On Optimal Sampling for Learning SDF Using MLPs Equipped With Positional Encoding
Bibliographic record
Abstract
Neural implicit fields, such as the neural signed distance field (SDF) of a shape, have emerged as a powerful representation for many applications, e.g., encoding a 3D shape and performing collision detection. Typically, implicit fields are encoded by Multi-layer Perceptrons (MLP) with positional encoding (PE) to capture high-frequency geometric details. However, a notable side effect of such PE-equipped MLPs is the noisy artifacts present in the learned implicit fields. While increasing the sampling rate could in general mitigate these artifacts, in this paper we aim to explain this adverse phenomenon through the lens of Fourier analysis. We devise a tool to determine the appropriate sampling rate for learning an accurate neural implicit field without undesirable side effects. Specifically, we propose a simple yet effective method to estimate the intrinsic frequency of a given network with randomized weights based on the Fourier analysis of the network's responses. It is observed that a PE-equipped MLP has an intrinsic frequency much higher than the highest frequency component in the PE layer. Sampling against this intrinsic frequency following the Nyquist-Sannon sampling theorem allows us to determine an appropriate training sampling rate. We empirically show in the setting of SDF fitting that this recommended sampling rate is sufficient to secure accurate fitting results, while further increasing the sampling rate would not further noticeably reduce the fitting error. Training PE-equipped MLPs simply with our sampling strategy leads to performances superior to the existing methods.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".