{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T03:07:30Z","timestamp":1784689650291,"version":"3.55.0"},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T00:00:00Z","timestamp":1741305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Inspur Cloud Information Technology Co., Ltd."},{"name":"Central Guidance for Local Science and Technology Development Fund of Shandong Province"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Given the significant potential of large language models (LLMs) in sequence modeling, emerging studies have begun applying them to time-series forecasting. Despite notable progress, existing methods still face two critical challenges: (1) their reliance on large amounts of paired text data, limiting the model applicability, and (2) a substantial modality gap between text and time series, leading to insufficient alignment and suboptimal performance. This paper introduces Hierarchical Text-Free Alignment (TS-HTFA) a novel method that leverages hierarchical alignment to fully exploit the representation capacity of LLMs for time-series analysis while eliminating the dependence on text data. Specifically, paired text data are replaced with adaptive virtual text based on QR decomposition word embeddings and learnable prompts. Furthermore, comprehensive cross-modal alignment is established at three levels: input, feature, and output, contributing to enhanced semantic symmetry between modalities. Extensive experiments on multiple time-series benchmarks demonstrate that TS-HTFA achieves state-of-the-art performance, significantly improving prediction accuracy and generalization.<\/jats:p>","DOI":"10.3390\/sym17030401","type":"journal-article","created":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T07:05:46Z","timestamp":1741331146000},"page":"401","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["TS-HTFA: Advancing Time-Series Forecasting via Hierarchical Text-Free Alignment with Large Language Models"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-5593-2653","authenticated-orcid":false,"given":"Pengfei","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6261-6702","authenticated-orcid":false,"given":"Huanran","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3955-0726","authenticated-orcid":false,"given":"Qi\u2019ao","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-7065-6059","authenticated-orcid":false,"given":"Silong","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-2344-6055","authenticated-orcid":false,"given":"Yiqiao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6079-991X","authenticated-orcid":false,"given":"Wenjing","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6389-6866","authenticated-orcid":false,"given":"Wei","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3881-4857","authenticated-orcid":false,"given":"Tianwen","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, East China Normal University, Shanghai 200062, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-8994-0919","authenticated-orcid":false,"given":"Liang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Inspur Cloud Information Technology Co., Ltd., Jinan 250101, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e1519","DOI":"10.1002\/widm.1519","article-title":"Deep Learning Models for Price Forecasting of Financial Time Series: A Review of Recent Advancements: 2020\u20132022","volume":"14","author":"Zhang","year":"2024","journal-title":"Wiley Interdiscip. Rev. Data Min. Knowl. Discov."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Gao, P., Liu, T., Liu, J.W., Lu, B.L., and Zheng, W.L. (2024, January 14\u201319). Multimodal Multi-View Spectral-Spatial-Temporal Masked Autoencoder for Self-Supervised Emotion Recognition. Proceedings of the ICASSP 2024\u20142024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Seoul, Republic of Korea.","DOI":"10.1109\/ICASSP48485.2024.10447194"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Liu, P., Wu, B., Li, N., Dai, T., Lei, F., Bao, J., Jiang, Y., and Xia, S.T. (2024, January 14\u201319). Wftnet: Exploiting global and local periodicity in long-term time series forecasting. Proceedings of the ICASSP 2024\u20142024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Seoul, Republic of Korea.","DOI":"10.1109\/ICASSP48485.2024.10446883"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2433","DOI":"10.1109\/JSEN.2022.3225338","article-title":"DUMA: Dual mask for multivariate time series anomaly detection","volume":"23","author":"Pan","year":"2022","journal-title":"IEEE Sensors J."