United States

Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems,
but they are still trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features.
In this paper, we propose to employ implicit stochastic gradient descent (ISGD) method to train PINNs for improving the stability of training process.
We heuristically analyze how ISGD overcome stiffness in the gradient flow dynamics of PINNs, especially for problems with multi-scale solutions.
We theoretically prove that for two-layer fully connected neural networks with large hidden nodes, randomly initialized ISGD converges to a globally optimal solution for the quadratic loss function.
Empirical results demonstrate that ISGD works well in practice and compares favorably to other gradient-based optimization methods such as SGD and Adam, while can also effectively address the numerical stiffness in training dynamics via gradient descent.

AAAI 2023

Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks

partial differential equations

physics-informed neural networks

gradient descent

machine learning

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers.<br><br><br>
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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

Naval Information Warfare Center Pacific is partnering with AFCEA San Diego chapter to host the workshop.

The NAML workshop is an opportunity for researchers from Navy research and development centers and our partner organizations to exchange technical ideas and to come together as a team.

The goals of NAML are:

* To spread awareness of current machine learning research relevant to Naval applications

* To connect machine learning researchers with experts in military requirements

* To build and strengthen collaborations within the defense research community

**Watch this video to hear about the AFCEA purpose.**

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NAML 2021

poster

As the quality of optical sensors improves, there is a need for processing large-scale images. In particular, the ability of devices to capture ultra-high definition (UHD) images and video places new demands on the image processing pipeline.
In this paper, we consider the task of low-light image enhancement (LLIE) and introduce a large-scale database consisting of images at 4K and 8K resolution. We conduct systematic benchmarking studies and provide a comparison of current LLIE algorithms. As a second contribution, we introduce LLFormer, a transformer-based low-light enhancement method. The core components of LLFormer are the axis-based multi-head selfattention and cross-layer attention fusion block, which significantly reduces the linear complexity. Extensive experiments on the new dataset and existing public datasets show that LLFormer outperforms state-of-the-art methods. We also show that employing existing LLIE methods trained on our benchmark as a pre-processing step significantly improves the performance of downstream tasks, e.g., face detection in low-light conditions. Code and dataset will be made available.

Ultra-High-Definition Low-Light Image Enhancement: A Benchmark and Transformer-Based Method

Human hand has amazing super-resolution ability in sensing the force and position of contact and this ability can be strengthened by practice. Inspired by this, we propose a method for robotic tactile super-resolution enhancement by learning spatiotemporal continuity of contact position and a tactile sensor composed of overlapping air chambers. Each overlapping air chamber is constructed of soft material and seals the barometer inside to mimic adapting receptors of human skin. Each barometer obtains the global receptive field of the contact surface with the pressure propagation in the hyperelastic seal overlapping air chambers. 
Neural networks with causal convolution are employed to resolve the pressure data sampled by barometers and to predict the contact position. The temporal consistency of spatial position contributes to the accuracy and stability of positioning. We obtain an average super-resolution (SR) factor of over 2500 with only four physical sensing nodes on the rubber surface (0.1 mm in the best case on 38 × 26 mm²), which outperforms the state-of-the-art. The effect of time series length on the location prediction accuracy of causal convolution is quantitatively analyzed in this article. 
We show that robots can accomplish challenging tasks such as haptic trajectory following, adaptive grasping, and human-robot interaction with the tactile sensor. This research provides new insight into tactile super-resolution sensing and could be beneficial to various applications in the robotics field. 

Improving Robotic Tactile Localization Super-Resolution via spatiotemporal Continuity Learning and Overlapping Air Chambers

Understanding intention behind event processes in texts is important to many applications. One challenging task in this line is event process typing, which aims to tag the process with one action label and one object label describing the overall action of the process and object the process likely affects respectively. To tackle this task, existing methods mainly rely on the matching of the event process level and label level representation, which ignores two important characteristics: Process Hierarchy and Label Hierarchy. In this paper, we propose a Hierarchical Optimal Transport (HOT) method to address the above problem. Specifically, we first explicitly extract the process hierarchy and label hierarchy. Then the HOT optimally matches the two types of hierarchy. Experimental results demonstrate that our proposed model outperforms previous methods. In particular, the MRR is improved by 10.55% and the recall@10 is improved by 14.54% in action label prediction.

