Topic models have been successfully used for analyzing text documents. However, with existing topic models, many documents are required for training. In this paper, we propose a neural network-based few-shot learning method that can learn a topic model from just a few documents. The neural networks in our model take a small number of documents as inputs, and output topic model priors. The proposed method trains the neural networks such that the expected test likelihood is improved when topic model parameters are estimated by maximizing the posterior probability using the priors based on the EM algorithm. Since each step in the EM algorithm is differentiable, the proposed method can backpropagate the loss through the EM algorithm to train the neural networks. The expected test likelihood is maximized by a stochastic gradient descent method using a set of multiple text corpora with an episodic training framework. In our experiments, we demonstrate that the proposed method achieves better perplexity than existing methods using three real-world text document sets.

Communication between workers and the master node to collect local stochastic gradients is a key bottleneck in a large-scale federated learning system. Various recent works have proposed to compress the local stochastic gradients to mitigate the communication overhead. However, robustness to malicious attacks is rarely considered in such a setting. In this work, we investigate the problem of Byzantine-robust federated learning with compression, where the attacks from Byzantine workers can be arbitrarily malicious. We point out that a vanilla combination of compressed stochastic gradient descent (SGD) and geometric median-based robust aggregation suffers from both stochastic and compression noise in the presence of Byzantine attacks. In light of this observation, we propose to jointly reduce the stochastic and compression noise so as to improve the Byzantine-robustness. For the stochastic noise, we adopt the stochastic average gradient algorithm (SAGA) to gradually eliminate the inner variations of regular workers. For the compression noise, we apply the gradient difference compression and achieve compression for free. We theoretically prove that the proposed algorithm reaches a neighborhood of the optimal solution at a linear convergence rate, and the asymptotic learning error is in the same order as that of the state-of-the-art uncompressed method. Finally, numerical experiments demonstrate effectiveness of the proposed method.

Variational inference is a popular alternative to Markov chain Monte Carlo methods that constructs a Bayesian posterior approximation by minimizing a discrepancy to the true posterior within a pre-specified family. This converts Bayesian inference into an optimization problem, enabling the use of simple and scalable stochastic optimization algorithms. However, a key limitation of variational inference is that the optimal approximation is typically not tractable to compute; even in simple settings the problem is nonconvex. Thus, recently developed statistical guarantees -- which all involve the (data) asymptotic properties of the optimal variational distribution -- are not reliably obtained in practice. In this work, we provide two major contributions: a theoretical analysis of the asymptotic convexity properties of variational inference in the popular setting with a Gaussian family; and consistent stochastic variational inference (CSVI), an algorithm that exploits these properties to find the optimal approximation in the asymptotic regime. CSVI consists of a tractable initialization procedure that finds the local basin of the optimal solution, and a scaled gradient descent algorithm that stays locally confined to that basin. Experiments on nonconvex synthetic and real-data examples show that compared with standard stochastic gradient descent, CSVI improves the likelihood of obtaining the globally optimal posterior approximation.

Symmetries have proven to be important ingredients in the analysis of neural networks. So far their use has mostly been implicit or seemingly coincidental. We undertake a systematic study of the role that symmetry plays. In particular, we clarify how symmetry interacts with the learning algorithm. The key ingredient in our study is played by Noether's celebrated theorem which, informally speaking, states that symmetry leads to conserved quantities (e.g., conservation of energy or conservation of momentum). In the realm of neural networks under gradient descent, model symmetries imply restrictions on the gradient path. E.g., we show that symmetry of activation functions leads to boundedness of weight matrices, for the specific case of linear activations it leads to balance equations of consecutive layers, data augmentation leads to gradient paths that have "momentum"-type restrictions, and time symmetry leads to a version of the Neural Tangent Kernel. Symmetry alone does not specify the optimization path, but the more symmetries are contained in the model the more restrictions are imposed on the path. Since symmetry also implies over-parametrization, this in effect implies that some part of this over-parametrization is cancelled out by the existence of the conserved quantities. Symmetry can therefore be thought of as one further important tool in understanding the performance of neural networks under gradient descent.

