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Learning a Compressed Sensing Measurement Matrix via Gradient Unrolling
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the averaged predictions from nearest neighbors and the ℓ1-AE decoder for label embedding predictions (ablation) | ℓ1-AE label embeddings · EURLex-4K and Wiki10-31K | P@1: 0.8062 vs 0.7949; 0.8617 vs 0.8560 | Helped |
| Use the averaged predictions from nearest neighbors and the ℓ1-AE decoder instead of SLEEC | Extreme multi-label prediction · EURLex-4K and Wiki10-31K, 1 model | P@1: 0.7600 -> 0.8062; 0.8356 -> 0.8617 | Helped |
| Use the ℓ1-min pos decoder instead of the learned neural decoder (ablation) | ℓ1-AE · Synthetic1 and Amazon | test RMSE: 0.465 -> 0.357; 0.638 -> 0.387; 0.129 -> 9.9e-3; 0.599 -> 0.023; 0.118 -> 1.4e-15; 0.565 -> 2.8e-15 | Helped |
| Increase the unrolled decoder depth (ablation) | ℓ1-AE + ℓ1-min pos · Synthetic1, 20 and 30 measurements | test RMSE: 0.097 -> 0.063 -> 9.6e-16; 9.9e-3 -> 1.2e-15 | Helped |
| Learn the measurement matrix from training samples | ℓ1-AE + ℓ1-min pos · Synthetic data with no extra structure | test RMSE: 0.8084 vs 0.8187; 0.1901 vs 0.1955; 0.0016 vs 0.0003 | No clear effect |
| Replace the projected-subgradient unrolling with ISTA unrolling (ablation) | Autoencoder measurement learning · Synthetic1, 10 measurements | test RMSE: 0.894 vs 0.465; 0.795 vs 0.357 | Hurt |
| Add a positivity constraint to ℓ1-minimization for nonnegative inputs (ablation) | ℓ1-min decoder · Nonnegative sparse recovery | recovery performance | Helped |
| Add a positivity constraint to model-based CoSaMP (ablation) | Model-based CoSaMP · Nonnegative structured sparse recovery | recovery performance | Helped |
| Use an ℓ1-AE-learned matrix with model-based CoSaMP instead of a Gaussian matrix | Model-based CoSaMP pos · Structured sparse recovery | recovery performance | Helped |
Closest papers by meaning
- The Price of Sparsity: Sufficient Conditions for Sparse Recovery using Sparse and Sparsified Measurements (NeurIPS 2025 · similarity 0.88)
- Non-Convex Tensor Recovery from Local Measurements (AAAI 2025 · similarity 0.87)
- Compressed Sensing using Generative Models (ICML 2017 · similarity 0.87)
- A Data-Driven and Distributed Approach to Sparse Signal Representation and Recovery (ICLR 2019 · similarity 0.87)
- Gradient Compressed Sensing: A Query-Efficient Gradient Estimator for High-Dimensional Zeroth-Order Optimization (ICML 2024 · similarity 0.86)
- A Unified Framework for Learning with Nonlinear Model Classes from Arbitrary Linear Samples (ICML 2024 · similarity 0.86)
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