We present a neat yet effective recursive operation on vision transformers that can improve parameter utilization without involving additional parameters. This is achieved by sharing weights across depth of transformer networks. The proposed method can obtain a substantial gain ( 2%) simply using naïve recursive operation, requires no special or sophisticated knowledge for designing principles of networks, and introduces minimum computational overhead to the training procedure. To reduce the additional computation caused by recursive operation while maintaining the superior accuracy, we propose an approximating method through multiple sliced group self-attentions across recursive layers which can reduce the cost consumption by 10 30% with minimal performance loss. We call our model Sliced Recursive Transformer (SReT), which is compatible with a broad range of other designs for efficient vision transformers. The flexible scalability has shown great potential for scaling up and constructing extremely deep and large dimensionality vision transformers. The architectures of transformer have achieved substantively breakthroughs recently in the fields of natural language processing (NLP) [Vaswani et al., 2017], computer vision (CV) [Dosovitskiy et al., 2021] and speech [Dong et al., 2018, Wang et al., 2021b]. In the vision area, Dosovitskiy et al. [Dosovitskiy et al., 2021] introduced the vision transformer (ViT) method that split a raw image to a patch sequence as input and directly applied transformer model [Vaswani et al., 2017] for the image classification task. ViT achieved impressive results and has inspired many follow-up works. However, the benefits of a transformer often come with a large computational cost and it is always of great challenge to achieve the optimal trade-off between the accuracy and model complexity. In this work, we are motivated by the following question: How can we improve the parameter utilization of a vision transformer, i.e., the representation ability without increasing the model size? We observe recursive operation as shown in Figure 1 is a simple while effective way to achieve this purpose.

The best performing Binary Neural Networks (BNNs) are usually attained using Adam optimization and its multi-step training variants. However, to the best of our knowledge, few studies explore the fundamental reasons why Adam is superior to other optimizers like SGD for BNN optimization or provide analytical explanations that support specific training strategies. To address this, in this paper we first investigate the trajectories of gradients and weights in BNNs during the training process. We show the regularization effect of second-order momentum in Adam is crucial to revitalize the weights that are dead due to the activation saturation in BNNs. We find that Adam, through its adaptive learning rate strategy, is better equipped to handle the rugged loss surface of BNNs and reaches a better optimum with higher generalization ability. Furthermore, we inspect the intriguing role of the real-valued weights in binary networks, and reveal the effect of weight decay on the stability and sluggishness of BNN optimization. Through extensive experiments and analysis, we derive a simple training scheme, building on existing Adam-based optimization, which achieves 70.5% top-1 accuracy on the ImageNet dataset using the same architecture as the state-of-the-art ReActNet while achieving 1.1% higher accuracy. Code and models are available at https://github.com/liuzechun/AdamBNN.

This work aims to empirically clarify a recently discovered perspective that label smoothing is incompatible with knowledge distillation (Müller et al., 2019). We begin by introducing the motivation behind on how this incompatibility is raised, i.e., label smoothing erases relative information between teacher logits. We provide a novel connection on how label smoothing affects distributions of semantically similar and dissimilar classes. Then we propose a metric to quantitatively measure the degree of erased information in sample's representation. After that, we study its one-sidedness and imperfection of the incompatibility view through massive analyses, visualizations and comprehensive experiments on Image Classification, Binary Networks, and Neural Machine Translation. Finally, we broadly discuss several circumstances wherein label smoothing will indeed lose its effectiveness. Recently a large body of studies is focusing on exploring the underlying relationships between these two methods, for instance, Müller et al. (Müller et al., 2019) discovered that label smoothing could improve calibration implicitly but will hurt the effectiveness of knowledge distillation. Yuan et al. (Yuan et al., 2019) considered knowledge distillation as a dynamical form of label smoothing as it delivered a regularization effect in training. The recent study (Lukasik et al., 2020) further noticed label smoothing could help mitigate label noise, they showed that when distilling models from noisy data, the teacher with label smoothing is helpful.

Previous studies dominantly target at self-supervised learning on real-valued networks and have achieved many promising results. However, on the more challenging binary neural networks (BNNs), this task has not yet been fully explored in the community. In this paper, we focus on this more difficult scenario: learning networks where both weights and activations are binary, meanwhile, without any human annotated labels. We observe that the commonly used contrastive objective is not satisfying on BNNs for competitive accuracy, since the backbone network contains relatively limited capacity and representation ability. Hence instead of directly applying existing self-supervised methods, which cause a severe decline in performance, we present a novel guided learning paradigm from real-valued to distill binary networks on the final prediction distribution, to minimize the loss and obtain desirable accuracy. Our proposed method can boost the simple contrastive learning baseline by an absolute gain of 5.5~15% on BNNs. We further reveal that it is difficult for BNNs to recover the similar predictive distributions as real-valued models when training without labels. Thus, how to calibrate them is key to address the degradation in performance. Extensive experiments are conducted on the large-scale ImageNet and downstream datasets. Our method achieves substantial improvement over the simple contrastive learning baseline, and is even comparable to many mainstream supervised BNN methods. Code will be made available.

Optimization of Binarized Neural Networks (BNNs) currently relies on real-valued latent weights to accumulate small update steps. In this paper, we argue that these latent weights cannot be treated analogously to weights in real-valued networks. Instead their main role is to provide inertia during training. We interpret current methods in terms of inertia and provide novel insights into the optimization of BNNs. We subsequently introduce the first optimizer specifically designed for BNNs, Binary Optimizer (Bop), and demonstrate its performance on CIFAR-10 and ImageNet. Together, the redefinition of latent weights as inertia and the introduction of Bop enable a better understanding of BNN optimization and open up the way for further improvements in training methodologies for BNNs.