InvertibleNetworks.jl: A Julia package for scalablenormalizing flows
Bibliographic record
Abstract
Normalizing flows is a density estimation method that provides efficient exact likelihood estimation and sampling (Dinh et al., 2014) from high-dimensional distributions.This method depends on the use of the change of variables formula, which requires an invertible transform.Thus normalizing flow architectures are built to be invertible by design (Dinh et al., 2014).In theory, the invertibility of architectures constrains the expressiveness, but the use of coupling layers allows normalizing flows to exploit the power of arbitrary neural networks, which do not need to be invertible, (Dinh et al., 2016) and layer invertibility means that, if properly implemented, many layers can be stacked to increase expressiveness without creating a training memory bottleneck.The package we present, InvertibleNetworks.jl, is a pure Julia (Bezanson et al., 2017) implementation of normalizing flows.We have implemented many relevant neural network layers, including GLOW 1x1 invertible convolutions (Kingma & Dhariwal, 2018), affine/additive coupling layers (Dinh et al., 2014), Haar wavelet multiscale transforms (Haar, 1909), and Hierarchical invertible neural transport (HINT) (Kruse et al., 2021), among others.These modular layers can be easily composed and modified to create different types of normalizing flows.As starting points, we have implemented RealNVP, GLOW, HINT, Hyperbolic networks (Lensink et al., 2022) and their conditional counterparts for users to quickly implement their individual applications.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.087 | 0.042 |
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".