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Self-Attentive Document Interaction Networks for Permutation Equivariant Ranking [article]

Rama Kumar Pasumarthi, Xuanhui Wang, Michael Bendersky, Marc Najork
<span title="2019-10-23">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It thus motivates us to study how to leverage cross-document interactions for learning-to-rank in the deep learning framework.  ...  We then propose a self-attention based document interaction network and show that it satisfies the permutation-equivariant requirement, and can generate scores for document sets of varying sizes.  ...  More recently, neural learning-to-rank algorithms [1, 4] and click models [5] capture document interactions using recurrent neural networks over document lists. ese methods, however, belong to the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.09676v2">arXiv:1910.09676v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rbbe2a75sndelectycoepbegve">fatcat:rbbe2a75sndelectycoepbegve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200908235256/https://arxiv.org/pdf/1910.09676v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/90/f6/90f6749ff9c1ea8ed52d0a8fd303b4b2115c0f91.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.09676v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

SetRank: Learning a Permutation-Invariant Ranking Model for Information Retrieval [article]

Liang Pang, Jun Xu, Qingyao Ai, Yanyan Lan, Xueqi Cheng, Jirong Wen
<span title="2020-05-07">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The self-attention mechanism not only helps SetRank to capture the local context information from cross-document interactions, but also to learn permutation-equivariant representations for the inputted  ...  In this paper, we propose a neural learning-to-rank model called SetRank which directly learns a permutation-invariant ranking model defined on document sets of any size.  ...  Deep Learning for Ranking Recently, deep learning methods such as deep neural networks and convolution neural networks have been widely applied to IR problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1912.05891v2">arXiv:1912.05891v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kabzequhcveblke5ggccsoqi4y">fatcat:kabzequhcveblke5ggccsoqi4y</a> </span>
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Set-to-Sequence Methods in Machine Learning: A Review

Mateusz Jurewicz, Leon Derczynski
<span title="2021-08-12">2021</span> <i title="AI Access Foundation"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4ax4efcwajcgvidb6hcg6mwx4a" style="color: black;">The Journal of Artificial Intelligence Research</a> </i> &nbsp;
representation to output a complex target permutation.  ...  Machine learning on sets towards sequential output is an important and ubiquitous task, with applications ranging from language modelling and meta-learning to multi-agent strategy games and power grid  ...  The authors would like to acknowledge Rasmus Pagh's assistance in the conceptualization of different set-to-sequence settings and general feedback on the early drafts of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1613/jair.1.12839">doi:10.1613/jair.1.12839</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ynsglcoo4vduhpy6xfkq3vvn5m">fatcat:ynsglcoo4vduhpy6xfkq3vvn5m</a> </span>
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Context-Aware Learning to Rank with Self-Attention [article]

Przemysław Pobrotyn, Tomasz Bartczak, Mikołaj Synowiec, Radosław Białobrzeski, Jarosław Bojar
<span title="2021-05-21">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In learning to rank, one is interested in optimising the global ordering of a list of items according to their utility for users.Popular approaches learn a scoring function that scores items individually  ...  Learning to rank is a key component of many e-commerce search engines.  ...  For optimisation of neural network models, we use Adam optimiser [22] with the learning rate tuned separately for each model. Details of hyperparameters used can be found in Appendix A.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.10084v4">arXiv:2005.10084v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/csadkne6ovelvoumvf6qacnv7i">fatcat:csadkne6ovelvoumvf6qacnv7i</a> </span>
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Set-to-Sequence Methods in Machine Learning: a Review [article]

Mateusz Jurewicz, Leon Strømberg-Derczynski
<span title="2021-03-17">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
representation to output a complex target permutation.  ...  Machine learning on sets towards sequential output is an important and ubiquitous task, with applications ranging from language modelling and meta-learning to multi-agent strategy games and power grid  ...  This function is represented as a neural network, which is then used to continuously adjust the learned permutation matrix.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2103.09656v1">arXiv:2103.09656v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7s7ll2xuyjcdpjkcaca7psy74m">fatcat:7s7ll2xuyjcdpjkcaca7psy74m</a> </span>
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A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups [article]

