Simplicity vs. Complexity in time series forecasting: a comparative study of iTransformer variants

Simplicity vs. Complexity in time series forecasting: a comparative study of iTransformer variants | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Simplicity vs. Complexity in time series forecasting: a comparative study of iTransformer variants Polycarp Shizawaliyi Yakoi, Xiangfu Meng, Chunli Yu, Victor Adeyi Odeh, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6518629/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract According to recent time series forecasting research, simpler models frequently perform better than their more complex counterparts, particularly over longer time horizons. By comparing two improved versions of the iTransformer—MiTransformer, which incorporates an external memory module, and DFiTransformer, which adds dual-frequency decomposition and Learnable Cross-Frequency Attention—this study investigates this assertion. Although both seek to increase forecasting accuracy, empirical findings across a number of benchmarks demonstrate that performance is frequently negatively impacted by complexity. The conclusion that simpler, well-structured architectures can provide superior generalisation and practical utility is further supported by the notable underperformance of the most complex model, DFiTransformer. Artificial Intelligence and Machine Learning Time Series Forecasting Transformer Architectures Model Complexity iTransformer Memory-Augmented Models Frequency-Aware Transformers Long-Term Forecasting Deep Learning for Time Series Inductive Bias Forecasting Model Evaluation Figures Figure 1 Figure 2 1. Introduction Time series forecasting (TSF) is a critical component in a wide range of domains, from energy and finance to meteorology and industrial automation. Models built upon the Transformer [ 1 ], like the iTransformer [ 2 ], have recently shown promising performance in modelling temporal dependencies, particularly for long sequences. However, as the design of these models grows increasingly complex—with layers of decomposition, cross-frequency modelling, or memory augmentation—the benefits of such added sophistication are increasingly being questioned. This study critically evaluates the trade-offs between complexity and performance by examining two variants of the base iTransformer model. The first, MiTransformer , augments the iTransformer by incorporating a Memory-Augmented Module (MAM), introduced in [ 3 ] to capture long-range dependencies. The second, DFiTransformer , introduces a Dual-Frequency Decomposition module that splits the embedded sequence into low- and high-frequency components, which are subsequently fused via a Learnable Cross-Frequency Attention (LCFA) mechanism to enhance frequency-aware learning. Despite their theoretical promise, both MiTransformer and DFiTransformer exhibit degraded forecasting accuracy compared to the simpler iTransformer across a suite of benchmarks. This result supports emerging findings in the literature that in some contexts, simpler models outperform their more complex counterparts [ 4 ][ 5 ][ 6 ], highlighting the importance of parsimony and interpretability, especially in real-world deployment contexts. To support our analysis, we include architecture diagrams (see Figs. 1 and 2 ) that illustrate the structural differences between MiTransformer and DFiTransformer. These visualizations help clarify the design intentions behind each model and provide context for interpreting their relative performance. 2. Related Work Transformer-based models have quickly become popular in TSF because of their capacity to capture long-range dependencies and adaptable attention mechanisms. Early adaptations such as the Informer [ 4 ] and Autoformer [ 5 ] introduced efficiency improvements via sparse attention and series decomposition. These models paved the way for further innovations aimed at enhancing the temporal modelling capabilities of transformers. Building on this foundation, the iTransformer [ 2 ] introduced an inverted structure that processes input along the variable dimension, demonstrating competitive performance with a remarkably simple architecture. This idea of “less is more” has recently gained renewed attention in the field, particularly with models like PatchTST [ 12 ], which emphasized architectural minimalism and achieved strong empirical results. In contrast, more complex designs have sought to boost performance by integrating advanced components. FiLM [ 13 ] explored frequency-based modelling, while FEDformer [ 6 ] introduced frequency-enhanced decompositions. Some models employ the inclusion of external memory systems to improve their capability to remember remote temporal patterns [ 9 ]. Inspired by memory networks [ 10 ], MAMs aim to address memory decay over long horizons. Similarly, the MiTransformer introduced in this study incorporates a MAM (introduced in [ 3 ]) into iTransformer, drawing inspiration from the effectiveness of memory-augmented transformers in both NLP and vision applications [ 14 ] [ 15 ]. It improves the performance of MAMs, which focus on overcoming the limitations of traditional attention in efficiently modelling long-term dependencies [ 10 ]. Although MAMs have been proposed to address long-range dependencies in sequential data, their benefits must be weighed against the increased complexity of inference and resource demands [ 11 ]. The DFiTransformer introduced here represents another complexity-oriented extension. It incorporates Dual-Frequency Decomposition to separate embedded signals into low- and high-frequency components, and fuses them using a Learnable Cross-Frequency Attention (LCFA) mechanism. This design shares conceptual ties with frequency-aware models like FEDformer and FiLM but adopts a learnable fusion strategy rather than fixed or heuristic mechanisms. Despite these architectural enhancements, our results indicate that such complexity may not yield better forecasting outcomes. Transformer-based models provide effective scalability and performance in time series tasks; however, enhancing architectural complexity does not automatically result in improved accuracy, particularly in the context of distribution shifts or extended prediction horizons [ 4 ] as evidenced in our study. The simpler iTransformer consistently outperforms both MiTransformer and DFiTransformer across various datasets and forecasting horizons. This observation echoes a growing body of research [ 2 ] [ 7 ] that advocates for simplicity in time series model design, citing benefits in generalization, interpretability, and practical deployment. 