arXiv research

New derivation of knot invariants from universal invariant.

New method evaluates LLMs fairness in universal prediction.

NODEs can approximate a wide range of diffeomorphisms with strong guarantees.

For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this construction imply that the corresponding largeness properties of closed manifolds dep…

Decomposes ultrametric spaces into scaled simplices.

We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found that some submarkets generate the higher momentum returns than other …

The paper optimizes portfolios with transaction costs in a large asset universe.

MAT combines meta-learning and adversarial training to defend against universal patches.

This paper fine-tunes LLMs for stock return prediction using financial news.

New analysis shows halting time is predictable for large models, improving optimization efficiency.

New algorithms for regression with adversarial responses on various metric spaces.

The abstract proves the existence of universal lottery tickets without needing further training.

Proposes a robust portfolio method for large asset universes.

The paper explores simple and relatively simple transformation groups and their universal coverings.

In this paper we explore coarse properties of cusp-decomposable manifolds first defined by Nguyên Phan. We describe the large scale geometry of the universal cover of a cusp-decomposable manifold and of quasi-isometries between two such universal covers. This description will provide us the tools to prove quasi-isometr…

In this article, a large data set containing every course taken by every undergraduate student in a major university in Canada over 10 years is analysed. Modern machine learning algorithms can use large data sets to build useful tools for the data provider, in this case, the university. In this article, two classifiers…

The study shows conditions for larger volumes in the universal cover of a manifold.

Simple technique turns any adversarial attack into a universal one using few test examples.

Formal manifolds with non-negative Ricci curvature have formal covers.

The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents. We show, that in the case of time series of the traded value, these Hurst exponen…

Study confirms the square-root law in price impact across Tokyo stocks.

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single stand…

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a linear combination of the feature vector $x^Tθ$ where $x\in {\cal R}^M$, within a G…

We present an algorithm for computing class-specific universal adversarial perturbations for deep neural networks. Such perturbations can induce misclassification in a large fraction of images of a specific class. Unlike previous methods that use iterative optimization for computing a universal perturbation, the propos…

Convolutional neural networks (CNN) have become one of the most popular machine learning tools and are being applied in various tasks, however, CNN models are vulnerable to universal perturbations, which are usually human-imperceptible but can cause natural images to be misclassified with high probability. One of the s…

Develops a new framework for large-scale geometry.

We present evidence, that if a large enough set of high resolution stock market data is analyzed, certain analogies with physics -- such as scaling and universality -- fail to capture the full complexity of such data. Despite earlier expectations, the mean value per trade, the mean number of trades per minute and the m…

A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in thr…

ELF simplifies normalizing flows, making them more efficient and universal.

For each $n$, we construct a separable metric space $\mathbb{U}_n$ that is universal in the coarse category of separable metric spaces with asymptotic dimension ($\mathop{asdim}$) at most $n$ and universal in the uniform category of separable metric spaces with uniform dimension ($\mathop{udim}$) at most $n$. Thus, $\m…

Graph Neural Networks struggle on random graphs without node identifiers.

Regularization is essential when training large neural networks. As deep neural networks can be mathematically interpreted as universal function approximators, they are effective at memorizing sampling noise in the training data. This results in poor generalization to unseen data. Therefore, it is no surprise that a ne…

Gradient descent dynamics in nonconvex models explained with universality.

Algorithm tackles large-scale portfolio optimization with higher moments, improving computational efficiency.

Transformers enable in-context learning with guarantees for a wide range of tasks.

New findings show Gaussian universality breaks down in high-dimensional linear factor mixtures.

The goal of this paper is to characterize function distributions that deep learning can or cannot learn in poly-time. A universality result is proved for SGD-based deep learning and a non-universality result is proved for GD-based deep learning; this also gives a separation between SGD-based deep learning and statistic…

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a s…

Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction dynamics between individual components is mediated by a global variable making the …

Unified framework proves neural networks' ability to mimic complex tasks.

New algorithm achieves consistent learning from context in bandit problems.

Abstract: Study of metrics on line bundles over complex varieties.

Consider a family of portfolio strategies with the aim of achieving the asymptotic growth rate of the best one. The idea behind Cover's universal portfolio is to build a wealth-weighted average which can be viewed as a buy-and-hold portfolio of portfolios. When an optimal portfolio exists, the wealth-weighted average c…

New findings show neural network training loss follows a power law over time.

We use methods of random matrix theory to analyze the cross-correlation matrix C of price changes of the largest 1000 US stocks for the 2-year period 1994-95. We find that the statistics of most of the eigenvalues in the spectrum of C agree with the predictions of random matrix theory, but there are deviations for a fe…

Semantic segmentation is a critical method in the field of autonomous driving. When performing semantic image segmentation, a wider field of view (FoV) helps to obtain more information about the surrounding environment, making automatic driving safer and more reliable, which could be offered by fisheye cameras. However…

Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain …

Understanding large-scale patterns in student course enrollment is a problem of great interest to university administrators and educational researchers. Yet important decisions are often made without a good quantitative framework of the process underlying student choices. We propose a probabilistic approach to modellin…