Research map / Time series / Long-term forecasting
Affirm: Interactive Mamba with Adaptive Fourier Filters for Long-term Time Series Forecasting
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Affirm, a lightweight time series forecaster combining an adaptive Fourier filter block (learnable thresholds plus global/local filters) with an interactive dual Mamba block, and reports SOTA-level accuracy with lower compute than Transformers.
Problem
Long-term time series forecasting (LTSF) where Transformers are computationally expensive, noise-sensitive, and overfit on small datasets, while linear and CNN models struggle with complex noisy data and long-range dependencies.
Approach
Replaces self-attention and feed-forward layers with an adaptive Fourier filter block (learnable low/high-pass thresholds and global/local frequency filters) and an interactive dual Mamba block using causal convolutions of two kernel sizes that cross-modulate each other, plus masked-autoencoder pretraining.
Key results
- Affirm achieves ETTh1 average MSE 0.411 vs PatchTST's 0.423 and Time-LLM's 0.408, with 9.78e+07 FLOPS versus Time-LLM's 7.3e+12.
- On Electricity (look-back 96, horizon 720), Affirm reaches MSE 0.216 with 1.7M parameters and 1.72G MACs, cutting MACs by 66.1% vs PatchTST.
- Ablation on ETTh1 shows removing AFFB raises average MSE from 0.411 to 0.434, and removing IDMB raises it to 0.423.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add IDMB (ablation) | Affirm · ETTh1 (avg.) | MSE: 0.423 -> 0.411 | Helped |
| Add AFFB (ablation) | Affirm · ETTh1 (avg.) | MSE: 0.434 -> 0.411 | Helped |
| Add LPF (ablation) | Affirm · ETTh1 (avg.) | MSE: 0.421 -> 0.411 | Helped |
| Add HPF (ablation) | Affirm · ETTh1 (avg.) | MSE: 0.417 -> 0.411 | Helped |
| Add LPF and HPF (ablation) | Affirm · ETTh1 (avg.) | MSE: 0.422 -> 0.411 | Helped |
| Add self-supervised pretraining (ablation) | Affirm · ETTh1 (avg.) | MSE: 0.415 -> 0.411 | Helped |
| Use Affirm instead of PatchTST | ETTh1 · ETTh1 (avg.) | MSE: 0.428 -> 0.411 | Helped |
| Use Affirm instead of PatchTST | Electricity · Electricity (avg.) | MSE: 0.167 -> 0.157 | Helped |
| Use Affirm instead of PatchTST | ETTm2 · ETTm2 (avg.) | MSE: 0.264 -> 0.252 | Helped |
| Use Affirm instead of Dlinear | Exchange · Exchange (avg.) | MSE: 0.297 -> 0.356 | Hurt |
| Use Affirm instead of Time-LLM | ETTm1 · ETTm1 (avg.) | MSE: 0.329 -> 0.344 | Hurt |
Surprising findings
- Vanilla Mamba substituted into PatchTST underperforms on lower-frequency datasets such as ETTh2 and Exchange, though it is comparable on Weather and ETTm1.
Limitations
- Time-LLM (LLaMA-7B-based) achieves slightly better accuracy on several benchmarks, requiring far more compute.
- Only evaluated on standard multivariate LTSF benchmarks with a fixed look-back per dataset.
Experimental setup
Datasets: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Exchange Traffic Weather
Benchmarks: ETTh1 ETTh2 ETTm1 ETTm2 Electricity Exchange Traffic Weather
Metrics: MSE MAE MACs parameters
Baselines: iTransformer PatchTST Crossformer DLinear RLinear TimeMixer TSLANet DTMamba Time-LLM GPT4TS
Builds on: Mamba PatchTST FiLM FreTS TSLANet
Closest papers by meaning
- Unlocking the Power of Patch: Patch-Based MLP for Long-Term Time Series Forecasting (AAAI 2025 · similarity 0.88)
- ARM: Refining Multivariate Forecasting with Adaptive Temporal-Contextual Learning (ICLR 2024 · similarity 0.88)
- Rethinking Fourier Transform from A Basis Functions Perspective for Long-term Time Series Forecasting (NeurIPS 2024 · similarity 0.87)
- CFPT: Empowering Time Series Forecasting through Cross-Frequency Interaction and Periodic-Aware Timestamp Modeling (ICML 2025 · similarity 0.87)
- OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain (NeurIPS 2025 · similarity 0.87)
- Towards a General Time Series Forecasting Model with Unified Representation and Adaptive Transfer (ICML 2025 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.