3. Methodology The usefulness of simplicity versus complexity in transformer-based models for multivariate TSF is examined in this work. We assess three model variations, iTransformer, MiTransformer, and DFiTransformer, which have different architectural complexities but are all based on the inverted transformer architecture. The baseline model, iTransformer , is distinguished by its inverted transformer architecture, which handles time series inputs without the need for a decoder. By eschewing common autoregressive elements, it prioritises simplicity and uses an effective encoder-only framework to enable direct sequence-to-sequence forecasting. By adding a Memory-Augmented Module (MAM) to every encoder layer, MiTransformer expands on iTransformer. This module gives the model the ability to explicitly store and retrieve long-term contextual information by introducing a fixed-size learnable memory that engages with the sequence through cross-attention. Although this seeks to reduce memory deterioration over long horizons, it simultaneously raises the complexity of the architecture and the computational expenses. The MiTransformer architecture is depicted in Fig. 1 . By adding a Dual-Frequency Decomposition module and a Learnable Cross-Frequency Attention (LCFA) mechanism, DFiTransformer adds complexity. DFiTransformer uses average pooling to break down the encoded sequence into high- and low-frequency components rather than changing the transformer architecture or adding memory units. Inter-frequency dependencies are then captured by fusing these elements using cross-attention. The transformer encoder stack receives the fused representation. The model does not include any memory-augmented layers and maintains the conventional full-attention encoder design in spite of this extra complexity. Figure 2 shows the architecture. Every model is assessed under the same conditions through various public datasets utilizing standard metrics (MSE and MAE). The aim of this controlled comparison is to investigate if architectural advancements, like memory enhancement or frequency alteration, reliably surpass the basic iTransformer baseline. 4. Experimental Setup Using Mean Squared Error (MSE) and Mean Absolute Error (MAE) as evaluation tools, we evaluate DFiTransformer, MiTransformer, and iTransformer across benchmark; lower values in both metrics suggest better performance. Forecasting horizons of 96, 192, 336, and 720 time steps were considered to evaluate the performance of both models over short- and long-term horizons under the multi-step forecasting framework, whereby the model forecasts the next L future steps given a fixed-length historical window. Input sequence lengths of 96 was used across models for fair comparison. 4.1 Datasets We evaluate the models on five widely-used multivariate time series datasets: Weather : Meteorological data from the US, including variables like temperature, humidity, and wind speed. Electricity Consumption Load (ECL) : Hourly electricity consumption data of 321 clients. Exchange : Daily exchange rates of eight foreign countries. ETTm1 and ETTm2 : Electric Transformer Temperature datasets with different temporal resolutions (15-min and 1-hour intervals). Each dataset is split into training, validation, and testing sets using a standard 7:2:1 ratio. 4.2 Models Compared iTransformer : The baseline inverted transformer architecture. MiTransformer : Enhances iTransformer with a memory-augmented module. DFiTransformer : Adds dual-frequency decomposition and Learnable Cross-Frequency Attention (LCFA) to iTransformer. All models are implemented in PyTorch and trained under consistent hyperparameter settings to ensure comparability. 4.3 Implementation Details The implementation is based on PyTorch and trained on an NVIDIA A8000 80G GPU. The Adam optimiser is used to train the model with a batch size of 32, a dropout rate of p = 0.1, and an initial learning rate of 0.0001 that decreases by two times each epoch. To avoid overfitting, we implement early stopping once the model has gone ten consecutive epochs without learning. 5. Results and Analysis We evaluate iTransformer, MiTransformer, and DFiTransformer across five widely-used time series forecasting benchmarks: using MSE and MAE as evaluation metrics. Forecasting horizons of 96, 192, 336, and 720 steps are considered to test performance at increasing levels of difficulty. Table 1 presents results of forecasting. Table 1 Forecasting results Models iTransformer MiTransformer DFiTransformer Metric MSE MAE MSE MAE MSE MAE Weather 96 0.174 0.214 0.179 0.218 0.187 0.232 192 0.221 0.254 0.224 0.257 0.242 0.275 336 0.278 0.296 0.285 0.301 0.299 0.313 720 0.358 0.347 0.359 0.350 0.373 0.364 Avg 0.258 0.278 0.262 0.282 0.275 0.296 ECL 96 0.148 0.240 0.166 0.256 0.191 0.297 192 0.162 0.253 0.177 0.267 0.207 0.310 336 0.178 0.269 0.195 0.285 0.222 0.323 720 0.225 0.317 0.234 0.318 0.249 0.343 Avg 0.178 0.270 0.193 0.282 0.217 0.318 Exchange 96 0.086 0.206 0.087 0.207 0.119 0.245 192 0.177 0.299 0.176 0.299 0.252 0.358 336 0.331 0.417 0.346 0.426 0.430 0.475 720 0.847 0.691 0.854 0.700 0.949 0.738 Avg 0.360 0.403 0.366 0.408 0.438 0.454 ETTm1 96 0.334 0.368 0.354 0.382 0.368 0.392 192 0.377 0.391 0.383 0.394 0.411 0.415 336 0.426 