We compute the overlap Dirac spectrum on three ensembles generated using 2+1 flavor domain wall fermions. The spectral density is determined up to $lambdasim$100 MeV with sub-percentage statistical uncertainty. The three ensembles have different latt
ice spacings and two of them have quark masses tuned to the physical point. We show that we can resolve the flavor content of the sea quarks and constrain their masses using the Dirac spectral density. We find that the density is close to a constant below $lambdale$ 20 MeV (but 10% higher than that in the 2-flavor chiral limit) as predicted by chiral perturbative theory ($chi$PT), and then increases linearly due to the strange quark mass. Using the next to leading order $chi$PT, one can extract the light and strange quark masses with $sim$20% uncertainties. Using the non-perturbative RI/MOM renormalization, we obtain the chiral condensates at $overline{textrm{MS}}$ 2 GeV as $Sigma=(260.3(0.7)(1.3)(0.7)(0.8) textrm{MeV})^3$ in the $N_f=2$ (keeping the strange quark mass at the physical point) chiral limit and $Sigma_0=(232.6(0.9)(1.2)(0.7)(0.8) textrm{MeV})^3$ in the $N_f=3$ chiral limit, where the four uncertainties come from the statistical fluctuation, renormalization constant, continuum extrapolation and lattice spacing determination. Note that {$Sigma/Sigma_0=1.40(2)(2)$ is much larger than 1} due to the strange quark mass effect.
Most differentiable neural architecture search methods construct a super-net for search and derive a target-net as its sub-graph for evaluation. There exists a significant gap between the architectures in search and evaluation. As a result, current m
ethods suffer from an inconsistent, inefficient, and inflexible search process. In this paper, we introduce EnTranNAS that is composed of Engine-cells and Transit-cells. The Engine-cell is differentiable for architecture search, while the Transit-cell only transits a sub-graph by architecture derivation. Consequently, the gap between the architectures in search and evaluation is significantly reduced. Our method also spares much memory and computation cost, which speeds up the search process. A feature sharing strategy is introduced for more balanced optimization and more efficient search. Furthermore, we develop an architecture derivation method to replace the traditional one that is based on a hand-crafted rule. Our method enables differentiable sparsification, and keeps the derived architecture equivalent to that of Engine-cell, which further improves the consistency between search and evaluation. Besides, it supports the search for topology where a node can be connected to prior nodes with any number of connections, so that the searched architectures could be more flexible. For experiments on CIFAR-10, our search on the standard space requires only 0.06 GPU-day. We further have an error rate of 2.22% with 0.07 GPU-day for the search on an extended space. We can also directly perform the search on ImageNet with topology learnable and achieve a top-1 error rate of 23.8% in 2.1 GPU-day.
We analyze the lattice spacing dependence for the pion unpolarized matrix element of a quark bilinear operator with Wilson link (quasi-PDF operator) in the rest frame, using 13 lattice spacings ranging from 0.032 fm to 0.121 fm. We compare results fo
r three different fermion actions with or without good chiral symmetry on dynamical gauge ensembles from three collaborations. This investigation is motivated by the fact that the gauge link generates an $1/a$ divergence, the cancelation of which in many ratios can be numerically tricky. Indeed, our results show that this cancelation deteriorates with decreasing lattice spacing, and that the RI/MOM method leaves a linearly divergent residue for quasi-PDFs. We also show that in the Landau gauge the interaction between the Wilson link and the external state results in a linear divergence which depends on the discretized fermion action.
We investigated the origin of the RI/MOM quark mass under the Landau gauge at the non-perturbative scale, using the chiral fermion with different quark masses and lattice spacings. Our result confirms that such a mass is non-vanishing based on the li
near extrapolation to the chiral and continuum limit, and shows that such a mass comes from the spontaneous chiral symmetry breaking induced by the near zero modes with the eigenvalue $lambda<{cal O}(5m_q)$, and is proportional to the quark matrix element of the trace anomaly at least down to $sim $1.3 GeV.
