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Federated Learning offers a way to train deep neural networks in a distributed fashion. While this addresses limitations related to distributed data, it incurs a communication overhead as the model parameters or gradients need to be exchanged regularly during training. This can be an issue with large scale distribution of learning asks and negate the benefit of the respective resource distribution. In this paper, we we propose to utilise parallel Adapters for Federated Learning. Using various datasets, we show that Adapters can be applied with different Federated Learning techniques. We highlight that our approach can achieve similar inference performance compared to training the full model while reducing the communication overhead drastically. We further explore the applicability of Adapters in cross-silo and cross-device settings, as well as different non-IID data distributions.

Though denoising diffusion probabilistic models (DDPMs) have achieved remarkable generation results, the low sampling efficiency of DDPMs still limits further applications. Since DDPMs can be formulated as diffusion ordinary differential equations (ODEs), various fast sampling methods can be derived from solving diffusion ODEs. However, we notice that previous sampling methods with fixed analytical form are not robust with the error in the noise estimated from pretrained diffusion models. In this work, we construct an error-robust Adams solver (ERA-Solver), which utilizes the implicit Adams numerical method that consists of a predictor and a corrector. Different from the traditional predictor based on explicit Adams methods, we leverage a Lagrange interpolation function as the predictor, which is further enhanced with an error-robust strategy to adaptively select the Lagrange bases with lower error in the estimated noise. Experiments on Cifar10, LSUN-Church, and LSUN-Bedroom datasets demonstrate that our proposed ERA-Solver achieves 5.14, 9.42, and 9.69 Fenchel Inception Distance (FID) for image generation, with only 10 network evaluations.

Let $X = \{X_{u}\}_{u \in U}$ be a real-valued Gaussian process indexed by a set $U$. It can be thought of as an undirected graphical model with every random variable $X_{u}$ serving as a vertex. We characterize this graph in terms of the covariance of $X$ through its reproducing kernel property. Unlike other characterizations in the literature, our characterization does not restrict the index set $U$ to be finite or countable, and hence can be used to model the intrinsic dependence structure of stochastic processes in continuous time/space. Consequently, the said characterization is not (and apparently cannot be) of the inverse-zero type. This poses novel challenges for the problem of recovery of the dependence structure from a sample of independent realizations of $X$, also known as structure estimation. We propose a methodology that circumvents these issues, by targeting the recovery of the underlying graph up to a finite resolution, which can be arbitrarily fine and is limited only by the available sample size. The recovery is shown to be consistent so long as the graph is sufficiently regular in an appropriate sense, and convergence rates are provided. Our methodology is illustrated by simulation and two data analyses.

With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDE problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training. However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains. This paper proposes a new kind of data-driven PDEs solver, physics-informed cell representations (PIXEL), elegantly combining classical numerical methods and learning-based approaches. We adopt a grid structure from the numerical methods to improve accuracy and convergence speed and overcome the spectral bias presented in PINNs. Moreover, the proposed method enjoys the same benefits in PINNs, e.g., using the same optimization frameworks to solve both forward and inverse PDE problems and readily enforcing PDE constraints with modern automatic differentiation techniques. We provide experimental results on various challenging PDEs that the original PINNs have struggled with and show that PIXEL achieves fast convergence speed and high accuracy. Project page: //namgyukang.github.io/PIXEL/

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial differential equations (PDEs) via embedding physical laws into the loss function. Many inverse problems can be tackled by simply combining the data from real life scenarios with existing PINN algorithms. In this paper, we present a multi-task learning method using uncertainty weighting to improve the training efficiency and accuracy of PINNs for inverse problems in linear elasticity and hyperelasticity. Furthermore, we demonstrate an application of PINNs to a practical inverse problem in structural analysis: prediction of external loads of diverse engineering structures based on limited displacement monitoring points. To this end, we first determine a simplified loading scenario at the offline stage. By setting unknown boundary conditions as learnable parameters, PINNs can predict the external loads with the support of measured data. When it comes to the online stage in real engineering projects, transfer learning is employed to fine-tune the pre-trained model from offline stage. Our results show that, even with noisy gappy data, satisfactory results can still be obtained from the PINN model due to the dual regularization of physics laws and prior knowledge, which exhibits better robustness compared to traditional analysis methods. Our approach is capable of bridging the gap between various structures with geometric scaling and under different loading scenarios, and the convergence of training is also greatly accelerated through not only the layer freezing but also the multi-task weight inheritance from pre-trained models, thus making it possible to be applied as surrogate models in actual engineering projects.

