Optimizing machine learning with poor starting points using Nesterov acceleration.
problem The challenge of achieving good performance with machine learning models starting from suboptimal initial conditions.
method Combining Robbins and Monro method for optimal starting points with Nesterov acceleration for poor starting points, especially with minibatch training.
result Nesterov acceleration can improve performance even with poor starting points, especially in the initial iterations.
Reweighted ALPS improves sampling from multimodal distributions using warm start points.
problem Sampling from multimodal distributions is hard due to exponential mixing times.
method Introduces Reweighted ALPS, a modified Annealed Leap-Point Sampler that uses warm start points.
result First polynomial-time bound for Re-ALPS in a general setting, under a natural assumption.
Bayesian optimization improves multi-start global optimization.
problem Global optimization challenges in real-world applications.
method Bayesian optimization framework to determine local search starting points.
result Bayesian optimization enhances the efficiency of multi-start local searches.
New method achieves optimal sample complexity without warm-start in bilevel optimization.
problem Optimizing smooth objective functions with fixed point constraints in meta-learning and equilibrium models.
method Fixed point iterations at lower-level and projected inexact gradient descent at upper-level.
result Achieves near optimal sample complexity O(ε−2) and ildeO(ε−1) samples. We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening…
New algorithms use outsourced data to improve model training efficiency.
problem Limited computational resources restrict model training efficiency.
method Simulation-based algorithms using outsourced data to find good initial points.
result The algorithms can find good initial points with high probability under suitable conditions.
Warm-start Bayesian optimization for related problems.
problem Optimizing stochastic simulators over multiple time periods or markets.
method Develops a joint statistical model and uses value of information to recommend evaluation points.
result Reduces solution time for sequences of related optimization problems.
A new algorithm computes elastic shape distances between curves efficiently.
problem Computing elastic shape distances between curves in high dimensions.
method Dynamic Programming for optimal diffeomorphisms and Kabsch-Umeyama algorithm for optimal rotation matrices.
result Efficient computation of elastic shape distances with improved efficiency for closed curves.
Using the topologist sine curve we present a new functorial construction of cone-like spaces, starting in the category of all path-connected topological spaces with a base point and continuous maps, and ending in the subcategory of all simply connected spaces. If one starts by a noncontractible n-dimensional Peano cont…
John's walk uses John's ellipsoids for uniform sampling from convex bodies.
problem Drawing uniform random samples from convex bodies efficiently.
method Affine-invariant random walk using John's ellipsoids for proposal distribution.
result The random walk mixes in O(n7) steps from a warm start. A new FFT-based method for fast rigid alignment of 2D closed curves.
problem Rigid alignment of 2D closed curves with application to shape analysis.
method FFT-based algorithm for optimal rigid alignment of closed curves with O(N log N) complexity.
result Order of magnitude speed-up in curve alignment compared to previous methods.
WSD uses a deterministic model to accelerate diffusion-based sampling.
problem Slow refinement process in diffusion models.
method Warm-start model that predicts an informed prior conditioned on input context.
result Significantly reduces the number of diffusion steps required for realistic samples.
New proof shows nonholonomic motions are geodesics, minimizing distance.
problem Nonholonomic motion equations are not variational.
method Proved geodesic property of nonholonomic trajectories using Riemannian metrics.
result Nonholonomic motions minimize distance in their manifold.
In this paper we provide the small-time heat kernel asymptotics at the cut locus in three relevant cases: generic low-dimensional Riemannian manifolds, generic 3D contact sub-Riemannian manifolds (close to the starting point) and generic 4D quasi-contact sub-Riemannian manifolds (close to a generic starting point). As …
Smooth 3D flows from non-smooth starting points.
problem Creating smooth Ricci flows from non-smooth initial conditions.
method Generalized singular Ricci flow applied to 3D complete manifolds.
result Existence of smooth Ricci flows starting from non-smooth initial conditions.
Establishes smooth Ricci flows from convex surfaces in 3D space.
problem Existence and uniqueness of Ricci flow starting from convex surfaces.
method Smooth Ricci flows starting from smooth convex surfaces.
result Uniform convergence of metrics to initial convex surface.
Paper introduces active and passive causal inference techniques.
problem Causal inference in machine learning.
method Categorizes causal inference techniques into active and passive approaches.
result Describes and discusses various causal inference methods.
Superposed Hawkes processes improve risk bounds and solve cold-start issues.
problem Improving risk bounds in temporal point processes.
method Least squares estimation of superposed Hawkes processes.
result Superposed Hawkes processes tighten risk bounds under certain conditions.
Unified framework for long-range and cold-start seasonal forecasts.
problem Forecasting seasonal profiles with limited historical data.
method Combining high-dimensional regression and matrix factorization.
result Framework accurately forecasts seasonal profiles on multiple datasets.
Consider a broken geodesics α([0,l]) on a compact Riemannian manifold (M,g) with boundary of dimension n≥3. The broken geodesics are unions of two geodesics with the property that they have a common end point. Assume that for every broken geodesic α([0,l]) starting at and ending to the boundary ∂M…
FAB-COST improves cold-start recommendation accuracy with less data.
problem Cold-start problem in recommendation systems.
method Contextual bandit algorithm using Expectation Propagation and Assumed Density Filtering.
result FAB-COST outperforms Laplace approximation on real data.
The Riemannian submersion π:SO0(1,n)→Hn is a principal bundle and its fiber at π(e) is the imbedding of SO(n) into SO0(1,n), where e is the identity of both SO0(1,n) and SO(n). In this study, we associate a curve, starting from the identity, in $\…
Research tackles unequal length time series for classification.
problem Unequal length time series in real-world data.
method Identified and evaluated two classes of unequal length mechanisms.
result Practical recommendations for handling unequal length time series.
