Logistic regression is exactly a NN with no hidden layers and a sigmoid activation function. A feedforward NN with additional layers is strictly more expressive than logistic regression.
Yes! The million dollar question is how much of that expressivity is actually required.
In many papers, the "baseline" logistic regression model is very stripped down: y~logit(.) but the neural network has had its expressiveness optimized in various ways. People aren't comparing against a 3 layer feedfoward network; there's augmentation and pre-training, architecture search and special learning schemes.
My claim is that if you want to claim that a problem needs the expressivity that (only) a neural network provides, you ought to be devoting a great deal of effort to the logistic regression model too. Make it a steelman, rather than a strawman, if you will.
In many papers, the "baseline" logistic regression model is very stripped down: y~logit(.) but the neural network has had its expressiveness optimized in various ways. People aren't comparing against a 3 layer feedfoward network; there's augmentation and pre-training, architecture search and special learning schemes.
My claim is that if you want to claim that a problem needs the expressivity that (only) a neural network provides, you ought to be devoting a great deal of effort to the logistic regression model too. Make it a steelman, rather than a strawman, if you will.