We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…
On-device research index
arXiv research
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.
168,657 papers · 148 categories
Trend · papers per month
48 results for “perturbation terms”
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.
The study explains why signature methods work in commodity futures term structure classification.
problem Lack of interpretability in signature methods for term structure classification.
method Introducing signature perturbations to explain the success of signature-based classification.
result The volatility of the convenience yield is the major discriminant for commodity markets classification.
Neural Networks have been shown to be sensitive to common perturbations such as blur, Gaussian noise, rotations, etc. They are also vulnerable to some artificial malicious corruptions called adversarial examples. The adversarial examples study has recently become very popular and it sometimes even reduces the term "adv…
New knot invariants derived using quantum cluster algebras.
problem Deriving new knot invariants from quantum cluster algebras.
method Interpreting -matrix of as cluster transformation, introducing auxiliary parameter .
result Derives perturbed-Alexander invariants with higher-order terms in .
Investigates fluid flow perturbations using geometric theory.
problem Analyzing linear perturbations in non-equilibrium fluid flows.
method Uses second order variations of the action and Jacobi fields.
result Demonstrates numerical simulations of perturbation dynamics.
Study privacy and accuracy in high-dimensional LASSO with perturbation mechanisms.
problem Privacy-preserving sparse linear regression in high dimensions.
method Analyzes output and objective perturbation mechanisms using AMP.
result Sparsity affects privacy-accuracy trade-off; stronger regularization improves privacy.
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior. As the minimization can only be carried out approximately, this approximation i…
We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a co…
This work proves Kerr black holes are dynamically stable under certain perturbations.
problem Dynamical stability of Kerr black holes under axially symmetric perturbations.
method Dimensional reduction to 2+1 Einstein-wave map system, construction of positive-definite energy functional, proving boundary terms vanish.
result Strictly conserved positive energy for axially symmetric linear perturbations of Kerr black holes.
A perturbative approach is used to derive approximations of arbitrary order to estimate high percentiles of sums of positive independent random variables that exhibit heavy tails. Closed-form expressions for the successive approximations are obtained both when the number of terms in the sum is deterministic and when it…
We show that the four derivative terms in the effective action of three-dimensional N=8 Yang-Mills theory are determined by supersymmetry. These terms receive both perturbative and non-perturbative corrections. Using our technique for constraining the effective action, we are able to determine the exact form of the eig…
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.
This paper establishes transversality for perturbed Vafa-Witten moduli spaces on 4-manifolds.
problem Transversality of Vafa-Witten moduli spaces on 4-manifolds with .
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.
Introduces RPU to explain randomization preference in dynamic settings.
problem Explains preference for randomization in dynamic investment problems.
method Introduces recursive perturbed utility (RPU) to incorporate randomization preference.
result Proves RPU-optimal portfolio policy is Gaussian and can be expressed in closed form.
Study robust learning without knowing perturbation sets, using interactions with attackers.
problem Learning robust predictors against unknown adversarial perturbations.
method Examined different interaction models with adversarial attackers, derived bounds on sample complexity and interactions.
result Upper bounds on sample complexity and lower bounds on interactions in various models.
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…
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.…
Adversarial training, in which a network is trained on both adversarial and clean examples, is one of the most trusted defense methods against adversarial attacks. However, there are three major practical difficulties in implementing and deploying this method - expensive in terms of extra memory and computation costs; …
EnLSTM network improves log generation from small datasets.
problem Generating well logs from small datasets with high accuracy.
method Combining ENN and C-LSTM networks with perturbation methods.
result 34% reduction in mean-square-error compared to existing models.
Researchers found a way to measure energy in black hole perturbations.
problem Lack of positive-definite and conserved energy in black hole stability.
method Dimensional reduction and construction of a positive-definite energy functional.
result Conserved Hamiltonian energy for axially symmetric perturbations of Kerr black holes.
