In this paper, we consider a model of an artificial neural network based on quantum-mechanical particles in [Formula: see text] potential. These particles play the role of neurons in our model. To simulate such a quantum-mechanical system, the Monte Carlo integration method is used. A form of the self-potential of a particle as well as two interaction potentials (exciting and inhibiting) are proposed. Examples of simplest logical elements (such as AND, OR and NOT) are shown. Further, we show an implementation of the simplest convolutional network in framework of our model.
AbstractWe consider semantic image segmentation. Our method is inspired by Bayesian deep learning which improves image segmentation accuracy by modeling the uncertainty of the network output. In contrast to uncertainty, our method directly learns to predict the erroneous pixels of a segmentation network, which is modeled as a binary classification problem. It can speed up training comparing to the Monte Carlo integration often used in Bayesian deep learning. It also allows us to train a branch to correct the labels of erroneous pixels. Our method consists of three stages: (i) predict pixel-wise error probability of the initial result, (ii) redetermine new labels for pixels with high error probability, and (iii) fuse the initial result and the redetermined result with respect to the error probability. We formulate the error-pixel prediction problem as a classification task and employ an error-prediction branch in the network to predict pixel-wise error probabilities. We also introduce a detail branch to focus the training process on the erroneous pixels. We have experimentally validated our method on the Cityscapes and ADE20K datasets. Our model can be easily added to various advanced segmentation networks to improve their performance. Taking DeepLabv3+ as an example, our network can achieve 82.88% of mIoU on Cityscapes testing dataset and 45.73% on ADE20K validation dataset, improving corresponding DeepLabv3+ results by 0.74% and 0.13% respectively.
We use variance minimization and Monte Carlo integration to calculate
the relativistic one-electron atomic (Z=92) wavefunctions (both the
2-component and 4-component forms) for the 1S1/2, 2S1/2, 2P1/2, 2P3/2,
3S1/2, 3P1/2, 3P3/2, 3D3/2 and 3D5/2 states. With these wavefunctions we
then evaluate the energy, a variety of simple properties and the decay
rates for a number of E1, M1, E2 and M2 transitions. Our results are in
excellent agreement with those in the literature.
Hybrid Petri nets have been extended to include general transitions that fire after a randomly distributed amount of time. With a single general one-shot transition the state space and evolution over time can be represented either as a
Parametric Location Tree
or as a
Stochastic Time Diagram
. Recent work has shown that both representations can be combined and then allow multiple stochastic firings. This work presents an algorithm for building the
Parametric Location Tree
with multiple general transition firings and shows how its transient probability distribution can be computed using multi-dimensional integration. We discuss the (dis-)advantages of an interval arithmetic and a geometric approach to compute the areas of integration. Furthermore, we provide details on how to perform a Monte Carlo integration either directly on these intervals or convex polytopes, or after transformation to standard simplices. A case study on a battery-backup system shows the feasibility of the approach and discusses the performance of the different integration approaches.
Erroneous pixel prediction for semantic image segmentation
