290.3800.4520.340 0.374 0.4020.414 0.4520.3580.397 0.4290.439 0.4960.4870.346 0.388 0.4560.452 0.4820.4860.5520.5700.537 0.476 0.458 0.5120.493 0.5510.5420.510 0.340 0.391 0.4300.439 0.4850.4790.491 0.479 10.397 0.437 0.520 0.504 0.6260.5591.0400.795 3.755 1.525 5.6021.9311.029 0.805 2.626 1.31711.12 2.979 9.3232.769
720 Avg 96 1920.4060.441 0.3540.394 0.2920.346 0.3320.3720.420 0.381 0.3300.446 0.412 0.372 0.3940.605 0.551 0.431 0.446 0.2990.3430.3790.422 0.3300.379 0.290 0.3420.462 0.468 0.4140.427 0.3380.375 0.3740.3870.4630.474 0.4370.449 0.3790.4190.515 0.511 0.450 0.459 0.5050.4750.5620.560 0.526 0.516 0.386 0.3980.5000.497 0.4390.452 0.3750.3980.8630.672 0.602 20.543 10.374 0.4004.721 3.647 4.431 0.672 0.5711.835 1.625 3.8741.697 1.729 6.736 2.1910.538 0.528
L336 720 Avg0.3660.394 0.417 0.421 0.3520.3830.371 0.398 0.454 0.3880.409 0.440 0.403 0.3570.3350.365 0.369 0.386 0.4250.421 0.3780.3320.369 0.3660.392 0.4160.420 0.351 0.3800.410 0.411 0.4780.450 0.4000.4060.4260.441 0.4450.459 0.5430.490 0.4480.4520.5530.496 0.621 0.671 0.588 0.5170.537 0.5610.4590.444 0.4950.464 0.5850.516 0.481 0.4560.4080.410 0.4350.428 0.4990.462 0.4290.4250.4000.407 0.4380.438 0.527 0.502 0.435 0.4370.7950.669 1.212 0.871 1.1660.823 0.961 0.7340.658 0.592 0.8980.721 1.1020.8410.7990.671
LL96 192 336 7200.173 0.262 0.229 0.301 0.2860.341 0.3780.40110.192 0.245 0.302 0.3990.281 0.317 0.352 0.4080.167 0.269 0.2240.303 0.2810.342 0.3970.4210.1650.255 0.220 0.292 0.2740.329 0.362 0.385[0.187 0.267 0.2490.309 0.321 0.351 0.4080.4030.421（[0.203 0.287 0.269 0.328 0.3250.366 0.4150.2550.339 0.281 0.340 0.3390.372 0.4330.4320.1920.274 0.2800.339 0.3340.361 0.4170.4130.189 0.280 0.2530.319 0.3140.357 0.4140.413[0.209 0.308 0.311 0.382 0.4420.466 0.675 0.587|0.3650.453 0.5330.563 1.3630.8871.078 0.8270.658 0.619 1.5490.972
日Avg 24 36 480.2660.326 2.0630.881 1.8680.892 1.7900.8840.284 2.723 2.027 2.2060.339 1.099 0.966 1.0220.2670.333 2.215 1.081 1.9630.963 2.1301.0240.2550.315 1.3190.754 1.4300.834 1.5530.8150.291 2.317 1.9720.333 0.934 0.920 2.2380.9403.228 2.679 2.6220.3050.349 1.260 1.080 1.0780.327 3.483 3.1030.371 1.287 2.294 1.148 1.8250.3060.347 0.945 0.8480.2930.342 2.527 1.020 2.615 1.0070.4090.436 8.313 2.144 6.631 1.9023.3791.338 1.410 0.810 5.764 1.677 4.755 1.4672.631 1.242 1.4790.915 4.4001.3824.7831.448
60 Avg 96 1921.979 0.957 1.925 0.903 0.1390.238 0.1530.2511.976 2.233 0.138 0.1520.983 1.017 0.234 0.2472.368 1.096 2.169 1.041 [0.1400.237 0.153 0.2491.470 0.788 1.4430.797 0.129 0.222 0.1570.2402.0270.928 2.1390.931 0.1680.272 0.1840.2892.857 2.847 10.193（ 0.201（1.157 1.144 0.308 0.3152.669 2.770 3.006 0.2011.085 1.125 2.178 1.161 2.077 0.3172.010 0.900 0.963 0.914 0.1690.2732.359 0.972 2.487 1.016 2.497 1.004 [0.187 0.3047.299 1.982 7.283 1.985 7.382 2.003 10.207 0.3074.763 5.264 5.137 |0.2740.3681.469 1.564 1.5444.832 1.465 4.8821.483 4.7241.445 [0.312 0.402
GCE336 720 Avg0.169 0.266 0.2060.2970.1680.2630.169 0.2670.1630.2590.1980.3000.2140.3290.2220.334 0.1820.2860.1990.3150.213 0.3160.2960.386 0.3000.3940.3480.433
0.4120.2940.632
Average Avg0.4140.294 [0.516 0.4070.628 0.3790.573004310.5620.436044606596043307010.4890570.510.634650620473.300668360750.6240.3400.621 0.3960.622 0.3920.8640.472 0.764 0.4160.7420.420 0.7550.423 0.741 0.422
336 7200.4500.3120.413 0.447 0.4130.2810.4330.2950.390 0.2630.6400.350 0.620 0.3360.383 0.6260.382 0.610 0.3760.6160.382 0.6220.337 0.6600.4080.6530.3550.3960.6130.386 0.658 30.4070.719 0.391 0.6960.379 0.7770.4200.732 0.423 0.7330.420
96 1920.254
0.1670.2630.2070.2950.2030.3010.197 0.2900.2200.3200.2460.3550.2310.3380.2000.3040.2120.3290.2300.3330.350 0.433
0.3880.2820.1660.2590.166 0.2630.161 0.2520.1920.295 0.5930.3210.2140.3270.361 0.222 0.338 0.1930.321 0.2960.2330.3450.265 0.360 0.229 0.3290.373 0.439 0.3110.3970.3400.420 0.338 0.422
0.2270.2080.323
mffors0.4070.2900.3900.2720.410 0.282 0.4230.287 0.4360.2960.360 0.2490.617 0.336 0.6290.3360.615 0.391 0.382
0.4030.276 0.280 0.2980.4660.3150.379 0.256 0.3920.264 0.4320.2860.587 0.366 0.6040.373 0.621（0.613 0.3880.612 0.338 0.6130.340 0.6180.3280.607 0.392 0.621 0.399 0.6220.3960.601
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(2022) and conduct experiments on full", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "data. The results are shown in Table 14. Overall, GPT2(6) FPT achieves comparable performance to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "score": 1.0, + "content": "PatchTST, Dlinear and outperforms other baselines by a large margin. Compared with the second", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 135, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 105, + 135, + 437, + 149 + ], + "score": 1.0, + "content": "best transformer-based baseline method FEDformer, GPT2(6) FPT yields an overall", + "type": "text" + }, + { + "bbox": [ + 437, + 136, + 465, + 147 + ], + "score": 0.87, + "content": "1 8 . 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 135, + 505, + 149 + ], + "score": 1.0, + "content": "relatively", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 146, + 506, + 161 + ], + "spans": [ + { + "bbox": [ + 104, + 146, + 506, + 161 + ], + "score": 1.0, + "content": "MSE reduction. It verifies the effectiveness of NLP pretrained model in time series forecasting, not", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 157, + 231, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 157, + 231, + 171 + ], + "score": 1.0, + "content": "limited to the few-shot setting.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4, + "bbox_fs": [ + 104, + 92, + 506, + 171 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 174, + 428, + 186 + ], + "lines": [ + { + "bbox": [ + 106, + 173, + 429, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 173, + 429, + 188 + ], + "score": 1.0, + "content": "Detail Experiment Table for Long-term Time-Series Forecasting in table 14", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 196, + 506, + 229 + ], + "lines": [ + { + "bbox": [ + 105, + 195, + 505, + 209 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 354, + 209 + ], + "score": 1.0, + "content": "Table 14: Full results on full data. We use prediction length", + "type": "text" + }, + { + "bbox": [ + 355, + 196, + 456, + 208 + ], + "score": 0.9, + "content": "O \\in \\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 195, + 505, + 209 + ], + "score": 1.0, + "content": "for ILI and", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 107, + 206, + 507, + 219 + ], + "spans": [ + { + "bbox": [ + 107, + 207, + 194, + 219 + ], + "score": 0.91, + "content": "O \\in \\{ 2 4 , 3 6 , 4 8 , 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 206, + 507, + 219 + ], + "score": 1.0, + "content": "for others. A lower MSE indicates better performance. Black: best, Red:", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 218, + 159, + 229 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 159, + 229 + ], + "score": 1.0, + "content": "second best.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 195, + 507, + 229 + ] + }, + { + "type": "table", + "bbox": [ + 109, + 248, + 581, + 588 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 109, + 248, + 581, + 588 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 248, + 581, + 588 + ], + "spans": [ + { + "bbox": [ + 109, + 248, + 581, + 588 + ], + "score": 0.982, + "html": "
Methods |GPT2(6)GPT2(0) DLinearPatchTSTTimesNetFEDformerAutoformer StationaryETSformerLightTSInformerReformer
MetricMSEMAE|MSEMAEMSE MAEMSEMAEMSEMAEMSEMAE|MSEMAEMSEMAE|MSEMAEMSEMAEMSEMAE
96 0.162 0.20420.212 0.181 0.248 0.2220.232 0.2660.176 0.2200.237 0.149 0.198 0.2820.1720.220 0.2190.2610.217 0.296 0.2760.3360.2660.336MSEMAE| 0.173 0.223[0.197 0.2810.1820.242 0.3000.3840.689 0.596
Wareet192 336 7200.2540.286 0.3260.3370.270 0.299 0.338 0.3450.2650.319 0.3330.3620.1940.241 0.2450.282 0.3140.3340.2800.306 0.3650.3590.403（0.3390.380 0.4280.307 0.3590.395 0.4190.4280.367 0.2450.285 0.321 0.338 0.4140.4100.237 0.312 0.2980.353 0.3520.2880.227 0.287 0.282 0.334 0.352 20.3860.5980.544 0.578 0.523 1.0590.7410.7520.638 0.639 0.5961.1300.792
Avg 960.2370.270 0.3760.397 0.4160.4180.252 0.422 0.4660.285 0.428 0.3750.248 0.300 0.3990.2250.264 0.3700.3990.3840.259 0.287 0.402 0.4360.4290.420（0.309 0.360 [0.376 0.4190.338 0.3820.4490.4590.288 0.314 0.513 0.4910.271 0.334 0.494 0.4790.261 0.312 10.424 40.4320.6340.548 0.8650.7130.8030.656 0.837 0.728
ULL192 336 720 Avg0.4420.433 0.4770.456 0.427 0.4260.450 0.488 0.464 0.485 0.478 0.465 0.4550.405 0.4220.416 0.4390.443 0.4720.490 0.4370.413 0.421 0.4220.436 0.4470.466 0.413 0.4300.5210.491 0.469 0.500 0.4580.4500.448 0.4590.465 0.506 0.507 0.4400.4600.5000.482 0.521 0.496 0.514 0.512 0.4960.4870.5340.504 0.5880.535 0.643 0.6160.5380.504 0.5740.521 0.562 0.5350.4750.462 0.518 30.488 0.547 0.5331.0080.792 1.107 0.809 1.181 0.8650.9230.766 1.0970.8351.257 0.889
TLL96 192 3360.2850.342 0.3540.389 0.3730.4070.318 0.368 0.383 0.407 0.4060.4270.2890.353 0.3830.418 0.4480.4650.274 0.336 0.3390.379 0.3290.3800.4520.340 0.374 0.4020.414 0.4520.3580.397 0.4290.439 0.4960.4870.346 0.388 0.4560.452 0.4820.4860.5520.5700.537 0.476 0.458 0.5120.493 0.5510.5420.510 0.340 0.391 0.4300.439 0.4850.4790.491 0.479 10.397 0.437 0.520 0.504 0.6260.5591.0400.795 3.755 1.525 5.6021.9311.029 0.805 2.626 1.31711.12 2.979 9.3232.769
720 Avg 96 1920.4060.441 0.3540.394 0.2920.346 0.3320.3720.420 0.381 0.3300.446 0.412 0.372 0.3940.605 0.551 0.431 0.446 0.2990.3430.3790.422 0.3300.379 0.290 0.3420.462 0.468 0.4140.427 0.3380.375 0.3740.3870.4630.474 0.4370.449 0.3790.4190.515 0.511 0.450 0.459 0.5050.4750.5620.560 0.526 0.516 0.386 0.3980.5000.497 0.4390.452 0.3750.3980.8630.672 0.602 20.543 10.374 0.4004.721 3.647 4.431 0.672 0.5711.835 1.625 3.8741.697 1.729 6.736 2.1910.538 0.528
L336 720 Avg0.3660.394 0.417 0.421 0.3520.3830.371 0.398 0.454 0.3880.409 0.440 0.403 0.3570.3350.365 0.369 0.386 0.4250.421 0.3780.3320.369 0.3660.392 0.4160.420 0.351 0.3800.410 0.411 0.4780.450 0.4000.4060.4260.441 0.4450.459 0.5430.490 0.4480.4520.5530.496 0.621 0.671 0.588 0.5170.537 0.5610.4590.444 0.4950.464 0.5850.516 0.481 0.4560.4080.410 0.4350.428 0.4990.462 0.4290.4250.4000.407 0.4380.438 0.527 0.502 0.435 0.4370.7950.669 1.212 0.871 1.1660.823 0.961 0.7340.658 0.592 0.8980.721 1.1020.8410.7990.671
LL96 192 336 7200.173 0.262 0.229 0.301 0.2860.341 0.3780.40110.192 0.245 0.302 0.3990.281 0.317 0.352 0.4080.167 0.269 0.2240.303 0.2810.342 0.3970.4210.1650.255 0.220 0.292 0.2740.329 0.362 0.385[0.187 0.267 0.2490.309 0.321 0.351 0.4080.4030.421（[0.203 0.287 0.269 0.328 0.3250.366 0.4150.2550.339 0.281 0.340 0.3390.372 0.4330.4320.1920.274 0.2800.339 0.3340.361 0.4170.4130.189 0.280 0.2530.319 0.3140.357 0.4140.413[0.209 0.308 0.311 0.382 0.4420.466 0.675 0.587|0.3650.453 0.5330.563 1.3630.8871.078 0.8270.658 0.619 1.5490.972
日Avg 24 36 480.2660.326 2.0630.881 1.8680.892 1.7900.8840.284 2.723 2.027 2.2060.339 1.099 0.966 1.0220.2670.333 2.215 1.081 1.9630.963 2.1301.0240.2550.315 1.3190.754 1.4300.834 1.5530.8150.291 2.317 1.9720.333 0.934 0.920 2.2380.9403.228 2.679 2.6220.3050.349 1.260 1.080 1.0780.327 3.483 3.1030.371 1.287 2.294 1.148 1.8250.3060.347 0.945 0.8480.2930.342 2.527 1.020 2.615 1.0070.4090.436 8.313 2.144 6.631 1.9023.3791.338 1.410 0.810 5.764 1.677 4.755 1.4672.631 1.242 1.4790.915 4.4001.3824.7831.448
60 Avg 96 1921.979 0.957 1.925 0.903 0.1390.238 0.1530.2511.976 2.233 0.138 0.1520.983 1.017 0.234 0.2472.368 1.096 2.169 1.041 [0.1400.237 0.153 0.2491.470 0.788 1.4430.797 0.129 0.222 0.1570.2402.0270.928 2.1390.931 0.1680.272 0.1840.2892.857 2.847 10.193（ 0.201（1.157 1.144 0.308 0.3152.669 2.770 3.006 0.2011.085 1.125 2.178 1.161 2.077 0.3172.010 0.900 0.963 0.914 0.1690.2732.359 0.972 2.487 1.016 2.497 1.004 [0.187 0.3047.299 1.982 7.283 1.985 7.382 2.003 10.207 0.3074.763 5.264 5.137 |0.2740.3681.469 1.564 1.5444.832 1.465 4.8821.483 4.7241.445 [0.312 0.402
GCE336 720 Avg0.169 0.266 0.2060.2970.1680.2630.169 0.2670.1630.2590.1980.3000.2140.3290.2220.334 0.1820.2860.1990.3150.213 0.3160.2960.386 0.3000.3940.3480.433
0.4120.2940.632
Average Avg0.4140.294 [0.516 0.4070.628 0.3790.573004310.5620.436044606596043307010.4890570.510.634650620473.300668360750.6240.3400.621 0.3960.622 0.3920.8640.472 0.764 0.4160.7420.420 0.7550.423 0.741 0.422
336 7200.4500.3120.413 0.447 0.4130.2810.4330.2950.390 0.2630.6400.350 0.620 0.3360.383 0.6260.382 0.610 0.3760.6160.382 0.6220.337 0.6600.4080.6530.3550.3960.6130.386 0.658 30.4070.719 0.391 0.6960.379 0.7770.4200.732 0.423 0.7330.420
96 1920.254
0.1670.2630.2070.2950.2030.3010.197 0.2900.2200.3200.2460.3550.2310.3380.2000.3040.2120.3290.2300.3330.350 0.433
0.3880.2820.1660.2590.166 0.2630.161 0.2520.1920.295 0.5930.3210.2140.3270.361 0.222 0.338 0.1930.321 0.2960.2330.3450.265 0.360 0.229 0.3290.373 0.439 0.3110.3970.3400.420 0.338 0.422
0.2270.2080.323
mffors0.4070.2900.3900.2720.410 0.282 0.4230.287 0.4360.2960.360 0.2490.617 0.336 0.6290.3360.615 0.391 0.382
0.4030.276 0.280 0.2980.4660.3150.379 0.256 0.3920.264 0.4320.2860.587 0.366 0.6040.373 0.621（0.613 0.3880.612 0.338 0.6130.340 0.6180.3280.607 0.392 0.621 0.399 0.6220.3960.601
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Methods MetricGPT2-backbone(6Layers) MSE MAE
LLE96 192 336 7200.376 ± 0.0072 0.418 ± 0.0013 0.408 ± 0.00060.421 ± 0.0054 0.441 ± 0.0014 0.439 ± 0.0002
LL96 192 336 7200.199 ± 0.0040 0.256 ± 0.0030 0.318 ± 0.0046 0.460 ± 0.01320.280 ± 0.0042 0.316 ± 0.0017 0.353 ± 0.0032 0.436 ± 0.0066
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Methods MetricGPT2(6)5% MSE MAEGPT2(6)10% MSE MAEETS MSE MAEARIMA MSE MAENaiveDrift MSE MAE
LL96 1920.376 0.4180.421 0.4410.331 0.4020.374 0.4112.954 10.2260.742 1.2120.481 0.5850.443 0.4950.764 1.5600.561 0.785
[uLL96 1920.386 0.4400.405 0.4380.390 0.4290.404 0.42352.237 186.4452.689 4.6540.693 0.7100.547 0.5571.539 2.8690.913 1.215
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Methods MetricGPT2(6)PatchTSTDLinearAutoformerAutoformer(Revin)FEDformerFEDformer(Revin)
MSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
L960.1990.2800.2060.2880.2360.3260.2320.3220.2240.3000.2290.3200.2230.298
1920.2560.3160.2640.3240.3060.3730.2910.3570.2960.3430.2940.3610.2880.336
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The", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 656, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 656, + 506, + 668 + ], + "score": 1.0, + "content": "source dataset is used to train the model and then forecasts without fine-tuning in the target dataset.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 667, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 506, + 680 + ], + "score": 1.0, + "content": "The target dataset is split into non-overlapping historical and test sequences. We use the historical", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "score": 1.0, + "content": "sequence as input to the model, and the obtained output is used to calculate errors with the test", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 104, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "sequences. Besides meta-learning-based models like N-BEATS, evaluated models’ parameters are", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "score": 1.0, + "content": "not allowed any adjustment using the forecasting phase. Also, same as Oreshkin et al. (2021), each", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 710, + 498, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 498, + 724 + ], + "score": 1.0, + "content": "data set adopts a specific metric (M4: sMAPE; M3: sMAPE; TOURISM: MAPE; ELECTR: ND)", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29 + } + ], + "page_idx": 20, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 310, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 312, + 754 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 312, + 754 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 72, + 295, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 70, + 297, + 87 + ], + "spans": [ + { + "bbox": [ + 105, + 70, + 297, + 87 + ], + "score": 1.0, + "content": "D.4 Mean and STD for Few-shot Learning", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 92, + 506, + 126 + ], + "lines": [ + { + "bbox": [ + 105, + 92, + 506, + 104 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 443, + 104 + ], + "score": 1.0, + "content": "Table 15 lists both mean and STD for GPT2(6), DLinear and PatchTST with 3 runs on", + "type": "text" + }, + { + "bbox": [ + 443, + 93, + 457, + 103 + ], + "score": 0.82, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 92, + 506, + 104 + ], + "score": 1.0, + "content": "ETTh2 and", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 102, + 506, + 115 + ], + "spans": [ + { + "bbox": [ + 105, + 102, + 506, + 115 + ], + "score": 1.0, + "content": "ETTm2. The results show a small variance in performance of GPT2(6) that represents the stability of", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 113, + 147, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 113, + 147, + 127 + ], + "score": 1.0, + "content": "GPT2(6).", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 92, + 506, + 127 + ] + }, + { + "type": "table", + "bbox": [ + 232, + 163, + 379, + 258 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 155, + 142, + 454, + 154 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 154, + 141, + 456, + 155 + ], + "spans": [ + { + "bbox": [ + 154, + 141, + 403, + 155 + ], + "score": 1.0, + "content": "Table 15: A subset of results showing both Mean and STD on", + "type": "text" + }, + { + "bbox": [ + 403, + 142, + 418, + 153 + ], + "score": 0.81, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 419, + 141, + 456, + 155 + ], + "score": 1.0, + "content": "datasets.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "table_body", + "bbox": [ + 232, + 163, + 379, + 258 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 232, + 163, + 379, + 258 + ], + "spans": [ + { + "bbox": [ + 232, + 163, + 379, + 258 + ], + "score": 0.974, + "html": "
Methods MetricGPT2-backbone(6Layers) MSE MAE
LLE96 192 336 7200.376 ± 0.0072 0.418 ± 0.0013 0.408 ± 0.00060.421 ± 0.0054 0.441 ± 0.0014 0.439 ± 0.0002
LL96 192 336 7200.199 ± 0.0040 0.256 ± 0.0030 0.318 ± 0.0046 0.460 ± 0.01320.280 ± 0.0042 0.316 ± 0.0017 0.353 ± 0.0032 0.436 ± 0.0066
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Methods MetricGPT2(6)5% MSE MAEGPT2(6)10% MSE MAEETS MSE MAEARIMA MSE MAENaiveDrift MSE MAE
LL96 1920.376 0.4180.421 0.4410.331 0.4020.374 0.4112.954 10.2260.742 1.2120.481 0.5850.443 0.4950.764 1.5600.561 0.785
[uLL96 1920.386 0.4400.405 0.4380.390 0.4290.404 0.42352.237 186.4452.689 4.6540.693 0.7100.547 0.5571.539 2.8690.913 1.215
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Methods MetricGPT2(6)PatchTSTDLinearAutoformerAutoformer(Revin)FEDformerFEDformer(Revin)
MSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAEMSEMAE
L960.1990.2800.2060.2880.2360.3260.2320.3220.2240.3000.2290.3200.2230.298
1920.2560.3160.2640.3240.3060.3730.2910.3570.2960.3430.2940.3610.2880.336
