We provide a theoretical framework to study a phenomenon that we call one-shot generalization. This phenomenon refers to the ability of an algorithm to perform transfer learning within a single task, meaning that it correctly classifies a test point that has a single exemplar in the training set. We propose a simple data model and use it to study this phenomenon in two ways. First, we prove a non-asymptotic base-line -- kernel methods based on nearest-neighbor classification cannot perform one-shot generalization, independently of the choice of the kernel and the size of the training set. Second, we empirically show that the most direct neural network architecture for our data model performs one-shot generalization almost perfectly. This stark differential leads us to believe that the one-shot generalization mechanism is partially responsible for the empirical success of neural networks.
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Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization and minimax problems through the lens of algorithmic stability in the framework of statistical learning theory. For empirical risk minimization (ERM) problems, we establish the optimal excess population risk bounds for both smooth and non-smooth cases by introducing on-average argument stability. For minimax problems, we develop a quantitative connection between on-average argument stability and generalization error which extends the existing results for uniform stability \cite{lei2021stability}. We further develop the first nearly optimal convergence rates for convex-concave problems both in expectation and with high probability, which, combined with our stability results, show that the optimal generalization bounds can be attained for both smooth and non-smooth cases. To the best of our knowledge, this is the first generalization analysis of SGMs when the gradients are sampled from a Markov process.
Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but is incomplete for neural networks with Hadamard products (NNs-Hp), e.g., StyleGAN and polynomial neural networks. In this work, we derive the finite-width NTK formulation for a special class of NNs-Hp, i.e., polynomial neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK. Based on our results, we elucidate the separation of PNNs over standard neural networks with respect to extrapolation and spectral bias. Our two key insights are that when compared to standard neural networks, PNNs are able to fit more complicated functions in the extrapolation regime and admit a slower eigenvalue decay of the respective NTK. Besides, our theoretical results can be extended to other types of NNs-Hp, which expand the scope of our work. Our empirical results validate the separations in broader classes of NNs-Hp, which provide a good justification for a deeper understanding of neural architectures.
Several existing works study either adversarial or natural distributional robustness of deep neural networks separately. In practice, however, models need to enjoy both types of robustness to ensure reliability. In this work, we bridge this gap and show that in fact, explicit tradeoffs exist between adversarial and natural distributional robustness. We first consider a simple linear regression setting on Gaussian data with disjoint sets of core and spurious features. In this setting, through theoretical and empirical analysis, we show that (i) adversarial training with $\ell_1$ and $\ell_2$ norms increases the model reliance on spurious features; (ii) For $\ell_\infty$ adversarial training, spurious reliance only occurs when the scale of the spurious features is larger than that of the core features; (iii) adversarial training can have an unintended consequence in reducing distributional robustness, specifically when spurious correlations are changed in the new test domain. Next, we present extensive empirical evidence, using a test suite of twenty adversarially trained models evaluated on five benchmark datasets (ObjectNet, RIVAL10, Salient ImageNet-1M, ImageNet-9, Waterbirds), that adversarially trained classifiers rely on backgrounds more than their standardly trained counterparts, validating our theoretical results. We also show that spurious correlations in training data (when preserved in the test domain) can improve adversarial robustness, revealing that previous claims that adversarial vulnerability is rooted in spurious correlations are incomplete.
Joint synthesis of images and segmentation masks with generative adversarial networks (GANs) is promising to reduce the effort needed for collecting image data with pixel-wise annotations. However, to learn high-fidelity image-mask synthesis, existing GAN approaches first need a pre-training phase requiring large amounts of image data, which limits their utilization in restricted image domains. In this work, we take a step to reduce this limitation, introducing the task of one-shot image-mask synthesis. We aim to generate diverse images and their segmentation masks given only a single labelled example, and assuming, contrary to previous models, no access to any pre-training data. To this end, inspired by the recent architectural developments of single-image GANs, we introduce our OSMIS model which enables the synthesis of segmentation masks that are precisely aligned to the generated images in the one-shot regime. Besides achieving the high fidelity of generated masks, OSMIS outperforms state-of-the-art single-image GAN models in image synthesis quality and diversity. In addition, despite not using any additional data, OSMIS demonstrates an impressive ability to serve as a source of useful data augmentation for one-shot segmentation applications, providing performance gains that are complementary to standard data augmentation techniques. Code is available at //github.com/ boschresearch/one-shot-synthesis
Designing learning systems which are invariant to certain data transformations is critical in machine learning. Practitioners can typically enforce a desired invariance on the trained model through the choice of a network architecture, e.g. using convolutions for translations, or using data augmentation. Yet, enforcing true invariance in the network can be difficult, and data invariances are not always known a piori. State-of-the-art methods for learning data augmentation policies require held-out data and are based on bilevel optimization problems, which are complex to solve and often computationally demanding. In this work we investigate new ways of learning invariances only from the training data. Using learnable augmentation layers built directly in the network, we demonstrate that our method is very versatile. It can incorporate any type of differentiable augmentation and be applied to a broad class of learning problems beyond computer vision. We provide empirical evidence showing that our approach is easier and faster to train than modern automatic data augmentation techniques based on bilevel optimization, while achieving comparable results. Experiments show that while the invariances transferred to a model through automatic data augmentation are limited by the model expressivity, the invariance yielded by our approach is insensitive to it by design.