0.420 0.444 0.430 0.444 0.437 720 0.491 0.459 0.517 0.470 0.560 0.493 Avg 0.407 0.410 0.425 0.419 0.446 0.434 ETTm2 96.000 0.180 0.264 0.182 0.263 0.196 0.275 192.000 0.250 0.309 0.250 0.306 0.256 0.313 336.000 0.311 0.348 0.318 0.351 0.332 0.358 720.000 0.412 0.407 0.414 0.405 0.414 0.404 Avg 0.288 0.332 0.291 0.331 0.300 0.338 1st 24 24 2 2 0 1 2nd 1 1 23 23 3 0 Across all datasets and forecasting horizons, the iTransformer consistently achieves the lowest average errors. MiTransformer , which adds a memory-augmented mechanism to the iTransformer, shows a marginal performance drop, particularly on long-term horizons. However, the DFiTransformer , despite being the most complex—introducing dual-frequency decomposition and cross-frequency attention—underperforms relative to both simpler models, especially on challenging datasets like Exchange and ECL. For example, on the Exchange dataset , iTransformer achieves an average MSE of 0.360 compared to 0.366 for MiTransformer and 0.438 for DFiTransformer. A similar trend holds for ECL, where the average MSEs are 0.178, 0.193, and 0.217 respectively. Notably, performance gaps widen with increasing prediction lengths, suggesting that added architectural complexity may hinder long-term generalization. These findings reinforce our central claim: architectural simplicity not only facilitates interpretability and efficiency but also tends to generalize better in practical forecasting scenarios . Even modest enhancements, such as the external memory module in MiTransformer, can introduce unnecessary overhead without clear performance benefits. The performance degradation observed in DFiTransformer further illustrates that increased model complexity does not guarantee improved outcomes, especially in the domain of time series forecasting. 6. Discussion: Simplicity vs Complexity in Forecasting Models Our comparative evaluation of three transformer-based models— iTransformer , MiTransformer , and DFiTransformer —reveals a consistent and important trend: simpler architectures can outperform more complex designs in time series forecasting . Studies have shown that simpler models, in some cases, outperform more complex ones due to their generalization ability and reduced computational demands [ 13 ] [ 14 ]. The iTransformer, employing a minimal inverted attention mechanism without auxiliary modules, delivers robust and consistent results across diverse datasets. In contrast, MiTransformer, which introduces a memory-augmented component, and DFiTransformer, which integrates frequency decomposition and cross-frequency attention, exhibit diminished performance despite increased architectural sophistication. These findings challenge the prevailing assumption that architectural complexity necessarily leads to better forecasting accuracy. In fact, the performance degradation observed in MiTransformer and DFiTransformer suggests that additional modules may introduce noise or overfitting—particularly problematic in real-world time series that are often noisy and non-stationary. This means that our findings agree with [ 15 ] and [ 16 ], who show that strong inductive biases or lightweight architectural designs can lead to superior generalization on long-range dependencies. Also, our findings echo those of [ 8 ], where a simple linear model outperformed state-of-the-art Transformer variants on long-term time-series forecasting. The implications are twofold. First, for practical deployment , models like iTransformer offer favourable trade-offs between accuracy, computational cost, and interpretability. Second, from a research perspective , our results call for a more nuanced understanding of architectural design: simplification, not complication, may be key to generalizable and scalable forecasting solutions. Our experimental results across six benchmark datasets reveal a consistent trend: increasing architectural complexity does not guarantee performance improvement in time series forecasting. The original iTransformer often outperforms both MiTransformer, which adds a memory augmentation module, and DFiTransformer, which combines memory with dual-frequency attention mechanisms. Among the three, DFiTransformer—the most complex—achieves the weakest performance on average. This hierarchy of results strongly supports the insight that simpler architectures not only generalize better but also offer practical advantages in terms of training efficiency and model interpretability [ 2 ] [ 12 ]. Therefore, our findings reinforce the principle that more is not always better —especially when it comes to deep learning for sequential data. These findings suggest that future model development should prioritize principled minimalism, seeking targeted, lightweight improvements rather than wholesale architectural expansion. 7. Conclusion This paper assessed two improved versions of the iTransformer—MiTransformer and DFiTransformer—each meant to enhance the base model via memory augmentation and frequency-aware mechanisms, respectively. Though they added complexity, both models fell short of the original iTransformer. These findings support the growing body of evidence indicating that in time series forecasting, architectural simplicity often produces better generalisation and robustness. Our results support the case that, particularly for long-term forecasting, more complex designs do not ensure better performance—highlighting the idea that "the simpler, the better" remains a useful design philosophy. Declarations Funding: Not applicable. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Acknowledgements : We thank and acknowledge our institution for providing computational resources for our experiments. Availability of data and materials: • Primary datasets: iTransformer official Google Drive (accessed 12/01/2025). Informer official Google Drive (accessed 22/09/2024). ETT Datasets. • Pre-processing code: A public GitHub repository will be activated upon acceptance. Competing interests : The authors declare no competing interests. 