Improved OOD detection across various shifts using multi-encoder fusion of RDMs.
problem Out-of-distribution detection across multiple types of distribution shifts.
method Statistical identification of encoder sensitivity, EncMin2L fusion, and Tippett minimum combination.
result Achieves AUROC ≥ 0.94 across four shift types, outperforming state-of-the-art detectors.
For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a-, b-, and c-increments. Statistics of the a-b-c-increments are computed for the Time & Sales records posted by the Chicago Mercantile Exchange Group for the futures traded on…
Minimum Description Length prevents overfitting in noisy data.
problem Learning from noisy data with overfitting risk.
method Minimum Description Length learning rule with tempered guarantees.
result Tempered agnostic finite sample learning guarantees and asymptotic behavior characterization.
Minimum attention improves reinforcement learning performance in high-dimensional dynamics.
problem Improving reinforcement learning performance in high-dimensional nonlinear dynamics.
method Applying minimum attention as a regularization technique in reinforcement learning, including model-based and model-free approaches.
result Minimum attention outperforms state-of-the-art algorithms in few-shot adaptation and variance reduction.
The minimum number of colors is a challenging knot invariant since, by definition, its calculation requires taking the minimum over infinitely many minima. In this article we estimate and in some cases calculate the minimum number of colors for the Turk's head knots on three strands.
Minimum braids are a complete invariant of knots and links. This paper defines minimum braids, describes how they can be generated, presents tables for knots up to ten crossings and oriented links up to nine crossings, and uses minimum braids to study graph trees, amphicheirality, unknotting numbers, and periodic table…
Study tightens bounds for interpolating noisy data using minimum l1-norm.
problem Predicting noisy data with minimum l1-norm interpolation.
method Provided matching upper and lower bounds for prediction error.
result Tight consistency up to negligible terms for d≫n. A new classification method based on Minimum Spanning Trees
problem Improving classification in supervised learning
method Proposing a classification algorithm based on Minimum Spanning Trees
result The proposed method is effective and computationally efficient
The paper finds minimum Dehn colors for knots and defines useful graphs for coloring.
problem Finding the minimum number of colors for Dehn colorings of knots.
method Analyzes Dehn colorings for knots and defines R-palette graphs. result For Dehn p-colorable knots, the minimum number of colors is at least ⌊log2pfloor+2. The paper calculates genus bounds for multibranched surfaces.
problem Finding genus bounds for multibranched surfaces.
method Using the first Betti number and boundary genus, the paper provides lower bounds for maximum and minimum genus.
result The maximum and minimum genus of GimesS1 equals twice that of G. Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of a knot K i…
Study shows how networks converge to minimum norm solutions with regularization.
problem Interpolating between known regions in shallow ReLU networks.
method Investigates empirical risk minimizers and weight decay regularizers.
result Empirical risk minimizers converge to minimum norm interpolants under specific conditions.
We find the minimum dilatation of pseudo-Anosov braids with many strands.
problem Finding the minimum dilatation of pseudo-Anosov braids with a large number of strands.
method Analyzing examples of Hironaka-Kin and Venzke to determine the minimum dilatation.
result The minimum dilatation is approximately 13.928 for large n. Study introduces AMVP and AMRR for dynamic portfolio optimization in volatile markets.
problem Optimizing portfolios in volatile and nonstationary financial markets.
method Adaptive Minimum-Variance Portfolio (AMVP) framework with ARFIMA-FIGARCH processes and non-Gaussian innovations.
result Demonstrated superior performance in risk reduction and portfolio stability during market breaks.
Minimum algebraic intersection found in hyperbolic surfaces, growing with genus.
problem Finding the minimum algebraic intersection form in hyperbolic surfaces.
method Analyzing algebraic intersection form in moduli space of hyperbolic surfaces.
result Minimum grows in the order of (logg)−2 with genus. Computed minimum crossing numbers for Turaev genus 2 links.
problem Verifying the Qazaqzeh-Chbili-Lowrance conjecture.
method Computed minimum crossing numbers for a specific family of links.
result Verified the Qazaqzeh-Chbili-Lowrance conjecture for the family.
