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STanHop: Sparse Tandem Hopfield Model for Memory-Enhanced Time Series Prediction
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Proposes STanHop-Net, a sparse tandem Hopfield network with a generalized sparse Hopfield (Tsallis alpha-entmax) layer and plug-in external memory modules for multivariate time series forecasting.
Problem
Multivariate time series prediction is hard due to noise and cross-series dependencies, and existing models respond slowly to sudden or rare events.
Approach
Generalizes the sparse modern Hopfield model by replacing the Gini entropy with Tsallis alpha-entropy so sparsity is learnable; stacks two tandem GSH sub-blocks (temporal and cross-series) with coarse-graining, and adds Plug-and-Play and Tune-and-Play external memory modules that retrieve from task-relevant memory sets.
Key results
- STanHop-Net ranks first or second in 47 of 58 settings against baselines including Crossformer and DLinear, with mean MSE/MAE over 10 runs.
- TuneMemory yields improvements such as -6.9% MSE on ILI OT at horizon 24 and -3.4% on ETTh1 at horizon 24.
- PlugMemory and TuneMemory give average performance boosts of about 12% and 3% respectively, per the conclusion.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use STanHop-Net instead of the strongest listed baseline | STanHop-Net · ETTh1, horizon 24 | MSE: 0.312 -> 0.294 | Helped |
| Use STanHop-Net instead of the strongest listed baseline | STanHop-Net · ETTm1, horizon 24 | MSE: 0.211 -> 0.195 | Helped |
| Use STanHop-Net instead of the strongest listed baseline | STanHop-Net · ECL, horizon 48 | MSE: 0.155 -> 0.152 | Helped |
| Use STanHop-Net instead of the strongest listed baseline | STanHop-Net · WTH, horizon 24 | MSE: 0.294 -> 0.292 | Helped |
| Use STanHop-Net instead of the strongest listed baseline | STanHop-Net · ILI, horizon 24 | MSE: 2.687 -> 3.121 | Hurt |
| Use STanHop-Net instead of the strongest listed baseline | STanHop-Net · Traffic, horizon 24 | MSE: 0.351 -> 0.505 | Hurt |
| Add task-relevant TuneMemory | STanHop-Net · ILI OT, horizon 12 | MSE: 4.011 -> 3.975 (-0.9%) | Helped |
| Use randomly selected bad external memory instead of task-relevant memory (ablation) | STanHop-Net · ILI OT, horizon 12 | MSE: 4.011 -> 4.340 (+8.2%) | Hurt |
| Add task-relevant TuneMemory | STanHop-Net · ILI OT, horizon 24 | MSE: 4.254 -> 3.960 (-6.9%) | Helped |
| Use randomly selected bad external memory instead of task-relevant memory (ablation) | STanHop-Net · ILI OT, horizon 24 | MSE: 4.254 -> 4.271 (+0.4%) | No clear effect |
| Add task-relevant TuneMemory | STanHop-Net · ILI OT, horizon 60 | MSE: 3.613 -> 3.572 (-1.1%) | Helped |
| Use randomly selected bad external memory instead of task-relevant memory (ablation) | STanHop-Net · ILI OT, horizon 60 | MSE: 3.613 -> 3.821 (+5.8%) | Hurt |
Surprising findings
- Randomly chosen ('bad') external memory sets can degrade performance, with TuneMemory-(b) increasing MSE by up to 8.2% on ILI OT.
Limitations
- Effectiveness of external memory depends on relevance of the memory set, requiring human effort and domain expertise.
- Generalized sparse Hopfield model has O(d^2) complexity.
Experimental setup
Datasets: ETTh1 ETTm1 Weather ECL ILI Traffic
Benchmarks: ETTh1 ETTm1 WTH ECL ILI Traffic
Metrics: MSE MAE
Baselines: FEDformer DLinear Informer Autoformer Crossformer Hopfield-based STanHop-Net (D) STanHop-Net (S)
Builds on: modern Hopfield model sparse modern Hopfield model Crossformer PatchTST
Closest papers by meaning
- TimePerceiver: An Encoder-Decoder Framework for Generalized Time-Series Forecasting (NeurIPS 2025 · similarity 0.85)
- Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts (ICLR 2025 · similarity 0.85)
- SynTSBench: Rethinking Temporal Pattern Learning in Deep Learning Models for Time Series (NeurIPS 2025 · similarity 0.85)
- Segment, Shuffle, and Stitch: A Simple Layer for Improving Time-Series Representations (NeurIPS 2024 · similarity 0.84)
- Sparse and Structured Hopfield Networks (ICML 2024 · similarity 0.84)
- TempoPFN: Synthetic Pre-training of Linear RNNs for Zero-shot Time Series Forecasting (NeurIPS 2026 · similarity 0.84)
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