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The", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 656, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 656, + 506, + 668 + ], + "score": 1.0, + "content": "source dataset is used to train the model and then forecasts without fine-tuning in the target dataset.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 667, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 506, + 680 + ], + "score": 1.0, + "content": "The target dataset is split into non-overlapping historical and test sequences. We use the historical", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "score": 1.0, + "content": "sequence as input to the model, and the obtained output is used to calculate errors with the test", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 104, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "sequences. Besides meta-learning-based models like N-BEATS, evaluated models’ parameters are", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 712 + ], + "score": 1.0, + "content": "not allowed any adjustment using the forecasting phase. Also, same as Oreshkin et al. (2021), each", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 710, + 498, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 498, + 724 + ], + "score": 1.0, + "content": "data set adopts a specific metric (M4: sMAPE; M3: sMAPE; TOURISM: MAPE; ELECTR: ND)", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29, + "bbox_fs": [ + 104, + 644, + 506, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 128 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 506, + 86 + ], + "score": 1.0, + "content": "Detailed Results Here, we list detailed performance of zero-shot learning in Table 18, Table", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "score": 1.0, + "content": "19 and Table 20. For each dataset, we separately list the performance of models under diverse", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "score": 1.0, + "content": "frequency. Compared to the most recent published method DLinear, GPT2(6) performs superior", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 119 + ], + "score": 1.0, + "content": "in most situations. Also, GPT2(6) does not use any information from the test data, but achieves a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 115, + 345, + 130 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 345, + 130 + ], + "score": 1.0, + "content": "comparable performance of meta-leaning based N-BEATS.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 168, + 174, + 444, + 336 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 202, + 140, + 408, + 152 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 201, + 139, + 408, + 154 + ], + "spans": [ + { + "bbox": [ + 201, + 139, + 408, + 154 + ], + "score": 1.0, + "content": "Table 18: Zero-shot performance on M4 (sMAPE).", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "table_body", + "bbox": [ + 168, + 174, + 444, + 336 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 168, + 174, + 444, + 336 + ], + "spans": [ + { + "bbox": [ + 168, + 174, + 444, + 336 + ], + "score": 0.983, + "html": "
Yearly (23k)Quarterly (24k)Monthly (48k)Others (5k)Average (100k)
N-BEATS-FR13.2679.59612.6764.69611.675
DLinear-M314.19318.85614.7659.19415.337
TimesNet-M315.65511.87716.1656.86314.553
PatchTST-M313.96610.92914.6647.08713.228
ETSformer-M327.84636.13425.11412.33827.748
LightTS-M313.78711.28915.1819.11713.623
Stationary-M314.98811.68616.0986.97714.327
FEDformer-M313.88711.51318.1547.52915.047
Autoformer-M314.55217.34125.0639.66620.022
Informer-M318.54216.90723.4547.34819.047
Reformer-M315.65211.05115.6047.00114.092
GPT(6)-M313.74010.78714.6307.08113.125
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Yearly (645)Quarterly (756)Monthly (1428)Others (174)Average (3003)
N-BEATS-M415.079.0713.194.2912.38
N-BEATS-FR16.439.0513.304.5112.61
DLinear-M417.439.7415.656.8114.03
TimesNet-M418.7512.2614.016.8814.17
PatchTST-M415.999.6214.719.4413.39
ETSformer-M420.5611.6516.9710.5716.03
LightTS-M415.639.4024.608.2817.90
Stationary-M417.0512.5616.828.1315.29
FEDformer-M416.009.4815.128.9413.53
Autoformer-M416.1813.9216.9114.6815.87
Informer-M419.7013.0015.9113.0315.82
Reformer-M416.039.7614.807.5313.37
GPT2(6)-M416.4210.1314.104.8113.06
", + "type": "table", + "image_path": "9d423a198b38020c34207ea08dbc16cb35199a4400937f10e7cbbf87527bd806.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 168, + 389, + 443, + 446.3333333333333 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 168, + 446.3333333333333, + 443, + 503.66666666666663 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 168, + 503.66666666666663, + 443, + 561.0 + ], + "spans": [], + "index": 12 + } + ] + } + ], + "index": 11 + }, + { + "type": "title", + "bbox": [ + 106, + 586, + 157, + 599 + ], + "lines": [ + { + "bbox": [ + 104, + 585, + 159, + 602 + ], + "spans": [ + { + "bbox": [ + 104, + 585, + 159, + 602 + ], + "score": 1.0, + "content": "E Proof", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 612, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 611, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 626 + ], + "score": 1.0, + "content": "In our numerical experiments, we obtain two interesting observations. First, the token similarity", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 623, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 505, + 636 + ], + "score": 1.0, + "content": "within a sample is larger in pretrained LM. We report the layer-wise average token cosine similarity in", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 634, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 506, + 647 + ], + "score": 1.0, + "content": "ETTh2 experiment in Figure 7. In particular, Figure 7 (a) shows that in a fine-tuned random initialed", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 645, + 505, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 645, + 505, + 658 + ], + "score": 1.0, + "content": "GPT2(6) model, the token similarity is around 0.1-0.2 among different layers. When switching to the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "frozen pre-trained GPT2-FPT model, the token similarity significantly increases in the deep layers", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "and eventually reaches more than 0.9 in the last layer. The ETTh2 dataset contains high volatility", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "hourly information related to the electricity transformer temperature. In this situation, higher token", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "similarity implies the high-frequency noise in the data is eased and only low-frequency information", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 713 + ], + "score": 1.0, + "content": "will be reserved. In other words, after going through the pretrained GPT2-FPT model, the signal-noise", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 711, + 419, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 419, + 723 + ], + "score": 1.0, + "content": "ratio is enhanced. We use the following theorem to characterize this behavior.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18.5 + } + ], + "page_idx": 21, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 299, + 740, + 312, + 754 + ], + "spans": [ + { + "bbox": [ + 299, + 740, + 312, + 754 + ], + "score": 1.0, + "content": "22", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 128 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 506, + 86 + ], + "score": 1.0, + "content": "Detailed Results Here, we list detailed performance of zero-shot learning in Table 18, Table", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 97 + ], + "score": 1.0, + "content": "19 and Table 20. For each dataset, we separately list the performance of models under diverse", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 506, + 108 + ], + "score": 1.0, + "content": "frequency. Compared to the most recent published method DLinear, GPT2(6) performs superior", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 119 + ], + "score": 1.0, + "content": "in most situations. Also, GPT2(6) does not use any information from the test data, but achieves a", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 115, + 345, + 130 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 345, + 130 + ], + "score": 1.0, + "content": "comparable performance of meta-leaning based N-BEATS.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 72, + 506, + 130 + ] + }, + { + "type": "table", + "bbox": [ + 168, + 174, + 444, + 336 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 202, + 140, + 408, + 152 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 201, + 139, + 408, + 154 + ], + "spans": [ + { + "bbox": [ + 201, + 139, + 408, + 154 + ], + "score": 1.0, + "content": "Table 18: Zero-shot performance on M4 (sMAPE).", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "table_body", + "bbox": [ + 168, + 174, + 444, + 336 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 168, + 174, + 444, + 336 + ], + "spans": [ + { + "bbox": [ + 168, + 174, + 444, + 336 + ], + "score": 0.983, + "html": "
Yearly (23k)Quarterly (24k)Monthly (48k)Others (5k)Average (100k)
N-BEATS-FR13.2679.59612.6764.69611.675
DLinear-M314.19318.85614.7659.19415.337
TimesNet-M315.65511.87716.1656.86314.553
PatchTST-M313.96610.92914.6647.08713.228
ETSformer-M327.84636.13425.11412.33827.748
LightTS-M313.78711.28915.1819.11713.623
Stationary-M314.98811.68616.0986.97714.327
FEDformer-M313.88711.51318.1547.52915.047
Autoformer-M314.55217.34125.0639.66620.022
Informer-M318.54216.90723.4547.34819.047
Reformer-M315.65211.05115.6047.00114.092
GPT(6)-M313.74010.78714.6307.08113.125
", + "type": "table", + "image_path": "69746595157fe631b52726ed8e3cc1dc08f6d81bd6c725a2c5e40e9ba46b9d32.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 168, + 174, + 444, + 228.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 168, + 228.0, + 444, + 282.0 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 168, + 282.0, + 444, + 336.0 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 202, + 355, + 408, + 367 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 201, + 354, + 408, + 369 + ], + "spans": [ + { + "bbox": [ + 201, + 354, + 408, + 369 + ], + "score": 1.0, + "content": "Table 19: Zero-shot performance on M3 (sMAPE).", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 168, + 389, + 443, + 561 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 168, + 389, + 443, + 561 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 168, + 389, + 443, + 561 + ], + "spans": [ + { + "bbox": [ + 168, + 389, + 443, + 561 + ], + "score": 0.983, + "html": "
Yearly (645)Quarterly (756)Monthly (1428)Others (174)Average (3003)
N-BEATS-M415.079.0713.194.2912.38
N-BEATS-FR16.439.0513.304.5112.61
DLinear-M417.439.7415.656.8114.03
TimesNet-M418.7512.2614.016.8814.17
PatchTST-M415.999.6214.719.4413.39
ETSformer-M420.5611.6516.9710.5716.03
LightTS-M415.639.4024.608.2817.90
Stationary-M417.0512.5616.828.1315.29
FEDformer-M416.009.4815.128.9413.53
Autoformer-M416.1813.9216.9114.6815.87
Informer-M419.7013.0015.9113.0315.82
Reformer-M416.039.7614.807.5313.37
GPT2(6)-M416.4210.1314.104.8113.06
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Yearly (518)Quarterly (427)Monthly (366)Average (1311)
N-BEATS-M423.5714.6619.3218.82
N-BEATS-FR23.4314.4520.4719.46
DLinear-M439.5918.3024.7628.51
TimesNet-M435.5919.2230.5428.84
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Stationary-M435.4235.1565.5843.75
FEDformer-M443.4119.8828.3931.55
Autoformer-M451.1934.9531.4740.39
Informer-M441.1630.9833.9235.82
Reformer-M433.8616.8523.7125.48
GPT2(6)-M427.1716.2121.9222.14
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We consider the self-attention for", + "type": "text" + }, + { + "bbox": [ + 345, + 325, + 350, + 334 + ], + "score": 0.32, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "-th query token. 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This phenomenon is especially important in few-shot forecasting tasks.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "score": 1.0, + "content": "Without enough token noise distillation ability, the model will more likely tend to overfit due to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 445, + 209, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 209, + 459 + ], + "score": 1.0, + "content": "insufficient training data.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 380, + 506, + 459 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 462, + 505, + 496 + ], + "lines": [ + { + "bbox": [ + 106, + 461, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 150, + 475 + ], + "score": 1.0, + "content": "We denote", + "type": "text" + }, + { + "bbox": [ + 151, + 464, + 161, + 473 + ], + "score": 0.85, + "content": "x _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 161, + 461, + 173, + 475 + ], + "score": 1.0, + "content": "as", + "type": "text" + }, + { + "bbox": [ + 173, + 464, + 178, + 472 + ], + "score": 0.78, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 461, + 262, + 475 + ], + "score": 1.0, + "content": "-th element of vector", + "type": "text" + }, + { + "bbox": [ + 262, + 464, + 270, + 473 + ], + "score": 0.71, + "content": "_ { \\textbf { \\em x } }", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 461, + 273, + 475 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 274, + 462, + 293, + 474 + ], + "score": 0.89, + "content": "W _ { i j }", + "type": "inline_equation" + }, + { + "bbox": [ + 293, + 461, + 363, + 475 + ], + "score": 1.0, + "content": "as the element at", + "type": "text" + }, + { + "bbox": [ + 363, + 464, + 368, + 472 + ], + "score": 0.74, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 461, + 415, + 475 + ], + "score": 1.0, + "content": "-th row and", + "type": "text" + }, + { + "bbox": [ + 415, + 463, + 421, + 474 + ], + "score": 0.84, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 461, + 506, + 475 + ], + "score": 1.0, + "content": "-th column of matrix", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 107, + 472, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 107, + 473, + 120, + 483 + ], + "score": 0.75, + "content": "W", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 472, + 141, + 486 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 141, + 474, + 157, + 486 + ], + "score": 0.89, + "content": "W _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 472, + 184, + 486 + ], + "score": 1.0, + "content": "as the", + "type": "text" + }, + { + "bbox": [ + 185, + 474, + 190, + 484 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 472, + 261, + 486 + ], + "score": 1.0, + "content": "-th row of matrix", + "type": "text" + }, + { + "bbox": [ + 261, + 474, + 275, + 483 + ], + "score": 0.57, + "content": "W", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 472, + 367, + 486 + ], + "score": 1.0, + "content": ". 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], + "score": 1.0, + "content": ", for all", + "type": "text" + }, + { + "bbox": [ + 290, + 632, + 303, + 644 + ], + "score": 0.88, + "content": "i , j", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 631, + 344, + 645 + ], + "score": 1.0, + "content": "from 1 to", + "type": "text" + }, + { + "bbox": [ + 344, + 633, + 351, + 642 + ], + "score": 0.79, + "content": "d", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 631, + 355, + 645 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35, + "is_list_end_line": true + } + ], + "index": 32, + "bbox_fs": [ + 127, + 537, + 506, + 645 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 658, + 504, + 681 + ], + "lines": [ + { + "bbox": [ + 105, + 657, + 506, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 657, + 506, + 672 + ], + "score": 1.0, + "content": "In the above assumptions, we ensure that for a given query patch, the difference between the clustering", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 669, + 326, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 669, + 326, + 681 + ], + "score": 1.0, + "content": "center and noises are large enough to be distinguished.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 657, + 506, + 681 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 723 + ], + "lines": [ + { + "bbox": [ + 105, + 686, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 347, + 700 + ], + "score": 1.0, + "content": "Theorem E.2 (formal statement of Theorem E.1). Let patch", + "type": "text" + }, + { + "bbox": [ + 348, + 689, + 358, + 699 + ], + "score": 0.84, + "content": "\\mathbf { \\Delta } _ { \\mathbf { \\mathcal { X } } _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 686, + 371, + 700 + ], + "score": 1.0, + "content": "be", + "type": "text" + }, + { + "bbox": [ + 372, + 687, + 383, + 698 + ], + "score": 0.87, + "content": "\\sigma ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 384, + 686, + 505, + 700 + ], + "score": 1.0, + "content": "-subgaussian random variable", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 152, + 711 + ], + "score": 1.0, + "content": "with mean", + "type": "text" + }, + { + "bbox": [ + 153, + 700, + 164, + 710 + ], + "score": 0.82, + "content": "\\pmb { \\mu _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 698, + 422, + 711 + ], + "score": 1.0, + "content": "and all n patches follow the same clustering center of query √", + "type": "text" + }, + { + "bbox": [ + 423, + 699, + 427, + 708 + ], + "score": 0.26, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". Per Assumptions", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 709, + 466, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 197, + 723 + ], + "score": 1.0, + "content": "aforementioned, when", + "type": "text" + }, + { + "bbox": [ + 198, + 709, + 309, + 723 + ], + "score": 0.91, + "content": "\\sqrt { d } \\ge 3 ( \\psi ( \\delta , d ) + \\nu _ { 2 } + \\nu _ { 4 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 711, + 399, + 723 + ], + "score": 1.0, + "content": ", then with probability", + "type": "text" + }, + { + "bbox": [ + 399, + 711, + 427, + 721 + ], + "score": 0.44, + "content": "1 - 5 \\delta", + "type": "inline_equation" + }, + { + "bbox": [ + 427, + 711, + 466, + 723 + ], + "score": 1.0, + "content": ", we have", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 686, + 505, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "interline_equation", + "bbox": [ + 106, + 85, + 498, + 180 + ], + "lines": [ + { + "bbox": [ + 113, + 85, + 498, + 180 + ], + "spans": [ + { + "bbox": [ + 113, + 85, + 498, + 180 + ], + "score": 0.9, + "content": "\\begin{array} { r l } & { \\left\\| \\frac { \\sum _ { i = 1 } ^ { n } \\exp \\left( \\frac { 1 } { \\sqrt { d } } x _ { l } W _ { Q } W _ { k } ^ { \\top } x _ { i } \\right) x _ { i } W _ { V } } { \\sum _ { j = 1 } ^ { n } \\exp \\left( \\frac { 1 } { \\sqrt { d } } x _ { l } W _ { Q } W _ { k } ^ { \\top } x _ { j } \\right) } - \\mu _ { l } W _ { V } \\right\\| _ { \\infty } \\leq 4 \\exp \\left( \\frac { \\psi ( \\delta , d ) } { \\sqrt { d } } \\right) \\sigma \\nu _ { 5 } \\sqrt { \\frac { 2 } { d n } \\log \\left( \\frac { 2 d } { \\delta } \\right) } } \\\\ & { + 7 \\left[ \\exp \\left( \\frac { \\nu _ { 2 } - \\nu _ { 4 } + \\psi ( \\delta , d ) } { \\sqrt { d } } \\right) - 1 \\right] \\| \\mu _ { l } W _ { V } \\| _ { \\infty } , } \\\\ & { \\gamma _ { h e r e } \\psi ( \\delta , d ) = 2 \\sigma \\nu _ { 1 } \\nu _ { 6 } \\sqrt { 2 \\log \\left( \\frac { 1 } { \\delta } \\right) } + 2 \\sigma ^ { 2 } \\nu _ { 6 } \\log \\left( \\frac { d } { \\delta } \\right) . } \\end{array}", + "type": "interline_equation", + "image_path": "03e8aead90232e9de3e9f6278192db285f1dffff876f6f9a925adb04cbaf9016.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 106, + 85, + 498, + 116.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 106, + 116.66666666666667, + 498, + 148.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 148.33333333333334, + 498, + 180.