A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.
The concentrating and diluting mechanisms of the normal kidney contribute in an impressive manner to the defense of water economy. In health, a given amount of solute may be excreted in a widely varying volume of water which is determined under most circumstances by the water needs of the organism. This ability to regulate the osmolality of the urine accounts for a range of urine concentrations which extends from marked hypotonicity to marked hypertonicity.1 In the course of advancing renal disease, the total amount of solute excretion per 24 hours may remain comparable to values achieved in health. It is a clinical observation of long standing, however, that the patient's ability to vary the volume of water in which this solute is contained becomes progressively limited. Hence, the range over which urine tonicity may be extended becomes more and more restricted. Typically, this restriction is manifested initially by a decrease in the maximum attainable urine osmolality, followed somewhat later by a progressive inability to decrease the tonicity of the urine. Ultimately, urine tonicity deviates little in either direction from the concurrent plasma osmolality, and the stage of so-called "permanent isosthenuria" or "fixed specific gravity" supervenes.The intrarenal mechanisms responsible for the impaired ability to concentrate and dilute the urine in chronic renal disease have never been adequately explained.
Current mechanisms for knowledge transfer in deep networks tend to either share the lower layers between tasks, or build upon representations trained on other tasks. However, existing work in non-deep multi-task and lifelong learning has shown success with using factorized representations of the model parameter space for transfer, permitting more flexible construction of task models. Inspired by this idea, we introduce a novel architecture for sharing latent factorized representations in convolutional neural networks (CNNs). The proposed approach, called a deconvolutional factorized CNN, uses a combination of deconvolutional factorization and tensor contraction to perform flexible transfer between tasks. Experiments on two computer vision data sets show that the DF-CNN achieves superior performance in challenging lifelong learning settings, resists catastrophic forgetting, and exhibits reverse transfer to improve previously learned tasks from subsequent experience without retraining.
Inspired by the possibility that generative models based on quantum circuits can provide a useful inductive bias for sequence modeling tasks, we propose an efficient training algorithm for a subset of classically simulable quantum circuit models. The gradient-free algorithm, presented as a sequence of exactly solvable effective models, is a modification of the density matrix renormalization group procedure adapted for learning a probability distribution. The conclusion that circuit-based models offer a useful inductive bias for classical datasets is supported by experimental results on the parity learning problem.
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