[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117784-en":3,"doc-seo-117784-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},117784,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Contextuality and inductive bias in quantum machine learning","Generalisation in machine learning depends on encoding data structures through an inductive bias in the model class. This work examines quantum contextuality as a route toward quantum machine learning advantage. A framework is introduced to define when a learning model is contextual, linking operational equivalence to the ability to encode a linearly conserved quantity in label space. The connection implies contextual model classes are generally more expressive than noncontextual ones, illustrated via a toy zero-sum game payoff-learning problem.","arXiv :2302 .01365v3 [ quant-ph] 18 Apr 2023  \nContextuality and inductive bias in quantum  \nmachine learning  \nJoseph Bowles∗1, Victoria J Wright2 , Máté Farkas2 , Nathan Killoran 1 , and Maria Schuld 1  \n1Xanadu, Toronto, ON, M5G 2C8, Canada  \n2 ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain  \nAbstract  \nGeneralisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the types of data structures that lend themselves naturally to quantum models. In this work we look to quantum contextuality—a form of nonclassicality with links to computational advantage—for answers to this question. We introduce a framework for studying contextuality in machine learning, which leads us to a definition of what it means for a learning model to be contextual. From this, we connect a central concept of contextuality, called operational equivalence, to the ability of a model to encode a linearly conserved quantity in its label space. A consequence of this connection is that contextuality is tied to expressivity: contextual model classes that encode the inductive bias are generally more expressive than their noncontextual counterparts. To demonstrate this, we construct an explicit toy learning problem—based on learning the payoff behaviour of a zero-sum game—for which this is the case. By leveraging tools from geometric quantum machine learning, we then describe how to construct quantum learning models with the associated inductive bias, and show through our toy problem that they outperform their corresponding classical surrogate models. This suggests that understanding learning problems of this form may lead to useful insights about the power of quantum machine learning.  \n1 Introduction  \nIn order for a learning model to generalise well from training data, it is often crucial to encode some knowledge about the structure of the data into the model itself [1, 2 , 3] . Convolutional neural networks [4, 5 , 6] are a classic illustration of this principle, whose success at image related tasks is often credited to the existence of model structures that relate to label invariance of the data under translation symmetries [7] . Together with the choice of loss function and hyperparameters, these structures form part of the basic assumptions that a learning model makes about the data, which is commonly referred to as the inductive bias of the model.  \nOne of the central challenges facing quantum machine learning is to identify data structures that can be encoded usefully into quantum learning models; in other words, what are the forms of inductive bias that naturally lend themselves to quantum computation [8, 9 , 10 , 11]? In answering this question, we should be wary of hoping for a one-size-fits-all approach in which  \n∗[joseph@xanadu.ai](joseph@xanadu.ai)  \nFigure 1: A. An example of the type of learning problem we consider in this work. Labels are generated for input training data xi via a conditional process P (yi j xi) . Here, the labels take the form yi = (yi(1) ; yi(2) ; yi(3) ) = (􀀆1; 􀀆1; 􀀆1) . The learning problem is to infer three probabilistic models P1 (y(1) jx), P2 (y(2) jx), P3 (y(3) jx) that sample the individual labels for unseen input data.  \nB. The data is assumed to satisfy a particular bias, which can be seen as a linear conservation law on the label space. Here, the sum of the expectation values of the labels is equal to zero for all x. We show that if a model encodes this as an inductive bias and is noncontextual, this implies constraints on the distributions Pk , amounting to a limit on expressivity of model classes that are restricted to only noncontextual learning models.  \nquantum models outperform neural network models at generic learning tasks. Rather, effort should be placed in understanding how th","cbCailsureIQb5Ng","https://ap.wps.com/l/cbCailsureIQb5Ng","pdf",1383539,1,40,"English","en",105,"# Introduction\n## Inductive bias and quantum machine learning\n## Contextuality as nonclassicality\n## Motivation and route through quantum foundations","[{\"question\":\"What role does inductive bias play in generalisation for quantum machine learning?\",\"answer\":\"Inductive bias encodes structures present in data into the assumptions of the model class, enabling generalisation beyond training samples.\"},{\"question\":\"How does the paper connect quantum contextuality to properties of learning models?\",\"answer\":\"It introduces a framework defining when a learning model is contextual and links contextuality to operational equivalence in relation to encoded conserved quantities.\"},{\"question\":\"Why are contextual model classes argued to be more expressive than noncontextual ones?\",\"answer\":\"The operational-equivalence connection ties contextuality to expressivity, implying contextual classes that encode the inductive bias generally outperform noncontextual counterparts.\"}]","Contextuality and inductive bias in quantum machine learning | 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role does inductive bias play in generalisation for quantum machine learning?","Question",{"text":75,"@type":76},"Inductive bias encodes structures present in data into the assumptions of the model class, enabling generalisation beyond training samples.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper connect quantum contextuality to properties of learning models?",{"text":80,"@type":76},"It introduces a framework defining when a learning model is contextual and links contextuality to operational equivalence in relation to encoded conserved quantities.",{"name":82,"@type":73,"acceptedAnswer":83},"Why are contextual model classes argued to be more expressive than noncontextual ones?",{"text":84,"@type":76},"The operational-equivalence connection ties contextuality to expressivity, implying contextual classes that encode the inductive bias generally outperform noncontextual 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