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 195, + 402, + 208 + ], + "lines": [ + { + "bbox": [ + 106, + 195, + 403, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 349, + 210 + ], + "score": 1.0, + "content": "Proof. See the proof of Lemma 2 in Wang et al. (2022) with", + "type": "text" + }, + { + "bbox": [ + 350, + 196, + 399, + 207 + ], + "score": 0.89, + "content": "k _ { 1 } = k = n", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 195, + 403, + 210 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 106, + 219, + 188, + 231 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 189, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 189, + 233 + ], + "score": 1.0, + "content": "E.2 Theorem E.4", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 106, + 239, + 310, + 251 + ], + "lines": [ + { + "bbox": [ + 106, + 240, + 310, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 310, + 253 + ], + "score": 1.0, + "content": "We first give the formal statement of Theorem E.4.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 253, + 505, + 300 + ], + "lines": [ + { + "bbox": [ + 105, + 252, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 338, + 266 + ], + "score": 1.0, + "content": "Theorem E.3 (formal statement of Theorem E.4). Let", + "type": "text" + }, + { + "bbox": [ + 339, + 253, + 379, + 265 + ], + "score": 0.91, + "content": "\\mathbf { \\mathscr { g } } _ { i } ~ \\in ~ \\mathbb { R } ^ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 252, + 400, + 266 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 400, + 253, + 442, + 265 + ], + "score": 0.92, + "content": "\\mathbf { \\Psi } _ { { \\mathbf { { y } } } _ { i } } \\in \\mathbb { R } ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 252, + 505, + 266 + ], + "score": 1.0, + "content": "be the feature", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 319, + 277 + ], + "score": 1.0, + "content": "map vector and forecasting targets for the sample", + "type": "text" + }, + { + "bbox": [ + 320, + 266, + 382, + 276 + ], + "score": 0.9, + "content": "i = 1 , 2 , . . . , N", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "respectively, and we assume", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 107, + 276, + 507, + 292 + ], + "spans": [ + { + "bbox": [ + 107, + 276, + 192, + 291 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\pmb { g } _ { i } \\pmb { g } _ { i } ^ { \\top } \\succeq \\sigma I } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 276, + 231, + 292 + ], + "score": 1.0, + "content": "for some", + "type": "text" + }, + { + "bbox": [ + 231, + 278, + 258, + 288 + ], + "score": 0.88, + "content": "\\sigma > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 276, + 374, + 292 + ], + "score": 1.0, + "content": ". 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As we assume positive definite, whic", + "type": "text" + }, + { + "bbox": [ + 201, + 442, + 289, + 457 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\frac { 1 } { N } \\sum _ { i = 1 } ^ { T } \\pmb { g } _ { i } \\pmb { g } _ { i } ^ { \\top } \\ \\succeq \\ \\sigma I } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 435, + 510, + 467 + ], + "score": 1.0, + "content": ", the hessian of optimization problem in (1) is also optimization problem in (1) is strongly convex with", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 465, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 211, + 479 + ], + "score": 1.0, + "content": "parameter proportional to", + "type": "text" + }, + { + "bbox": [ + 211, + 468, + 218, + 476 + ], + "score": 0.76, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 465, + 506, + 479 + ], + "score": 1.0, + "content": ". Then via standard stochastic gradient decent analysis (e.g., section 3.1", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 476, + 279, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 279, + 489 + ], + "score": 1.0, + "content": "in Lacoste-Julien et al. (2012)), we obtain:", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "interline_equation", + "bbox": [ + 116, + 490, + 483, + 525 + ], + "lines": [ + { + "bbox": [ + 116, + 490, + 483, + 525 + ], + "spans": [ + { + "bbox": [ + 116, + 490, + 483, + 525 + ], + "score": 0.94, + "content": "\\frac { 1 } { t } \\sum _ { j = 1 } ^ { t } \\left( \\frac { 1 } { 2 N } \\sum _ { i = 1 } ^ { N } \\lVert W _ { j } g _ { i } - y _ { i } \\rVert _ { 2 } ^ { 2 } \\right) - \\frac { 1 } { 2 N } \\sum _ { i = 1 } ^ { N } \\lVert W ^ { * } g _ { i } - y _ { i } \\rVert _ { 2 } ^ { 2 } \\le \\mathcal { O } \\left( \\frac { \\log t } { \\sigma t } \\right) = \\tilde { O } ( \\sigma ^ { - 1 } t ^ { - 1 } ) .", + "type": "interline_equation", + "image_path": "fa2f6218b315bcc42ead442a9450c3dee342ec8654ba78bcebb5c6f2bb89b41b.jpg" + } + ] + } + ], + "index": 23, + "virtual_lines": [ + { + "bbox": [ + 116, + 490, + 483, + 501.6666666666667 + ], + "spans": [], + "index": 22 + }, + { + "bbox": [ + 116, + 501.6666666666667, + 483, + 513.3333333333334 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 116, + 513.3333333333334, + 483, + 525.0 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 529, + 408, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 409, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 185, + 543 + ], + "score": 1.0, + "content": "Therefore, to reach", + "type": "text" + }, + { + "bbox": [ + 185, + 532, + 190, + 540 + ], + "score": 0.76, + "content": "\\epsilon", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 528, + 339, + 543 + ], + "score": 1.0, + "content": "optimization gap, we just need to set", + "type": "text" + }, + { + "bbox": [ + 340, + 528, + 405, + 542 + ], + "score": 0.92, + "content": "t = \\tilde { \\mathcal { O } } ( \\sigma ^ { - 1 } \\epsilon ^ { - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 528, + 409, + 543 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 106, + 552, + 506, + 674 + ], + "lines": [ + { + "bbox": [ + 105, + 553, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 565 + ], + "score": 1.0, + "content": "The second observation is that for the pretrained GPT2-FPT model, the last transformer layer’s", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 564, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 576 + ], + "score": 1.0, + "content": "outputs, i.e., feature maps, are spread widely throughout the feature space. We report the t-SNE", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 575, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 575, + 505, + 587 + ], + "score": 1.0, + "content": "visualization of the feature maps for GPT2-FPT and an end-to-end model PatchTST in Figure 8. In", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 586, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 506, + 598 + ], + "score": 1.0, + "content": "Figure 8 (a) and (b), we color the samples chunked from the one single time series into the same", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "score": 1.0, + "content": "color and the same configuration of the T-SNE is applied. One may observe that the feature maps of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "score": 1.0, + "content": "GPT2-FPT has less concentration compared to PatchTST. It implies the GPT2-FPT’s feature maps", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 619, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 505, + 631 + ], + "score": 1.0, + "content": "corresponding to different samples are more distinctive which eventually facilitates the learning ability", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 629, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 505, + 642 + ], + "score": 1.0, + "content": "of the last MLP layer. Researchers Wang & Isola (2020) have found that contrastive learning-based", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 104, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "representation learning may result in a uniform distribution of training data, and such behavior plays", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 651, + 506, + 665 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 506, + 665 + ], + "score": 1.0, + "content": "an important role in its good downstream task performance. We use the following theorem to justify", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 663, + 118, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 118, + 674 + ], + "score": 1.0, + "content": "it.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 675, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 230, + 689 + ], + "score": 1.0, + "content": "Theorem E.4 (informal). Let", + "type": "text" + }, + { + "bbox": [ + 230, + 678, + 240, + 688 + ], + "score": 0.82, + "content": "\\mathbf { \\pmb { g } } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 675, + 260, + 689 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 260, + 678, + 270, + 687 + ], + "score": 0.78, + "content": "\\mathbf { \\nabla } _ { \\mathbf { \\psi } _ { 3 } } \\psi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 675, + 505, + 689 + ], + "score": 1.0, + "content": "be the feature map vector and forecasting targets for the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 687, + 507, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 136, + 702 + ], + "score": 1.0, + "content": "sample", + "type": "text" + }, + { + "bbox": [ + 137, + 689, + 195, + 700 + ], + "score": 0.91, + "content": "i = 1 , 2 , . . . , N", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 687, + 308, + 702 + ], + "score": 1.0, + "content": "respectively, and we assume", + "type": "text" + }, + { + "bbox": [ + 317, + 687, + 507, + 703 + ], + "score": 1.0, + "content": "PNi=1 gig⊤i ⪰ σI for some σ > 0. Under mild", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "conditions, if we train an MLP layer that maps feature maps to forecasting targets via the stochastic", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 711, + 489, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 452, + 723 + ], + "score": 1.0, + "content": "gradient descent, the total step to reach some optimization tolerance is on the order of", + "type": "text" + }, + { + "bbox": [ + 453, + 711, + 486, + 723 + ], + "score": 0.93, + "content": "\\mathcal { O } ( \\sigma ^ { - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 711, + 489, + 723 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5 + } + ], + "page_idx": 23, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 313, + 754 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 313, + 754 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 15 + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 494, + 196, + 505, + 207 + ], + "lines": [] + }, + { + "type": "discarded", + "bbox": [ + 495, + 530, + 504, + 540 + ], + "lines": [ + { + "bbox": [ + 497, + 533, + 503, + 538 + ], + "spans": [ + { + "bbox": [ + 497, + 533, + 503, + 538 + ], + "score": 1.0, + "content": "■", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "interline_equation", + "bbox": [ + 106, + 85, + 498, + 180 + ], + "lines": [ + { + "bbox": [ + 113, + 85, + 498, + 180 + ], + "spans": [ + { + "bbox": [ + 113, + 85, + 498, + 180 + ], + "score": 0.9, + "content": "\\begin{array} { r l } & { \\left\\| \\frac { \\sum _ { i = 1 } ^ { n } \\exp \\left( \\frac { 1 } { \\sqrt { d } } x _ { l } W _ { Q } W _ { k } ^ { \\top } x _ { i } \\right) x _ { i } W _ { V } } { \\sum _ { j = 1 } ^ { n } \\exp \\left( \\frac { 1 } { \\sqrt { d } } x _ { l } W _ { Q } W _ { k } ^ { \\top } x _ { j } \\right) } - \\mu _ { l } W _ { V } \\right\\| _ { \\infty } \\leq 4 \\exp \\left( \\frac { \\psi ( \\delta , d ) } { \\sqrt { d } } \\right) \\sigma \\nu _ { 5 } \\sqrt { \\frac { 2 } { d n } \\log \\left( \\frac { 2 d } { \\delta } \\right) } } \\\\ & { + 7 \\left[ \\exp \\left( \\frac { \\nu _ { 2 } - \\nu _ { 4 } + \\psi ( \\delta , d ) } { \\sqrt { d } } \\right) - 1 \\right] \\| \\mu _ { l } W _ { V } \\| _ { \\infty } , } \\\\ & { \\gamma _ { h e r e } \\psi ( \\delta , d ) = 2 \\sigma \\nu _ { 1 } \\nu _ { 6 } \\sqrt { 2 \\log \\left( \\frac { 1 } { \\delta } \\right) } + 2 \\sigma ^ { 2 } \\nu _ { 6 } \\log \\left( \\frac { d } { \\delta } \\right) . } \\end{array}", + "type": "interline_equation", + "image_path": "03e8aead90232e9de3e9f6278192db285f1dffff876f6f9a925adb04cbaf9016.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 106, + 85, + 498, + 116.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 106, + 116.66666666666667, + 498, + 148.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 106, + 148.33333333333334, + 498, + 180.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 195, + 402, + 208 + ], + "lines": [ + { + "bbox": [ + 106, + 195, + 403, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 349, + 210 + ], + "score": 1.0, + "content": "Proof. See the proof of Lemma 2 in Wang et al. (2022) with", + "type": "text" + }, + { + "bbox": [ + 350, + 196, + 399, + 207 + ], + "score": 0.89, + "content": "k _ { 1 } = k = n", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 195, + 403, + 210 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 106, + 195, + 403, + 210 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 219, + 188, + 231 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 189, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 189, + 233 + ], + "score": 1.0, + "content": "E.2 Theorem E.4", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 106, + 239, + 310, + 251 + ], + "lines": [ + { + "bbox": [ + 106, + 240, + 310, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 310, + 253 + ], + "score": 1.0, + "content": "We first give the formal statement of Theorem E.4.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5, + "bbox_fs": [ + 106, + 240, + 310, + 253 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 253, + 505, + 300 + ], + "lines": [ + { + "bbox": [ + 105, + 252, + 505, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 338, + 266 + ], + "score": 1.0, + "content": "Theorem E.3 (formal statement of Theorem E.4). Let", + "type": "text" + }, + { + "bbox": [ + 339, + 253, + 379, + 265 + ], + "score": 0.91, + "content": "\\mathbf { \\mathscr { g } } _ { i } ~ \\in ~ \\mathbb { R } ^ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 379, + 252, + 400, + 266 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 400, + 253, + 442, + 265 + ], + "score": 0.92, + "content": "\\mathbf { \\Psi } _ { { \\mathbf { { y } } } _ { i } } \\in \\mathbb { R } ^ { T }", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 252, + 505, + 266 + ], + "score": 1.0, + "content": "be the feature", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 264, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 319, + 277 + ], + "score": 1.0, + "content": "map vector and forecasting targets for the sample", + "type": "text" + }, + { + "bbox": [ + 320, + 266, + 382, + 276 + ], + "score": 0.9, + "content": "i = 1 , 2 , . . . , N", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 264, + 505, + 277 + ], + "score": 1.0, + "content": "respectively, and we assume", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 107, + 276, + 507, + 292 + ], + "spans": [ + { + "bbox": [ + 107, + 276, + 192, + 291 + ], + "score": 0.9, + "content": "\\begin{array} { r } { \\frac { 1 } { N } \\sum _ { i = 1 } ^ { N } \\pmb { g } _ { i } \\pmb { g } _ { i } ^ { \\top } \\succeq \\sigma I } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 276, + 231, + 292 + ], + "score": 1.0, + "content": "for some", + "type": "text" + }, + { + "bbox": [ + 231, + 278, + 258, + 288 + ], + "score": 0.88, + "content": "\\sigma > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 276, + 374, + 292 + ], + "score": 1.0, + "content": ". 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As we assume positive definite, whic", + "type": "text" + }, + { + "bbox": [ + 201, + 442, + 289, + 457 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\frac { 1 } { N } \\sum _ { i = 1 } ^ { T } \\pmb { g } _ { i } \\pmb { g } _ { i } ^ { \\top } \\ \\succeq \\ \\sigma I } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 435, + 510, + 467 + ], + "score": 1.0, + "content": ", the hessian of optimization problem in (1) is also optimization problem in (1) is strongly convex with", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 465, + 506, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 211, + 479 + ], + "score": 1.0, + "content": "parameter proportional to", + "type": "text" + }, + { + "bbox": [ + 211, + 468, + 218, + 476 + ], + "score": 0.76, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 465, + 506, + 479 + ], + "score": 1.0, + "content": ". Then via standard stochastic gradient decent analysis (e.g., section 3.1", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 476, + 279, + 489 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 279, + 489 + ], + "score": 1.0, + "content": "in Lacoste-Julien et al. 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We report the t-SNE", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 575, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 575, + 505, + 587 + ], + "score": 1.0, + "content": "visualization of the feature maps for GPT2-FPT and an end-to-end model PatchTST in Figure 8. In", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 586, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 506, + 598 + ], + "score": 1.0, + "content": "Figure 8 (a) and (b), we color the samples chunked from the one single time series into the same", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 506, + 610 + ], + "score": 1.0, + "content": "color and the same configuration of the T-SNE is applied. One may observe that the feature maps of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 607, + 506, + 621 + ], + "score": 1.0, + "content": "GPT2-FPT has less concentration compared to PatchTST. It implies the GPT2-FPT’s feature maps", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 619, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 505, + 631 + ], + "score": 1.0, + "content": "corresponding to different samples are more distinctive which eventually facilitates the learning ability", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 629, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 505, + 642 + ], + "score": 1.0, + "content": "of the last MLP layer. Researchers Wang & Isola (2020) have found that contrastive learning-based", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 104, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "representation learning may result in a uniform distribution of training data, and such behavior plays", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 651, + 506, + 665 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 506, + 665 + ], + "score": 1.0, + "content": "an important role in its good downstream task performance. We use the following theorem to justify", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 663, + 118, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 118, + 674 + ], + "score": 1.0, + "content": "it.