This work improves explanation quality for time series predictions by learning perturbations.
problem Explaining predictions on multivariate time series data with time dependencies.
method Learning both masks and associated perturbations to explain predictions.
result Learning perturbations significantly improves explanation quality on time series data.
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.
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.
Complex Chern-Simons theory reveals peacock patterns in perturbative series.
problem Understanding the structure of partition functions in complex Chern-Simons theory.
method Analyzing the partition function as a holomorphic function and using resurgence theory.
result Perturbative series are resurgent, with trans-series involving non-perturbative variables.
Graph neural networks detect structural perturbations from time series data.
problem Detecting structural causes of disturbances in complex systems.
method Graph neural network approach to infer structural perturbations from functional time series.
result Data-driven approach outperforms typical reconstruction methods and meets Bayesian inference accuracy.
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 present in this paper an empirical framework motivated by the practitioner point of view on stability. The goal is to both assess clustering validity and yield market insights by providing through the data perturbations we propose a multi-view of the assets' clustering behaviour. The perturbation framework is illust…
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…
The large k asymptotics (perturbation series) for integrals of the form ∫FμeikS, where μ is a smooth top form and S is a smooth function on a manifold F, both of which are invariant under the action of a symmetry group G, may be computed using the stationary phase approximation…
The Habiro ring of a number field uses power series to study algebraic K-theory.
problem Analyzing algebraic K-theory of number fields.
method Introduces Habiro ring and modules graded by K3(K). result Establishes connections between Habiro ring and Chern-Simons theory.
CRITS improves time series classification with interpretable local explanations.
problem Lack of detailed explanations in time series classification models.
method CRITS uses convolutional kernels, max-pooling, and rectified linear units to extract feature weights.
result CRITS provides intrinsically interpretable local explanations without requiring gradients or random perturbations.
Adversarial Training (AT) and Virtual Adversarial Training (VAT) are the regularization techniques that train Deep Neural Networks (DNNs) with adversarial examples generated by adding small but worst-case perturbations to input examples. In this paper, we propose xAT and xVAT, new adversarial training algorithms, that …
DualVDT improves time-series forecasting with a novel dual reparametrized structure.
problem Time-series forecasting with improved performance and analytical rigor.
method Dual reparametrized variational mechanisms on VAE, latent score based generative model, reverse time stochastic differential equation, variational ancestral sampling, KL divergence reduction.
result Advanced performance in time-series forecasting with reduced KL divergence.
The paper proposes a method to generate diverse counterfactual explanations for anomaly detection in time series data.
problem Lack of helpful explanations for anomaly detection models in time series data.
method Model-agnostic algorithm that generates diverse counterfactual examples for anomaly detection models.
result The method produces counterfactual examples that are not considered anomalous by the detection model and satisfy validity, plausibility, and closeness criteria.
CCE improves anomaly detection metrics by measuring both confidence and consistency.
problem Existing anomaly detection metrics lack discriminative power, hyperparameter dependency, and robustness to perturbations.
method CCE uses Bayesian estimation to quantify uncertainty and constructs global and event-level confidence and consistency scores.
result CCE demonstrates strict boundedness, robustness, and linear time complexity.
The minority game (MG) model introduced recently provides promising insights into the understanding of the evolution of prices, indices and rates in the financial markets. In this paper we perform a time series analysis of the model employing tools from statistics, dynamical systems theory and stochastic processes. Usi…
We give an introductory survey on the universal Vassiliev invariant called the perturbative series expansion of the Chern-Simons theory of links in euclidean space, and on its relation with the Kontsevich integral. We also prove an original geometric property of the anomaly of Bott, Taubes, Altschuler, Freidel and D. T…
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.
A new stable similarity measure for time series using persistent homology.
problem Constructing a robust measure of time series similarity.
method Persistent homology for stability, bi-conditional periodicity score for similarity.
result Stability of the bi-conditional periodicity score under perturbations and dimension reduction.
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.
Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explici…
Study of mean curvature flows with conical singularities using mathematical techniques.
problem Understanding the dynamics of mean curvature flows near conical singularities.
method Feynman-Kac formula and invariant cone method for noncompact settings.
result Generic initial perturbations avoid conical singularities in mean curvature flows.
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal…
Proposes a stability evaluation criterion for learning models using distributional perturbations.
problem Ensuring reliable deployment of learning models in out-of-sample environments.
method Uses optimal transport discrepancy with moment constraints to quantify minimal perturbation required for model deterioration.
result Validates the practical utility of the stability evaluation criterion across various real-world applications.
Study evaluates local explanation methods for time series forecasting.
problem Lack of local interpretability methods for multivariate time series forecasting.
method Proposed two novel evaluation metrics: Area Over the Perturbation Curve for Regression and Ablation Percentage Threshold.
result Comprehensive comparison of local explanation models on two datasets.
This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial da…
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…
Invariants of hyperbolic knots connect to quantum modularity.
problem Understanding quantum invariants of hyperbolic knots.
method Introducing matrix invariants and their properties.
result Matrix invariants relate to quantum modularity conjectures.
