A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on links formed by pseudocircle arrangements, focusing on three unavoidable cases.
New simplicial complexes show unavoidable link of spheres in high dimensions.
The reductivity of a spherical curve is the minimal number of a local transformation called an inverse-half-twisted splice required to obtain a reducible spherical curve from the spherical curve. It is unknown if there exists a spherical curve whose reductivity is four. In this paper, an unavoidable set of configuratio…
This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in w…
Paper bridges AI/ML and causal modeling to reduce bias.
The reductivity of a spherical curve represents how reduced the spherical curve is. It is unknown if there exists a spherical curve whose reductivity is four. In this paper we give an unavoidable set for spherical curves with reductivity four by considering 4-gons.
We show that we can obtain a reducible spherical curve from any non-trivial spherical curve by four or less inverse-half-twisted splices, i.e., the reductivity, which represents how reduced a spherical curve is, is four or less. We also discuss unavoidable sets of tangles for spherical curves.
Kernel method improves instrumental variable regression rates.
We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of…
We show that there exist infinitely many pairs of distinct knots in the 3-sphere such that each pair can yield homeomorphic lens spaces by the same Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot, a satellite knot or a hyperbolic knot, except that both cannot be satellite knots simultaneo…
Defines crisis transitions in pure exchange economies rigorously.
New algorithm recovers graph structure from noisy data.
Before the operation of a motor imagery based brain-computer interface (BCI) adopting machine learning techniques, a cumbersome training procedure is unavoidable. The development of a practical BCI posed the challenge of classifying single-trial EEG with a small training set. In this letter, we addressed this problem b…
We study the effects of approximate inference on the performance of Thompson sampling in the -armed bandit problems. Thompson sampling is a successful algorithm for online decision-making but requires posterior inference, which often must be approximated in practice. We show that even small constant inference error …
Abstract: Study of surface transitions and IDE inflections via contact geometry.
The interest rates (or nominal yields) can be negative, this is an unavoidable fact which has already been visible during the Great Depression (1929-39). Nowadays we can find negative rates easily by e.g. auditing. Several theoretical and practical ideas how to model and eventually overcome empirical negative rates can…
Harmonization schemes limit accuracy due to domain information.
We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown. Recent results in this setting have demonstrated efficient learning algorithms with regret growing with the square root of the number of decision steps. We present new efficient algorithms that ach…
In this paper we consider the problem of finding stable maxima of expensive (to evaluate) functions. We are motivated by the optimisation of physical and industrial processes where, for some input ranges, small and unavoidable variations in inputs lead to unacceptably large variation in outputs. Our approach uses multi…
regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, regularization typically selects too many features and that so-called false positives are unavoidable. In this pape…
Structured missing data complicates machine learning, presenting new challenges.
Stock prices predicted using a Transformer model.
Cosine similarity can force points to grow in magnitude, causing convergence issues.
Optimal regularity theory for stable minimal hypersurfaces with small singular set.
Develops a parameter-free SGD algorithm with optimal convergence rate.
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the measure and running non-convex gradient descent on the positions and weights of…
New method bounds hardware noise without assumptions.
The paper explores robustness in linear regression models under adversarial attacks.
Contextual bandits study how reward variance affects regret bounds.
We give a necessary and sufficient geometric structural condition for a stable codimension 1 integral varifold on a smooth Riemannian manifold to correspond to an embedded smooth hypersurface away from a small set of generally unavoidable singularities; when this condition is satisfied, the singular set is empty if the…
In practice, one must recognize the inevitable incompleteness of information while making decisions. In this paper, we consider the optimal redeeming problem of stock loans under a state of incomplete information presented by the uncertainty in the (bull or bear) trends of the underlying stock. This is called drift unc…
Sharp bounds for high-probability estimation of discrete distributions.
Current Flash X-ray single-particle diffraction Imaging (FXI) experiments, which operate on modern X-ray Free Electron Lasers (XFELs), can record millions of interpretable diffraction patterns from individual biomolecules per day. Due to the stochastic nature of the XFELs, those patterns will to a varying degree includ…
Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number of such surfaces grows in relation to the size of the underlying triangulation.…
New proof of a 111-year-old result using gauge theory.
Developing a visual platform for faster astronomical source cataloging.
The zeta and eta-functions associated with massless and massive Dirac operators, in a D-dimensional (D odd or even) manifold without boundary, are rigorously constructed. Several mathematical subtleties involved in this process are stressed, as the intrisic ambiguity present in the definition of the associated fermion …
Study sparsity benefits in infinite feature contextual bandits.
Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes network, then every unambiguous causal conclusion produced by a consistent method f…
Determining possible failure scenarios is a critical step in the evaluation of autonomous vehicle systems. Real-world vehicle testing is commonly employed for autonomous vehicle validation, but the costs and time requirements are high. Consequently, simulation-driven methods such as Adaptive Stress Testing (AST) have b…
This work builds the connection between the regularity theory of optimal transportation map, Monge-Ampère equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse. According to the regularity theory of Monge-Ampère equation, if the support of the …
We study combinatorial multi-armed bandit with probabilistically triggered arms (CMAB-T) and semi-bandit feedback. We resolve a serious issue in the prior CMAB-T studies where the regret bounds contain a possibly exponentially large factor of , where is the minimum positive probability that an arm is trigg…
Understanding the nature of dark energy, the mysterious force driving the accelerated expansion of the Universe, is a major challenge of modern cosmology. The next generation of cosmological surveys, specifically designed to address this issue, rely on accurate measurements of the apparent shapes of distant galaxies. H…
Multi-view clustering is an important yet challenging task due to the difficulty of integrating the information from multiple representations. Most existing multi-view clustering methods explore the heterogeneous information in the space where the data points lie. Such common practice may cause significant information …
Constraining linear layers in neural networks to respect symmetry transformations from a group is a common design principle for invariant networks that has found many applications in machine learning. In this paper, we consider a fundamental question that has received little attention to date: Can these networks ap…
Extreme learning machine (ELM) as a neural network algorithm has shown its good performance, such as fast speed, simple structure etc, but also, weak robustness is an unavoidable defect in original ELM for blended data. We present a new machine learning framework called LARSEN-ELM for overcoming this problem. In our pa…
Paper warns of metric deformation in manifold learning, leading to incorrect answers.
The paper proves neural networks are almost always surjective, impacting model safety.