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We study the Compressed Sensing (CS) problem, which is the problem of finding the most sparse vector that satisfies a set of linear measurements up to some numerical tolerance. We introduce an $\ell_2$ regularized formulation of CS which we reformulate as a mixed integer second order cone program. We derive a second order cone relaxation of this problem and show that under mild conditions on the regularization parameter, the resulting relaxation is equivalent to the well studied basis pursuit denoising problem. We present a semidefinite relaxation that strengthens the second order cone relaxation and develop a custom branch-and-bound algorithm that leverages our second order cone relaxation to solve small-scale instances of CS to certifiable optimality. When compared against solutions produced by three state of the art benchmark methods on synthetic data, our numerical results show that our approach produces solutions that are on average $6.22\%$ more sparse. When compared only against the experiment-wise best performing benchmark method on synthetic data, our approach produces solutions that are on average $3.10\%$ more sparse. On real world ECG data, for a given $\ell_2$ reconstruction error our approach produces solutions that are on average $9.95\%$ more sparse than benchmark methods ($3.88\%$ more sparse if only compared against the best performing benchmark), while for a given sparsity level our approach produces solutions that have on average $10.77\%$ lower reconstruction error than benchmark methods ($1.42\%$ lower error if only compared against the best performing benchmark). When used as a component of a multi-label classification algorithm, our approach achieves greater classification accuracy than benchmark compressed sensing methods. This improved accuracy comes at the cost of an increase in computation time by several orders of magnitude.

LambdaBeam is a state-of-the-art execution-guided algorithm for program synthesis that incorporates higher-order functions, lambda functions, and iterative loops into the Domain-Specific Language (DSL). LambdaBeam generates every program from the start. Yet, many program blocks or subprograms occur frequently in a given domain, e.g., loops to traverse a list. Thus, repeating programs can be used to enhance the synthesis algorithm. However, LambdaBeam fails to leverage this potential. For this purpose, we introduce AbstractBeam: A novel program synthesis framework that employs Library Learning to identify such program repetitions, integrates them into the DSL, and thus utilizes their potential to boost LambdaBeam's synthesis algorithm. Our experimental evaluations demonstrate that AbstractBeam significantly improves LambdaBeam's performance in the LambdaBeam integer list manipulation domain. Additionally, AbstractBeam's program generation is more efficient compared to LambdaBeam's synthesis. Finally, our findings indicate that Library Learning is effective in domains not specifically crafted to highlight its benefits.

Dance, as an art form, fundamentally hinges on the precise synchronization with musical beats. However, achieving aesthetically pleasing dance sequences from music is challenging, with existing methods often falling short in controllability and beat alignment. To address these shortcomings, this paper introduces Beat-It, a novel framework for beat-specific, key pose-guided dance generation. Unlike prior approaches, Beat-It uniquely integrates explicit beat awareness and key pose guidance, effectively resolving two main issues: the misalignment of generated dance motions with musical beats, and the inability to map key poses to specific beats, critical for practical choreography. Our approach disentangles beat conditions from music using a nearest beat distance representation and employs a hierarchical multi-condition fusion mechanism. This mechanism seamlessly integrates key poses, beats, and music features, mitigating condition conflicts and offering rich, multi-conditioned guidance for dance generation. Additionally, a specially designed beat alignment loss ensures the generated dance movements remain in sync with the designated beats. Extensive experiments confirm Beat-It's superiority over existing state-of-the-art methods in terms of beat alignment and motion controllability.

Deep model fusion/merging is an emerging technique that merges the parameters or predictions of multiple deep learning models into a single one. It combines the abilities of different models to make up for the biases and errors of a single model to achieve better performance. However, deep model fusion on large-scale deep learning models (e.g., LLMs and foundation models) faces several challenges, including high computational cost, high-dimensional parameter space, interference between different heterogeneous models, etc. Although model fusion has attracted widespread attention due to its potential to solve complex real-world tasks, there is still a lack of complete and detailed survey research on this technique. Accordingly, in order to understand the model fusion method better and promote its development, we present a comprehensive survey to summarize the recent progress. Specifically, we categorize existing deep model fusion methods as four-fold: (1) "Mode connectivity", which connects the solutions in weight space via a path of non-increasing loss, in order to obtain better initialization for model fusion; (2) "Alignment" matches units between neural networks to create better conditions for fusion; (3) "Weight average", a classical model fusion method, averages the weights of multiple models to obtain more accurate results closer to the optimal solution; (4) "Ensemble learning" combines the outputs of diverse models, which is a foundational technique for improving the accuracy and robustness of the final model. In addition, we analyze the challenges faced by deep model fusion and propose possible research directions for model fusion in the future. Our review is helpful in deeply understanding the correlation between different model fusion methods and practical application methods, which can enlighten the research in the field of deep model fusion.