This paper studies the geometry of minimum-volume confidence sets for multinomial parameters.
problem Determining if minimum-volume confidence sets for multinomial outcomes are disjoint.
method Enumerating and covering the continuous regions of the exact p-value function to study the geometry of minimum-volume confidence sets.
result The geometry of minimum-volume confidence sets for multinomial parameters is studied, providing insights into their structure and properties.
Building on previous results on the quadratic helicity in magnetohydrodynamics (MHD) we investigate particular minimum helicity states. Those are eigenfunctions of the curl operator and are shown to constitute solutions of the quasi-stationary incompressible ideal MHD equations. We then show that these states have inde…
The paper calculates minimum Dehn colors for knots using symmetric local biquandle cocycles.
problem Determining the minimum number of Dehn colors for knots.
method Using symmetric local biquandle cocycle invariants to evaluate minimum Dehn colors.
result There exist knots distinguished by minimum numbers of Dehn colors.
Inference for normal and Monte Carlo distributions using minimum relative entropy.
problem Inference from partial information on expectations and covariances.
method Minimum relative entropy sub-manifolds, analytical formulas, Monte Carlo simulations.
result Improved numerical implementation for inference from partial information.
ML helps select variables for minimum-variance portfolios, reducing risk and improving performance.
problem Optimizing minimum-variance portfolios with relevant predictors.
method Parameterized minimum-variance portfolio weights using a large pool of firm-level characteristics and their transformations.
result ML-selected predictors lead to lower risk and better performance in minimum-variance portfolios.
We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time windo…
Paper proves edge-connectivity equals minimum degree for graphs with non-negative curvature.
problem Edge-connectivity vs. minimum degree in graphs with non-negative curvature.
method Analyzes finite connected graphs with non-negative Lin-Lu-Yau curvature.
result Edge-connectivity equals minimum degree for graphs with non-negative curvature.
New approach finds minimum width for deep, narrow MLPs.
problem Finding the minimum width for deep, narrow MLPs to approximate continuous functions.
method Proposes a framework to simplify finding minimum width into determining a geometrical function w(dx,dy) based on input and output dimensions. result Proves that w(dx,dy) equals the optimal minimum width for deep, narrow MLPs to achieve universality. We consider the relations between different measures of complexity for free homotopy classes of curves on a surface Σ, including the minimum number of self-intersections, the minimum length of the words representing them in a geometric presentation of π1(Σ), and the minimum degree of the coverings of Σ to which …
Unified framework for geometric computation of minimum-area homotopy.
problem Computing the minimum homotopy area of a closed curve.
method Unified combinatorial word approach combining geometric and algebraic methods.
result Unified geometric proof and constructive algorithm for minimum area homotopy.
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
In this paper we study the minimum dilatation pseudo-Anosov mapping classes coming from fibrations over the circle of a single 3-manifold, the mapping torus for the "simplest pseudo-Anosov braid". The dilatations that arise include the minimum dilatations for orientable mapping classes for genus g=2,3,4,5,8 as well as …
Originally, the SW-equations discovered by Seiberg-Witten are 1st-order PDE, which solutions (A,φ), with φ\ne 0, are known as SW-monopoles. It is known that the solutions of these 1st-order eq correspond to the minimum of SW-functional. However, it is not true, that for all spin^{c} class α, the minimum is always attai…
Investigates the long-only minimum variance portfolio in factor models.
problem Understanding the long-only minimum variance portfolio in factor models.
method Investigates the long-only global minimum variance portfolio in a factor model of returns, providing explicit and geometric descriptions for different factor models.
result Provides rigorous and explicit descriptions of the long-only solution in terms of covariance matrix parameters and geometric descriptions for multiple factors.
Paper shows minimum 10 vertices for hyperbolic origami 2-torus.
problem Finding minimum vertices for hyperbolic origami 2-torus.
method Geodesic triangulation and isometric polyhedral embedding.
result 10 vertices are the minimum required for a hyperbolic origami 2-torus.