},{"key":"ref_5","unstructured":"Bai, S., Kolter, J.Z., and Koltun, V. (2018). An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv."},{"key":"ref_6","unstructured":"Wang, H., Peng, J., Huang, F., Wang, J., Chen, J., and Xiao, Y. (2022, January 25\u201329). MICN: Multi-scale local and global context modeling for long-term series forecasting. Proceedings of the International Conference on Learning Representations, Virtual Event."},{"key":"ref_7","unstructured":"Wu, H., Hu, T., Liu, Y., Zhou, H., Wang, J., and Long, M. (2022, January 25\u201329). TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. Proceedings of the The Eleventh International Conference on Learning Representations, Virtual Event."},{"key":"ref_8","unstructured":"Zeng, A., Chen, M., Zhang, L., and Xu, Q. (2023, January 7\u201314). Are transformers effective for time series forecasting?. Proceedings of the AAAI Conference on Artificial Intelligence, Washington, DC, USA."},{"key":"ref_9","unstructured":"Das, A., Kong, W., Leach, A., Sen, R., and Yu, R. (2023). Long-term Forecasting with TiDE: Time-series Dense Encoder. arXiv."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6851","DOI":"10.1109\/TKDE.2023.3342137","article-title":"Promptcast: A new prompt-based learning paradigm for time series forecasting","volume":"36","author":"Xue","year":"2023","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_11","unstructured":"Cao, D., Jia, F., Arik, S.O., Pfister, T., Zheng, Y., Ye, W., and Liu, Y. (2023). Tempo: Prompt-based generative pre-trained transformer for time series forecasting. arXiv."},{"key":"ref_12","unstructured":"Chang, C., Peng, W.C., and Chen, T.F. (2023). Llm4ts: Two-stage fine-tuning for time-series forecasting with pre-trained llms. arXiv."},{"key":"ref_13","unstructured":"Jin, M., Wang, S., Ma, L., Chu, Z., Zhang, J.Y., Shi, X., Chen, P.Y., Liang, Y., Li, Y.F., and Pan, S. (2023). Time-llm: Time series forecasting by reprogramming large language models. arXiv."},{"key":"ref_14","unstructured":"Sun, C., Li, Y., Li, H., and Hong, S. (2023). TEST: Text prototype aligned embedding to activate LLM\u2019s ability for time series. arXiv."},{"key":"ref_15","unstructured":"Wang, Z., and Ji, H. (March, January 22). Open vocabulary electroencephalography-to-text decoding and zero-shot sentiment classification. Proceedings of the AAAI Conference on Artificial Intelligence, Online."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Qiu, J., Han, W., Zhu, J., Xu, M., Weber, D., Li, B., and Zhao, D. (2023, January 6\u201310). Can brain signals reveal inner alignment with human languages?. Proceedings of the Findings of the Association for Computational Linguistics: EMNLP 2023, Singapore.","DOI":"10.18653\/v1\/2023.findings-emnlp.120"},{"key":"ref_17","unstructured":"Li, J., Liu, C., Cheng, S., Arcucci, R., and Hong, S. (2024, January 3\u20135). Frozen language model helps ECG zero-shot learning. Proceedings of the Medical Imaging with Deep Learning, PMLR, Paris, France."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jia, F., Wang, K., Zheng, Y., Cao, D., and Liu, Y. (2024, January 26\u201327). GPT4MTS: Prompt-based Large Language Model for Multimodal Time-series Forecasting. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v38i21.30383"},{"key":"ref_19","unstructured":"Yu, H., Guo, P., and Sano, A. (2024). ECG Semantic Integrator (ESI): A Foundation ECG Model Pretrained with LLM-Enhanced Cardiological Text. arXiv."},{"key":"ref_20","unstructured":"Kim, J.W., Alaa, A., and Bernardo, D. (2024). EEG-GPT: Exploring Capabilities of Large Language Models for EEG Classification and Interpretation. arXiv."},{"key":"ref_21","unstructured":"Zhou, T., Ma, Z., Wen, Q., Wang, X., Sun, L., and Jin, R. (2022, January 17\u201323). FEDformer: Frequency enhanced decomposed transformer for long-term series forecasting. Proceedings of the International Conference on Machine Learning, PMLR, Baltimore, MD, USA."