A Category-theoretical Meta-analysis of Definitions of Disentanglement
- URL: http://arxiv.org/abs/2305.06886v2
- Date: Mon, 29 May 2023 13:26:17 GMT
- Title: A Category-theoretical Meta-analysis of Definitions of Disentanglement
- Authors: Yivan Zhang, Masashi Sugiyama
- Abstract summary: Disentangling the factors of variation in data is a fundamental concept in machine learning.
This paper presents a meta-analysis of existing definitions of disentanglement.
- Score: 97.34033555407403
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Disentangling the factors of variation in data is a fundamental concept in
machine learning and has been studied in various ways by different researchers,
leading to a multitude of definitions. Despite the numerous empirical studies,
more theoretical research is needed to fully understand the defining properties
of disentanglement and how different definitions relate to each other. This
paper presents a meta-analysis of existing definitions of disentanglement,
using category theory as a unifying and rigorous framework. We propose that the
concepts of the cartesian and monoidal products should serve as the core of
disentanglement. With these core concepts, we show the similarities and crucial
differences in dealing with (i) functions, (ii) equivariant maps, (iii)
relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our
understanding of disentanglement and its various formulations and can help
researchers navigate different definitions and choose the most appropriate one
for their specific context.
Related papers
- Normalization in Proportional Feature Spaces [49.48516314472825]
normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling.
The selection of an appropriate normalization method needs to take into account the type and characteristics of the involved features.
arXiv Detail & Related papers (2024-09-17T17:46:27Z) - Geometric Understanding of Discriminability and Transferability for Visual Domain Adaptation [27.326817457760725]
Invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities.
Recently, empirical connections between transferability and discriminability have received increasing attention.
In this work, we systematically analyze the essentials of transferability and discriminability from the geometric perspective.
arXiv Detail & Related papers (2024-06-24T13:31:08Z) - Domain Embeddings for Generating Complex Descriptions of Concepts in
Italian Language [65.268245109828]
We propose a Distributional Semantic resource enriched with linguistic and lexical information extracted from electronic dictionaries.
The resource comprises 21 domain-specific matrices, one comprehensive matrix, and a Graphical User Interface.
Our model facilitates the generation of reasoned semantic descriptions of concepts by selecting matrices directly associated with concrete conceptual knowledge.
arXiv Detail & Related papers (2024-02-26T15:04:35Z) - Definition-independent Formalization of Soundscapes: Towards a Formal
Methodology [0.873811641236639]
Soundscapes have been studied by researchers from various disciplines, each with different perspectives, goals, approaches, and terminologies.
We present a potential formalization that is independent of the underlying soundscape definition.
We show a practical application of our presented formalization.
arXiv Detail & Related papers (2023-10-20T10:22:15Z) - Enriching Disentanglement: From Logical Definitions to Quantitative Metrics [59.12308034729482]
Disentangling the explanatory factors in complex data is a promising approach for data-efficient representation learning.
We establish relationships between logical definitions and quantitative metrics to derive theoretically grounded disentanglement metrics.
We empirically demonstrate the effectiveness of the proposed metrics by isolating different aspects of disentangled representations.
arXiv Detail & Related papers (2023-05-19T08:22:23Z) - Evaluating the Robustness of Interpretability Methods through
Explanation Invariance and Equivariance [72.50214227616728]
Interpretability methods are valuable only if their explanations faithfully describe the explained model.
We consider neural networks whose predictions are invariant under a specific symmetry group.
arXiv Detail & Related papers (2023-04-13T17:59:03Z) - The role of feature space in atomistic learning [62.997667081978825]
Physically-inspired descriptors play a key role in the application of machine-learning techniques to atomistic simulations.
We introduce a framework to compare different sets of descriptors, and different ways of transforming them by means of metrics and kernels.
We compare representations built in terms of n-body correlations of the atom density, quantitatively assessing the information loss associated with the use of low-order features.
arXiv Detail & Related papers (2020-09-06T14:12:09Z) - A category theoretical argument for causal inference [0.0]
The goal of this paper is to design a causal inference method accounting for complex interactions between causal factors.
The proposed method relies on a category theoretical reformulation of the definitions of dependent variables, independent variables and latent variables.
As an application, we show how the proposed method can be used to design a genome-wide association algorithm for the field of genetics.
arXiv Detail & Related papers (2020-04-09T05:48:46Z) - Expressiveness and machine processability of Knowledge Organization
Systems (KOS): An analysis of concepts and relations [0.0]
The potential of both the expressiveness and machine processability of each Knowledge Organization System is extensively regulated by its structural rules.
Ontologies explicitly define diverse types of relations, and are by their nature machine-processable.
arXiv Detail & Related papers (2020-03-11T12:35:52Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.