Paper proposes a new Taylor moment expansion for non-linear Gaussian filtering and smoothing.
problem Non-linear Gaussian filtering and smoothing in continuous-discrete state-space models.
method Taylor moment expansion (TME) for moment functions directly and in time variable.
result Significantly outperforms state-of-the-art methods in terms of estimation accuracy and numerical stability.
Taylorized training improves neural network training at finite width.
problem Understanding and improving neural network training at finite width.
method Training the k-th order Taylor expansion of the neural network at initialization.
result Taylorized training agrees with full neural network training better as k increases and can significantly close the performance gap.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
problem Limitations of Taylor diagram in capturing non-linear relationships and sensitivity to outliers.
method Proposes a kernelized version of the Taylor diagram that uses maximum mean discrepancy and kernel mean embedding.
result Kernelized Taylor diagram visualizes data populations with minimal assumptions of data distributions.
TaylorPODA uses Taylor expansions to improve feature attributions for opaque models.
problem Lack of systematic framework for quantifying feature contributions in opaque models.
method Taylor expansion framework with postulates (precision, federation, zero-discrepancy, adaptation).
result TaylorPODA achieves competitive results and provides principled explanations.
New approximations for Asian basket spread options using stochastic Taylor expansions.
problem Pricing Asian basket spread options under the Black-Scholes model.
method Stochastic Taylor expansion applied to a log-normal proxy model.
result Highly accurate approximations for Asian and spread options, without numerical integration.
A framework connects Taylor methods with Fisher-efficient NG.
problem Combining Taylor-based methods with Fisher-efficient NG.
method Constructs a theoretical framework linking Taylor approximation and NG.
result Mathematical justification for combining higher order methods with NG.
Proposes a Taylor framework to unify and analyze attribution methods.
problem Lack of a unified guideline for feature contribution assignment in machine learning models.
method Introduces a Taylor attribution framework to model the attribution problem and reformulates fourteen mainstream methods.
result Empirically validates the Taylor reformulations and reveals a positive correlation between performance and principles followed.
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Developed Taylor series for muscle-finger system analysis.
problem Understanding the complex relationship between muscle activity and finger movement.
method Used Dendrite Net to develop Taylor series and construct relation spectrum.
result Found muscle synergy and coupling in hand movement.
Study finds Deep Taylor Decomposition is unreliable for explaining neural networks.
problem Reliability of Deep Taylor Decomposition for explaining neural networks.
method Investigated the theoretical foundations of Deep Taylor Decomposition (DTD) and found it under-constrained.
result DTD is unreliable because its theoretical foundations are under-constrained and roots do not align with input.
An expanding literature articulates the view that Taylor rules are helpful in predicting exchange rates. In a changing world however, Taylor rule parameters may be subject to structural instabilities, for example during the Global Financial Crisis. This paper forecasts exchange rates using such Taylor rules with Time V…
Unified framework for analyzing machine learning model attributions.
problem Lack of a general and theoretical framework for understanding attribution methods.
method Proposes a Taylor attribution framework to unify and analyze seven mainstream attribution methods.
result Established three principles for good attribution and empirically validated the Taylor reformulations.
New sampling scheme improves ML accuracy in physics simulations.
problem Improving accuracy of ML models in physics simulations.
method Taylor-based data sampling scheme for DNNs.
result Reduces error in DNN solutions of ODE systems.
The first aperiodic monotiling, introduced by Taylor, was based on a trapezoidal prototile equipped with 14 distinct decorations. A presentation of the closely related Taylor-Socolar aperiodic monotiling is based on a hexagonal prototile equipped with 7 decorations. This paper gives decoration-free algebraic descriptio…
Paper provides convergence guarantees for rectifier networks using neural Taylor approximations.
problem Smoothness and convexity issues in modern convolutional networks.
method Neural Taylor approximations and Taylor loss for optimization.
result Guarantees match lower bounds for convex nonsmooth functions and accurately capture optimization dynamics.