Defines MER for Bayesian learning, a gap between achievable and optimal performance.
problem Analyzing the best performance of Bayesian learning under generative models.
method Two methods for deriving upper bounds for MER: conditional mutual information and minimum estimation error.
result Quantifies the rate at which MER decays to zero with more data and relates it to model richness.
We prove that every simple graph of order 12 which has minimum degree 6 contains a K_6 minor.
Mathematical framework for minimum enclosing ball problem.
problem Determining the smallest sphere enclosing a set in d-dimensional space.
method Theoretical framework based on enclosing and partitioning theorems.
result Bounds and relations between circumradius, inradius, diameter, and width.
Consider the problem of estimating the minimum entropy of pseudo-Anosov maps on a surface of genus g with n punctures. We determine the behaviour of this minimum number for a certain large subset of the (g,n) plane, up to a multiplicative constant. In particular it has been shown that for fixed n, this minimum …
Study on folded ribbon knots and their minimum length.
problem Finding the minimum length of folded ribbon knots.
method Using Kauffman's model of folded ribbon knots and analyzing their properties.
result Proved bounds on the minimum folded ribbonlength for various types of knots.
New framework for DNN training guarantees convergence to global minimum.
problem Training deep neural networks to converge to global minimum.
method Reformulated minimization problem with recursive algorithmic framework, using bounded style assumptions.
result Convergence to an ε-(global) minimum with O(1/ε^3) gradient computations.
Even knots with more than 30 crossings are not fertile.
problem Understanding fertility in knots with specific crossing numbers.
method Analyzing minimum crossing number diagrams and changing over-under information.
result Even knots with more than 30 crossings cannot be obtained from a minimum crossing number diagram by changing over-under information.
Optimal estimator derived for partially observable LTI systems.
problem Optimal estimator for partially observable LTI systems.
method State-space representation for derivation of optimal estimator.
result Derivation of minimum error variance estimator for partially observable LTI systems.
We study the generalization properties of minimum-norm solutions for three over-parametrized machine learning models including the random feature model, the two-layer neural network model and the residual network model. We proved that for all three models, the generalization error for the minimum-norm solution is compa…
Two types of 4-manifolds disagree on minimum Euler characteristic.
problem Disagreement between topological and smooth 4-manifolds.
method Comparison of topological and smooth 4-manifolds with a fixed fundamental group.
result Minimum Euler characteristic differs between topological and smooth 4-manifolds.
Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.
problem Determining the minimum vertex degree for non-negative Lin-Lu-Yau curvature.
method Investigation of Ollivier-Ricci curvature and Lin-Lu-Yau modification on locally finite graphs.
result Lower bound on minimum vertex degree ensuring non-negative Lin-Lu-Yau curvature.
Study minimum ribbonlength of immersed flat knots and links.
problem Finding the minimum ribbonlength for immersed planar knots and links.
method Embedding into disk diagram space to find length minimizers.
result Computed minimal ribbonlength for some knot and link diagrams.
Hill-ADAM optimizes loss landscapes by exploring state space deterministically.
problem Escaping local minima in loss landscapes.
method Hill-ADAM alternates between minimizing and maximizing error to explore the loss space.
result Hill-ADAM finds the global minimum state in loss landscapes.
Exponential models of distributions are widely used in machine learning for classiffication and modelling. It is well known that they can be interpreted as maximum entropy models under empirical expectation constraints. In this work, we argue that for classiffication tasks, mutual information is a more suitable informa…
Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minima while eventually visiting a global minimum on longer time-scales. LD is based on the first-order Langevin diffusion which is reversible in time. We study two variants th…
A wide range of fundamental machine learning tasks that are addressed by the maximum a posteriori estimation can be reduced to a general minimum conical hull problem. The best-known solution to tackle general minimum conical hull problems is the divide-and-conquer anchoring learning scheme (DCA), whose runtime complexi…
We show that the minimum of asymptotic translation lengths of all point-pushing pseudo-Anosov maps on any one punctured Riemann surface is one.