The challenges of training deep neural networks can be classified into 3 main categories:

1) Training Data : in order to start training a neural net for a specific task, we need to acquire a training set, in which a single training example consists of intput-output pairs (x, y). Using these training examples, the network can finally figure out a relation between the input x and the output y. For most mainstream tasks, training sets are available online, but unfortunately if you are working on a task that is not so popular then you will have to acquire training data yourself. Fortunately when you manually generate a reasonable amount of training data you can use a technique called data synthesis that enables you to automatically generate more training data using the manually-generated data set.

2) Network Structure and parameters : Now that we have our training data, we need to choose a specific structure and assign parameter values, which depends heavily on the task at hand. Again for mainstream tasks, choices of structure and parameters have been proposed in the literature, but if your are working on a novel task then you will have to go through an agonizing systematic approach, where you choose random structure and parameter values, by repeating this process you will finally reach a range of structures and parameter values that should work fine for the task at hand.

3) Training Resources : Usually a deep neural network system would have millions of parameters and thousands of training instances, and as a result the computational complexity required to train such system can be huge. Usually a huge system with multi-GPUs is required to train deepNNs.

Training deep neural networks, especially deep convolutional neural networks (CNNs) and deep recurrent neural networks (RNNs), can be challenging due to various difficulties and obstacles. Researchers and practitioners have devised several techniques to address these challenges. Here are some common difficulties and the corresponding solutions:

1. Vanishing and Exploding Gradients:

• Difficulty: During backpropagation, gradients may become extremely small (vanishing) or large (exploding) as they propagate through layers, making training difficult.
• Solution: Techniques like weight initialization (Xavier/Glorot initialization), gradient clipping, and using activation functions like ReLU help mitigate these issues.

2. Overfitting:

• Difficulty: Models may memorize the training data rather than generalizing to unseen data, leading to overfitting.
• Solution: Regularization techniques like dropout, L1/L2 regularization, and early stopping are used to prevent overfitting. Data augmentation can also help by creating variations in the training data.

3. Optimization Challenges:

• Difficulty: Finding the optimal set of weights in high-dimensional spaces can be challenging. Standard optimization techniques may get stuck in local minima.
• Solution: Advanced optimization algorithms like Adam, RMSprop, and learning rate schedules are used to improve convergence.

4. Computational Resources:

• Difficulty: Training deep networks requires substantial computational resources, including GPUs and TPUs.
• Solution: Cloud computing platforms and distributed training frameworks help make deep learning more accessible. Smaller architectures like MobileNet and EfficientNet reduce computational requirements while maintaining performance.

5. Dataset Size:

• Difficulty: Deep networks often require large datasets for effective training.
• Solution: Transfer learning allows leveraging pre-trained models on larger datasets (e.g., ImageNet) as a starting point for tasks with limited data. Techniques like fine-tuning adapt these models to specific tasks.

6. Hyperparameter Tuning:

• Difficulty: Selecting the right hyperparameters (e.g., learning rate, batch size) can be challenging and time-consuming.
• Solution: Grid search, random search, and automated hyperparameter optimization tools like Hyperopt and Optuna help find suitable hyperparameters.

7. Architectural Complexity:

• Difficulty: Designing deep network architectures that balance performance and computational efficiency can be tricky.
• Solution: Neural architecture search (NAS) and automated machine learning (AutoML) tools explore architecture design space to find optimal models.

8. Regularization and Normalization:

• Difficulty: Ensuring model generalization and avoiding overfitting requires careful selection and application of regularization techniques.
• Solution: Techniques like batch normalization, layer normalization, and dropout are applied to stabilize and regularize training.

9. Data Imbalance:

• Difficulty: In classification tasks, imbalanced datasets can lead to biased models.
• Solution: Techniques like oversampling, undersampling, and class-weighted loss functions address data imbalance.

10. Parallelization:

• Difficulty: Distributing and parallelizing training across multiple devices or nodes efficiently is complex.
• Solution: Distributed deep learning frameworks like TensorFlow and PyTorch support parallel training, making use of multi-GPU setups and distributed clusters.

11. Explainability and Interpretability:

• Difficulty: Deep networks' lack of interpretability can be a challenge in domains requiring transparent decision-making.
• Solution: Techniques like gradient-based saliency maps (e.g., Grad-CAM), attention mechanisms, and model-agnostic interpretability methods enhance model interpretability.

Addressing these challenges is an ongoing area of research in deep learning, with new techniques and tools continuously emerging to make training deep neural networks more accessible and efficient.