# Discrete Mode Decomposition Meets Shapley Value for Robust Signal Prediction in Tactile Internet [](https://opensource.org/licenses/MIT)[](https://www.python.org/downloads/)[](https://pytorch.org/)[](https://infocom2026.ieee-infocom.org/) ## 🏆 Accepted at IEEE INFOCOM 2026 **Authors:** Ali Vahedi and Qi Zhang **Affiliation:** DIGIT and Department of Electrical and Computer Engineering, Aarhus University, Denmark **Acknowledgments:** This research was supported by:- TOAST project, funded by the European Union's Horizon Europe research and innovation program under the Marie Skłodowska-Curie Actions Doctoral Network (Grant Agreement No. 101073465)- Danish Council for Independent Research project eTouch (Grant No. 1127-00339B)- NordForsk Nordic University Cooperation on Edge Intelligence (Grant No. 168043) --- ## 📖 Abstract The Tactile Internet (TI) requires ultra-low latency and high reliability to ensure stability and transparency in touch-enabled teleoperation. However, variable delays and packet loss present significant challenges to maintaining immersive haptic communication. This work proposes a novel predictive framework that integrates **Discrete Mode Decomposition (DMD)** with **Shapley Mode Value (SMV)** for accurate and timely haptic signal prediction. - **DMD** decomposes haptic signals into interpretable intrinsic modes- **SMV** evaluates each mode's contribution to prediction accuracy, aligned with goal-oriented semantic communication- Combined **DMD+SMV** accelerates inference, enabling efficient communication and smooth teleoperation ### Key Results| Method | 1-Sample Accuracy | 100-Sample Accuracy | 1-Sample Latency | 100-Sample Latency ||--------|-------------------|---------------------|------------------|---------------------|| **DMD+SMV (Ours)** | **98.9%** | **92.5%** | **0.056ms** | **2ms** || DMD | 96.9% | 90.0% | 0.05ms | 6.91ms || Baseline | 73.6% | 67.3% | 0.04ms | 1640.76ms | --- ## 🏗️ Project Structure ```dmd-smv-tactile-internet/├── README.md # This file├── LICENSE # MIT License├── requirements.txt # Python dependencies├── setup.py # Package installation├── pyproject.toml # Modern Python packaging│├── configs/ # Configuration files│ ├── default_config.yaml # Default training configuration│ ├── transformer_config.yaml # Transformer-specific settings│ ├── resnet_config.yaml # ResNet-specific settings│ └── lstm_config.yaml # LSTM-specific settings│├── src/ # Source code│ ├── __init__.py│ ├── dmd/ # Discrete Mode Decomposition│ │ ├── __init__.py│ │ ├── decomposition.py # Core DMD algorithm│ │ ├── wiener_filter.py # Discrete Wiener filtering│ │ ├── hilbert_transform.py # Discrete Hilbert transform│ │ └── optimization.py # ADMM optimization│ ││ ├── smv/ # Shapley Mode Value│ │ ├── __init__.py│ │ ├── shapley_value.py # Shapley value computation│ │ ├── monte_carlo.py # Monte Carlo approximation│ │ └── mode_valuation.py # Mode valuation utilities│ ││ ├── models/ # Neural Network architectures│ │ ├── __init__.py│ │ ├── transformer.py # Transformer architecture│ │ ├── resnet.py # ResNet-32 architecture│ │ ├── lstm.py # LSTM architecture│ │ └── base_model.py # Base model class│ ││ ├── data/ # Data handling│ │ ├── __init__.py│ │ ├── dataset.py # Dataset classes│ │ ├── dataloader.py # DataLoader utilities│ │ └── preprocessing.py # Data preprocessing│ ││ ├── training/ # Training utilities│ │ ├── __init__.py│ │ ├── trainer.py # Main training loop│ │ ├── losses.py # Loss functions│ │ └── callbacks.py # Training callbacks│ ││ ├── evaluation/ # Evaluation utilities│ │ ├── __init__.py│ │ ├── metrics.py # Accuracy, PSNR, etc.│ │ ├── inference.py # Inference engine│ │ └── benchmarks.py # Benchmarking utilities│ ││ └── utils/ # Utility functions│ ├── __init__.py│ ├── logger.py # Logging utilities│ ├── visualization.py # Plotting and visualization│ ├── config.py # Configuration management│ └── seed.py # Reproducibility utilities│├── experiments/ # Experiment scripts│ ├── train_all_models.py # Train all architectures│ ├── evaluate_accuracy.py # Accuracy evaluation│ ├── evaluate_inference.py # Inference time evaluation│ ├── ablation_study.py # Ablation studies│ └── generate_figures.py # Generate paper figures│├── scripts/ # Utility scripts│ ├── download_data.py # Download dataset│ ├── prepare_data.py # Prepare data for training│ └── run_experiments.sh # Run all experiments│├── tests/ # Unit tests│ ├── test_dmd.py # Test DMD module│ ├── test_smv.py # Test SMV module│ ├── test_models.py # Test neural networks│ └── test_metrics.py # Test evaluation metrics│├── notebooks/ # Jupyter notebooks│ ├── 01_data_exploration.ipynb│ ├── 02_dmd_visualization.ipynb│ ├── 03_smv_analysis.ipynb│ └── 04_results_analysis.ipynb│├── results/ # Results storage│ ├── figures/ # Generated figures│ └── logs/ # Training logs│└── docs/ # Documentation ├── installation.md ├── usage.md └── api_reference.md``` --- ## 🚀 Quick Start ### Installation ```bash# Clone the repositorygit clone https://github.com/alivahedi/dmd-smv-tactile-internet.gitcd dmd-smv-tactile-internet # Create virtual environmentpython -m venv venvsource venv/bin/activate # On Windows: venv\Scripts\activate # Install dependenciespip install -r requirements.txt # Install package in development modepip install -e .