Vanishing gradient problem is a phenomenon that occurs during the training of deep neural networks, where the gradients that are used to update the network become extremely small or "vanish" as they are backpropogated from the output layers to the earlier layers.

The vanishing gradient problem can somewhat be mitigated using the ReLU (Rectified Linear Unit) activation function, for which the gradient in most cases would have a value of 1, unlike tanh of sigmoid activations which in most cases would have a gradient that is nearly a 0

Dear Abu RayHan,

The vanishing gradient problem, a significant challenge in deep learning, hinders the training of deep neural networks. It arises due to the nature of backpropagation, the algorithm commonly employed for training such networks. During backpropagation, gradients are computed and propagated backward through the layers of a network to update the weights. The vanishing gradient problem occurs when these gradients become extremely small as they propagate through deep networks. Since the gradients are multiplied in each layer as part of the backpropagation process, their diminishment can lead to exponentially decreasing gradients as they move backward from the output layers to the initial layers. Consequently, the weights in shallow layers receive vanishingly small updates, severely impeding their learning. This issue adversely affects the training of deep neural networks in several ways.

Firstly, the network's convergence becomes slow, as the initial layers receive negligible gradient updates, delaying their learning progress.

Secondly, shallow layers may fail to learn meaningful features, hampering the network's capacity to extract useful representations from the data.

Lastly, deep networks may become prone to overfitting, as the shallow layers struggle to update efficiently due to the vanishing gradients.

To address the vanishing gradient problem, various techniques and architectures have been developed. One such approach is the initialization of weights using carefully chosen methods. For instance, employing weight initialization techniques like Xavier or He initialization can alleviate the vanishing gradient problem to some extent by avoiding excessively small or large initial weights. Additionally, activation functions play a crucial role in mitigating this problem. Non-linear activation functions such as ReLU (Rectified Linear Unit) have gained popularity due to their ability to combat vanishing gradients. ReLU ensures that gradients do not vanish by avoiding saturation for positive inputs, allowing for efficient backpropagation through deep networks.

Furthermore, advanced architectures like Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRU) have been designed specifically to alleviate the vanishing gradient problem in recurrent neural networks (RNNs). These architectures incorporate gating mechanisms to selectively propagate gradients through time, enabling better information flow across distant time steps.

The vanishing gradient problem in deep learning refers to a situation where gradients of the loss function, with respect to the model's parameters, become exceedingly small as they are propagated backward through the layers of a deep neural network during training. This phenomenon results in earlier layers receiving very small weight updates, leading to a slow or stagnant training process. To combat this issue, various techniques and architectures have been introduced. Among the most notable solutions are the introduction of activation functions like the Rectified Linear Unit (ReLU) and its variants, and architectures like skip connections, as seen in Residual Networks (ResNet). These approaches aim to ensure a smoother and more effective flow of gradient information through the network, facilitating deeper and more robust model training.

It's a typical problem we could meet when learning and using DL. But there are so many answers on the internet to your question, maybe you've got them.

In brief, when the gradients of the loss function with respect to the network parameters become too small, the network stops learning or learns very slowly. And I tried different activation function to mitigate this problem, for example, Rectified Linear Units (ReLU) in ANN structure.

Moreover, I found a useful but concise answer to share with you, link here:

https://www.kdnuggets.com/2022/02/vanishing-gradient-problem.html

The vanishing gradient problem is a challenge that can occur during the training of deep neural networks, particularly in the context of gradient-based optimization algorithms like stochastic gradient descent (SGD). It pertains to the way gradients (derivatives of the loss function with respect to the model's parameters) are computed and propagated backward through the layers of a deep neural network during the training process. The problem can lead to slow convergence or the complete failure of training in deep networks.

The core of any deep learning architecture is the Gradient descent algorithm and Backpropagation.

In Backpropagation, you essentially compute gradients of the Loss function with the respect to the weights starting at the output layer and going back to the input layer chaining the gradients (aka chain rule) as you go, and these gradients are in the order of few thousands a part ( about 0.001 or 0.0001) at every layer and they almost vanish when you multiply them all.

The Vanishing Gradient Problem in deep learning is like that one elusive sock that always seems to disappear in the laundry. You know it's there somewhere, but no matter how hard you look, it just vanishes into thin air. But unlike the sock, this problem has serious implications for the training of deep neural networks.

So what exactly is this vanishing gradient problem? Well, imagine you're trying to teach a neural network to recognize cats. You feed it a bunch of cat pictures and expect it to learn from them. But here's the catch - the network learns by adjusting its weights based on the error it makes during training. And this adjustment is done using a technique called backpropagation.

Now, let's say you have multiple layers in your network. During backpropagation, the error signal gets propagated backwards through these layers, and each layer adjusts its weights accordingly. The problem arises when this error signal becomes too small as it travels backward through each layer. It gradually diminishes until it practically disappears - hence the name "vanishing gradient."

This vanishing gradient problem wreaks havoc on deep neural networks because those poor little gradients can't provide enough information for proper weight adjustments in deeper layers. As a result, these deeper layers don't learn much from their mistakes and end up being useless blobs of neurons.

But fear not! The brilliant minds of deep learning have come up with some nifty techniques and architectures to tackle this pesky issue. One such technique is called "gradient clipping." It's like putting a leash on those runaway gradients so they don't vanish into thin air anymore. By setting an upper limit on how large or small gradients can be, we ensure they stay within a reasonable range and prevent them from disappearing altogether.

Another approach is using activation functions that are less prone to causing vanishing gradients. For instance, instead of using sigmoid or tanh functions that squash values between 0 and 1, we can opt for ReLU (Rectified Linear Unit) activation function. ReLU is like a superhero that saves the day by only activating when its input is positive, thus preventing gradients from vanishing.

To illustrate how these techniques have solved the vanishing gradient problem, let's consider the example of image classification. In the past, deep neural networks struggled to accurately classify images with many layers due to vanishing gradients. But with gradient clipping and ReLU activation functions, networks like ResNet and DenseNet have achieved remarkable results in image recognition tasks.

In conclusion, the vanishing gradient problem may seem like a disappearing sock in your laundry, but it's a serious issue that affects the training of deep neural networks. Fortunately, techniques such as gradient clipping and using appropriate activation functions have emerged as superheroes to mitigate this problem. So next time you encounter a vanishing gradient, just remember that there are solutions out there - no need to panic!

Reference:

Nguyen-Duc T., Nguyen H., Pham V.T., Nguyen L.M., Tran D.N. (2020) A Novel Approach for Vanishing Gradient Problem in Deep Learning Using Rectified Linear Unit Activation Function. In: Le T., Le N., Hoang D., Pham C., Nguyen N. (eds) Advanced Computational Methods for Knowledge Engineering. Springer Proceedings in Mathematics & Statistics, vol 312. Springer, Cham