We prove a Freed-Uhlenbeck style generic smoothness theorem for the moduli space of solutions to the Vafa--Witten equations on a closed symplectic four-manifold by using a method developed by Feehan for the study of the -monopole equations on smooth closed four-manifolds. We introduce a set of perturbation terms…
In this paper, we take the first steps towards a novel unified framework for the analysis of perturbations in both the Time and Frequency domains. The identification of type and source of such perturbations is fundamental for monitoring reactor cores and guarantee safety while running at nominal conditions. A 3D Convol…
Improved generalization bounds for SGD in non-convex learning.
problem Understanding generalization properties of SGD in non-convex settings.
method Introducing Type II perturbed SGD (T2pm-SGD) to analyze generalization error bounds.
result Tighter generalization error bounds for SGD in non-convex learning, especially for sub-Gaussian and bounded loss functions.
Local minimizers are convex and close to Wulff shapes.
problem Finding local minimizers in anisotropic isoperimetric problems.
method Showed local minimizers are geodesically convex and small smooth perturbations of tangent Wulff shapes.
result Local minimizers are quantitatively close to Wulff shapes.
We compute the Ricci curvature of a curved noncommutative three torus. The computation is done both for conformal and non-conformal perturbations of the flat metric. To perturb the flat metric, the standard volume form on the noncommutative three torus is perturbed and the corresponding perturbed Laplacian is analyzed.…
Motivated by the HRRT-formula for holographic entanglement entropy, we consider the following question: what are the position and the surface area of extremal surfaces in a perturbed geometry, given their anchor on the asymptotic boundary? We derive explicit expressions for the change in position and surface area, ther…
Smooth knots with odd Conway polynomial terms have inscribed trefoils.
problem Finding inscribed trefoils for smooth knots with specific polynomial terms.
method Using a perturbation of the double-cover of the orientation class and analyzing planar configurations.
result Smooth knots with odd quadratic terms of the Conway polynomial have inscribed trefoils.
Generalizes Fefferman's structure to CR three-manifolds with additional data.
problem Finding conditions for conformal isometry and existence of metrics.
method Introduces perturbations of Fefferman's conformal circle bundle and investigates existence of metrics.
result Provides conditions for existence of metrics satisfying Einstein equations.
In the framework of fibred cusp operators on a manifold associated to a boundary fibration $Φ: \pa X\to Y$, the homotopy groups of the space of invertible smoothing perturbations of the identity are computed in terms of the K-theory of . It is shown that there is a periodicity, namely the odd and the even h…
We introduce a gauge-theoretic integer lift of the Rohlin invariant of a smooth 4-manifold X with the homology of . The invariant has two terms; one is a count of solutions to the Seiberg-Witten equations on X, and the other is essentially the index of the Dirac operator on a non-compact manifold with e…
In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general -manifold is finite. We conjectured (and proved for the case of -loops) that, after adding counterterms of the expecte…
Geodesic spheres in certain symmetric spaces are quantitatively stable under small perturbations.
problem Stability of geodesic spheres in symmetric spaces under perturbations.
method Quantitative stability analysis using spectral gap of the Laplacian on geodesic spheres.
result Geodesic spheres are uniformly stable with respect to small -volume preserving perturbations.
Fair pricing and hedging under small perturbations of the numéraire on a finite probability spaceq-fin.PR
The paper examines fair pricing and hedging stability under small numéraire perturbations.
problem Fair pricing and hedging stability under numéraire perturbations.
method Reformulating the stochastic control problem to show stability and deriving asymptotic formulas.
result Fair price and hedging strategy are stable with small numéraire perturbations.
Novel tensor perturbation bounds for orthogonal iteration methods.
problem Developing robust bounds for tensor reconstruction and subspace estimation.
method Blockwise tensor perturbation bounds for high-order orthogonal iteration (HOOI).
result Upper bounds for singular subspace estimation converge linearly and tensor reconstruction error bound is characterized by a simple quantity.