Graph neural networks (GNNs) are a type of deep learning models that learning over graphs, and have been successfully applied in many domains. Despite the effectiveness of GNNs, it is still challenging for GNNs to efficiently scale to large graphs. As a remedy, distributed computing becomes a promising solution of training large-scale GNNs, since it is able to provide abundant computing resources. However, the dependency of graph structure increases the difficulty of achieving high-efficiency distributed GNN training, which suffers from the massive communication and workload imbalance. In recent years, many efforts have been made on distributed GNN training, and an array of training algorithms and systems have been proposed. Yet, there is a lack of systematic review on the optimization techniques from graph processing to distributed execution. In this survey, we analyze three major challenges in distributed GNN training that are massive feature communication, the loss of model accuracy and workload imbalance. Then we introduce a new taxonomy for the optimization techniques in distributed GNN training that address the above challenges. The new taxonomy classifies existing techniques into four categories that are GNN data partition, GNN batch generation, GNN execution model, and GNN communication protocol.We carefully discuss the techniques in each category. In the end, we summarize existing distributed GNN systems for multi-GPUs, GPU-clusters and CPU-clusters, respectively, and give a discussion about the future direction on scalable GNNs.

Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.

Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are correct and that people can easily and reliably understand them. While the former has been addressed in prior work, the latter is often overlooked, resulting in informal model understanding derived from a handful of local explanations. In this paper, we introduce explanation summary (ExSum), a mathematical framework for quantifying model understanding, and propose metrics for its quality assessment. On two domains, ExSum highlights various limitations in the current practice, helps develop accurate model understanding, and reveals easily overlooked properties of the model. We also connect understandability to other properties of explanations such as human alignment, robustness, and counterfactual minimality and plausibility.

We present CoDEx, a set of knowledge graph completion datasets extracted from Wikidata and Wikipedia that improve upon existing knowledge graph completion benchmarks in scope and level of difficulty. In terms of scope, CoDEx comprises three knowledge graphs varying in size and structure, multilingual descriptions of entities and relations, and tens of thousands of hard negative triples that are plausible but verified to be false. To characterize CoDEx, we contribute thorough empirical analyses and benchmarking experiments. First, we analyze each CoDEx dataset in terms of logical relation patterns. Next, we report baseline link prediction and triple classification results on CoDEx for five extensively tuned embedding models. Finally, we differentiate CoDEx from the popular FB15K-237 knowledge graph completion dataset by showing that CoDEx covers more diverse and interpretable content, and is a more difficult link prediction benchmark. Data, code, and pretrained models are available at //bit.ly/2EPbrJs.

The design of deep graph models still remains to be investigated and the crucial part is how to explore and exploit the knowledge from different hops of neighbors in an efficient way. In this paper, we propose a novel RNN-like deep graph neural network architecture by incorporating AdaBoost into the computation of network; and the proposed graph convolutional network called AdaGCN~(AdaBoosting Graph Convolutional Network) has the ability to efficiently extract knowledge from high-order neighbors and integrate knowledge from different hops of neighbors into the network in an AdaBoost way. We also present the architectural difference between AdaGCN and existing graph convolutional methods to show the benefits of our proposal. Finally, extensive experiments demonstrate the state-of-the-art prediction performance and the computational advantage of our approach AdaGCN.

Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. At present, the vast majority of GCNs use a neighborhood aggregation framework to learn a continuous and compact vector, then performing a pooling operation to generalize graph embedding for the classification task. These approaches have two disadvantages in the graph classification task: (1)when only the largest sub-graph structure ($k$-hop neighbor) is used for neighborhood aggregation, a large amount of early-stage information is lost during the graph convolution step; (2) simple average/sum pooling or max pooling utilized, which loses the characteristics of each node and the topology between nodes. In this paper, we propose a novel framework called, dual attention graph convolutional networks (DAGCN) to address these problems. DAGCN automatically learns the importance of neighbors at different hops using a novel attention graph convolution layer, and then employs a second attention component, a self-attention pooling layer, to generalize the graph representation from the various aspects of a matrix graph embedding. The dual attention network is trained in an end-to-end manner for the graph classification task. We compare our model with state-of-the-art graph kernels and other deep learning methods. The experimental results show that our framework not only outperforms other baselines but also achieves a better rate of convergence.