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Termination is a fundamental question in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete probabilistic choice and demonic bounded nondeterminism. The qualitative question asks if the program terminates almost surely, no matter how nondeterminism is resolved; the quantitative question asks for a bound on the probability of termination. Despite a long and rich literature on the topic, no sound and relatively complete proof systems were known for this problem. We provide the first sound and relatively complete proof rules for proving qualitative and quantitative termination in the assertion language of arithmetic. Our proof rules use supermartingales as estimates of likelihood of the prgroam's evolution - the key insight is to use appropriately defined finite-state sub-instances. Our completeness result shows how to construct a suitable supermartingales from an almost-surely terminating program. We also show that proofs of termination in many existing proof systems can be transformed to proofs in our system, pointing to its applicability in practice. As an application of our proof rule, we show a proof of almost sure termination for the two-dimensional random walker.

Video object segmentation (VOS) aims to distinguish and track target objects in a video. Despite the excellent performance achieved by off-the-shell VOS models, existing VOS benchmarks mainly focus on short-term videos lasting about 5 seconds, where objects remain visible most of the time. However, these benchmarks poorly represent practical applications, and the absence of long-term datasets restricts further investigation of VOS in realistic scenarios. Thus, we propose a novel benchmark named LVOS, comprising 720 videos with 296,401 frames and 407,945 high-quality annotations. Videos in LVOS last 1.14 minutes on average, approximately 5 times longer than videos in existing datasets. Each video includes various attributes, especially challenges deriving from the wild, such as long-term reappearing and cross-temporal similar objects. Compared to previous benchmarks, our LVOS better reflects VOS models' performance in real scenarios. Based on LVOS, we evaluate 20 existing VOS models under 4 different settings and conduct a comprehensive analysis. On LVOS, these models suffer a large performance drop, highlighting the challenge of achieving precise tracking and segmentation in real-world scenarios. Attribute-based analysis indicates that key factor to accuracy decline is the increased video length, emphasizing LVOS's crucial role. We hope our LVOS can advance development of VOS in real scenes. Data and code are available at //lingyihongfd.github.io/lvos.github.io/.

Stochastic gradient descent (SGD) has emerged as the quintessential method in a data scientist's toolbox. Using SGD for high-stakes applications requires, however, careful quantification of the associated uncertainty. Towards that end, in this work, we establish a high-dimensional Central Limit Theorem (CLT) for linear functionals of online SGD iterates for overparametrized least-squares regression with non-isotropic Gaussian inputs. Our result shows that a CLT holds even when the dimensionality is of order exponential in the number of iterations of the online SGD, which, to the best of our knowledge, is the first such result. In order to use the developed result in practice, we further develop an online approach for estimating the expectation and the variance terms appearing in the CLT, and establish high-probability bounds for the developed online estimator. Furthermore, we propose a two-step fully online bias-correction methodology which together with the CLT result and the variance estimation result, provides a fully online and data-driven way to numerically construct confidence intervals, thereby enabling practical high-dimensional algorithmic inference with SGD. We also extend our results to a class of single-index models, based on the Gaussian Stein's identity. We also provide numerical simulations to verify our theoretical findings in practice.

Sequential recommendation is one of the important branches of recommender system, aiming to achieve personalized recommended items for the future through the analysis and prediction of users' ordered historical interactive behaviors. However, along with the growth of the user volume and the increasingly rich behavioral information, how to understand and disentangle the user's interactive multi-intention effectively also poses challenges to behavior prediction and sequential recommendation. In light of these challenges, we propose a Contrastive Learning sequential recommendation method based on Multi-Intention Disentanglement (MIDCL). In our work, intentions are recognized as dynamic and diverse, and user behaviors are often driven by current multi-intentions, which means that the model needs to not only mine the most relevant implicit intention for each user, but also impair the influence from irrelevant intentions. Therefore, we choose Variational Auto-Encoder (VAE) to realize the disentanglement of users' multi-intentions, and propose two types of contrastive learning paradigms for finding the most relevant user's interactive intention, and maximizing the mutual information of positive sample pairs, respectively. Experimental results show that MIDCL not only has significant superiority over most existing baseline methods, but also brings a more interpretable case to the research about intention-based prediction and recommendation.

This paper tackles the problem of constructing Bezout matrices for Newton polynomials in a basis-preserving approach that operates directly with the given Newton basis, thus avoiding the need for transformation from Newton basis to monomial basis. This approach significantly reduces the computational cost and also mitigates numerical instability caused by basis transformation. For this purpose, we investigate the internal structure of Bezout matrices in Newton basis and design a basis-preserving algorithm that generates the Bezout matrix in the specified basis used to formulate the input polynomials. Furthermore, we show an application of the proposed algorithm on constructing confederate resultant matrices for Newton polynomials. Experimental results demonstrate that the proposed methods perform superior to the basis-transformation-based ones.

