A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper identifies potential adversarial samples near decision boundaries of neural networks.
problem Vulnerability of deep neural networks to small perturbations of inputs.
method Developed a method to explore near decision boundaries of trained classifiers to identify potential adversarial samples.
result Potential adversarial samples represent only 61% of the test data but cover more than 82% of adversarial samples produced by iFGSM and 92% of those by DeepFool on CIFAR10.
We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the k-th tensor powers of a positive line bundle L in a k1-neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential kφ …
We consider scattering by an abstract compactly supported perturbation in R^n. To include the traditional cases of potential, obstacle and metric scattering without going into their particular nature we adopt the "black box" formalism developed jointly with Sjostrand [23]. It is quite likely that one could extend the r…
problem Understanding the tradeoff between natural accuracy and perturbation stability in wider neural networks for adversarial robustness.
method Careful examination of the relationship between network width, robust regularization parameter λ, and perturbation stability using neural tangent kernels.
result Wider networks can achieve better natural accuracy but worse perturbation stability, leading to potentially worse overall model robustness.
The Ma-Trudinger-Wang curvature --- or cross-curvature --- is an object arising in the regularity theory of optimal transportation. If the transportation cost is derived from a Hamiltonian action, we show its cross-curvature can be expressed in terms of the associated Jacobi fields. Using this expression, we show the l…
Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result becomes false for some arbitrarily small, smooth perturbations of the potential.
We study stability of non-compact gradient Kaehler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kaehler potential of the soliton will converge to the original soliton under Kaehler-Ricci …
Image classifiers are sensitive to small changes, affecting most images in a class.
problem Sensitivity of image classifiers to small perturbations.
method Demonstrated sensitivity for any classifier over images, showing that for most classes, a tiny perturbation can change the classification of a majority of images.
result Image classifiers are sensitive to small perturbations, affecting most images in a class.
We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators and free energies are co…
This note is devoted to Keller-Lieb-Thirring spectral estimates for Schrödinger operators on infinite cylinders: the absolute value of the ground state level is bounded by a function of a norm of the potential. Optimal potentials with small norms are shown to depend on a single variable. The proof is a perturbation arg…
We study the classical action functional $\SMC_V$ on the free loop space of a closed, finite dimensional Riemannian manifold M and the symplectic action $\AMC_V$ on the free loop space of its cotangent bundle. The critical points of both functionals can be identified with the set of perturbed closed geodesics in M.…
We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of th…
Perturbed geodesics are trajectories of particles moving on a semi-Riemannian manifold in the presence of a potential. Our purpose here is to extend to perturbed geodesics on semi-Riemannian manifolds the well known Morse Index Theorem. When the metric is indefinite, the Morse index of the energy functional becomes inf…
This paper examines how graph topology affects adversarial attacks on vertex classification.
problem Adversarial attacks on vertex classification are vulnerable to graph topology changes.
method Examined two topological graph characteristics and their impact on adversary perturbation budgets.
result Training sets including high-degree vertices or those ensuring all unlabeled nodes have neighbors can significantly increase the adversary's perturbation budget.