Describe the challenges and methods associated with training very deep neural networks, such as those used in state-of-the-art image recognition models.

Training very deep neural networks presents challenges like vanishing/exploding gradients, increased computational requirements, and overfitting. Methods to address these include the use of residual connections (as in ResNet) to facilitate gradient flow, batch normalization to stabilize learning, and dropout to prevent overfitting. Advanced optimizers like Adam and learning rate scheduling also help in managing the training process efficiently.