On the Natural Gradient of the Evidence Lower Bound
Authors: Nihat Ay, Jesse van Oostrum, Adwait Datar
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This article studies the Fisher-Rao gradient, also referred to as the natural gradient, of the evidence lower bound (ELBO) which plays a central role in generative machine learning. It reveals that the gap between the evidence and its lower bound, the ELBO, has essentially a vanishing natural gradient within unconstrained optimization. As a result, maximization of the ELBO is equivalent to minimization of the Kullback-Leibler divergence from a target distribution, the primary objective function of learning. Building on this insight, we derive a condition under which this equivalence persists even when optimization is constrained to a model. This condition yields a geometric characterization, which we formalize through the notion of a cylindrical model. |
| Researcher Affiliation | Academia | Nihat Ay EMAIL Institute for Data Science Foundations Hamburg University of Technology 21073 Hamburg, Germany Santa Fe Institute Santa Fe, NM 87501, USA Leipzig University 04109 Leipzig, Germany Jesse van Oostrum EMAIL Institute for Data Science Foundations Hamburg University of Technology 21073 Hamburg, Germany Adwait Datar EMAIL Institute for Data Science Foundations Hamburg University of Technology 21073 Hamburg, Germany |
| Pseudocode | No | The paper contains mathematical derivations, theorems, propositions, and definitions but does not include any explicitly labeled or formatted pseudocode or algorithm blocks. |
| Open Source Code | Yes | The code for reproducing the data and figures in this paper is made available at Datar et al. (2024). ... Datar, Adwait, Jesse van Oostrum, and Nihat Ay. Code for paper: On the natural gradient of the evidence lower bound. https://github.com/addat10/Nat-Gradient-ELBO.git, 2024. |
| Open Datasets | No | The paper uses illustrative examples with |
| Dataset Splits | No | The paper presents theoretical analysis and uses illustrative examples with simulated data to demonstrate theoretical concepts. It does not describe experiments with real-world datasets that would require explicit training/test/validation splits. |
| Hardware Specification | No | The paper focuses on theoretical derivations and illustrative examples. There is no mention of specific hardware used for any computations or figure generation. |
| Software Dependencies | No | The paper mentions that code for reproducing figures is available but does not specify any software dependencies with version numbers (e.g., Python, specific libraries, or frameworks). |
| Experiment Setup | No | The paper describes theoretical concepts and their geometric implications, using examples to illustrate these concepts. It does not detail an experimental setup in the typical sense (e.g., hyperparameters, training configurations, model initialization, optimizers) for evaluating a machine learning model or algorithm. |