We develop closed-form approximations for European put options under stochastic volatility models.
problem Tackling the pricing of European put options under stochastic volatility models with time-dependent parameters.
method Using a second-order Taylor expansion around the mean of the argument, we write the option price as an expectation of a Black-Scholes formula. We then simplify the resulting expectations and derive closed-form pricing formulas under the assumption of piecewise-constant parameters.
result We derive closed-form pricing formulas and bounds on the remainder term generated by the Taylor expansion, showing that the errors are well within acceptable ranges for practical applications.
A new method explains anomalies in one-class models using deep Taylor decomposition.
problem Understanding why one-class models classify data points as anomalies.
method Recompose one-class SVM as a neural network, perform deep Taylor decomposition.
result The method reliably explains a wide set of data anomalies and outperforms baselines.
We provide new exact Taylor's series with fixed coefficients and without the remainder. We demonstrate the usefulness of this contribution by using it to obtain very simple solutions to (non-linear) PDEs. We also apply the method to the portfolio model.
We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the …
Paper develops a new algorithm to find shortest paths on surfaces.
problem Finding shortest paths on surfaces with defined metrics.
method Uses Taylor expansion of exponential map for numerical computation.
result Developed a new algorithm to find geodesics efficiently.
TEAM uses Taylor expansion to generate adversarial examples.
problem Vulnerability of deep neural networks to adversarial examples.
method Approximates DNN output using Taylor expansion and optimizes with Lagrange multiplier method.
result Improves robustness of DNNs through adversarial training.
The paper modifies asset pricing models using Taylor series expansions and market-based averages.
problem Improving asset pricing models to better reflect market dynamics.
method Derives new pricing equations using Taylor series expansions and market-based averages.
result New expressions for asset prices and volatilities derived from market data.
Examines how central bank policies affect stock markets and asset prices.
problem Understanding the impact of monetary policy on stock markets and asset prices.
method Used Taylor rule equations to analyze data from 1990 to 2020 for US and UK, testing with various econometric methods.
result Monetary policy can explain asset price volatility and output gap better than just inflation rate.
The Adomian decomposition method is shown to be equivalent to the Taylor series approach.
problem Incorrectly perceived complexity of the Adomian decomposition method.
method Demonstrates the Adomian decomposition method as equivalent to the Taylor series approach.
result The Adomian decomposition method is simpler and more straightforward.
New learning algorithm for real analytic functions without gradient descent.
problem Learning real analytic functions without gradient descent.
method Taylor approximation and sampling data distribution.
result Nonuniform learning result for real analytic functions.
The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
problem Calculating Bachelier option prices and variance reduction in correlated cases.
method Taylor expansions and classical Itô calculus to derive option prices, uses negative powers of future mean volatility.
result The paper provides a new method to calculate Bachelier option prices and applies it to reduce variance in Monte Carlo simulations.
In this paper we propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model, based on Taylor expansions and the calculation of mixed exponential-power moments of a Gaussian distribution. Our numerical results show that a second order expansion provides accurate prices o…
Proves a special case of the Gaussian kinematic formula using large sphere limits.
problem Proving a special case of the Gaussian kinematic formula.
method Viewing the GKF as the limit of spherical kinematic formulas for large dimension spheres.
result Proves a special case of the Gaussian kinematic formula.
Extends Bonnet-Myers theorem with new generalizations.
problem Generalizing Bonnet-Myers theorem.
method Complementary generalization of existing extensions by Calabi and Cheeger-Gromov-Taylor.
result New theorem extending previous extensions of Bonnet-Myers.
We introduce Taylor expansions that do not require the differentiability. We also provide new solutions to partial differential equations. We apply our methods to finance.
New insights on pruning deep networks by preserving function locality.
problem Designing effective pruning methods for deep neural networks.
method Revisited loss modeling using first and second order Taylor expansions, emphasizing locality.
result Both first and second order Taylor expansions can achieve similar performance in pruning.
