Revisiting Subgradient Method: Complexity and Convergence Beyond Lipschitz Continuity

The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this algorithm are mainly derived for Lipschitz continuous objective functions. In this work, we first extend the typical complexity results for the subgradient method to convex and weakly convex minimization without assuming Lipschitz continuity. Specifically, we establish $\mathcal{O}(1/\sqrt{T})$ bound in terms of the suboptimality gap ``$f(x) - f^*$'' for convex case and $\mathcal{O}(1/{T}^{1/4})$ bound in terms of the gradient of the Moreau envelope function for weakly convex case. Furthermore, we provide convergence results for non-Lipschitz convex and weakly convex objective functions using proper diminishing rules on the step sizes. In particular, when $f$ is convex, we show $\mathcal{O}(\log(k)/\sqrt{k})$ rate of convergence in terms of the suboptimality gap. With an additional quadratic growth condition, the rate is improved to $\mathcal{O}(1/k)$ in terms of the squared distance to the optimal solution set. When $f$ is weakly convex, asymptotic convergence is derived. The central idea is that the dynamics of properly chosen step sizes rule fully controls the movement of the subgradient method, which leads to boundedness of the iterates, and then a trajectory-based analysis can be conducted to establish the desired results. To further illustrate the wide applicability of our framework, we extend the complexity results to the truncated subgradient, the stochastic subgradient, the incremental subgradient, and the proximal subgradient methods for non-Lipschitz functions.

Ensemble Modeling with Contrastive Knowledge Distillation for Sequential Recommendation

Sequential recommendation aims to capture users' dynamic interest and predicts the next item of users' preference. Most sequential recommendation methods use a deep neural network as sequence encoder to generate user and item representations. Existing works mainly center upon designing a stronger sequence encoder. However, few attempts have been made with training an ensemble of networks as sequence encoders, which is more powerful than a single network because an ensemble of parallel networks can yield diverse prediction results and hence better accuracy. In this paper, we present Ensemble Modeling with contrastive Knowledge Distillation for sequential recommendation (EMKD). Our framework adopts multiple parallel networks as an ensemble of sequence encoders and recommends items based on the output distributions of all these networks. To facilitate knowledge transfer between parallel networks, we propose a novel contrastive knowledge distillation approach, which performs knowledge transfer from the representation level via Intra-network Contrastive Learning (ICL) and Cross-network Contrastive Learning (CCL), as well as Knowledge Distillation (KD) from the logits level via minimizing the Kullback-Leibler divergence between the output distributions of the teacher network and the student network. To leverage contextual information, we train the primary masked item prediction task alongside the auxiliary attribute prediction task as a multi-task learning scheme. Extensive experiments on public benchmark datasets show that EMKD achieves a significant improvement compared with the state-of-the-art methods. Besides, we demonstrate that our ensemble method is a generalized approach that can also improve the performance of other sequential recommenders. Our code is available at this link: https://github.com/hw-du/EMKD.

VGOS: Voxel Grid Optimization for View Synthesis from Sparse Inputs

Neural Radiance Fields (NeRF) has shown great success in novel view synthesis due to its state-of-the-art quality and flexibility. However, NeRF requires dense input views (tens to hundreds) and a long training time (hours to days) for a single scene to generate high-fidelity images. Although using the voxel grids to represent the radiance field can significantly accelerate the optimization process, we observe that for sparse inputs, the voxel grids are more prone to overfitting to the training views and will have holes and floaters, which leads to artifacts. In this paper, we propose VGOS, an approach for fast (3-5 minutes) radiance field reconstruction from sparse inputs (3-10 views) to address these issues. To improve the performance of voxel-based radiance field in sparse input scenarios, we propose two methods: (a) We introduce an incremental voxel training strategy, which prevents overfitting by suppressing the optimization of peripheral voxels in the early stage of reconstruction. (b) We use several regularization techniques to smooth the voxels, which avoids degenerate solutions. Experiments demonstrate that VGOS achieves state-of-the-art performance for sparse inputs with super-fast convergence. Code will be available at https://github.com/SJoJoK/VGOS.

