Performance of Hyperbolic Geometry Models on Top-N Recommendation Tasks

We introduce a simple autoencoder based on hyperbolic geometry for solving standard collaborative filtering problem. In contrast to many modern deep learning techniques, we build our solution using only a single hidden layer. Remarkably, even with such a minimalistic approach, we not only outperform the Euclidean counterpart but also achieve a competitive performance with respect to the current state-of-the-art. We additionally explore the effects of space curvature on the quality of hyperbolic models and propose an efficient data-driven method for estimating its optimal value.

Sample Efficient Ensemble Learning with Catalyst.RL

We present Catalyst.RL, an open-source PyTorch framework for reproducible and sample efficient reinforcement learning (RL) research. Main features of Catalyst.RL include large-scale asynchronous distributed training, efficient implementations of various RL algorithms and auxiliary tricks, such as n-step returns, value distributions, hyperbolic reinforcement learning, etc. To demonstrate the effectiveness of Catalyst.RL, we applied it to a physics-based reinforcement learning challenge "NeurIPS 2019: Learn to Move -- Walk Around" with the objective to build a locomotion controller for a human musculoskeletal model. The environment is computationally expensive, has a high-dimensional continuous action space and is stochastic. Our team took the 2nd place, capitalizing on the ability of Catalyst.RL to train high-quality and sample-efficient RL agents in only a few hours of training time. The implementation along with experiments is open-sourced so results can be reproduced and novel ideas tried out.

Universality Theorems for Generative Models

Despite the fact that generative models are extremely successful in practice, the theory underlying this phenomenon is only starting to catch up with practice. In this work we address the question of the universality of generative models: is it true that neural networks can approximate any data manifold arbitrarily well? We provide a positive answer to this question and show that under mild assumptions on the activation function one can always find a feedforward neural network that maps the latent space onto a set located within the specified Hausdorff distance from the desired data manifold. We also prove similar theorems for the case of multiclass generative models and cycle generative models, trained to map samples from one manifold to another and vice versa.

Hyperbolic Image Embeddings

Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made using linear hyperplanes, Euclidean distances, or spherical geodesic distances (cosine similarity). In this work, we demonstrate that in many practical scenarios hyperbolic embeddings provide a better alternative.

Generalized Tensor Models for Recurrent Neural Networks

Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs enjoys the property of depth efficiency --- a shallow network of exponentially large width is necessary to realize the same score function as computed by such an RNN. Such networks, however, are not very often applied to real life tasks. In this work, we attempt to reduce the gap between theory and practice by extending the theoretical analysis to RNNs which employ various nonlinearities, such as Rectified Linear Unit (ReLU), and show that they also benefit from properties of universality and depth efficiency. Our theoretical results are verified by a series of extensive computational experiments.

Tensorized Embedding Layers for Efficient Model Compression

The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing. However, when the vocabulary is large (e.g., 800k unique words in the One-Billion-Word dataset), the corresponding weight matrices can be enormous, which precludes their deployment in a limited resource setting. We introduce a novel way of parametrizing embedding layers based on the Tensor Train (TT) decomposition, which allows compressing the model significantly at the cost of a negligible drop or even a slight gain in performance. Importantly, our method does not take the pre-trained model and compress its weights but rather supplants the standard embedding layers with their TT-based counterparts. The resulting model is then trained end-to-end, however, it can capitalize on larger batches due to the reduced memory requirements. We evaluate our method on a wide range of benchmarks in sentiment analysis, neural machine translation, and language modeling, and analyze the trade-off between performance and compression ratios for a wide range of architectures, from MLPs to LSTMs and Transformers.

Geometry Score: A Method For Comparing Generative Adversarial Networks

One of the biggest challenges in the research of generative adversarial networks (GANs) is assessing the quality of generated samples and detecting various levels of mode collapse. In this work, we construct a novel measure of performance of a GAN by comparing geometrical properties of the underlying data manifold and the generated one, which provides both qualitative and quantitative means for evaluation. Our algorithm can be applied to datasets of an arbitrary nature and is not limited to visual data. We test the obtained metric on various real-life models and datasets and demonstrate that our method provides new insights into properties of GANs.

Expressive power of recurrent neural networks

Deep neural networks are surprisingly efficient at solving practical tasks, but the theory behind this phenomenon is only starting to catch up with the practice. Numerous works show that depth is the key to this efficiency. A certain class of deep convolutional networks -- namely those that correspond to the Hierarchical Tucker (HT) tensor decomposition -- has been proven to have exponentially higher expressive power than shallow networks. I.e. a shallow network of exponential width is required to realize the same score function as computed by the deep architecture. In this paper, we prove the expressive power theorem (an exponential lower bound on the width of the equivalent shallow network) for a class of recurrent neural networks -- ones that correspond to the Tensor Train (TT) decomposition. This means that even processing an image patch by patch with an RNN can be exponentially more efficient than a (shallow) convolutional network with one hidden layer. Using theoretical results on the relation between the tensor decompositions we compare expressive powers of the HT- and TT-Networks. We also implement the recurrent TT-Networks and provide numerical evidence of their expressivity.

Art of singular vectors and universal adversarial perturbations

Vulnerability of Deep Neural Networks (DNNs) to adversarial attacks has been attracting a lot of attention in recent studies. It has been shown that for many state of the art DNNs performing image classification there exist universal adversarial perturbations --- image-agnostic perturbations mere addition of which to natural images with high probability leads to their misclassification. In this work we propose a new algorithm for constructing such universal perturbations. Our approach is based on computing the so-called $(p, q)$-singular vectors of the Jacobian matrices of hidden layers of a network. Resulting perturbations present interesting visual patterns, and by using only 64 images we were able to construct universal perturbations with more than 60 \% fooling rate on the dataset consisting of 50000 images. We also investigate a correlation between the maximal singular value of the Jacobian matrix and the fooling rate of the corresponding singular vector, and show that the constructed perturbations generalize across networks.