Marc Finzi, Max Welling, Andrew Gordon Wilson
<span title="2021-04-19">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Symmetries and equivariance are fundamental to the generalization of neural networks on domains such as images, graphs, and point clouds.  ...  We release our software library to enable researchers to construct equivariant layers for arbitrary matrix groups.  ...  Acknowledgements We would like to thank Roberto Bondesan and Robert Young for useful discussions about equivariance and Lie algebra representations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.09459v1">arXiv:2104.09459v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vulnpee2hfhj3h5uqv7m4rigau">fatcat:vulnpee2hfhj3h5uqv7m4rigau</a> </span>
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Learning Ordinal Embedding from Sets

Aïssatou Diallo, Johannes Fürnkranz
<span title="2021-07-27">2021</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
approach in a scalable learning framework.  ...  Without having access to features of the items to be embedded, we show the applicability of our model on toy datasets for the task of reconstruction and demonstrate the validity of the obtained embeddings  ...  The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e23080964">doi:10.3390/e23080964</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i64ponvbmnfalfd7sibp4m4dry">fatcat:i64ponvbmnfalfd7sibp4m4dry</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210729210333/https://res.mdpi.com/d_attachment/entropy/entropy-23-00964/article_deploy/entropy-23-00964.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/64/70/647033bb760ec60bac347777a6afc13f0f9fabe0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e23080964"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networks [article]

Haorui Wang, Haoteng Yin, Muhan Zhang, Pan Li
<span title="2022-04-25">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Graph neural networks (GNN) have shown great advantages in many graph-based learning tasks but often fail to predict accurately for a task-based on sets of nodes such as link/motif prediction and so on  ...  PEG imposes permutation equivariance w.r.t. the original node features and rotation equivariance w.r.t. the positional features simultaneously.  ...  INTRODUCTION Graph neural networks (GNN), inheriting from the power of neural networks (Hornik et al., 1989) , have recently become the de facto standard for machine learning with graph-structured data  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2203.00199v3">arXiv:2203.00199v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2jn2x3bbrbbxvakv7kh74gkplu">fatcat:2jn2x3bbrbbxvakv7kh74gkplu</a> </span>
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Quantum walk neural networks with feature dependent coins

Stefan Dernbach, Arman Mohseni-Kabir, Siddharth Pal, Miles Gepner, Don Towsley
<span title="2019-09-23">2019</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j7jxtbkpgnastjy3xdfamy6f7u" style="color: black;">Applied Network Science</a> </i> &nbsp;
Recent neural networks designed to operate on graph-structured data have proven effective in many domains.  ...  A quantum walk neural network is based on learning the coin operators that determine the behavior of quantum random walks, the quantum parallel to classical random walks.  ...  This method is equivariant with respect to the node ordering of the graph (i.e. permuting the neighborhood of v i equally permutes the values of f k (v i )).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s41109-019-0188-2">doi:10.1007/s41109-019-0188-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qljpf5qcsrcavipjc2m5ayxz2a">fatcat:qljpf5qcsrcavipjc2m5ayxz2a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200210142955/https://appliednetsci.springeropen.com/track/pdf/10.1007/s41109-019-0188-2" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ab/4e/ab4e583a326d43fb6b211df5e5f843cf195e0c8e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s41109-019-0188-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> springer.com </button> </a>

On the Equivalence between Positional Node Embeddings and Structural Graph Representations [article]

Balasubramaniam Srinivasan, Bruno Ribeiro
<span title="2020-09-22">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks.  ...  We also show that the concept of transductive and inductive learning is unrelated to node embeddings and graph representations, clearing another source of confusion in the literature.  ...  A neural network is used to learn the joint probability via MCMC, in an unsupervised fashion.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.00452v3">arXiv:1910.00452v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4bx2573owvbephefgwp36i5yiu">fatcat:4bx2573owvbephefgwp36i5yiu</a> </span>
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A Deep Generative Model for Reordering Adjacency Matrices [article]

