This yields learnable kernel transformations that are jointly optimized with downstream tasks.

Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may not be realistic for real-world data. Additionally, baking in fixed group equivariance may impose overly restrictive constraints on model architecture. This highlights the need for methods that can dynamically discover and apply symmetries as soft constraints. For neural network architectures, equivariance is commonly achieved through group transformations of a canonical weight tensor, resulting in weight sharing over a given group $G$. In this work, we propose to learn such a weight-sharing scheme by defining a collection of learnable doubly stochastic matrices that act as soft permutation matrices on canonical weight tensors, which can take regular group representations as a special case. This yields learnable kernel transformations that are jointly optimized with downstream tasks. We show that when the dataset exhibits strong symmetries, the permutation matrices will converge to regular group representations and our weight-sharing networks effectively become regular group convolutions. Additionally, the flexibility of the method enables it to effectively pick up on partial symmetries.

Vision Transformers (ViTs) have achieved impressive performance over various computer vision tasks. However, modelling global correlations with multi-head self-attention (MSA) layers leads to two widely recognized issues: the massive computational resource consumption and the lack of intrinsic inductive bias for modelling local visual patterns. To solve both issues, we devise a simple yet effective method named Single-Path Vision Transformer pruning (SPViT), to efficiently and automatically compress the pre-trained ViTs into compact models with proper locality added. Specifically, we first propose a novel weight-sharing scheme between MSA and convolutional operations, delivering a single-path space to encode all candidate operations. In this way, we cast the operation search problem as finding which subset of parameters to use in each MSA layer, which significantly reduces the computational cost and optimization difficulty, and the convolution kernels can be well initialized using pre-trained MSA parameters. Relying on the single-path space, we further introduce learnable binary gates to encode the operation choices, which are jointly optimized with network parameters to automatically determine the configuration of each layer. We conduct extensive experiments on two representative ViTs showing that our SPViT achieves a new SOTA for pruning on ImageNet-1k. For example, our SPViT can trim 52.0% FLOPs for DeiT-B and get an impressive 0.6% top-1 accuracy gain simultaneously. The source code is available at https://github.com/ziplab/SPViT.

Contributions We propose a method to learn such weight-sharing schemes from data. As a proof of concept, we focus on being invariant We propose a novel Bayesian neural network architecture to two types of transformations applied on images, that can learn invariances from data namely rotations and flips. However, our algorithm can be alone by inferring a posterior distribution over applied to any other choice of symmetry, as long as the corresponding different weight-sharing schemes. We show that weight-sharing scheme is available. Apart from our model outperforms other non-invariant architectures, achieving good performance during inference, our model is when trained on datasets that contain able to learn such invariances from data. This is achieved by specific invariances. The same holds true when specifying a probability distribution over the weight-sharing no data augmentation is performed.

Probabilistic models of natural images are usually evaluated by measuring performance on rather indirect tasks, such as denoising and inpainting. A more direct way to evaluate a generative model is to draw samples from it and to check whether statistical properties of the samples match the statistics of natural images. This method is seldom used with high-resolution images, because current models produce samples that are very different from natural images, as assessed by even simple visual inspection. We investigate the reasons for this failure and we show that by augmenting existing models so that there are two sets of latent variables, one set modelling pixel intensities and the other set modelling image-specific pixel covariances, we are able to generate high-resolution images that look much more realistic than before. The overall model can be interpreted as a gated MRF where both pair-wise dependencies and mean intensities of pixels are modulated by the states of latent variables. Finally, we confirm that if we disallow weight-sharing between receptive fields that overlap each other, the gated MRF learns more efficient internal representations, as demonstrated in several recognition tasks.