We derive a simple and model-independent formula for the change in the generalization gap due to a gradient descent update. We then compare the change in the test error for stochastic gradient descent to the change in test error from an equivalent number of gradient descent updates and show explicitly that stochastic gradient descent acts to regularize generalization error by decorrelating nearby updates. These calculations depends on the details of the model only through the mean and covariance of the gradient distribution, which may be readily measured for particular models of interest. We discuss further improvements to these calculations and comment on possible implications for stochastic optimization. Note added: this paper appeared in the "Workshop on Integration of Deep Learning Theories" at NeurIPS in 2018 [1]. Given the current interest in this topic (see e.g.

We study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that unbiased estimators have unacceptable performance for such nonlinear networks in this regime. We derive explicit generalization lower bounds for general biased estimators, in the cases of linear regression and of two-layered networks. In the linear case the bound is asymptotically tight. In the nonlinear case, we provide a comparison of our bounds with an empirical study of the stochastic gradient descent algorithm. The analysis uses elements from the theory of large random matrices.

International Conference on Learning Representations (ICLR) recently announced the ICLR 2021 Outstanding Paper Awards winners. It recognised eight papers out of the 860 submitted this year. The papers were evaluated for both technical quality and the potential to create a practical impact. The committee was chaired by Ivan Titov (U. This paper deals with parameterising hypercomplex multiplications using arbitrarily learnable parameters compared with the fully-connected layer counterpart.

Deep learning (DL) relies on massive amounts of labeled data, and improving its labeled sample-efficiency remains one of the most important problems since its advent. Semi-supervised learning (SSL) leverages unlabeled data that are more accessible than their labeled counterparts. Active learning (AL) selects unlabeled instances to be annotated by a human-in-the-loop in hopes of better performance with less labeled data. Given the accessible pool of unlabeled data in pool-based AL, it seems natural to use SSL when training and AL to update the labeled set; however, algorithms designed for their combination remain limited. In this work, we first prove that convergence of gradient descent on sufficiently wide ReLU networks can be expressed in terms of their Gram matrix' eigen-spectrum. Equipped with a few theoretical insights, we propose convergence rate control (CRC), an AL algorithm that selects unlabeled data to improve the problem conditioning upon inclusion to the labeled set, by formulating an acquisition step in terms of improving training dynamics. Extensive experiments show that SSL algorithms coupled with CRC can achieve high performance using very few labeled data.

Many learning tasks in machine learning can be viewed as taking a gradient step towards minimizing the average loss of a batch of examples in each training iteration. When noise is prevalent in the data, this uniform treatment of examples can lead to overfitting to noisy examples with larger loss values and result in poor generalization. Inspired by the expert setting in on-line learning, we present a flexible approach to learning from noisy examples. Specifically, we treat each training example as an expert and maintain a distribution over all examples. We alternate between updating the parameters of the model using gradient descent and updating the example weights using the exponentiated gradient update. Unlike other related methods, our approach handles a general class of loss functions and can be applied to a wide range of noise types and applications. We show the efficacy of our approach for multiple learning settings, namely noisy principal component analysis and a variety of noisy classification problems.

Recent studies revealed complex convergence dynamics in gradient-based methods, which has been little understood so far. Changing the step size to balance between high convergence rate and small generalization error may not be sufficient: maximizing the test accuracy usually requires a larger learning rate than minimizing the training loss. To explore the dynamic bounds of convergence rate, this study introduces \textit{differential capability} into an optimization process, which measures whether the test accuracy increases as fast as a model approaches the decision boundary in a classification problem. The convergence analysis showed that: 1) a higher convergence rate leads to slower capability growth; 2) a lower convergence rate results in faster capability growth and decay; 3) regulating a convergence rate in either direction reduces differential capability.