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Counting k-cliques in a graph is an important problem in graph analysis with many applications such as community detection and graph partitioning. Counting k-cliques is typically done by traversing search trees starting at each vertex in the graph. Parallelizing k-clique counting has been well-studied on CPUs and many solutions exist. However, there are no performant solutions for k-clique counting on GPUs. Parallelizing k-clique counting on GPUs comes with numerous challenges such as the need for extracting fine-grain multi-level parallelism, sensitivity to load imbalance, and constrained physical memory capacity. While there has been work on related problems such as finding maximal cliques and generalized sub-graph matching on GPUs, k-clique counting in particular has yet to be explored in depth. In this paper, we present the first parallel GPU solution specialized for the k-clique counting problem. Our solution supports both graph orientation and pivoting for eliminating redundant clique discovery. It incorporates both vertex-centric and edge-centric parallelization schemes for distributing work across thread blocks, and further partitions work within each thread block to extract fine-grain multi-level parallelism while tolerating load imbalance. It also includes optimizations such as binary encoding of induced sub-graphs and sub-warp partitioning to limit memory consumption and improve the utilization of execution resources. Our evaluation shows that our best GPU implementation outperforms the best state-of-the-art parallel CPU implementation by a geometric mean of 12.39x, 6.21x, and 18.99x for k=4, 7, and 10, respectively. We also perform a detailed evaluation of the trade-offs involved in the choice of parallelization scheme, and the incremental speedup of each optimization to provide an in-depth understanding of the optimization space. ...

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Calculus of Variation combined with Differential Geometry as tools of modelling and solving problems in image processing and computer vision were introduced in the late 80's and the 90s of the 20th century. The beginning of an extensive work in these directions was marked by works such as Geodesic Active Contours (GAC), the Beltrami framework, level set method of Osher and Sethian the works of Charpiat et al. and the works by Chan and Vese to name just a few. In many cases the optimization of these functional are done by the gradient descent method via the calculation of the Euler-Lagrange equations. Straightforward use of the resulted EL equations in the gradient descent scheme leads to non-geometric and in some cases non sensical equations. It is costumary to modify these EL equations or even the functional itself in order to obtain geometric and/or sensical equations. The aim of this note is to point to the correct way to derive the EL and the gradient descent equations such that the resulted gradient descent equation is geometric and makes sense.

The ability to learn new concepts continually is necessary in this ever-changing world. However, deep neural networks suffer from catastrophic forgetting when learning new categories. Many works have been proposed to alleviate this phenomenon, whereas most of them either fall into the stability-plasticity dilemma or take too much computation or storage overhead. Inspired by the gradient boosting algorithm to gradually fit the residuals between the target model and the previous ensemble model, we propose a novel two-stage learning paradigm FOSTER, empowering the model to learn new categories adaptively. Specifically, we first dynamically expand new modules to fit the residuals between the target and the output of the original model. Next, we remove redundant parameters and feature dimensions through an effective distillation strategy to maintain the single backbone model. We validate our method FOSTER on CIFAR-100 and ImageNet-100/1000 under different settings. Experimental results show that our method achieves state-of-the-art performance. Code is available at: //github.com/G-U-N/ECCV22-FOSTER.

Let $\mathbf{H}$ be the Cartesian product of a family of finite abelian groups. Via a polynomial approach, we give sufficient conditions for a partition of $\mathbf{H}$ induced by weighted poset metric to be reflexive, which also become necessary for some special cases. Moreover, by examining the roots of the Krawtchouk polynomials, we establish non-reflexive partitions of $\mathbf{H}$ induced by combinatorial metric. When $\mathbf{H}$ is a vector space over a finite field $\mathbb{F}$, we consider the property of admitting MacWilliams identity (PAMI) and the MacWilliams extension property (MEP) for partitions of $\mathbf{H}$. With some invariance assumptions, we show that two partitions of $\mathbf{H}$ admit MacWilliams identity if and only if they are mutually dual and reflexive, and any partition of $\mathbf{H}$ satisfying the MEP is in fact an orbit partition induced by some subgroup of $\Aut_{\mathbb{F}}(\mathbf{H})$, which is necessarily reflexive. As an application of the aforementioned results, we establish partitions of $\mathbf{H}$ induced by combinatorial metric that do not satisfy the MEP, which further enable us to provide counter-examples to a conjecture proposed by Pinheiro, Machado and Firer in \cite{39}.

