arXiv research

Let $(M,g,\si)$ be a compact spin manifold of dimension $n \geq 2$. Let $λ_1^+(\tilde{g})$ be the smallest positive eigenvalue of the Dirac operator in the metric $\tilde{g} \in [g]$ conformal to $g$. We then define $\lamin(M,[g],\si) = \inf_{\tilde{g} \in [g]} λ_1^+(\tilde{g}) \Vol(M,\tilde{g})^{1/n} $. We show that $…

Develops a more powerful selective inference method for stepwise feature selection.

New algorithm improves signal reconstruction from noisy measurements with side information.

The moduli space of holomorphic fiber bundles ${\cal M}_n(\Si)$ over a compact Riemann surface $\Si$ is considered. A formula for the regularised determinant and an other for the symplectic form at trivial bundle are proposed.

We propose a novel adversarial speaker adaptation (ASA) scheme, in which adversarial learning is applied to regularize the distribution of deep hidden features in a speaker-dependent (SD) deep neural network (DNN) acoustic model to be close to that of a fixed speaker-independent (SI) DNN acoustic model during adaptatio…

This paper ranks pre-trained DNNs using a novel SI measure.

New method reduces computational cost for selective inference.

Paper extends SI method for detecting CPs in complex systems' frequency domain.

In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding of a numerical algorithm into a neural network form, resulting in a substantial …

SI-CLAD improves clustering-based anomaly detection by controlling false positives.

Develops new reinforcement learning methods for complex constrained decision-making problems.

Let SI(S_g) denote the hyperelliptic Torelli group of a closed surface S_g of genus g. This is the subgroup of the mapping class group of S_g consisting of elements that act trivially on H_1(S_g;Z) and that commute with some fixed hyperelliptic involution of S_g. We prove that the cohomological dimension of SI(S_g) is …

A k-submanifold L of an open n-manifold M is called weakly integrable (WI) [resp. strongly integrable (SI)] if there exists a submersion Φ:M\to R^{n-k} such that L\subset Φ^{-1}(0) [resp. L= Φ^{-1}(0)]. In this work we study the following problem, first stated in a particular case by Costa et al. (Invent. Math. 1988): …

The assumption in the main result of [Peter W. Michor: Basic Differential Forms for Actions of Lie Groups, Proc. AMS 124, 5 (1996) 1633-1642] is removed. Thus: A section of a Riemannian $G$-manifold $M$ is a closed submanifold $\Si$ which meets each orbit orthogonally. It is shown that the algebra of $G$-invariant diff…

In this paper we consider on a complete Riemannian manifold $M$ an immersed totally geodesic hypersurface $\Si$ existing together with an immersed submanifold $N$ without focal points. No curvature condition is needed. We obtained several connectedness results relating the topologies of $M$ and $\Si$ which depend on th…

We study minimal graphic functions on complete Riemannian manifolds $\Si$ with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with …

Enhances selective inference for generalized lasso using parametric programming.

LSI enables joint learning of latent variables and generative models.

Paper proposes a new method for selective inference in robust regression.

This work uses a SI-DNN to predict AC-OPF solutions efficiently.

Study uses RNN to detect CPs with SI to control false positives.

Proposes a new method to improve selective inference for Lasso models.

New method predicts unobserved interactions between sets of elements.

Study on second homology group of genus 3 hyperelliptic Torelli group.

Paper introduces PTL-SI for statistical inference in TL-HDR, controlling FPR.

We give a definition of an integer-valued function $\sum_i α_i x ^*_i$ derived from arrow diagrams for the ambient isotopy classes of oriented spherical curves. Then, we introduce certain elements of the free $\mathbb{Z}$-module generated by the arrow diagrams with at most $l$ arrows, called relators of Type~($\check{…

STAND-DA improves AD in DA target domains with limited data.

In the context of Multi Instance Learning, we analyze the Single Instance (SI) learning objective. We show that when the data is unbalanced and the family of classifiers is sufficiently rich, the SI method is a useful learning algorithm. In particular, we show that larger data imbalance, a quality that is typically per…

We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with $Z_{\Si (L)}$ grading. As one of applications of the sp…

Paper presents a fast and adaptive filter for SI suppression in full-duplex transceivers.

Unified understanding of three continual learning regularisation methods.

A new method reduces feature screening cost from $O(np)$ to $O(\sqrt{n}p)$.

Let $(M,g)$ be a compact Riemannian manifold of dimension $n\geq 3$. For a metric $g$ on $M$, we let $\la_2(g)$ be the second eigenvalue of the Yamabe operator $L_g:= \frac{4(n-1)}{n-2} Δ_g + \scal_g$. Then, the second Yamabe invariant is defined as $$ \si_2(M) \definedas \sup \inf_{h \in [g]} \la_2(h) \Vol(M,h)^{2/n}.…

SETrLUSI combines diverse knowledge from multiple domains for faster convergence.

A quantum circuit designed for efficient statistical model preparation and training.

Starting with a Lie algebroid ${\cal A}$ over a space $M$ we lift its action to the canonical transformations on the affine bundle ${\cal R}$ over the cotangent bundle $T^*M$. Such lifts are classified by the first cohomology $H^1({\cal A})$. The resulting object is a Hamiltonian algebroid ${\cal A}^H$ over ${\cal R}$ …

We analyze symmetries in overparametrized neural networks using a mean-field approach.

Developed accurate empirical potentials for Si:H nanowires using multi-fidelity Gaussian process.

Let M be a compact manifold equipped with a Riemannian metric g and a spin structure \si. We let $λ(M,[g],\si)= \inf_{\tilde{g} \in [g]} λ_1^+(\tilde{g}) Vol(M,\tilde{g})^{1/n}$ where $λ_1^+(\tilde{g})$ is the smallest positive eigenvalue of the Dirac operator D in the metric $\tilde{g}$. A previous result stated that …

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have limited expressive power due to the Gaussian assumption of latent variables. In t…

Paper introduces a method to assess the statistical reliability of changepoints using selective inference and dynamic programming.

A novel text-independent speaker identification (SI) method is proposed. This method uses the Mel-frequency Cepstral coefficients (MFCCs) and the dynamic information among adjacent frames as feature sets to capture speaker's characteristics. In order to utilize dynamic information, we design super-MFCCs features by cas…

Most structure inference methods either rely on exhaustive search or are purely data-driven. Exhaustive search robustly infers the structure of arbitrarily complex data, but it is slow. Data-driven methods allow efficient inference, but do not generalize when test data have more complex structures than training data. I…

Sharp thresholds and contiguity for community detection in contextual SBM.

DC-SIS selects features faster than mRMR for Parkinson's vocal diagnosis.

New method quantifies reliability of neural network image segmentation.

Let $(M,g,\si)$ be a compact Riemannian spin manifold of dimension $\geq 2$. For any metric $\tilde g$ conformal to $g$, we denote by $\tildeλ$ the first positive eigenvalue of the Dirac operator on $(M,\tilde g,\si)$. We show that $$\inf_{\tilde{g} \in [g]} \tildeλ\Vol(M,\tilde g)^{1/n} \leq (n/2) \Vol(S^n)^{1/n}.$$ T…

In this paper, we propose a two-step training procedure for source separation via a deep neural network. In the first step we learn a transform (and it's inverse) to a latent space where masking-based separation performance using oracles is optimal. For the second step, we train a separation module that operates on the…