arXiv research

Study on rigidity with non-negative intermediate curvature on low-dimensional manifolds.

Preserves positive intermediate curvature on manifolds.

The study connects manifold topology to metrics with positive intermediate curvature.

For a pair of points in a smooth closed convex planar curve $γ$, its mid-line is the line containing its mid-point and the intersection point of the corresponding pair of tangent lines. It is well known that the envelope of the mid-lines ($EML$) is formed by the union of three affine invariants sets: Affine Envelope Sy…

New rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.

Study on spaces of metrics with intermediate curvature bounds.

Proves metrics with positive intermediate Ricci curvature on complex manifolds.

Extends Perelman's theorem to positive intermediate curvature conditions.

The study proves that certain manifolds with boundary cannot have metrics with positive intermediate curvatures.

Study finds metrics with positive intermediate Ricci curvature on specific low-dimensional manifolds.

Sharp dimension constraints for positive intermediate curvature metrics are established.

This paper introduces a novel approach to measuring privacy risks in deep computer vision models based on intermediate outputs.

The paper proves manifold splitting theorems with nonnegative intermediate curvature.

A framework to explain decoder-only sequence classification models using intermediate predictions.

Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.

We use a local argument to prove if an $r$-dimensional torus acts isometrically and effectively on a connected $n$-dimensional manifold which has positive $k^\mathrm{th}$-intermediate Ricci curvature at some point, then $r \leq \lfloor \frac{n+k}{2} \rfloor$. This symmetry rank bound generalizes those established by Gr…

We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.

Knowledge distillation (KD) is a popular method for reducing the computational overhead of deep network inference, in which the output of a teacher model is used to train a smaller, faster student model. Hint training (i.e., FitNets) extends KD by regressing a student model's intermediate representation to a teacher mo…

A cost-effective framework for gradual domain adaptation using multifidelity.

Gradual domain adaptation improves model transfer between domains with intermediate training.

Study shows Gromov's Betti number bound fails for certain intermediate Ricci curvatures.

Study analyzes financial intermediation costs in decentralized lending protocols.

Intermediate logic of all convex polyhedra is axiomatized.

Study estimates heterogeneous principal causal effects with binary treatments and intermediate variables.

Log-Sobolev inequality proven for submanifolds in specific types of manifolds.

Optimizes transport on submanifolds for curvature inequalities.

Extends metric properties over surgeries to higher codimensions.

Proves positive Euler characteristic for certain manifolds with positive second intermediate Ricci curvature.

Study improves understanding of Ricci curvature in manifolds.

Study finds almost contact structures in thermal QCD-like theories at intermediate coupling.

Study manifolds with positive intermediate Ricci curvature and large symmetry rank.

Neural networks are vulnerable to adversarial examples, malicious inputs crafted to fool trained models. Adversarial examples often exhibit black-box transfer, meaning that adversarial examples for one model can fool another model. However, adversarial examples are typically overfit to exploit the particular architectu…

Self-supervised and supervised methods learn similar intermediate visual representations but diverge in final layers.

In this paper, we diagnose deep neural networks for 3D point cloud processing to explore utilities of different intermediate-layer network architectures. We propose a number of hypotheses on the effects of specific intermediate-layer network architectures on the representation capacity of DNNs. In order to prove the hy…

We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of the theory is that the value functions of the primal and dual problems are finit…

The study allows for connected sums in manifolds with positive intermediate Ricci curvature.

New curvature concept shows certain manifolds can't have positive curvature.

Study of Calabi-Yau manifold degenerations near complex structure limits.

The paper finds many manifolds with intermediate Ricci curvature for small k.

We suggest an intermediate currency approach that allows us to price options on all FX markets simultaneously under the same risk-neutral measure which ensures consistency of FX option prices across all markets. In particular, it is sufficient to calibrate a model to the volatility smile on the domestic market as, due …

We consider the problem of optimal investment with intermediate consumption in a general semimartingale model of an incomplete market, with preferences being represented by a utility stochastic field. We show that the key conclusions of the utility maximization theory hold under the assumptions of no unbounded profit w…

Proves new Sobolev inequalities for submanifolds in manifolds with nonnegative intermediate Ricci curvature.

We study the geometry of multidimensional scalar $2^{nd}$ order PDEs (i.e. PDEs with $n$ independent variables) with one unknown function, viewed as hypersurfaces $\mathcal{E}$ in the Lagrangian Grassmann bundle $M^{(1)}$ over a $(2n+1)$-dimensional contact manifold $(M,\mathcal{C})$. We develop the theory of character…

We give an optimal estimate for the norm of any submanifold's second fundamental form in terms of its focal radius and the lower sectional curvature bound of the ambient manifold. This is a special case of a similar theorem for intermediate Ricci curvature, and leads to a $C^{1,α}$ compactness result for submanifolds, …

To reduce the large computation and storage cost of a deep convolutional neural network, the knowledge distillation based methods have pioneered to transfer the generalization ability of a large (teacher) deep network to a light-weight (student) network. However, these methods mostly focus on transferring the probabili…

Sparse curves on surfaces grow at a specific intermediate rate.

New method uses SoS densities and α-divergences for efficient sequential transport maps.

Proves non-existence of metrics with positive curvature for certain connected sums.