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 31, + "bbox_fs": [ + 104, + 553, + 506, + 674 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 676, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 675, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 230, + 689 + ], + "score": 1.0, + "content": "Theorem E.4 (informal). Let", + "type": "text" + }, + { + "bbox": [ + 230, + 678, + 240, + 688 + ], + "score": 0.82, + "content": "\\mathbf { \\pmb { g } } _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 675, + 260, + 689 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 260, + 678, + 270, + 687 + ], + "score": 0.78, + "content": "\\mathbf { \\nabla } _ { \\mathbf { \\psi } _ { 3 } } \\psi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 675, + 505, + 689 + ], + "score": 1.0, + "content": "be the feature map vector and forecasting targets for the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 687, + 507, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 136, + 702 + ], + "score": 1.0, + "content": "sample", + "type": "text" + }, + { + "bbox": [ + 137, + 689, + 195, + 700 + ], + "score": 0.91, + "content": "i = 1 , 2 , . . . , N", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 687, + 308, + 702 + ], + "score": 1.0, + "content": "respectively, and we assume", + "type": "text" + }, + { + "bbox": [ + 317, + 687, + 507, + 703 + ], + "score": 1.0, + "content": "PNi=1 gig⊤i ⪰ σI for some σ > 0. Under mild", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "conditions, if we train an MLP layer that maps feature maps to forecasting targets via the stochastic", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 711, + 489, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 452, + 723 + ], + "score": 1.0, + "content": "gradient descent, the total step to reach some optimization tolerance is on the order of", + "type": "text" + }, + { + "bbox": [ + 453, + 711, + 486, + 723 + ], + "score": 0.93, + "content": "\\mathcal { O } ( \\sigma ^ { - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 711, + 489, + 723 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 675, + 507, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 75, + 501, + 210 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 75, + 501, + 210 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 75, + 501, + 210 + ], + "spans": [ + { + "bbox": [ + 108, + 75, + 501, + 210 + ], + "score": 0.964, + "type": "image", + "image_path": "79fecec56b601d1b0ff7b61c13b1d97ca3f9cb2fb39776d4de5e5c3d06cf057c.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 108, + 75, + 501, + 120.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 120.0, + 501, + 165.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 108, + 165.0, + 501, + 210.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 218, + 506, + 252 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 217, + 505, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 217, + 505, + 230 + ], + "score": 1.0, + "content": "Figure 6: The performance and token similarity within samples with respect to each layer with", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 228, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 241 + ], + "score": 1.0, + "content": "different random replace ratios. Pretrained parameters are replaced by random initial parameters", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 240, + 239, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 239, + 253 + ], + "score": 1.0, + "content": "according to certain proportions.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 108, + 266, + 503, + 355 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 266, + 503, + 355 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 266, + 503, + 355 + ], + "spans": [ + { + "bbox": [ + 108, + 266, + 503, + 355 + ], + "score": 0.963, + "type": "image", + "image_path": "a7654d71b5e66b610362d200b813e492a8d5636060557d6cb648b6245edf1738.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 108, + 266, + 503, + 295.6666666666667 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 108, + 295.6666666666667, + 503, + 325.33333333333337 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 108, + 325.33333333333337, + 503, + 355.00000000000006 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 362, + 504, + 385 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "Figure 7: The token similarity within samples with respect to each layer. (a) GPT2-noPretrain-model;", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 374, + 398, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 398, + 385 + ], + "score": 1.0, + "content": "(b) GPT2-Pretrained-model; (c) Pretrained attention is replaced by PCA.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + } + ], + "index": 8.25 + }, + { + "type": "text", + "bbox": [ + 107, + 407, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "The Theorem E.4 considers the covariate matrix of feature maps being positive definite that indicates", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 417, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 213, + 430 + ], + "score": 1.0, + "content": "the set of all feature maps", + "type": "text" + }, + { + "bbox": [ + 213, + 417, + 233, + 430 + ], + "score": 0.92, + "content": "\\left\\{ \\pmb { g } _ { i } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 417, + 506, + 430 + ], + "score": 1.0, + "content": "spans the whole feature spaces, and the higher spread level gives a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 131, + 441 + ], + "score": 1.0, + "content": "larger", + "type": "text" + }, + { + "bbox": [ + 131, + 431, + 138, + 439 + ], + "score": 0.7, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 429, + 505, + 441 + ], + "score": 1.0, + "content": ". In this case, if we only want to learn an MLP layer, the problem reduces to a well-conditioned", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 440, + 417, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 417, + 452 + ], + "score": 1.0, + "content": "least-squared regression problem. Then the fast convergence rate is achieved.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 456, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "score": 1.0, + "content": "Efficiently learning the last MLP layer plays a very important role in time series forecasting and", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "can substantially impact the prediction performance. In Zeng et al. (2023), the authors show that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 477, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 505, + 491 + ], + "score": 1.0, + "content": "learning a single MLP layer can also bring very promising performance. In few-shot forecasting, the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 488, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 506, + 502 + ], + "score": 1.0, + "content": "pre-trained GPT2 model may still preserve highly diverse feature maps than end-to-end type models", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 500, + 368, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 368, + 513 + ], + "score": 1.0, + "content": "and eventually leads to fast learning speed on the last MLP layer.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 516, + 505, + 582 + ], + "lines": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "Another possible benefit of wide spared feature maps is enhancing the model memorization ability", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 525, + 507, + 541 + ], + "spans": [ + { + "bbox": [ + 104, + 525, + 507, + 541 + ], + "score": 1.0, + "content": "when using a multi-layer decoder structure. In the literature on network memorization ability (e.g.,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "score": 1.0, + "content": "Vardi et al. (2021); Yun et al. (2020)), the deep learning model tends to have better memorization", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "score": 1.0, + "content": "ability when feature maps are well separated. In forecasting tasks, capturing extreme or rare behavior", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 560, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 572 + ], + "score": 1.0, + "content": "is very important. The pretrained GPT gains more capacity in the decoder to correctly forecast", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 572, + 202, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 202, + 583 + ], + "score": 1.0, + "content": "uncommon time series.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5 + }, + { + "type": "title", + "bbox": [ + 107, + 598, + 315, + 612 + ], + "lines": [ + { + "bbox": [ + 104, + 596, + 317, + 616 + ], + "spans": [ + { + "bbox": [ + 104, + 596, + 317, + 616 + ], + "score": 1.0, + "content": "F N-gram Explanation for Universality", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 623, + 505, + 723 + ], + "lines": [ + { + "bbox": [ + 106, + 623, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 506, + 636 + ], + "score": 1.0, + "content": "Why does the proposed pretrained-frozen-model work so effectively? We have achieved state-of-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 633, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 647 + ], + "score": 1.0, + "content": "the-art performance in time series analysis using a language model that is mostly trained on natural", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "language data. The answer lies in the universality of the frozen structure, which includes attention", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "layers and Feed Forward layers. We can represent images and time series forecasting tasks as an", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 666, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 104, + 666, + 506, + 680 + ], + "score": 1.0, + "content": "n-gram estimation problem, akin to text analysis, by employing a patching approach. This method", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "score": 1.0, + "content": "treats subsequences of time series or image patches as individual tokens. Central to sequential", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 173, + 702 + ], + "score": 1.0, + "content": "prediction is the", + "type": "text" + }, + { + "bbox": [ + 174, + 690, + 181, + 699 + ], + "score": 0.78, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 688, + 405, + 702 + ], + "score": 1.0, + "content": "-order Markov process, and a simple way to capture the", + "type": "text" + }, + { + "bbox": [ + 405, + 690, + 412, + 699 + ], + "score": 0.79, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "-order Markov process", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 699, + 506, + 714 + ], + "spans": [ + { + "bbox": [ + 104, + 699, + 116, + 714 + ], + "score": 1.0, + "content": "is", + "type": "text" + }, + { + "bbox": [ + 117, + 702, + 124, + 710 + ], + "score": 0.75, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 124, + 699, + 313, + 714 + ], + "score": 1.0, + "content": "-gram language model. To predict next token", + "type": "text" + }, + { + "bbox": [ + 314, + 702, + 326, + 711 + ], + "score": 0.81, + "content": "w _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 699, + 417, + 714 + ], + "score": 1.0, + "content": ", we need to compute", + "type": "text" + }, + { + "bbox": [ + 418, + 700, + 502, + 712 + ], + "score": 0.92, + "content": "p ( w _ { 0 } | w _ { 1 } , \\dots , w _ { n - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 699, + 506, + 714 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 710, + 506, + 725 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 247, + 725 + ], + "score": 1.0, + "content": "which can be further computed as", + "type": "text" + }, + { + "bbox": [ + 247, + 711, + 389, + 723 + ], + "score": 0.9, + "content": "p ( w _ { 0 } w _ { 1 } \\dots w _ { n - 1 } ) / p ( w _ { 1 } \\dots w _ { n - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 710, + 472, + 725 + ], + "score": 1.0, + "content": ". 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(a) GPT2-noPretrain-model;", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 374, + 398, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 398, + 385 + ], + "score": 1.0, + "content": "(b) GPT2-Pretrained-model; (c) Pretrained attention is replaced by PCA.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + } + ], + "index": 8.25 + }, + { + "type": "text", + "bbox": [ + 107, + 407, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 406, + 505, + 419 + ], + "score": 1.0, + "content": "The Theorem E.4 considers the covariate matrix of feature maps being positive definite that indicates", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 417, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 213, + 430 + ], + "score": 1.0, + "content": "the set of all feature maps", + "type": "text" + }, + { + "bbox": [ + 213, + 417, + 233, + 430 + ], + "score": 0.92, + "content": "\\left\\{ \\pmb { g } _ { i } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 417, + 506, + 430 + ], + "score": 1.0, + "content": "spans the whole feature spaces, and the higher spread level gives a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 429, + 505, + 441 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 131, + 441 + ], + "score": 1.0, + "content": "larger", + "type": "text" + }, + { + "bbox": [ + 131, + 431, + 138, + 439 + ], + "score": 0.7, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 429, + 505, + 441 + ], + "score": 1.0, + "content": ". In this case, if we only want to learn an MLP layer, the problem reduces to a well-conditioned", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 440, + 417, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 417, + 452 + ], + "score": 1.0, + "content": "least-squared regression problem. Then the fast convergence rate is achieved.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 406, + 506, + 452 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 456, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 506, + 470 + ], + "score": 1.0, + "content": "Efficiently learning the last MLP layer plays a very important role in time series forecasting and", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "can substantially impact the prediction performance. In Zeng et al. (2023), the authors show that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 477, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 477, + 505, + 491 + ], + "score": 1.0, + "content": "learning a single MLP layer can also bring very promising performance. In few-shot forecasting, the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 488, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 506, + 502 + ], + "score": 1.0, + "content": "pre-trained GPT2 model may still preserve highly diverse feature maps than end-to-end type models", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 500, + 368, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 368, + 513 + ], + "score": 1.0, + "content": "and eventually leads to fast learning speed on the last MLP layer.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 455, + 506, + 513 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 516, + 505, + 582 + ], + "lines": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "Another possible benefit of wide spared feature maps is enhancing the model memorization ability", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 525, + 507, + 541 + ], + "spans": [ + { + "bbox": [ + 104, + 525, + 507, + 541 + ], + "score": 1.0, + "content": "when using a multi-layer decoder structure. In the literature on network memorization ability (e.g.,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 506, + 551 + ], + "score": 1.0, + "content": "Vardi et al. (2021); Yun et al. (2020)), the deep learning model tends to have better memorization", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "score": 1.0, + "content": "ability when feature maps are well separated. In forecasting tasks, capturing extreme or rare behavior", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 560, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 572 + ], + "score": 1.0, + "content": "is very important. The pretrained GPT gains more capacity in the decoder to correctly forecast", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 572, + 202, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 202, + 583 + ], + "score": 1.0, + "content": "uncommon time series.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5, + "bbox_fs": [ + 104, + 515, + 507, + 583 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 598, + 315, + 612 + ], + "lines": [ + { + "bbox": [ + 104, + 596, + 317, + 616 + ], + "spans": [ + { + "bbox": [ + 104, + 596, + 317, + 616 + ], + "score": 1.0, + "content": "F N-gram Explanation for Universality", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 623, + 505, + 723 + ], + "lines": [ + { + "bbox": [ + 106, + 623, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 506, + 636 + ], + "score": 1.0, + "content": "Why does the proposed pretrained-frozen-model work so effectively? We have achieved state-of-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 633, + 506, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 647 + ], + "score": 1.0, + "content": "the-art performance in time series analysis using a language model that is mostly trained on natural", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "language data. The answer lies in the universality of the frozen structure, which includes attention", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 655, + 506, + 669 + ], + "score": 1.0, + "content": "layers and Feed Forward layers. We can represent images and time series forecasting tasks as an", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 666, + 506, + 680 + ], + "spans": [ + { + "bbox": [ + 104, + 666, + 506, + 680 + ], + "score": 1.0, + "content": "n-gram estimation problem, akin to text analysis, by employing a patching approach. This method", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 690 + ], + "score": 1.0, + "content": "treats subsequences of time series or image patches as individual tokens. 