This paper focuses on developing a reduction-based algebraic multigrid method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based algebraic multigrid (AMG) approach, $\ell$AIR (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion dominated problems in two or three dimensions. Motivated by the success of $\ell$AIR in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy minimization AMG methods with the local approximation of ideal operators used in $\ell$AIR. The resulting constrained $\ell$AIR (C$\ell$AIR) algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that has been previously difficult for reduction-based methods.
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清華大學智能產(chan)業研究院（AIR）招(zhao)聘深(shen)度強化方向的(de)本科/碩士/博(bo)士實習生，主要研究方向側(ce)重前沿(yan) offline RL/multi-agent RL 算法研究及轉化落(luo)地。團隊(dui)同時注重與行(xing)業頭部企業密切協作(zuo)，賦能相應產(chan)業，實現高水平的(de)產(chan)學研轉化。
Large-scale datasets with point-wise semantic and instance labels are crucial to 3D instance segmentation but also expensive. To leverage unlabeled data, previous semi-supervised 3D instance segmentation approaches have explored self-training frameworks, which rely on high-quality pseudo labels for consistency regularization. They intuitively utilize both instance and semantic pseudo labels in a joint learning manner. However, semantic pseudo labels contain numerous noise derived from the imbalanced category distribution and natural confusion of similar but distinct categories, which leads to severe collapses in self-training. Motivated by the observation that 3D instances are non-overlapping and spatially separable, we ask whether we can solely rely on instance consistency regularization for improved semi-supervised segmentation. To this end, we propose a novel self-training network InsTeacher3D to explore and exploit pure instance knowledge from unlabeled data. We first build a parallel base 3D instance segmentation model DKNet, which distinguishes each instance from the others via discriminative instance kernels without reliance on semantic segmentation. Based on DKNet, we further design a novel instance consistency regularization framework to generate and leverage high-quality instance pseudo labels. Experimental results on multiple large-scale datasets show that the InsTeacher3D significantly outperforms prior state-of-the-art semi-supervised approaches. Code is available: //github.com/W1zheng/InsTeacher3D.
We introduce a novel random integration algorithm that boasts both high convergence order and polynomial tractability for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration in periodic isotropic Sobolev space and the isotropic Sobolev space with compact support, our approach attains a nearly optimal root mean square error (RMSE) bound. In contrast to previous nearly optimal algorithms, our method exhibits polynomial tractability, ensuring that the number of samples does not scale exponentially with increasing dimensions. Our integration algorithm also enjoys nearly optimal bound for weighted Korobov space. Furthermore, the algorithm can be applied without the need for prior knowledge of weights, distinguishing it from the component-by-component algorithm. For integration in the Wiener algebra, the sample complexity of our algorithm is independent of the decay rate of Fourier coefficients. The effectiveness of the integration is confirmed through numerical experiments.
This work proposes a framework of benchmark functions designed to facilitate the creation of test cases for numerical optimisation techniques. The framework, written in Python 3, is designed to be easy to install, use, and expand. The collection includes some of the most used multi-modal continuous functions present in literature, which can be instantiated using an arbitrary number of dimensions. Meta-information of each benchmark function, like search boundaries and position of known optima, are included and made easily accessible through class methods. Built-in interactive visualisation capabilities, baseline techniques, and rigorous testing protocols complement the features of the framework. The framework can be found here: \url{//gitlab.com/luca.baronti/python_benchmark_functions
This paper explores the utilization of LLMs for data preprocessing (DP), a crucial step in the data mining pipeline that transforms raw data into a clean format conducive to easy processing. Whereas the use of LLMs has sparked interest in devising universal solutions to DP, recent initiatives in this domain typically rely on GPT APIs, raising inevitable data breach concerns. Unlike these approaches, we consider instruction-tuning local LLMs (7 -- 13B models) as universal DP task solvers that operate on a local, single, and low-priced GPU, ensuring data security and enabling further customization. We select a collection of datasets across four representative DP tasks and construct instruction tuning data using data configuration, knowledge injection, and reasoning data distillation techniques tailored to DP. By tuning Mistral-7B, Llama 3-8B, and OpenOrca-Platypus2-13B, our models, namely, Jellyfish-7B/8B/13B, deliver competitiveness compared to GPT-3.5/4 models and strong generalizability to unseen tasks while barely compromising the base models' abilities in NLP tasks. Meanwhile, Jellyfish offers enhanced reasoning capabilities compared to GPT-3.5. Our models are available at: //huggingface.co/NECOUDBFM/Jellyfish . Our instruction dataset is available at: //huggingface.co/datasets/NECOUDBFM/Jellyfish-Instruct .