The change in Holographic entanglement entropy (HEE) for small fluctuations about pure anti De Sitter (AdS) is obtained by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface. However, it is known that change in the embedding appears in second orde…
Study reveals class-dependent effects in perturbation-based feature attribution metrics for time series classification.
problem Varying effectiveness of perturbation-based metrics across different classes in time series models.
method Systematic empirical analysis across multiple datasets, model architectures, and perturbation strategies.
result Perturbation-based metrics show varying effectiveness across classes, with some metrics performing better for certain classes.
In \cite{LZ2} it is proved that for certain class of perturbations of the hyperbolic equation , there exist changes of coordinate, called quasi-Miura transformations, that reduce the perturbed equations to the unperturbed one. We prove in the present paper that if in addition the perturbed equations posse…
The paper is devoted to the study of BRST charge in perturbed two dimensional conformal field theory. The main goal is to write the operator equation expressing the conservation law of BRST charge in perturbed theory in terms of purely algebraic operations on the corresponding operator algebra, which are defined via th…
Implicit Regularization Makes Overparameterized Asymmetric Matrix Sensing Robust to Perturbationscs.LG
Paper shows robustness of gradient descent in matrix sensing despite perturbations.
problem Understanding robustness of gradient descent in matrix sensing.
method Developed perturbed gradient flow to capture noise and improve robustness.
result Gradient descent is robust to perturbations in matrix sensing.
PRoA assesses deep learning robustness against practical functional perturbations.
problem Inadequate practical robustness verification methods for deep learning systems.
method Probabilistic robustness assessment based on adaptive concentration.
result Statistical guarantees on probabilistic robustness against functional perturbations.
Modelling Cellular Perturbations with the Sparse Additive Mechanism Shift Variational Autoencoderstat.ML
SAMS-VAE models cellular perturbations using sparse additive mechanisms.
problem Modeling effects of diverse interventions on cells.
method Sparse Additive Mechanism Shift Variational Autoencoder (SAMS-VAE).
result SAMS-VAE identifies disentangled, perturbation-specific latent subspaces.
Recent advances show that deep neural networks are not robust to deliberately crafted adversarial examples which many are generated by adding human imperceptible perturbation to clear input. Consider norms attacks, Project Gradient Descent (PGD) and the Carlini and Wagner (C\&W) attacks are the two main methods, …
Quantum mechanics applied to option pricing with a time-dependent bubble.
problem Option pricing with a time-dependent arbitrage bubble.
method Application of Dirac's interaction picture to the Black-Scholes equation.
result Exact and approximate solutions for option pricing with a square bubble.
The paper shows robustness of Hilbert space-valued stochastic volatility models to perturbations.
problem Robustness of Hilbert space-valued stochastic volatility models to measurement or approximation errors.
method Quantifying the error induced by volatility perturbations and studying robustness of volatility process with finite dimensional approximations.
result Explicit bounds for the induced error in terms of approximation of the underlying parameter.
SIGNNAP learns stable and identifiable node representations in GNNs against graph perturbations.
problem Fragility of GNN models to graph perturbations leading to unreliable node representations.
method SIGNNAP proposes a novel model that learns stable and identifiable node representations in an unsupervised manner, formalizing stability and identifiability through a contrastive objective and preserving smoothness with existing GNN backbones.
result SIGNNAP demonstrates effectiveness in learning stable and identifiable node representations in GNNs against graph perturbations on six benchmarks.
Study on stability of GCNNs under graph perturbations.
problem Limited theoretical understanding of GCNN stability.
method Proposes a probabilistic framework to analyze GCNN stability under various graph perturbations.
result Demonstrates the importance of data distribution in stability analysis.
We show that under suitable non-degeneracy conditions, complete gradient flow lines of the scalar curvature functional of a riemannian manifold perturb into eternal forced mean curvature flows with large forcing term.