7,887 research outputs found
On-Line Learning Theory of Soft Committee Machines with Correlated Hidden Units - Steepest Gradient Descent and Natural Gradient Descent -
The permutation symmetry of the hidden units in multilayer perceptrons causes
the saddle structure and plateaus of the learning dynamics in gradient learning
methods. The correlation of the weight vectors of hidden units in a teacher
network is thought to affect this saddle structure, resulting in a prolonged
learning time, but this mechanism is still unclear. In this paper, we discuss
it with regard to soft committee machines and on-line learning using
statistical mechanics. Conventional gradient descent needs more time to break
the symmetry as the correlation of the teacher weight vectors rises. On the
other hand, no plateaus occur with natural gradient descent regardless of the
correlation for the limit of a low learning rate. Analytical results support
these dynamics around the saddle point.Comment: 7 pages, 6 figure
Effect of manganese doping on the size effect of lead zirconate titanate thin films and the extrinsic nature of dead layers
We have investigated the size effect in lead zirconate titanate (PZT) thin
films with a range of manganese (Mn) doping concentrations. We found that the
size effect in the conventional Pt/PZT/Pt thin-film capacitors could be
systematically reduced and almost completely eliminated by increasing Mn doping
concentration. The interfacial layer at the electrode-film interface appears to
disappear almost entirely for the PZT films with 2% Mn doping levels, confirmed
by the fits using the conventional in-series capacitor model. Our work
indicates that the size effect in ferroelectrics is extrinsic in nature,
supporting the work by Saad et al. Other implications of our results have also
been discussed. By comparing a variety of experimental studies in the
literature we propose a scenario that the dead layer between PZT (or barium
strontium titanate, BST) and metal electrodes such as Pt and Au might have a
defective pyrochlore/fluorite structure (possibly with a small portion of
ferroelectric perovskite phase).Comment: 21 pages, 6 figure
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