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The Unreasonable Effectiveness of Linear Prediction as a Perceptual Metric
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Proposes LASI, a data-free, training-free full-reference perceptual similarity metric built from inference-time pixel-level weighted least squares autoregressive embeddings, competitive with LPIPS and PIM on BAPPS.
Problem
Full-reference image quality assessment needs perceptual similarity metrics aligned with human judgments, but current best methods rely on deep features trained on large data or annotated human judgments.
Approach
Construct per-pixel perceptual embeddings by solving a weighted least squares autoregressive prediction problem over a causal neighborhood at inference time, with L2 distance between embeddings averaged over pixels as the similarity; no training, no data, no deep features, and fully differentiable.
Key results
- LASI scores 73.8 on BAPPS-2AFC Traditional vs 61.2 for MS-SSIM and 75.7 for PIM, and 81.4 on CNN vs LPIPS 83.7.
- On BAPPS-JND Traditional, LASI reaches 55.9 mAP vs 36.2 for MS-SSIM and 46.9 for LPIPS (fts. only).
- In the worst case LASI is within 5.8% of the best unsupervised method, with no training or data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase LASI neighborhood size N (ablation) | LASI · BAPPS-2AFC | score | Helped |
| Increase LASI neighborhood size N (ablation) | LASI · BAPPS-2AFC | WLS prediction loss | Helped |
| Compute the WLS problem separately for each channel and average the results (ablation) | LASI · downstream perceptual tasks | performance | Hurt |
| Use LASI instead of MS-SSIM | BAPPS-2AFC Traditional · BAPPS-2AFC Traditional | score: 20.6% | Helped |
| Use LASI instead of MS-SSIM | LASI · BAPPS-2AFC categories | score: 20.6%; 2.6%; 8.7%; 2.7%; 8.4%; 8.7% | Helped |
| Use LASI instead of MS-SSIM | BAPPS-JND CNN · BAPPS-JND CNN | mAP: -0.9% | No clear effect |
| Use LASI instead of MS-SSIM | BAPPS-JND Traditional · BAPPS-JND Traditional | mAP: 54.4% | Helped |
Surprising findings
- Increasing the embedding dimensionality (neighborhood size) consistently improves both the WLS prediction loss and perceptual 2-AFC performance, unlike learned deep features where classification accuracy can correlate negatively with perception.
Limitations
- Benchmarked mainly on small 64x64 patches from BAPPS, so generalization to larger images or other datasets is unclear.
- Computational cost grows cubically with embedding dimensionality.
Experimental setup
Datasets: BAPPS
Benchmarks: BAPPS-2AFC BAPPS-JND
Metrics: 2-AFC agreement score mean average precision
Baselines: LPIPS PIM A-DISTS MS-SSIM L2
Builds on: MS-SSIM LPIPS Maximum Differentiation competition lossless compression with weighted least squares prediction
Closest papers by meaning
- Perception Encoder: The best visual embeddings are not at the output of the network (NeurIPS 2025 · similarity 0.87)
- Discriminating image representations with principal distortions (ICLR 2025 · similarity 0.87)
- Perceptual Inductive Bias Is What You Need Before Contrastive Learning (CVPR 2025 · similarity 0.86)
- Multidimensional Observer Model and Perceptual Dimensions of Human Image Quality Assessment (NeurIPS 2026 · similarity 0.86)
- Towards flexible perception with visual memory (ICML 2025 · similarity 0.85)
- LipSim: A Provably Robust Perceptual Similarity Metric (ICLR 2024 · similarity 0.85)
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