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.
Proposes a novel path generation and evaluation method for video games.
Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
One-shot path planning for multiple agents using neural networks.
Introduces q-paths for generalizing geometric annealing paths in machine learning.
Transports along path in fibre bundles are axiomatically introduced. Their general functional form and some their simple properties are investigated. The relationships of the transports along paths and lifting of paths are studied.
This paper describes and evaluates the use of Generative Adversarial Networks (GANs) for path planning in support of smart mobility applications such as indoor and outdoor navigation applications, individualized wayfinding for people with disabilities (e.g., vision impairments, physical disabilities, etc.), path planni…
A new method predicts future paths using a Monte-Carlo approach.
A positive path in the linear symplectic group $\Sp(2n)$ is a smooth path which is everywhere tangent to the positive cone. These paths are generated by negative definite (time-dependent) quadratic Hamiltonian functions on Euclidean space. A special case are autonomous positive paths, which are generated by time-indepe…
Flow Matching enables robust training of CNFs with various probability paths.
This paper optimizes paths for generative models using kinetic energy.
Paper presents a copula-based method to efficiently generate correlated sample paths from multi-step time series models.
A toolkit for path-norms enhances neural network generalization bounds.
The (parallel) linear transports along paths in vector bundles are axiomatically described. Their general form and certain properties are found. It is shown that these transports are locally (i.e. along every fixed path) always Euclidean ones in a senses that there exist frames in which their matrices are unit. The inv…
Extend classical theory of affine processes to path-dependent setting
New method generates realistic financial price paths with drawdowns.
The linear transports along paths in vector bundles introduced in Ref. [1] are applied to the special case of tensor bundles over a given differentiable manifold. Links with the transports along paths generated by derivations of tensor algebras are investigated. A possible generalization of the theory of geodesics is p…
Path-independent equilibrium models improve network performance on harder problems.
New AI method generates SDE paths without explicit coefficients.
Dupire's functional Itô calculus provides an alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices. In this paper, we introduce a measure of path-dependence of functionals within the functional Itô calculus framework. Name…
Study of motion constraints and path-following on 3D space.
Study lattice paths from twist knots and double twist knots.
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire's functional Ito calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent deriv…
Generative model for TPPs using signatures and distributional discrepancies.
Develops methods to find most probable paths on complex manifolds.
Foundation for robust finance using rough path theory.
The paper calculates sensitivities for financial derivatives using path weighting methods.
In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the solution in terms of path d…
This work derives closed-form expressions computing the expectation of co-presence and of number of co-occurrences of nodes on paths sampled from a network according to general path weights (a bag of paths). The underlying idea is that two nodes are considered as similar when they often appear together on (preferably s…
The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically eval…
Develops methods to simulate rare transitions in molecular systems.
Study on Frechet distance properties for paths and graphs.
The study proves unique path lifting properties and their implications on quotient spaces and covering maps.
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
Generative Flow Networks solve shortest path problems in graphs.
The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths acting in it is considered. The consistency between linear transports along paths i…
Deep network solves maze path planning without training.
Modern navigation services often provide multiple paths connecting the same source and destination for users to select. Hence, ranking such paths becomes increasingly important, which directly affects the service quality. We present PathRank, a data-driven framework for ranking paths based on historical trajectories us…
Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying lat…
The study compares different game-theoretic attribution methods and finds that interventional Shapley values yield less consistent results than Aumann-Shapley due to path symmetry.
Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph convolution framework that involves every path linking the message sender and recei…
Complexity measures for neural nets with general activations using path-based norms.
We solve the paradox of score-based methods by minimizing path variance.
New methods use machine learning to simulate rare transitions in molecular systems.
We characterize the existence of horizontal path lifts for general connections on arbitrary fiber bundles with a new property that also gives fresh insight into linear and -connections.
In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computati…
Develops a new model-free approach to portfolio theory using rough paths.
In the framework of path integral the evolution operator kernel for the Merton-Garman Hamiltonian is constructed. Based on this kernel option formula is obtained, which generalizes the well-known Black-Scholes result. Possible approximation numerical schemes for path integral calculations are proposed.