While transformers have gained recognition as a versatile tool for artificial intelligence (AI), an unexplored challenge arises in the context of chess — a classical AI benchmark. Here, incorporating vision Transform...
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Prior knowledge of the medical domain has consistently enriched medical image analysis, yet its full potential remains to be explored. Our Deformable Symmetry Attention (DSA) aims to leverage anatomical symmetry prior...
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Geo-tagged images are publicly available in large quantities, whereas labels such as object classes are rather scarce and expensive to collect. Meanwhile, contrastive learning has achieved tremendous success in variou...
As machine learning models become larger, and are increasingly trained on large and uncurated data sets in weakly supervised mode, it becomes important to establish mechanisms for inspecting, interacting, and revising...
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Predictions on subseasonal-to-seasonal (S2S) timescales—ranging from two weeks to two months—are crucial for early warning systems but remain challenging owing to chaos in the climate system. Teleconnections, such a...
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While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of...
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The memorization effects of deep networks show that they will first memorize training data with clean labels and then those with noisy labels. The early stopping method therefore can be exploited for learning with noi...
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Recent work has highlighted the label alignment property (LAP) in supervised learning, where the vector of all labels in the dataset is mostly in the span of the top few singular vectors of the data matrix. Drawing in...
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Video summarization methods generate a compact representation of the original video preserving the essential content of the input video. Video summaries utilize less storage space compared to the original video. The s...
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The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The L2 Physics- Informed Loss is the de-facto standard in training Physics-In...
ISBN:
(纸本)9781713871088
The Physics-Informed Neural Network (PINN) approach is a new and promising way to solve partial differential equations using deep learning. The L2 Physics- Informed Loss is the de-facto standard in training Physics-Informed Neural Networks. In this paper, we challenge this common practice by investigating the relationship between the loss function and the approximation quality of the learned solution. In particular, we leverage the concept of stability in the literature of partial differential equation to study the asymptotic behavior of the learned solution as the loss approaches zero. With this concept, we study an important class of high-dimensional non-linear PDEs in optimal control, the Hamilton-Jacobi- Bellman (HJB) Equation, and prove that for general Lp Physics-Informed Loss, a wide class of HJB equation is stable only if p is sufficiently large. Therefore, the commonly used L2 loss is not suitable for training PINN on those equations, while L∞ loss is a better choice. Based on the theoretical insight, we develop a novel PINN training algorithm to minimize the L∞ loss for HJB equations which is in a similar spirit to adversarial training. The effectiveness of the proposed algorithm is empirically demonstrated through experiments.
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