Residual connections, also known as skip connections, are a crucial architectural feature in deep learning, particularly in neural networks like ResNet. They allow the input of a layer to bypass one or more layers and be added directly to the output of a subsequent layer. This mechanism helps to mitigate issues such as vanishing and exploding gradients, which can hinder the training of deep networks.

The primary function of residual connections is to facilitate the learning of residual functions, which are often easier to optimize than the original functions. For instance, if a function is difficult to learn, its residual can be defined as the difference between the desired output and the input, making it simpler for the network to adjust its weights accordingly. This is particularly beneficial in very deep networks, where training can become challenging due to the depth of the architecture ¹².

Moreover, residual connections introduce multiple paths for gradients during backpropagation, which helps in maintaining effective gradient flow. This results in improved convergence during training and allows for the construction of deeper networks without a significant increase in training difficulty ¹⁵.