arXiv research

In this paper, we obtain several new intrinsic and extrinsic differential sphere theorems via Ricci flow. For intrinsic case, we show that a closed simply connected $n(\ge 4)$-dimensional Riemannian manifold $M$ is diffeomorphic to $S^n$ if one of the following conditions holds pointwisely: $$ (i)\ R_0>\left(1-\frac{24…

Paper proposes a new sparse group k-max regularization for sparsity constraints.

RAM extends attention-based mechanism for existence determination.

The famous pinching problem says that on a compact simply connected $n$-manifold if its sectional curvature satisfies $K_{min} > (1/4)K_{max} > 0$, then the manifold is homeomorphic to the sphere. In [8, problem 12], S. T. Yau proposed the following problem: If we replace $K_{max}$ by the scalar curvature, can we deduc…

The paper calculates bounds for unknotting rational tangles using knot Floer homology.

Let $(M,g)$ be a compact Ricci-flat 4-manifold. For $p \in M$ let $K_{max}(p)$ (respectively $K_{min}(p)$) denote the maximum (respectively the minimum) of sectional curvatures at $p$. We prove that if $K_{max} (p) \le \ -c K_{min}(p)$ for all $p \in M$, for some constant $c$ with $0 \leq c < \frac{2+\sqrt 6}{4}$, th…

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger c…

Algorithm solves two-sided matching markets with unknown preferences and constraints.

New algorithm reduces unfairness in bandit problems by balancing exploration and exploitation.

Study on scalar curvature minimizability loss and saddle point solutions.

We study how well one can recover sparse principal components of a data matrix using a sketch formed from a few of its elements. We show that for a wide class of optimization problems, if the sketch is close (in the spectral norm) to the original data matrix, then one can recover a near optimal solution to the optimiza…

We consider the optimization problem associated with training simple ReLU neural networks of the form $\mathbf{x}\mapsto \sum_{i=1}^{k}\max\{0,\mathbf{w}_i^\top \mathbf{x}\}$ with respect to the squared loss. We provide a computer-assisted proof that even if the input distribution is standard Gaussian, even if the dime…

Some new differentiable sphere theorems are obtained via the Ricci flow and stable currents. We prove that if $M^n$ is a compact manifold whose normalized scalar curvature and sectional curvature satisfy the pointwise pinching condition $R_0>σ_{n}K_{\max}$, where $σ_n\in (\frac{1}{4},1)$ is an explicit positive constan…

Improved algorithm for misspecified MLMDPs with bounded regret and space/time complexities.

Proposes a new optimization-based method for aggregating sets in neural networks.

Turbo-Aggregate reduces secure aggregation time from quadratic to nearly linear.

In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an $(n-m) \times n$ ($m>0$) CS matrix $A$ and a positive $k$, we are interested in computing $\displaystyle α_k = \max_{\{z: Az=0,z\neq 0\}}\max_{\{K: |K|\leq k\}}$ ${\|z_K \|_{1}}{\|z\|_{1}}$, where …

Study aggregation of statistical evidence under unknown dependence using group-invariance.

New LCM aggregator improves GNN performance and efficiency.

Unified approach to aggregating models and preferences.

In order to scale standard Gaussian process (GP) regression to large-scale datasets, aggregation models employ factorized training process and then combine predictions from distributed experts. The state-of-the-art aggregation models, however, either provide inconsistent predictions or require time-consuming aggregatio…

Aggregation challenges causal interpretation of IV estimators.

SACP aggregates nonconformity scores from multiple predictors to create more efficient uncertainty sets.

We consider the forecast aggregation problem in repeated settings, where the forecasts are done on a binary event. At each period multiple experts provide forecasts about an event. The goal of the aggregator is to aggregate those forecasts into a subjective accurate forecast. We assume that experts are Bayesian; namely…

We introduce a novel aggregation method to efficiently perform image denoising. Preliminary filters are aggregated in a non-linear fashion, using a new metric of pixel proximity based on how the pool of filters reaches a consensus. We provide a theoretical bound to support our aggregation scheme, its numerical performa…

Paper analyzes sparse aggregation in GLMs with Kullback-Leibler risk bounds.

Aggregates predictions from multiple regression models using random projections and kernel methods.

The paper introduces a method to control false splits in tree-based data aggregation.

Estimates variance function using aggregation methods in regression models.

This work analyzes two methods for combining multiple binary labels in bipartite ranking.

PREMA recovers detailed data from aggregated views.

Paper presents a novel approach for global feature aggregation in Graph Neural Networks.

New algorithm for aggregate inference in HMMs with continuous observations.

A robust aggregation method improves federated learning's accuracy in corrupted settings.

BAFFLE uses blockchain to federate learning without a central aggregator.

New method aggregates nodes in sparse graphical models.

U-aggregation combines multiple models without labels for better risk prediction.

Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep Set learning. This work investigates a core component of Deep Set architecture: ag…

BOA improves financial forecasting by combining expert models.

MEVA aggregates model predictions to improve accuracy without needing model details.

New aggregation method improves GNN robustness to structural perturbations.

A new algorithm estimates aggregate marginals from noisy data in an online manner.

Non-affine aggregation rules cannot preserve monotonicity in convex learning.

Study improves fair opinion aggregation by balancing voter attributes.

Fishnets improve set and graph learning with scalable, robust aggregation.

CAggNet improves medical image segmentation by fusing coarse and fine features.