On the Performance of Legendre State-Space Models in Short-Term Time Series Forecasting
Bibliographic record
Abstract
State-space models (SSMs) are a class of fundamental models in control theory. SSMs are well-known for their concise mathematical representations and capability of capturing the evolving dynamics of systems. They have also proven useful in time series modeling. Recent studies suggest that SSMs are able to conceptually generalize to classic machine learning models (CNNs, RNNs and RNN-variants) as well as provide theoretical justification for the design of novel sequence models. In this work, we investigate one type of SSM, the Legendre Memory Unit (LMU) and LMU’s parallelized variant (LMUFFT), and propose a stacking strategy leveraging the LMUFFT backbone and a Deep Adaptive Input Normalization (DAIN) scheme. Model performance is evaluated using short-term time series forecasting tasks formulated from real-world data. The proposed structure outperforms the traditional machine learning models in efficiency and prediction capability. Our results also suggest that this family of state-space models has potential in the realm of machine learning research. By shedding light on the benefits of SSMs in short-term time series forecasting, we hope to pique the interest of machine learning researchers in the use of SSMs and inspire further investigation into novel model designs based on these models.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".