Recently proposed adversarial training methods show the robustness to both adversarial and original examples and achieve state-of-the-art results in supervised and semi-supervised learning. All the existing adversarial training methods consider only how the worst perturbed examples (i.e., adversarial examples) could af…
This is the first paper in a series which proposes and develops the polyfold Fredholm structure--Kuranishi structure correspondence, identifying these two abstract perturbative structures which are indispensable for constructing and understanding symplectic invariants in the most general settings. In this paper, I pres…
This paper tackles gauge fixing and regularity for perturbations around spherical backgrounds.
problem Understanding gauge freedom and regularity in perturbation theory for symmetric tensors.
method Analyzing Hodge-type decomposition for axially symmetric and axistationary tensors, showing existence and uniqueness of gauge tensors.
result Stationary and axially symmetric second order perturbations can be rendered in a canonical form with only one degree of differentiability loss near the origin.
We develop a new method to price SOFR futures contracts considering convexity, skew, and smile.
problem Analyzing and pricing SOFR futures contracts with convexity, skew, and smile adjustments.
method A perturbative formalism based on a time-ordered exponential series to solve the backward-Kolmogorov diffusion PDE.
result An analytic pricing formula for SOFR futures contracts that incorporates convexity, skew, and smile adjustments.
The speculation game is an agent-based toy model to investigate the dynamics of the financial market. Our model has achieved the reproduction of 10 of the well-known stylized facts for financial time series. However, there is also a divergence from the behavior of real market. The market price of the model tends to be …
New findings show learnable distributions remain learnable even with noisy or adversarial perturbations.
problem Learning from perturbed samples in high-dimensional spaces.
method Developed a perturbation-quantization framework to analyze additive noise and adversarial corruption models.
result Sample compressible families remain learnable even under noisy or adversarial perturbations.
The paper explores hidden torus symmetries in integrable systems and their stability.
problem Structural stability of singularities in integrable systems.
method Use of hidden torus actions near singular orbits and integrable perturbations.
result Persistence of toric symmetries and structural stability of Kalashnikov's parabolic orbits.
New methods reveal symmetries in Chern-Simons theory.
problem Understanding symmetries in Chern-Simons theory.
method Introduced a special basis in the center of the universal enveloping algebra to present group factors in arbitrary representations.
result Computed Vassiliev invariants and proved the tug-the-hook symmetry of the colored HOMFLY polynomial.
Adversarial training can lead to overfitting without compromising robustness.
problem Explaining benign overfitting in adversarially robust linear classification.
method Theoretical analysis and numerical experiments on adversarial training.
result Adversarially trained linear classifiers can achieve near-optimal risks despite overfitting noisy data.
The purpose of the paper is to introduce some conjectures regarding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and 3-manifolds into two power series of type P and NP, convergent in …
Co-TSFA improves time series forecasting by distinguishing between short-lived and persistent anomalies.
problem Standard forecasting models fail to distinguish between short-lived and persistent anomalies, leading to overreaction or underreaction.
method Co-TSFA learns to ignore forecast-irrelevant anomalies and respond to forecast-relevant ones through input-only and input-output augmentations and a latent-output alignment loss.
result Co-TSFA improves performance under anomalous conditions while maintaining accuracy on normal data.
Improved GSPGS estimators reduce bias in noisy function measurements.
problem Reduced bias in noisy function measurements.
method Generalized Simultaneous Perturbation-based Gradient Search (GSPGS) with various estimators.
result Estimators requiring more function measurements have lower bias.
RINS-T solves time series inverse problems robustly without pretraining.
problem Recovering original signals from corrupted time series data.
method Implicit neural solvers with robust optimization techniques.
result RINS-T achieves high recovery performance without pretraining.
Matching correlated VAR time series databases by recovering matching permutations.
problem Matching perturbed and permuted correlated VAR time series.
method Probabilistic framework modeling, maximum likelihood estimator (MLE), linear assignment, convex relaxations.
result Recovery guarantees for perfect or partial recovery of matching permutations, thresholds for σ. Model predicts stock price volatility using stochastic differential equations.
problem Predicting stock price volatility in financial markets.
method Continuous cascade model using stochastic differential equations with two independent Brownian motions.
result The model accurately reproduces empirical volatility and multifractality.
Consider a supervised dataset D=[A∣b], where b is the outcome column, rows of D correspond to observations, and columns of A are the features of the dataset. A central problem in machine learning and pattern recognition is to select the most important features from D to be able to predic…
This paper presents a new method for solving systems with polynomial stiffness.
problem Finding analytical solutions to nonlinear differential equations with polynomial stiffness is challenging.
method The paper introduces a geometric/algebraic method using generating series and shuffle product.
result The method provides a recursive schematic that can be automated and applied to systems with polynomial stiffness.
This the first in a series of papers whose ultimate goal is to establish the full nonlinear stability of the Kerr family for ∣a∣≪m. The paper builds on the strategy laid out in \cite{KS} in the context of the nonlinear stability of Schwarzschild for axially symmetric polarized perturbations. In fact the central id…
ISOMORPH creates a digital twin for supply chain logistics, advancing time-series forecasting benchmarks.
problem Lack of public benchmarks for supply chain logistics time-series forecasting.
method Developed a digital twin simulator with interpretable parameters and modular topology, generating datasets and verifying conservation laws.
result Foundation models achieve MASE values exceeding public benchmarks at low-to-moderate horizons, supporting UQ.
SOAR improves deep networks' robustness against adversarial examples.
problem Improving deep neural networks' robustness against adversarial examples.
method Formulated adversarial robustness problem under robust optimization framework, approximated loss function using second-order Taylor series expansion.
result SOAR significantly improves robustness of networks against adversarial perturbations.