arXiv research

Estimates simplicial volume for complex hyperbolic surfaces.

Novikov theorem extended to rational Pontryagin classes for cyclic group $C_4$.

The structure set $\ST^{TOP}(M)$ of an $n$-dimensional topological manifold $M$ for $n \geqslant 5$ has a homotopy invariant functorial abelian group structure, by the algebraic version of the Browder-Novikov-Sullivan-Wall surgery theory. An element $(N,f) \in \ST^{TOP}(M)$ is an equivalence class of $n$-dimensional ma…

Class ambiguity is typical in image classification problems with a large number of classes. When classes are difficult to discriminate, it makes sense to allow k guesses and evaluate classifiers based on the top-k error instead of the standard zero-one loss. We propose top-k multiclass SVM as a direct method to optimiz…

In order to push the performance on realistic computer vision tasks, the number of classes in modern benchmark datasets has significantly increased in recent years. This increase in the number of classes comes along with increased ambiguity between the class labels, raising the question if top-1 error is the right perf…

Paper introduces a new loss function for deep imbalanced classification.

Proposes top-label calibration and M2B framework for multiclass to binary calibration.

We study the bounded fundamental class in the top dimensional bounded cohomology of negatively curved manifolds with infinite volume. We prove that the bounded fundamental class of $M$ vanishes if $M$ is geometrically finite. Furthermore, when $M$ is a $\mathbb{R}$-rank one locally symmetric space, we show that the bou…

Paper analyzes trade-offs in top-k classification accuracies and proposes a new loss function.

Injective map from top cohomology of moduli spaces to handlebodies.

Study on top-$k$ classification with new loss functions and algorithms.

Reduces high granularity and dimensionality in hierarchical categorical variables.

We show that every Lie algebroid $A$ over a manifold $P$ has a natural representation on the line bundle $Q_A = \wedge^{top}A \otimes \wedge^{top} T^*P$. The line bundle $Q_A$ may be viewed as the Lie algebroid analog of the orientation bundle in topology, and sections of $Q_A$ may be viewed as transverse measures to $…

New scoring rules compare probabilistic top lists in classification.

We show that for closed orientable manifolds the $k$-dimensional stable systole admits a metric-independent volume bound if and only if there are cohomology classes of degree $k$ that generate cohomology in top-degree. Moreover, it turns out that in the nonorientable case such a bound does not exist for stable systoles…

Establishing criteria for top cell inertness in complexes.

For information retrieval and binary classification, we show that precision at the top (or precision at k) and recall at the top (or recall at k) are maximised by thresholding the posterior probability of the positive class. This finding is a consequence of a result on constrained minimisation of the cost-sensitive exp…

It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré Duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation betwee…

We show that the Debarre-de Jong conjecture that the Fano scheme of lines on a smooth hypersurface of degree at most n in n-dimensional projective space must have its expected dimension, and the Beheshti-Starr conjecture that bounds the dimension of the Fano scheme of lines for hypersurfaces of degree at least n in n-d…

The study finds obstructions for certain Weyl curvature tensors on manifolds.

For any compact oriented manifold $M$, we show that that the top degree multi-vector fields transverse to the zero section of $\wedge^{\text{top}}TM$ are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of its zero locus and a finite number of numerical invariants. Th…

The paper analyzes top-k classification and proposes consistent loss functions.

New method calculates Thurston norm for 3-manifolds with toroidal boundaries.

Negative curvature manifolds have vanishing bounded volume class if and only if Cheeger constant is positive.

We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ri…

The topological fundamental group $π_{1}^{top}$ is a topological invariant that assigns to each space a quasi-topological group and is discrete on spaces which are well behaved locally. For a totally path-disconnected, Hausdorff, unbased space $X$, we compute the topological fundamental group of the "hoop earring" spac…

New findings on Johnson kernel's top homology group.

DS-Softmax speeds up softmax inference by learning sparse experts.

The study restricts circle actions on certain manifolds to dimensions 4, 8, and 16.

Study approximates top Lyapunov exponents for surface mapping classes.

Study top dimensional cohomology groups of congruence subgroups of SL_n(Z).

The paper proves the existence of a special Kähler metric on a minimal ruled surface.

The Maskit embedding M of a surface Σis the space of geometrically finite groups on the boundary of quasifuchsian space for which the `top' end is homeomorphic to Σ, while the `bottom' end consists of two triply punctured spheres, the remains of Σwhen two fixed disjoint curves have been pinched. As such representations…

Let $M$ be a compact connected manifold of dimension $n$ endowed with a conformal class $C$ of Riemannian metrics of volume one. For any integer $k\geq0$, we consider the conformal invariant $λ_k ^c (C)$ defined as the supremum of the $k$-th eigenvalue $λ_k (g)$ of the Laplace-Beltrami operator $Δ_g$, where $g$ runs ov…

Completed volumes match with combinatorial classes of the double ramification cycle.

Improved uncertainty estimates for classification models reduce calibration error.

A framework for binary classification on top samples.

Similar simplices can be inscribed in most smoothly embedded spheres.

New configuration space integrals show nontrivial formal smooth structures on 4-manifold bundles.

Extends linear classification framework to nonlinear SVM-based ranking problems.

The paper addresses calibration in label ranking, a structured prediction task.

DeepTopPush improves accuracy at the top for complex classification tasks.

Introduces top-$k$ regularization for better feature selection in machine learning.

Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large scale hierarchical classification. However, accuracy of top-down approaches is poor…

Bottom-up algorithms outperform top-down in hierarchical community detection at intermediate levels.

This research uses Siamese networks to identify partial mouse brain images from the Allen atlas.

The study uncovers the breakdown of Gaussian universality in high-dimensional empirical risk minimization.

In (\cite{zhang2014nonlinear,zhang2014nonlinear2}), we have viewed machine learning as a coding and dimensionality reduction problem, and further proposed a simple unsupervised dimensionality reduction method, entitled deep distributed random samplings (DDRS). In this paper, we further extend it to supervised learning …