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Group invariance principles for causal generative models [article]

Michel Besserve, Naji Shajarisales, Bernhard Schölkopf, Dominik Janzing
2017 arXiv   pre-print
Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches.  ...  We show that the group theoretic view provides a very general tool to study the structure of data generating mechanisms with direct applications to machine learning.  ...  ., then it can be considered as a generative model whose cause Z has an invariant distribution on the unit hypercube [0, 1] K , the generic group being the group combining translations modulo 1 for each  ... 
arXiv:1705.02212v1 fatcat:bvd4l3dfpbbhpfdbrpgnbin5zq

Spacetime orientation and the meaning of Lorentz invariance in general relativity [article]

Zhongmin Qian
2018 arXiv   pre-print
We examine the principle of Lorentz invariance under the general theory of relativity, and demonstrate the importance of a concept of the spacetime orientation as part of the causal structure of spacetime  ...  The parity violation at the level of weak interactions and other similar discrete symmetries breaking show that the invariance of laws under the full group of Lorentz transformations can not be taken granted  ...  The author would like to thank Dominic Joyce for the helpful comments.  ... 
arXiv:1802.05290v1 fatcat:nvytz6gzfrfdvc3klrvhtbdihi

Geometric unification theory of the grand unification and gravitational interactions and new physics [article]

C. Huang, Yong-Chang Huang
2020 arXiv   pre-print
The Lagrangians of the grand unification and gravitational interactions are unifiedly deduced from quantitative causal principle (QCP) and satisfy the gauge invariant principle of general gauge fields  ...  composed of the invariant quantities in corresponding spacetime structures.  ...  All the deduced Lagrangians in this paper in current particle physics standard model are invariant in all general coordinate transformations (for tangent bundle) and gauge transformations (for principal  ... 
arXiv:1703.01177v6 fatcat:gx5y2ad3uvhb3fe4phfljn6iey

Page 7914 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
Gauge models which generalize the Schwinger model are dis- cussed.  ...  ., isotony, Einstein causality, relativistic covariance) as well as the local primitive causality condition (i.e, 7(V) = %(V"') for every nonempty convex region V, where V” denotes the causal completion  ... 

Causality and the speed of sound

George F. R. Ellis, Roy Maartens, Malcolm A. H. MacCallum
2007 General Relativity and Gravitation  
A usual causal requirement on a viable theory of matter is that the speed of sound be at most the speed of light. In view of various recent papers querying this limit, the question is revisited here.  ...  We have strongly made the case for a particular viewpoint based on an understanding of present day physics.  ...  Comment 5: It appears that none of the above causality-violating theories can be based on a microscopic matter model that obeys special relativity principles.  ... 
doi:10.1007/s10714-007-0479-2 fatcat:tizkrzqwl5fhpp4nbfnc7gm6eq

Causal Groupoid Symmetries

Sergio Pissanetzky
2014 Applied Mathematics  
Consequently, we focus on invariants, particularly group-theoretical block systems. The symmetry of S by itself is characterized by its symmetric group, which generates a trivial block system over S.  ...  Proposed here is a new framework for the analysis of complex systems as a non-explicitly programmed mathematical hierarchy of subsystems using only the fundamental principle of causality, the mathematics  ...  They have plenty of invariant non-trivial structures, but these differ from those at the λ point for a given causal model.  ... 
doi:10.4236/am.2014.54059 fatcat:2tjaqxmyabeirc24rajxuaj53u

Discovering Invariant Rationales for Graph Neural Networks [article]

Ying-Xin Wu, Xiang Wang, An Zhang, Xiangnan He, Tat-Seng Chua
2022 arXiv   pre-print
Then it approaches the causal rationales that are invariant across different distributions while filtering out the spurious patterns that are unstable.  ...  Unfortunately, the leading rationalization models often rely on data biases, especially shortcut features, to compose rationales and make predictions without probing the critical and causal patterns.  ...  This class of algorithms improves the robustness and generalization for GNNs, which helps the models better generalize in unseen groups or out-of-distribution datasets.  ... 
arXiv:2201.12872v1 fatcat:aaktipxdprbwtplkekzi366svu

Equivariant and Invariant Grounding for Video Question Answering [article]

Yicong Li, Xiang Wang, Junbin Xiao, Tat-Seng Chua
2022 arXiv   pre-print
Taking a causal look at VideoQA, we devise a self-interpretable framework, Equivariant and Invariant Grounding for Interpretable VideoQA (EIGV).  ...  Such black-box nature calls for visual explainability that reveals "What part of the video should the model look at to answer the question?".  ...  As a correction, the grounding indicator makes a discrete selection over the clip-wise attention result to generate a disjoint group of the causal scene.  ... 
arXiv:2207.12783v1 fatcat:emlmphxvsrhlzbjsip4r2vsvvy

