In this paper, we propose the deep finite volume method (DFVM), a novel deep learning method for solving %high-order (order $\geq 2$) partial differential equations (PDEs). The key idea is to design a new loss function based on the local conservation property over the so-called {\it control volumes}, derived from the original PDE. Since the DFVM is designed according to a {\it weak instead of strong} form of the PDE, it may achieve better accuracy than the strong-form-based deep learning method such as the well-known PINN, when the to-be-solved PDE has an insufficiently smooth solution. Moreover, since the calculation of second-order derivatives of neural networks has been transformed to that of first-order derivatives which can be implemented directly by the Automatic Differentiation mechanism(AD), the DFVM usually has a computational cost much lower than that of the methods which need to compute second-order derivatives by the AD. Our numerical experiments show that compared to some deep learning methods in the literature such as the PINN, DRM, and WAN, the DFVM obtains the same or higher accurate approximate solutions by consuming significantly lower computational cost. Moreover, for some PDE with a nonsmooth solution, the relative error of approximate solutions by DFVM is two orders of magnitude less than that by the PINN.
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In this paper, we address the task of aberration-aware depth-from-defocus (DfD), which takes account of spatially variant point spread functions (PSFs) of a real camera. To effectively obtain the spatially variant PSFs of a real camera without requiring any ground-truth PSFs, we propose a novel self-supervised learning method that leverages the pair of real sharp and blurred images, which can be easily captured by changing the aperture setting of the camera. In our PSF estimation, we assume rotationally symmetric PSFs and introduce the polar coordinate system to more accurately learn the PSF estimation network. We also handle the focus breathing phenomenon that occurs in real DfD situations. Experimental results on synthetic and real data demonstrate the effectiveness of our method regarding both the PSF estimation and the depth estimation.
In this paper, we introduce a new flow-based method for global optimization of Lipschitz functions, called Stein Boltzmann Sampling (SBS). Our method samples from the Boltzmann distribution that becomes asymptotically uniform over the set of the minimizers of the function to be optimized. Candidate solutions are sampled via the \emph{Stein Variational Gradient Descent} algorithm. We prove the asymptotic convergence of our method, introduce two SBS variants, and provide a detailed comparison with several state-of-the-art global optimization algorithms on various benchmark functions. The design of our method, the theoretical results, and our experiments, suggest that SBS is particularly well-suited to be used as a continuation of efficient global optimization methods as it can produce better solutions while making a good use of the budget.
We propose a new method, Adversarial In-Context Learning (adv-ICL), to optimize prompt for in-context learning (ICL) by employing one LLM as a generator, another as a discriminator, and a third as a prompt modifier. As in traditional adversarial learning, adv-ICL is implemented as a two-player game between the generator and discriminator, where the generator tries to generate realistic enough output to fool the discriminator. In each round, given an input prefixed by task instructions and several exemplars, the generator produces an output. The discriminator is then tasked with classifying the generator input-output pair as model-generated or real data. Based on the discriminator loss, the prompt modifier proposes possible edits to the generator and discriminator prompts, and the edits that most improve the adversarial loss are selected. We show that adv-ICL results in significant improvements over state-of-the-art prompt optimization techniques for both open and closed-source models on 11 generation and classification tasks including summarization, arithmetic reasoning, machine translation, data-to-text generation, and the MMLU and big-bench hard benchmarks. In addition, because our method uses pre-trained models and updates only prompts rather than model parameters, it is computationally efficient, easy to extend to any LLM and task, and effective in low-resource settings.
We propose a novel data-driven linear inverse model, called Colored-LIM, to extract the linear dynamics and diffusion matrix that define a linear stochastic process driven by an Ornstein-Uhlenbeck colored-noise. The Colored-LIM is a new variant of the classical linear inverse model (LIM) which relies on the white noise assumption. Similar to LIM, the Colored-LIM approximates the linear dynamics from a finite realization of a stochastic process and then solves the diffusion matrix based on, for instance, a generalized fluctuation-dissipation relation, which can be done by solving a system of linear equations. The main difficulty is that in practice, the colored-noise process can be hardly observed while it is correlated to the stochastic process of interest. Nevertheless, we show that the local behavior of the correlation function of the observable encodes the dynamics of the stochastic process and the diffusive behavior of the colored-noise. In this article, we review the classical LIM and develop Colored-LIM with a mathematical background and rigorous derivations. In the numerical experiments, we examine the performance of both LIM and Colored-LIM. Finally, we discuss some false attempts to build a linear inverse model for colored-noise driven processes, and investigate the potential misuse and its consequence of LIM in the appendices.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
Non-IID data present a tough challenge for federated learning. In this paper, we explore a novel idea of facilitating pairwise collaborations between clients with similar data. We propose FedAMP, a new method employing federated attentive message passing to facilitate similar clients to collaborate more. We establish the convergence of FedAMP for both convex and non-convex models, and propose a heuristic method to further improve the performance of FedAMP when clients adopt deep neural networks as personalized models. Our extensive experiments on benchmark data sets demonstrate the superior performance of the proposed methods.
In this paper, we proposed to apply meta learning approach for low-resource automatic speech recognition (ASR). We formulated ASR for different languages as different tasks, and meta-learned the initialization parameters from many pretraining languages to achieve fast adaptation on unseen target language, via recently proposed model-agnostic meta learning algorithm (MAML). We evaluated the proposed approach using six languages as pretraining tasks and four languages as target tasks. Preliminary results showed that the proposed method, MetaASR, significantly outperforms the state-of-the-art multitask pretraining approach on all target languages with different combinations of pretraining languages. In addition, since MAML's model-agnostic property, this paper also opens new research direction of applying meta learning to more speech-related applications.
The key issue of few-shot learning is learning to generalize. In this paper, we propose a large margin principle to improve the generalization capacity of metric based methods for few-shot learning. To realize it, we develop a unified framework to learn a more discriminative metric space by augmenting the softmax classification loss function with a large margin distance loss function for training. Extensive experiments on two state-of-the-art few-shot learning models, graph neural networks and prototypical networks, show that our method can improve the performance of existing models substantially with very little computational overhead, demonstrating the effectiveness of the large margin principle and the potential of our method.
In this paper, we introduce the Reinforced Mnemonic Reader for machine reading comprehension tasks, which enhances previous attentive readers in two aspects. First, a reattention mechanism is proposed to refine current attentions by directly accessing to past attentions that are temporally memorized in a multi-round alignment architecture, so as to avoid the problems of attention redundancy and attention deficiency. Second, a new optimization approach, called dynamic-critical reinforcement learning, is introduced to extend the standard supervised method. It always encourages to predict a more acceptable answer so as to address the convergence suppression problem occurred in traditional reinforcement learning algorithms. Extensive experiments on the Stanford Question Answering Dataset (SQuAD) show that our model achieves state-of-the-art results. Meanwhile, our model outperforms previous systems by over 6% in terms of both Exact Match and F1 metrics on two adversarial SQuAD datasets.
In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax
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