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Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transport cost between two different data sets; if some changes happen to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently find the variable to pivot within expected $O(1)$ time, and complete each pivoting operation within expected $O(|V|)$ time where $V$ is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transport cost that needs at least one traversal over all $|E| = O(|V|^2)$ variables, where $|E|$ denotes the number of edges in the network. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.

This work pioneers evaluating emergent planning capabilities based on situational awareness in large language models. We contribute (i) novel benchmarks and metrics for standardized assessment; (ii) a unique dataset to spur progress; and (iii) demonstrations that prompting and multi-agent schemes significantly enhance planning performance in context-sensitive planning tasks. Positioning this within a situated agent and automated planning research, we highlight inherent reliability challenges--efficiently mapping world states to actions without environmental guidance remains open despite simulated domain advances. Although out-of-scope, limitations around validation methodology and data availability indicate exciting directions, including fine-tuning on expanded planning corpora and optimizations for triggering fast latent planning. By conclusively demonstrating current methods' promise and limitations via rigorous comparison, we catalyze investigating reliable goal-directed reasoning for situated agents.

Most of existing correspondence pruning methods only concentrate on gathering the context information as much as possible while neglecting effective ways to utilize such information. In order to tackle this dilemma, in this paper we propose Graph Context Transformation Network (GCT-Net) enhancing context information to conduct consensus guidance for progressive correspondence pruning. Specifically, we design the Graph Context Enhance Transformer which first generates the graph network and then transforms it into multi-branch graph contexts. Moreover, it employs self-attention and cross-attention to magnify characteristics of each graph context for emphasizing the unique as well as shared essential information. To further apply the recalibrated graph contexts to the global domain, we propose the Graph Context Guidance Transformer. This module adopts a confident-based sampling strategy to temporarily screen high-confidence vertices for guiding accurate classification by searching global consensus between screened vertices and remaining ones. The extensive experimental results on outlier removal and relative pose estimation clearly demonstrate the superior performance of GCT-Net compared to state-of-the-art methods across outdoor and indoor datasets. The source code will be available at: //github.com/guobaoxiao/GCT-Net/.

Abductive reasoning is logical reasoning that makes educated guesses to infer the most likely reasons to explain the observations. However, the abductive logical reasoning over knowledge graphs (KGs) is underexplored in KG literature. In this paper, we initially and formally raise the task of abductive logical reasoning over KGs, which involves inferring the most probable logic hypothesis from the KGs to explain an observed entity set. Traditional approaches use symbolic methods, like searching, to tackle the knowledge graph problem. However, the symbolic methods are unsuitable for this task, because the KGs are naturally incomplete, and the logical hypotheses can be complex with multiple variables and relations. To address these issues, we propose a generative approach to create logical expressions based on observations. First, we sample hypothesis-observation pairs from the KG and use supervised training to train a generative model that generates hypotheses from observations. Since supervised learning only minimizes structural differences between generated and reference hypotheses, higher structural similarity does not guarantee a better explanation for observations. To tackle this issue, we introduce the Reinforcement Learning from the Knowledge Graph (RLF-KG) method, which minimizes the differences between observations and conclusions drawn from the generated hypotheses according to the KG. Experimental results demonstrate that transformer-based generative models can generate logical explanations robustly and efficiently. Moreover, with the assistance of RLF-KG, the generated hypothesis can provide better explanations for the observations, and the method of supervised learning with RLF-KG achieves state-of-the-art results on abductive knowledge graph reasoning on three widely used KGs.

In recent years, considerable attention has been devoted to the regularization models due to the presence of high-dimensional data in scientific research. Sparse support vector machine (SVM) are useful tools in high-dimensional data analysis, and they have been widely used in the area of econometrics. Nevertheless, the non-smoothness of objective functions and constraints present computational challenges for many existing solvers in the presence of ultra-high dimensional covariates. In this paper, we design efficient and parallelizable algorithms for solving sparse SVM problems with high dimensional data through feature space split. The proposed algorithm is based on the alternating direction method of multiplier (ADMM). We establish the rate of convergence of the proposed ADMM method and compare it with existing solvers in various high and ultra-high dimensional settings. The compatibility of the proposed algorithm with parallel computing can further alleviate the storage and scalability limitations of a single machine in large-scale data processing.

Supervised speech enhancement has gained significantly from recent advancements in neural networks, especially due to their ability to non-linearly fit the diverse representations of target speech, such as waveform or spectrum. However, these direct-fitting solutions continue to face challenges with degraded speech and residual noise in hearing evaluations. By bridging the speech enhancement and the Information Bottleneck principle in this letter, we rethink a universal plug-and-play strategy and propose a Refining Underlying Information framework called RUI to rise to the challenges both in theory and practice. Specifically, we first transform the objective of speech enhancement into an incremental convergence problem of mutual information between comprehensive speech characteristics and individual speech characteristics, e.g., spectral and acoustic characteristics. By doing so, compared with the existing direct-fitting solutions, the underlying information stems from the conditional entropy of acoustic characteristic given spectral characteristics. Therefore, we design a dual-path multiple refinement iterator based on the chain rule of entropy to refine this underlying information for further approximating target speech. Experimental results on DNS-Challenge dataset show that our solution consistently improves 0.3+ PESQ score over baselines, with only additional 1.18 M parameters. The source code is available at //github.com/caoruitju/RUI_SE.

Gait recognition is a biometric technology that has received extensive attention. Most existing gait recognition algorithms are unimodal, and a few multimodal gait recognition algorithms perform multimodal fusion only once. None of these algorithms may fully exploit the complementary advantages of the multiple modalities. In this paper, by considering the temporal and spatial characteristics of gait data, we propose a multi-stage feature fusion strategy (MSFFS), which performs multimodal fusions at different stages in the feature extraction process. Also, we propose an adaptive feature fusion module (AFFM) that considers the semantic association between silhouettes and skeletons. The fusion process fuses different silhouette areas with their more related skeleton joints. Since visual appearance changes and time passage co-occur in a gait period, we propose a multiscale spatial-temporal feature extractor (MSSTFE) to learn the spatial-temporal linkage features thoroughly. Specifically, MSSTFE extracts and aggregates spatial-temporal linkages information at different spatial scales. Combining the strategy and modules mentioned above, we propose a multi-stage adaptive feature fusion (MSAFF) neural network, which shows state-of-the-art performance in many experiments on three datasets. Besides, MSAFF is equipped with feature dimensional pooling (FD Pooling), which can significantly reduce the dimension of the gait representations without hindering the accuracy. //github.com/ShinanZou/MSAFF

This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.