In recent years, Physics-informed neural networks (PINNs) have been widely used to solve partial differential equations alongside numerical methods because PINNs can be trained without observations and deal with continuous-time problems directly. In contrast, optimizing the parameters of such models is difficult, and individual training sessions must be performed to predict the evolutions of each different initial condition. To alleviate the first problem, observed data can be injected directly into the loss function part. To solve the second problem, a network architecture can be built as a framework to learn a finite difference method. In view of the two motivations, we propose Five-point stencil CNNs (FCNNs) containing a five-point stencil kernel and a trainable approximation function for reaction-diffusion type equations including the heat, Fisher's, Allen-Cahn, and other reaction-diffusion equations with trigonometric function terms. We show that FCNNs can learn finite difference schemes using few data and achieve the low relative errors of diverse reaction-diffusion evolutions with unseen initial conditions. Furthermore, we demonstrate that FCNNs can still be trained well even with using noisy data.

With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate this parameter is limited. In this study we described and compared confounding-adjustment methods to address this gap. The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression and two little-known implementations of g-computation for this problem. Motivated by a cohort investigation in the Longitudinal Study of Australian Children, we conducted a simulation study that found the IPW estimator, weighted quantile regression and g-computation implementations minimised bias when the relevant models were correctly specified, with g-computation additionally minimising the variance. These methods provide appealing alternatives to the common "ignore or transform" approach and multivariable quantile regression, enhancing our capability to obtain meaningful causal effect estimates with skewed outcome data.

Missing data is common in datasets retrieved in various areas, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the logic behind the imputation is explainable, which is especially difficult for complex methods that are for example, based on deep learning. This motivates us to introduce a conditional Distribution based Imputation of Missing Values (DIMV) algorithm. This approach works based on finding the conditional distribution of a feature with missing entries based on the fully observed features. As will be illustrated in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods under comparison; (ii) is explainable; (iii) can provide an approximated confidence region for the missing values in a given sample; (iv) works for both small and large scale data; (v) in many scenarios, does not require a huge number of parameters as deep learning approaches and therefore can be used for mobile devices or web browsers; and (vi) is robust to the normally distributed assumption that its theoretical grounds rely on. In addition to DIMV, we also introduce the DPER* algorithm improving the speed of DPER for estimating the mean and covariance matrix from the data, and we confirm the speed-up via experiments.

Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path in a large graph, neural networks allow learning from data to predict the most likely answer in more complex tasks such as image classification, which cannot be reduced to an exact algorithm. To get the best of both worlds, this thesis explores combining both concepts leading to more robust, better performing, more interpretable, more computationally efficient, and more data efficient architectures. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. When integrating an algorithm into a neural architecture, it is important that the algorithm is differentiable such that the architecture can be trained end-to-end and gradients can be propagated back through the algorithm in a meaningful way. To make algorithms differentiable, this thesis proposes a general method for continuously relaxing algorithms by perturbing variables and approximating the expectation value in closed form, i.e., without sampling. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable renderers, and differentiable logic gate networks. Finally, this thesis presents alternative training strategies for learning with algorithms.

Since deep neural networks were developed, they have made huge contributions to everyday lives. Machine learning provides more rational advice than humans are capable of in almost every aspect of daily life. However, despite this achievement, the design and training of neural networks are still challenging and unpredictable procedures. To lower the technical thresholds for common users, automated hyper-parameter optimization (HPO) has become a popular topic in both academic and industrial areas. This paper provides a review of the most essential topics on HPO. The first section introduces the key hyper-parameters related to model training and structure, and discusses their importance and methods to define the value range. Then, the research focuses on major optimization algorithms and their applicability, covering their efficiency and accuracy especially for deep learning networks. This study next reviews major services and toolkits for HPO, comparing their support for state-of-the-art searching algorithms, feasibility with major deep learning frameworks, and extensibility for new modules designed by users. The paper concludes with problems that exist when HPO is applied to deep learning, a comparison between optimization algorithms, and prominent approaches for model evaluation with limited computational resources.