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ICNNs achieve convexity by enforcing certain constraints on the weights of the network. Specifically, the weights associated with the input connections are constrained to be non-negative. This ensures that the function learned by the network is convex with respect to the input. Implementing this involves specific architectural choices and training methodologies. It’s not just about slapping on a regular neural network and hoping for the best. The architecture is carefully designed to maintain this convexity. For example, activation functions play a critical role. Common choices include ReLU (Rectified Linear Unit) and its variants, as they preserve the non-negativity required for convexity. The training process also needs to be tailored. Techniques like weight normalization and specific regularization terms are often used to ensure that the weights remain non-negative throughout training. This might involve adding penalties to the loss function if weights become negative, encouraging the optimization algorithm to keep them positive.