We systematically investigate the complexity of counting subgraph patterns modulo fixed integers. For example, it is known that the parity of the number of $k$-matchings can be determined in polynomial time by a simple reduction to the determinant. We generalize this to an $n^{f(t,s)}$-time algorithm to compute modulo $2^t$ the number of subgraph occurrences of patterns that are $s$ vertices away from being matchings. This shows that the known polynomial-time cases of subgraph detection (Jansen and Marx, SODA 2015) carry over into the setting of counting modulo $2^t$. Complementing our algorithm, we also give a simple and self-contained proof that counting $k$-matchings modulo odd integers $q$ is Mod_q-W[1]-complete and prove that counting $k$-paths modulo $2$ is Parity-W[1]-complete, answering an open question by Bj\"orklund, Dell, and Husfeldt (ICALP 2015).
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The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have distinct colors and include the maximum number of colors. We study the approximation complexity of the problem and we provide an inapproximability lower bound. Then we present a heuristic for the problem and an experimental evaluation of our heuristic, both on synthetic and real-world graphs.
We show that for each single crossing graph $H$, a polynomially bounded weight function for all $H$-minor free graphs $G$ can be constructed in Logspace such that it gives nonzero weights to all the cycles in $G$. This class of graphs subsumes almost all classes of graphs for which such a weight function is know to be constructed in Logspace. As a consequence, we obtain that for the class of $H$-minor free graphs where $H$ is a single crossing graph, reachability can be solved in UL, and bipartite maximum matching can be solved in SPL, which are small subclasses of the parallel complexity class NC. In the restrictive case of bipartite graphs, our maximum matching result improves upon the recent result of Eppstein and Vazirani, where they show an NC bound for constructing perfect matching in general single crossing minor free graphs.
Siamese tracking has achieved groundbreaking performance in recent years, where the essence is the efficient matching operator cross-correlation and its variants. Besides the remarkable success, it is important to note that the heuristic matching network design relies heavily on expert experience. Moreover, we experimentally find that one sole matching operator is difficult to guarantee stable tracking in all challenging environments. Thus, in this work, we introduce six novel matching operators from the perspective of feature fusion instead of explicit similarity learning, namely Concatenation, Pointwise-Addition, Pairwise-Relation, FiLM, Simple-Transformer and Transductive-Guidance, to explore more feasibility on matching operator selection. The analyses reveal these operators' selective adaptability on different environment degradation types, which inspires us to combine them to explore complementary features. To this end, we propose binary channel manipulation (BCM) to search for the optimal combination of these operators. BCM determines to retrain or discard one operator by learning its contribution to other tracking steps. By inserting the learned matching networks to a strong baseline tracker Ocean, our model achieves favorable gains by $67.2 \rightarrow 71.4$, $52.6 \rightarrow 58.3$, $70.3 \rightarrow 76.0$ success on OTB100, LaSOT, and TrackingNet, respectively. Notably, Our tracker, dubbed AutoMatch, uses less than half of training data/time than the baseline tracker, and runs at 50 FPS using PyTorch. Code and model will be released at //github.com/JudasDie/SOTS.
Localizing individuals in crowds is more in accordance with the practical demands of subsequent high-level crowd analysis tasks than simply counting. However, existing localization based methods relying on intermediate representations (\textit{i.e.}, density maps or pseudo boxes) serving as learning targets are counter-intuitive and error-prone. In this paper, we propose a purely point-based framework for joint crowd counting and individual localization. For this framework, instead of merely reporting the absolute counting error at image level, we propose a new metric, called density Normalized Average Precision (nAP), to provide more comprehensive and more precise performance evaluation. Moreover, we design an intuitive solution under this framework, which is called Point to Point Network (P2PNet). P2PNet discards superfluous steps and directly predicts a set of point proposals to represent heads in an image, being consistent with the human annotation results. By thorough analysis, we reveal the key step towards implementing such a novel idea is to assign optimal learning targets for these proposals. Therefore, we propose to conduct this crucial association in an one-to-one matching manner using the Hungarian algorithm. The P2PNet not only significantly surpasses state-of-the-art methods on popular counting benchmarks, but also achieves promising localization accuracy. The codes will be available at: //github.com/TencentYoutuResearch/CrowdCounting-P2PNet.
