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.
Taylorized training improves neural network training at finite width.
Kernelized Taylor diagram visualizes data populations with fewer assumptions.
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
TaylorPODA uses Taylor expansions to improve feature attributions for opaque models.
New approximations for Asian basket spread options using stochastic Taylor expansions.
Proposes a Taylor framework to unify and analyze attribution methods.
Taylor expansions improve reinforcement learning policies.
Developed Taylor series for muscle-finger system analysis.
Study finds Deep Taylor Decomposition is unreliable for explaining neural networks.
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.
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…
New sampling scheme improves ML accuracy in physics simulations.
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.
Paper develops a new algorithm to find shortest paths on surfaces.
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 …
This technical report constructs a theoretical framework to relate standard Taylor approximation based optimisation methods with Natural Gradient (NG), a method which is Fisher efficient with probabilistic models. Such a framework will be shown to also provide mathematical justification to combine higher order methods …
Modern convolutional networks, incorporating rectifiers and max-pooling, are neither smooth nor convex; standard guarantees therefore do not apply. Nevertheless, methods from convex optimization such as gradient descent and Adam are widely used as building blocks for deep learning algorithms. This paper provides the fi…
The Adomian decomposition method is shown to be equivalent to the Taylor series approach.
The paper modifies asset pricing models using Taylor series expansions and market-based averages.
Examines how central bank policies affect stock markets and asset prices.
New learning algorithm for real analytic functions without gradient descent.
The paper calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
Proves a special case of the Gaussian kinematic formula using large sphere limits.
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…
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.
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.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
We consider closed-form approximations for European put option prices within the Heston and GARCH diffusion stochastic volatility models with time-dependent parameters. Our methodology involves writing the put option price as an expectation of a Black-Scholes formula and performing a second-order Taylor expansion aroun…
Paper develops formulas for shape derivatives in wave scattering.
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.
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…
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 with a torsion-free affine connection the operator acting on the space is defined to be the composition of the differential …
Expanding the rough Heston model in
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 …
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove that as the surface tension tends to zero, when the Rayleigh-Taylor condition is satisfied, solutions converge to the Euler …
We describe Taylor towers for spaces of knots arising from Goodwillie-Weiss calculus of the embedding functor and extend the configuration space integrals of Bott and Taubes from spaces of knots to the stages of the towers. We show that certain combinations of integrals, indexed by trivalent diagrams, yield cohomology …
Approximates option prices in Barndorff-Nielsen and Shephard models using Taylor expansion.
Deep networks are able to learn highly predictive models of video data. Due to video length, a common strategy is to train them on small video snippets. We apply the deep Taylor / LRP technique to understand the deep network's classification decisions, and identify a "border effect": a tendency of the classifier to loo…
SOAR improves deep networks' robustness against adversarial examples.
Let M and N be smooth manifolds. For an open V of M let emb(V,N) be the space of embeddings from V to N. By results of Goodwillie and Goodwillie-Klein, the cofunctor V |--> emb(V,N) is analytic if dim(N)-dim(M) > 2. We deduce that its Taylor series converges to it. For details about the Taylor series, see Part I.
Taylor's law of temporal fluctuation scaling, variance mean, is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity o…
Paper introduces cubature method for stochastic Volterra equations.
We associate a Taylor tower supplied by calculus of the embedding functor to the space of long knots and study its cohomology spectral sequence. The combinatorics of the spectral sequence along the line of total degree zero leads to chord diagrams with relations as in finite type knot theory. We show that the spectral …