Finite-Time Analysis of Discrete-Time Stochastic Interpolants
Authors: Yuhao Liu, Yu Chen, Rui Hu, Longbo Huang
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, numerical experiments are conducted on the discrete-time sampler to corroborate our theoretical findings. |
| Researcher Affiliation | Academia | 1IIIS, Tsinghua University, Beijing, China. Correspondence to: Longbo Huang <EMAIL>. |
| Pseudocode | No | The paper describes the discrete-time sampler using Equation (7), which is a mathematical formula for an update rule, but it does not present a structured pseudocode or algorithm block. |
| Open Source Code | No | The paper does not contain any explicit statement about releasing source code or provide a link to a code repository. |
| Open Datasets | Yes | We implement the discretized sampler as defined in Equation (7), and evaluate its performance on on two-dimensional datasets (primarily from Grathwohl et al. 2019) and Gaussian mixtures. |
| Dataset Splits | No | The paper mentions using "sampled data points" and generating data from "Gaussian mixtures" to visualize densities and estimate KL divergence. It does not provide specific training/test/validation dataset splits for reproducibility. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments, such as CPU/GPU models or memory specifications. |
| Software Dependencies | No | The paper mentions the use of 'Adam optimizer (Kingma & Ba, 2015)' and 'ReLU activation functions (Nair & Hinton, 2010)' but does not provide specific version numbers for any software libraries, programming languages, or development environments. |
| Experiment Setup | Yes | We employ I(t, x0, x1) = tx1 + (1 t)x0, γ(t) = p 2t(1 t) and ϵ = 1 in our experiments. We set t0 = 0.001 and t N = 0.999 to ensure that the initial density ρ(t0) is close to ρ0 and the estimated density ρ(t N) closely approximates ρ1. To train the estimator ˆb F (t, x), we leverage a simple quadratic objective (see Appendix A for details) whose optimizer is the real drift b F (t, x). We employ the Adam optimizer (Kingma & Ba, 2015) to train the network using the gradient computed on the empirical loss. The MLP architecture consists of three hidden layers, each with 256 neurons, followed by Re LU activation functions (Nair & Hinton, 2010). |