Although Physics-Informed Neural Networks (PINNs) have been successfully applied in a wide variety of science and engineering fields, they can fail to accurately predict the underlying solution in slightly challenging convection-diffusion-reaction problems. In this paper, we investigate the reason of this failure from a domain distribution perspective, and identify that learning multi-scale fields simultaneously makes the network unable to advance its training and easily get stuck in poor local minima. We show that the widespread experience of sampling more collocation points in high-loss layer regions hardly help optimize and may even worsen the results. These findings motivate the development of a novel curriculum learning method that encourages neural networks to prioritize learning on easier non-layer regions while downplaying learning on harder layer regions. The proposed method helps PINNs automatically adjust the learning emphasis and thereby facilitate the optimization procedure. Numerical results on typical benchmark equations show that the proposed curriculum learning approach mitigates the failure modes of PINNs and can produce accurate results for very sharp boundary and interior layers. Our work reveals that for equations whose solutions have large scale differences, paying less attention to high-loss regions can be an effective strategy for learning them accurately.
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Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately solve the multi-material diffusion equation. The new method applies continuity conditions at the material interface derived from the property of the diffusion equation, and combines the distinctive spatial separation strategy and the loss term normalization strategy to solve the problem that the residual points cannot be arranged at the material interface, the problem that it is difficult to express non-smooth functions with a single neural network, and the problem that the neural network is difficult to optimize the loss function with different magnitudes of loss terms, which finally provides the available prediction function for a class of multi-material diffusion problems. Numerical experiments verify the robustness and effectiveness of the new method.
Visual Grounding (VG) refers to locating a region described by expressions in a specific image, which is a critical topic in vision-language fields. To alleviate the dependence on labeled data, existing unsupervised methods try to locate regions using task-unrelated pseudo-labels. However, a large proportion of pseudo-labels are noisy and diversity scarcity in language taxonomy. Inspired by the advances in V-L pretraining, we consider utilizing the VLP models to realize unsupervised transfer learning in downstream grounding task. Thus, we propose CLIP-VG, a novel method that can conduct self-paced curriculum adapting of CLIP via exploiting pseudo-language labels to solve VG problem. By elaborating an efficient model structure, we first propose a single-source and multi-source curriculum adapting method for unsupervised VG to progressively sample more reliable cross-modal pseudo-labels to obtain the optimal model, thus achieving implicit knowledge exploiting and denoising. Our method outperforms the existing state-of-the-art unsupervised VG method Pseudo-Q in both single-source and multi-source scenarios with a large margin, i.e., 6.78%~10.67% and 11.39%~24.87% on RefCOCO/+/g datasets, even outperforms existing weakly supervised methods. The code and models will be released at \url{//github.com/linhuixiao/CLIP-VG}.
In multi-agent reinforcement learning (MARL), many popular methods, such as VDN and QMIX, are susceptible to a critical multi-agent pathology known as relative overgeneralization (RO), which arises when the optimal joint action's utility falls below that of a sub-optimal joint action in cooperative tasks. RO can cause the agents to get stuck into local optima or fail to solve cooperative tasks that require significant coordination between agents within a given timestep. Recent value-based MARL algorithms such as QPLEX and WQMIX can overcome RO to some extent. However, our experimental results show that they can still fail to solve cooperative tasks that exhibit strong RO. In this work, we propose a novel approach called curriculum learning for relative overgeneralization (CURO) to better overcome RO. To solve a target task that exhibits strong RO, in CURO, we first fine-tune the reward function of the target task to generate source tasks that are tailored to the current ability of the learning agent and train the agent on these source tasks first. Then, to effectively transfer the knowledge acquired in one task to the next, we use a transfer learning method that combines value function transfer with buffer transfer, which enables more efficient exploration in the target task. We demonstrate that, when applied to QMIX, CURO overcomes severe RO problem and significantly improves performance, yielding state-of-the-art results in a variety of cooperative multi-agent tasks, including the challenging StarCraft II micromanagement benchmarks.
Nonlinear dynamics is a pervasive phenomenon observed in various scientific and engineering disciplines. However, uncovering analytical expressions that describe nonlinear dynamics from limited data remains a challenging and essential task. In this paper, we propose a new deep symbolic learning method called the ``finite expression method'' (FEX) to identify the governing equations within the space of functions containing a finite set of analytic expressions, based on observed dynamic data. The core idea is to leverage FEX to generate analytical expressions of the governing equations by learning the derivatives of partial differential equation (PDE) solutions using convolutions. Our numerical results demonstrate that FEX outperforms all existing methods (such as PDE-Net, SINDy, GP, and SPL) in terms of numerical performance across various problems, including time-dependent PDE problems and nonlinear dynamical systems with time-varying coefficients. Furthermore, the results highlight that FEX exhibits flexibility and expressive power in accurately approximating symbolic governing equations, while maintaining low memory and favorable time complexity.