Generalizable NeRF aims to synthesize novel views for unseen scenes. Common practices involve constructing variance-based cost volumes for geometry reconstruction and encoding 3D descriptors for decoding novel views. However, existing methods show limited generalization ability in challenging conditions due to inaccurate geometry, sub-optimal descriptors, and decoding strategies. We address these issues point by point. First, we find the variance-based cost volume exhibits failure patterns as the features of pixels corresponding to the same point can be inconsistent across different views due to occlusions or reflections. We introduce an Adaptive Cost Aggregation (ACA) approach to amplify the contribution of consistent pixel pairs and suppress inconsistent ones. Unlike previous methods that solely fuse 2D features into descriptors, our approach introduces a Spatial-View Aggregator (SVA) to incorporate 3D context into descriptors through spatial and inter-view interaction. When decoding the descriptors, we observe the two existing decoding strategies excel in different areas, which are complementary. A Consistency-Aware Fusion (CAF) strategy is proposed to leverage the advantages of both. We incorporate the above ACA, SVA, and CAF into a coarse-to-fine framework, termed Geometry-aware Reconstruction and Fusion-refined Rendering (GeFu). GeFu attains state-of-the-art performance across multiple datasets. Code is available at //github.com/TQTQliu/GeFu .

We consider a graph coloring algorithm that processes vertices in order taken uniformly at random and assigns colors to them using First-Fit strategy. We show that this algorithm uses, in expectation, at most $(\frac{1}{2} + o(1))\cdot \ln n \,/\, \ln\ln n$ different colors to color any forest with $n$ vertices. We also construct a family of forests that shows that this bound is best possible.

Automatic KB completion for commonsense knowledge graphs (e.g., ATOMIC and ConceptNet) poses unique challenges compared to the much studied conventional knowledge bases (e.g., Freebase). Commonsense knowledge graphs use free-form text to represent nodes, resulting in orders of magnitude more nodes compared to conventional KBs (18x more nodes in ATOMIC compared to Freebase (FB15K-237)). Importantly, this implies significantly sparser graph structures - a major challenge for existing KB completion methods that assume densely connected graphs over a relatively smaller set of nodes. In this paper, we present novel KB completion models that can address these challenges by exploiting the structural and semantic context of nodes. Specifically, we investigate two key ideas: (1) learning from local graph structure, using graph convolutional networks and automatic graph densification and (2) transfer learning from pre-trained language models to knowledge graphs for enhanced contextual representation of knowledge. We describe our method to incorporate information from both these sources in a joint model and provide the first empirical results for KB completion on ATOMIC and evaluation with ranking metrics on ConceptNet. Our results demonstrate the effectiveness of language model representations in boosting link prediction performance and the advantages of learning from local graph structure (+1.5 points in MRR for ConceptNet) when training on subgraphs for computational efficiency. Further analysis on model predictions shines light on the types of commonsense knowledge that language models capture well.

Within the rapidly developing Internet of Things (IoT), numerous and diverse physical devices, Edge devices, Cloud infrastructure, and their quality of service requirements (QoS), need to be represented within a unified specification in order to enable rapid IoT application development, monitoring, and dynamic reconfiguration. But heterogeneities among different configuration knowledge representation models pose limitations for acquisition, discovery and curation of configuration knowledge for coordinated IoT applications. This paper proposes a unified data model to represent IoT resource configuration knowledge artifacts. It also proposes IoT-CANE (Context-Aware recommendatioN systEm) to facilitate incremental knowledge acquisition and declarative context driven knowledge recommendation.

Many natural language processing tasks solely rely on sparse dependencies between a few tokens in a sentence. Soft attention mechanisms show promising performance in modeling local/global dependencies by soft probabilities between every two tokens, but they are not effective and efficient when applied to long sentences. By contrast, hard attention mechanisms directly select a subset of tokens but are difficult and inefficient to train due to their combinatorial nature. In this paper, we integrate both soft and hard attention into one context fusion model, "reinforced self-attention (ReSA)", for the mutual benefit of each other. In ReSA, a hard attention trims a sequence for a soft self-attention to process, while the soft attention feeds reward signals back to facilitate the training of the hard one. For this purpose, we develop a novel hard attention called "reinforced sequence sampling (RSS)", selecting tokens in parallel and trained via policy gradient. Using two RSS modules, ReSA efficiently extracts the sparse dependencies between each pair of selected tokens. We finally propose an RNN/CNN-free sentence-encoding model, "reinforced self-attention network (ReSAN)", solely based on ReSA. It achieves state-of-the-art performance on both Stanford Natural Language Inference (SNLI) and Sentences Involving Compositional Knowledge (SICK) datasets.