Cuong Phu Le

Pavlo Melnyk, Michael Felsberg, Mårten Wadenbäck et al.

In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of O$(n)$. Namely, we propose O$(n)$-equivariant neurons with spherical decision surfaces that generalize to any dimension $n$, which we call Deep Equivariant Hyperspheres. We demonstrate how to combine them in a network that directly operates on the basis of the input points and propose an invariant operator based on the relation between two points and a sphere, which as we show, turns out to be a Gram matrix. Using synthetic and real-world data in $n$D, we experimentally verify our theoretical contributions and find that our approach is superior to the competing methods for O$(n)$-equivariant benchmark datasets (classification and regression), demonstrating a favorable speed/performance trade-off. The code is available at https://github.com/pavlo-melnyk/equivariant-hyperspheres.

Dung Hoang-Anh, Cuong Pham Trung Le, Jianfei Cai et al.

Zero-shot quantization aims to learn a quantized model from a pre-trained full-precision model with no access to original real training data. The common idea in zero-shot quantization approaches is to generate synthetic data for quantizing the full-precision model. While it is well-known that deep neural networks with low sharpness have better generalization ability, none of the previous zero-shot quantization works considers the sharpness of the quantized model as a criterion for generating training data. This paper introduces a novel methodology that takes into account quantized model sharpness in synthetic data generation to enhance generalization. Specifically, we first demonstrate that sharpness minimization can be attained by maximizing gradient matching between the reconstruction loss gradients computed on synthetic and real validation data, under certain assumptions. We then circumvent the problem of the gradient matching without real validation set by approximating it with the gradient matching between each generated sample and its neighbors. Experimental evaluations on CIFAR-100 and ImageNet datasets demonstrate the superiority of the proposed method over the state-of-the-art techniques in low-bit quantization settings.