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In International conference on machine learning, in International conference on machine learning Zeng A, Chen M, Zhang L, Xu Q (2023) Are transformers effective for time series forecasting? in AAAI conference on artificial intelligence Chen H, Luong V, Mukherjee L, Singh V (2025) SimpleTM: A Simple Baseline for Multivariate Time Series Forecasting, in The Thirteenth International Conference on Learning Representations Rae J, Hunt JJ, Danihelka I, Harley T, Senior rW, Wayne G, Graves A, Lillicrap T (2016) Scaling memory-augmented neural networks with sparse reads and writes. Adv Neural Inf Process Syst, 29 Sukhbaatar S, Weston J, Fergus R (2015) End-to-end memory networks. Adv Neural Inf Process Syst, 28 Chen Q, Li Y, Ma C, Wang J (2023) Memory-Augmented Neural Networks for Sequential Data: A Survey and Outlook. ACM-CSUR Nie Y, Nguyen NH, Sinthong P, Kalagnanam J (2022) A time series is worth 64 words: Long-term forecasting with transformers, arXiv preprint arXiv:2211.14730 , Lim B, Zohren S (2021) Time-series forecasting with deep learning: a survey. Philosophical Trans Royal Soc A 379(2194):20200209 Elsayed S, Thyssens D, Rashed AJHS, Schmidt-Thieme L (2021) Do we really need deep learning models for time series forecasting? arXiv preprint arXiv:2101.02118. , Wu H, Hu T, Liu Y, Zhou H, Wang J, Long M (2022) Timesnet: Temporal 2d-variation modeling for general time series analysis, arXiv preprint arXiv:2210.02186 , Gu A, Dao T (2023) Mamba: Linear-time sequence modeling with selective state spaces, arXiv preprint arXiv:2312.00752 , Kaiser Ł, Nachum O, Roy A, Bengio S (2017) Learning to remember rare events., arXiv preprint arXiv:1703.03129 , Additional Declarations The authors declare no competing interests. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6518629","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":447338780,"identity":"ce76b753-8dad-4bd8-bac0-e4a876d8d905","order_by":0,"name":"Polycarp Shizawaliyi Yakoi","email":"","orcid":"https://orcid.org/0009-0006-9696-7276","institution":"School of Electronic and Information Engineering, Liaoning Technical University","correspondingAuthor":false,"prefix":"","firstName":"Polycarp","middleName":"Shizawaliyi","lastName":"Yakoi","suffix":""},{"id":447338930,"identity":"a2098d42-421e-433e-a472-708bb4ec2805","order_by":1,"name":"Xiangfu Meng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmElEQVRIiWNgGAWjYLCChAoJOX4StZyxMJZsIEkLY1tF4gaitei2n30m8XCeBOMGBuaHj24Qo8XsTLqxQeI2CWZzBjZj4xyitBxIY3wA1MJm2cDDJk2clvPPGA4kzpHgMThAtJYbIFsaJCRI0fKM2SDhmISBZDPRfjmfxib5o6auvp+9+eFjorQgADNpykfBKBgFo2AU4AMAkvEsqA2bCokAAAAASUVORK5CYII=","orcid":"","institution":"School of Electronic and Information Engineering, Liaoning Technical University","correspondingAuthor":true,"prefix":"","firstName":"Xiangfu","middleName":"","lastName":"Meng","suffix":""},{"id":447339639,"identity":"58c669b8-331a-44e5-8703-b499cb3477b9","order_by":2,"name":"Chunli Yu","email":"","orcid":"","institution":"School of Electronic and Information Engineering, Liaoning Technical University","correspondingAuthor":false,"prefix":"","firstName":"Chunli","middleName":"","lastName":"Yu","suffix":""},{"id":447339640,"identity":"72e8a92a-9da5-44fa-bb40-62d8ca617ff8","order_by":3,"name":"Victor Adeyi Odeh","email":"","orcid":"https://orcid.org/0000-0001-6765-957X","institution":"School of Information and Communication Engineering, University of Electronic Science and Technology of China","correspondingAuthor":false,"prefix":"","firstName":"Victor","middleName":"Adeyi","lastName":"Odeh","suffix":""},{"id":447339641,"identity":"9c679d8d-cec4-4c6f-b6b1-e7f484b1ddf5","order_by":4,"name":"Danladi Suleman","email":"","orcid":"https://orcid.org/0000-0002-9958-8320","institution":"University of the Sunshine Coast, School of Science, Technology and Engineering, UniSC Moreton Bay, QLD Australia","correspondingAuthor":false,"prefix":"","firstName":"Danladi","middleName":"","lastName":"Suleman","suffix":""}],"badges":[],"createdAt":"2025-04-24 08:23:14","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6518629/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6518629/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":81350397,"identity":"b848afc0-b03f-42aa-9b4d-98604f64f6af","added_by":"auto","created_at":"2025-04-25 06:11:29","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":24705,"visible":true,"origin":"","legend":"\u003cp\u003eMiTransformer Architecture\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6518629/v1/a191b6389eead64b9a56fc93.png"},{"id":81350398,"identity":"0467d0cd-7377-428c-9c98-a08ed7f515a4","added_by":"auto","created_at":"2025-04-25 06:11:29","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":35139,"visible":true,"origin":"","legend":"\u003cp\u003eDFiTransformer architecture\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6518629/v1/ec5ef00a58b4fc4c6a0ff15d.png"},{"id":81351315,"identity":"f8c4101d-7979-4ab4-abeb-14e32da0c87d","added_by":"auto","created_at":"2025-04-25 06:27:30","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1274540,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6518629/v1/4c5d2322-8ab6-4c9f-885f-5f9d28130122.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSimplicity vs. Complexity in time series forecasting: a comparative study of iTransformer variants\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eTime series forecasting (TSF) is a critical component in a wide range of domains, from energy and finance to meteorology and industrial automation. Models built upon the Transformer [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], like the iTransformer [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], have recently shown promising performance in modelling temporal dependencies, particularly for long sequences. However, as the design of these models grows increasingly complex\u0026mdash;with layers of decomposition, cross-frequency modelling, or memory augmentation\u0026mdash;the benefits of such added sophistication are increasingly being questioned.