Gaussian Integral Linear Operators for Precomputed Graphics
Bibliographic record
Abstract
Integral linear operators play a key role in many graphics problems, but solutions obtained via Monte Carlo methods often suffer from high variance. A common strategy to improve the efficiency of integration across various inputs is to precompute the kernel function. Traditional methods typically rely on basis expansions for both the input and output functions. However, using fixed output bases can restrict the precision of output reconstruction and limit the compactness of the kernel representation. In this work, we introduce a new method that approximates both the kernel and the input function using Gaussian mixtures. This formulation allows the integral operator to be evaluated analytically, leading to improved flexibility in kernel storage and output representation. Moreover, our method naturally supports the sequential application of multiple operators and enables closed-form operator composition, which is particularly beneficial in tasks involving chains of operators. We demonstrate the versatility and effectiveness of our approach across a variety of graphics problems, including environment map relighting, boundary value problems, and fluorescence rendering.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".