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To predict next token", + "type": "text" + }, + { + "bbox": [ + 314, + 702, + 326, + 711 + ], + "score": 0.81, + "content": "w _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 699, + 417, + 714 + ], + "score": 1.0, + "content": ", we need to compute", + "type": "text" + }, + { + "bbox": [ + 418, + 700, + 502, + 712 + ], + "score": 0.92, + "content": "p ( w _ { 0 } | w _ { 1 } , \\dots , w _ { n - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 699, + 506, + 714 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 710, + 506, + 725 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 247, + 725 + ], + "score": 1.0, + "content": "which can be further computed as", + "type": "text" + }, + { + "bbox": [ + 247, + 711, + 389, + 723 + ], + "score": 0.9, + "content": "p ( w _ { 0 } w _ { 1 } \\dots w _ { n - 1 } ) / p ( w _ { 1 } \\dots w _ { n - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 710, + 472, + 725 + ], + "score": 1.0, + "content": ". Hence, the core of", + "type": "text" + }, + { + "bbox": [ + 473, + 713, + 479, + 721 + ], + "score": 0.77, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 710, + 506, + 725 + ], + "score": 1.0, + "content": "-gram", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 277, + 507, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 397, + 292 + ], + "score": 1.0, + "content": "language model is to estimate the probability of observing a sequence of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 398, + 280, + 405, + 288 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 406, + 277, + 464, + 292 + ], + "score": 1.0, + "content": "tokens. When", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 464, + 280, + 471, + 288 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 471, + 277, + 507, + 292 + ], + "score": 1.0, + "content": "is large,", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 289, + 506, + 302 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 140, + 302 + ], + "score": 1.0, + "content": "most of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 141, + 291, + 148, + 299 + ], + "score": 0.72, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 149, + 289, + 506, + 302 + ], + "score": 1.0, + "content": "token sequences will not be observed from data, leading to the sparse data problem, a", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 299, + 506, + 314 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 219, + 314 + ], + "score": 1.0, + "content": "common challenge faced by", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 219, + 302, + 226, + 310 + ], + "score": 0.75, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 227, + 299, + 473, + 314 + ], + "score": 1.0, + "content": "-gram language model. As a result, a large body of research in", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 473, + 302, + 480, + 310 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 480, + 299, + 506, + 314 + ], + "score": 1.0, + "content": "-gram", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 310, + 506, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 310, + 427, + 325 + ], + "score": 1.0, + "content": "language model is focused on how to effectively estimate probability of having", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 428, + 313, + 434, + 321 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 435, + 310, + 506, + 325 + ], + "score": 1.0, + "content": "-token sequences", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "even when they are NOT observed from data. We hypothesize that the transformer model pretrained", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 286, + 347 + ], + "score": 1.0, + "content": "by GPT-2 essentially allows us to estimate", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 287, + 333, + 361, + 345 + ], + "score": 0.92, + "content": "p ( w _ { 0 } w _ { 1 } \\dots w _ { n - 1 } )", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 361, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "from observations of significantly", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "shorter token sequences. In this section, we will show that the function of estimating probabilities of", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "score": 1.0, + "content": "longer sequences from observation of shorter sequences is universal and is independent from domain", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 364, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 506, + 379 + ], + "score": 1.0, + "content": "as long as data exhibit a skew distribution (e.g., follows a power law). We note that our work is closely", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 376, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 389 + ], + "score": 1.0, + "content": "related to the discussion presented in Elhage et al. (2021); Olsson et al. (2022), where the authors", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 387, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 323, + 400 + ], + "score": 1.0, + "content": "also connect the function of transformer to compute of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 323, + 389, + 330, + 397 + ], + "score": 0.79, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 330, + 387, + 506, + 400 + ], + "score": 1.0, + "content": "-grams. We however note that our key result", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "score": 1.0, + "content": "is to show the universality in computing probability of longer sequences from observations of shorter", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "score": 1.0, + "content": "sequences, which can’t be found in any existing studies. Although the discussion is restricted to", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 420, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 506, + 433 + ], + "score": 1.0, + "content": "discrete tokens, it should be generalized to continuous signals as we can always quantize continuous", + "type": "text", + "cross_page": true + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 431, + 469, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 469, + 443 + ], + "score": 1.0, + "content": "signals into a finite number of discrete tokens, similar to what BEiT Bao et al. 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(c) The token similarity within samples within different continuous sequence", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 240, + 142, + 257 + ], + "spans": [ + { + "bbox": [ + 104, + 240, + 142, + 257 + ], + "score": 1.0, + "content": "lengths.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 277, + 505, + 442 + ], + "lines": [ + { + "bbox": [ + 105, + 277, + 507, + 292 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 397, + 292 + ], + "score": 1.0, + "content": "language model is to estimate the probability of observing a sequence of", + "type": "text" + }, + { + "bbox": [ + 398, + 280, + 405, + 288 + ], + "score": 0.76, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 277, + 464, + 292 + ], + "score": 1.0, + "content": "tokens. 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As a result, a large body of research in", + "type": "text" + }, + { + "bbox": [ + 473, + 302, + 480, + 310 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 299, + 506, + 314 + ], + "score": 1.0, + "content": "-gram", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 310, + 506, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 310, + 427, + 325 + ], + "score": 1.0, + "content": "language model is focused on how to effectively estimate probability of having", + "type": "text" + }, + { + "bbox": [ + 428, + 313, + 434, + 321 + ], + "score": 0.74, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 310, + 506, + 325 + ], + "score": 1.0, + "content": "-token sequences", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 334 + ], + "score": 1.0, + "content": "even when they are NOT observed from data. We hypothesize that the transformer model pretrained", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 333, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 286, + 347 + ], + "score": 1.0, + "content": "by GPT-2 essentially allows us to estimate", + "type": "text" + }, + { + "bbox": [ + 287, + 333, + 361, + 345 + ], + "score": 0.92, + "content": "p ( w _ { 0 } w _ { 1 } \\dots w _ { n - 1 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 333, + 505, + 347 + ], + "score": 1.0, + "content": "from observations of significantly", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "shorter token sequences. In this section, we will show that the function of estimating probabilities of", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "score": 1.0, + "content": "longer sequences from observation of shorter sequences is universal and is independent from domain", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 364, + 506, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 506, + 379 + ], + "score": 1.0, + "content": "as long as data exhibit a skew distribution (e.g., follows a power law). We note that our work is closely", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 376, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 389 + ], + "score": 1.0, + "content": "related to the discussion presented in Elhage et al. (2021); Olsson et al. 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We however note that our key result", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 411 + ], + "score": 1.0, + "content": "is to show the universality in computing probability of longer sequences from observations of shorter", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 409, + 505, + 421 + ], + "score": 1.0, + "content": "sequences, which can’t be found in any existing studies. Although the discussion is restricted to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 420, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 106, + 420, + 506, + 433 + ], + "score": 1.0, + "content": "discrete tokens, it should be generalized to continuous signals as we can always quantize continuous", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 431, + 469, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 469, + 443 + ], + "score": 1.0, + "content": "signals into a finite number of discrete tokens, similar to what BEiT Bao et al. (2022) did.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 447, + 505, + 502 + ], + "lines": [ + { + "bbox": [ + 105, + 447, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 505, + 459 + ], + "score": 1.0, + "content": "To gain a better understanding, let’s start by examining a \"zero-layer\" Transformer model. This model", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "operates by taking a token, embedding it, and transforming it back to produce logits that predict the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "subsequent token. Because it cannot transfer information from other tokens, it relies solely on the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 479, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 493 + ], + "score": 1.0, + "content": "current token to predict the next one. Consequently, the optimal behavior of this model is to closely", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 491, + 254, + 503 + ], + "spans": [ + { + "bbox": [ + 105, + 491, + 254, + 503 + ], + "score": 1.0, + "content": "resemble the bigram log-likelihood.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 106, + 507, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "score": 1.0, + "content": "Then we move on to the so-called \"attention-only\" transformer, which doesn’t have MLP layers.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 517, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 505, + 531 + ], + "score": 1.0, + "content": "As discussed in a recent work Elhage et al. 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This can be intuitively understood as each attention head", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 551, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 551, + 506, + 564 + ], + "score": 1.0, + "content": "having the ability to selectively attend from the current token (\"B\") to a previous token (\"A\") and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 450, + 574 + ], + "score": 1.0, + "content": "transfer relevant information to fine-tune the probability of potential subsequent tokens", + "type": "text" + }, + { + "bbox": [ + 450, + 562, + 471, + 573 + ], + "score": 0.39, + "content": "\\mathrm { ( \" } \\mathrm { C \" } )", + "type": "inline_equation" + }, + { + "bbox": [ + 471, + 561, + 506, + 574 + ], + "score": 1.0, + "content": ". Olsson", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 572, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 586 + ], + "score": 1.0, + "content": "et al. (2022) further discusses a multi-layer transformer can do more complex n-gram estimation", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "using an induction heads mechanism. 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This rule seems to largely decouple A and B, which means they do not memorize a fixed", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 104, + 626, + 507, + 641 + ], + "spans": [ + { + "bbox": [ + 104, + 626, + 297, + 641 + ], + "score": 1.0, + "content": "table of n-gram statistics. The rule [A][B] . . .", + "type": "text" + }, + { + "bbox": [ + 297, + 628, + 342, + 639 + ], + "score": 0.84, + "content": "[ \\mathbf { A } ] [ \\mathbf { B } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 626, + 507, + 641 + ], + "score": 1.0, + "content": "applies regardless of what A and B are,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 249, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 249, + 650 + ], + "score": 1.0, + "content": "which can abstract to new patterns.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 504, + 723 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "Building upon these discussions, we are now prepared to substantiate the following argument: For", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 665, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 677 + ], + "score": 1.0, + "content": "sequential data following a power law, there is a potentially universal solution to the final", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "estimation of n-gram probabilities. That’s the reason behind the universality of pretrained LM’s", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 370, + 700 + ], + "score": 1.0, + "content": "performance in cross-domain tasks. 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(2021), one-layer attention-only Transformers can be", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 528, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 104, + 528, + 506, + 543 + ], + "score": 1.0, + "content": "comprehended as a combination of a bigram model and multiple \"skip-trigram\" models (impacting", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 540, + 506, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 506, + 552 + ], + "score": 1.0, + "content": "the probabilities of sequences \"A. . . BC\"). 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Olsson", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 572, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 586 + ], + "score": 1.0, + "content": "et al. (2022) further discusses a multi-layer transformer can do more complex n-gram estimation", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "using an induction heads mechanism. 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The rule [A][B] . . .", + "type": "text" + }, + { + "bbox": [ + 297, + 628, + 342, + 639 + ], + "score": 0.84, + "content": "[ \\mathbf { A } ] [ \\mathbf { B } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 626, + 507, + 641 + ], + "score": 1.0, + "content": "applies regardless of what A and B are,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 638, + 249, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 249, + 650 + ], + "score": 1.0, + "content": "which can abstract to new patterns.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 32, + "bbox_fs": [ + 104, + 506, + 507, + 650 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 504, + 723 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "Building upon these discussions, we are now prepared to substantiate the following argument: For", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 665, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 677 + ], + "score": 1.0, + "content": "sequential data following a power law, there is a potentially universal solution to the final", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "estimation of n-gram probabilities. 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The lemma below shows an important structure of", + "type": "text" + }, + { + "bbox": [ + 426, + 181, + 434, + 190 + ], + "score": 0.8, + "content": "J", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 179, + 439, + 192 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "interline_equation", + "bbox": [ + 111, + 191, + 437, + 262 + ], + "lines": [ + { + "bbox": [ + 111, + 191, + 437, + 262 + ], + "spans": [ + { + "bbox": [ + 111, + 191, + 437, + 262 + ], + "score": 0.77, + "content": "\\begin{array} { r l } & { \\mathit { \\mathcal { e m m a } } \\mathrm { G . 1 . } \\quad | J | _ { 2 } \\leq | A | _ { 2 } \\sum _ { i = 1 } ^ { N } \\left( P _ { i , i } + \\frac { 1 } { 2 } \\right) \\left| x _ { i } - \\sum _ { j = 1 } ^ { N } P _ { i , j } x _ { j } \\right| ^ { 2 } + \\Delta } \\\\ & { \\mathrm { v h e r e } \\qquad \\Delta = | A | _ { 2 } \\sum _ { i \\neq j } ^ { N } P _ { i , j } \\left| x _ { j } - \\sum _ { k = 1 } ^ { N } P _ { i , k } x _ { k } \\right| ^ { 2 } + \\frac { | A | _ { 2 } } { 2 } \\sum _ { j = 1 } ^ { N } | x _ { i } | ^ { 2 } } \\\\ & { P _ { i , j } = \\frac { \\exp \\left( x _ { i } ^ { \\top } A x _ { j } \\right) } { \\sum _ { k = 1 } ^ { N } \\exp \\left( x _ { i } ^ { \\top } A x _ { k } \\right) } } \\end{array}", + "type": "interline_equation", + "image_path": "4cd6514bb45f06614e96f155b39188714feeb3c8d07f7c166f9d9ac8c07aebfa.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 111, + 191, + 437, + 214.66666666666666 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 111, + 214.66666666666666, + 437, + 238.33333333333331 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 111, + 238.33333333333331, + 437, + 262.0 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 487, + 224, + 505, + 235 + ], + "lines": [ + { + "bbox": [ + 486, + 224, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 486, + 224, + 506, + 235 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 273, + 505, + 317 + ], + "lines": [ + { + "bbox": [ + 105, + 272, + 506, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 272, + 397, + 290 + ], + "score": 1.0, + "content": "Proof. 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According to the analysis from the work, we have the gradient", + "type": "text" + }, + { + "bbox": [ + 397, + 274, + 456, + 291 + ], + "score": 0.93, + "content": "\\begin{array} { r } { J _ { i , j } = \\frac { \\partial f _ { i } ( \\boldsymbol { X } ) } { x _ { j } } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 272, + 506, + 290 + ], + "score": 1.0, + "content": "is given by", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 114, + 289, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 114, + 290, + 297, + 305 + ], + "score": 0.84, + "content": "J _ { i , j } = P _ { i , j } I + X ^ { \\top } Q ^ { i } \\left( X A \\delta _ { i , j } + E _ { j , i } X A ^ { \\top } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 290, + 448, + 305 + ], + "score": 0.78, + "content": "Q ^ { i } = \\mathrm { d i a g } ( P _ { i , : } ) - P _ { i , : } P _ { i , : } ^ { \\top }", + "type": "inline_equation" + }, + { + "bbox": [ + 454, + 289, + 478, + 306 + ], + "score": 1.0, + "content": "Here", + "type": "text" + }, + { + "bbox": [ + 478, + 291, + 505, + 304 + ], + "score": 0.87, + "content": "P _ { i , : } \\in", + "type": "inline_equation" + } + ], + "index": 12 + }, + { + "bbox": [ + 107, + 302, + 326, + 320 + ], + "spans": [ + { + "bbox": [ + 107, + 304, + 122, + 317 + ], + "score": 0.91, + "content": "\\mathbb { R } _ { + } ^ { N }", + "type": "inline_equation" + }, + { + "bbox": [ + 122, + 302, + 181, + 320 + ], + "score": 1.0, + "content": "represents the", + "type": "text" + }, + { + "bbox": [ + 182, + 306, + 186, + 314 + ], + "score": 0.78, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 302, + 255, + 320 + ], + "score": 1.0, + "content": "-th row of matrix", + "type": "text" + }, + { + "bbox": [ + 255, + 306, + 264, + 315 + ], + "score": 0.79, + "content": "P", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 302, + 326, + 320 + ], + "score": 1.0, + "content": ". We thus have", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 272, + 506, + 320 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 110, + 321, + 404, + 407 + ], + "lines": [ + { + "bbox": [ + 110, + 321, + 404, + 407 + ], + "spans": [ + { + "bbox": [ + 110, + 321, + 404, + 407 + ], + "score": 0.94, + "content": "\\begin{array} { r c l } { | J | _ { 2 } } & { \\leq } & { \\sum _ { i , j = 1 } ^ { N } | J _ { i , j } | _ { 2 } } \\\\ & { \\leq } & { \\sum _ { i , j = 1 } ^ { N } P _ { i , j } + \\sum _ { i = 1 } ^ { N } | X ^ { \\top } Q ^ { i } X | _ { 2 } | A | _ { 2 } + \\sum _ { i , j = 1 } ^ { N } | X ^ { \\top } Q ^ { i } E _ { j , i } X | _ { 2 } | A | _ { 2 } } \\\\ & { \\leq } & { N + | A | _ { 2 } \\sum _ { i = 1 } ^ { N } \\bigg ( \\sum _ { j = 1 } ^ { N } P _ { i , j } | x _ { j } | ^ { 2 } - \\left| \\sum _ { j = 1 } ^ { N } P _ { i , j } x _ { j } \\right| ^ { 2 } \\bigg ) + | A | _ { 2 } \\sum _ { i , j = 1 } ^ { N } | X ^ { \\top } Q ^ { i } e _ { j } x _ { i } ^ { \\top } | } \\\\ & { \\leq } & { N + | A | _ { 2 } \\sum _ { i = 1 } ^ { N } \\sum _ { j = 1 } ^ { N } P _ { i , j } \\left| x _ { j } - \\sum _ { k = 1 } ^ { N } P _ { i , k } x _ { k } \\right| ^ { 2 } + | A | _ { 2 } \\sum _ { i , j = 1 } ^ { N } P _ { i , j } \\left| x _ { i } ^ { \\top } \\left( x _ { j } - X ^ { \\top } P _ { i , : } \\right) \\right| } \\\\ & { \\leq } & { | A | _ { 2 } \\sum _ { i = 1 } ^ { N } \\left( P _ { i , i } + \\frac { 1 } { 2 } \\right) \\left| x _ { i } - X ^ { \\top } P _ { i , : } \\right| ^ { 2 } + \\underbrace { N + | A | _ { 2 } \\sum _ { i \\neq j } ^ { N } P _ { i , j } \\left| x _ { j } - X ^ { \\top } P _ { i , : } \\right| ^ { 2 } + \\frac { | A | _ { 2 } } { 2 } \\sum _ { j = 1 } ^ { N } | x _ { i } | ^ { 2 } } _ { : = \\Delta } } \\end{array}", + "type": "interline_equation", + "image_path": "f73908bccee20ffd926de213097a7999ea143607f3fba7cdb4a63ed65324d14b.