High-order meshes provide a more accurate geometrical approximation of an object's boundary (where stress usually concentrates, especially in the presence of contacts) than linear elements, for a negligible additional cost when used in a finite element simulation. High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order finite element formulation (high-order basis) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact model. Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of non-linear meshes or non-linear finite element basis. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order basis and high-order geometry. Additionally, we show that collision proxies can be naturally incorporated into this formulation. We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.
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This paper is about fast slosh free fluid transportation. Existing approaches are either computationally heavy or only suitable for specific robots and container shapes. We model the end effector as a point mass suspended by a spherical pendulum and study the requirements for slosh free motion and the validity of the point mass model. In this approach, slosh free trajectories are generated by controlling the pendulum's pivot and simulating the motion of the point mass. We cast the trajectory optimization problem as a quadratic program; this strategy can be used to obtain valid control inputs. Through simulations and experiments on a 7 DoF Franka Emika Panda robot we validate the effectiveness of the proposed approach.
Reinforcement learning has been demonstrated as a flexible and effective approach for learning a range of continuous control tasks, such as those used by robots to manipulate objects in their environment. But in robotics particularly, real-world rollouts are costly, and sample efficiency can be a major limiting factor when learning a new skill. In game environments, the use of world models has been shown to improve sample efficiency while still achieving good performance, especially when images or other rich observations are provided. In this project, we explore the use of a world model in a deformable robotic manipulation task, evaluating its effect on sample efficiency when learning to fold a cloth in simulation. We compare the use of RGB image observation with a feature space leveraging built-in structure (keypoints representing the cloth configuration), a common approach in robot skill learning, and compare the impact on task performance and learning efficiency with and without the world model. Our experiments showed that the usage of keypoints increased the performance of the best model on the task by 50%, and in general, the use of a learned or constructed reduced feature space improved task performance and sample efficiency. The use of a state transition predictor(MDN-RNN) in our world models did not have a notable effect on task performance.
We propose estimators based on kernel ridge regression for nonparametric causal functions such as dose, heterogeneous, and incremental response curves. Treatment and covariates may be discrete or continuous in general spaces. Due to a decomposition property specific to the RKHS, our estimators have simple closed form solutions. We prove uniform consistency with finite sample rates via original analysis of generalized kernel ridge regression. We extend our main results to counterfactual distributions and to causal functions identified by front and back door criteria. We achieve state-of-the-art performance in nonlinear simulations with many covariates, and conduct a policy evaluation of the US Job Corps training program for disadvantaged youths.
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in $H({\rm curl})$ and $H({\rm div})$ (e.g. for electromagnetic or radiation diffusion problems) a specially constructed interpolation-histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.
BERT has shown a lot of sucess in a wide variety of NLP tasks. But it has a limitation dealing with long inputs due to its attention mechanism. Longformer, ETC and BigBird addressed this issue and effectively solved the quadratic dependency problem. However we find that these models are not sufficient, and propose LittleBird, a novel model based on BigBird with improved speed and memory footprint while maintaining accuracy. In particular, we devise a more flexible and efficient position representation method based on Attention with Linear Biases (ALiBi). We also show that replacing the method of global information represented in the BigBird with pack and unpack attention is more effective. The proposed model can work on long inputs even after being pre-trained on short inputs, and can be trained efficiently reusing existing pre-trained language model for short inputs. This is a significant benefit for low-resource languages where large amounts of long text data are difficult to obtain. As a result, our experiments show that LittleBird works very well in a variety of languages, achieving high performance in question answering tasks, particularly in KorQuAD2.0, Korean Question Answering Dataset for long paragraphs.