This paper is concerned with the multi-frequency factorization method for imaging the support of a wave-number-dependent source function. It is supposed that the source function is given by the Fourier transform of some time-dependent source with a priori given radiating period. Using the multi-frequency far-field data at a fixed observation direction, we provide a computational criterion for characterizing the smallest strip containing the support and perpendicular to the observation direction. The far-field data from sparse observation directions can be used to recover a $\Theta$-convex polygon of the support. The inversion algorithm is proven valid even with multi-frequency near-field data in three dimensions. The connections to time-dependent inverse source problems are discussed in the near-field case. We also comment on possible extensions to source functions with two disconnected supports. Numerical tests in both two and three dimensions are implemented to show effectiveness and feasibility of the approach. This paper provides numerical analysis for a frequency-domain approach to recover the support of an admissible class of time-dependent sources.
Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.
Emotion recognition in conversation (ERC) aims to detect the emotion label for each utterance. Motivated by recent studies which have proven that feeding training examples in a meaningful order rather than considering them randomly can boost the performance of models, we propose an ERC-oriented hybrid curriculum learning framework. Our framework consists of two curricula: (1) conversation-level curriculum (CC); and (2) utterance-level curriculum (UC). In CC, we construct a difficulty measurer based on "emotion shift" frequency within a conversation, then the conversations are scheduled in an "easy to hard" schema according to the difficulty score returned by the difficulty measurer. For UC, it is implemented from an emotion-similarity perspective, which progressively strengthens the model's ability in identifying the confusing emotions. With the proposed model-agnostic hybrid curriculum learning strategy, we observe significant performance boosts over a wide range of existing ERC models and we are able to achieve new state-of-the-art results on four public ERC datasets.
Knowledge graphs (KGs) capture knowledge in the form of head--relation--tail triples and are a crucial component in many AI systems. There are two important reasoning tasks on KGs: (1) single-hop knowledge graph completion, which involves predicting individual links in the KG; and (2), multi-hop reasoning, where the goal is to predict which KG entities satisfy a given logical query. Embedding-based methods solve both tasks by first computing an embedding for each entity and relation, then using them to form predictions. However, existing scalable KG embedding frameworks only support single-hop knowledge graph completion and cannot be applied to the more challenging multi-hop reasoning task. Here we present Scalable Multi-hOp REasoning (SMORE), the first general framework for both single-hop and multi-hop reasoning in KGs. Using a single machine SMORE can perform multi-hop reasoning in Freebase KG (86M entities, 338M edges), which is 1,500x larger than previously considered KGs. The key to SMORE's runtime performance is a novel bidirectional rejection sampling that achieves a square root reduction of the complexity of online training data generation. Furthermore, SMORE exploits asynchronous scheduling, overlapping CPU-based data sampling, GPU-based embedding computation, and frequent CPU--GPU IO. SMORE increases throughput (i.e., training speed) over prior multi-hop KG frameworks by 2.2x with minimal GPU memory requirements (2GB for training 400-dim embeddings on 86M-node Freebase) and achieves near linear speed-up with the number of GPUs. Moreover, on the simpler single-hop knowledge graph completion task SMORE achieves comparable or even better runtime performance to state-of-the-art frameworks on both single GPU and multi-GPU settings.
Sequential recommendation as an emerging topic has attracted increasing attention due to its important practical significance. Models based on deep learning and attention mechanism have achieved good performance in sequential recommendation. Recently, the generative models based on Variational Autoencoder (VAE) have shown the unique advantage in collaborative filtering. In particular, the sequential VAE model as a recurrent version of VAE can effectively capture temporal dependencies among items in user sequence and perform sequential recommendation. However, VAE-based models suffer from a common limitation that the representational ability of the obtained approximate posterior distribution is limited, resulting in lower quality of generated samples. This is especially true for generating sequences. To solve the above problem, in this work, we propose a novel method called Adversarial and Contrastive Variational Autoencoder (ACVAE) for sequential recommendation. Specifically, we first introduce the adversarial training for sequence generation under the Adversarial Variational Bayes (AVB) framework, which enables our model to generate high-quality latent variables. Then, we employ the contrastive loss. The latent variables will be able to learn more personalized and salient characteristics by minimizing the contrastive loss. Besides, when encoding the sequence, we apply a recurrent and convolutional structure to capture global and local relationships in the sequence. Finally, we conduct extensive experiments on four real-world datasets. The experimental results show that our proposed ACVAE model outperforms other state-of-the-art methods.
Recently, neural networks have been widely used in e-commerce recommender systems, owing to the rapid development of deep learning. We formalize the recommender system as a sequential recommendation problem, intending to predict the next items that the user might be interacted with. Recent works usually give an overall embedding from a user's behavior sequence. However, a unified user embedding cannot reflect the user's multiple interests during a period. In this paper, we propose a novel controllable multi-interest framework for the sequential recommendation, called ComiRec. Our multi-interest module captures multiple interests from user behavior sequences, which can be exploited for retrieving candidate items from the large-scale item pool. These items are then fed into an aggregation module to obtain the overall recommendation. The aggregation module leverages a controllable factor to balance the recommendation accuracy and diversity. We conduct experiments for the sequential recommendation on two real-world datasets, Amazon and Taobao. Experimental results demonstrate that our framework achieves significant improvements over state-of-the-art models. Our framework has also been successfully deployed on the offline Alibaba distributed cloud platform.
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