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].
Geometry and Expressive Power of Conditional Restricted Boltzmann Machines
Authors: Guido Montúfar, Nihat Ay, Keyan Ghazi-Zahedi
JMLR 2015 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We address the representational power of these models, proving results on their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models. In this paper we address the representational power of CRBMs, contributing theoretical insights to the optimal number of hidden units. We proved an extensive series of results that generalize recent theoretical work on the representational power of RBMs in a non-trivial way. |
| Researcher Affiliation | Academia | Guido Mont ufar EMAIL Max Planck Institute for Mathematics in the Sciences 04103 Leipzig, Germany Nihat Ay EMAIL Max Planck Institute for Mathematics in the Sciences 04103 Leipzig, Germany Department of Mathematics and Computer Science Leipzig University 04009 Leipzig, Germany Santa Fe Institute Santa Fe, NM 87501, USA Keyan Ghazi-Zahedi EMAIL Max Planck Institute for Mathematics in the Sciences 04103 Leipzig, Germany |
| Pseudocode | Yes | Algorithm 1 Algorithmic illustration of the proof of Theorem 7. Input: Strictly positive joint distribution p, target conditional distribution q( | ), and ϵ > 0 Output: Transformation p of the input p with P y |p (y|x) q(y|x)| ϵ for all x Initialize B {Here B {0, 1}k denotes the set of inputs x that have been readily processed in the current iteration} while B {0, 1}k do Choose (disjoint) cylinder sets C1, . . . , CK packing {0, 1}k \- B If needed, perform at most K sharing steps resetting the Ci rows of p for all i [K], taking p( |x) close to δ0 for all x Ci for all i [K] and leaving all other rows close to their current values, according to Corollary 28 for each i [K] do Perform at most 2n 1 sharing steps taking p( |x) close to q( |x) for all x Bi, where Bi is some star contained in Ci, and leaving the ({0, 1}k \- Ci)-rows close to their current values, according to Corollary 27 end for B B ( i [K]Bi) end while |
| Open Source Code | No | The paper does not contain any explicit statements about the release of source code, nor does it provide any links to a code repository. |
| Open Datasets | No | This paper is theoretical and does not present experimental results based on specific datasets. Therefore, no information about open datasets is provided. |
| Dataset Splits | No | This paper is theoretical and does not use any datasets for experimental evaluation, so there is no mention of dataset splits. |
| Hardware Specification | No | This paper is theoretical and does not describe any experimental setups or computational runs that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | This paper is theoretical and does not describe any experimental implementations. Therefore, no specific software dependencies with version numbers are provided. |
| Experiment Setup | No | This paper is theoretical and does not include any experimental evaluation. Therefore, it does not describe specific experimental setup details such as hyperparameters or training configurations. |