``` ### Download Dataset ```bash# Download the Kinaesthetic Interactions Datasetpython scripts/download_data.py``` ### Quick Training Example ```pythonfrom src.dmd import DiscreteModeDcompositionfrom src.smv import ShapleyModeValuefrom src.models import TransformerPredictorfrom src.training import Trainer # Initialize DMDdmd = DiscreteModeDcomposition(noise_variance=0.01) # Decompose signalmodes, center_frequencies = dmd.decompose(signal) # Compute Shapley Mode Valuessmv = ShapleyModeValue()mode_values = smv.compute(modes, model, validation_data) # Train Transformer with important modestrainer = Trainer(model=TransformerPredictor(), config=config)trainer.train(train_data, val_data)``` ### Run Full Experiment Pipeline ```bash# Run all experimentsbash scripts/run_experiments.sh # Or run individual experimentspython experiments/train_all_models.py --config configs/default_config.yamlpython experiments/evaluate_accuracy.py --checkpoint best_model.ptpython experiments/generate_figures.py --output results/figures/``` --- ## 📊 Reproducing Paper Results ### Training All Models ```bashpython experiments/train_all_models.py \ --architectures transformer resnet lstm \ --methods baseline dmd dmd_smv \ --window_sizes 1 5 10 25 50 100 \ --epochs 200 \ --seed 42``` ### Generate Main Results Figure (Figure 3) ```bashpython experiments/generate_figures.py \ --figure accuracy_inference \ --output results/figures/figure3.pdf``` ### Ablation Study (Mode Update Frequency) ```bashpython experiments/ablation_study.py \ --update_intervals 40 90 100 \ --architecture transformer \ --output results/ablation/``` --- ## 📈 Results ### Accuracy Comparison (Figure 3) Our DMD+SMV framework achieves:- **98.9%** accuracy for 1-sample prediction (Transformer)- **92.5%** accuracy for 100-sample prediction (Transformer)- **820× speedup** compared to baseline methods ### PSNR Results (Figure 4) - **29.5 dB** PSNR at W=1 for human side- **27.5 dB** PSNR at W=1 for robot side- Consistent **9-10 dB improvement** over baseline across all horizons ### Inference Time (Table I & II) | Architecture | DMD+SMV | DMD | Baseline ||--------------|---------|-----|----------|| Transformer | 2.85ms | 7.30ms | 1640ms || ResNet-32 | 4.30ms | 10.45ms | 2059ms || LSTM | 6.00ms | 15.2ms | 2616ms | ### FLOPs and FLOPS Comparison (Table III) | Architecture | FLOPs (DMD) | FLOPs (DMD+SMV) | FLOPS (DMD) | FLOPS (DMD+SMV) ||--------------|-------------|-----------------|-------------|-----------------|| LSTM | 3.4×10⁷ | 2.1×10⁶ | 2.24×10⁹ | 0.35×10⁹ || ResNet-32 | 11.2×10⁷ | 8.6×10⁶ | 10.72×10⁹ | 2×10⁹ || Transformer | 19.3×10⁷ | 14.8×10⁶ | **26.4×10⁹** | **5.19×10⁹** | --- ## 🔗 Links - **Paper:** IEEE INFOCOM 2025 Proceedings- **Code:** [github.com/Ali-Vahedifar/Discrete-Mode-Decomposition](https://github.com/Ali-Vahedifar/Discrete-Mode-Decomposition.git)- **Dataset:** [Kinaesthetic Interactions Dataset (Zenodo)](https://doi.org/10.5281/zenodo.14924062) --- ## 🔧 Configuration ### Default Configuration ```yaml# configs/default_config.yamltraining: epochs: 200 batch_size: 64 learning_rate: 0.001 lr_decay_epochs: [80, 120, 170] lr_decay_factor: 0.005 dropout: 0.1 dmd: noise_variance: 0.01 epsilon1: 1e-6 epsilon2: 1e-6 kappa1: 1e-3 kappa2: 1e-3 smv: tolerance: 0.01 max_iterations: 1000 evaluation: window_sizes: [1, 5, 10, 25, 50, 100] num_runs: 10``` --- ## 📚 Citation If you use this code in your research, please cite our paper: ```bibtex@inproceedings{vahedifar2025dmd, title={Discrete Mode Decomposition Meets Shapley Value: Robust Signal Prediction in Tactile Internet}, author={Vahedifar, Mohammad Ali and Zhang, Qi}, booktitle={IEEE INFOCOM 2026 - IEEE Conference on Computer Communications}, year={2026}, organization={IEEE}}``` --- ## 📧 Contact - **Ali Vahedi**: av@ece.au.dk **Institution:** DIGIT and Department of Electrical and Computer Engineering, Aarhus University, Denmark --- ## 📄 License This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details. --- ## 🙏 Acknowledgments - [TOAST Doctoral Network](https://toast-dn.eu/) - EU Horizon Europe Program- [Danish Council for Independent Research](https://dff.dk/) - eTouch Project- [NordForsk](https://www.nordforsk.org/) - Nordic Edge Intelligence Cooperation- [Kinaesthetic Interactions Dataset](https://doi.org/10.5281/zenodo.14924062) --- ## 📜 Changelog ### v1.0.0 (2026)- Initial release- Full implementation of DMD and SMV algorithms- Support for Transformer, ResNet-32, and LSTM architectures- Comprehensive evaluation framework- Paper reproduction scripts