[D] After training, do models need to use their initial dataset to make predictions or just the trained weights?

I'm rather new to ML so please correct me if I'm wrong, but after a model is trained, the net result is a trained weight matrix that can be applied to new data. Therefore, the model won't have to do the computationally heavy training on the old dataset again.

If that is correct, why do ML predictions take so much time/computational power? Shouldn't it just be matrix multiplication through a neural network (which seems like a fairly simple calculation to …

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