This study introduces an innovative framework that employs large language models (LLMs) to automate the design and generation of curricula for reinforcement learning (RL). As mobile networks evolve towards the 6G era, managing their increasing complexity and dynamic nature poses significant challenges. Conventional RL approaches often suffer from slow convergence and poor generalization due to conflicting objectives and the large state and action spaces associated with mobile networks. To address these shortcomings, we introduce curriculum learning, a method that systematically exposes the RL agent to progressively challenging tasks, improving convergence and generalization. However, curriculum design typically requires extensive domain knowledge and manual human effort. Our framework mitigates this by utilizing the generative capabilities of LLMs to automate the curriculum design process, significantly reducing human effort while improving the RL agent's convergence and performance. We deploy our approach within a simulated mobile network environment and demonstrate improved RL convergence rates, generalization to unseen scenarios, and overall performance enhancements. As a case study, we consider autonomous coordination and user association in mobile networks. Our obtained results highlight the potential of combining LLM-based curriculum generation with RL for managing next-generation wireless networks, marking a significant step towards fully autonomous network operations.
Recent advancements in learning algorithms have demonstrated that the sharpness of the loss surface is an effective measure for improving the generalization gap. Building upon this concept, Sharpness-Aware Minimization (SAM) was proposed to enhance model generalization and achieved state-of-the-art performance. SAM consists of two main steps, the weight perturbation step and the weight updating step. However, the perturbation in SAM is determined by only the gradient of the training loss, or cross-entropy loss. As the model approaches a stationary point, this gradient becomes small and oscillates, leading to inconsistent perturbation directions and also has a chance of diminishing the gradient. Our research introduces an innovative approach to further enhancing model generalization. We propose the Adaptive Adversarial Cross-Entropy (AACE) loss function to replace standard cross-entropy loss for SAM's perturbation. AACE loss and its gradient uniquely increase as the model nears convergence, ensuring consistent perturbation direction and addressing the gradient diminishing issue. Additionally, a novel perturbation-generating function utilizing AACE loss without normalization is proposed, enhancing the model's exploratory capabilities in near-optimum stages. Empirical testing confirms the effectiveness of AACE, with experiments demonstrating improved performance in image classification tasks using Wide ResNet and PyramidNet across various datasets. The reproduction code is available online
We present a novel approach of discretizing variable coefficient diffusion operators in the context of meshfree generalized finite difference methods. Our ansatz uses properties of derived operators and combines the discrete Laplace operator with reconstruction functions approximating the diffusion coefficient. Provided that the reconstructions are of a sufficiently high order, we prove that the order of accuracy of the discrete Laplace operator transfers to the derived diffusion operator. We show that the new discrete diffusion operator inherits the diagonal dominance property of the discrete Laplace operator. Finally, we present the possibility of discretizing anisotropic diffusion operators with the help of derived operators. Our numerical results for Poisson's equation and the heat equation show that even low-order reconstructions preserve the order of the underlying discrete Laplace operator for sufficiently smooth diffusion coefficients. In experiments, we demonstrate the applicability of the new discrete diffusion operator to interface problems with point clouds not aligning to the interface and numerically show first-order convergence.
In this paper, we propose a novel joint deep reinforcement learning (DRL)-based solution to optimize the utility of an uncrewed aerial vehicle (UAV)-assisted communication network. To maximize the number of users served within the constraints of the UAV's limited bandwidth and power resources, we employ deep Q-Networks (DQN) and deep deterministic policy gradient (DDPG) algorithms for optimal resource allocation to ground users with heterogeneous data rate demands. The DQN algorithm dynamically allocates multiple bandwidth resource blocks to different users based on current demand and available resource states. Simultaneously, the DDPG algorithm manages power allocation, continuously adjusting power levels to adapt to varying distances and fading conditions, including Rayleigh fading for non-line-of-sight (NLoS) links and Rician fading for line-of-sight (LoS) links. Our joint DRL-based solution demonstrates an increase of up to 41% in the number of users served compared to scenarios with equal bandwidth and power allocation.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
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