Filter then Attend: Improving attention-based Time Series Forecasting with Spectral Filtering
Pith reviewed 2026-05-18 20:23 UTC · model grok-4.3
The pith
Adding learnable spectral filters before transformers improves long time series forecasts and allows smaller models.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Prepending learnable frequency filters to transformer architectures improves their spectral utilization in long time-series forecasting tasks. This yields 5-10 percent relative performance gains across instances while adding roughly 1000 parameters, and it enables reduced embedding dimensions that result in smaller yet more effective models compared to the unfiltered baselines.
What carries the argument
A learnable spectral filtering layer placed before the transformer that processes the input to enhance frequency content utilization ahead of attention.
If this is right
- Transformer forecasters achieve 5-10 percent relative accuracy gains when the filter layer is added.
- Embedding dimensions can be reduced while preserving or improving forecast quality.
- The models better exploit the full frequency spectrum, as confirmed by synthetic experiments.
Where Pith is reading between the lines
- The filtering step could extend to other attention-based sequence models that exhibit low-frequency bias.
- Smaller filtered models may lower memory and compute needs during deployment for repeated forecasting.
Load-bearing premise
The performance gains arise specifically from improved frequency handling by the filters rather than from extra capacity or regularization effects.
What would settle it
Running the same transformer models with the learnable filter replaced by a non-learnable or random layer of similar parameter count; if the 5-10 percent gains disappear, it would support that the learnable spectral filtering is responsible.
read the original abstract
Transformer-based models are at the forefront in long time-series forecasting (LTSF). While in many cases, these models are able to achieve state of the art results, they suffer from a bias toward low-frequencies in the data and high computational and memory requirements. Recent work has established that learnable frequency filters can be an integral part of a deep forecasting model by enhancing the model's spectral utilization. These works choose to use a multilayer perceptron to process their filtered signals and thus do not solve the issues found with transformer-based models. In this paper, we establish that adding a filter to the beginning of transformer-based models enhances their performance in long time-series forecasting. We add learnable filters, which only add an additional $\approx 1000$ parameters to several transformer-based models and observe in multiple instances 5-10 \% relative improvement in forecasting performance. Additionally, we find that with filters added, we are able to decrease the embedding dimension of our models, resulting in transformer-based architectures that are both smaller and more effective than their non-filtering base models. We also conduct synthetic experiments to analyze how the filters enable Transformer-based models to better utilize the full spectrum for forecasting.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript proposes prepending a learnable spectral filter layer (adding ~1000 parameters) to transformer-based models for long-term time series forecasting. It reports 5-10% relative improvements over several baselines on public datasets, shows that the filtered models can use smaller embedding dimensions while remaining more accurate, and includes synthetic experiments to argue that the filters improve utilization of the full frequency spectrum rather than only low frequencies.
Significance. If the performance gains can be causally attributed to frequency-selective filtering rather than generic capacity or regularization, the method would offer a lightweight, practical fix for the documented low-frequency bias in attention-based forecasters while simultaneously enabling smaller models. The parameter count and model-size reduction claims are attractive if they survive controlled ablation.
major comments (2)
- [§4] §4 (Experiments) and associated tables: the 5-10% relative gains and the claim that filters permit reduced embedding dimension are reported without a matched-parameter control that disables frequency selectivity (e.g., a non-FFT linear projection or fixed random filter with identical parameter count). Because the abstract and synthetic-experiment discussion attribute both the accuracy lift and the ability to shrink the embedding dimension specifically to improved spectral utilization, the absence of this control leaves the central causal claim untested.
- [Synthetic Experiments] Synthetic spectrum analysis section: the experiments are invoked to demonstrate that filters enable better use of higher frequencies, yet the description provides no quantitative isolation (e.g., spectrum of attention weights or prediction error decomposed by frequency band) that would distinguish the filter's frequency response from other effects of the added layer.
minor comments (2)
- [Abstract] Abstract: the phrase 'in multiple instances' is vague; listing the specific model–dataset pairs that achieve the 5-10% band would improve clarity.
- [Method] Notation: the precise parameterization of the learnable filter coefficients (number of taps, initialization, constraint to real-valued or complex) is not stated in the main text, complicating reproducibility.
Simulated Author's Rebuttal
We thank the referee for the constructive feedback. The points raised regarding the need for matched-parameter controls and more quantitative analysis in the synthetic experiments are valid and will strengthen the causal claims in the paper. We address each comment below and will revise the manuscript accordingly.
read point-by-point responses
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Referee: [§4] §4 (Experiments) and associated tables: the 5-10% relative gains and the claim that filters permit reduced embedding dimension are reported without a matched-parameter control that disables frequency selectivity (e.g., a non-FFT linear projection or fixed random filter with identical parameter count). Because the abstract and synthetic-experiment discussion attribute both the accuracy lift and the ability to shrink the embedding dimension specifically to improved spectral utilization, the absence of this control leaves the central causal claim untested.
Authors: We agree that a matched-parameter control is necessary to isolate the contribution of frequency selectivity from generic capacity or regularization effects. In the revised manuscript, we will add ablation experiments comparing the learnable spectral filter against (i) a non-FFT linear projection with the same ~1000 parameters and (ii) a fixed random filter with identical parameter count. These controls will be evaluated on the same datasets and model configurations, directly testing whether the observed gains and embedding-dimension reductions are attributable to learnable frequency response. Preliminary results from these runs indicate that the learnable filter outperforms both controls, and the full results will be reported in updated tables and text. revision: yes
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Referee: [Synthetic Experiments] Synthetic spectrum analysis section: the experiments are invoked to demonstrate that filters enable better use of higher frequencies, yet the description provides no quantitative isolation (e.g., spectrum of attention weights or prediction error decomposed by frequency band) that would distinguish the filter's frequency response from other effects of the added layer.
Authors: We acknowledge that the current synthetic experiments would benefit from additional quantitative measures to more rigorously separate the filter's frequency-selective effects. In the revision, we will augment the synthetic spectrum analysis by including (i) prediction error decomposed across frequency bands and (ii) spectral analysis of attention weights with and without the filter layer. These metrics will provide explicit evidence of improved higher-frequency utilization and will be added to the section along with supporting figures. revision: yes
Circularity Check
Minor self-citation present but central claims rest on external benchmarks and experiments
full rationale
The paper introduces learnable spectral filters as a lightweight addition (~1000 parameters) to transformer-based LTSF models and reports 5-10% relative gains plus the ability to reduce embedding dimension. These results are obtained by direct comparison against standard public datasets and baselines rather than by re-deriving the filter parameters from the target metrics. The abstract and synthetic experiments invoke prior work on frequency filters, but this citation is not load-bearing for the new empirical claims; the performance numbers remain independently falsifiable. No self-definitional equations, fitted-input predictions, or ansatz smuggling appear in the derivation chain.
Axiom & Free-Parameter Ledger
free parameters (1)
- learnable filter coefficients
axioms (1)
- domain assumption Transformer models exhibit a bias toward low-frequency components in time-series data
discussion (0)
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