Proposes a new method to identify important input features using maximally invariant data perturbation.
problem Lack of formal mathematical definitions for feature scoring in complex machine learning models.
method Formulates the problem as linear programming to find the maximally invariant data perturbation.
result Identifies relevant parts of images effectively, distinguishing important input features.
The paper explores maximal perturbations to hide certain attributes in data while keeping the model's performance intact.
problem Protecting sensitive attributes from both model and human detection.
method Adversarial perturbations applied to raw data to conditionally damage model's classification of one attribute while preserving the rest.
result Maximal perturbations can hide certain attributes from both model and human detection, impacting model performance but not human perception.
Proposes a stochastic optimization method for feature attribution.
problem Improving feature attribution methods for complex models.
method Reformulates the optimization problem as a differentiable function solvable by gradient-based algorithms, particularly stochastic optimization.
result The proposed method effectively identifies relevant parts of images.
New quantum invariant is asymptotically multiplicative under cyclic covers.
problem Quantum invariants are not multiplicative under finite covers.
method Introduced a perturbative power series invariant of cusped hyperbolic 3-manifolds.
result The power series is asymptotically multiplicative under cyclic covers.
The study shows instability of Nikodym maximal function bounds on Riemannian manifolds under metric perturbation.
problem Instability of Nikodym maximal function bounds on Riemannian manifolds under metric perturbation.
method Analyzing the instability of $L^{ rac{d+2}2}$ bounds for the Nikodym maximal function over manifolds of constant sectional curvature and extending to any d-dimensional Riemannian manifold with a local totally geodesic submanifold. result The instability of the bounds for the Nikodym maximal function on Riemannian manifolds under metric perturbation.
We show that the perturbative g invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra g, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate …
This paper tackles incomplete multi-view clustering with spectral perturbation theory.
problem Realistic clustering scenario where data instances are missing in certain views.
method Spectral perturbation theory and matrix completion method for incomplete similarity matrix.
result The minimization of perturbation risk bounds maximizes the final fusion result across all views.
The paper tackles extrapolation of gene knockouts effects on RNA counts.
problem Modeling effects of gene knockouts on RNA counts for new perturbations.
method Formulated as a latent variable model with additive perturbation effects, proved identifiability, proposed PDAE for estimation.
result PDAE can accurately predict effects of unseen but identifiable perturbations.
New invariant from non-acyclic flat connections.
problem Constructing a higher-loop perturbative invariant.
method Integral of a Chern-Simons volume form over moduli space of flat connections.
result Generalization of Chern-Simons invariant to non-acyclic connections.
Jacobian regularization boosts neural network robustness without degrading generalization.
problem Ensuring robustness of machine learning models against input perturbations.
method Developed a computationally efficient Jacobian regularization technique.
result Significant improvements in robustness measured against random and adversarial perturbations.
A new framework learns cyclic causal graphs from incomplete data.
problem Learning causal models in systems with feedback loops and missing data.
method MissNODAGS framework, alternating imputation and likelihood maximization.
result Improved performance compared to imputation followed by causal learning.
Evolutionary algorithm finds optimal pixel perturbations to improve neural network generalization.
problem Minimal data corruption by pixel modifications causes overfitting in neural networks.
method Evolutionary algorithm with a novel cost function to maximize generalization gap and domain divergence.
result Method outperforms previous pixel-based data distribution shift methods on CNNs.
Power series invariant of hyperbolic 3-manifolds matches knot invariants.
problem Understanding topological invariants of hyperbolic 3-manifolds.
method Perturbative power series associated with ideally triangulated cusped hyperbolic 3-manifolds.
result The power series agrees with Kashaev and Andersen-Kashaev invariants to all orders.
New framework maximizes perturbed samples for inverse classification with budget constraints.
problem Maximizing perturbed samples for desired classification outcomes under budget constraints.
method Gradient methods, stochastic processes, Lagrangian relaxations, Gumbel trick.
result Stochastic process-based algorithms outperform in different budget settings.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
State-of-the-art classifiers are vulnerable to small adversarial perturbations.
problem Vulnerability of state-of-the-art classifiers to adversarial perturbations.
method Assumed smooth generative model, derived upper bounds on robustness, proved adversarial perturbation transfer.
result Existence of adversarial perturbations that transfer well across different classifiers with small risk.