},{"key":"ref_22","unstructured":"Nie, Y., Nguyen, N.H., Sinthong, P., and Kalagnanam, J. (2023, January 1\u20135). A Time Series is Worth 64 Words: Long-term Forecasting with Transformers. Proceedings of the International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_23","unstructured":"Zhang, Y., and Yan, J. (2023, January 1\u20135). Crossformer: Transformer utilizing cross-dimension dependency for multivariate time series forecasting. Proceedings of the International Conference on Learning Representations, Kigali, Rwanda."},{"key":"ref_24","unstructured":"Liu, Y., Hu, T., Zhang, H., Wu, H., Wang, S., Ma, L., and Long, M. (2023). itransformer: Inverted transformers are effective for time series forecasting. arXiv."},{"key":"ref_25","unstructured":"Zhou, T., Niu, P., Wang, X., Sun, L., and Jin, R. (2023). One Fits All: Power General Time Series Analysis by Pretrained LM. arXiv."},{"key":"ref_26","unstructured":"Pan, Z., Jiang, Y., Garg, S., Schneider, A., Nevmyvaka, Y., and Song, D. (2024, January 21\u201327). S2 IP-LLM: Semantic Space Informed Prompt Learning with LLM for Time Series Forecasting. Proceedings of the Forty-First International Conference on Machine Learning, Vienna, Austria."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Liu, X., Hu, J., Li, Y., Diao, S., Liang, Y., Hooi, B., and Zimmermann, R. (2024, January 13\u201317). Unitime: A language-empowered unified model for cross-domain time series forecasting. Proceedings of the ACM on Web Conference 2024, Singapore.","DOI":"10.1145\/3589334.3645434"},{"key":"ref_28","unstructured":"Liu, C., Xu, Q., Miao, H., Yang, S., Zhang, L., Long, C., Li, Z., and Zhao, R. (2025). TimeCMA: Towards LLM-Empowered Time Series Forecasting via Cross-Modality Alignment. arXiv."},{"key":"ref_29","unstructured":"Hu, Y., Li, Q., Zhang, D., Yan, J., and Chen, Y. (2025, January 24\u201328). Context-Alignment: Activating and Enhancing LLM Capabilities in Time Series. Proceedings of the International Conference on Learning Representations, Singapore."},{"key":"ref_30","unstructured":"Liu, P., Guo, H., Dai, T., Li, N., Bao, J., Ren, X., Jiang, Y., and Xia, S.T. (2025). CALF: Aligning LLMs for Time Series Forecasting via Cross-modal Fine-Tuning. arXiv."},{"key":"ref_31","unstructured":"Shen, J., Li, L., Dery, L.M., Staten, C., Khodak, M., Neubig, G., and Talwalkar, A. (2023, January 23\u201329). Cross-Modal Fine-Tuning: Align then Refine. Proceedings of the International Conference on Machine Learning, Honolulu, HI, USA."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chen, P.Y. (2024, January 20\u201327). Model Reprogramming: Resource-Efficient Cross-Domain Machine Learning. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v38i20.30267"},{"key":"ref_33","unstructured":"Pang, Z., Xie, Z., Man, Y., and Wang, Y.X. (2024, January 7\u201311). Frozen Transformers in Language Models Are Effective Visual Encoder Layers. Proceedings of the Twelfth International Conference on Learning Representations, Vienna, Austria."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Lai, Z., Wu, J., Chen, S., Zhou, Y., and Hovakimyan, N. (2024, January 16\u201322). Residual-based Language Models are Free Boosters for Biomedical Imaging Tasks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPRW63382.2024.00515"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Jin, Y., Hu, G., Chen, H., Miao, D., Hu, L., and Zhao, C. (2023, January 7\u201314). Cross-Modal Distillation for Speaker Recognition. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada.","DOI":"10.1609\/aaai.v37i11.26525"},{"key":"ref_36","unstructured":"Vinod, R., Chen, P.Y., and Das, P. (2023). Reprogramming Pretrained Language Models for Protein Sequence Representation Learning. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhao, Z., Fan, W., Li, J., Liu, Y., Mei, X., Wang, Y., Wen, Z., Wang, F., Zhao, X., and Tang, J. (2024). Recommender systems in the era of large language models (llms). IEEE Trans. Knowl. Data Eng.","DOI":"10.1109\/TKDE.2024.3392335"},{"key":"ref_38","unstructured":"Hu, E.J., Shen, Y., Wallis, P., Allen-Zhu, Z., Li, Y., Wang, S., Wang, L., and Chen, W. (2021). Lora: Low-rank adaptation of large language models. