Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Fisher information dissipation for time-inhomogeneous stochastic differential equations
Authors: Qi Feng, Xinzhe Zuo, Wuchen Li
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical examples demonstrate the convergence results for the time-dependent Langevin dynamics. Several numerical experiments are provided to justify our theoretical results. |
| Researcher Affiliation | Academia | Qi Feng EMAIL Department of Mathematics Florida State University Tallahassee, FL 32306, USA; Xinzhe Zuo EMAIL Department of Mathematics University of California, Los Angeles Los Angeles, CA 90095, USA; Wuchen Li EMAIL Department of Mathematics University of South Carolina Columbia, SC 29208, USA |
| Pseudocode | No | The paper describes mathematical formulations and derivations, along with numerical schemes like Euler-Maruyama in equations, but does not present any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link regarding the availability of source code for the methodology described. |
| Open Datasets | No | The paper's numerical experiments use synthetic data. For example, it states, "We first sample M = 10^6 particles from N(0, 1)" and simulates stochastic differential equations, rather than using external publicly available datasets. |
| Dataset Splits | No | The numerical experiments are based on simulations rather than external datasets with predefined splits. There are no mentions of training, validation, or test splits. |
| Hardware Specification | No | The paper does not specify any particular hardware (e.g., GPU, CPU models) used for running the numerical experiments. |
| Software Dependencies | No | The paper mentions using the "Euler-Maruyama scheme" for discretization but does not specify any software libraries, frameworks, or their version numbers. |
| Experiment Setup | Yes | We first sample M = 10^6 particles from N(0, 1). Then we evolve (37) using the Euler-Maruyama scheme shown below for N = 10000 steps with a step size of h = 0.002: Xn+1 = Xn - h∇V (Xn) + √(2C log(nh + t0))Bn , where Bn ∼ N(0, √h), and t0 = e. [...] we choose K = 50 in our numerical experiment. [...] In two-dimension (Fig. 3), we used M = 10^6 particles, N = 10000 steps with a stepsize of h = 0.001. |