We present a novel technique for constructing differentiable order-type operations, including soft ranking, soft top-k selection, and soft permutations. Our approach leverages an efficient closed-form formula for the inverse of the function LapSum, defined as the sum of Laplace distributions. This formulation ensures low computational and memory complexity in selecting the highest activations, enabling losses and gradients to be computed in $O(n \log n)$ time. Through extensive experiments, we demonstrate that our method outperforms state-of-the-art techniques for high-dimensional vectors and large $k$ values. Furthermore, we provide efficient implementations for both CPU and CUDA environments, underscoring the practicality and scalability of our method for large-scale ranking and differentiable ordering problems.

Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models, we typically apply linear interpolation in the latent space. However, this interpolation uses implicitly the fact that Gaussian is unimodal. Thus, the problem of interpolating in the case when the latent density is non-Gaussian is an open problem. In this article, we present a general and unified approach to interpolation, which simultaneously allows us to search for geodesics and interpolating curves in latent space in the case of arbitrary density. Our results have a strong theoretical background based on the introduced quality measure of an interpolating curve. In particular, we show that maximizing the quality measure of the curve can be equivalently understood as a search of geodesic for a certain redefinition of the Riemannian metric on the space. We provide examples in three important cases. First, we show that our approach can be easily applied to finding geodesics on manifolds. Next, we focus our attention in finding interpolations in pretrained generative models. We show that our model effectively works in the case of arbitrary density. Moreover, we can interpolate in the subset of the space consisting of data possessing a given feature. The last case is focused on finding interpolation in the space of chemical compounds.

The problem of reducing processing time of large deep learning models is a fundamental challenge in many real-world applications. Early exit methods strive towards this goal by attaching additional Internal Classifiers (ICs) to intermediate layers of a neural network. ICs can quickly return predictions for easy examples and, as a result, reduce the average inference time of the whole model. However, if a particular IC does not decide to return an answer early, its predictions are discarded, with its computations effectively being wasted. To solve this issue, we introduce Zero Time Waste (ZTW), a novel approach in which each IC reuses predictions returned by its predecessors by (1) adding direct connections between ICs and (2) combining previous outputs in an ensemble-like manner. We conduct extensive experiments across various multiple modes, datasets, and architectures to demonstrate that ZTW achieves a significantly better accuracy vs. inference time trade-off than other early exit methods. On the ImageNet dataset, it obtains superior results over the best baseline method in 11 out of 16 cases, reaching up to 5 percentage points of improvement on low computational budgets.

Most autoencoder-based generative machine learning models use a two-factor cost function composed of reconstruction error and prior distribution distance. The latter is often evaluated with kernel–based methods. We notice that the impact of the batch size is different on each of the factors: kernel distribution profits from larger batches, while the reconstruction term achieves peak performance on smaller ones. Thus, we define a batch size reconstruction-distribution trade-off. Instead of searching for an optimum global size of the batch, we propose to use small batches for the sake of reconstruction together with a vector enhanced with previously computed latent data for the sake of prior distribution optimization. We evaluate our method on standard benchmarks and illustrate that it can improve the model’s generative scores.

The problem of reducing processing time of large deep learning models is a fundamental challenge in many real-world applications. Early exit methods strive towards this goal by attaching additional Internal Classifiers (ICs) to intermediate layers of a neural network. ICs can quickly return predictions for easy examples and, as a result, reduce the average inference time of the whole model. However, if a particular IC does not decide to return an answer early, its predictions are discarded, with its computations effectively being wasted. To solve this issue, we introduce Zero Time Waste (ZTW), a novel approach in which each IC reuses predictions returned by its predecessors by (1) adding direct connections between ICs and (2) combining previous outputs in an ensemble-like manner. We conduct extensive experiments across various datasets and architectures to demonstrate that ZTW achieves a significantly better accuracy vs. inference time trade-off than other recently proposed early exit methods.

The computation of the distance to the true distribution is a key component of most state-of-the-art generative models. Inspired by prior works on the Sliced-Wasserstein Auto-Encoders (SWAE) and the Wasserstein Auto-Encoders with MMD-based penalty (WAE-MMD), we propose a new generative model - a Cramer-Wold Auto-Encoder (CWAE). A fundamental component of CWAE is the characteristic kernel, the construction of which is one of the goals of this paper, from here on referred to as the Cramer-Wold kernel. Its main distinguishing feature is that it has a closed-form of the kernel product of radial Gaussians. Consequently, CWAE model has a~closed-form for the distance between the posterior and the normal prior, which simplifies the optimization procedure by removing the need to sample in order to compute the loss function. At the same time, CWAE performance often improves upon WAE-MMD and SWAE on standard benchmarks.

In this paper, we present a new active learning strategy whose main focus is to have the ability to adapt to the unknown (or changing) learning scenario. We introduce the learners' ensemble based approach and model it as the multi-armed bandit problem. Presented application of simple exploration-exploitation trade-off algorithms from the UCB and EXP3 families show an improvement over using the classical strategies. Evaluation on data from UCI database compare three different selection algorithms. In our tests, presented method shows promising results.

This paper proposes a classification framework based on simple classifiers organized in a tree‐like structure. It is observed that simple classifiers, even though they have high error rate, find similarities among classes in the problem domain. The authors propose to trade on this property by recognizing classes that are mistaken and constructing overlapping subproblems. The subproblems are then solved by other classifiers, which can be very simple, giving as a result a hierarchical classifier (HC). It is shown that HC, together with the proposed training algorithm and evaluation methods, performs well as a classification framework. It is also proven that such constructs give better accuracy than the root classifier it is built upon.

Text-to-phoneme conversion is a common problem in speech processing. This can be done using a rule-based system or a neural network. In this paper we propose a solution to this problem using a modular hybrid system that uses basic rules to subdivide the original problem into easier tasks which are then solved by dedicated neural networks. Such a solution can be more rapidly constructed, and is easily extendable. A voting committee concept is used to enhance generalization abilities of the system.

A model representing neural networks is proposed. It uses the functional graphs notion defined by R. Jakubowski (1977). This is a system of nodes connected with functional edges between which binary relations can be defined. Multilayer artificial neural networks can easily be defined using functional edges to model neurons, and parametrized binary relations to model synaptic connections. Learning is also defined in terms of functional graphs. The proposed description can produce descriptions of whole classes of networks.