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This paper presents a high-order discontinuous Galerkin finite element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced by Romenski et al., in multiple space dimensions. In the absence of algebraic source terms, the model is endowed with a curl constraint on the relative velocity field. In this paper, the hyperbolicity of the system is studied for the first time in the multidimensional case, showing that the original model is only weakly hyperbolic in multiple space dimensions. To restore strong hyperbolicity, two different methodologies are used: i) the explicit symmetrization of the system, which can be achieved by adding terms that contain linear combinations of the curl involution, similar to the Godunov-Powell terms in the MHD equations; ii) the use of the hyperbolic generalized Lagrangian multiplier (GLM) curl-cleaning approach forwarded. The PDE system is solved using a high-order ADER discontinuous Galerkin method with a posteriori sub-cell finite volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model. To illustrate the performance of the method, several different test cases and benchmark problems have been run, showing the high-order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.

Recent years have witnessed the growing popularity of domain-specific accelerators (DSAs), such as Google's TPUs, for accelerating various applications such as deep learning, search, autonomous driving, etc. To facilitate DSA designs, high-level synthesis (HLS) is used, which allows a developer to compile a high-level description in the form of software code in C and C++ into a design in low-level hardware description languages (such as VHDL or Verilog) and eventually synthesized into a DSA on an ASIC (application-specific integrated circuit) or FPGA (field-programmable gate arrays). However, existing HLS tools still require microarchitecture decisions, expressed in terms of pragmas (such as directives for parallelization and pipelining). To enable more people to design DSAs, it is desirable to automate such decisions with the help of deep learning for predicting the quality of HLS designs. This requires us a deeper understanding of the program, which is a combination of original code and pragmas. Naturally, these programs can be considered as sequence data, for which large language models (LLM) can help. In addition, these programs can be compiled and converted into a control data flow graph (CDFG), and the compiler also provides fine-grained alignment between the code tokens and the CDFG nodes. However, existing works either fail to leverage both modalities or combine the two in shallow or coarse ways. We propose ProgSG allowing the source code sequence modality and the graph modalities to interact with each other in a deep and fine-grained way. To alleviate the scarcity of labeled designs, a pre-training method is proposed based on a suite of compiler's data flow analysis tasks. Experimental results on two benchmark datasets show the superiority of ProgSG over baseline methods that either only consider one modality or combine the two without utilizing the alignment information.

We prove Wasserstein inverse reinforcement learning enables the learner's reward values to imitate the expert's reward values in a finite iteration for multi-objective optimizations. Moreover, we prove Wasserstein inverse reinforcement learning enables the learner's optimal solutions to imitate the expert's optimal solutions for multi-objective optimizations with lexicographic order.

We introduce Reactive Action and Motion Planner (RAMP), which combines the strengths of search-based and reactive approaches for motion planning. In essence, RAMP is a hierarchical approach where a novel variant of a Model Predictive Path Integral (MPPI) controller is used to generate trajectories which are then followed asynchronously by a local vector field controller. We demonstrate, in the context of a table clearing application, that RAMP can rapidly find paths in the robot's configuration space, satisfy task and robot-specific constraints, and provide safety by reacting to static or dynamically moving obstacles. RAMP achieves superior performance through a number of key innovations: we use Signed Distance Function (SDF) representations directly from the robot configuration space, both for collision checking and reactive control. The use of SDFs allows for a smoother definition of collision cost when planning for a trajectory, and is critical in ensuring safety while following trajectories. In addition, we introduce a novel variant of MPPI which, combined with the safety guarantees of the vector field trajectory follower, performs incremental real-time global trajectory planning. Simulation results establish that our method can generate paths that are comparable to traditional and state-of-the-art approaches in terms of total trajectory length while being up to 30 times faster. Real-world experiments demonstrate the safety and effectiveness of our approach in challenging table clearing scenarios.