The convolution operation suffers from a limited receptive filed, while global modeling is fundamental to dense prediction tasks, such as semantic segmentation. In this paper, we apply graph convolution into the semantic segmentation task and propose
an improved Laplacian. The graph reasoning is directly performed in the original feature space organized as a spatial pyramid. Different from existing methods, our Laplacian is data-dependent and we introduce an attention diagonal matrix to learn a better distance metric. It gets rid of projecting and re-projecting processes, which makes our proposed method a light-weight module that can be easily plugged into current computer vision architectures. More importantly, performing graph reasoning directly in the feature space retains spatial relationships and makes spatial pyramid possible to explore multiple long-range contextual patterns from different scales. Experiments on Cityscapes, COCO Stuff, PASCAL Context and PASCAL VOC demonstrate the effectiveness of our proposed methods on semantic segmentation. We achieve comparable performance with advantages in computational and memory overhead.
The open source HIP platform for GPU computing provides an uniform framework to support both the NVIDIA and AMD GPUs, and also the possibility to porting the CUDA code to the HIP- compatible one. We present the porting progress on the Overlap fermion
inverter (GWU-code) and also the general Lattice QCD inverter package - QUDA. The manual of using QUDA on HIP and also the tips of porting general CUDA code into the HIP framework are also provided.
The correspondence between residual networks and dynamical systems motivates researchers to unravel the physics of ResNets with well-developed tools in numeral methods of ODE systems. The Runge-Kutta-Fehlberg method is an adaptive time stepping that
renders a good trade-off between the stability and efficiency. Can we also have an adaptive time stepping for ResNets to ensure both stability and performance? In this study, we analyze the effects of time stepping on the Euler method and ResNets. We establish a stability condition for ResNets with step sizes and weight parameters, and point out the effects of step sizes on the stability and performance. Inspired by our analyses, we develop an adaptive time stepping controller that is dependent on the parameters of the current step, and aware of previous steps. The controller is jointly optimized with the network training so that variable step sizes and evolution time can be adaptively adjusted. We conduct experiments on ImageNet and CIFAR to demonstrate the effectiveness. It is shown that our proposed method is able to improve both stability and accuracy without introducing additional overhead in inference phase.
We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of $N_f = 2+1$ DWF configurations with three lattice spacings and three volu
mes, and several pion masses including the physical pion mass. With fully non-perturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 33(4)(4)% and 37(5)(4)% respectively in the $overline{MS}$ scheme at $mu = 2$ GeV. A quarter of the trace anomaly gives a 23(1)(1)% contribution to the proton mass based on the sum rule, given 9(2)(1)% contribution from the $u, d,$ and $s$ quark scalar condensates. The $u,d,s$ and glue momentum fractions in the $overline{MS}$ scheme are in good agreement with global analyses at $mu = 2$ GeV.
We present the first nonperturbatively-renormalized determination of the glue momentum fraction $langle x rangle_g$ in the nucleon, based on lattice-QCD simulations at physical pion mass using the cluster-decomposition error reduction (CDER) techniqu
e. We provide the first practical strategy to renormalize the glue energy-momentum tensor (EMT) nonperturbatively in the RI/MOM scheme, and convert the results to the $overline{textrm{MS}}$ scheme with 1-loop matching. The simulation results show that the CDER technique can reduce the statistical uncertainty of its renormalization constant by a factor of ${cal O}$(300) in calculations using typical state-of-the-art lattice volume, and the nonperturbatively-renormalized $langle x rangle_g$ is shown to be independent of the lattice definitions of the glue EMT up to discretization errors. We determine the renormalized $langle x rangle_g^{overline{textrm{MS}}}(2textrm{ GeV})$ to be 0.47(4)(11) at physical pion mass, which is consistent with the experimentally-determined value.
Improving information flow in deep networks helps to ease the training difficulties and utilize parameters more efficiently. Here we propose a new convolutional neural network architecture with alternately updated clique (CliqueNet). In contrast to p
rior networks, there are both forward and backward connections between any two layers in the same block. The layers are constructed as a loop and are updated alternately. The CliqueNet has some unique properties. For each layer, it is both the input and output of any other layer in the same block, so that the information flow among layers is maximized. During propagation, the newly updated layers are concatenated to re-update previously updated layer, and parameters are reused for multiple times. This recurrent feedback structure is able to bring higher level visual information back to refine low-level filters and achieve spatial attention. We analyze the features generated at different stages and observe that using refined features leads to a better result. We adopt a multi-scale feature strategy that effectively avoids the progressive growth of parameters. Experiments on image recognition datasets including CIFAR-10, CIFAR-100, SVHN and ImageNet show that our proposed models achieve the state-of-the-art performance with fewer parameters.
