We analyze the one-pass stochastic gradient descent dynamics of a two-layer neural network with quadratic activations in a teacher--student framework. In the high-dimensional regime, where the input dimension $N$ and the number of samples $M$ diverge at fixed ratio $α= M/N$, and for finite hidden widths $(p,p^*)$ of the student and teacher, respectively, we study the low-dimensional ordinary differential equations that govern the evolution of the student--teacher and student--student overlap matrices. We show that overparameterization ($p>p^*$) only modestly accelerates escape from a plateau of poor generalization by modifying the prefactor of the exponential decay of the loss. We then examine how unconstrained weight norms introduce a continuous rotational symmetry that results in a nontrivial manifold of zero-loss solutions for $p>1$. From this manifold the dynamics consistently selects the closest solution to the random initialization, as enforced by a conserved quantity in the ODEs governing the evolution of the overlaps. Finally, a Hessian analysis of the population-loss landscape confirms that the plateau and the solution manifold correspond to saddles with at least one negative eigenvalue and to marginal minima in the population-loss geometry, respectively.

Many researchers have sought ways of model compression to reduce the size of a deep neural network (DNN) with minimal performance degradation in order to use DNNs in embedded systems. Among the model compression methods, a method called knowledge transfer is to train a student network with a stronger teacher network. In this paper, we propose a novel knowledge transfer method which uses convolutional operations to paraphrase teacher's knowledge and to translate it for the student. This is done by two convolutional modules, which are called a paraphraser and a translator. The paraphraser is trained in an unsupervised manner to extract the teacher factors which are defined as paraphrased information of the teacher network. The translator located at the student network extracts the student factors and helps to translate the teacher factors by mimicking them. We observed that our student network trained with the proposed factor transfer method outperforms the ones trained with conventional knowledge transfer methods.

In knowledge distillation, previous feature distillation methods mainly focus on the design of loss functions and the selection of the distilled layers, while the effectofthefeatureprojector between thestudent andtheteacher remains underexplored.

Whilesomerecent works propose to distill an ensemble model into a single model to reduce such costs,thereisstillaperformance gapbetween theensemble anddistilledmodels.

The above scheme proves particularly relevant when the student network is overparameterized (namely, when larger layer sizes are employed) as compared to the underlying teacher network. Under these operating conditions, it is tempting to speculate that the student ability to handle the given task could be eventually stored in a sub-portion of the whole network.

The above scheme proves particularly relevant when the student network is overparameterized (namely, when larger layer sizes are employed) as compared to the underlying teacher network. Under these operating conditions, it is tempting to speculate that the student ability to handle the given task could be eventually stored in a sub-portion of the whole network.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/