New method μP2 improves neural network training by scaling perturbations layerwise.
problem Improving neural network performance as models scale up.
method Layerwise perturbation scaling in the infinite-width limit of neural networks.
result Layerwise perturbation scaling ensures all layers are effectively perturbed in the limit.
The paper constructs new bimetric conformal invariants using metric perturbations.
problem Developing new conformal invariants in Riemannian geometry.
method Using linear metric perturbations and conformal invariants.
result New bimetric conformal invariants on 4D manifolds are derived.
The universal perturbative invariants of rational homology spheres can be extracted from the Chern-Simons partition function by combining perturbative and nonperturbative results. We spell out the general procedure to compute these invariants, and we work out in detail the case of Seifert spaces. By extending some prev…
In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
New approach to quantum knot invariants using perturbed Gaussian generating functions.
problem Developing universal quantum knot invariants.
method Introducing generating functions of the form PeG where G is quadratic and P is a perturbation, and developing a calculus for such functions. result The rank one invariant ZD dominates sl2-colored Jones polynomials and relates to knot genus and Whitehead doubling. Researchers construct a gauge-invariant energy functional for axially symmetric perturbations around Kerr black holes.
problem Understanding energy of axially symmetric perturbations around Kerr black holes.
method Hamiltonian dimensional reduction to a 2+1 Einstein-wave map system, constructing a positive-definite, gauge-invariant energy functional. result The energy functional serves as a Hamiltonian for the constrained evolution of linear perturbations.
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.
We derive a gauge theoretic invariant of integral homology 3-spheres which counts gauge orbits of irreducible, perturbed flat SU(3) connections with sign given by spectral flow. To compensate for the dependence of this sum on perturbations, the invariant includes contributions from the reducible, perturbed flat orbits.…
We examine the issue of sensitivity with respect to model parameters for the problem of utility maximization from final wealth in an incomplete Samuelson model and mainly, but not exclusively, for utility functions of positive power-type. The method consists in moving the parameters through change of measure, which we …
IMSAT learns discrete representations by maximizing information and enforcing invariance.
problem Learning useful discrete representations from data.
method Information Maximizing Self-Augmented Training (IMSAT) with data augmentation and information-theoretic dependency maximization.
result IMSAT achieves state-of-the-art results for clustering and unsupervised hash learning.
New knot invariants derived using quantum cluster algebras.
problem Deriving new knot invariants from quantum cluster algebras.
method Interpreting R-matrix of Uq(sl2) as cluster transformation, introducing auxiliary parameter ε. result Derives perturbed-Alexander invariants with higher-order terms in ε. 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…
DAA attacks adversarial defenses by optimizing a perturbed data distribution.
problem PGD adversarial attacks do not optimize risk maximization.
method DAA optimizes a perturbed data distribution to maximize generalization risk.
result DAA outperforms state-of-the-art defenses on MadryLab leaderboards.
The integrality of the Kontsevich integral and perturbative invariants is discussed. We show that the denominator of the degree n part of the Kontsevich integral of any knot or link is a divisor of (2!3!...n!)4(n+1)!. We also show that the denominator of of the degree n part of the universal perturbative invari…
Study of knot invariant growth for twisted knots.
problem Understanding the behavior of a knot invariant for families of knots.
method Analyzing the perturbed Alexander invariant for twisted knots.
result Coefficients of the invariant grow linearly as the number of twists increases.
We study the relationship between Bar-Natan's perturbation in Khovanov homology and Szabo's geometric spectral sequence, and construct a link invariant that generalizes both into a common theory. We study a few properties of the new invariant, and introduce a family of s-invariants from the new theory in the same spiri…
The volume conjecture is extended to all orders for hyperbolic 3-manifolds using complex Chern-Simons theory.
problem Extending the volume conjecture to all orders for hyperbolic 3-manifolds.
method Deriving formulas for the perturbative expansion of the partition function of complex Chern-Simons theory and comparing it to Witten-Reshetikhin-Turaev invariants.
result The conjecture that the perturbative expansion of the partition function of complex Chern-Simons theory matches the Witten-Reshetikhin-Turaev invariants at roots of unity in the limit of infinitely many invariants.
