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We study spectral properties of a spinless quantum particle confined to an infinite planar layer with hard walls, which interacts with a periodic lattice of point perturbations and a homogeneous magnetic field perpendicular to the layer. It is supposed that the lattice cell contains a finite number of impurities and the flux through the cell is rational. Using the Landau-Zak transformation, we convert the problem into investigation of the corresponding fiber operators which is performed by means of Krein's formula. This yields an explicit description of the spectral bands, which may be absolutely continuous or degenerate, depending on the parameters of the model.

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Feature distillation, a primary method in knowledge distillation, always leads to significant accuracy improvements. Most existing methods distill features in the teacher network through a manually designed transformation. In this paper, we propose a novel distillation method named task-oriented feature distillation (TOFD) where the transformation is convolutional layers that are trained in a data-driven manner by task loss. As a result, the task-oriented information in the features can be captured and distilled to students. Moreover, an orthogonal loss is applied to the feature resizing layer in TOFD to improve the performance of knowledge distillation. Experiments show that TOFD outperforms other distillation methods by a large margin on both image classification and 3D classification tasks. Codes have been released in Github[3].

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