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MIRE: Matched Implicit Neural Representations
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Proposes MIRE, which greedily selects a per-layer activation function from a dictionary of seven parametric activation atoms (Sinc, RC, RRC, PSWF, Gabor, Gaussian, sinusoid) to build a signal-matched implicit neural representation.
Problem
INRs typically use a single fixed activation function across all layers, and their activation parameters require exhaustive per-signal grid searches before training, limiting representation power and generalization.
Approach
Builds a layer-wise activation sequence by matching pursuit-style dictionary learning: for each new hidden layer, every activation atom in the dictionary is trained with trainable parameters, the lowest-MSE atom is locked in, and the process repeats, so the INR is matched to the signal and parameter grid search is avoided.
Key results
- On Kodak image representation, MIRE achieves the highest PSNR and SSIM among compared INRs (WIRE, SIREN, GAUSS, MFN), with the Parrot example's matched sequence being Sinc, Gaussian, Gabor Wavelet.
- On occupancy field representation, MIRE attains the highest IoU on Stanford Lucy and Thai Statue, recovering finer high-frequency detail than WIRE and SIREN.
- MIRE gives consistent PSNR across random activation-parameter initialization distributions, whereas WIRE and SIREN perform well only under narrow initialization ranges.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use signal-matched activation functions selected from the dictionary | MIRE · Image representation (Kodak) | PSNR | Helped |
| use signal-matched activation functions selected from the dictionary | MIRE · Image inpainting (Kodak) | PSNR | Helped |
| use signal-matched activation functions selected from the dictionary | MIRE · Stanford Lucy and Thai Statue occupancy fields | IoU | Helped |
| use signal-matched activation functions selected from the dictionary | MIRE · Chair and Hotdog novel view synthesis | performance metrics | Helped |
| vary activation-parameter initialization across uniform and normal distributions (ablation) | MIRE · Parrot image representation | PSNR consistency | Helped |
| initialize activation parameters from U(−10, 10) (ablation) | WIRE · Parrot image representation | PSNR | Mixed |
| initialize activation parameters from U(−100, 100) (ablation) | SIREN · Parrot image representation | PSNR | Helped |
Surprising findings
- Existing INRs such as WIRE and SIREN are highly sensitive to the activation-parameter initialization distribution, performing well only under specific ranges.
Limitations
- Greedy layer-wise search trains each atom for a fixed number of epochs per layer, so the search cost scales with dictionary size and depth.
- Discretized approximation of PSWFs via natural cubic spline is used rather than closed-form functions.
Experimental setup
Datasets: Kodak Stanford 3D (Thai Statue, Stanford Lucy) NeRF Chair NeRF Hotdog
Benchmarks: Kodak Stanford 3D Thai Statue Stanford Lucy NeRF Chair NeRF Hotdog
Metrics: PSNR SSIM IoU
Baselines: WIRE SIREN GAUSS MFN INCODE FINER
Builds on: SIREN WIRE GAUSS NeRF MFN
Closest papers by meaning
- VI^3NR: Variance Informed Initialization for Implicit Neural Representations (CVPR 2025 · similarity 0.89)
- Implicit Representations via Operator Learning (ICML 2024 · similarity 0.89)
- A sampling theory perspective on activations for implicit neural representations (ICML 2024 · similarity 0.89)
- Implicit Neural Representations and the Algebra of Complex Wavelets (ICLR 2024 · similarity 0.88)
- Learning Transferable Features for Implicit Neural Representations (NeurIPS 2024 · similarity 0.88)
- ReLUs Are Sufficient for Learning Implicit Neural Representations (ICML 2024 · similarity 0.87)
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