The ad-hoc retrieval task is to rank related documents given a query and a document collection. A series of deep learning based approaches have been proposed to solve such problem and gained lots of attention. However, we argue that they are inherently based on local word sequences, ignoring the subtle long-distance document-level word relationships. To solve the problem, we explicitly model the document-level word relationship through the graph structure, capturing the subtle information via graph neural networks. In addition, due to the complexity and scale of the document collections, it is considerable to explore the different grain-sized hierarchical matching signals at a more general level. Therefore, we propose a Graph-based Hierarchical Relevance Matching model (GHRM) for ad-hoc retrieval, by which we can capture the subtle and general hierarchical matching signals simultaneously. We validate the effects of GHRM over two representative ad-hoc retrieval benchmarks, the comprehensive experiments and results demonstrate its superiority over state-of-the-art methods.
We propose a scalable Gromov-Wasserstein learning (S-GWL) method and establish a novel and theoretically-supported paradigm for large-scale graph analysis. The proposed method is based on the fact that Gromov-Wasserstein discrepancy is a pseudometric on graphs. Given two graphs, the optimal transport associated with their Gromov-Wasserstein discrepancy provides the correspondence between their nodes and achieves graph matching. When one of the graphs has isolated but self-connected nodes ($i.e.$, a disconnected graph), the optimal transport indicates the clustering structure of the other graph and achieves graph partitioning. Using this concept, we extend our method to multi-graph partitioning and matching by learning a Gromov-Wasserstein barycenter graph for multiple observed graphs; the barycenter graph plays the role of the disconnected graph, and since it is learned, so is the clustering. Our method combines a recursive $K$-partition mechanism with a regularized proximal gradient algorithm, whose time complexity is $\mathcal{O}(K(E+V)\log_K V)$ for graphs with $V$ nodes and $E$ edges. To our knowledge, our method is the first attempt to make Gromov-Wasserstein discrepancy applicable to large-scale graph analysis and unify graph partitioning and matching into the same framework. It outperforms state-of-the-art graph partitioning and matching methods, achieving a trade-off between accuracy and efficiency.
This paper presents our semantic parsing system for the evaluation task of open domain semantic parsing in NLPCC 2019. Many previous works formulate semantic parsing as a sequence-to-sequence(seq2seq) problem. Instead, we treat the task as a sketch-based problem in a coarse-to-fine(coarse2fine) fashion. The sketch is a high-level structure of the logical form exclusive of low-level details such as entities and predicates. In this way, we are able to optimize each part individually. Specifically, we decompose the process into three stages: the sketch classification determines the high-level structure while the entity labeling and the matching network fill in missing details. Moreover, we adopt the seq2seq method to evaluate logical form candidates from an overall perspective. The co-occurrence relationship between predicates and entities contribute to the reranking as well. Our submitted system achieves the exactly matching accuracy of 82.53% on full test set and 47.83% on hard test subset, which is the 3rd place in NLPCC 2019 Shared Task 2. After optimizations for parameters, network structure and sampling, the accuracy reaches 84.47% on full test set and 63.08% on hard test subset(Our code and data are available at //github.com/zechagl/NLPCC2019-Semantic-Parsing).
Question answering over knowledge graphs (KGQA) has evolved from simple single-fact questions to complex questions that require graph traversal and aggregation. We propose a novel approach for complex KGQA that uses unsupervised message passing, which propagates confidence scores obtained by parsing an input question and matching terms in the knowledge graph to a set of possible answers. First, we identify entity, relationship, and class names mentioned in a natural language question, and map these to their counterparts in the graph. Then, the confidence scores of these mappings propagate through the graph structure to locate the answer entities. Finally, these are aggregated depending on the identified question type. This approach can be efficiently implemented as a series of sparse matrix multiplications mimicking joins over small local subgraphs. Our evaluation results show that the proposed approach outperforms the state-of-the-art on the LC-QuAD benchmark. Moreover, we show that the performance of the approach depends only on the quality of the question interpretation results, i.e., given a correct relevance score distribution, our approach always produces a correct answer ranking. Our error analysis reveals correct answers missing from the benchmark dataset and inconsistencies in the DBpedia knowledge graph. Finally, we provide a comprehensive evaluation of the proposed approach accompanied with an ablation study and an error analysis, which showcase the pitfalls for each of the question answering components in more detail.
This paper seeks to model human language by the mathematical framework of quantum physics. With the well-designed mathematical formulations in quantum physics, this framework unifies different linguistic units in a single complex-valued vector space, e.g. words as particles in quantum states and sentences as mixed systems. A complex-valued network is built to implement this framework for semantic matching. With well-constrained complex-valued components, the network admits interpretations to explicit physical meanings. The proposed complex-valued network for matching (CNM) achieves comparable performances to strong CNN and RNN baselines on two benchmarking question answering (QA) datasets.
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.
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