Matches in SemOpenAlex for { <https://semopenalex.org/work/W4377164015> ?p ?o ?g. }
- W4377164015 abstract "Abstract We develop a new formulation of deep learning based on the Mori–Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete dynamical systems, and it allows us to directly propagate quantities of interest (conditional expectations and probability density functions) forward and backward through the network by means of exact linear operator equations. Such new equations can be used as a starting point to develop new effective parameterizations of deep neural networks and provide a new framework to study deep learning via operator-theoretic methods. The proposed MZ formulation of deep learning naturally introduces a new concept, i.e., the memory of the neural network, which plays a fundamental role in low-dimensional modeling and parameterization. By using the theory of contraction mappings, we develop sufficient conditions for the memory of the neural network to decay with the number of layers. This allows us to rigorously transform deep networks into shallow ones, e.g., by reducing the number of neurons per layer (using projection operators), or by reducing the total number of layers (using the decay property of the memory operator)." @default.
- W4377164015 created "2023-05-21" @default.
- W4377164015 creator A5062986633 @default.
- W4377164015 creator A5091985936 @default.
- W4377164015 date "2023-05-21" @default.
- W4377164015 modified "2023-10-14" @default.
- W4377164015 title "The Mori–Zwanzig formulation of deep learning" @default.
- W4377164015 cites W1978501336 @default.
- W4377164015 cites W1980286668 @default.
- W4377164015 cites W1992758828 @default.
- W4377164015 cites W2018773952 @default.
- W4377164015 cites W2027311462 @default.
- W4377164015 cites W2037905990 @default.
- W4377164015 cites W2039529522 @default.
- W4377164015 cites W2053450287 @default.
- W4377164015 cites W2070792261 @default.
- W4377164015 cites W2073502465 @default.
- W4377164015 cites W2084333107 @default.
- W4377164015 cites W2088087785 @default.
- W4377164015 cites W2092807065 @default.
- W4377164015 cites W2096737643 @default.
- W4377164015 cites W2103455761 @default.
- W4377164015 cites W2124138287 @default.
- W4377164015 cites W2131866773 @default.
- W4377164015 cites W2164193727 @default.
- W4377164015 cites W2165698076 @default.
- W4377164015 cites W2194775991 @default.
- W4377164015 cites W2302255633 @default.
- W4377164015 cites W2408541014 @default.
- W4377164015 cites W2482944896 @default.
- W4377164015 cites W2600297185 @default.
- W4377164015 cites W2789015616 @default.
- W4377164015 cites W2796243079 @default.
- W4377164015 cites W2885195348 @default.
- W4377164015 cites W2962947529 @default.
- W4377164015 cites W2963139910 @default.
- W4377164015 cites W2963480349 @default.
- W4377164015 cites W2963512172 @default.
- W4377164015 cites W2963670229 @default.
- W4377164015 cites W2963838606 @default.
- W4377164015 cites W2963894861 @default.
- W4377164015 cites W2969434393 @default.
- W4377164015 cites W2973022759 @default.
- W4377164015 cites W2979313281 @default.
- W4377164015 cites W2992005611 @default.
- W4377164015 cites W2995681639 @default.
- W4377164015 cites W2997942693 @default.
- W4377164015 cites W3043715697 @default.
- W4377164015 cites W3098203661 @default.
- W4377164015 cites W3103191065 @default.
- W4377164015 cites W3104298728 @default.
- W4377164015 cites W3104905240 @default.
- W4377164015 cites W3105174114 @default.
- W4377164015 cites W3206241734 @default.
- W4377164015 cites W4238209390 @default.
- W4377164015 cites W4255975175 @default.
- W4377164015 doi "https://doi.org/10.1007/s40687-023-00390-2" @default.
- W4377164015 hasPublicationYear "2023" @default.
- W4377164015 type Work @default.
- W4377164015 citedByCount "0" @default.
- W4377164015 crossrefType "journal-article" @default.
- W4377164015 hasAuthorship W4377164015A5062986633 @default.
- W4377164015 hasAuthorship W4377164015A5091985936 @default.
- W4377164015 hasBestOaLocation W43771640151 @default.
- W4377164015 hasConcept C104317684 @default.
- W4377164015 hasConcept C108583219 @default.
- W4377164015 hasConcept C121332964 @default.
- W4377164015 hasConcept C121864883 @default.
- W4377164015 hasConcept C142362112 @default.
- W4377164015 hasConcept C153349607 @default.
- W4377164015 hasConcept C154945302 @default.
- W4377164015 hasConcept C158448853 @default.
- W4377164015 hasConcept C17020691 @default.
- W4377164015 hasConcept C185592680 @default.
- W4377164015 hasConcept C28826006 @default.
- W4377164015 hasConcept C2984842247 @default.
- W4377164015 hasConcept C33923547 @default.
- W4377164015 hasConcept C41008148 @default.
- W4377164015 hasConcept C50644808 @default.
- W4377164015 hasConcept C55493867 @default.
- W4377164015 hasConcept C558565934 @default.
- W4377164015 hasConcept C73301696 @default.
- W4377164015 hasConcept C80444323 @default.
- W4377164015 hasConcept C86339819 @default.
- W4377164015 hasConcept C99874945 @default.
- W4377164015 hasConceptScore W4377164015C104317684 @default.
- W4377164015 hasConceptScore W4377164015C108583219 @default.
- W4377164015 hasConceptScore W4377164015C121332964 @default.
- W4377164015 hasConceptScore W4377164015C121864883 @default.
- W4377164015 hasConceptScore W4377164015C142362112 @default.
- W4377164015 hasConceptScore W4377164015C153349607 @default.
- W4377164015 hasConceptScore W4377164015C154945302 @default.
- W4377164015 hasConceptScore W4377164015C158448853 @default.
- W4377164015 hasConceptScore W4377164015C17020691 @default.
- W4377164015 hasConceptScore W4377164015C185592680 @default.
- W4377164015 hasConceptScore W4377164015C28826006 @default.
- W4377164015 hasConceptScore W4377164015C2984842247 @default.
- W4377164015 hasConceptScore W4377164015C33923547 @default.
- W4377164015 hasConceptScore W4377164015C41008148 @default.
- W4377164015 hasConceptScore W4377164015C50644808 @default.