Attention modules for Convolutional Neural Networks (CNNs) are an effective method to enhance performance on multiple computer-vision tasks. While existing methods appropriately model channel-, spatial- and self-attention, they primarily operate in a feedforward bottom-up manner. Consequently, the attention mechanism strongly depends on the local information of a single input feature map and does not incorporate relatively semantically-richer contextual information available at higher layers that can specify "what and where to look" in lower-level feature maps through top-down information flow. Accordingly, in this work, we propose a lightweight top-down attention module (TDAM) that iteratively generates a "visual searchlight" to perform channel and spatial modulation of its inputs and outputs more contextually-relevant feature maps at each computation step. Our experiments indicate that TDAM enhances the performance of CNNs across multiple object-recognition benchmarks and outperforms prominent attention modules while being more parameter and memory efficient. Further, TDAM-based models learn to "shift attention" by localizing individual objects or features at each computation step without any explicit supervision resulting in a 5% improvement for ResNet50 on weakly-supervised object localization. Source code and models are publicly available at: //github.com/shantanuj/TDAM_Top_down_attention_module .
In this paper, we consider a transformation of $k$ disjoint paths in a graph. For a graph and a pair of $k$ disjoint paths $\mathcal{P}$ and $\mathcal{Q}$ connecting the same set of terminal pairs, we aim to determine whether $\mathcal{P}$ can be transformed to $\mathcal{Q}$ by repeatedly replacing one path with another path so that the intermediates are also $k$ disjoint paths. The problem is called Disjoint Paths Reconfiguration. We first show that Disjoint Paths Reconfiguration is PSPACE-complete even when $k=2$. On the other hand, we prove that, when the graph is embedded on a plane and all paths in $\mathcal{P}$ and $\mathcal{Q}$ connect the boundaries of two faces, Disjoint Paths Reconfiguration can be solved in polynomial time. The algorithm is based on a topological characterization for rerouting curves on a plane using the algebraic intersection number. We also consider a transformation of disjoint $s$-$t$ paths as a variant. We show that the disjoint $s$-$t$ paths reconfiguration problem in planar graphs can be determined in polynomial time, while the problem is PSPACE-complete in general.
We present and analyze the Krylov-Bellman Boosting (KBB) algorithm for policy evaluation in general state spaces. It alternates between fitting the Bellman residual using non-parametric regression (as in boosting), and estimating the value function via the least-squares temporal difference (LSTD) procedure applied with a feature set that grows adaptively over time. By exploiting the connection to Krylov methods, we equip this method with two attractive guarantees. First, we provide a general convergence bound that allows for separate estimation errors in residual fitting and LSTD computation. Consistent with our numerical experiments, this bound shows that convergence rates depend on the restricted spectral structure, and are typically super-linear. Second, by combining this meta-result with sample-size dependent guarantees for residual fitting and LSTD computation, we obtain concrete statistical guarantees that depend on the sample size along with the complexity of the function class used to fit the residuals. We illustrate the behavior of the KBB algorithm for various types of policy evaluation problems, and typically find large reductions in sample complexity relative to the standard approach of fitted value iterationn.
We focus on the setting of contextual batched bandit (CBB), where a batch of rewards is observed from the environment in each episode. But the rewards of the non-executed actions are unobserved (i.e., partial-information feedbacks). Existing approaches for CBB usually ignore the rewards of the non-executed actions, resulting in feedback information being underutilized. In this paper, we propose an efficient reward imputation approach using sketching for CBB, which completes the unobserved rewards with the imputed rewards approximating the full-information feedbacks. Specifically, we formulate the reward imputation as a problem of imputation regularized ridge regression, which captures the feedback mechanisms of both the non-executed and executed actions. To reduce the time complexity of reward imputation, we solve the regression problem using randomized sketching. We prove that our reward imputation approach obtains a relative-error bound for sketching approximation, achieves an instantaneous regret with a controllable bias and a smaller variance than that without reward imputation, and enjoys a sublinear regret bound against the optimal policy. Moreover, we present two extensions of our approach, including the rate-scheduled version and the version for nonlinear rewards, making our approach more feasible. Experimental results demonstrated that our approach can outperform the state-of-the-art baselines on synthetic and real-world datasets.
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also intrigues great interests in the time series community. Among multiple advantages of transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review transformer schemes for time series modeling by highlighting their strengths as well as limitations through a new taxonomy to summarize existing time series transformers in two perspectives. From the perspective of network modifications, we summarize the adaptations of module level and architecture level of the time series transformers. From the perspective of applications, we categorize time series transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.
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