Warm-starting neural networks can lead to worse performance than fresh starts.
problem Warm-starting neural networks can degrade performance compared to fresh starts.
method Analyzed and provided a simple trick to overcome the degradation of warm-starting.
result A simple trick can overcome the degradation of warm-starting in several important situations.
Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphi…
On a Riemannian surface, the energy of a map into a Riemannian manifold is a conformal invariant functional, and its critical points are the harmonic maps. Our main result is a generalization of this theorem when the starting manifold is even dimensional. We then build a conformal invariant functional for the maps betw…
In 1931 Elie Cartan constructed a geometry which was rarely considered. Cartan proposed a way to define an infinitesimal metric ds starting from a variational problem on hypersurfaces in an n-dimensional manifold M. This distance depends not only of the point $\textsc{m}\in\mathcal{M}$ but on the orient…
Smooth Ricci flow from conical singularities with curvature decay.
problem Ricci flow on manifolds with isolated conical singularities.
method Smooth Ricci flow starting from conical metrics with curvature decay.
result Existence of smooth Ricci flow with curvature decay and isolated singularities.
Given a configuration x of n distinct points in hyperbolic 3-space H3, Michael Atiyah associated n polynomials p1,…,pn of a variable t∈CP1, of degree n−1, and conjectured that they are linearly independent over C, no matter which configuration x one s…
Developed an efficient iterative algorithm for SVI model.
problem SVI model's optimizer's strong dependence on input starting point.
method Fixed-point and least-square optimizer.
result Convergence results for fixed-point iterative algorithm in certain situations.
Paper proposes a simple estimator for DPP correlation kernels.
problem Estimating the correlation kernel matrix of DPPs.
method Closed-form estimator for correlation kernel, easy to implement.
result Consistency and asymptotic normality of the estimator proved.
A simple patch copying method reduces black-box adversarial attack queries by 81%.
problem The effectiveness of black-box adversarial attacks depends on the initialization method.
method Copying small patches from other images as initialization points.
result Reduces the number of queries required for a state-of-the-art Boundary Attack by 81%
Study pinched submanifolds in symmetric spaces, proving flow behaviors.
problem Analyzing mean curvature flow in symmetric spaces.
method Proved flow behaviors for pinched submanifolds in rank one symmetric spaces.
result Submanifolds in symmetric spaces either collapse or converge smoothly.
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential g…
Study shows asymptotic behavior of metric near singular points of a Monge-Ampère equation.
problem Analyzing singularities of a metric defined by a Monge-Ampère equation.
method Using the tropical Monge-Ampère equation and asymptotic analysis.
result The solution is not C1,1 across singular points and asymptotic to the Gross-Wilson metric. Improved log-concave sampling to O(d1/2) with warm starts.
problem Sampling from strongly log-concave distributions efficiently.
method Warm starts and discretized underdamped Langevin diffusion.
result Achieved O(d1/2) complexity for high-accuracy sampling. Backplay improves RL efficiency with demonstrations.
problem Improving sample efficiency in sparse reward environments.
method Constructs a curriculum using a single demonstration to start training near the end of the demo.
result Backplay outperforms other methods in grid worlds and a complex game.
We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable semigroups of completely bounded mappings. We then explore several applications of that method to injective operator spaces, fixed points of completely contractive mappings, Toeplitz operators, dy…
We prove that the Ricci flow on CP^n blown-up at one point starting with any rotationally symmetric Kahler metric must develop Type I singularities. In particular, if the total volume does not go to zero at the singular time, the parabolic blow-up limit of the Type I Ricci flow along the exceptional divisor is a comple…
We introduce the \emph{metric spectrum}, which measures the exponential rate of approximation to an isolated invariant set of points starting in its stable set, and relate it to the Lyapunov spectrum. We determine the metric spectrum of each Morse component of the finest Morse decomposition of a linear induced flow on …
In this paper, several modifications are introduced to the functional approximation method iterLap to reduce the approximation error, including stopping rule adjustment, proposal of new residual function, starting point selection for numerical optimisation, scaling of Hessian matrix. Illustrative examples are also prov…
Study properties of self-similar continua with finite intersection property.
problem Characterize self-similar continua with finite intersection property.
method Prove intersection graph criterion, finite order theorem, and parameter matching theorem.
result All Jordan arcs starting from a intersection point in such continuum on a plane should have the same slope parameter at that point.
We calculate moments of decision times for diffusion models.
problem Modeling decision times in cognitive tasks.
method Derive expressions for the first three moments of decision times.
result Explicit formulae for third and higher moments are provided.
We find the complete set of fundamental invariants for systems of ordinary differential equations of order ≥4 under the group of point transformations generalizing similar results for contact invariants of a single ODE and point invariants of systems of the second and the third order. It turns out that starting fr…
CDLF predicts product life-cycles in cold-start phases with high accuracy.
problem Forecasting new products in early phases when data is scarce.
method Conditional Diffusion Life-cycle Forecaster (CDLF) combining static descriptors, reference trajectories, and new observations.
result CDLF outperforms classical models in accuracy and probabilistic forecasting.
We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main four theorems on the theory of deformations of quadrics and Bianchi's treatment of the …
We will discuss some sharp estimates for CMC graphs in a Riemannian 3-manifold MxR whose boundary is contained in a slice. We will start by giving sharp lower bounds for the geodesic curvature of the boundary and improve these bounds when assuming additional restrictions on the maximum height that such a surface reache…
The paper estimates the volume of singular points in evolving surfaces.
problem Estimating the volume of singular points in evolving surfaces.
method Uniform and sharp volume estimates for singular sets of mean curvature flows.
result Uniform and sharp volume estimates for singular sets of mean curvature flows.