Sequential Recommendation with Probabilistic Logical Reasoning

Deep learning and symbolic learning are two frequently employed methods in Sequential Recommendation (SR). Recent neural-symbolic SR models demonstrate their potential to enable SR to be equipped with concurrent perception and cognition capacities. However, neural-symbolic SR remains a challenging problem due to open issues like representing users and items in logical reasoning. In this paper, we combine the Deep Neural Network (DNN) SR models with logical reasoning and propose a general framework named Sequential Recommendation with Probabilistic Logical Reasoning (short for SR-PLR). This framework allows SR-PLR to benefit from both similarity matching and logical reasoning by disentangling feature embedding and logic embedding in the DNN and probabilistic logic network. To better capture the uncertainty and evolution of user tastes, SR-PLR embeds users and items with a probabilistic method and conducts probabilistic logical reasoning on users' interaction patterns. Then the feature and logic representations learned from the DNN and logic network are concatenated to make the prediction. Finally, experiments on various sequential recommendation models demonstrate the effectiveness of the SR-PLR.

DREAM: Adaptive Reinforcement Learning based on Attention Mechanism for Temporal Knowledge Graph Reasoning

Temporal knowledge graphs (TKGs) model the temporal evolution of events and have recently attracted increasing attention. Since TKGs are intrinsically incomplete, it is necessary to reason out missing elements. Although existing TKG reasoning methods have the ability to predict missing future events, they fail to generate explicit reasoning paths and lack explainability. As reinforcement learning (RL) for multi-hop reasoning on traditional knowledge graphs starts showing superior explainability and performance in recent advances, it has opened up opportunities for exploring RL techniques on TKG reasoning. However, the performance of RL-based TKG reasoning methods is limited due to: (1) lack of ability to capture temporal evolution and semantic dependence jointly; (2) excessive reliance on manually designed rewards. To overcome these challenges, we propose an adaptive reinforcement learning model based on attention mechanism (DREAM) to predict missing elements in the future. Specifically, the model contains two components: (1) a multi-faceted attention representation learning method that captures semantic dependence and temporal evolution jointly; (2) an adaptive RL framework that conducts multi-hop reasoning by adaptively learning the reward functions. Experimental results demonstrate DREAM outperforms state-of-the-art models on public dataset

Generative Image Inpainting with Segmentation Confusion Adversarial Training and Contrastive Learning

This paper presents a new adversarial training framework for image inpainting with segmentation confusion adversarial training (SCAT) and contrastive learning. SCAT plays an adversarial game between an inpainting generator and a segmentation network, which provides pixel-level local training signals and can adapt to images with free-form holes. By combining SCAT with standard global adversarial training, the new adversarial training framework exhibits the following three advantages simultaneously: (1) the global consistency of the repaired image, (2) the local fine texture details of the repaired image, and (3) the flexibility of handling images with free-form holes. Moreover, we propose the textural and semantic contrastive learning losses to stabilize and improve our inpainting model's training by exploiting the feature representation space of the discriminator, in which the inpainting images are pulled closer to the ground truth images but pushed farther from the corrupted images. The proposed contrastive losses better guide the repaired images to move from the corrupted image data points to the real image data points in the feature representation space, resulting in more realistic completed images. We conduct extensive experiments on two benchmark datasets, demonstrating our model's effectiveness and superiority both qualitatively and quantitatively.

OppLoD: the Opponency based Looming Detector, Model Extension of Looming Sensitivity from LGMD to LPLC2

