arXiv research

This study explains how adversarial interaction creates non-homogeneous patterns using a pseudo-Reaction-Diffusion model.

Turing complete flow on 4-sphere preserves volume.

Modified dynamical systems retain Turing universality.

New neural stack and Turing Machine architectures prove stability and computational power.

In recent years, Neural Turing Machines have gathered attention by joining the flexibility of neural networks with the computational capabilities of Turing machines. However, Neural Turing Machines are notoriously hard to train, which limits their applicability. We propose reservoir memory machines, which are still abl…

This study calculates the maximum error of a famous estimation method.

Researchers prove Transformers are Turing-complete and analyze their components.

This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator-prey system in population-dynamics. The spatial movement of the capital and labour force are taken into account by cross-diffusion effect. First, we are showing two possible ways for modeling thi…

We propose Turing Learning, a novel system identification method for inferring the behavior of natural or artificial systems. Turing Learning simultaneously optimizes two populations of computer programs, one representing models of the behavior of the system under investigation, and the other representing classifiers. …

This study shows neural nets can approximate Turing machines with meaningful statistical properties.

One type of switch simplifies operations on lattice knots.

The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial intelligence. In the intervening years, the idea of cognition as computation has emerged …

The Navier-Stokes equations on certain manifolds can perform universal computation.

New framework for manifold convolutions using toric embeddings.

Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these alternatives have not yet been fully explored. We study the computational power of two…

A new restart criterion for k-means++ improves clustering quality and adapts to data difficulty.

Abstract sketches historical development of Lie brackets, crossed modules, and Lie-Rinehart algebras.

In this paper, we study quatization condition of logsymplectic struc- ture using integrality of such structue on the complement of associated divisor D.

In this article, we introduce a new mode for training Generative Adversarial Networks (GANs). Rather than minimizing the distance of evidence distribution $\tilde{p}(x)$ and the generative distribution $q(x)$, we minimize the distance of $\tilde{p}(x_r)q(x_f)$ and $\tilde{p}(x_f)q(x_r)$. This adversarial pattern can be…

A framework to quantify deployment risk in ML systems, especially for rare states.

New tools quantify deep generative models' performance.

Neural Turing Machines (NTMs) are an instance of Memory Augmented Neural Networks, a new class of recurrent neural networks which decouple computation from memory by introducing an external memory unit. NTMs have demonstrated superior performance over Long Short-Term Memory Cells in several sequence learning tasks. A n…

We construct a financial "Turing test" to determine whether human subjects can differentiate between actual vs. randomized financial returns. The experiment consists of an online video-game (http://arora.ccs.neu.edu) where players are challenged to distinguish actual financial market returns from random temporal permut…

We improve current instability-based methods for the selection of the number of clusters $k$ in cluster analysis by developing a normalized cluster instability measure that corrects for the distribution of cluster sizes, a previously unaccounted driver of cluster instability. We show that our normalized instability mea…

Survey on computational models in dynamical systems, including new universality concepts.

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannes…

Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the early work of Laplace and the seminal contribution of Good and Turing. One of the b…

Study computability of real numbers from group properties.

The goal of this paper, using lifting theory it is to produce almost paracomplex struc- tures on the tangent bundle of almost Lorentzian r-paracontact manifold endowed with almost Lorentzian r-paracontact structure. Finally, we discuss the effect over dynamics systems of the produced geometrical structures.

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

Modeling HFT interactions reveals market instability.

New proof of instability for certain Einstein metrics.

Popular culture has contemplated societies of thinking machines for generations, envisioning futures from utopian to dystopian. These futures are, arguably, here now-we find ourselves at the doorstep of technology that can at least simulate the appearance of thinking, acting, and feeling. The real question is: now what…

Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolution…

Study stability and instability of Ricci-flat metrics under generalized Ricci flow.

Some exotic compact objects possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event horizon exhibits a linear instability of a peculiar kind: either there are solu…

Interval Neural Networks detect instabilities in image reconstructions.

Note on instabilities in super-time-stepping methods for Heston model.

Binary perceptron's instability linked to replica symmetry breaking.

A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For example, real-time studies of instabilities in nonlinear fibre optics frequently …

The study examines stability and instability of Poincaré-Einstein metrics using Ricci flow.

Many industrial machine learning (ML) systems require frequent retraining to keep up-to-date with constantly changing data. This retraining exacerbates a large challenge facing ML systems today: model training is unstable, i.e., small changes in training data can cause significant changes in the model's predictions. In…

We present the preliminary high-level design and features of DynamicPPL.jl, a modular library providing a lightning-fast infrastructure for probabilistic programming. Besides a computational performance that is often close to or better than Stan, DynamicPPL provides an intuitive DSL that allows the rapid development of…

Study shows instability of naked singularities in perfect fluid models.

Study on spectral stability of Riemannian coverings.

Clinical models can be unstable, leading to unreliable predictions.

Private KL distribution estimation improved with instance-optimality.

We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the generalized word problem in braid groups, in the special case of cyclic subgroups. We ill…