arXiv research

Boosts barely robust learners to be more adversarially robust.

While adversarial training can improve robust accuracy (against an adversary), it sometimes hurts standard accuracy (when there is no adversary). Previous work has studied this tradeoff between standard and robust accuracy, but only in the setting where no predictor performs well on both objectives in the infinite data…

The present paper deals with mirror symmetry aspects of compact ``barely'' $G_2$ manifolds, that is, $G_2$ manifolds of the form (CY$\times S^1)/\mathbb{Z}_2$. We propose that the mirror of any barely $G_2$ manifold is another barely one and which is constructed as a fibration of the \emph{mirror} of the CY base. Also,…

We calculate explicitly the Betti numbers of a class of barely G2 manifolds - that is, G2 manifolds that are realised as a product of a Calabi-Yau manifold and a circle, modulo an involution. The particular class which we consider are those spaces where the Calabi-Yau manifolds are complete intersections of hypersurfac…

We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the $SU(2)$ theory on a compact oriented simply connected simple type Riemann manifold with $b_2^+ \geq 3$. As the corollaries,…

We consider in a market model the cooperative emergence of value due to a positive feedback between perception of needs and demand. Here we consider also a negative feedback from production of the traded products, and find that this cooperativity is robust, provided that the production rate is slow. Cooperativity is fo…

After surveying existing proofs that every closed, orientable 3-manifold is parallelizable, we give three proofs using minimal background. In particular, our proofs use neither spin structures nor the theory of Stiefel-Whitney classes.

DIP-FAT improves adversarial training by diversifying perturbations.

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different events, and their respective i…

Study on hemisphere threshold for Escobar functional on Riemannian manifolds, revealing mass and boundary invariant behaviors.

Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing classifiers, leading to ridiculous misclassification results. In…

Improves Gaussian process regression without bias.

While deep learning has received a surge of interest in a variety of fields in recent years, major deep learning models barely use complex numbers. However, speech, signal and audio data are naturally complex-valued after Fourier Transform, and studies have shown a potentially richer representation of complex nets. In …

The aggregation of k-ary preferences is a historical and important problem, since it has many real-world applications, such as peer grading, presidential elections and restaurant ranking. Meanwhile, variants of Plackett-Luce model has been applied to aggregate k-ary preferences. However, there are two urgent issues sti…

With the help of transfer entropy, we analyze information flows between communities of complex networks. We show that the transfer entropy provides a coherent description of interactions between communities, including non-linear interactions. To put some flesh on the bare bones, we analyze transfer entropies between co…

Statistical leverage scores emerged as a fundamental tool for matrix sketching and column sampling with applications to low rank approximation, regression, random feature learning and quadrature. Yet, the very nature of this quantity is barely understood. Borrowing ideas from the orthogonal polynomial literature, we in…

New algorithm improves GAN stability and quality.

Recent advances in visual tracking are based on siamese feature extractors and template matching. For this category of trackers, latest research focuses on better feature embeddings and similarity measures. In this work, we focus on building holistic object representations for tracking. We propose a framework that is d…

Deep neural networks have been widely adopted in recent years, exhibiting impressive performances in several application domains. It has however been shown that they can be fooled by adversarial examples, i.e., images altered by a barely-perceivable adversarial noise, carefully crafted to mislead classification. In thi…

Attention tokens are group elements, negated algebra norms.

Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…

CREDIT learns to master pair trading with risk-aware RL, outperforming existing methods.

Multifractal analysis is one of the important approaches that enables us to measure the complexity of various data via the scaling properties. We compare the most common techniques used for multifractal exponents estimation from both theoretical and practical point of view. Particularly, we discuss the methods based on…

Reinforcement Learning (RL) is a research area that has blossomed tremendously in recent years and has shown remarkable potential for artificial intelligence based opponents in computer games. This success is primarily due to vast capabilities of Convolutional Neural Networks (ConvNet), enabling algorithms to extract u…

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use few literal expressions, equations, functions, etc. We barely suppose that the re…

Graph representation learning is of paramount importance for a variety of graph analytical tasks, ranging from node classification to community detection. Recently, graph convolutional networks (GCNs) have been successfully applied for graph representation learning. These GCNs generate node representation by aggregatin…

This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate students, having nevertheless a limited mathematical background. Overall this text is a…

The complex networks approach has been gaining popularity in analysing investor behaviour and stock markets, but within this approach, initial public offerings (IPO) have barely been explored. We fill this gap in the literature by analysing investor clusters in the first two years after the IPO filing in the Helsinki S…

The dependency structure of credit risk parameters is a key driver for capital consumption and receives regulatory and scientific attention. The impact of parameter imperfections on the quality of expected loss (EL) in the sense of a fair, unbiased estimate of risk expenses however is barely covered. So far there are n…

While deep learning is remarkably successful on perceptual tasks, it was also shown to be vulnerable to adversarial perturbations of the input. These perturbations denote noise added to the input that was generated specifically to fool the system while being quasi-imperceptible for humans. More severely, there even exi…

We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics …

We introduce a matrix representation of a chord on a tangle which leads us to representing tangle chord diagrams as stacks of matrices that we call books. We show that band sum moves, Reidemeister moves as well as orientation changes are implemented on \widetilde{Z}_f - a framed link invariant constructed from the Kont…

New tighter confidence bounds for sequential kernel regression.

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine learning and predictive modeling, distributed optimization methods have recently garne…

MiCA regulation led to a shift in stablecoin dominance.

Deep neural networks (DNNs) are one of the most prominent technologies of our time, as they achieve state-of-the-art performance in many machine learning tasks, including but not limited to image classification, text mining, and speech processing. However, recent research on DNNs has indicated ever-increasing concern o…

An intriguing property of deep neural networks is their inherent vulnerability to adversarial inputs, which significantly hinders their application in security-critical domains. Most existing detection methods attempt to use carefully engineered patterns to distinguish adversarial inputs from their genuine counterparts…

Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter is often too restrictive when applied to complex empirical data. Here we show tha…

Deep learning models, which are increasingly being used in the field of medical image analysis, come with a major security risk, namely, their vulnerability to adversarial examples. Adversarial examples are carefully crafted samples that force machine learning models to make mistakes during testing time. These maliciou…

The paper studies learning dynamics in two-layer neural networks.

XCS constitutes the most deeply investigated classifier system today. It bears strong potentials and comes with inherent capabilities for mastering a variety of different learning tasks. Besides outstanding successes in various classification and regression tasks, XCS also proved very effective in certain multi-step en…

Recent studies have introduced end-to-end TTS, which integrates the production of context and acoustic features in statistical parametric speech synthesis. As a result, a single neural network replaced laborious feature engineering with automated feature learning. However, little is known about what types of context in…

This paper studies universal rates of ERM for binary classification under agnostic learning.

Many real-world datasets are labeled with natural orders, i.e., ordinal labels. Ordinal regression is a method to predict ordinal labels that finds a wide range of applications in data-rich domains, such as natural, health and social sciences. Most existing ordinal regression approaches work well for independent and id…

The paper explores sampling problems and shows minimal exploration is needed.

This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional d…

Neural networks enjoy widespread use, but many aspects of their training, representation, and operation are poorly understood. In particular, our view into the training process is limited, with a single scalar loss being the most common viewport into this high-dimensional, dynamic process. We propose a new window into …

The digitalization of the legal domain has been ongoing for a couple of years. In that process, the application of different machine learning (ML) techniques is crucial. Tasks such as the classification of legal documents or contract clauses as well as the translation of those are highly relevant. On the other side, di…