On Convolutions, Intrinsic Dimension, and Diffusion Models
Authors: Kin Kwan Leung, Rasa Hosseinzadeh, Gabriel Loaiza-Ganem
TMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work we bridge this gap by formally proving the correctness of FLIPD under realistic assumptions. Additionally, we show that an analogous result holds when Gaussian convolutions are replaced with uniform ones, and discuss the relevance of this result. The correctness of FLIPD as an estimator of LID therefore hinges on Equation 1 holding in general, and as previously mentioned, Kamkari et al. (2024b) only proved Equation 1 in the case where M is an affine submanifold of RD. We refer the reader to Kamkari et al. (2024b) for a more thorough derivation of FLIPD, along with illustrative examples, and empirical results. |
| Researcher Affiliation | Industry | Kin Kwan Leung EMAIL Layer 6 AI Rasa Hosseinzadeh EMAIL Layer 6 AI Gabriel Loaiza-Ganem EMAIL Layer 6 AI |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. It focuses on mathematical derivations and proofs. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the methodology described in this work, nor does it provide a link to a code repository. |
| Open Datasets | No | This theoretical paper does not conduct experiments using specific datasets and therefore does not provide access information for any datasets. It discusses data generically in the context of the manifold hypothesis, such as 'image data' and 'natural images', but these are illustrative rather than specific datasets used for evaluation. |
| Dataset Splits | No | This theoretical paper does not conduct experiments on specific datasets, so there is no mention of training/test/validation splits. |
| Hardware Specification | No | This theoretical paper does not describe experimental procedures that would require specific hardware, thus no hardware specifications are mentioned. |
| Software Dependencies | No | This theoretical paper does not describe experimental procedures that would require specific software dependencies with version numbers for reproducibility. While it mentions other works using tools like PyTorch and CUDA, it does not specify software used for its own methodology. |
| Experiment Setup | No | This theoretical paper does not conduct experiments, and therefore does not describe any experimental setup details such as hyperparameters or training configurations. |