The Effect of Batch Normalization in the Symmetric Phase

Author(s):  
Shiro Takagi ◽  
Yuki Yoshida ◽  
Masato Okada
Author(s):  
Sushma Shrestha ◽  
Abeer Alsadoon ◽  
P. W. C. Prasad ◽  
Indra Seher ◽  
Omar Hisham Alsadoon

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Gustavo O. Heymans ◽  
Marcus Benghi Pinto

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.


2021 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Isah Charles Saidu ◽  
Lehel Csató

We present a sample-efficient image segmentation method using active learning, we call it Active Bayesian UNet, or AB-UNet. This is a convolutional neural network using batch normalization and max-pool dropout. The Bayesian setup is achieved by exploiting the probabilistic extension of the dropout mechanism, leading to the possibility to use the uncertainty inherently present in the system. We set up our experiments on various medical image datasets and highlight that with a smaller annotation effort our AB-UNet leads to stable training and better generalization. Added to this, we can efficiently choose from an unlabelled dataset.


1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.


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