Event Process Typing via Hierarchical Optimal Transport

Time or money? That is a question! In this paper, we consider this dilemma in the pricing regime, in which we try to find the optimal pricing scheme for identical items with heterogenous time-sensitive buyers. We characterize the revenue-optimal solution and propose an efficient algorithm to find it in a Bayesian setting. Our results also demonstrate the tight ratio between the value of wasted time and the seller's revenue, as well as that of two common-used pricing schemes, the $k$-step function and the fixed pricing. To explore the nature of the optimal scheme in the general setting, we present the closed forms over the product distribution and show by examples that positive correlation between the valuation of the item and the cost per unit time could help increase revenue. To the best of our knowledge, it is the first step towards understanding the impact of the time factor as a part of the buyer cost in pricing problems, in the computational view.

Optimal Pricing Schemes for Identical Items with Time-Sensitive Buyers

The prevalence of region-based urban data has enabled us to explore the correlations of regions for better urban planning and smart-city solutions, in which region embedding plays an important role. However, this is a challenging problem considering the following two factors: different city data for region embedding and the effectiveness for various downstream applications. 
In this paper, we propose a novel framework, named \textbf{HREP} (\textbf{H}eterogeneous \textbf{R}egion \textbf{E}mbedding with \textbf{P}rompt learning), considering both intra-region and inter-region correlations, which includes two major modules, \textbf{H}eterogeneous graph learning for \textbf{R}egion \textbf{E}mbedding (\textbf{HRE}) and prompt learning for different downstream tasks. In the HRE module, we construct a region heterogeneous graph according to three categories of data, capturing inter-region contexts, e.g., human mobility and region geographic neighbors, and intra-region contexts, e.g., POI information. Specially, we design a \textit{relation-aware graph embedding} to learn region embedding and relation embeddings of edge types based on the heterogeneous graph. Then we introduce self-attention to capture the global correlation of regions. Moreover, we develop a \textit{attention-based fusion module} to integrate sharing information among different types of correlations. 
To enable region embedding to be effectively utilized in downstream tasks, we migrate the prompt learning, i.e., continuous prompt
prefix-tuning, which can guide the learning of downstream tasks, leading to better prediction results. Extensive experimental results on real-world datasets show that our model outperforms all state-of-the-art methods dramatically.

Heterogeneous Region Embedding with Prompt Learning

Attention modules, which adaptively weight and refine features according to the importance of the input, have become a critical technique to boost the capability of convolutional neural networks. However, most existing attention modules are heuristic without a sound interpretation, and thus, require empirical engineering to design structure and operators within the modules. To handle the above issue, based on our 'less is more important' observation, we propose an Attention Module guided by Probability Density Function (PDF), dubbed PdfAM, which enjoys a rational motivation and requires few empirical structure designs. Concretely, we observe that pixels with less occurrence are prone to be textural details or foreground objects with much importance to aid vision tasks. Thus, with PDF values adopted as a smooth and anti-noise alternative to the pixel occurrence frequency, we design our PdfAM by first estimating the PDF based on some distribution assumption, and then predicting a 3D attention map via applying a negative correlation between the attention weights and the estimated PDF values. Furthermore, we develop learnable PDF-rescale parameters so as to adaptively transform the estimated PDF and predict a customized negative correlation. Experiments show that our PdfAM consistently boosts various networks under both high- and low-level vision tasks, and also performs favorably against other attention modules in terms of accuracy and convergence.