Oh-Hyun Kwon, Chiun-How Kao, Chun-houh Chen, Kwan-Liu Ma
<span title="2022-02-21">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper introduces a fundamentally new approach to matrix visualization of a graph, where a machine learning model learns to generate diverse matrix reorderings of a graph.  ...  However, this trial-and-error approach is laborious and disorganized, which is especially challenging for novices.  ...  To achieve this, we have designed a novel neural network architecture to address unique challenges in learning a deep generative model for matrix reordering.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.04971v2">arXiv:2110.04971v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3ac4h5ggyzagnevhs3be4wmw2m">fatcat:3ac4h5ggyzagnevhs3be4wmw2m</a> </span>
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Equivariant Maps for Hierarchical Structures [article]

Renhao Wang, Marjan Albooyeh, Siamak Ravanbakhsh
<span title="2020-11-24">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
While using invariant and equivariant maps, it is possible to apply deep learning to a range of primitive data structures, a formalism for dealing with hierarchy is lacking.  ...  More generally, we show that any equivariant map for the hierarchy has this form.  ...  Conclusion This paper presents a procedure to design neural networks equivariant to hierarchical symmetries and nested structures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.03627v2">arXiv:2006.03627v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2m2jkjm2bbbwllcr3woc47vvna">fatcat:2m2jkjm2bbbwllcr3woc47vvna</a> </span>
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Weisfeiler and Leman go Machine Learning: The Story so far [article]

Christopher Morris, Yaron Lipman, Haggai Maron, Bastian Rieck, Nils M. Kriege, Martin Grohe, Matthias Fey, Karsten Borgwardt
<span title="2021-12-18">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We discuss the theoretical background, show how to use it for supervised graph- and node representation learning, discuss recent extensions, and outline the algorithm's connection to (permutation-)equivariant  ...  In recent years, algorithms and neural architectures based on the Weisfeiler-Leman algorithm, a well-known heuristic for the graph isomorphism problem, emerged as a powerful tool for machine learning with  ...  Equivariance as a design principle for neural networks The vast majority of graph learning tasks belong to one of two groups: invariant or equivariant.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2112.09992v1">arXiv:2112.09992v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r5ahhxsvhrbotfi6grerkzxuui">fatcat:r5ahhxsvhrbotfi6grerkzxuui</a> </span>
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Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs [article]

Ryan L. Murphy, Balasubramaniam Srinivasan, Vinayak Rao, Bruno Ribeiro
<span title="2019-02-25">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions).  ...  This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions.  ...  Our goal in this paper is to model and learn permutation-sensitive functions f that can be used to construct flexible and learnable permutation-invariant neural networks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.01900v3">arXiv:1811.01900v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lvfsu53tgbe5faxsd534d4uaku">fatcat:lvfsu53tgbe5faxsd534d4uaku</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826020201/https://arxiv.org/pdf/1811.01900v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ed/03/ed037940ec3b35dba5edcd7c22742f9ab6e52ed9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.01900v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks [article]

Matthew Li and Laurent Demanet and Leonardo Zepeda-Núñez
<span title="2021-10-28">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce an end-to-end deep learning architecture called the wide-band butterfly network (WideBNet) for approximating the inverse scattering map from wide-band scattering data.  ...  WideBNet is able to produce images that are competitive with optimization-based approaches, but at a fraction of the cost, and we also demonstrate numerically that it learns to super-resolve scatterers  ...  We also thank George Barbastathis for detailed feedback on an earlier draft, and for invaluable references. In addition, we thank the two anonymous referees for their helpful comments and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.12413v2">arXiv:2011.12413v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t4zouzrjz5alrnipp2n5a6uivu">fatcat:t4zouzrjz5alrnipp2n5a6uivu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211117161417/https://arxiv.org/pdf/2011.12413v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e9/96/e9968c24d8a16f99f862535088cd6cad47cc5626.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.12413v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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