Taylor's law found in stock market illiquidity, with varying exponents.
problem Understanding the temporal fluctuation scaling in stock illiquidity.
method Investigation of high-frequency illiquidity data from multiple exchanges and industries.
result Taylor's law holds with varying exponents (b > 2 for A-shares, b < 2 for B-shares) across different markets and sectors.
Analyzes explaining nonlinear model predictions.
problem Understanding the contribution of inputs to outputs in nonlinear models.
method Merges integrated gradient and deep Taylor decomposition methods.
result Provides a natural reference point for model at use.
In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R^3. Also we compute, by using the Taylor expan…
New samplers reduce NFEs for diffusion models.
problem High NFEs in diffusion models.
method Quasi-Taylor samplers based on ideal derivatives.
result Reduced NFEs for image synthesis.
Deep networks analyze video snippets to predict outcomes, revealing a border effect that can be adjusted for better accuracy.
problem Improving the accuracy of deep networks trained on small video snippets.
method Applied the deep Taylor / LRP technique to understand and identify a border effect, tuning the step size to improve accuracy.
result The step size used to build video snippets can be adjusted to improve deep network accuracy without retraining.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
problem Defining and analyzing Ruelle-Taylor resonances for Anosov actions.
method Combining microlocal methods and J. Taylor's cohomological theory, defining Ruelle-Taylor resonances and proving Fredholm theory.
result Ruelle-Taylor resonances form a discrete subset of Cκ with λ=0 being a leading resonance. New SVM models correct mean of volatility processes to satisfy efficient market hypothesis.
problem Capturing complex market behavior while maintaining efficient market hypothesis.
method Propose mean-corrections for generalized Taylor SVM models.
result Models satisfy efficient market hypothesis and capture complex market behavior.
Paper develops formulas for shape derivatives in wave scattering.
problem Computing high order shape derivatives for wave scattering is challenging.
method Introduces elegant recurrence formulas using differential forms and Lie derivatives.
result Unified framework for computing high order shape perturbations in scattering problems.
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…
Iterative tilting fine-tunes diffusion models for reward-tilted distributions.
problem Fine-tuning diffusion models for reward-tilted distributions.
method Decomposes large reward tilts into smaller, tractable tilts via first-order Taylor expansion, avoiding backpropagation.
result Validated on a two-dimensional Gaussian mixture, achieving exact closed-form solutions.
In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by Lévy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting parameterized curve. We apply this method to devel…
Study complex structures with totally real sections, providing integrability equations.
problem Existence and integrability of complex structures with totally real sections.
method Explicit integrability equations derived from fiberwise Taylor expansions.
result Detailed fiberwise Taylor expansions and integrability equations in a geometric case.
In this paper we study the Taylor series of an operator-valued function related to the differential of the exponential map. For a smooth manifold M with a torsion-free affine connection the operator Ep(v) acting on the space TpM is defined to be the composition of the differential …
Study shows how noise and distractions affect neural network explanations.
problem Lack of consideration for noise and distractions in neural network explanations.
method Examined the impact of noise and distracting elements on neural network interpretation models.
result Noise and distracting elements influence the results of neural network explanations.
Expanding the rough Heston model in H
problem Analyzing the dependence of the fractional Riccati equation on the Hurst parameter H method Deriving a Taylor expansion of the Riccati solution in H result Local uniform convergence and analyticity of the fractional Riccati solution
This work continues the study of a homotopy-theoretic construction of the author inspired by the Bott-Taubes integrals. Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots. Their techniques were later used by Cattaneo et al. to construct real…
This paper provides intuition on the relationship of accrual and mark-to-market valuation for cash and forward interest rate trades. Discounted cashflow valuation is compared to spread-based valuation for forward trades, which explains the trader's view on valuation. This is followed by Taylor series approximation for …