Looming detection plays an important role in insect collision prevention systems. As a vital capability evolutionary survival, it has been extensively studied in neuroscience and is attracting increasing research interest in robotics due to its close relationship with collision detection and navigation. Visual cues such as angular size, angular velocity, and expansion have been widely studied for looming detection by means of optic flow or elementary neural computing research. However, a critical visual motion cue has been long neglected because it is so easy to be confused with expansion, that is radial-opponent-motion (ROM). Recent research on the discovery of LPLC2, a ROM-sensitive neuron in Drosophila, has revealed its ultra-selectivity because it only responds to stimuli with focal, outward movement. This characteristic of ROM-sensitivity is consistent with the demand for collision detection because it is strongly associated with danger looming that is moving towards the center of the observer. Thus, we hope to extend the well-studied neural model of the lobula giant movement detector (LGMD) with ROM-sensibility in order to enhance robustness and accuracy at the same time. In this paper, we investigate the potential to extend an image velocity-based looming detector, the lobula giant movement detector (LGMD), with ROM-sensibility. To achieve this, we propose the mathematical definition of ROM and its main property, the radial motion opponency (RMO). Then, a synaptic neuropile that analogizes the synaptic processing of LPLC2 is proposed in the form of lateral inhibition and attention. Thus, our proposed model is the first to perform both image velocity selectivity and ROM sensitivity. Systematic experiments are conducted to exhibit the huge potential of the proposed bio-inspired looming detector.

Long-Document Cross-Lingual Summarization

Cross-Lingual Summarization (CLS) aims at generating summaries in one language for the given documents in another language. CLS has attracted wide research attention due to its practical significance in the multi-lingual world. Though great contributions have been made, existing CLS works typically focus on short documents, such as news articles, short dialogues and guides. Different from these short texts, long documents such as academic articles and business reports usually discuss complicated subjects and consist of thousands of words, making them non-trivial to process and summarize. To promote CLS research on long documents, we construct Perseus, the first long-document CLS dataset which collects about 94K Chinese scientific documents paired with English summaries. The average length of documents in Perseus is more than two thousand tokens. As a preliminary study on long-document CLS, we build and evaluate various CLS baselines, including pipeline and end-to-end methods. Experimental results on Perseus show the superiority of the end-to-end baseline, outperforming the strong pipeline models equipped with sophisticated machine translation systems. Furthermore, to provide a deeper understanding, we manually analyze the model outputs and discuss specific challenges faced by current approaches. We hope that our work could benchmark long-document CLS and benefit future studies.

MicroAST: Towards Super-Fast Ultra-Resolution Arbitrary Style Transfer

Arbitrary style transfer (AST) transfers arbitrary artistic styles onto content images. Despite the recent rapid progress, existing AST methods are either incapable or too slow to run at ultra-resolutions (e.g., 4K) with limited resources, which heavily hinders their further applications. In this paper, we tackle this dilemma by learning a straightforward and lightweight model, dubbed MicroAST. The key insight is to completely abandon the use of cumbersome pre-trained Deep Convolutional Neural Networks (e.g., VGG) at inference. Instead, we design two micro encoders (content and style encoders) and one micro decoder for style transfer. The content encoder aims at extracting the main structure of the content image. The style encoder, coupled with a modulator, encodes the style image into learnable dual-modulation signals that modulate both intermediate features and convolutional filters of the decoder, thus injecting more sophisticated and flexible style signals to guide the stylizations. In addition, to boost the ability of the style encoder to extract more distinct and representative style signals, we also introduce a new style signal contrastive loss in our model. Compared to the state of the art, our MicroAST not only produces visually superior results but also is 5-73 times smaller and 6-18 times faster, for the first time enabling super-fast (about 0.5 seconds) AST at 4K ultra-resolutions. Code is available at https://github.com/EndyWon/MicroAST.

An Investigation into Whitening Loss for Self-supervised Learning

A desirable objective in self-supervised learning (SSL) is to avoid feature collapse. Whitening loss guarantees collapse avoidance by minimizing the distance between embeddings of positive pairs under the conditioning that the embeddings from different views are whitened. In this paper, we propose a framework with an informative indicator to analyze whitening loss, which provides a clue to demystify several interesting phenomena as well as a pivoting point connecting to other SSL methods. We reveal that batch whitening (BW) based methods do not impose whitening constraints on the embedding, but they only require the embedding to be full-rank. This full-rank constraint is also sufficient to avoid dimensional collapse. Based on our analysis, we propose channel whitening with random group partition (CW-RGP), which exploits the advantages of BW-based methods in preventing collapse and avoids their disadvantages requiring large batch size. Experimental results on ImageNet classification and COCO object detection reveal that the proposed CW-RGP possesses a promising potential for learning good representations. The code is available at https://github.com/winci-ai/CW-RGP.