Improved algorithm speeds up generation of universal adversarial perturbations.
problem Slow generation of universal adversarial perturbations.
method Optimized algorithm based on orientation of perturbation vectors.
result Significantly faster generation of universal perturbations with higher fooling rates.
We consider closed and orientable immersed hypersurfaces of translational manifolds. Given a vector field on such a hypersurface, we define a perturbation of its Gauss map, which allows us to obtain topological invariants for the immersion that depends on the geometry of the manifold and the ambient space. We use these…
New counterexample shows curved surfaces can deform geodesics without diffeomorphism.
problem Can curved surfaces deform geodesics without changing their lengths?
method Constructs a perturbed surface with longer geodesics but no contracting diffeomorphism.
result No diffeomorphism can contract all tangent vectors on a surface with longer geodesics.
The purpose of this paper is to study finite dimensional equivariant moduli problems from the viewpoint of stratification theory. We show that there exists a stratified obstruction system for a finite dimensional equivariant moduli problem. In addition, we define a coindex for a G-vector bundle which is determined by t…
Study perturbations of submodules in Drury-Arveson space, finding smooth vector bundles with Hermitian connections.
problem Geometry of perturbations in Drury-Arveson space.
method Analysis of smooth vector bundles with Hermitian connections and computation of parallel transport operators.
result Found natural Hermitian connections on perturbed submodules.
Formula calculates invariant for 3-manifolds with torus boundaries.
problem Calculating an invariant for 3-manifolds with torus boundaries.
method Generalized Chern-Simons invariant and provided a gluing formula.
result A gluing formula for the invariant d(M,ρ). Study analyzes perturbations in singular subspaces under random noise.
problem Understanding singular vector and subspace changes in signal-plus-noise models.
method Generalized Davis-Kahan-Wedin theorem for any unitarily invariant norm, considering ℓ∞ and ℓ2,∞ bounds. result Fine-grained insights into singular vector and subspace perturbations, including ℓ∞ and ℓ2,∞ bounds. We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact Kähler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal Kähler metric proved by Calabi.
In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set $\fc$ of m vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a pertu…
The paper smooths out equations on 4-manifolds to show smooth moduli spaces.
problem Understanding the structure of solutions to Vafa-Witten equations on 4-manifolds.
method Constructing perturbation terms to ensure transversality and showing moduli spaces are smooth.
result For generic perturbation, the general part of the moduli space is a smooth 0-dimensional manifold.
Fast algorithm for rescaling vectors with clipping, improving training efficiency.
problem Efficiently rescale vectors to a desired length while maintaining them within a domain after clipping.
method Analytical solution for optimal rescaling using fast and differentiable algorithm.
result Optimal rescaling can be found analytically, improving training efficiency for neural networks.
Improved perturbation reduces matrix condition number to O(n) with minimal storage.
problem Reducing the condition number of deterministic matrices for efficient algorithmic use.
method Introduced pattern matrices and sparse perturbations with dependent entries.
result Condition number reduced to O(n) with O(n) random numbers in O(log n) precision.
This paper establishes transversality for perturbed Vafa-Witten moduli spaces on 4-manifolds.
problem Transversality of Vafa-Witten moduli spaces on 4-manifolds with C≡0. method Constructing perturbation terms to ensure the moduli space is a smooth manifold of dimension zero.
result For generic perturbation terms, the moduli space of solutions is a smooth manifold of dimension zero.
Perturbs area-minimizing hypersurfaces to reduce singular set's dimension.
problem Reduces the dimension of the singular set of area-minimizing hypersurfaces.
method Perturbs a smooth hypersurface to minimize the Minkowski dimension of the singular set.
result The singular set of the perturbed minimizing current has Minkowski dimension less than n-9.
Study local perturbations of vector bundles with polynomial curvature solutions.
problem Existence and stability of solutions to geometric PDEs under deformations.
method Geometric invariant theory, moment map framework, polystability conditions.
result Existence and uniqueness of solutions under local polystability conditions.
