On Lazy Training in Differentiable Programming
This challenges the idea that lazy training explains neural network success, with implications for theoretical understanding in non-convex optimization.
The paper shows that 'lazy training' in neural networks, where parameters barely change during optimization, arises from a scaling choice that linearizes models, making them equivalent to kernel methods, and finds that this regime degrades performance in deep convolutional networks for vision tasks.
In a series of recent theoretical works, it was shown that strongly over-parameterized neural networks trained with gradient-based methods could converge exponentially fast to zero training loss, with their parameters hardly varying. In this work, we show that this "lazy training" phenomenon is not specific to over-parameterized neural networks, and is due to a choice of scaling, often implicit, that makes the model behave as its linearization around the initialization, thus yielding a model equivalent to learning with positive-definite kernels. Through a theoretical analysis, we exhibit various situations where this phenomenon arises in non-convex optimization and we provide bounds on the distance between the lazy and linearized optimization paths. Our numerical experiments bring a critical note, as we observe that the performance of commonly used non-linear deep convolutional neural networks in computer vision degrades when trained in the lazy regime. This makes it unlikely that "lazy training" is behind the many successes of neural networks in difficult high dimensional tasks.