Gradient-based meta-learning (GBML) with deep neural nets (DNNs) has become a popular approach for few-shot learning. However, due to the non-convexity of DNNs and the complex bi-level optimization in GBML, the theoretical properties of GBML with DNNs remain largely unknown. In this paper, we first develop a novel theoretical analysis to answer the following questions: Does GBML with DNNs have global convergence guarantees? We provide a positive answer to this question by proving that GBML with over-parameterized DNNs is guaranteed to converge to global optima at a linear rate. The second question we aim to address is: How does GBML achieve fast adaption to new tasks with experience on past similar tasks? To answer it, we prove that GBML is equivalent to a functional gradient descent operation that explicitly propagates experience from the past tasks to new ones. Finally, inspired by our theoretical analysis, we develop a new kernel-based meta-learning approach. We show that the proposed approach outperforms GBML with standard DNNs on the Omniglot dataset when the number of past tasks for meta-training is small. The code is available at https://github.com/ AI-secure/Meta-Neural-Kernel .

Modern deep learning models are enormously complex function approximators, with many state-of-the-art architectures employing millions or even billions of trainable parameters [Radford et al., 2019, Adiwardana et al., 2020]. While the raw parameter count provides only a crude approximation of a model's capacity, more sophisticated metrics such as those based on PAC-Bayes [McAllester, 1999, Dziugaite and Roy, 2017, Neyshabur et al., 2017b], VC dimension [Vapnik and Chervonenkis, 1971], and parameter norms [Bartlett et al., 2017, Neyshabur et al., 2017a] also suggest that modern architectures have very large capacity. Moreover, from the empirical perspective, practical models are flexible enough to perfectly fit the training data, even if the labels are pure noise [Zhang et al., 2017]. Surprisingly, these same high-capacity models generalize well when trained on real data, even without any explicit control of capacity. These observations are in conflict with classical generalization theory, which contends that models of intermediate complexity should generalize best, striking a balance between the bias and the variance of their predictive functions. To reconcile theory with observation, it has been suggested that deep neural networks may enjoy some form of implicit regularization induced by gradient-based training algorithms that biases the trained models towards simpler functions.

Deep neural networks (DNNs) have become the de facto learning mechanism in different domains. Their tendency to perform unreliably on out-of-distribution (OOD) inputs hinders their adoption in critical domains. Several approaches have been proposed for detecting OOD inputs. However, existing approaches still lack robustness. In this paper, we shed light on the robustness of OOD detection (OODD) approaches by revealing the important role of optimization methods. We show that OODD approaches are sensitive to the type of optimization method used during training deep models. Optimization methods can provide different solutions to a non-convex problem and so these solutions may or may not satisfy the assumptions (e.g., distributions of deep features) made by OODD approaches. Furthermore, we propose a robustness score that takes into account the role of optimization methods. This provides a sound way to compare OODD approaches. In addition to comparing several OODD approaches using our proposed robustness score, we demonstrate that some optimization methods provide better solutions for OODD approaches.

It becomes urgent to design effective anti-spoofing algorithms for vulnerable automatic speaker verification systems due to the advancement of high-quality playback devices. Current studies mainly treat anti-spoofing as a binary classification problem between bonafide and spoofed utterances, while lack of indistinguishable samples makes it difficult to train a robust spoofing detector. In this paper, we argue that for anti-spoofing, it needs more attention for indistinguishable samples over easily-classified ones in the modeling process, to make correct discrimination a top priority. Therefore, to mitigate the data discrepancy between training and inference, we propose to leverage a balanced focal loss function as the training objective to dynamically scale the loss based on the traits of the sample itself. Besides, in the experiments, we select three kinds of features that contain both magnitude-based and phase-based information to form complementary and informative features. Experimental results on the ASVspoof2019 dataset demonstrate the superiority of the proposed methods by comparison between our systems and top-performing ones. Systems trained with the balanced focal loss perform significantly better than conventional cross-entropy loss. With complementary features, our fusion system with only three kinds of features outperforms other systems containing five or more complex single models by 22.5% for min-tDCF and 7% for EER, achieving a min-tDCF and an EER of 0.0124 and 0.55% respectively. Furthermore, we present and discuss the evaluation results on real replay data apart from the simulated ASVspoof2019 data, indicating that research for anti-spoofing still has a long way to go.

In this paper, we present a new idea for Transfer Learning (TL) based on Gibbs Sampling. Gibbs sampling is an algorithm in which instances are likely to transfer to a new state with a higher possibility with respect to a probability distribution. We find that such an algorithm can be employed to transfer instances between domains. Restricted Boltzmann Machine (RBM) is an energy based model that is very feasible for being trained to represent a data distribution and also for performing Gibbs sampling. We used RBM to capture data distribution of the source domain and use it in order to cast target instances into new data with a distribution similar to the distribution of source data. Using datasets that are commonly used for evaluation of TL methods, we show that our method can successfully enhance target classification by a considerable ratio. Additionally, the proposed method has the advantage over common DA methods that it needs no target data during the process of training of models.

