3,616 research outputs found
Deep Limits of Residual Neural Networks
Neural networks have been very successful in many applications; we often,
however, lack a theoretical understanding of what the neural networks are
actually learning. This problem emerges when trying to generalise to new data
sets. The contribution of this paper is to show that, for the residual neural
network model, the deep layer limit coincides with a parameter estimation
problem for a nonlinear ordinary differential equation. In particular, whilst
it is known that the residual neural network model is a discretisation of an
ordinary differential equation, we show convergence in a variational sense.
This implies that optimal parameters converge in the deep layer limit. This is
a stronger statement than saying for a fixed parameter the residual neural
network model converges (the latter does not in general imply the former). Our
variational analysis provides a discrete-to-continuum -convergence
result for the objective function of the residual neural network training step
to a variational problem constrained by a system of ordinary differential
equations; this rigorously connects the discrete setting to a continuum
problem
Model based learning for accelerated, limited-view 3D photoacoustic tomography
Recent advances in deep learning for tomographic reconstructions have shown
great potential to create accurate and high quality images with a considerable
speed-up. In this work we present a deep neural network that is specifically
designed to provide high resolution 3D images from restricted photoacoustic
measurements. The network is designed to represent an iterative scheme and
incorporates gradient information of the data fit to compensate for limited
view artefacts. Due to the high complexity of the photoacoustic forward
operator, we separate training and computation of the gradient information. A
suitable prior for the desired image structures is learned as part of the
training. The resulting network is trained and tested on a set of segmented
vessels from lung CT scans and then applied to in-vivo photoacoustic
measurement data
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