\u003c/p\u003e \u003cp\u003eThis study critically evaluates the trade-offs between complexity and performance by examining two variants of the base iTransformer model. The first, \u003cb\u003eMiTransformer\u003c/b\u003e, augments the iTransformer by incorporating a Memory-Augmented Module (MAM), introduced in [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] to capture long-range dependencies. The second, \u003cb\u003eDFiTransformer\u003c/b\u003e, introduces a \u003cb\u003eDual-Frequency Decomposition\u003c/b\u003e module that splits the embedded sequence into low- and high-frequency components, which are subsequently fused via a \u003cb\u003eLearnable Cross-Frequency Attention (LCFA)\u003c/b\u003e mechanism to enhance frequency-aware learning.\u003c/p\u003e \u003cp\u003eDespite their theoretical promise, both MiTransformer and DFiTransformer exhibit degraded forecasting accuracy compared to the simpler iTransformer across a suite of benchmarks. This result supports emerging findings in the literature that in some contexts, simpler models outperform their more complex counterparts [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e][\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e][\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], highlighting the importance of parsimony and interpretability, especially in real-world deployment contexts.\u003c/p\u003e \u003cp\u003eTo support our analysis, we include architecture diagrams (see Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) that illustrate the structural differences between MiTransformer and DFiTransformer. These visualizations help clarify the design intentions behind each model and provide context for interpreting their relative performance.\u003c/p\u003e"},{"header":"2. Related Work","content":"\u003cp\u003eTransformer-based models have quickly become popular in TSF because of their capacity to capture long-range dependencies and adaptable attention mechanisms. Early adaptations such as the \u003cb\u003eInformer\u003c/b\u003e [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] and \u003cb\u003eAutoformer\u003c/b\u003e [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] introduced efficiency improvements via sparse attention and series decomposition. These models paved the way for further innovations aimed at enhancing the temporal modelling capabilities of transformers.\u003c/p\u003e \u003cp\u003eBuilding on this foundation, the \u003cb\u003eiTransformer\u003c/b\u003e [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] introduced an inverted structure that processes input along the variable dimension, demonstrating competitive performance with a remarkably simple architecture. This idea of \u0026ldquo;less is more\u0026rdquo; has recently gained renewed attention in the field, particularly with models like \u003cb\u003ePatchTST\u003c/b\u003e [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], which emphasized architectural minimalism and achieved strong empirical results.\u003c/p\u003e \u003cp\u003eIn contrast, more complex designs have sought to boost performance by integrating advanced components. \u003cb\u003eFiLM\u003c/b\u003e [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] explored frequency-based modelling, while \u003cb\u003eFEDformer\u003c/b\u003e [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] introduced frequency-enhanced decompositions. Some models employ the inclusion of external memory systems to improve their capability to remember remote temporal patterns [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Inspired by memory networks [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], MAMs aim to address memory decay over long horizons.\u003c/p\u003e \u003cp\u003eSimilarly, the MiTransformer introduced in this study incorporates a MAM (introduced in [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]) into iTransformer, drawing inspiration from the effectiveness of memory-augmented transformers in both NLP and vision applications [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. It improves the performance of MAMs, which focus on overcoming the limitations of traditional attention in efficiently modelling long-term dependencies [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Although MAMs have been proposed to address long-range dependencies in sequential data, their benefits must be weighed against the increased complexity of inference and resource demands [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe \u003cb\u003eDFiTransformer\u003c/b\u003e introduced here represents another complexity-oriented extension. It incorporates \u003cb\u003eDual-Frequency Decomposition\u003c/b\u003e to separate embedded signals into low- and high-frequency components, and fuses them using a \u003cb\u003eLearnable Cross-Frequency Attention (LCFA)\u003c/b\u003e mechanism. This design shares conceptual ties with frequency-aware models like FEDformer and FiLM but adopts a learnable fusion strategy rather than fixed or heuristic mechanisms.\u003c/p\u003e \u003cp\u003eDespite these architectural enhancements, our results indicate that such complexity may not yield better forecasting outcomes. Transformer-based models provide effective scalability and performance in time series tasks; however, enhancing architectural complexity does not automatically result in improved accuracy, particularly in the context of distribution shifts or extended prediction horizons [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e] as evidenced in our study. The simpler iTransformer consistently outperforms both MiTransformer and DFiTransformer across various datasets and forecasting horizons. This observation echoes a growing body of research [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] that advocates for simplicity in time series model design, citing benefits in generalization, interpretability, and practical deployment.