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Experiments

The paper's experiments are one protocol applied to three tasks, documented in enough detail to rerun them.

  • Benchmarks

    Every model's size, costs and final metrics on all three tasks, with convergence plots and qualitative comparisons.

  • Ablations

    FUTON's basis, bandwidth, rank, combiner and head, varied one at a time on images.

  • Reproducing the paper

    The data, the training scripts and their configs, and the run directories that hold every result.

The protocol at a glance

Task Signals Budget Steps One step sees Schedule Scored on
Images 24 Kodak images about 197k 1000 the whole image cosine, to a hundredth all pixels
Occupancy 5 Stanford shapes about 131k 1000 \(2^{18}\) random voxels cosine, to a hundredth all voxels
Radiance fields 8 Blender scenes about 74k, its color network included 25,000 4096 rays exponential, to a tenth (torch-ngp's recipe) all 200 test views

Every model of a task follows the same rules:

  • Hyperparameters. Those of its authors' code, wherever the budget allows them.
  • FUTON's size. Its components per axis and head are chosen per task on the data its baselines were tuned on: half the resolution and 64 units on images and radiance fields, where FUTON reads its basis from a table of 2048 points per axis, and half the resolution and a linear head on volumes. Its CP rank is the largest multiple of 5 that keeps it smaller than every baseline. The bandwidth and head ablations show the choice on images.
  • Learning rate. From the grid {3e-1, 1e-1, 3e-2, 1e-2, 3e-3, 1e-3, 3e-4, 1e-4}, chosen on two signals of the task.
  • Optimizer. PyTorch's default Adam.
  • Run. Seed 0 on an NVIDIA A100, the model compiled with torch.compile in a warm-up pass that keeps compilation out of the clock.
  • Costs. From the same runs: the training time counts the training steps alone, every evaluation records how long it took and its peak memory, and every training step its own peak. Each cost in the tables is the median over the signals of a task, so a run slowed by other work on its GPU does not move it.
  • Metrics. On the full signal, LPIPS with its VGG network. The tables report the mean over the signals of a task with a within-signal standard error (a plain one for IoU, which saturates on every shape), the best value in bold and the second in italics.