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 110, + 321, + 404, + 349.6666666666667 + ], + "spans": [], + "index": 14 + }, + { + "bbox": [ + 110, + 349.6666666666667, + 404, + 378.33333333333337 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 110, + 378.33333333333337, + 404, + 407.00000000000006 + ], + "spans": [], + "index": 16 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 420, + 506, + 513 + ], + "lines": [ + { + "bbox": [ + 105, + 419, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 480, + 434 + ], + "score": 1.0, + "content": "As indicated by Lemma 1, one of the key components in the upper bound of Jacobian is", + "type": "text" + }, + { + "bbox": [ + 480, + 421, + 505, + 433 + ], + "score": 0.89, + "content": "| x _ { i } -", + "type": "inline_equation" + } + ], + "index": 17 + }, + { + "bbox": [ + 107, + 432, + 507, + 448 + ], + "spans": [ + { + "bbox": [ + 107, + 432, + 167, + 448 + ], + "score": 0.93, + "content": "\\textstyle \\sum _ { j = 1 } ^ { N } P _ { i , j } x _ { j } | ^ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 167, + 432, + 507, + 448 + ], + "score": 1.0, + "content": ". 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X ^ { \\top } P _ { i , : } | ^ { 2 } = \\sum _ { i = 1 } ^ { N } \\left| x _ { i } - \\bar { x } - X ^ { \\top } X A x _ { i } \\right| ^ { 2 } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 551, + 509, + 576 + ], + "score": 1.0, + "content": "By assuming that all the input patterns are", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 101, + 564, + 510, + 593 + ], + "spans": [ + { + "bbox": [ + 101, + 564, + 212, + 593 + ], + "score": 1.0, + "content": "i=1 zero centralized, we have", + "type": "text" + }, + { + "bbox": [ + 212, + 573, + 238, + 583 + ], + "score": 0.84, + "content": "\\bar { x } = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 564, + 261, + 593 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 262, + 572, + 480, + 586 + ], + "score": 0.89, + "content": "\\begin{array} { r } { \\sum _ { i = 1 } ^ { N } | x _ { i } - X ^ { \\top } X A x _ { i } | ^ { 2 } = \\mathrm { t r } \\left( ( I - 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Let", + "type": "text" + }, + { + "bbox": [ + 176, + 613, + 194, + 626 + ], + "score": 0.89, + "content": "W _ { Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 194, + 612, + 214, + 626 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 215, + 613, + 233, + 624 + ], + "score": 0.9, + "content": "W _ { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 612, + 318, + 626 + ], + "score": 1.0, + "content": "be matrices of size", + "type": "text" + }, + { + "bbox": [ + 319, + 613, + 351, + 624 + ], + "score": 0.91, + "content": "D \\times m", + "type": "inline_equation" + }, + { + "bbox": [ + 352, + 612, + 376, + 626 + ], + "score": 1.0, + "content": ". Let", + "type": "text" + }, + { + "bbox": [ + 377, + 613, + 474, + 625 + ], + "score": 0.9, + "content": "\\lambda _ { 1 } \\ \\ge \\ \\lambda _ { 2 } \\ \\ge \\ . . . \\ \\ge \\ \\lambda _ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "be the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 623, + 508, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 623, + 169, + 639 + ], + "score": 1.0, + "content": "eigenvalues of", + "type": "text" + }, + { + "bbox": [ + 169, + 626, + 195, + 636 + ], + "score": 0.89, + "content": "X ^ { \\top } X", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 623, + 348, + 639 + ], + "score": 1.0, + "content": "ranked in descending order, and let", + "type": "text" + }, + { + "bbox": [ + 348, + 625, + 448, + 637 + ], + "score": 0.88, + "content": "v _ { i } \\in \\mathbb { R } ^ { D } , i = 1 , \\dots , D", + "type": "inline_equation" + }, + { + "bbox": [ + 449, + 623, + 508, + 639 + ], + "score": 1.0, + "content": "be the corre-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 101, + 630, + 510, + 657 + ], + "spans": [ + { + "bbox": [ + 101, + 630, + 284, + 657 + ], + "score": 1.0, + "content": "sponding eigenvectors. 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Then", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 261, + 452, + 274 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 452, + 274 + ], + "score": 1.0, + "content": "we analyze the performance of various layers to clarify our selection of GPT2(6) FPT.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9.5 + }, + { + "type": "table", + "bbox": [ + 214, + 317, + 394, + 510 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 105, + 290, + 504, + 313 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 289, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 250, + 304 + ], + "score": 1.0, + "content": "Table 21: Model analysis results on", + "type": "text" + }, + { + "bbox": [ + 250, + 291, + 266, + 301 + ], + "score": 0.86, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 266, + 289, + 390, + 304 + ], + "score": 1.0, + "content": "data. We use prediction length", + "type": "text" + }, + { + "bbox": [ + 390, + 290, + 490, + 303 + ], + "score": 0.91, + "content": "O \\in \\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 289, + 506, + 304 + ], + "score": 1.0, + "content": "for", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 301, + 267, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 301, + 138, + 314 + ], + "score": 1.0, + "content": "ILI and", + "type": "text" + }, + { + "bbox": [ + 139, + 301, + 223, + 313 + ], + "score": 0.93, + "content": "O \\in \\{ 2 4 , 3 6 , \\hat { 4 } 8 , 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 301, + 267, + 314 + ], + "score": 1.0, + "content": "for others.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "table_body", + "bbox": [ + 214, + 317, + 394, + 510 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 214, + 317, + 394, + 510 + ], + "spans": [ + { + "bbox": [ + 214, + 317, + 394, + 510 + ], + "score": 0.979, + "html": "
MethodsGPT2(6)No FreezeNo Pretrain
MetricMSEMAEMSEMAEMSEMAE
wwheees960.1750.2300.1830.2290.1990.254
1920.2270.2760.2750.3000.2620.302
3360.2860.3220.2970.3310.3260.345
7200.3660.3790.3800.3880.4050.396
960.5430.5060.6710.5640.8820.643
LL1920.7480.5800.9070.6321.3890.817
3360.7540.5950.9310.6552.9681.149
720------
960.3760.4210.4400.4490.4650.457
1920.4180.4410.5030.4780.6140.536
LLa3360.4080.4390.6910.5720.5960.529
720------
LL960.3860.4050.4290.4320.3940.410
1920.4400.4380.4960.4700.4320.432
3360.4850.4590.5350.4890.4910.464
7200.5570.4990.7860.5920.5640.503
960.1990.2800.2170.2930.3010.353
LL1920.2560.3160.3000.3500.3210.365
3360.3180.3530.3310.3680.3710.398
7200.4600.4390.4600.4360.6590.528
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It verifies", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 557, + 423, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 557, + 423, + 572 + ], + "score": 1.0, + "content": "that frozen pre-trained attention layers are effective for time series forecasting.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 106, + 574, + 505, + 629 + ], + "lines": [ + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 505, + 586 + ], + "score": 1.0, + "content": "Parameters Initialization Compared with the random initial model, self-attention frozen pre-trained", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 585, + 504, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 475, + 597 + ], + "score": 1.0, + "content": "model GPT2(6) FPT achieves better performance on most datasets and yields an overall", + "type": "text" + }, + { + "bbox": [ + 475, + 585, + 504, + 596 + ], + "score": 0.85, + "content": "2 1 . 2 \\%", + "type": "inline_equation" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 595, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 211, + 610 + ], + "score": 1.0, + "content": "relative MSE reduction on", + "type": "text" + }, + { + "bbox": [ + 211, + 596, + 226, + 606 + ], + "score": 0.86, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 226, + 595, + 262, + 610 + ], + "score": 1.0, + "content": "data and", + "type": "text" + }, + { + "bbox": [ + 262, + 596, + 289, + 607 + ], + "score": 0.87, + "content": "1 4 . 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 595, + 396, + 610 + ], + "score": 1.0, + "content": "relative MSE reduction on", + "type": "text" + }, + { + "bbox": [ + 396, + 596, + 415, + 607 + ], + "score": 0.86, + "content": "10 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 595, + 506, + 610 + ], + "score": 1.0, + "content": "data. It again suggests", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 607, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 505, + 619 + ], + "score": 1.0, + "content": "that a model pre-trained on cross-domain data can achieve significant performance improvement in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 616, + 202, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 202, + 632 + ], + "score": 1.0, + "content": "time series forecasting.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 106, + 634, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 648 + ], + "score": 1.0, + "content": "The Number of GPT2 Layers For most transformer-based methods in time-series forecasting", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "score": 1.0, + "content": "Zhou et al. (2022); Wu et al. (2021); Nie et al. (2022), no more than 3 encoder layers are included.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "However, most pre-trained models with at least 12 layers may suffer from overfitting in time series", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "forecasting. To better balance performance and computational efficiency, we test using various", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "score": 1.0, + "content": "numbers of layers on ETTh2. 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Firstly,", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 104, + 228, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 104, + 228, + 506, + 241 + ], + "score": 1.0, + "content": "we compare GPT2(6) FPT with the same model without freezing (No Freeze) and random initial", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 240, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 505, + 253 + ], + "score": 1.0, + "content": "model (No Pre-train). For the end-to-end paradigm No Pre-train GPT2-backbone (6 Layers), we", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 250, + 506, + 263 + ], + "spans": [ + { + "bbox": [ + 106, + 250, + 506, + 263 + ], + "score": 1.0, + "content": "directly train all parameters of the model. We summarize the results in Table 21 and Table 22. Then", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 261, + 452, + 274 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 452, + 274 + ], + "score": 1.0, + "content": "we analyze the performance of various layers to clarify our selection of GPT2(6) FPT.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9.5, + "bbox_fs": [ + 104, + 207, + 506, + 274 + ] + }, + { + "type": "table", + "bbox": [ + 214, + 317, + 394, + 510 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 105, + 290, + 504, + 313 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 289, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 289, + 250, + 304 + ], + "score": 1.0, + "content": "Table 21: Model analysis results on", + "type": "text" + }, + { + "bbox": [ + 250, + 291, + 266, + 301 + ], + "score": 0.86, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 266, + 289, + 390, + 304 + ], + "score": 1.0, + "content": "data. We use prediction length", + "type": "text" + }, + { + "bbox": [ + 390, + 290, + 490, + 303 + ], + "score": 0.91, + "content": "O \\in \\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 289, + 506, + 304 + ], + "score": 1.0, + "content": "for", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 301, + 267, + 314 + ], + "spans": [ + { + "bbox": [ + 106, + 301, + 138, + 314 + ], + "score": 1.0, + "content": "ILI and", + "type": "text" + }, + { + "bbox": [ + 139, + 301, + 223, + 313 + ], + "score": 0.93, + "content": "O \\in \\{ 2 4 , 3 6 , \\hat { 4 } 8 , 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 301, + 267, + 314 + ], + "score": 1.0, + "content": "for others.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "table_body", + "bbox": [ + 214, + 317, + 394, + 510 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 214, + 317, + 394, + 510 + ], + "spans": [ + { + "bbox": [ + 214, + 317, + 394, + 510 + ], + "score": 0.979, + "html": "
MethodsGPT2(6)No FreezeNo Pretrain
MetricMSEMAEMSEMAEMSEMAE
wwheees960.1750.2300.1830.2290.1990.254
1920.2270.2760.2750.3000.2620.302
3360.2860.3220.2970.3310.3260.345
7200.3660.3790.3800.3880.4050.396
960.5430.5060.6710.5640.8820.643
LL1920.7480.5800.9070.6321.3890.817
3360.7540.5950.9310.6552.9681.149
720------
960.3760.4210.4400.4490.4650.457
1920.4180.4410.5030.4780.6140.536
LLa3360.4080.4390.6910.5720.5960.529
720------
LL960.3860.4050.4290.4320.3940.410
1920.4400.4380.4960.4700.4320.432
3360.4850.4590.5350.4890.4910.464
7200.5570.4990.7860.5920.5640.503
960.1990.2800.2170.2930.3010.353
LL1920.2560.3160.3000.3500.3210.365
3360.3180.3530.3310.3680.3710.398
7200.4600.4390.4600.4360.6590.528
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It again suggests", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 607, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 505, + 619 + ], + "score": 1.0, + "content": "that a model pre-trained on cross-domain data can achieve significant performance improvement in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 616, + 202, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 202, + 632 + ], + "score": 1.0, + "content": "time series forecasting.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35, + "bbox_fs": [ + 105, + 574, + 506, + 632 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 634, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 648 + ], + "score": 1.0, + "content": "The Number of GPT2 Layers For most transformer-based methods in time-series forecasting", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 506, + 657 + ], + "score": 1.0, + "content": "Zhou et al. (2022); Wu et al. (2021); Nie et al. (2022), no more than 3 encoder layers are included.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "However, most pre-trained models with at least 12 layers may suffer from overfitting in time series", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "forecasting. To better balance performance and computational efficiency, we test using various", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 505, + 690 + ], + "score": 1.0, + "content": "numbers of layers on ETTh2. Additionally, we train a completely random initialized non-pretrained", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 371, + 701 + ], + "score": 1.0, + "content": "GPT2 as a comparison. The results are shown in Figure 9, for both", + "type": "text" + }, + { + "bbox": [ + 371, + 689, + 385, + 699 + ], + "score": 0.86, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 386, + 689, + 403, + 701 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 404, + 689, + 423, + 699 + ], + "score": 0.86, + "content": "10 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 423, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "data, the pre-trained", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "model is unable to do well with few layers but significantly outperforms non-pre-trained GPT2 with", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "more attention blocks transferred from NLP. It indicates that pre-trained attention layers produce", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 307, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 505, + 321 + ], + "score": 1.0, + "content": "a great benefit in time series forecasting. Also, the pre-trained model achieves better performance", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 454, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 454, + 331 + ], + "score": 1.0, + "content": "between 3 and 9 layers. Thus GPT2 with 6 layers is chosen as our default architecture.", + "type": "text", + "cross_page": true + } + ], + "index": 17 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 633, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 214, + 105, + 394, + 298 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 77, + 503, + 100 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 75, + 505, + 91 + ], + "spans": [ + { + "bbox": [ + 105, + 75, + 319, + 91 + ], + "score": 1.0, + "content": "Table 22: No Pretrain and No Freeze results on", + "type": "text" + }, + { + "bbox": [ + 320, + 78, + 339, + 88 + ], + "score": 0.86, + "content": "10 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 75, + 482, + 91 + ], + "score": 1.0, + "content": "data. We use prediction length", + "type": "text" + }, + { + "bbox": [ + 482, + 77, + 505, + 89 + ], + "score": 0.79, + "content": "O \\in", + "type": "inline_equation" + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 88, + 362, + 101 + ], + "spans": [ + { + "bbox": [ + 107, + 88, + 186, + 101 + ], + "score": 0.76, + "content": "\\{ 9 6 , 1 9 2 , 3 3 6 , 7 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 88, + 233, + 101 + ], + "score": 1.0, + "content": "for ILI and", + "type": "text" + }, + { + "bbox": [ + 234, + 88, + 318, + 100 + ], + "score": 0.9, + "content": "O \\in \\{ 2 4 , 3 6 , 4 8 , 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 88, + 362, + 101 + ], + "score": 1.0, + "content": "for others.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "table_body", + "bbox": [ + 214, + 105, + 394, + 298 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 214, + 105, + 394, + 298 + ], + "spans": [ + { + "bbox": [ + 214, + 105, + 394, + 298 + ], + "score": 0.978, + "html": "
MethodsGPT2(6)No FreezeNo Pretrain
MetricMSEMAEMSEMAEMSEMAE
weeeet960.1630.2150.1680.2210.1750.229
1920.2100.2540.2380.2860.2440.287
3360.2560.2920.2890.3180.3010.325
7200.3210.3390.3980.3830.3900.378
LLE960.4580.4560.6050.5320.6800.560
1920.5700.5160.7130.5790.7380.602
3360.6080.5350.7470.5860.8930.641
7200.7250.5910.9450.6882.9941.169
960.3310.3740.3690.3940.4220.433
LLa1920.4020.4110.4640.4550.4820.466
3360.4060.4330.4200.4390.5400.496
7200.4490.4640.5350.5150.5640.519
LL960.3900.4040.4290.4300.3850.401
1920.4290.4230.4630.4460.4260.421
3360.4690.4390.5100.4700.5060.455
7200.5690.4980.7800.5910.5760.505
LLa960.1880.2690.2430.3110.2440.315
1920.2510.3090.3070.3520.3180.363
3360.3070.3460.3370.3640.4090.412
7200.4260.4170.4710.4400.4730.450
