arXiv research

Study L^2-Betti numbers in prime characteristic for a conjecture about 2-complex towers.

Study shows some contractible complexes can't have certain immersions.

Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…

In this paper we extend Witten-Helffer-Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor-Turaev torsi…

This paper uncovers the low-rank structure of neural network Hessians.

Given a Kähler fiber space $p:X\to Y$ whose generic fiber is of general type, we prove that the fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on the relative canonical bundle $K_{X/Y}$ of $p$. We also propose a conjectural generalization of this result for relative twisted Kähler-Eins…

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 …

The paper proves Sard's theorem for polynomial maps in infinite dimensions.

Given a sequence of regular finite coverings of complete Riemannian manifolds, we consider the covering solenoid associated with the sequence. We study the leaf-wise Laplacian on the covering solenoid. The main result is that the spectrum of the Laplacian on the covering solenoid equals the closure of the union of the …

We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are separable. A consequence is that closed hyperbolic 3-manifolds have finite-sheeted Haken covers, which resolves the virtual Haken …

We give an alternate proof of Wise's Malnormal Special Quotient Theorem (MSQT), avoiding cubical small cancellation theory. We also show how to deduce Wise's Quasiconvex Hierarchy Theorem from the MSQT and theorems of Hsu--Wise and Haglund--Wise.

We point out a new view on slow invariant manifolds (SIM) in dynamical systems which departs from a purely geometric covariant characterization implying coordinate independency. The fundamental idea is to treat the SIM as a well-defined geometric object in phase space and elucidate characterizing geometric properties t…

Many real datasets contain values missing not at random (MNAR). In this scenario, investigators often perform list-wise deletion, or delete samples with any missing values, before applying causal discovery algorithms. List-wise deletion is a sound and general strategy when paired with algorithms such as FCI and RFCI, b…

xDeepInt learns both vector-wise and bit-wise feature interactions.

We prove a freeness theorem for low-rank subgroups of one-relator groups. Let $F$ be a free group, and let $w\in F$ be a non-primitive element. The primitivity rank of $w$, $π(w)$, is the smallest rank of a subgroup of $F$ containing $w$ as an imprimitive element. Then any subgroup of the one-relator group $G=F/\langle…

Proposes SROF for row-wise fusion in federated learning for multivariate responses.

Improves early stopping in deep networks by adjusting stepsizes.

Defines fiber-wise linear differential operators on vector bundles.

New bounds show limitations of sample-wise information-theoretic generalization.

Layer-wise preconditioning methods improve neural network optimization and feature learning.

Answering a question asked by Agol and Wise, we show that a desired stronger form of Wise's malnormal special quotient theorem does not hold. The counterexamples are generalizations of triangle groups, built using the Ramanujan graphs constructed by Lubotzky--Phillips--Sarnak.

Proposes QEP to mitigate quantization error propagation in layer-wise post-training quantization.

The study proves Gaussian universality of deep random features learning.

The paper proves Gorenstein contractions for multiscale differentials on nodal curves.

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece $γ$ of the boundary must be algebraic and eith…

In this on-going work, I explore certain theoretical and empirical implications of data transformations under the PCA. In particular, I state and prove three theorems about PCA, which I paraphrase as follows: 1). PCA without discarding eigenvector rows is injective, but looses this injectivity when eigenvector rows are…

A new conformal prediction framework for two-stage models identifies stage-wise uncertainty.

Unified framework LPCD optimizes quantization of complex submodules.

We develop and analyze efficient "coordinate-wise" methods for finding the leading eigenvector, where each step involves only a vector-vector product. We establish global convergence with overall runtime guarantees that are at least as good as Lanczos's method and dominate it for slowly decaying spectrum. Our methods a…

Random layer-wise pruning profiles are as effective as metric-based ones for various datasets.

Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of the existing algorithms tend to investigate the ensemble information at the obje…

This paper explains double descent in linear neural networks, identifying new factors.

Layer-wise networks have a closed-form solution and a stopping criterion.

The paper compares two methods for handling missing data in causal discovery.

A Finsler space $(M,F)$ is called flag-wise positively curved, if for any $x\in M$ and any tangent plane $\mathbf{P}\subset T_xM$, we can find a nonzero vector $y\in \mathbf{P}$, such that the flag curvature $K^F(x,y, \mathbf{P})>0$. Though compact positively curved spaces are very rare in both Riemannian and Finsler g…

Layer-wise networks have a closed-form solution and a stopping criterion.

New method quantifies uncertainty at class level for better decision-making.

New methods estimate point-wise dependency from neural MI models.

Using recent results of Agol, Przytycki-Wise and Wise we show that twisted Alexander polynomials detect the Thurston norm of any irreducible 3-manifold which is not a closed graph manifold.

AdaTrans adapts to feature and sample transfer in high-dimensional regression.

This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample complexity bound that is order-wise optimal with respect to the incoherence paramete…

Few-shot learning aims to train efficient predictive models with a few examples. The lack of training data leads to poor models that perform high-variance or low-confidence predictions. In this paper, we propose to meta-learn the ensemble of epoch-wise empirical Bayes models (E3BM) to achieve robust predictions. "Epoch…

Linear NDCG is used for measuring the performance of the Web content quality assessment in ECML/PKDD Discovery Challenge 2010. In this paper, we will prove that the DCG error equals a new pair-wise loss.

BlockEcho method improves imputation of block-wise missing data.

StrTransformer recovers sources without labels by optimizing latent matrices and enforcing structural constraints.

Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities.

In the classical best arm identification (Best-$1$-Arm) problem, we are given $n$ stochastic bandit arms, each associated with a reward distribution with an unknown mean. We would like to identify the arm with the largest mean with probability at least $1-δ$, using as few samples as possible. Understanding the sample c…

New adversarial attack method based on deep feature distributions.