Noisy labels in large E-commerce product data (i.e., product items are placed into incorrect categories) are a critical issue for product categorization task because they are unavoidable, non-trivial to remove and degrade prediction performance significantly. Training a product title classification model which is robust to noisy labels in the data is very important to make product classification applications more practical. In this paper, we study the impact of instance-dependent noise to performance of product title classification by comparing our data denoising algorithm and different noise-resistance training algorithms which were designed to prevent a classifier model from over-fitting to noise. We develop a simple yet effective Deep Neural Network for product title classification to use as a base classifier. Along with recent methods of stimulating instance-dependent noise, we propose a novel noise stimulation algorithm based on product title similarity. Our experiments cover multiple datasets, various noise methods and different training solutions. Results uncover the limit of classification task when noise rate is not negligible and data distribution is highly skewed.
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could fail when pseudo-invariant features and geometric skews exist. Inspired by IRM, in this paper we propose a novel formulation for domain generalization, dubbed invariant information bottleneck (IIB). IIB aims at minimizing invariant risks for nonlinear classifiers and simultaneously mitigating the impact of pseudo-invariant features and geometric skews. Specifically, we first present a novel formulation for invariant causal prediction via mutual information. Then we adopt the variational formulation of the mutual information to develop a tractable loss function for nonlinear classifiers. To overcome the failure modes of IRM, we propose to minimize the mutual information between the inputs and the corresponding representations. IIB significantly outperforms IRM on synthetic datasets, where the pseudo-invariant features and geometric skews occur, showing the effectiveness of proposed formulation in overcoming failure modes of IRM. Furthermore, experiments on DomainBed show that IIB outperforms $13$ baselines by $0.9\%$ on average across $7$ real datasets.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
The field of few-shot learning has recently seen substantial advancements. Most of these advancements came from casting few-shot learning as a meta-learning problem. Model Agnostic Meta Learning or MAML is currently one of the best approaches for few-shot learning via meta-learning. MAML is simple, elegant and very powerful, however, it has a variety of issues, such as being very sensitive to neural network architectures, often leading to instability during training, requiring arduous hyperparameter searches to stabilize training and achieve high generalization and being very computationally expensive at both training and inference times. In this paper, we propose various modifications to MAML that not only stabilize the system, but also substantially improve the generalization performance, convergence speed and computational overhead of MAML, which we call MAML++.
We consider the task of weakly supervised one-shot detection. In this task, we attempt to perform a detection task over a set of unseen classes, when training only using weak binary labels that indicate the existence of a class instance in a given example. The model is conditioned on a single exemplar of an unseen class and a target example that may or may not contain an instance of the same class as the exemplar. A similarity map is computed by using a Siamese neural network to map the exemplar and regions of the target example to a latent representation space and then computing cosine similarity scores between representations. An attention mechanism weights different regions in the target example, and enables learning of the one-shot detection task using the weaker labels alone. The model can be applied to detection tasks from different domains, including computer vision object detection. We evaluate our attention Siamese networks on a one-shot detection task from the audio domain, where it detects audio keywords in spoken utterances. Our model considerably outperforms a baseline approach and yields a 42.6% average precision for detection across 10 unseen classes. Moreover, architectural developments from computer vision object detection models such as a region proposal network can be incorporated into the model architecture, and results show that performance is expected to improve by doing so.
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