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1,856
Training Products of Experts by Minimizing Contrastive Divergence
, 2002
"... It is possible to combine multiple latentvariable models of the same data by multiplying their probability distributions together and then renormalizing. This way of combining individual “expert ” models makes it hard to generate samples from the combined model but easy to infer the values of the l ..."
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Cited by 850 (75 self)
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is unnecessary. Training a PoE by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule. Fortunately, a PoE can be trained using a different objective function called “contrastive divergence ” whose
Renormalization group flows from holography  Supersymmetry and a ctheorem
 ADV THEOR. MATH. PHYS
, 1999
"... We obtain first order equations that determine a supersymmetric kink solution in fivedimensional N = 8 gauged supergravity. The kink interpolates between an exterior antide Sitter region with maximal supersymmetry and an interior antide Sitter region with one quarter of the maximal supersymmetry. ..."
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Cited by 294 (25 self)
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. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N = 4 superYangMills theory broken to an N = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained
Differential Renormalization
, 1992
"... Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure for massless φ 4 theory is therefore studied in order to te ..."
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Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure for massless φ 4 theory is therefore studied in order
Renormalization of Hamiltonians
, 1997
"... Abstract. A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in the perturbative expansion, is projected on a smal ..."
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Abstract. A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in the perturbative expansion, is projected on a
Trees in renorming theory
 Proc. London Math. Soc 78
, 1999
"... Renorming theory is that branch of functional analysis which investigates problems of the form: for which Banach spaces X does there exist a norm on X, equivalent to the given norm, with some good geometrical property of smoothness or strict convexity? The hope is to give answers in terms of familia ..."
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Cited by 44 (3 self)
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Renorming theory is that branch of functional analysis which investigates problems of the form: for which Banach spaces X does there exist a norm on X, equivalent to the given norm, with some good geometrical property of smoothness or strict convexity? The hope is to give answers in terms
Renormalization Group
, 2009
"... The renormalization procedure in the last chapter has eliminated all UVdivergences from the Feynman integrals arising from large momenta in D = 4 − ε dimensions. This was necessary to obtain finite correlation functions in the limit ε → 0. We have seen in Chapter 7 that the dependence on the cutoff ..."
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on the cutoff or any other mass scale, introduced in the regularization process, changes the Ward identities derived from scale transformations by an additional term—the anomaly of scale invariance. The precise consequences of this term for the renormalized proper vertex functions were first investigated
Renormalization Group
, 2010
"... The renormalization procedure in the last chapter has eliminated all UVdivergences from the Feynman integrals arising from large momenta in D = 4 − ε dimensions. This was necessary to obtain finite correlation functions in the limit ε → 0. We have seen in Chapter 7 that the dependence on the cutoff ..."
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on the cutoff or any other mass scale, introduced in the regularization process, changes the Ward identities derived from scale transformations by an additional term—the anomaly of scale invariance. The precise consequences of this term for the renormalized proper vertex functions were first investigated
Testable Consequences of CurvedSpacetime Renormalization
, 1998
"... I consider certain renormalization effects in curved spacetime quantum field theory. In the very early universe these effects resemble those of a cosmological constant, while in the present universe they give rise to a significant finite renormalization of the gravitational constant. The relevant re ..."
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renormalization term and its relation to elementary particle masses was first found by Parker and Toms in 1985, as a consequence of the “new partially summed form ” of the propagator in curved spacetime. The significance of the term is based on the contribution of massive particles to the vacuum. In the present
Boundary terms Unbound! Holographic Renormalization Of . . .
, 2009
"... A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a pform field strength. This requires the introduction of appropriate surface terms – also known as ‘boundary counterterms’ – in the action. The variation of the action with respect to the boundary m ..."
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Cited by 5 (0 self)
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A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a pform field strength. This requires the introduction of appropriate surface terms – also known as ‘boundary counterterms’ – in the action. The variation of the action with respect to the boundary
54 On the Renormalization of Quantum Electrodynamics
, 1950
"... ABSTRACT. The subtraction procedure of Dyson is modified in order to eliminate a certain difficulty in the renormalization programme, namely the socalled ‘ b ’ divergencies, The conclusions of Dyson concerning the finiteness of the renormalized S matrix are confirmed. I T has been shown to be very ..."
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1950) If we definep”=pA+p’(lA) wherep ’ is the energymomentum vector of a free electron then 2 ~ =) 257 j: W,PL:)~~,(~~, pi) where the effects of the contribution of the mass renormalization term to Cy have been taken into account. A, ( V’,,P’,,P”) will now contain the infinities arising from
Results 1  10
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1,856