A Group-Theoretic Approach to Computational Abstraction: Symmetry-Driven Hierarchical Clustering
Authors: Haizi Yu, Igor Mineyev, Lav R. Varshney
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Humans abstraction ability plays a key role in concept learning and knowledge discovery. This theory paper presents the mathematical formulation for computationally emulating human-like abstractions computational abstraction and abstraction processes developed hierarchically from innate priors like symmetries. |
| Researcher Affiliation | Academia | Haizi Yu EMAIL Coordinated Science Laboratory Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801, USA; Igor Mineyev EMAIL Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL 61801, USA; Lav R. Varshney EMAIL Coordinated Science Laboratory Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801, USA |
| Pseudocode | Yes | Algorithm 1: Computing base partitions by tracing orbits: O(|X|).; Algorithm 2: Computing partitions generated from more than one generators inductively by taking the meet of two partitions computed earlier: O(|P||Q|). |
| Open Source Code | No | The paper does not explicitly state that source code for their methodology is provided, nor does it include a link to a code repository. It mentions using 'the computer algebra system GAP (The GAP Group, 2018)' and 'the GAP package Cryst Cat (Felsch and G ahler, 2000)' which are third-party tools. |
| Open Datasets | Yes | In the chemistry application, raw data were taken as the compound formulas in the molecule database from the Materials Project (Jain et al., 2013).; images of handwritten 8 from the MNIST dataset exhibited more symmetries compared to other digits. |
| Dataset Splits | No | The paper describes conceptual divisions of input space for computational abstraction (e.g., 'a finite subspace Y = Zn[ b,b]'), but does not provide specific training, validation, or test dataset splits for machine learning experiments. |
| Hardware Specification | No | The paper describes a theoretical framework and algorithms. It does not provide any specific details about the hardware (e.g., GPU, CPU models, memory) used for any implementations or conceptual experiments. |
| Software Dependencies | Yes | The computer algebra system GAP (The GAP Group, 2018) offers methods for constructing the subgroup lattice for a given group, and stores several data libraries for special groups and their subgroup lattices. Common practices includes enumerating subgroups up to conjugacy (also supported in GAP), then computing abstractions within the conjugacy class is easy by Theorem 9. To identify the top , we start with the transformation group of X = Rn and then consider special subgroups of F(Rn) and special subspaces of Rn. ... and implemented in the GAP package Cryst Cat (Felsch and G ahler, 2000). |
| Experiment Setup | No | The paper is theoretical, presenting a mathematical formulation and algorithms. It discusses algorithmic implementations and examples but does not describe a traditional experimental setup with specific hyperparameters, training configurations, or system-level settings for model training or evaluation. |