New invariants for 3-manifolds derived from equivariant Cerf theory.
problem Existence of perturbative SU(n) Casson invariants on integer homology spheres. method Equivariant Cerf theory for Morse functions, adapted to infinite-dimensional setting.
result Existence and explicit formula for SU(4) Casson invariants. The paper solves utility maximization under partial information using transformations and perturbation methods.
problem Maximizing recursive utility under partial information.
method Transforming to full information, using variational formulation, stochastic game approach, and terminal perturbation method.
result Explicit saddle points and optimal terminal wealth obtained.
GraphCL learns node representations by maximizing similarity between perturbed node features.
problem Learning node representations in graph data without labeled data.
method Contrastive learning of node embeddings using graph neural networks and a loss function.
result Significantly outperforms state-of-the-art in unsupervised node classification benchmarks.
MissNODAG learns cyclic causal graphs from incomplete data.
problem Causal discovery in systems with feedback loops and missing data.
method Differentiable framework integrating additive noise model and expectation-maximization.
result MissNODAG uncovers cyclic structures and missingness mechanisms from partially observed data.
Paper finds positive metric entropy in perturbed geodesic flow.
problem Understanding dynamics outside KAM tori in nearly integrable systems.
method Lagrangian perturbation of geodesic flow on a flat 3-torus.
result Positive metric entropy found outside some KAM tori.
Ensemble Adversarial Training improves model robustness to black-box attacks.
problem Vulnerability of adversarial training to black-box attacks and novel attacks.
method Augmenting training data with perturbations from other models.
result Ensemble Adversarial Training yields models with strong robustness to black-box attacks.
The paper studies invariant complex manifolds in holomorphic slow-fast systems.
problem Existence of invariant complex manifolds in holomorphic systems.
method Geometric singular perturbation theory, Fenichel and Briot-Bouquet theories.
result Conditions are provided to guarantee the existence of one-dimensional invariant complex manifolds.
We construct power series invariants of rational homology 3-spheres from quantum PSU(n)-invariants. The power series can be regarded as perturbative invariants corresponding to the contribution of the trivial connection in the hypothetical Witten's integral. This generalizes a result of Ohtsuki (the n=2 case) which l…
Prove that collapsing CSC metrics can be perturbed to invariant collapsing CSC metrics.
problem Prove that collapsing constant scalar curvature metrics can be perturbed to invariant collapsing constant scalar curvature metrics.
method Prove that a sequence of constant scalar curvature metrics which is collapsing with bounded curvature to a manifold can be perturbed to a sequence of invariant collapsing constant scalar curvature metrics.
result Prove that a sequence of constant scalar curvature metrics which is collapsing with bounded curvature to a manifold can be perturbed to a sequence of invariant collapsing constant scalar curvature metrics.
We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes in multiple ways. In the background of a non-abelian irreducible flat connection, perturbative G_C invariants turn out to be interesting topological invariants, wh…
In this paper we prescribe a fourth order conformal invariant on the standard n−sphere, with n≥5, and study the related fourth order elliptic equation. We first find some existence results in the perturbative case. After some blow up analysis we build a homotopy to pass from the perturbative case to the non-pert…
We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also shed a new light to LeBrun's curvature inequalities.
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). A new method for high-dimensional inference using random perturbations.
problem High-dimensional statistical inference challenges.
method Perturb-max approach: random perturbations followed by optimization.
result Expected value of perturb-max inference can generate unbiased samples from Gibbs distribution.
We consider quantum invariants of 3-manifolds associated with arbitrary simple Lie algebras. Using the symmetry principle we show how to decompose the quantum invariant as the product of two invariants, one of them is the invariant corresponding to the projective group. We then show that the projective quantum invarian…