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function. All parameters are concatenated into one vector = [vec(W) >;vec(V)>] . In the following questions, the neural network, the activation and loss function can be any of their combinations. Of course, you can consider multiple choices of them or even cover all of them.

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Newton's method uses the Hessian of the loss function, a matrix of second derivatives, to calculate the learning direction. Since it uses high order information, the learning direction points to the minimum of the loss function with higher accuracy. The drawback is that calculating the Hessian matrix is very computationally expensive.

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H n ( x n − x n − 1) = ( g n − g n − 1) This yields the so-called “secant conditions” which ensures that H n + 1 behaves like the Hessian at least for the diference ( x n − x n − 1). Assuming H n is invertible (which is true if it is psd), then multiplying both sides by H n − 1 yields. H n − 1 y n = s n.

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Dec 27, 2019 · in regions of the loss function where the hessian has high values means that the curvature of the functions is high, and therefore the learning rate or scaling factor should be small in regions of the loss function where the. hessain has small values, the curvature if low and therefore you shouldn't be wasting time and the learning rate will therefore increase

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Softmax and cross-entropy loss. We've just seen how the softmax function is used as part of a machine learning network, and how to compute its derivative using the multivariate chain rule. While we're at it, it's worth to take a look at a loss function that's commonly used along with softmax for training a network: cross-entropy.

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May 09, 2019 · The curvature (Hessian) of a function is the second-order derivative of the function, which depicts how quickly the gradient of the function changes. Computing Hessian (curvature) takes longer time than computing just gradient but knowing Hessian can accelerate learning convergence.