Fourier Feature Regression Eval

fourier-feature-regression-eval

Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains — Tancik et al. (2020) (arXiv:2006.10739, 2020)

What this evaluates

Evaluates how well coordinate-based MLPs with different input feature mappings (none, basic, positional encoding, Gaussian random Fourier features) can learn high-frequency functions across various low-dimensional regression tasks in computer vision and graphics.

Datasets

• Natural images — total ?; splits: train (-1), test (-1)
• Text images — total ?; splits: train (-1), test (-1)
• 3D shape — total ?; splits: train (-1), test (-1)
• Shepp-Logan phantoms — total ?; splits: train (-1), test (-1)
• ATLAS dataset — total ?; splits: train (-1), test (-1)
• NeRF ATLAS scene — total ?; splits: train (-1), test (-1)

Metrics

• PSNR (primary) — range: dB
  • Peak Signal-to-Noise Ratio computed from the mean squared error between predicted and ground truth values. Higher is better.
• IoU (primary) — range: [0, 1]
  • Intersection over Union between predicted binary occupancy and ground truth occupancy on points sampled near the mesh surface. Higher is better.

Input / output format

Input: 2D or 3D spatial coordinates (pixel or voxel locations) passed to a coordinate-based MLP.

Output: Continuous values (RGB color, volume density, or atomic response) or binary occupancy (0/1), depending on the task.

Scoring recipe

if task == '3D_shape':
    pred_occ = sigmoid(mlp_output) > 0.5
    iou = intersection(pred_occ, gold_occ) / union(pred_occ, gold_occ)
    return iou
else:
    mse = mean_squared_error(pred_vals, gold_vals)
    max_val = max(gold_vals) # or 255 for images
    psnr = 10 * log10(max_val**2 / mse)
    return psnr

Common pitfalls

• Direct vs indirect supervision: Direct tasks use ground truth labels per coordinate, while indirect tasks pass network outputs through a forward model (e.g., integral projection, Fourier transform, volume rendering) before computing loss.
• The scale parameter (σ) for Fourier feature mappings is highly task-dependent and requires hyperparameter sweeping; the paper notes scale is more critical than the distribution shape.
• PSNR is the standard metric for all tasks except 3D shape regression, which exclusively uses IoU.

Evidence (verbatim from paper)

All results are reported in PSNR except 3D shape, which uses IoU (higher is better for all).

Citation

@misc{tancik2020fourier,
  title={Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains},
  author={Tancik et al. (2020)},
  year={2020},
  note={arXiv:2006.10739}
}

• arXiv: 2006.10739