Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically address the imposition of Dirichlet/Neumann boundary conditions over irregular domain boundaries. In this paper, we present a framework to neurally solve partial differential equations over domains with irregularly shaped (non-rectilinear) geometric boundaries. Our network takes in the shape of the domain as an input (represented using an unstructured point cloud, or any other parametric representation such as Non-Uniform Rational B-Splines) and is able to generalize to novel (unseen) irregular domains; the key technical ingredient to realizing this model is a novel approach for identifying the interior and exterior of the computational grid in a differentiable manner. We also perform a careful error analysis which reveals theoretical insights into several sources of error incurred in the model-building process. Finally, we showcase a wide variety of applications, along with favorable comparisons with ground truth solutions.

遗憾已被广泛用作评估分布式多代理系统在线优化算法的性能的首选指标。但是，与代理相关的数据/模型变化可以显着影响决策，并需要在代理之间达成共识。此外，大多数现有的作品都集中在开发（强烈或非严格地）凸出的方法上，对于一般非凸损失的分布式在线优化中的遗憾界限，几乎没有得到很少的结果。为了解决这两个问题，我们提出了一种新型的综合遗憾，并使用新的基于网络的基于遗憾的度量标准来评估分布式在线优化算法。我们具体地定义了复合遗憾的静态和动态形式。通过利用我们的综合遗憾的动态形式，我们开发了一种基于共识的在线归一化梯度（CONGD）的伪convex损失方法，事实证明，它显示了与最佳器路径变化的规律性术语有关的透明性行为。对于一般的非凸损失，我们首先阐明了基于最近进步的分布式在线非凸学习的遗憾，因此没有确定性算法可以实现sublinear的遗憾。然后，我们根据离线优化的Oracle开发了分布式的在线非凸优化（Dinoco），而无需进入梯度。迪诺科（Dinoco）被证明是统一的遗憾。据我们所知，这是对一般分布在线非convex学习的第一个遗憾。

在分布式深度学习的背景下，陈旧的权重或梯度的问题可能导致算法性能差。这个问题通常通过延迟耐受算法来解决，并在目标函数和步进尺寸上有一些温和的假设。在本文中，我们提出了一种不同的方法来开发一种新算法，称为$ \ textbf {p} $ redicting $ \ textbf {c} $ lipping $ \ textbf {a} $ synchronous $ \ textbf {s} textbf {g} $ radient $ \ textbf {d} $ escent（aka，pc-asgd）。具体而言，PC -ASGD有两个步骤 - $ \ textIt {预测步骤} $利用泰勒扩展利用梯度预测来减少过时的权重的稳固性，而$ \ textit {clivipping step} $选择性地降低了过时的权重，以减轻过时的权重他们的负面影响。引入权衡参数以平衡这两个步骤之间的影响。从理论上讲，考虑到平滑的物镜函数弱键和非凸的延迟延迟的延迟，我们介绍了收敛速率。还提出了一种实用的PC-ASGD变体，即采用条件来帮助确定权衡参数。对于经验验证，我们在两个基准数据集上使用两个深神经网络体系结构演示了该算法的性能。

我们提出了一种新的多功能增强学习的新型政策梯度方法，其利用了两个不同的差异减少技术，并且不需要在迭代上进行大量批次。具体而言，我们提出了一种基于势头的分散策略梯度跟踪（MDPGT），其中使用新的基于动量的方差减少技术来接近具有重要性采样的本地策略梯度代理，并采用中间参数来跟踪两个连续的策略梯度代理。此外，MDPGT可证明$ \ mathcal {o}的最佳可用样本复杂性（n ^ { - 1} \ epsilon ^ {-3}）$，用于汇聚到全球平均值的$ \ epsilon $ -stationary点n $本地性能函数（可能是非旋转）。这优于在分散的无模型增强学习中的最先进的样本复杂性，并且当用单个轨迹初始化时，采样复杂性与现有的分散的政策梯度方法获得的样本复杂性匹配。我们进一步验证了高斯策略函数的理论索赔。当所需的误差容忍$ \ epsilon $足够小时，MDPGT导致线性加速，以前已经在分散的随机优化中建立，但不是为了加强学习。最后，我们在多智能体增强学习基准环境下提供了实证结果，以支持我们的理论发现。

This paper focuses on designing efficient models with low parameters and FLOPs for dense predictions. Even though CNN-based lightweight methods have achieved stunning results after years of research, trading-off model accuracy and constrained resources still need further improvements. This work rethinks the essential unity of efficient Inverted Residual Block in MobileNetv2 and effective Transformer in ViT, inductively abstracting a general concept of Meta-Mobile Block, and we argue that the specific instantiation is very important to model performance though sharing the same framework. Motivated by this phenomenon, we deduce a simple yet efficient modern \textbf{I}nverted \textbf{R}esidual \textbf{M}obile \textbf{B}lock (iRMB) for mobile applications, which absorbs CNN-like efficiency to model short-distance dependency and Transformer-like dynamic modeling capability to learn long-distance interactions. Furthermore, we design a ResNet-like 4-phase \textbf{E}fficient \textbf{MO}del (EMO) based only on a series of iRMBs for dense applications. Massive experiments on ImageNet-1K, COCO2017, and ADE20K benchmarks demonstrate the superiority of our EMO over state-of-the-art methods, \eg, our EMO-1M/2M/5M achieve 71.5, 75.1, and 78.4 Top-1 that surpass \textbf{SoTA} CNN-/Transformer-based models, while trading-off the model accuracy and efficiency well.