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eThe usefulness of simplicity versus complexity in transformer-based models for multivariate TSF is examined in this work. We assess three model variations, iTransformer, MiTransformer, and DFiTransformer, which have different architectural complexities but are all based on the inverted transformer architecture.\u003c/p\u003e \u003cp\u003eThe baseline model, \u003cb\u003eiTransformer\u003c/b\u003e, is distinguished by its inverted transformer architecture, which handles time series inputs without the need for a decoder. By eschewing common autoregressive elements, it prioritises simplicity and uses an effective encoder-only framework to enable direct sequence-to-sequence forecasting.\u003c/p\u003e \u003cp\u003eBy adding a \u003cb\u003eMemory-Augmented Module (MAM)\u003c/b\u003e to every encoder layer, \u003cb\u003eMiTransformer\u003c/b\u003e expands on iTransformer. This module gives the model the ability to explicitly store and retrieve long-term contextual information by introducing a fixed-size learnable memory that engages with the sequence through cross-attention. Although this seeks to reduce memory deterioration over long horizons, it simultaneously raises the complexity of the architecture and the computational expenses. The MiTransformer architecture is depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eBy adding a \u003cb\u003eDual-Frequency Decomposition module\u003c/b\u003e and a \u003cb\u003eLearnable Cross-Frequency Attention (LCFA)\u003c/b\u003e mechanism, \u003cb\u003eDFiTransformer\u003c/b\u003e adds complexity. DFiTransformer uses average pooling to break down the encoded sequence into high- and low-frequency components rather than changing the transformer architecture or adding memory units. Inter-frequency dependencies are then captured by fusing these elements using cross-attention. The transformer encoder stack receives the fused representation. The model does not include any memory-augmented layers and maintains the conventional full-attention encoder design in spite of this extra complexity. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the architecture.\u003c/p\u003e \u003cp\u003eEvery model is assessed under the same conditions through various public datasets utilizing standard metrics (MSE and MAE). The aim of this controlled comparison is to investigate if architectural advancements, like memory enhancement or frequency alteration, reliably surpass the basic iTransformer baseline.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Experimental Setup","content":"\u003cp\u003eUsing Mean Squared Error (MSE) and Mean Absolute Error (MAE) as evaluation tools, we evaluate DFiTransformer, MiTransformer, and iTransformer across benchmark; lower values in both metrics suggest better performance. Forecasting horizons of 96, 192, 336, and 720 time steps were considered to evaluate the performance of both models over short- and long-term horizons under the multi-step forecasting framework, whereby the model forecasts the next L future steps given a fixed-length historical window. Input sequence lengths of 96 was used across models for fair comparison.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Datasets\u003c/h2\u003e \u003cp\u003eWe evaluate the models on five widely-used multivariate time series datasets:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eWeather\u003c/b\u003e: Meteorological data from the US, including variables like temperature, humidity, and wind speed.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eElectricity Consumption Load (ECL)\u003c/b\u003e: Hourly electricity consumption data of 321 clients.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eExchange\u003c/b\u003e: Daily exchange rates of eight foreign countries.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eETTm1 and ETTm2\u003c/b\u003e: Electric Transformer Temperature datasets with different temporal resolutions (15-min and 1-hour intervals).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eEach dataset is split into training, validation, and testing sets using a standard 7:2:1 ratio.\u003c/p\u003e \u003cp\u003e \u003cb\u003e4.2 Models Compared\u003c/b\u003e \u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eiTransformer\u003c/b\u003e: The baseline inverted transformer architecture.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eMiTransformer\u003c/b\u003e: Enhances iTransformer with a memory-augmented module.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eDFiTransformer\u003c/b\u003e: Adds dual-frequency decomposition and Learnable Cross-Frequency Attention (LCFA) to iTransformer.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eAll models are implemented in PyTorch and trained under consistent hyperparameter settings to ensure comparability.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Implementation Details\u003c/h2\u003e \u003cp\u003eThe implementation is based on PyTorch and trained on an NVIDIA A8000 80G GPU. The Adam optimiser is used to train the model with a batch size of 32, a dropout rate of p\u0026thinsp;=\u0026thinsp;0.1, and an initial learning rate of 0.0001 that decreases by two times each epoch. To avoid overfitting, we implement early stopping once the model has gone ten consecutive epochs without learning.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Results and Analysis","content":"\u003cp\u003eWe evaluate iTransformer, MiTransformer, and DFiTransformer across five widely-used time series forecasting benchmarks: using MSE and MAE as evaluation metrics. Forecasting horizons of 96, 192, 336, and 720 steps are considered to test performance at increasing levels of difficulty. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents results of forecasting.