Learning Interpolations between Boltzmann Densities
Authors: Bálint Máté, François Fleuret
TMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In 4 we run experiments on Gaussian mixtures and on the Boltzmann density of a quantum particle in a double-well potential, and report improvements in KL-divergence, effective sample size, mode coverage and also training speed. To quantify the results of the experiments, for each model we report a subset of the following metrics. For all runs we report the reverse KL-divergence (minus log Z), and the effective sample size, ... Table 1: Results of training the same flow architecture with different objectives on the targets (2) and (18). |
| Researcher Affiliation | Academia | Bálint Máté EMAIL Department of Computer Science, Department of Physics University of Geneva; François Fleuret EMAIL Department of Computer Science University of Geneva |
| Pseudocode | No | The paper describes the mathematical framework and methodology in sections 2 and 3, but does not present any structured pseudocode or algorithm blocks. |
| Open Source Code | Yes | The implementation of our experiments is available at https://github.com/balintmate/boltzmann-interpolations. |
| Open Datasets | No | The experiments are conducted on synthetically defined target distributions: 'Gaussian mixtures' described by equations (2) and (18), and the 'Boltzmann density of a quantum mechanical particle in a double-well potential' derived from an action function (27). These are defined within the paper or its referenced work, and no external, publicly available datasets are explicitly provided with access information. |
| Dataset Splits | No | The paper describes generating samples from a base density and transforming them to a target density, rather than using pre-existing datasets with explicit training, validation, or test splits. Batch sizes are mentioned for optimization, not for dataset partitioning. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU/CPU models, processor types, or memory amounts used for running the experiments. It only mentions general training and model architecture details. |
| Software Dependencies | No | The paper lists several software libraries used, including JAX, Haiku, Optax, NumPy, Hydra, Matplotlib, Jupyter, and Weights & Biases, but does not provide specific version numbers for any of these dependencies. |
| Experiment Setup | Yes | Optimization. We train with a batch size of 256 using the Adam optimizer (Kingma & Ba, 2017) and evaluate on batches of size 4096. The trajectories of the flow are computed by a 4th-order Runge-Kutta solver with 50 integration steps. The N = 64 and N = 32 runs in 4.2 are trained for 2.5 × 10^5 and 10^5 iterations, respectively. All other models are trained for 10^4 iterations. The initial learning rate of 3 × 10^-3 is annealed to 0 following a cosine schedule. Architectures. The parametrization of Vt and ft are given by a weighted average of 4 MLPs. The weighting is done by evenly spaced RBF time-kernels, one for each model. In the case of the Gaussian targets the MLPs has two hidden layers with 64 neurons per layer, in the case of the quantum particle the MLPs has 3 hidden layers with 128 neurons per layer. Between the linear layers we use swish nonlinearities. |