We aim to bridge the gap between our common-sense few-sample human learning and large-data machine learning. We derive a theory of human-like few-shot learning from von-Neuman-Landauer's principle. modelling human learning is difficult as how people learn varies from one to another. Under commonly accepted definitions, we prove that all human or animal few-shot learning, and major models including Free Energy Principle and Bayesian Program Learning that model such learning, approximate our theory, under Church-Turing thesis. We find that deep generative model like variational autoencoder (VAE) can be used to approximate our theory and perform significantly better than baseline models including deep neural networks, for image recognition, low resource language processing, and character recognition.

Despite significant progress in object categorization, in recent years, a number of important challenges remain; mainly, the ability to learn from limited labeled data and to recognize object classes within large, potentially open, set of labels. Zero-shot learning is one way of addressing these challenges, but it has only been shown to work with limited sized class vocabularies and typically requires separation between supervised and unsupervised classes, allowing former to inform the latter but not vice versa. We propose the notion of vocabulary-informed learning to alleviate the above mentioned challenges and address problems of supervised, zero-shot, generalized zero-shot and open set recognition using a unified framework. Specifically, we propose a weighted maximum margin framework for semantic manifold-based recognition that incorporates distance constraints from (both supervised and unsupervised) vocabulary atoms. Distance constraints ensure that labeled samples are projected closer to their correct prototypes, in the embedding space, than to others. We illustrate that resulting model shows improvements in supervised, zero-shot, generalized zero-shot, and large open set recognition, with up to 310K class vocabulary on Animal with Attributes and ImageNet datasets.

We consider infinite horizon Markov decision processes (MDPs) with fast-slow structure, meaning that certain parts of the state space move "fast" (and in a sense, are more influential) while other parts transition more "slowly." Such structure is common in real-world problems where sequential decisions need to be made at high frequencies, yet information that varies at a slower timescale also influences the optimal policy. Examples include: (1) service allocation for a multi-class queue with (slowly varying) stochastic costs, (2) a restless multi-armed bandit with an environmental state, and (3) energy demand response, where both day-ahead and real-time prices play a role in the firm's revenue. Models that fully capture these problems often result in MDPs with large state spaces and large effective time horizons (due to frequent decisions), rendering them computationally intractable. We propose an approximate dynamic programming algorithmic framework based on the idea of "freezing" the slow states, solving a set of simpler finite-horizon MDPs (the lower-level MDPs), and applying value iteration (VI) to an auxiliary MDP that transitions on a slower timescale (the upper-level MDP). We also extend the technique to a function approximation setting, where a feature-based linear architecture is used. On the theoretical side, we analyze the regret incurred by each variant of our frozen-state approach. Finally, we give empirical evidence that the frozen-state approach generates effective policies using just a fraction of the computational cost, while illustrating that simply omitting slow states from the decision modeling is often not a viable heuristic.

We present Muse, a text-to-image Transformer model that achieves state-of-the-art image generation performance while being significantly more efficient than diffusion or autoregressive models. Muse is trained on a masked modeling task in discrete token space: given the text embedding extracted from a pre-trained large language model (LLM), Muse is trained to predict randomly masked image tokens. Compared to pixel-space diffusion models, such as Imagen and DALL-E 2, Muse is significantly more efficient due to the use of discrete tokens and requiring fewer sampling iterations; compared to autoregressive models, such as Parti, Muse is more efficient due to the use of parallel decoding. The use of a pre-trained LLM enables fine-grained language understanding, translating to high-fidelity image generation and the understanding of visual concepts such as objects, their spatial relationships, pose, cardinality etc. Our 900M parameter model achieves a new SOTA on CC3M, with an FID score of 6.06. The Muse 3B parameter model achieves an FID of 7.88 on zero-shot COCO evaluation, along with a CLIP score of 0.32. Muse also directly enables a number of image editing applications without the need to fine-tune or invert the model: inpainting, outpainting, and mask-free editing. More results are available at https://muse-model.github.io

Reinforcement Learning (RL) is currently one of the most commonly used techniques for traffic signal control (TSC), which can adaptively adjusted traffic signal phase and duration according to real-time traffic data. However, a fully centralized RL approach is beset with difficulties in a multi-network scenario because of exponential growth in state-action space with increasing intersections. Multi-agent reinforcement learning (MARL) can overcome the high-dimension problem by employing the global control of each local RL agent, but it also brings new challenges, such as the failure of convergence caused by the non-stationary Markov Decision Process (MDP). In this paper, we introduce an off-policy nash deep Q-Network (OPNDQN) algorithm, which mitigates the weakness of both fully centralized and MARL approaches. The OPNDQN algorithm solves the problem that traditional algorithms cannot be used in large state-action space traffic models by utilizing a fictitious game approach at each iteration to find the nash equilibrium among neighboring intersections, from which no intersection has incentive to unilaterally deviate. One of main advantages of OPNDQN is to mitigate the non-stationarity of multi-agent Markov process because it considers the mutual influence among neighboring intersections by sharing their actions. On the other hand, for training a large traffic network, the convergence rate of OPNDQN is higher than that of existing MARL approaches because it does not incorporate all state information of each agent. We conduct an extensive experiments by using Simulation of Urban MObility simulator (SUMO), and show the dominant superiority of OPNDQN over several existing MARL approaches in terms of average queue length, episode training reward and average waiting time.