Class Is Invariant to Context and Vice Versa: On Learning Invariance for Out-Of-Distribution Generalization [article]

Jiaxin Qi, Kaihua Tang, Qianru Sun, Xian-Sheng Hua, Hanwang Zhang
2022 arXiv   pre-print
Out-Of-Distribution generalization (OOD) is all about learning invariance against environmental changes.  ...  If the context in every class is evenly distributed, OOD would be trivial because the context can be easily removed due to an underlying principle: class is invariant to context.  ...  Mahajan, D., Tople, S., Sharma, A.: Domain generalization using causal matching. 59. Vapnik, V.: Principles of risk minimization for learning theory.  ... 
arXiv:2208.03462v1 fatcat:uu2pusxocjfh5fjprc424z5evy

Page 4299 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
This leads us to define a general structure which we call a ‘causal spin foam’. We also demonstrate that the causal evolution models for spin networks fall in the general class of causal spin foams.”  ...  group for the quantum construction.  ... 

Frontiers of Quantum Gravity: shared challenges, converging directions [article]

Jan de Boer, Bianca Dittrich, Astrid Eichhorn, Steven B. Giddings, Steffen Gielen, Stefano Liberati, Etera R. Livine, Daniele Oriti, Kyriakos Papadodimas, Antonio D. Pereira, Mairi Sakellariadou, Sumati Surya (+1 others)
2022 arXiv   pre-print
In practice however, recent years have shown the emergence of common techniques, results and physical ideas arising from different sub-communities, suggesting exciting new prospects for collaboration and  ...  tensor models and group field theory, (v) the central role played by causality in causal dynamical triangulations and causal set theory, (vi) the use of tensor networks in AdS/CFT, group field theory and  ...  [37] and group field theories (also seen as an alternative implementation of renormalization for spin foam models) [38] .  ... 
arXiv:2207.10618v1 fatcat:l6g2p6sjcrfy5l343l2qizdozq

Invariant Information Bottleneck for Domain Generalization [article]

Bo Li, Yifei Shen, Yezhen Wang, Wenzhen Zhu, Colorado J. Reed, Jun Zhang, Dongsheng Li, Kurt Keutzer, Han Zhao
2022 arXiv   pre-print
Specifically, we first present a novel formulation for invariant causal prediction via mutual information.  ...  Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization.  ...  ICP assumes that the data are generated according to a structural causal model (SCM) (Pearl 2010) .  ... 
arXiv:2106.06333v6 fatcat:aha2tsr7ezhqlawex7zxgi4abi

Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective [article]

Yuejiang Liu, Riccardo Cadei, Jonas Schweizer, Sherwin Bahmani, Alexandre Alahi
2022 arXiv   pre-print
for out-of-distribution generalization and low-shot transfer.  ...  We first introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables, namely invariant variables, style confounders, and spurious  ...  We thank Bastien Van Delft, Brian Alan Sifringer and Yifan Sun for thoughtful feedback on early drafts, Parth Kothari and Hossein Bahari for valuable suggestions on experiments, as well as reviewers for  ... 
arXiv:2111.14820v4 fatcat:u34zervh4nakrbzc7uoqmtwqyq

Symmetry and causality properties of physical fields

H. P. Jakobsen, B. Orsted, I. E. Segal, B. Speh, M. Vergne
1978 Proceedings of the National Academy of Sciences of the United States of America  
Representations of groups of causality-preserving transformations on locally Minkowskian space-times, by actions on classes of wave functions of designated transformation properties, are analyzed, in extension  ...  Kostant for his participation in some of our discussions, particularly at an early stage in this work. This research was supported in part by the National Science Foundation under Grant MCS 76-02762.  ...  The global groups are generated by these components together with an operation of space reversal, which as an automorphism of the infinitesimal causal group can be considered the same in all cases.  ... 
doi:10.1073/pnas.75.4.1609 pmid:16592512 pmcid:PMC392386 fatcat:5q6gt6ec7vfj7psyzrqbizntzi

Relativity Theory Does Not Imply that the Future Already Exists: A Counterexample [chapter]

Rafael D. Sorkin
2007 Relativity and the Dimensionality of the World  
I offer the classical sequential growth models of causal set theory as counterexamples.  ...  One should also mention here an important difference between diffeomorphism-invariance and relabeling-invariance: the former is expressed by an invariance group arising as the automorphism group of a background  ...  General covariance for causets can thus be interpreted as invariance under relabeling, in analogy to the interpretation of general covariance as coordinate-invariance in the continuum.  ... 
doi:10.1007/978-1-4020-6318-3_9 fatcat:lc5xjsu73zehlifqh7brmofn3m
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