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Lee, Y.L., Tsai, Y.H., Chiu, W.C., and Lee, C.Y. (2023, January 17\u201324). Multimodal prompting with missing modalities for visual recognition. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Vancouver, BC, Canada.","DOI":"10.1109\/CVPR52729.2023.01435"},{"key":"ref_40","unstructured":"Villani, C. (2021). Topics in Optimal Transportation, American Mathematical Society."},{"key":"ref_41","unstructured":"Cuturi, M. (2013). Sinkhorn Distances: Lightspeed Computation of Optimal Transport. Adv. Neural Inf. Process. Syst., 26."},{"key":"ref_42","unstructured":"Liu, Y., Qin, G., Huang, X., Wang, J., and Long, M. (2024). Autotimes: Autoregressive time series forecasters via large language models. arXiv."},{"key":"ref_43","first-page":"9","article-title":"Language models are unsupervised multitask learners","volume":"1","author":"Radford","year":"2019","journal-title":"OpenAI Blog"},{"key":"ref_44","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_45","unstructured":"Wu, H., Xu, J., Wang, J., and Long, M. (2021, January 6\u201314). Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting. Proceedings of the Advances in Neural Information Processing Systems, Red Hook, NY, USA."},{"key":"ref_46","unstructured":"Woo, G., Liu, C., Sahoo, D., Kumar, A., and Hoi, S.C.H. (2022). ETSformer: Exponential Smoothing Transformers for Time-series Forecasting. arXiv."},{"key":"ref_47","unstructured":"Tan, M., Merrill, M., Gupta, V., Althoff, T., and Hartvigsen, T. Are language models actually useful for time series forecasting? In Proceedings of the NeurIPS, Vancouver, BC, Canada, 9\u201315 December 2024."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Challu, C., Olivares, K.G., Oreshkin, B.N., Garza, F., Mergenthaler, M., and Dubrawski, A. (2022). N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting. arXiv.","DOI":"10.1609\/aaai.v37i6.25854"},{"key":"ref_49","unstructured":"Oreshkin, B.N., Carpov, D., Chapados, N., and Bengio, Y. (2019). N-BEATS: Neural basis expansion analysis for interpretable time series forecasting. arXiv."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Qiu, X., Hu, J., Zhou, L., Wu, X., Du, J., Zhang, B., Guo, C., Zhou, A., Jensen, C.S., and Sheng, Z. (2024). TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods. arXiv.","DOI":"10.14778\/3665844.3665863"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1016\/j.ijforecast.2018.06.001","article-title":"The M4 Competition: Results, Findings, Conclusion and Way Forward","volume":"34","author":"Makridakis","year":"2018","journal-title":"Int. J. Forecast."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Jiang, Y., Pan, Z., Zhang, X., Garg, S., Schneider, A., Nevmyvaka, Y., and Song, D. (2024). Empowering Time Series Analysis with Large Language Models: A Survey. arXiv.","DOI":"10.24963\/ijcai.2024\/895"},{"key":"ref_53","unstructured":"Jin, M., Zhang, Y., Chen, W., Zhang, K., Liang, Y., Yang, B., Wang, J., Pan, S., and Wen, Q. (2024, January 21\u201327). Position: What Can Large Language Models Tell Us about Time Series Analysis. Proceedings of the Forty-First International Conference on Machine Learning, Vienna, Austria."},{"key":"ref_54","unstructured":"Guo, D., Yang, D., Zhang, H., Song, J., Zhang, R., Xu, R., Zhu, Q., Ma, S., Wang, P., and Bi, X. (2025). Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv."},{"key":"ref_55","unstructured":"Kong, Y., Yang, Y., Wang, S., Liu, C., Liang, Y., Jin, M., Zohren, S., Pei, D., Liu, Y., and Wen, Q. (2025). Position: Empowering Time Series Reasoning with Multimodal LLMs. arXiv."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/401\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:48:52Z","timestamp":1760028532000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/401"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,7]]},"references-count":55,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030401"],"URL":"https:\/\/doi.org\/10.3390\/sym17030401","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,7]]}}}