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  "author": "Joan Bruna",
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  "extra_authors": [
            
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    {
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      "extra_author": "Soumith Chintala",
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      "extra_author": "Soumith Chintala",
            
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      "extra_author": "Yann LeCun",
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      "extra_author": "Yann LeCun",
            
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    },
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    {
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      "extra_author": "Serkan Piantino",
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      "orcid": ""
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      "orcid": ""
            
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    },
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    {
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      "extra_author": "Arthur Szlam",
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      "extra_author": "Arthur Szlam",
            
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      "orcid": ""
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      "orcid": ""
            
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    },
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    {
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      "extra_author": "Mark Tygert",
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      "extra_author": "Mark Tygert",
            
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      "orcid": ""
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  "name": 
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"a-mathematical-motivation-for-complex-valued-convolutional-networks",
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  "notes": "A complex-valued convolutional network (convnet) 
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  "notes": "A complex-valued convolutional network (convnet) 
            
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implements the repeated application of the following composition of 
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implements the repeated application of the following composition of 
            
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three operations, recursively applying the composition to an input 
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three operations, recursively applying the composition to an input 
            
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vector of nonnegative real numbers: (1) convolution with 
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vector of nonnegative real numbers: (1) convolution with 
            
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complex-valued vectors followed by (2) taking the absolute value of 
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complex-valued vectors followed by (2) taking the absolute value of 
            
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every entry of the resulting vectors followed by (3) local 
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every entry of the resulting vectors followed by (3) local 
            
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averaging.",
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averaging.",
            
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  "title": "A Mathematical Motivation for Complex-valued Convolutional 
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  "title": "A Mathematical Motivation for Complex-valued Convolutional 
            
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Networks",
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Networks",
            
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}