We investigate spatio-temporal prediction and introduce a novel prediction algorithm. Our approach is based on the point processes, which we use to model the event arrivals in both space and time. Although we specifically use the Hawkes process, other processes can be readily used as provided remarks in the paper. Moreover, we partition the given spatial region into subregions by an adaptive decision tree and model each subregion with individual and interacting point processes. With individual point processes for each subregion, we estimate the time and location of the events using the past event times and locations. Furthermore, thanks to the nonstationary and self-exciting point generation mechanism in the Hawkes process and the adaptive partitioning of the space, we model the data as nonstationary in both time and space. Finally, we provide a gradient based joint optimization algorithm for the adaptive tree parameter and the point process parameters. With the joint optimization, our algorithm can infer the source statistics and adaptive partitioning of the region. We also provide a training algorithm for the online setup, where we update the model parameters with newly arrived points. We provide experimental results on both simulated data and real-life data where we compare our approach with the standard approaches and demonstrate significant performance improvements thanks to the adaptive spatial partitioning mechanism and the joint optimization procedure.

Autoencoders have been widely used for dimensional reduction and feature extraction. Various types of autoencoders have been proposed by introducing regularization terms. Most of these regularizations improve representation learning by constraining the weights in the encoder part, which maps input into hidden nodes and affects the generation of features. In this study, we show that a constraint to the decoder can also significantly improve its performance because the decoder determines how the latent variables contribute to the reconstruction of input. Inspired by the structural modal analysis method in mechanical engineering, a new modal autoencoder (MAE) is proposed by othogonalising the columns of the readout weight matrix. The new regularization helps to disentangle explanatory factors of variation and forces the MAE to extract fundamental modes in data. The learned representations are functionally independent in the reconstruction of input and perform better in consecutive classification tasks. The results were validated on the MNIST variations and USPS classification benchmark suite. Comparative experiments clearly show that the new algorithm has a surprising advantage. The new MAE introduces a very simple training principle for autoencoders and could be promising for the pre-training of deep neural networks.

In this paper, we propose a novel learning scheme called epoch-evolving Gaussian Process Guided Learning (GPGL), which aims at characterizing the correlation information between the batch-level distribution and the global data distribution. Such correlation information is encoded as context labels and needs renewal every epoch. With the guidance of the context label and ground truth label, GPGL scheme provides a more efficient optimization through updating the model parameters with a triangle consistency loss. Furthermore, our GPGL scheme can be further generalized and naturally applied to the current deep models, outperforming the existing batch-based state-of-the-art models on mainstream datasets (CIFAR-10, CIFAR-100, and Tiny-ImageNet) remarkably.

Prediction of spatio-temporal chaotic systems is important in various fields, such as Numerical Weather Prediction (NWP). While data assimilation methods have been applied in NWP, machine learning techniques, such as Reservoir Computing (RC), are recently recognized as promising tools to predict spatio-temporal chaotic systems. However, the sensitivity of the skill of the machine learning based prediction to the imperfectness of observations is unclear. In this study, we evaluate the skill of RC with noisy and sparsely distributed observations. We intensively compare the performances of RC and Local Ensemble Transform Kalman Filter (LETKF) by applying them to the prediction of the Lorenz 96 system. Although RC can successfully predict the Lorenz 96 system if the system is perfectly observed, we find that RC is vulnerable to observation sparsity compared with LETKF. To overcome this limitation of RC, we propose to combine LETKF and RC. In our proposed method, the system is predicted by RC that learned the analysis time series estimated by LETKF. Our proposed method can successfully predict the Lorenz 96 system using noisy and sparsely distributed observations. Most importantly, our method can predict better than LETKF when the process-based model is imperfect.

Searching for accurate Machine and Deep Learning models is a computationally expensive and awfully energivorous process. A strategy which has been gaining recently importance to drastically reduce computational time and energy consumed is to exploit the availability of different information sources, with different computational costs and different "fidelity", typically smaller portions of a large dataset. The multi-source optimization strategy fits into the scheme of Gaussian Process based Bayesian Optimization. An Augmented Gaussian Process method exploiting multiple information sources (namely, AGP-MISO) is proposed. The Augmented Gaussian Process is trained using only "reliable" information among available sources. A novel acquisition function is defined according to the Augmented Gaussian Process. Computational results are reported related to the optimization of the hyperparameters of a Support Vector Machine (SVM) classifier using two sources: a large dataset - the most expensive one - and a smaller portion of it. A comparison with a traditional Bayesian Optimization approach to optimize the hyperparameters of the SVM classifier on the large dataset only is reported.