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Using only sign of gradient is a way to go, but might result in slow convergence. Nevertheless it is a valid variation of the method. The Geometry of Sign Gradient Descent Sign-based optimization methods have become popular in machine learning due to their favorable communication cost in distributed optimization and their surprisingly good performance in ...


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Think about the convergence behavior of your algorithm (assuming a fixed learning rate) — once it gets x to within learning_rate of the optimum, it will jump to the other side, and the sign will change. Then it will jump back to exactly the previous value, and oscillate between those two values until you choose to terminate it, never getting any closer to ...


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Batch Normalization (BN) does not prevent the vanishing or exploding gradient problem in a sense that these are impossible. Rather it reduces the probability for these to occur. Accordingly, the original paper states: In traditional deep networks, too-high learning rate may result in the gradients that explode or vanish, as well as getting stuck in poor ...


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ReLU is considered as an activation function, on similar fashion can we use Gradient Clipping also as an activation function? ReLU is an activation function. Gradient clipping is a technique to keep the problem of exploding gradient at bay. I wish also to stress that the best technique to control for vanishing/exploding gradients is, at the moment, batch ...


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Yes we have. MSE loss function is usually used for regression problems. We can have different loss functions according to our needs. Follow the article below. https://towardsdatascience.com/common-loss-functions-in-machine-learning-46af0ffc4d23 If you wish to learn as to what does gradient does in the algorithm you can visit this article: https://...


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Just focusing on "sign" part. The sign of the gradient tells in which direction to move but only "locally". Once you move you have a new surface and then may be now the steepest portion(which leads to global minima/maxima) is not there and then you need to decide again the direction based on the sign and this might not be optimal. As ...


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(Copied from my answer on stats.SE. (This meta.SE answer seems to approve of this copy-paste pattern.)) The original Adam paper briefly explains what it means by "invariant to diagonal rescaling of the gradients" at the end of section 2.1. I would try to explain it in some more detail. Like stochastic gradient descent (SGD), Adam is an iterative method ...


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The setting: We have a neural network $\phi_{\mathbf{w}}:\mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ with weights $\mathbf{w} \in \mathbb{R}^{q}$. A loss function $\hat{L}: \mathbb{R}^{m} \times \mathbb{R}^{m} \rightarrow \mathbb{R}$ evaluates the quality of a prediction. If $x \in \mathbb{R}^{n}$ shall be mapped to $y \in \mathbb{R}^{m}$ by the neural ...


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This is because the derivative wrt $b$ is $1$: $\frac{\partial E}{\partial b} = 1$ dout is the derivative of loss function wrt prediction. Using chain rule, $$ \frac{dE}{dw} = \frac{dE}{dy}\frac{dy}{ds}\frac{ds}{dw} $$ The last term is the vector of input features $x$. In your case dout is the combination of the first two terms. For example, for MSE loss and ...


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You can get that from the weight updates, not sure if it is the best approach -Save the model -Save the weights of the first layer -Load the model and Compile the model with SGD w/o momentum -Set all the weights = that of the previous model -Train with the input and output i.e. the Array for epoch=1 and batch_size=1 -Get the weights again -Calculate the ...


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Several options: You can use the defintion of the derivative to have an approximation.... def f(x): return x[0]**2 + 3*x[1]**3 def der(f, x, der_index=[]): # der_index: variable w.r.t. get gradient epsilon = 2.34E-10 grads = [] for idx in der_index: x_ = x.copy() x_[idx]+=epsilon grads.append((f(x_) - f(x))/...


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