Learnable token perturbations boost extrapolation in LLMs.
problem Limited flexibility of current discrete perturbations in large language models.
method Learnable continuous latent vector transformations in embedding space, unbiased estimating equations, stochastic gradient descent optimization.
result Significant gains in out-of-domain settings over state-of-the-art methods.
We propose an extension of the recently-proposed volume conjecture for closed hyperbolic 3-manifolds, to all orders in perturbative expansion. We first derive formulas for the perturbative expansion of the partition function of complex Chern-Simons theory around a hyperbolic flat connection, which produces infinitely-m…
New invariant counts graph configurations in 3D manifolds.
problem Counting graph configurations in 3D manifolds.
method Using combings instead of parallelizations for a more flexible definition.
result Universal finite type invariant of three-manifolds.
Deterministic bounds for tensor singular values and vectors, differing from matrix cases.
problem Spectral learning of higher-order orthogonally decomposable tensors.
method Deterministic perturbation bounds for singular values and vectors of orthogonally decomposable tensors.
result Perturbation affects each essential singular value/vector in isolation, independent of multiplicity and distance from other singular values.
The paper studies nilpotent structures in oriented neutral vector bundles and neutral hyperKähler structures.
problem Nilpotent structures in oriented neutral vector bundles and their relation to neutral hyperKähler structures.
method Defined H-nilpotent structures for Lie subgroups of SO(2n,2n) related to neutral hyperKähler structures. result Existence of complex and paracomplex structures forming neutral hyperKähler structures if and only if there exists an H-nilpotent structure. The paper proves new theorems about specific types of operator perturbations.
problem Analyzing conformal perturbations of Dirac and signature operators.
method Developed Kastler-Kalau-Walze type theorems for specific operator types.
result Established new theorems for six-dimensional manifolds with boundary.
The paper studies vector fields on manifolds and their embeddings into tangent bundles.
problem Characterizing and understanding vector fields on manifolds and their embeddings.
method Forming Sasaki metrics and studying embeddings of cross sections defined by vector fields.
result Minimal unit vector fields on spheres are related to contact structures.
We developed a perturbation model for affine gravity theories.
problem Cosmological perturbations in theories without metric.
method Segregated perturbations into symmetric and antisymmetric components, decomposing into irreducible elements.
result Fully addressed gauge freedom in affine gravity theories.
We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are provided.
We consider perturbed quadharmonic operators, Δ4+V, acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential V satisfying a bound from below by a non-positive function depending on the distance from a point. Under a bounded geometry assumption on the Hermitian vecto…
Study vector fields with complex singularities, proving bounds and formulas.
problem Understanding the Milnor number of vector fields with specific singularities.
method Global and local formulas expressing Milnor/Poincare-Hopf contributions, sharp lower bounds under perturbations.
result Sharp lower bounds for Milnor number contributions under holomorphic perturbations.
Complex functional maps link tangent bundles, preserving orientation and angles.
problem Linking tangent bundles for orientation-aware correspondence.
method Endow tangent bundles with complex structures to enable robust transfer of tangent vector fields.
result Establishes orientation-aware correspondence without relying on descriptors or extra regularization.
We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often es…
Study proves 3-manifolds with parallel vector fields have odd Betti numbers.
problem Determining when 3-manifolds can have parallel vector fields.
method Analyzing Kähler mapping tori and Lorentzian manifolds.
result Betti numbers of 3-manifolds with parallel vector fields are always odd.
A perturbative SU(3) Casson invariant ΛSU(3)(X) for integral homology 3-spheres is defined. Besides being fully perturbative, it has nice properties: (1) 4.ΛSU(3)(X) is an integer. (2) It is preseved under orientation change. (3) A connected sum formula holds. Explicit calculations of the invariant for $1/k…
For a closed oriented 3-manifold Y we define n(Y) to be the minimal non-negative number such that in each homotopy class of non-singular vector fields of Y there is a Morse-Smale vector field with less or equal to n(Y) periodic orbits. We combine the construction process of Morse-Smale flows given in [2] with h…
New deep learning method preserves orientation in shape matching.
problem Symmetry issues in shape matching.
method Orientation-aware functional maps using complex functional representations and DiffusionNet.
result Stable correspondence predictions with robust orientation preservation.
