We present an efficient technique, which allows to train classification networks which are verifiably robust against norm-bounded adversarial attacks. This framework is built upon the work of Gowal et al., who applies the interval arithmetic to bound the activations at each layer and keeps the prediction invariant to the input perturbation. While that method is faster than competitive approaches, it requires careful tuning of hyper-parameters and a large number of epochs to converge. To speed up and stabilize training, we supply the cost function with an additional term, which encourages the model to keep the interval bounds at hidden layers small. Experimental results demonstrate that we can achieve comparable (or even better) results using a smaller number of training iterations, in a more stable fashion. Moreover, the proposed model is not so sensitive to the exact specification of the training process, which makes it easier to use by practitioners.

Independent Component Analysis (ICA) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis (MWeICA) algorithm, a new ICA method which is based on approximate diagonalization of weighted covariance matrices. Our idea is based on theoretical result, which says that linear independence of weighted data (for gaussian weights) guarantees independence. Experiments show that MWeICA achieves better results to most state-of-the-art ICA methods, with similar computational time.

Several deep models, esp. the generative, compare the samples from two distributions (e.g. WAE like AutoEncoder models, set-processing deep networks, etc) in their cost functions. Using all these methods one cannot train the model directly taking small size (in extreme -- one element) batches, due to the fact that samples are to be compared. We propose a generic approach to training such models using one-element mini-batches. The idea is based on splitting the batch in latent into parts: previous, i.e. historical, elements used for latent space distribution matching and the current ones, used both for latent distribution computation and the minimization process. Due to the smaller memory requirements, this allows to train networks on higher resolution images then in the classical approach.

We show how to construct smooth and realistic interpolations for generative models, with arbitrary, not necessarily Gaussian, prior. The crucial idea is based on the construction on the realisticity index of a curve, which maximisation, as we show, leads to a search of a geodesic with respect to the corresponding Riemann structure.

We use a hypernetwork to automatically generate continuous functional representation of images at test time without any additional training. More precisely, the hypernetwork takes an image and returns weights to a target network representing the image. Since obtained representation is continuous, we can easily inspect the image at various resolutions. Finally, because we use a single hypernetwork responsible for creating individual image models, similar images have similar weights of their target networks. As a consequence, interpolation in the space of weights of target networks representing images shows properties similar to that of generative models. To experimentally evaluate the proposed mechanism, we apply it to image super-resolution. Despite of using a single model for various scale factors, we obtained the results comparable to existing super-resolution methods.

Non-linear source separation is a challenging open problem with many applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA) model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a simple, closed--form optimization target instead of a discriminator--based independence measure. Our results show that CW-ICA achieves comparable results to ANICA, while foregoing the need for adversarial training.

In this paper, we propose a simple, fast and easy to implement algorithm LOSSGRAD (locally optimal step-size in gradient descent), which automatically modifies the step-size in gradient descent during neural networks training. Given a function $f$, a point $x$, and the gradient $\nabla_x f$ of $f$, we aim to find the step-size $h$ which is (locally) optimal, i.e. satisfies: $$ h=arg\,min_{t \geq 0} f(x-t \nabla_x f). $$ Making use of quadratic approximation, we show that the algorithm satisfies the above assumption. We experimentally show that our method is insensitive to the choice of initial learning rate while achieving results comparable to other methods.

In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that methods can be divided into two groups. First consists of methods which are a modification of standard normality tests, while the second is based on classical distances between samples. It turns out that both groups are correct generative models, but the second one gives a slightly faster decrease rate of Fr\'{e}chet Inception Distance (FID).

We propose a general, theoretically justified mechanism for processing missing data by neural networks. Our idea is to replace typical neuron's response in the first hidden layer by its expected value. This approach can be applied for various types of networks at minimal cost in their modification. Moreover, in contrast to recent approaches, it does not require complete data for training. Experimental results performed on different types of architectures show that our method gives better results than typical imputation strategies and other methods dedicated for incomplete data.

We propose a general, theoretically justified mechanism for processing missing data by neural networks. Our idea is to replace typical neuron's response in the first hidden layer by its expected value. This approach can be applied for various types of networks at minimal cost in their modification. Moreover, in contrast to recent approaches, it does not require complete data for training. Experimental results performed on different types of architectures show that our method gives better results than typical imputation strategies and other methods dedicated for incomplete data.