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Also, the pre-trained model achieves better performance", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 319, + 454, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 454, + 331 + ], + "score": 1.0, + "content": "between 3 and 9 layers. Thus GPT2 with 6 layers is chosen as our default architecture.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16.5 + }, + { + "type": "image", + "bbox": [ + 128, + 347, + 480, + 528 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 128, + 347, + 480, + 528 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 128, + 347, + 480, + 528 + ], + "spans": [ + { + "bbox": [ + 128, + 347, + 480, + 528 + ], + "score": 0.974, + "type": "image", + "image_path": "96d0bc0d960fc52be108097d406b2bb72722f38e72cd8dbdedf59b0206be9cd2.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 128, + 347, + 480, + 407.3333333333333 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 128, + 407.3333333333333, + 480, + 467.66666666666663 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 128, + 467.66666666666663, + 480, + 528.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 536, + 505, + 560 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "Figure 9: Comparison of pre-trained and non-pre-trained GPT2 with various layers on ETTh2. Color", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 547, + 469, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 251, + 560 + ], + "score": 1.0, + "content": "represents various prediction length", + "type": "text" + }, + { + "bbox": [ + 251, + 547, + 312, + 560 + ], + "score": 0.93, + "content": "O \\in \\{ 9 6 , 1 9 2 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 547, + 469, + 560 + ], + "score": 1.0, + "content": "and line style means different models .", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5 + } + ], + "index": 20.25 + }, + { + "type": "title", + "bbox": [ + 107, + 582, + 257, + 594 + ], + "lines": [ + { + "bbox": [ + 105, + 579, + 258, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 258, + 597 + ], + "score": 1.0, + "content": "H.2 No Pre-training but Freezing", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 603, + 505, + 636 + ], + "lines": [ + { + "bbox": [ + 105, + 602, + 506, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 506, + 616 + ], + "score": 1.0, + "content": "For comprehensively ablation on pre-training and freezing strategies, we also add experiment for", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "score": 1.0, + "content": "random initialized GPT2(6) with freezing. The results in Table 23 shows that only input and output", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 624, + 483, + 637 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 483, + 637 + ], + "score": 1.0, + "content": "modules can not work and pre-trained knowledge play an importance part in time series tasks.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25 + }, + { + "type": "table", + "bbox": [ + 191, + 671, + 419, + 708 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 180, + 654, + 430, + 666 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 179, + 651, + 431, + 668 + ], + "spans": [ + { + "bbox": [ + 179, + 651, + 431, + 668 + ], + "score": 1.0, + "content": "Table 23: Ablation on random initialized model with freezing.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "table_body", + "bbox": [ + 191, + 671, + 419, + 708 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 191, + 671, + 419, + 708 + ], + "spans": [ + { + "bbox": [ + 191, + 671, + 419, + 708 + ], + "score": 0.971, + "html": "
MethodsGPT2(6)No FreezeNo PretrainNo Pretrain + Freeze
MetricMSEMAEMSEMAEMSEMAEMSEMAE
LLa960.3760.4210.4400.4490.4650.4570.5400.497
1920.4180.4410.5030.4780.6140.5360.7210.580
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MethodsGPT2(6)No FreezeNo Pretrain
MetricMSEMAEMSEMAEMSEMAE
weeeet960.1630.2150.1680.2210.1750.229
1920.2100.2540.2380.2860.2440.287
3360.2560.2920.2890.3180.3010.325
7200.3210.3390.3980.3830.3900.378
LLE960.4580.4560.6050.5320.6800.560
1920.5700.5160.7130.5790.7380.602
3360.6080.5350.7470.5860.8930.641
7200.7250.5910.9450.6882.9941.169
960.3310.3740.3690.3940.4220.433
LLa1920.4020.4110.4640.4550.4820.466
3360.4060.4330.4200.4390.5400.496
7200.4490.4640.5350.5150.5640.519
LL960.3900.4040.4290.4300.3850.401
1920.4290.4230.4630.4460.4260.421
3360.4690.4390.5100.4700.5060.455
7200.5690.4980.7800.5910.5760.505
LLa960.1880.2690.2430.3110.2440.315
1920.2510.3090.3070.3520.3180.363
3360.3070.3460.3370.3640.4090.412
7200.4260.4170.4710.4400.4730.450
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Color", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 547, + 469, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 251, + 560 + ], + "score": 1.0, + "content": "represents various prediction length", + "type": "text" + }, + { + "bbox": [ + 251, + 547, + 312, + 560 + ], + "score": 0.93, + "content": "O \\in \\{ 9 6 , 1 9 2 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 547, + 469, + 560 + ], + "score": 1.0, + "content": "and line style means different models .", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5 + } + ], + "index": 20.25 + }, + { + "type": "title", + "bbox": [ + 107, + 582, + 257, + 594 + ], + "lines": [ + { + "bbox": [ + 105, + 579, + 258, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 258, + 597 + ], + "score": 1.0, + "content": "H.2 No Pre-training but Freezing", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 603, + 505, + 636 + ], + "lines": [ + { + "bbox": [ + 105, + 602, + 506, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 506, + 616 + ], + "score": 1.0, + "content": "For comprehensively ablation on pre-training and freezing strategies, we also add experiment for", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "score": 1.0, + "content": "random initialized GPT2(6) with freezing. 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MethodsGPT2(6)No FreezeNo PretrainNo Pretrain + Freeze
MetricMSEMAEMSEMAEMSEMAEMSEMAE
LLa960.3760.4210.4400.4490.4650.4570.5400.497
1920.4180.4410.5030.4780.6140.5360.7210.580
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MethodsInput & Output+LN+ POS
MetricMSEMAEMSEMAEMSEMAE
LL960.3950.4100.3920.4090.3860.405
1920.4440.4380.4360.4350.4400.438
3360.5100.4720.4950.4670.4850.459
7200.6070.5170.5640.5030.5570.499
960.1980.2820.1980.2790.1990.280
La1920.2610.3240.2630.3250.2560.316
3360.3360.3770.3220.3560.3180.353
7200.4730.4440.4570.4350.4600.436
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Figure 10 shows that the performance improvement for GPT2(6) FPT is almost flattened.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 436, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 104, + 436, + 506, + 451 + ], + "score": 1.0, + "content": "These results illustrate that such a cross-domain FPT model is extremely efficient in few-shot time", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "score": 1.0, + "content": "series forecasting and only requires a few fine-tuning samples to reach a SOTA performance. 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Line color represents different models and line", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 693, + 326, + 707 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 261, + 707 + ], + "score": 1.0, + "content": "style means various prediction lengths", + "type": "text" + }, + { + "bbox": [ + 262, + 694, + 322, + 706 + ], + "score": 0.93, + "content": "\\mathrm { ~ \\ i ~ { ~ O ~ } ~ } \\in \\{ 9 6 , 1 9 2 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 693, + 326, + 707 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40.5 + } + ], + "index": 36.75 + } + ], + "page_idx": 30, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 310, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 312, + 755 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 312, + 755 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 72, + 278, + 84 + ], + "lines": [ + { + "bbox": [ + 106, + 72, + 279, + 86 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 279, + 86 + ], + "score": 1.0, + "content": "H.3 Fine-Tuning Parameters Selection", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 95, + 506, + 162 + ], + "lines": [ + { + "bbox": [ + 105, + 96, + 507, + 109 + ], + "spans": [ + { + "bbox": [ + 105, + 96, + 507, + 109 + ], + "score": 1.0, + "content": "In this section, we conduct ablation experiments to study which parameters are important to fine-tune.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 106, + 506, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 106, + 506, + 119 + ], + "score": 1.0, + "content": "Since the input embedding and output layers are randomly initialized for adapting to a new domain,", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 118, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 105, + 118, + 506, + 131 + ], + "score": 1.0, + "content": "they must be trained. Then, we study adding layer normalization and positional embeddings to the list", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 128, + 505, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 505, + 141 + ], + "score": 1.0, + "content": "of fine-tuning parameters. Table 24 shows the results that re-train parameters of layer normalization", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 140, + 507, + 151 + ], + "spans": [ + { + "bbox": [ + 106, + 140, + 507, + 151 + ], + "score": 1.0, + "content": "and positional embeddings can bring certain benefits, especially in longer prediction lengths. 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MethodsInput & Output+LN+ POS
MetricMSEMAEMSEMAEMSEMAE
LL960.3950.4100.3920.4090.3860.405
1920.4440.4380.4360.4350.4400.438
3360.5100.4720.4950.4670.4850.459
7200.6070.5170.5640.5030.5570.499
960.1980.2820.1980.2790.1990.280
La1920.2610.3240.2630.3250.2560.316
3360.3360.3770.3220.3560.3180.353
7200.4730.4440.4570.4350.4600.436
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Figure 10 shows that the performance improvement for GPT2(6) FPT is almost flattened.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 436, + 506, + 451 + ], + "spans": [ + { + "bbox": [ + 104, + 436, + 506, + 451 + ], + "score": 1.0, + "content": "These results illustrate that such a cross-domain FPT model is extremely efficient in few-shot time", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 461 + ], + "score": 1.0, + "content": "series forecasting and only requires a few fine-tuning samples to reach a SOTA performance. 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Line color represents different models and line", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 693, + 326, + 707 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 261, + 707 + ], + "score": 1.0, + "content": "style means various prediction lengths", + "type": "text" + }, + { + "bbox": [ + 262, + 694, + 322, + 706 + ], + "score": 0.93, + "content": "\\mathrm { ~ \\ i ~ { ~ O ~ } ~ } \\in \\{ 9 6 , 1 9 2 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 693, + 326, + 707 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40.5 + } + ], + "index": 36.75 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 72, + 405, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 407, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 407, + 86 + ], + "score": 1.0, + "content": "H.5 Knowledge transfer with other Pre-trained Transformer Models", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 92, + 506, + 191 + ], + "lines": [ + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "score": 1.0, + "content": "We investigate how other pre-trained transformer models perform and whether other domains can also", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 505, + 116 + ], + "score": 1.0, + "content": "help. Another NLP pre-trained model BERT Devlin et al. (2019) and the CV pre-trained model BEiT", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 237, + 127 + ], + "score": 1.0, + "content": "Bao et al. (2022) are trained on", + "type": "text" + }, + { + "bbox": [ + 237, + 115, + 252, + 126 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 115, + 302, + 127 + ], + "score": 1.0, + "content": "ETTh2 and", + "type": "text" + }, + { + "bbox": [ + 303, + 115, + 317, + 126 + ], + "score": 0.84, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 115, + 506, + 127 + ], + "score": 1.0, + "content": "ETTm2. Similar to GPT2, we only reserve 6", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "score": 1.0, + "content": "layers and freeze attention blocks. Our results are shown in Table 25 that BERT(6) FPT and BEiT(6)", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 506, + 149 + ], + "score": 1.0, + "content": "FPT are comparable to PatchTST and remarkably surpass other baselines. We come to the conclusion", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 506, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 506, + 160 + ], + "score": 1.0, + "content": "that the universality of our proposed architecture holds across other pre-trained-transformer models.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 159, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 159, + 505, + 171 + ], + "score": 1.0, + "content": "Moreover, the domain of successful knowledge transfer in time series forecasting is not limited to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "score": 1.0, + "content": "natural language. 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Black: best,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 229, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 229, + 317, + 241 + ], + "score": 1.0, + "content": "Red: second best, Violet: third best. ’-’ means that", + "type": "text" + }, + { + "bbox": [ + 317, + 230, + 333, + 240 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 229, + 506, + 241 + ], + "score": 1.0, + "content": "time series is not sufficient to constitute a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 240, + 157, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 157, + 254 + ], + "score": 1.0, + "content": "training set.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + }, + { + "type": "table_body", + "bbox": [ + 182, + 255, + 425, + 397 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 182, + 255, + 425, + 397 + ], + "spans": [ + { + "bbox": [ + 182, + 255, + 425, + 397 + ], + "score": 0.98, + "html": "
MethodsMetricETTh2ETTm2
9619233672096192336720
GPT2-backbone(6 Layers)MSE0.3760.421 0.408-0.1990.2560.3180.460
MAE0.4190.441 0.439-0.2800.3160.3530.436
BERT-backbond(6 Layers)MSE MAE0.397 0.4180.480 0.4650.481 0.472- =0.222 0.3000.281 0.3350.331 0.3670.441 0.428
BEiT-backbond(6 Layers)MSE MAE|0.405 0.4180.448 0.446 0.5000.5240.208 0.2910.272 0.3260.3310.452
DLinearZeng et al. (2023)MSE MAE0.4420.617 0.4560.5421.424- -0.2360.3060.362 0.3800.433 0.674
PatchTSTNie et al. (2022)MSE MAE[0.401 0.4210.452 0.4550.4690.849 0.464- -0.3260.373 [0.2060.2640.423 0.3340.583 0.454
FEDformerZhou et al. (2022)MSE MAE0.390 0.4240.457 0.4650.4830.477- -0.2880.324 0.2990.290 0.378 0.5230.3670.483
AutoformerWu et al. (2021)MSE MAE0.428 0.496 0.486 0.468 0.504 0.496- -0.320 0.361 [0.232 0.291 0.3220.3570.427 0.478 0.5170.510 0.533 0.538
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MethodsClassical methods XGBoost RocketRNNTCNTrans. Re.MLP DLinear LightTS.TimesNetGPT2(6)
LSTNet LSSLIn.Pyra.Auto. Station.FED.ETS. Flow.29.7
EthanolConcentration43.745.239.931.128.932.731.931.630.831.632.731.228.133.832.635.734.2
FaceDetection63.364.765.766.752.867.368.667.065.768.468.066.066.367.668.067.568.669.2
Handwriting15.858.825.824.653.332.027.432.829.436.731.628.032.533.827.026.132.132.7
Heartbeat73.275.677.172.775.676.177.180.575.674.673.773.771.277.675.175.178.077.2
JapaneseVowels86.596.298.198.498.998.797.898.998.496.299.298.495.998.996.296.298.498.6
PEMS-SF98.375.186.786.168.882.182.781.583.282.787.380.9 86.083.875.188.489.687.9
SelfRegulationSCP184.690.884.090.884.692.290.490.188.184.089.488.789.692.587.389.891.893.2
SelfRegulationSCP2 SpokenArabicDigits48.953.352.852.255.653.956.753.353.350.657.254.4 55.056.150.551.157.259.4
UWaveGestureLibrary69.6 75.971.2 94.4100.0 87.8100.095.698.4 85.697.0100.099.6100.0100.0100.0 100.098.881.4 82.1100.0 80.399.0 85.399.2 88.1
Average72.571.885.9 70.988.4 70.371.985.6 71.585.6 72.183.4 70.885.9 71.187.5 72.785.3 70.785.0 71.086.6 73.067.570.473.6
66.074.0
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It is widely believed that longer input lengths", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "have the potential to generate superior results. However, in practice, certain algorithms might fall", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "score": 1.0, + "content": "short in effectively utilizing long input signals due to overfitting issues either. Here, we conducted", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "score": 1.0, + "content": "long-term forecasting experiments by comparing our approach with the best reported values from", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "different baseline papers. This was done to avoid any biases stemming from selective tuning of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 710, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 724 + ], + "score": 1.0, + "content": "baseline parameters. While some may argue in favor of a fairer comparison using a fixed input length,", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35.5 + } + ], + "page_idx": 31, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 298, + 740, + 313, + 754 + ], + "spans": [ + { + "bbox": [ + 298, + 740, + 313, + 754 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 15 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 72, + 405, + 84 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 407, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 407, + 86 + ], + "score": 1.0, + "content": "H.5 Knowledge transfer with other Pre-trained Transformer Models", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 92, + 506, + 191 + ], + "lines": [ + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 105 + ], + "score": 1.0, + "content": "We investigate how other pre-trained transformer models perform and whether other domains can also", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 505, + 116 + ], + "spans": [ + { + "bbox": [ + 106, + 104, + 505, + 116 + ], + "score": 1.0, + "content": "help. Another NLP pre-trained model BERT Devlin et al. (2019) and the CV pre-trained model BEiT", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 115, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 237, + 127 + ], + "score": 1.0, + "content": "Bao et al. (2022) are trained on", + "type": "text" + }, + { + "bbox": [ + 237, + 115, + 252, + 126 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 115, + 302, + 127 + ], + "score": 1.0, + "content": "ETTh2 and", + "type": "text" + }, + { + "bbox": [ + 303, + 115, + 317, + 126 + ], + "score": 0.84, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 115, + 506, + 127 + ], + "score": 1.0, + "content": "ETTm2. Similar to GPT2, we only reserve 6", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 506, + 138 + ], + "score": 1.0, + "content": "layers and freeze attention blocks. Our results are shown in Table 25 that BERT(6) FPT and BEiT(6)", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 506, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 506, + 149 + ], + "score": 1.0, + "content": "FPT are comparable to PatchTST and remarkably surpass other baselines. We come to the conclusion", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 147, + 506, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 147, + 506, + 160 + ], + "score": 1.0, + "content": "that the universality of our proposed architecture holds across other pre-trained-transformer models.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 159, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 159, + 505, + 171 + ], + "score": 1.0, + "content": "Moreover, the domain of successful knowledge transfer in time series forecasting is not limited to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 169, + 506, + 182 + ], + "score": 1.0, + "content": "natural language. Knowledge from the CV domain can also help, supported by BEiT’s experimental", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 180, + 137, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 137, + 192 + ], + "score": 1.0, + "content": "results.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 93, + 506, + 192 + ] + }, + { + "type": "table", + "bbox": [ + 182, + 255, + 425, + 397 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 107, + 207, + 505, + 252 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 207, + 506, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 207, + 366, + 220 + ], + "score": 1.0, + "content": "Table 25: Results of frozen pretrained transformer variants on", + "type": "text" + }, + { + "bbox": [ + 366, + 208, + 381, + 218 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 207, + 506, + 220 + ], + "score": 1.0, + "content": "ETTh2 and ETTm2. We use", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 218, + 507, + 231 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 176, + 231 + ], + "score": 1.0, + "content": "prediction length", + "type": "text" + }, + { + "bbox": [ + 177, + 218, + 275, + 231 + ], + "score": 0.9, + "content": "O \\in \\{ 9 6 , 1 \\bar { 9 } 2 , 3 3 6 , 7 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 276, + 218, + 507, + 231 + ], + "score": 1.0, + "content": ". A lower MSE indicates better performance. Black: best,", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 229, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 106, + 229, + 317, + 241 + ], + "score": 1.0, + "content": "Red: second best, Violet: third best. ’-’ means that", + "type": "text" + }, + { + "bbox": [ + 317, + 230, + 333, + 240 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 229, + 506, + 241 + ], + "score": 1.0, + "content": "time series is not sufficient to constitute a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 240, + 157, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 240, + 157, + 254 + ], + "score": 1.0, + "content": "training set.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + }, + { + "type": "table_body", + "bbox": [ + 182, + 255, + 425, + 397 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 182, + 255, + 425, + 397 + ], + "spans": [ + { + "bbox": [ + 182, + 255, + 425, + 397 + ], + "score": 0.98, + "html": "
