arXiv research

Neighbor embeddings balance attraction and repulsion to visualize data.

Proves properties of neural network basins of attraction and their expressiveness.

Proposes a method to learn system dynamics and region of attraction from trajectories.

ARS visualization improves t-SNE dynamics with tunable attraction and repulsion.

Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.

This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It is assumed that attractive spots in the environment are responsible for modifyi…

Given a free group $F_n$, a fully irreducible automorphism $f \in \aut$, and a generic element $x \in F_n$, the elements $f^k(x)$ converge in the appropriate sense to an object called an attracting lamination of $f$. When the action of $f$ on $\frac{F_n}{[F_n, F_n]}$ has finite order, we introduce a homological version…

SGD tends to favor simpler subnetworks, improving generalization.

We investigate how the choice of decision makers can be varied under the presence of risk and uncertainty. Our analysis is based on the approach we have previously applied to individual decision makers, which we now generalize to the case of decision makers that are members of a society. The approach employs the mathem…

Study on existence of ground states on curved spaces with conditions on potential growth.

We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we show that its attracting (and repelling) tree is a nongeometric $\mathbb R$-tree all of whose branch points are trivalent

Hidden regular variation is a sub-model of multivariate regular variation and facilitates accurate estimation of joint tail probabilities. We generalize the model of hidden regular variation to what we call hidden domain of attraction. We exhibit examples that illustrate the need for a more general model and discuss de…

RAHMC improves sampling from multimodal distributions using dissipative dynamics.

Researchers identify valid auxiliary functions for extreme value distributions and their max-domains of attraction.

Most recommender systems recommend a list of items. The user examines the list, from the first item to the last, and often chooses the first attractive item and does not examine the rest. This type of user behavior can be modeled by the cascade model. In this work, we study cascading bandits, an online learning variant…

Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for processes which encompass the fractionally differentiated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.

Motivated by applications to insurance mathematics, we prove some heavy-traffic limit theorems for process which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a nonGaussian stable distribution.

The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Mark…

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points…

PoEL protocol aims to efficiently create and secure liquidity for blockchain networks.

This paper analyses the relationship between BitCoin price and supply-demand fundamentals of BitCoin, global macro-financial indicators and BitCoin attractiveness for investors. Using daily data for the period 2009-2014 and applying time-series analytical mechanisms, we find that BitCoin market fundamentals and BitCoin…

The study proves a theorem about subword complexity for free group automorphisms.

Study fixed point indices and words at infinity for graph selfmaps.

Enhances contrastive learning for better representation learning on wild images.

New method finds basins of attraction without needing system models.

This work models the interconnection of company's investment managers' representations and the market attraction of its shares. The models that reflect the connection of the company's market effectiveness indices and parameters of its economic activity are created on the basis of the Mean-Variance Analysis and Regressi…

Bayesian supertrees method uses variational Bayes for overlapping taxon subsets.

Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning models efficiently. First-order methods such as gradient descent are usually the methods of choice for training machine learning models. However, these methods converge to saddle points for certain ch…

A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degr…

Compactifies geodesic flows on hyperbolic surfaces, revealing attractive circles at infinity.

Study bounds topological entropy of toroidal attractors.

ICLR 2021 challenge in computational geometry and topology attracted 16 teams.

We introduce a new model for online ranking in which the click probability factors into an examination and attractiveness function and the attractiveness function is a linear function of a feature vector and an unknown parameter. Only relatively mild assumptions are made on the examination function. A novel algorithm f…

Study ping-pong dynamics in hyperbolic-like groups with non-simple points.

We consider the problem of diversity enhancing clustering, i.e, developing clustering methods which produce clusters that favour diversity with respect to a set of protected attributes such as race, sex, age, etc. In the context of fair clustering, diversity plays a major role when fairness is understood as demographic…

GCAO improves clustering of high-dimensional data by grouping low-density boundary points.

Study on consensus formation in manifolds with curvature constraints.

The paper defines a path metric on a stable component of polynomial families.

We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This type of problems have recently attracted a great deal of interest, mainly due to th…

Isobenefit Lines can offer a certain range of applicability in Location Theory and Gravitational Models for Urban and Geography Economics, in positional decision processes made by citizens, and, last but not least, in land value and property market theories and analysis. The value of a land, or a property, in a generic…

Recently, a general method for analyzing the statistical accuracy of the EM algorithm has been developed and applied to some simple latent variable models [Balakrishnan et al. 2016]. In that method, the basin of attraction for valid initialization is required to be a ball around the truth. Using Stein's Lemma, we exten…

This master thesis focuses on practical application of Convolutional Neural Network models on the task of road labeling with bike attractivity score. We start with an abstraction of real world locations into nodes and scored edges in partially annotated dataset. We enhance information available about each edge with pho…

Continuous control tasks in reinforcement learning are important because they provide an important framework for learning in high-dimensional state spaces with deceptive rewards, where the agent can easily become trapped into suboptimal solutions. One way to avoid local optima is to use a population of agents to ensure…

Framework analyzes neural network dynamics for better understanding and optimization.

Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we introduce dynamics in 1-, 2- and 3-dimensional topological surgery, by means of attracti…

The web link selection problem is to select a small subset of web links from a large web link pool, and to place the selected links on a web page that can only accommodate a limited number of links, e.g., advertisements, recommendations, or news feeds. Despite the long concerned click-through rate which reflects the at…

High-fee pools attract more liquidity but execute less volume; low-fee pools have more stable LPs.

In recent years, multi-armed bandit (MAB) framework has attracted a lot of attention in various applications, from recommender systems and information retrieval to healthcare and finance, due to its stellar performance combined with certain attractive properties, such as learning from less feedback. The multi-armed ban…