Less Is More Important: An Attention Module Guided by Probability Density Function for Convolutional Neural Networks

Attention mechanisms, such as local and non-local attention, play a fundamental role in recent deep learning based speech enhancement (SE) systems. However, a natural speech contains many fast-changing and relatively briefly acoustic events, therefore, capturing the most informative speech features by indiscriminately using local and non-local attention is challenged. We observe that the noise type and speech feature vary within a sequence of speech and the local and non-local can respectively process different types of corrupted speech regions. To leverage this, we propose Selector-Enhancer, a dual-attention based convolution neural network (CNN) with a feature-filter that can dynamically select regions from low-resolution speech features and feed them to local or non-local attention operations. In particular, the proposed feature-filter is trained by using reinforcement learning (RL) with a developed difficulty-regulated reward that related to network performance, model complexity and “the difficulty of the SE task”. The results show that our method achieves comparable or superior performance to existing approaches. In particular, Selector-Enhancer is effective for real-world denoising, where the number and types of noise are varies on a single noisy mixture.

Selector-Enhancer: Learning Dynamic Selection of Local and Non-local Attention Operation for Speech Enhancement

Despite success in many challenging problems, reinforcement learning (RL) is still confronted with sample inefficiency, which can be mitigated by introducing prior knowledge to agents. However, many transfer techniques in reinforcement learning make the limiting assumption that the teacher is an expert. In this paper, we use the action prior from the Reinforcement Learning as Inference framework - that is, a distribution over actions at each state which resembles a teacher policy, rather than a Bayesian prior - to recover state-of-the-art policy distillation techniques. Then, we propose a class of adaptive methods that can robustly exploit action priors by combining reward shaping and auxiliary regularization losses. In contrast to prior work, we develop algorithms for leveraging suboptimal action priors that may nevertheless impart valuable knowledge - which we call soft action priors. The proposed algorithms adapt by adjusting the strength of teacher feedback according to an estimate of the teacher's usefulness in each state. We perform tabular experiments, which show that the proposed methods achieve state-of-the-art performance, surpassing it when learning from suboptimal priors. Finally, we demonstrate the robustness of the adaptive algorithms in continuous action deep RL problems, in which adaptive algorithms considerably improved stability when compared to existing policy distillation methods.

Soft Action Priors: Towards Robust Policy Transfer

Satisfaction of the strict saddle property has become a standard assumption in non-convex optimization, and it ensures that many first-order optimization
algorithms will almost always escape saddle points. However, functions exist in machine learning that do not satisfy this property, such as the loss function of a neural network with at least two hidden layers. First-order methods such as gradient descent may converge to non-strict saddle points of such functions, and there do not currently exist any first-order methods that reliably escape non-strict saddle points. To address this need, we demonstrate that regularizing a function with a linear term enforces the strict saddle property, and we provide justification for only regularizing locally, i.e., when the norm of the gradient falls below a certain threshold. We analyze bifurcations that may result from this form of regularization, and then we provide a selection rule for regularizers that depends only on the gradient of an objective function. This rule is shown to guarantee that gradient descent will escape the neighborhoods around a broad class of non-strict saddle points, and this behavior is demonstrated on numerical examples of non-strict saddle points common in the optimization literature.

Linear Regularizers Enforce the Strict Saddle Property

Multimodal named entity recognition (MNER) is a critical step in information extraction, which aims to detect entity spans and classify them to corresponding entity types given a sentence-image pair. Existing methods either (1) obtain named entities with coarse-grained visual clues from attention mechanisms, or (2) first detect fine-grained visual regions with toolkits and then recognize named entities. However, they suffer from improper alignment between entity types and visual regions or error propagation in the two-stage manner, which finally imports irrelevant visual information into texts. In this paper, we propose a novel end-to-end framework named MNER-QG that can simultaneously perform MRC-based multimodal named entity recognition and query grounding. Specifically, with the assistance of queries, MNER-QG can provide prior knowledge of entity types and visual regions, and further enhance representations of both text and image. To conduct the query grounding task, we provide manual annotations and weak supervisions that are obtained via training a highly flexible visual grounding model with transfer learning. We conduct extensive experiments on two public MNER datasets, Twitter2015 and Twitter2017. Experimental results show that MNER-QG outperforms the current state-of-the-art models on the MNER task, and also improves the query grounding performance.

Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks

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