MethodsMetricETTh2ETTm2
9619233672096192336720
GPT2-backbone(6 Layers)MSE0.3760.421 0.408-0.1990.2560.3180.460
MAE0.4190.441 0.439-0.2800.3160.3530.436
BERT-backbond(6 Layers)MSE MAE0.397 0.4180.480 0.4650.481 0.472- =0.222 0.3000.281 0.3350.331 0.3670.441 0.428
BEiT-backbond(6 Layers)MSE MAE|0.405 0.4180.448 0.446 0.5000.5240.208 0.2910.272 0.3260.3310.452
DLinearZeng et al. (2023)MSE MAE0.4420.617 0.4560.5421.424- -0.2360.3060.362 0.3800.433 0.674
PatchTSTNie et al. (2022)MSE MAE[0.401 0.4210.452 0.4550.4690.849 0.464- -0.3260.373 [0.2060.2640.423 0.3340.583 0.454
FEDformerZhou et al. (2022)MSE MAE0.390 0.4240.457 0.4650.4830.477- -0.2880.324 0.2990.290 0.378 0.5230.3670.483
AutoformerWu et al. (2021)MSE MAE0.428 0.496 0.486 0.468 0.504 0.496- -0.320 0.361 [0.232 0.291 0.3220.3570.427 0.478 0.5170.510 0.533 0.538
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MethodsClassical methods XGBoost RocketRNNTCNTrans. Re.MLP DLinear LightTS.TimesNetGPT2(6)
LSTNet LSSLIn.Pyra.Auto. Station.FED.ETS. Flow.29.7
EthanolConcentration43.745.239.931.128.932.731.931.630.831.632.731.228.133.832.635.734.2
FaceDetection63.364.765.766.752.867.368.667.065.768.468.066.066.367.668.067.568.669.2
Handwriting15.858.825.824.653.332.027.432.829.436.731.628.032.533.827.026.132.132.7
Heartbeat73.275.677.172.775.676.177.180.575.674.673.773.771.277.675.175.178.077.2
JapaneseVowels86.596.298.198.498.998.797.898.998.496.299.298.495.998.996.296.298.498.6
PEMS-SF98.375.186.786.168.882.182.781.583.282.787.380.9 86.083.875.188.489.687.9
SelfRegulationSCP184.690.884.090.884.692.290.490.188.184.089.488.789.692.587.389.891.893.2
SelfRegulationSCP2 SpokenArabicDigits48.953.352.852.255.653.956.753.353.350.657.254.4 55.056.150.551.157.259.4
UWaveGestureLibrary69.6 75.971.2 94.4100.0 87.8100.095.698.4 85.697.0100.099.6100.0100.0100.0 100.098.881.4 82.1100.0 80.399.0 85.399.2 88.1
Average72.571.885.9 70.988.4 70.371.985.6 71.585.6 72.183.4 70.885.9 71.187.5 72.785.3 70.785.0 71.086.6 73.067.570.473.6
66.074.0
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It is widely believed that longer input lengths", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 505, + 680 + ], + "score": 1.0, + "content": "have the potential to generate superior results. However, in practice, certain algorithms might fall", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "score": 1.0, + "content": "short in effectively utilizing long input signals due to overfitting issues either. Here, we conducted", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 506, + 702 + ], + "score": 1.0, + "content": "long-term forecasting experiments by comparing our approach with the best reported values from", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "different baseline papers. This was done to avoid any biases stemming from selective tuning of", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 710, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 724 + ], + "score": 1.0, + "content": "baseline parameters. While some may argue in favor of a fairer comparison using a fixed input length,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 524, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 524, + 505, + 536 + ], + "score": 1.0, + "content": "we are starting to shift our focus towards pursuing more accurate algorithms that possess enhanced", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 534, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 506, + 548 + ], + "score": 1.0, + "content": "capabilities for handling longer inputs. Instead of restricting the input length to a fixed small value, it", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 546, + 505, + 559 + ], + "spans": [ + { + "bbox": [ + 104, + 546, + 505, + 559 + ], + "score": 1.0, + "content": "is pragmatic to tune both the input length and model parameters based on performance, as it is often", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 557, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 557, + 505, + 570 + ], + "score": 1.0, + "content": "the primary concern in practical usage. Exploring the utilization of extremely long inputs, such as", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 568, + 337, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 337, + 579 + ], + "score": 1.0, + "content": "Chatgpt or LLM, is among our future research directions.", + "type": "text", + "cross_page": true + } + ], + "index": 14 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 656, + 506, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 109, + 100, + 507, + 219 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 209, + 78, + 402, + 89 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 207, + 75, + 402, + 91 + ], + "spans": [ + { + "bbox": [ + 207, + 75, + 402, + 91 + ], + "score": 1.0, + "content": "Table 27: Full results for the anomaly detection.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 109, + 100, + 507, + 219 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 100, + 507, + 219 + ], + "spans": [ + { + "bbox": [ + 109, + 100, + 507, + 219 + ], + "score": 0.98, + "html": "
Methods MetricsPSMD RPMSLF1SMAP RPSWaTF1PSM RF1AvgF1 %
F1RPF1R
GPT(6)88.8984.9886.8982.0082.9182.4590.6060.9572.8892.2096.3494.2398.6295.68 97.1386.72
TimesNet*87.9181.5484.6189.5475.3681.8490.1456.4069.3990.7595.4093.0298.5196.2097.3485.24
PatchTST87.2682.1484.6288.3470.9678.7090.6455.4668.8291.1080.9485.7298.8493.4796.0882.79
ETSformer87.4479.2383.1385.1384.9385.0392.2555.7569.5090.0280.3684.9199.3185.2891.7682.87
FEDformer87.9582.3985.0877.1480.0778.5790.4758.1070.7690.1796.4293.1997.3197.1697.2384.97
LightTS87.1078.4282.5382.4075.7878.9592.5855.2769.2191.9894.7293.3398.3795.9797.1584.23
DLinear83.6271.5277.1084.3485.4284.8892.3255.4169.2680.9195.3087.5298.2889.2693.5582.46
Stationary88.3381.2184.6268.5589.1477.5089.3759.0271.0968.0396.7579.8897.8296.7697.2982.08
Autoformer88.0682.3585.1177.2780.9279.0590.4058.6271.1289.8595.8192.7499.0888.1593.2984.26
Pyraformer85.6180.6183.0483.8185.9384.8692.5457.7171.0987.9296.0091.7871.6796.0282.0882.57
Anomaly Transformer"*88.9182.2385.4979.6187.3783.3191.8558.1171.1872.5197.3283.1068.3594.7279.4080.50
Informer86.6077.2381.6581.7786.4884.0690.1157.1369.9270.2996.7581.4364.2796.3377.1078.83
Reformer82.5869.2475.3285.5183.3184.4090.9157.4470.4072.50 96.5382.8059.9395.3873.6177.31
LogTransformer83.4670.1376.2173.0587.3779.5789.1557.5969.9768.67 97.3280.5263.0698.0076.7476.60
Transformer83.5876.1379.5671.5787.3778.6889.3757.1269.7068.84 96.5380.3762.7596.5676.0776.88
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MethodsMask RatioGPT2(3)MSE MAETimesNetMSE MAEPatchTSTMSE MAEETSformerMSEMAELightTSMSE MAEDLinearMSE MAEFEDformerMSE MAEStationaryMSEMAEAutoformerMSE MAEInformerMSE MAEReformer|MSE MAE
12.5%[L] 25%37.5%50%Avg0.017 0.0850.022 0.0960.0290.1110.040 0.1280.0280.1050.0230.1010.0230.1010.0290.1110.036 0.1240.0270.1070.0410.1300.0440.1350.0490.1430.055 0.1510.0470.1400.0960.2290.0960.2290.1330.2710.1860.3230.1200.2530.0930.2060.0930.2060.1130.2310.1340.2550.104 0.2180.0800.1930.080 0.1930.1030.2190.132 0.2480.0930.2060.0520.1660.0520.1660.069 0.1910.089 0.2180.062 0.17710.0320.1190.0320.1190.0390.1310.0470.1450.0360.126[0.0460.144|0.0460.1440.0570.1610.0670.1740.0510.1500.0630.180|0.0630.1800.0790.2000.093 0.2180.0710.188[0.042 0.1460.0420.1460.0630.1820.082 0.2080.0550.166
12.5%L 25%0.0170.0760.0200.0800.0220.0870.0180.0800.0200.0850.0230.09110.0260.0940.0280.0990.030 0.1040.0340.1100.0290.1020.1080.2390.1640.2940.2370.3560.3230.4210.2080.32710.0340.1270.042 0.1430.0510.1590.062 0.1660.0850.1960.1060.2220.131 0.2470.0960.2080.0560.1590.080 0.1950.110 0.2310.156 0.2760.1010.2150.0210.0880.0240.0960.0270.1030.0300.1080.0260.0990.0230.0920.0260.1010.0300.1080.1330.2700.1350.2720.1550.2930.108 0.2280.1360.2620.1750.3000.211 0.3290.1570.280
L 37.5%50%Avg0.0220.087
0.0250.0950.0210.0840.0260.0980.0220.0880.0590.1740.046 0.1510.0350.1190.0290.1050.2000.3330.1560.292
12.5%LLT 25%37.5%0.0430.1400.054 0.1560.0570.1590.069 0.1780.0930.2010.107 0.2170.120 0.2300.1260.2630.169 0.3040.220 0.3470.240 0.3450.265 0.3640.151 0.2670.180 0.29210.0700.1900.106 0.23610.0600.1650.080 0.1890.102 0.2120.074 0.1820.0900.2030.109 0.2220.1140.2340.140 0.2620.1740.29310.0740.1940.1020.2270.135 0.2610.179 0.2980.122 0.245
0.0720.084
50%0.1070.1020.2150.1410.248
0.1730.187
0.2020.4020.3290.3340.4040.2840.3730.2010.3060.1170.2460.0940.2010.0940.2010.1370.2480.1030.2140.215 0.3250.1610.2790.122 0.245
Avg0.0691730.0780.1150.224
12.5%LLE 25%37.5%0.0390.044
44
0.1250.1350.0400.0460.1300.1410.0570.1520.0610.15810.1870.3190.2790.3900.1010.2310.1150.2460.1000.1270.2160.24710.0950.2120.1370.2580.0420.0490.1470.1330.0490.1470.0440.1380.050 0.1490.3050.4310.3220.4440.163 0.2890.206 0.3310.2520.3700.316 0.4190.2340.352
0.0510.147
50%Avg0.0590.0.0600.1620.0730.1740.6020.5720.3670.4360.136 0.2680.1190.2500.1830.2990.1420.2590.2990.2320.3410.0650.1700.0680.1730.3690.472472
0.0480.1410.0490.1460.0650.1630.1630.2790.05330.1520.0550.1560.3370.452
12.5%GEE 25%37.5%50%Avg0.080 0.1940.0870.0940.080 0.1940.2030.2110.0850.2020.089）0.2060.0940.21310.055 0.16010.1960.3210.2070.3320.102 0.2290.1210.2520.0920.2140.118 0.2470.1070.23710.0930.2100.0970.2140.089 0.2100.0960.2200.218 0.32610.1900.3080.197 0.312
0.0650.1750.0760.1890.2190.219 0.326
0.1010.0900.2200.2070.1000.0920.2210.0910.2080.2350.357570.1600.2930.1310.2620.1750.3050.1320.2600.1580.2840.1080.2280.2280.1130.2390.2280.3310.2220.328
0.2030.3150.210 0.3190.2000.313
0.0920.2100.0720.1830.2140.3390.130 0.2590.100 0.2180.1010.225
12.5%wrees 25%37.5%50%Avg0.0260.040490.0250.0450.0290.0520.0290.0490.0570.141[0.0470.1010.052 0.111[0.0390.084|0.0480.1030.041 0.1070.0270.0510.0260.0470.0370.09310.031 0.076
0.0280.00.0310.0530.0650.155
0.0400.091
0.0370.0650.0310.0560.0380.0630.1020.2070.0650.1330.0660.1340.1830.3120.0370.0680.0370.0670.053 0.114
0.0300.0540.0600.144
0.0460.0990.0380.087
0.0760.1710.0550.1170.052 0.1100.0990.2030.0320.0590.0310.0570.0450.104
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Methods MetricsPSMD RPMSLF1SMAP RPSWaTF1PSM RF1AvgF1 %
F1RPF1R
GPT(6)88.8984.9886.8982.0082.9182.4590.6060.9572.8892.2096.3494.2398.6295.68 97.1386.72
TimesNet*87.9181.5484.6189.5475.3681.8490.1456.4069.3990.7595.4093.0298.5196.2097.3485.24
PatchTST87.2682.1484.6288.3470.9678.7090.6455.4668.8291.1080.9485.7298.8493.4796.0882.79
ETSformer87.4479.2383.1385.1384.9385.0392.2555.7569.5090.0280.3684.9199.3185.2891.7682.87
FEDformer87.9582.3985.0877.1480.0778.5790.4758.1070.7690.1796.4293.1997.3197.1697.2384.97
LightTS87.1078.4282.5382.4075.7878.9592.5855.2769.2191.9894.7293.3398.3795.9797.1584.23
DLinear83.6271.5277.1084.3485.4284.8892.3255.4169.2680.9195.3087.5298.2889.2693.5582.46
Stationary88.3381.2184.6268.5589.1477.5089.3759.0271.0968.0396.7579.8897.8296.7697.2982.08
Autoformer88.0682.3585.1177.2780.9279.0590.4058.6271.1289.8595.8192.7499.0888.1593.2984.26
Pyraformer85.6180.6183.0483.8185.9384.8692.5457.7171.0987.9296.0091.7871.6796.0282.0882.57
Anomaly Transformer"*88.9182.2385.4979.6187.3783.3191.8558.1171.1872.5197.3283.1068.3594.7279.4080.50
Informer86.6077.2381.6581.7786.4884.0690.1157.1369.9270.2996.7581.4364.2796.3377.1078.83
Reformer82.5869.2475.3285.5183.3184.4090.9157.4470.4072.50 96.5382.8059.9395.3873.6177.31
LogTransformer83.4670.1376.2173.0587.3779.5789.1557.5969.9768.67 97.3280.5263.0698.0076.7476.60
Transformer83.5876.1379.5671.5787.3778.6889.3757.1269.7068.84 96.5380.3762.7596.5676.0776.88
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MethodsMask RatioGPT2(3)MSE MAETimesNetMSE MAEPatchTSTMSE MAEETSformerMSEMAELightTSMSE MAEDLinearMSE MAEFEDformerMSE MAEStationaryMSEMAEAutoformerMSE MAEInformerMSE MAEReformer|MSE MAE
12.5%[L] 25%37.5%50%Avg0.017 0.0850.022 0.0960.0290.1110.040 0.1280.0280.1050.0230.1010.0230.1010.0290.1110.036 0.1240.0270.1070.0410.1300.0440.1350.0490.1430.055 0.1510.0470.1400.0960.2290.0960.2290.1330.2710.1860.3230.1200.2530.0930.2060.0930.2060.1130.2310.1340.2550.104 0.2180.0800.1930.080 0.1930.1030.2190.132 0.2480.0930.2060.0520.1660.0520.1660.069 0.1910.089 0.2180.062 0.17710.0320.1190.0320.1190.0390.1310.0470.1450.0360.126[0.0460.144|0.0460.1440.0570.1610.0670.1740.0510.1500.0630.180|0.0630.1800.0790.2000.093 0.2180.0710.188[0.042 0.1460.0420.1460.0630.1820.082 0.2080.0550.166
12.5%L 25%0.0170.0760.0200.0800.0220.0870.0180.0800.0200.0850.0230.09110.0260.0940.0280.0990.030 0.1040.0340.1100.0290.1020.1080.2390.1640.2940.2370.3560.3230.4210.2080.32710.0340.1270.042 0.1430.0510.1590.062 0.1660.0850.1960.1060.2220.131 0.2470.0960.2080.0560.1590.080 0.1950.110 0.2310.156 0.2760.1010.2150.0210.0880.0240.0960.0270.1030.0300.1080.0260.0990.0230.0920.0260.1010.0300.1080.1330.2700.1350.2720.1550.2930.108 0.2280.1360.2620.1750.3000.211 0.3290.1570.280
L 37.5%50%Avg0.0220.087
0.0250.0950.0210.0840.0260.0980.0220.0880.0590.1740.046 0.1510.0350.1190.0290.1050.2000.3330.1560.292
12.5%LLT 25%37.5%0.0430.1400.054 0.1560.0570.1590.069 0.1780.0930.2010.107 0.2170.120 0.2300.1260.2630.169 0.3040.220 0.3470.240 0.3450.265 0.3640.151 0.2670.180 0.29210.0700.1900.106 0.23610.0600.1650.080 0.1890.102 0.2120.074 0.1820.0900.2030.109 0.2220.1140.2340.140 0.2620.1740.29310.0740.1940.1020.2270.135 0.2610.179 0.2980.122 0.245
0.0720.084
50%0.1070.1020.2150.1410.248
0.1730.187
0.2020.4020.3290.3340.4040.2840.3730.2010.3060.1170.2460.0940.2010.0940.2010.1370.2480.1030.2140.215 0.3250.1610.2790.122 0.245
Avg0.0691730.0780.1150.224
12.5%LLE 25%37.5%0.0390.044
44
0.1250.1350.0400.0460.1300.1410.0570.1520.0610.15810.1870.3190.2790.3900.1010.2310.1150.2460.1000.1270.2160.24710.0950.2120.1370.2580.0420.0490.1470.1330.0490.1470.0440.1380.050 0.1490.3050.4310.3220.4440.163 0.2890.206 0.3310.2520.3700.316 0.4190.2340.352
0.0510.147
50%Avg0.0590.0.0600.1620.0730.1740.6020.5720.3670.4360.136 0.2680.1190.2500.1830.2990.1420.2590.2990.2320.3410.0650.1700.0680.1730.3690.472472
0.0480.1410.0490.1460.0650.1630.1630.2790.05330.1520.0550.1560.3370.452
12.5%GEE 25%37.5%50%Avg0.080 0.1940.0870.0940.080 0.1940.2030.2110.0850.2020.089）0.2060.0940.21310.055 0.16010.1960.3210.2070.3320.102 0.2290.1210.2520.0920.2140.118 0.2470.1070.23710.0930.2100.0970.2140.089 0.2100.0960.2200.218 0.32610.1900.3080.197 0.312
0.0650.1750.0760.1890.2190.219 0.326
0.1010.0900.2200.2070.1000.0920.2210.0910.2080.2350.357570.1600.2930.1310.2620.1750.3050.1320.2600.1580.2840.1080.2280.2280.1130.2390.2280.3310.2220.328
0.2030.3150.210 0.3190.2000.313
0.0920.2100.0720.1830.2140.3390.130 0.2590.100 0.2180.1010.225
12.5%wrees 25%37.5%50%Avg0.0260.040490.0250.0450.0290.0520.0290.0490.0570.141[0.0470.1010.052 0.111[0.0390.084|0.0480.1030.041 0.1070.0270.0510.0260.0470.0370.09310.031 0.076
0.0280.00.0310.0530.0650.155
0.0400.091
0.0370.0650.0310.0560.0380.0630.1020.2070.0650.1330.0660.1340.1830.3120.0370.0680.0370.0670.053 0.114
0.0300.0540.0600.144
0.0460.0990.0380.087
0.0760.1710.0550.1170.052 0.1100.0990.2030.0320.0590.0310.0570.0450.104
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MethodsGPT2(6）TimesNetPatchTSTN-HiTSN-BEATSETSformerLightTSDLinear FEDformer Stationary Autoformer Informer Reformer
SMAPE13.53113.38713.47713.41813.43618.00914.24716.96513.72813.71713.97414.72716.169
heeaMASE3.0152.9963.0193.0453.0434.4873.1094.2833.0483.0783.1343.4183.800
OWA0.7930.7860.7920.7930.7941.1150.8271.0580.8030.8070.8220.8810.973
tttniSMAPE10.17710.10010.3810.20210.12413.37611.36412.14510.79210.95811.33811.36013.313
MASE1.1941.1821.2331.1941.1691.9061.3281.5201.2831.3251.3651.4011.775
OWA0.8980.8900.9210.8990.8861.3021.0001.1060.9580.9811.0121.0271.252
SMAPE12.89412.67012.95912.79112.67714.58814.01413.51414.26013.91713.95814.06220.128
nnyauoMASE0.9560.9330.9700.9690.9371.3681.0531.0371.1021.0971.1031.1412.614
OWA0.8970.8780.9050.8990.8801.1490.9810.9561.0120.9981.0021.0241.927
SMAPE4.9404.8914.9525.0614.9257.26715.8806.7094.9546.3025.48524.46032.491
DirttMASE3.2283.3023.3473.2163.3915.24011.4344.9533.2644.0643.86520.96033.355
OWA1.0291.0351.0491.0401.0531.5913.4741.4871.0361.3041.1875.8798.679
SMAPE11.99111.82912.05911.92711.85114.71813.52513.63912.84012.78012.90914.08618.200
aaeeeeeMASE1.6001.5851.6231.6131.5992.4082.1112.0951.7011.7561.7712.7184.223
OWA0.8610.8510.8690.8610.8551.1721.0511.0510.9180.9300.9391.2301.775
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MethodsGPT2(6）TimesNetPatchTSTN-HiTSN-BEATSETSformerLightTSDLinear FEDformer Stationary Autoformer Informer Reformer
SMAPE13.53113.38713.47713.41813.43618.00914.24716.96513.72813.71713.97414.72716.169
heeaMASE3.0152.9963.0193.0453.0434.4873.1094.2833.0483.0783.1343.4183.800
OWA0.7930.7860.7920.7930.7941.1150.8271.0580.8030.8070.8220.8810.973
tttniSMAPE10.17710.10010.3810.20210.12413.37611.36412.14510.79210.95811.33811.36013.313
MASE1.1941.1821.2331.1941.1691.9061.3281.5201.2831.3251.3651.4011.775
OWA0.8980.8900.9210.8990.8861.3021.0001.1060.9580.9811.0121.0271.252
SMAPE12.89412.67012.95912.79112.67714.58814.01413.51414.26013.91713.95814.06220.128
nnyauoMASE0.9560.9330.9700.9690.9371.3681.0531.0371.1021.0971.1031.1412.614
OWA0.8970.8780.9050.8990.8801.1490.9810.9561.0120.9981.0021.0241.927
SMAPE4.9404.8914.9525.0614.9257.26715.8806.7094.9546.3025.48524.46032.491
DirttMASE3.2283.3023.3473.2163.3915.24011.4344.9533.2644.0643.86520.96033.355
OWA1.0291.0351.0491.0401.0531.5913.4741.4871.0361.3041.1875.8798.679
SMAPE11.99111.82912.05911.92711.85114.71813.52513.63912.84012.78012.90914.08618.200
aaeeeeeMASE1.6001.5851.6231.6131.5992.4082.1112.0951.7011.7561.7712.7184.223
OWA0.8610.8510.8690.8610.8551.1721.0511.0510.9180.9300.9391.2301.775
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