arXiv research

New invariant computed for Brieskorn homology spheres.

We give a complete description of the closure of the space of one-generator closed subgroups of PSL2(R) for the Chabauty topology, by computing explicitly the matrices associated with elements of Aut(D) = PSL2(R), and finding quantities parametrizing the limit cases. Along the way, we investigate under what conditions …

We study surfaces of constant mean curvature which are invariant by oneparameter group of either rotational isometries or parabolic isometries, immersed into the homogeneous manifold PSL2(R,tau). Also, we give some applications.

We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the …

Study on homological Dehn functions of groups of type $FP_2$.

Minimal annuli constructed in PSL2 via variational method.

We construct uncountably many discrete groups of type $FP$; in particular we construct groups of type $FP$ that do not embed in any finitely presented group. We compute the ordinary, $\ell^2$- and compactly-supported cohomology of these groups. For each $n\geq 4$ we construct a closed aspherical $n$-manifold that admit…

FP uses random projections to train networks without feedback, achieving comparable performance to backpropagation.

GGFPS improves model performance by sampling molecules more efficiently.

In this paper we create many examples of hyperbolic groups with subgroups satisfying interesting finiteness properties. We give the first examples of subgroups of hyperbolic groups which are of type $FP_2$ but not finitely presented. We give uncountably many groups of type $FP_2$ with similar properties to those subgro…

The study examines discrete subgroups of PSL2 over non-archimedean fields.

FP-UCB algorithm achieves bounded regret for finitely parameterized multi-armed bandits.

New method improves feature selection by integrating stability paths.

Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, the performance gain is at the expense of a reduction in float…

The paper uses Tannakian reconstruction to understand hyperbolic log-orbi curves.

L-CNNs approximate gauge actions, revealing fixed points with no lattice artifacts.

Formanek and Procesi have demonstrated that Aut(F_n) is not linear for n >2. Their technique is to construct nonlinear groups of a special form, which we call FP-groups, and then to embed a special type of automorphism group, which we call a poison group, in Aut(F_n), from which they build an FP-group. We first prove t…

In this paper, we study the interaction between the geodesic orbit (g.o.~in short) property and certain flag curvature conditions. A Finsler manifold is called g.o.~if each constant speed geodesic is the orbit of a one-parameter subgroup. Besides the non-negatively curved condition, we also concern the (FP) condition f…

We implement a systematic asset allocation model using the Historical Simulation with Flexible Probabilities (HS-FP) framework developed by Meucci. The HS-FP framework is a flexible non-parametric estimation approach that considers future asset class behavior to be conditional on time and market environments, and deriv…

Since machine learning models have been applied to neuroimaging data, researchers have drawn conclusions from the derived weight maps. In particular, weight maps of classifiers between two conditions are often described as a proxy for the underlying signal differences between the conditions. Recent studies have however…

Previously one of the authors constructed uncountable families of groups of type $FP$ and of $n$-dimensional Poincaré duality groups for each $n\geq 4$. We strengthen these results by showing that these groups comprise uncountably many quasi-isometry classes. We deduce that for each $n\geq 4$ there are uncountably many…

In this paper, we introduce the flag-wise positively curved condition for Finsler spaces (the (FP) Condition), which means that in each tangent plane, we can find a flag pole in this plane such that the corresponding flag has positive flag curvature. Applying the Killing navigation technique, we find a list of compact …

New work shows FP potential monotonicity equals low-degree polynomial estimators limits.

New representation of PSL2(R) on infinite hyperbolic space via convex bodies.

AI agent plays CSGO deathmatch with human-like style.

We extend first-order model agnostic meta-learning algorithms (including FOMAML and Reptile) to image segmentation, present a novel neural network architecture built for fast learning which we call EfficientLab, and leverage a formal definition of the test error of meta-learning algorithms to decrease error on out of d…

This paper extends FP's method to complex hyperbolic branched covers to find Einstein metrics.

The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the r…

WILD-SCAV benchmarks AI in complex 3D FPS environments.

FP-BMA improves generalization by encouraging flat posteriors in Bayesian Model Averaging.

Develops a neural network approach to solve inverse stochastic problems from particle observations.

The paper classifies PD_4-complexes based on their fundamental group properties.

Prognostics and Health Management (PHM) is an emerging engineering discipline which is concerned with the analysis and prediction of equipment health and performance. One of the key challenges in PHM is to accurately predict impending failures in the equipment. In recent years, solutions for failure prediction have evo…

One of the key challenges in predictive maintenance is to predict the impending downtime of an equipment with a reasonable prediction horizon so that countermeasures can be put in place. Classically, this problem has been posed in two different ways which are typically solved independently: (1) Remaining useful life (R…

This is a survey on the global theory of constant mean curvature surfaces in Riemannian homogeneous 3-manifolds. These ambient 3-manifolds include the eight canonical Thurston 3-dimensional geometries, i.e. R3, H3, S3, H2 \times R, S2 \times R, the Heisenberg space Nil3, the universal cover of PSL2(R) and the Lie group…

Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.

Hougthon's groups H_n is a family of groups where each H_n consists of `translations at infinity' on n rays of discrete points emanating from the origin on the plane. Brown shows H_n has type FP_n-1 but not FP_n by constructing infinite dimensional cell complex on which H_n acts with certain conditions. We modify his i…

A novel score-based method solves high-dimensional Fokker-Planck equations with improved accuracy and speed.

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.

New method learns diffusion transition density for Bayesian inference.

The paper defines Benoist-Hulin groups and explores their properties.

Winograd convolution is widely used in deep neural networks (DNNs). Existing work for DNNs considers only the subset Winograd algorithms that are equivalent to Toom-Cook convolution. We investigate a wider range of Winograd algorithms for DNNs and show that these additional algorithms can significantly improve floating…

If S is a subgroup of a direct product of two limit groups, and S is of type FP(2) over the rationals, then S has a subgroup of finite index that is a direct product of at most two limit groups.

We show that the Basilica Thompson group introduced by Belk and Forrest is not finitely presented, and in fact is not of type FP_2. The proof involves developing techniques for proving non-simple connectedness of certain subcomplexes of CAT(0) cube complexes.

We study the asymptotic growth of homology groups and the cellular volume of classifying spaces as one passes to normal subgroups $G_n<G$ of increasing finite index in a fixed finitely generated group $G$, assuming $\bigcap_n G_n =1$. We focus in particular on finitely presented residually free groups, calculating thei…

New method finds Fuchsian representations dominating others in surface group representations.

New optimization method improves AUC for binary classification and changepoint detection.

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on the global convergence. Sparse PCA algorithms based on a convex formulation, for…