Geometrically proves twisted Poincaré duality for orientable Poisson manifolds.
problem Establishing twisted Poincaré duality for Poisson manifolds.
method Geometrically reinterprets algebraic constructions of twisted Poisson modules and Poisson chain complexes.
result Explicit chain isomorphism between Poisson cochain and chain complexes with coefficients in Poisson modules.
Beyond existing multi-view clustering, this paper studies a more realistic clustering scenario, referred to as incomplete multi-view clustering, where a number of data instances are missing in certain views. To tackle this problem, we explore spectral perturbation theory. In this work, we show a strong link between per…
We show that the Spivak normal fibration of an orientable 4-dimensional Poincaré complex has a vector bundle reduction.
Given a discrete subgroup Γ of finite co-volume of PGL(2,R), we define and study parabolic vector bundles on the quotient Σ of the (extended) hyperbolic plane by Γ. If Γ contains an orientation-reversing isometry, then the above is equivalent to studying real and quaternionic parabolic vecto…
The paper calculates expected distances on partially oriented flag manifolds.
problem Understanding distances on partially oriented flag manifolds.
method Computing expected distances on low-dimensional examples.
result Computed expected distances on partially oriented flag manifolds.
The paper modifies Vafa-Witten equations on 4-manifolds for better solution estimates.
problem Constructing a priori estimates for solutions of Vafa-Witten equations on 4-manifolds.
method Introducing perturbation terms to the Vafa-Witten equations and proving transversality.
result The singularities of solutions can be removed, and moduli spaces constructed.
Proposes an efficient method for ordered counterfactual explanations.
problem Insufficient explanation of perturbation vectors for executing actions.
method Mixed-Integer Linear Optimization (MILP) approach for evaluating and extracting optimal pairs of actions and orders.
result Demonstrated effectiveness of the proposed method on real datasets.
We consider remodeling the planar search patterns, in the presence of the river-type perturbation represented by the weak vector field, basing on the time-optimal paths as Finslerian solutions to the Zermelo navigation problem via Randers metric.
The paper calculates spectral torsion for rescaled Dirac operators on manifolds.
problem Computing spectral torsion for rescaled Dirac operators.
method Using trilinear Clifford multiplication and functional of differential one-forms.
result Computed spectral torsion for four types of rescaled Dirac operators.
For any compact oriented manifold M, we show that that the top degree multi-vector fields transverse to the zero section of ∧topTM are classified, up to orientation preserving diffeomorphism, in terms of the topology of the arrangement of its zero locus and a finite number of numerical invariants. Th…
Study linear perturbations in Schwarzschild black hole spacetime.
problem Linear perturbations of Schwarzschild black hole spacetime.
method Investigate linearised perturbation of constant mass aspect function foliation at null infinity.
result Linearised perturbations of Bondi energy and mass vanish, and all linear momentum can be achieved.
We give a new construction of the one-variable Alexander polynomial of an oriented knot or link, and show that it generalizes to a vector valued invariant of oriented tangles.
Universal perturbations misclassify text with high accuracy.
problem Vulnerability of text classifiers to small perturbations.
method Algorithm to compute universal adversarial perturbations.
result Deep neural networks are highly vulnerable to universal adversarial perturbations.
A new method for reconstructing flows from perturbed distributions.
problem Reconstructing flows from perturbed probability distributions.
method Integrable vector fields and Green's functions.
result A nonparametric flow can be computed to generate samples from a perturbed distribution.
Given a state-of-the-art deep neural network classifier, we show the existence of a universal (image-agnostic) and very small perturbation vector that causes natural images to be misclassified with high probability. We propose a systematic algorithm for computing universal perturbations, and show that state-of-the-art …
We elaborate on an idea of M. Abouzaid of equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A∞-algebra. This is a variation on K. Fukaya's definition of Morse-A∞-categories for closed oriented manifolds involving families of Morse funct…