In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem of compressed sensing with GNNs has since been extensively analyzed when the measurement matrix and/or network weights follow a subgaussian distribution. We move beyond the subgaussian assumption, to measurement matrices that are derived by sampling uniformly at random rows of a unitary matrix (including subsampled Fourier measurements as a special case). Specifically, we prove the first known restricted isometry guarantee for generative compressed sensing with subsampled isometries, and provide recovery bounds with nearly order-optimal sample complexity, addressing an open problem of Scarlett et al. (2022, p. 10). Recovery efficacy is characterized by the coherence, a new parameter, which measures the interplay between the range of the network and the measurement matrix. Our approach relies on subspace counting arguments and ideas central to high-dimensional probability. Furthermore, we propose a regularization strategy for training GNNs to have favourable coherence with the measurement operator. We provide compelling numerical simulations that support this regularized training strategy: our strategy yields low coherence networks that require fewer measurements for signal recovery. This, together with our theoretical results, supports coherence as a natural quantity for characterizing generative compressed sensing with subsampled isometries.

We present the Caltech Fish Counting Dataset (CFC), a large-scale dataset for detecting, tracking, and counting fish in sonar videos. We identify sonar videos as a rich source of data for advancing low signal-to-noise computer vision applications and tackling domain generalization in multiple-object tracking (MOT) and counting. In comparison to existing MOT and counting datasets, which are largely restricted to videos of people and vehicles in cities, CFC is sourced from a natural-world domain where targets are not easily resolvable and appearance features cannot be easily leveraged for target re-identification. With over half a million annotations in over 1,500 videos sourced from seven different sonar cameras, CFC allows researchers to train MOT and counting algorithms and evaluate generalization performance at unseen test locations. We perform extensive baseline experiments and identify key challenges and opportunities for advancing the state of the art in generalization in MOT and counting.

We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva [Algorithmica, 2018] and Bonomo et al. [Graphs Combin., 2009]. This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound. The running times of the clique-width based algorithms for b-Coloring and Fall Coloring are tight under the Exponential Time Hypothesis.

In recent years, change point detection for high dimensional data has become increasingly important in many scientific fields. Most literature develop a variety of separate methods designed for specified models (e.g. mean shift model, vector auto-regressive model, graphical model). In this paper, we provide a unified framework for structural break detection which is suitable for a large class of models. Moreover, the proposed algorithm automatically achieves consistent parameter estimates during the change point detection process, without the need for refitting the model. Specifically, we introduce a three-step procedure. The first step utilizes the block segmentation strategy combined with a fused lasso based estimation criterion, leads to significant computational gains without compromising the statistical accuracy in identifying the number and location of the structural breaks. This procedure is further coupled with hard-thresholding and exhaustive search steps to consistently estimate the number and location of the break points. The strong guarantees are proved on both the number of estimated change points and the rates of convergence of their locations. The consistent estimates of model parameters are also provided. The numerical studies provide further support of the theory and validate its competitive performance for a wide range of models. The developed algorithm is implemented in the R package LinearDetect.

Multi-object tracking (MOT) is a crucial component of situational awareness in military defense applications. With the growing use of unmanned aerial systems (UASs), MOT methods for aerial surveillance is in high demand. Application of MOT in UAS presents specific challenges such as moving sensor, changing zoom levels, dynamic background, illumination changes, obscurations and small objects. In this work, we present a robust object tracking architecture aimed to accommodate for the noise in real-time situations. We propose a kinematic prediction model, called Deep Extended Kalman Filter (DeepEKF), in which a sequence-to-sequence architecture is used to predict entity trajectories in latent space. DeepEKF utilizes a learned image embedding along with an attention mechanism trained to weight the importance of areas in an image to predict future states. For the visual scoring, we experiment with different similarity measures to calculate distance based on entity appearances, including a convolutional neural network (CNN) encoder, pre-trained using Siamese networks. In initial evaluation experiments, we show that our method, combining scoring structure of the kinematic and visual models within a MHT framework, has improved performance especially in edge cases where entity motion is unpredictable, or the data presents frames with significant gaps.

Bid optimization for online advertising from single advertiser's perspective has been thoroughly investigated in both academic research and industrial practice. However, existing work typically assume competitors do not change their bids, i.e., the wining price is fixed, leading to poor performance of the derived solution. Although a few studies use multi-agent reinforcement learning to set up a cooperative game, they still suffer the following drawbacks: (1) They fail to avoid collusion solutions where all the advertisers involved in an auction collude to bid an extremely low price on purpose. (2) Previous works cannot well handle the underlying complex bidding environment, leading to poor model convergence. This problem could be amplified when handling multiple objectives of advertisers which are practical demands but not considered by previous work. In this paper, we propose a novel multi-objective cooperative bid optimization formulation called Multi-Agent Cooperative bidding Games (MACG). MACG sets up a carefully designed multi-objective optimization framework where different objectives of advertisers are incorporated. A global objective to maximize the overall profit of all advertisements is added in order to encourage better cooperation and also to protect self-bidding advertisers. To avoid collusion, we also introduce an extra platform revenue constraint. We analyze the optimal functional form of the bidding formula theoretically and design a policy network accordingly to generate auction-level bids. Then we design an efficient multi-agent evolutionary strategy for model optimization. Offline experiments and online A/B tests conducted on the Taobao platform indicate both single advertiser's objective and global profit have been significantly improved compared to state-of-art methods.

Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.

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