In 3D face reconstruction, orthogonal projection has been widely employed to substitute perspective projection to simplify the fitting process. This approximation performs well when the distance between camera and face is far enough. However, in some scenarios that the face is very close to camera or moving along the camera axis, the methods suffer from the inaccurate reconstruction and unstable temporal fitting due to the distortion under the perspective projection. In this paper, we aim to address the problem of single-image 3D face reconstruction under perspective projection. Specifically, a deep neural network, Perspective Network (PerspNet), is proposed to simultaneously reconstruct 3D face shape in canonical space and learn the correspondence between 2D pixels and 3D points, by which the 6DoF (6 Degrees of Freedom) face pose can be estimated to represent perspective projection. Besides, we contribute a large ARKitFace dataset to enable the training and evaluation of 3D face reconstruction solutions under the scenarios of perspective projection, which has 902,724 2D facial images with ground-truth 3D face mesh and annotated 6DoF pose parameters. Experimental results show that our approach outperforms current state-of-the-art methods by a significant margin. The code and data are available at //github.com/cbsropenproject/6dof_face.

Reinforcement learning (RL) exhibits impressive performance when managing complicated control tasks for robots. However, its wide application to physical robots is limited by the absence of strong safety guarantees. To overcome this challenge, this paper explores the control Lyapunov barrier function (CLBF) to analyze the safety and reachability solely based on data without explicitly employing a dynamic model. We also proposed the Lyapunov barrier actor-critic (LBAC), a model-free RL algorithm, to search for a controller that satisfies the data-based approximation of the safety and reachability conditions. The proposed approach is demonstrated through simulation and real-world robot control experiments, i.e., a 2D quadrotor navigation task. The experimental findings reveal this approach's effectiveness in reachability and safety, surpassing other model-free RL methods.

Transportation of probability measures underlies many core tasks in statistics and machine learning, from variational inference to generative modeling. A typical goal is to represent a target probability measure of interest as the push-forward of a tractable source measure through a learned map. We present a new construction of such a transport map, given the ability to evaluate the score of the target distribution. Specifically, we characterize the map as a zero of an infinite-dimensional score-residual operator and derive a Newton-type method for iteratively constructing such a zero. We prove convergence of these iterations by invoking classical elliptic regularity theory for partial differential equations (PDE) and show that this construction enjoys rapid convergence, under smoothness assumptions on the target score. A key element of our approach is a generalization of the elementary Newton method to infinite-dimensional operators, other forms of which have appeared in nonlinear PDE and in dynamical systems. Our Newton construction, while developed in a functional setting, also suggests new iterative algorithms for approximating transport maps.

We implement a method from computer sciences to address a challenge in Paleolithic archaeology: how to infer cognition differences from material culture. Archaeological material culture is linked to cognition: more complex ancient technologies are assumed to have required complex cognition. We present an application of Petri net analysis to compare Neanderthal tar production technologies and tie the results to cognitive requirements. We applied three complexity metrics, each relying on their own unique definitions of complexity, to the modelled production sequences. Based on the results, we suggest that Neanderthal working memory requirements may have been similar to human preferences regarding working memory use today. This method also enables us to distinguish the high-order cognitive functions combining traits like planning, inhibitory control, and learnings that were likely required by different ancient technological processes. The Petri net approach can contribute to our understanding of technology and cognitive evolution as it can be used on different materials and technologies, across time and species.

Structural data well exists in Web applications, such as social networks in social media, citation networks in academic websites, and threads data in online forums. Due to the complex topology, it is difficult to process and make use of the rich information within such data. Graph Neural Networks (GNNs) have shown great advantages on learning representations for structural data. However, the non-transparency of the deep learning models makes it non-trivial to explain and interpret the predictions made by GNNs. Meanwhile, it is also a big challenge to evaluate the GNN explanations, since in many cases, the ground-truth explanations are unavailable. In this paper, we take insights of Counterfactual and Factual (CF^2) reasoning from causal inference theory, to solve both the learning and evaluation problems in explainable GNNs. For generating explanations, we propose a model-agnostic framework by formulating an optimization problem based on both of the two casual perspectives. This distinguishes CF^2 from previous explainable GNNs that only consider one of them. Another contribution of the work is the evaluation of GNN explanations. For quantitatively evaluating the generated explanations without the requirement of ground-truth, we design metrics based on Counterfactual and Factual reasoning to evaluate the necessity and sufficiency of the explanations. Experiments show that no matter ground-truth explanations are available or not, CF^2 generates better explanations than previous state-of-the-art methods on real-world datasets. Moreover, the statistic analysis justifies the correlation between the performance on ground-truth evaluation and our proposed metrics.

Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization capability, model optimization, and model selection and design. We conclude by proposing several interesting future directions.