arXiv research

Study of loss functions for learning to defer, proving consistency.

Study improves $H$-consistency bounds for regression analysis.

Enhanced $H$-consistency bounds derived under relaxed conditions.

This paper tackles deferral learning with multiple experts, providing strong theoretical guarantees.

Study on $H$-consistency bounds for machine learning surrogates.

Enhanced consistency bounds derived for classification under a new noise condition.

Unified surrogate loss framework for multi-label learning with strong consistency guarantees.

New method improves consistency in preference learning for neural networks.

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

Study on calibration and consistency of adversarial surrogate losses.

This paper introduces new loss functions for balanced multi-class classification.

Develops algorithms for optimizing multi-label metrics with provable guarantees.

Paper establishes a universal growth rate for smooth surrogate losses in classification.

Study on learning to defer with multiple experts using new surrogate losses.

Study of estimation errors in surrogate loss minimizers, providing stronger guarantees than existing methods.

This thesis tackles learning with multi-class abstention and multi-expert deferral, improving model reliability and efficiency.

New algorithms optimize metrics for binary classification with class imbalance.

Classifies special homogeneous curves with polynomial equations.

Given a hyperbolic subgroup $H$ of a hyperbolic group $G$ for which a Cannon-Thurston map $\hat i:\partial H \ra \partial G$ exists, we study the limit set $Λ_H$ of $H$ with respect to its action on $\partial G$. We prove that the set of conical limit points is exactly the subset of $Λ_H$ consisting of the points to wh…

The paper revisits discriminative vs. generative classifiers, showing naive Bayes requires fewer samples.

Let $G/H$ be a compact homogeneous space, and let $\hat{g}_0$ and $\hat{g}_1$ be $G$-invariant Riemannian metrics on $G/H$. We consider the problem of finding a $G$-invariant Einstein metric $g$ on the manifold $G/H\times [0,1]$ subject to the constraint that $g$ restricted to $G/H\times \{0\}$ and $G/H\times \{1\}$ co…

We improve adversarial robustness calibration analysis for broader hypothesis sets.

Theoretical analysis of cross-entropy loss functions and their robustness.

We study Tian's $α$-invariant in comparison with the $α_1$-invariant for pairs $(S_d,H)$ consisting of a smooth surface $S_d$ of degree $d$ in the projective three-dimensional space and a hyperplane section $H$. A conjecture of Tian asserts that $α(S_d,H)=α_1(S_d,H)$. We show that this is indeed true for $d=4$ (the res…

We introduce spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$. Intuitively spherical T-duality exchanges $H$ with the second Chern class $c_2(P)$. Unless $dim(M)\leq 4$, not all pairs admit spherical T-duals and the spheric…

The holonomy algebra $\g$ of an $n+2$-dimensional Lorentzian manifold $(M,g)$ admitting a parallel distribution of isotropic lines is contained in the subalgebra $\simil(n)=(\Real\oplus\so(n))\zr\Real^n\subset\so(1,n+1)$. An important invariant of $\g$ is its $\so(n)$-projection $\h\subset\so(n)$, which is a Riemannian…

A framework for ranking with abstention, offering theoretical guarantees and practical effectiveness.

Let $T$ be a circle and $LT$ be its loop group. Let $\mathcal{M}$ be an infinite dimensional manifold equipped with a nice $LT$-action. We construct an analytic $LT$-equivariant index for $\mathcal{M}$, and justify it in terms of noncommutative geometry. More precisely, we construct a Hilbert space $\mathcal{H}$ consis…

Study improves top-k set prediction with low cardinality.

Online L2D algorithm for multiclass classification with varying experts.

New framework for learning from imbalanced data with theoretical guarantees.

Study of groups and their quasi-isometrically embedded subgroups.

In earlier papers, we introduced spherical T-duality, which relates pairs of the form $(P,H)$ consisting of an oriented $S^3$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$ called the 7-flux. Intuitively, the spherical T-dual is another such pair $(\hat P, \hat H)$ and spherical T-duality exchanges the 7-flux with …

The paper studies a special Grassmannian space and shows it's an orbit of a unitary group.

A new method for learning to defer decisions with expert advice improves over standard methods.

ORAT improves model robustness against outliers and adversarial attacks.

Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.

Unified model for prediction and deferral selects top-k entities efficiently.

The paper classifies differentiable structures on a line with two origins.

Unified framework for deferring queries to top-k experts, improving accuracy-cost trade-offs.

Unified RMOT framework for non-modelable risk factors reduces audit bounds.

A novel framework for regression with multiple experts, addressing challenges in infinite and continuous label spaces.

Let $T$ be a circle group, and $LT$ be its loop group. We hope to establish an index theory for infinite-dimensional manifolds which $LT$ acts on, including Hamiltonian $LT$-spaces, from the viewpoint of $KK$-theory. We have already constructed several objects in the previous paper \cite{T}, including a Hilbert space $…