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Overcoming the limitations of deep learning
These two possible problems can be overcome by:
- Minimizing the use of the sigmoid and tanh activation functions
- Using a momentum-based stochastic gradient descent
- Proper initialization of weights and biases, such as xavier initialization
- Regularization (add regularization loss along with data loss and minimize that)
For more detail, along with mathematical representations of the vanishing and exploding gradient, you can read this article: Intelligent Signals : Unstable Deep Learning. Why and How to solve them ?