FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2969219076> ?p ?o ?g. }

• W2969219076 endingPage "475" @default.
• W2969219076 startingPage "446" @default.
• W2969219076 abstract "We study a deep linear network endowed with the following structure: A matrix $X$ is obtained by multiplying $K$ matrices (called factors and corresponding to the action of the layers). The action of each layer (i.e., factor) is obtained by applying a fixed linear operator to a vector of parameters satisfying a constraint. The number of layers is not limited. Assuming that $X$ is given and factors have been estimated, the error between the product of the estimated factors and $X$ (i.e., the reconstruction error) is either the statistical or the empirical risk. We provide necessary and sufficient conditions on the network topology under which a stability property holds. The stability property requires that the error on the parameters defining the near-optimal factors scales linearly with the reconstruction error (i.e., the risk). Therefore, under these conditions on the network topology, any successful learning task leads to stably defined features that can be interpreted. In order to do so, we first evaluate how the Segre embedding and its inverse distort distances. Then we show that any deep structured linear network can be cast as a generic multilinear problem that uses the Segre embedding. This is the tensorial lifting. Using the tensorial lifting, we provide a necessary and sufficient condition for the identifiability of the factors up to a scale rearrangement. We finally provide a necessary and sufficient condition called the deep-Null Space Property (because of the analogy with the usual Null Space Property in the compressed sensing framework) which guarantees that the stability property holds. We illustrate the theory with a practical example where the deep structured linear network is a convolutional linear network. We obtain a condition on the scattering of the supports which is strong but not empty. A simple test on the network topology can be implemented to test whether the condition holds." @default.
• W2969219076 created "2019-08-29" @default.
• W2969219076 creator A5016303776 @default.
• W2969219076 creator A5068623131 @default.
• W2969219076 date "2019-01-01" @default.
• W2969219076 modified "2023-10-18" @default.
• W2969219076 title "Multilinear Compressive Sensing and an Application to Convolutional Linear Networks" @default.
• W2969219076 cites W1787224781 @default.
• W2969219076 cites W1902027874 @default.
• W2969219076 cites W1953819449 @default.
• W2969219076 cites W1970377488 @default.
• W2969219076 cites W2020390700 @default.
• W2969219076 cites W2024254345 @default.
• W2969219076 cites W2034683677 @default.
• W2969219076 cites W2048687561 @default.
• W2969219076 cites W2068943743 @default.
• W2969219076 cites W2078397124 @default.
• W2969219076 cites W2078626246 @default.
• W2969219076 cites W2095168618 @default.
• W2969219076 cites W2102019642 @default.
• W2969219076 cites W2118550318 @default.
• W2969219076 cites W2124172487 @default.
• W2969219076 cites W2127114523 @default.
• W2969219076 cites W2134332047 @default.
• W2969219076 cites W2137902180 @default.
• W2969219076 cites W2140089781 @default.
• W2969219076 cites W2140867429 @default.
• W2969219076 cites W2145096794 @default.
• W2969219076 cites W2166116275 @default.
• W2969219076 cites W2195388612 @default.
• W2969219076 cites W2274086169 @default.
• W2969219076 cites W2611328865 @default.
• W2969219076 cites W2963494673 @default.
• W2969219076 cites W2963855280 @default.
• W2969219076 cites W3104684837 @default.
• W2969219076 cites W4250955649 @default.
• W2969219076 doi "https://doi.org/10.1137/18m119834x" @default.
• W2969219076 hasPublicationYear "2019" @default.
• W2969219076 type Work @default.
• W2969219076 sameAs 2969219076 @default.
• W2969219076 citedByCount "9" @default.
• W2969219076 countsByYear W29692190762020 @default.
• W2969219076 countsByYear W29692190762021 @default.
• W2969219076 countsByYear W29692190762022 @default.
• W2969219076 countsByYear W29692190762023 @default.
• W2969219076 crossrefType "journal-article" @default.
• W2969219076 hasAuthorship W2969219076A5016303776 @default.
• W2969219076 hasAuthorship W2969219076A5068623131 @default.
• W2969219076 hasBestOaLocation W29692190761 @default.
• W2969219076 hasConcept C105795698 @default.
• W2969219076 hasConcept C112972136 @default.
• W2969219076 hasConcept C11413529 @default.
• W2969219076 hasConcept C114614502 @default.
• W2969219076 hasConcept C119857082 @default.
• W2969219076 hasConcept C121332964 @default.
• W2969219076 hasConcept C122770356 @default.
• W2969219076 hasConcept C124101348 @default.
• W2969219076 hasConcept C124851039 @default.
• W2969219076 hasConcept C126255220 @default.
• W2969219076 hasConcept C154945302 @default.
• W2969219076 hasConcept C158693339 @default.
• W2969219076 hasConcept C17902559 @default.
• W2969219076 hasConcept C184720557 @default.
• W2969219076 hasConcept C203763787 @default.
• W2969219076 hasConcept C28826006 @default.
• W2969219076 hasConcept C33923547 @default.
• W2969219076 hasConcept C41008148 @default.
• W2969219076 hasConcept C41608201 @default.
• W2969219076 hasConcept C62520636 @default.
• W2969219076 hasConcept C84545080 @default.
• W2969219076 hasConceptScore W2969219076C105795698 @default.
• W2969219076 hasConceptScore W2969219076C112972136 @default.
• W2969219076 hasConceptScore W2969219076C11413529 @default.
• W2969219076 hasConceptScore W2969219076C114614502 @default.
• W2969219076 hasConceptScore W2969219076C119857082 @default.
• W2969219076 hasConceptScore W2969219076C121332964 @default.
• W2969219076 hasConceptScore W2969219076C122770356 @default.
• W2969219076 hasConceptScore W2969219076C124101348 @default.
• W2969219076 hasConceptScore W2969219076C124851039 @default.
• W2969219076 hasConceptScore W2969219076C126255220 @default.
• W2969219076 hasConceptScore W2969219076C154945302 @default.
• W2969219076 hasConceptScore W2969219076C158693339 @default.
• W2969219076 hasConceptScore W2969219076C17902559 @default.
• W2969219076 hasConceptScore W2969219076C184720557 @default.
• W2969219076 hasConceptScore W2969219076C203763787 @default.
• W2969219076 hasConceptScore W2969219076C28826006 @default.
• W2969219076 hasConceptScore W2969219076C33923547 @default.
• W2969219076 hasConceptScore W2969219076C41008148 @default.
• W2969219076 hasConceptScore W2969219076C41608201 @default.
• W2969219076 hasConceptScore W2969219076C62520636 @default.
• W2969219076 hasConceptScore W2969219076C84545080 @default.
• W2969219076 hasFunder F4320306076 @default.
• W2969219076 hasIssue "3" @default.
• W2969219076 hasLocation W29692190761 @default.
• W2969219076 hasLocation W29692190762 @default.
• W2969219076 hasLocation W29692190763 @default.
• W2969219076 hasLocation W29692190764 @default.
• W2969219076 hasLocation W29692190765 @default.

• next