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eForecasting results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eiTransformer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eMiTransformer\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003eDFiTransformer\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eMetric\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eWeather\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.174\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.214\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.179\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.218\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.187\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.232\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.221\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.254\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.224\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.257\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.242\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.275\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.278\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.296\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.285\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.301\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.299\u003c/p\u003e \u003c/td\u003e 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align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAvg\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.258\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.278\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.262\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.282\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.275\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.296\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eECL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e 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\u003cp\u003e\u003cb\u003e24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2nd\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAcross all datasets and forecasting horizons, the \u003cb\u003eiTransformer\u003c/b\u003e consistently achieves the lowest average errors. \u003cb\u003eMiTransformer\u003c/b\u003e, which adds a memory-augmented mechanism to the iTransformer, shows a marginal performance drop, particularly on long-term horizons. However, the \u003cb\u003eDFiTransformer\u003c/b\u003e, despite being the most complex\u0026mdash;introducing dual-frequency decomposition and cross-frequency attention\u0026mdash;underperforms relative to both simpler models, especially on challenging datasets like Exchange and ECL.\u003c/p\u003e \u003cp\u003eFor example, on the \u003cb\u003eExchange dataset\u003c/b\u003e, iTransformer achieves an average MSE of 0.360 compared to 0.366 for MiTransformer and 0.438 for DFiTransformer. A similar trend holds for ECL, where the average MSEs are 0.178, 0.193, and 0.217 respectively. Notably, performance gaps widen with increasing prediction lengths, suggesting that added architectural complexity may hinder long-term generalization.\u003c/p\u003e \u003cp\u003eThese findings reinforce our central claim: \u003cb\u003earchitectural simplicity not only facilitates interpretability and efficiency but also tends to generalize better in practical forecasting scenarios\u003c/b\u003e. Even modest enhancements, such as the external memory module in MiTransformer, can introduce unnecessary overhead without clear performance benefits. The performance degradation observed in DFiTransformer further illustrates that increased model complexity does not guarantee improved outcomes, especially in the domain of time series forecasting.\u003c/p\u003e"},{"header":"6. Discussion: Simplicity vs Complexity in Forecasting Models","content":"\u003cp\u003eOur comparative evaluation of three transformer-based models\u0026mdash;\u003cb\u003eiTransformer\u003c/b\u003e, \u003cb\u003eMiTransformer\u003c/b\u003e, and \u003cb\u003eDFiTransformer\u003c/b\u003e\u0026mdash;reveals a consistent and important trend: \u003cb\u003esimpler architectures can outperform more complex designs in time series forecasting\u003c/b\u003e. Studies have shown that simpler models, in some cases, outperform more complex ones due to their generalization ability and reduced computational demands [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe iTransformer, employing a minimal inverted attention mechanism without auxiliary modules, delivers robust and consistent results across diverse datasets. In contrast, MiTransformer, which introduces a memory-augmented component, and DFiTransformer, which integrates frequency decomposition and cross-frequency attention, exhibit diminished performance despite increased architectural sophistication.\u003c/p\u003e \u003cp\u003eThese findings challenge the prevailing assumption that architectural complexity necessarily leads to better forecasting accuracy. In fact, the performance degradation observed in MiTransformer and DFiTransformer suggests that additional modules may introduce noise or overfitting\u0026mdash;particularly problematic in real-world time series that are often noisy and non-stationary. This means that our findings agree with [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] and [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e], who show that strong inductive biases or lightweight architectural designs can lead to superior generalization on long-range dependencies. Also, our findings echo those of [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], where a simple linear model outperformed state-of-the-art Transformer variants on long-term time-series forecasting.