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Differentiable and Learnable Wireless Simulation with Geometric Transformers
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Introduces Wi-GATr, an E(3)-equivariant Geometric Algebra Transformer with a wireless-specific GA tokenizer that serves as a fully learnable neural surrogate for wireless channel prediction, inverse localization, and diffusion-based scene reconstruction.
Problem
Wireless ray tracing simulators are limited by modelling assumptions and parameter accuracy, while existing fully-learnt neural surrogates rely on 2D image representations that are lossy and not differentiable w.r.t. antenna pose, and are sample-inefficient.
Approach
Tokenize wireless scenes (mesh faces, antennas, links) into projective geometric algebra elements and process them with an E(3)-equivariant GATr transformer, yielding a differentiable, sample-efficient, symmetry-robust surrogate that can also serve as a score network for a DDPM for inverse problems.
Key results
- On WiPTR, Wi-GATr reaches 0.41 dB MAE on unseen floor plans vs 0.69 for Transformer and 1.28 for PLViT with full data.
- Wi-GATr is invariant to rotation/translation (MAE 0.74 dB on Wi3R under rotations vs 78.68 dB for the Transformer).
- On real DICHASUS measurements, Wi-GATr outperforms hybrid methods by >35% and a calibrated ray tracer by >70% in error.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | wireless signal prediction · Wi3R unseen floor plans | MAE (dB): 1.32 -> 0.74 | Helped |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | wireless signal prediction · WiPTR unseen floor plans | MAE (dB): 0.69 -> 0.41 | Helped |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | wireless signal prediction · WiPTR OOD layout | MAE (dB): 0.86 -> 0.43 | Helped |
| use the SEGNN equivariant model instead of Wi-GATr | wireless signal prediction · Wi3R OOD layout | MAE (dB): 2.34 -> 7.03 | Hurt |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | diffusion model · canonicalized scenes: signal prediction | variational upper bound on negative log likelihood: 3.00 -> 1.62 | Helped |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | diffusion model · canonicalized scenes: receiver localization | variational upper bound on negative log likelihood: 8.28 -> 3.64 | Helped |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | diffusion model · canonicalized scenes: geometry reconstruction | variational upper bound on negative log likelihood: -3.61 -> -3.95 | Helped |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | diffusion model · arbitrary rotations: receiver localization | variational upper bound on negative log likelihood: 105.68 -> 3.64 | Helped |
| use the Wi-GATr equivariant architecture instead of a vanilla transformer | diffusion model · arbitrary rotations: geometry reconstruction | variational upper bound on negative log likelihood: 389.34 -> -3.95 | Helped |
| train the transformer diffusion model with random-rotation data augmentation (ablation) | Transformer diffusion model · arbitrary rotations: signal prediction | variational upper bound on negative log likelihood: 9.57 -> 17.65 | Hurt |
| train the transformer diffusion model with random-rotation data augmentation (ablation) | Transformer diffusion model · arbitrary rotations: receiver localization | variational upper bound on negative log likelihood: 105.68 -> 14.45 | Helped |
| train the transformer diffusion model with random-rotation data augmentation (ablation) | Transformer diffusion model · arbitrary rotations: geometry reconstruction | variational upper bound on negative log likelihood: 389.34 -> -2.34 | Helped |
Surprising findings
- A vanilla Transformer with data augmentation performs far worse than the non-augmented one on the diffusion tasks (e.g., 15.66 vs 3.00 on canonicalized signal prediction).
- Sionna RT is inaccurate for indoor WiPTR scenes because it lacks transmissions and higher-order diffraction, despite being very fast.
Limitations
- Learnable approaches need training data and data collection overhead, unlike model-based simulators.
- Less configurable than model-based ray tracers, with many configuration choices learned implicitly.
- Diffusion-based geometry generation shows about 26% line-of-sight intersection error on generated scenes.
Experimental setup
Datasets: Wi3R WiPTR ProcTHOR-10k Wi3Rooms DICHASUS
Benchmarks: Wi3R WiPTR DICHASUS
Metrics: mean absolute error (dB) variational lower bound on NLL localization error relative delay spread error
Baselines: Transformer Transformer without tokenizer SEGNN PLViT Learned Materials Neural Materials Wireless InSite Sionna RT
Builds on: GATr DDPM SEGNN PLViT
Closest papers by meaning
- Physics Unrolled Neural Operator for Wireless Field Modeling (NeurIPS 2026 · similarity 0.85)
- Radio Frequency Ray Tracing with Neural Object Representation for Enhanced RF Modeling (CVPR 2025 · similarity 0.84)
- RxGS: Receiver-Generalizable 3D Gaussian Splatting for Radio-Frequency Data Synthesis (NeurIPS 2026 · similarity 0.83)
- GSRF: Complex-Valued 3D Gaussian Splatting for Efficient Radio-Frequency Data Synthesis (NeurIPS 2025 · similarity 0.83)
- NeWRF: A Deep Learning Framework for Wireless Radiation Field Reconstruction and Channel Prediction (ICML 2024 · similarity 0.83)
- GeRaF: Neural Geometry Reconstruction from Radio Frequency Signals (NeurIPS 2025 · similarity 0.82)
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