Stereo depth estimation using synchronous optimization with segment based regularization
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Regularization
Classification of discontinuities
Maxima and minima
Recent work has noted that all bad local minima can be removed from neural network loss landscapes, by adding a single unit with a particular parameterization. We show that the core technique from these papers can be used to remove all bad local minima from any loss landscape, so long as the global minimum has a loss of zero. This procedure does not require the addition of auxiliary units, or even that the loss be associated with a neural network. The method of action involves all bad local minima being converted into bad (non-local) minima at infinity in terms of auxiliary parameters.
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Maxima and minima
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Abstract We present a novel method that constructs and navigates a network of local minima of potential fields defined over multidimensional spaces. Though motivated by problems of motion planning for robotic manipulators, similar techniques have been proposed for use in other domains such as molecular chemistry and drug design. The method is based on building a roadmap of paths connecting local minima of a potential function. The novel approach consists of an up‐hill search strategy used to climb out of local minima and find new nearby local minima, without doubling back on previous local minima. With this up‐hill search strategy, one can find local minima otherwise difficult to encounter, and one can focus the search to specific local minima and specific directions from those local minima. The construction of the roadmap can be done in parallel with very little communication. We present extensive simulation results. © 2001 John Wiley & Sons, Inc.
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Maxima and minima
Saturation (graph theory)
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We applied an extended version of the Niching-CMA-ES heuristic to search for local minima of the Cooke triplet, a renowned photographic lens design, of which 21 local minima were already known. The considered problem is defined by 6 input (decision) variables, namely the curvatures of the three lenses present in the Cooke triplet, and is driven by a single objective function, that is the RMS spot size. The applied approach found: (i) 19 out of the 21 known minima in a single run; (ii) 540 new local minima with objective values lower/equal to those of the known 21 minima; (iii) a large number of infeasible designs.
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The training of neural net classifiers is often hampered by the occurrence of local minima, which results in the attainment of inferior classification performance. It has been shown that the occurrence of local minima in the criterion function is often related to specific patterns of defects in the classifier. In particular, three main causes for local minima were identified. Such an understanding of the physical correlates of local minima suggests sensible ways of choosing the weights from which the training process is initiated. A method of initialization is introduced and shown to decrease the possibility of local minima occurring on various test problems.
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Abstract Discontinuities that have unfavourable orientation and are continuous within overall engineering rock regions can have a dominant effect on the strength, deformability and permeability of the rock mass. The concepts of geometrical parameters of basic discontinuities and engineering discontinuities are proposed in this communication. Further, the engineering discontinuities are divided into key discontinuities and non‐key discontinuities. Within any region of the rock mass, the spacing, trace length and probability of engineering discontinuities can be estimated from the geometrical parameters of the basic discontinuities. In general, the geometrical parameters are different from those of the basic discontinuities. Finally, two examples are given to illustrate how to apply these parameters to rock engineering problems.
Classification of discontinuities
Geomechanics
Discontinuity (linguistics)
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Large solid material masses inevitably contain discontinuities. In many cases they occur in one or several parallel sets with individual discontinuities spaced at regular intervals. The numerical treatment of the combined effect of motion across discontinuities and deformation of the intervening intact blocks poses a formidable challenge. Two general complementary approaches are considered for stress wave interaction: explicit, in which the motions across the discontinuities and the deformation within the blocks are represented separately; and implicit, wherein a single effective medium is defined so as to deform on average like an assemblage of blocks and discontinuities. The implicit composite model admits arbitrary constitutive behavior in both the intact blocks and discontinuities, and by enforcing internal compatibility and stress equilibrium derives a super-element representing the combined anistropic behavior due to both discontinuities and continuous blocks, in close agreement with the explicit model.
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With the purpose of solving the local minima of standard Back-Propagation(BP) algorithm,a modified error function was proposed to escape from the local minima and converge to the global minima.A modified XOR was used.The result contrast indicates that the new back-propagation algorithm can fast escape from the local minima and converge to the global minima,which is just within the expectation.
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Backpropagation
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Maxima and minima
Momentum (technical analysis)
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