\u003c/p\u003e \u003cp\u003eThe implications are twofold. First, for \u003cb\u003epractical deployment\u003c/b\u003e, models like iTransformer offer favourable trade-offs between accuracy, computational cost, and interpretability. Second, from a \u003cb\u003eresearch perspective\u003c/b\u003e, our results call for a more nuanced understanding of architectural design: \u003cb\u003esimplification, not complication, may be key\u003c/b\u003e to generalizable and scalable forecasting solutions.\u003c/p\u003e \u003cp\u003eOur experimental results across six benchmark datasets reveal a consistent trend: increasing architectural complexity does not guarantee performance improvement in time series forecasting. The original iTransformer often outperforms both MiTransformer, which adds a memory augmentation module, and DFiTransformer, which combines memory with dual-frequency attention mechanisms. Among the three, DFiTransformer\u0026mdash;the most complex\u0026mdash;achieves the weakest performance on average. This hierarchy of results strongly supports the insight that simpler architectures not only generalize better but also offer practical advantages in terms of training efficiency and model interpretability [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Therefore, our findings reinforce the principle that \u003cb\u003emore is not always better\u003c/b\u003e\u0026mdash;especially when it comes to deep learning for sequential data. These findings suggest that future model development should prioritize principled minimalism, seeking targeted, lightweight improvements rather than wholesale architectural expansion.\u003c/p\u003e"},{"header":"7. Conclusion","content":"\u003cp\u003eThis paper assessed two improved versions of the iTransformer\u0026mdash;MiTransformer and DFiTransformer\u0026mdash;each meant to enhance the base model via memory augmentation and frequency-aware mechanisms, respectively. Though they added complexity, both models fell short of the original iTransformer. These findings support the growing body of evidence indicating that in time series forecasting, architectural simplicity often produces better generalisation and robustness. Our results support the case that, particularly for long-term forecasting, more complex designs do not ensure better performance\u0026mdash;highlighting the idea that \"the simpler, the better\" remains a useful design philosophy.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding:\u003c/h2\u003e\n\u003cp\u003eNot applicable. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e: We thank and acknowledge our institution for providing computational resources for our experiments.\u003c/p\u003e\n\u003ch2\u003eAvailability of data and materials:\u003c/h2\u003e\n\u003cp\u003e\u0026bull; Primary datasets:\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003eiTransformer official Google Drive (accessed 12/01/2025).\u003c/li\u003e\n\u003cli\u003eInformer official Google Drive (accessed 22/09/2024).\u003c/li\u003e\n\u003cli\u003eETT Datasets.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u0026bull; Pre-processing code: A public GitHub repository will be activated upon acceptance.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e: The authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eVaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser Ł, Polosukhin I (2017) Attention is all you need, in \u003cem\u003e31st Conference on Neural Information Processing Systems (NIPS 2017)\u003c/em\u003e, Long Beach, CA, USA\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLiu Y, Hu T, Zhang H, Wu H, Wang S, Ma L, Long M (2024) itransformer: Inverted transformers are effective for time series forecasting, in \u003cem\u003eICLR 2024\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYakoi PS, Meng X, Yu C, Odeh VA, Zhang Y, Zhao Z (2025) LTSMiTransformer: Learnable Temporal Sparsity and Memory for Efficient Long-Term Time Series Forecasting\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H, Zhang W (2021) Informer: Beyond efficient transformer for long sequence time-series forecasting, in \u003cem\u003eProceedings of the AAAI conference on artificial intelligence\u003c/em\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWu LM (2021) Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting, in \u003cem\u003e35th Conference on Neural Information Processing Systems (NeurIPS\u003c/em\u003e 2021\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou T, Ma Z, Wen Q, Wang X, Sun L, Jin R (2022) Fedformer: Frequency enhanced decomposed transformer for long-term series forecasting. 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By comparing two improved versions of the iTransformer\u0026mdash;MiTransformer, which incorporates an external memory module, and DFiTransformer, which adds dual-frequency decomposition and Learnable Cross-Frequency Attention\u0026mdash;this study investigates this assertion. Although both seek to increase forecasting accuracy, empirical findings across a number of benchmarks demonstrate that performance is frequently negatively impacted by complexity. The conclusion that simpler, well-structured architectures can provide superior generalisation and practical utility is further supported by the notable underperformance of the most complex model, DFiTransformer.\u003c/p\u003e","manuscriptTitle":"Simplicity vs. Complexity in time series forecasting: a comparative study of iTransformer variants","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-25 06:11:25","doi":"10.21203/rs.3.rs-6518629/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f7572a3d-e80d-4608-8834-ace0a5fe40b9","owner":[],"postedDate":"April 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":47613967,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2025-04-25T06:11:25+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-25 06:11:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6518629","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6518629","identity":"rs-6518629","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}