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.
We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal component analysis. As the ambient dimension tends to infinity, and with proper tim…
A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a N-way model of O(LN) into a simple matrix equation of O(NL2) with a real-time capability. To avoid numerical instability d…
Identifying changes in the generative process of sequential data, known as changepoint detection, has become an increasingly important topic for a wide variety of fields. A recently developed approach, which we call EXact Online Bayesian Changepoint Detection (EXO), has shown reasonable results with efficient computati…
Online detection of abrupt changes in high-dimensional data streams.
problem Detecting abrupt changes in high-dimensional, streaming data with multiple subspaces.
method Dynamic sparse subspace learning approach with multiple structural change-point model, Bayesian information criterion for penalty coefficients selection, and Pruned Exact Linear Time algorithm.
result Effectiveness demonstrated through simulation and real gesture data studies.
We consider online detection strategies for identifying a change point in a stream of quantum particles allegedly prepared in identical states. We show that the identification of the change point can be done without error via sequential local measurements while attaining the optimal performance bound set by quantum mec…
Paper addresses online alignment of large language models under uncertain preference feedback.
problem Online alignment of large language models with misspecified preference feedback.
method Formulates an oracle-robust objective as a worst-case optimization problem for log-linear policies, and develops projected stochastic composite updates.
result Shows that the robust objective admits an exact closed-form decomposition and achieves O(ε−2) oracle complexity.
Unified framework for efficient online training of RNNs.
problem Efficient and biologically plausible online training of recurrent neural networks.
method Organizes algorithms based on criteria like past vs. future facing, tensor structure, stochastic vs. deterministic, and closed form vs. numerical.
result Algorithms cluster according to criteria, revealing conceptual connections.
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equation…
By using Bäcklund transformation for the sine-Gordon equation, new periodic exact solutions of the constant astigmatism equation zyy+(1/z)xx+2=0 are generated from a seed which corresponds to Lipschitz surfaces of constant astigmatism.
Researchers found a new exact solution for pricing Aunt Michaela options using modified Black-Scholes equation.
problem Pricing Aunt Michaela options with a specific maturity condition.
method Computed a new exact series solution of a modified Black-Scholes equation using Maple.
result The modified Black-Scholes equation with Aunt Michaela option is exactly solvable using associated Laguerre polynomials or Whittaker M functions.
We propose two methods to obtain exact solutions for the Almgren-Chriss model about optimal execution of portfolio transactions. In the first method we rewrite the Almgren-Chriss equation and find two exact solutions. In the second method, employing a general reparametrized time, we show that the Almgren-Chriss equatio…
Changepoints are abrupt variations in the generative parameters of a data sequence. Online detection of changepoints is useful in modelling and prediction of time series in application areas such as finance, biometrics, and robotics. While frequentist methods have yielded online filtering and prediction techniques, mos…
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.
Let f,g:R→R be integrable functions, f nowhere zero, and φ(u)=∫du/f(u) be invertible. An exact solution to the generalized nonhomogeneous inviscid Burgers' equation ut+g(u).ux=f(u) is given, by quadratures.
Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.
We outline a new geometric method of constructing exact solutions of gravitational field equations parametrized by generic off-diagonal metrics, anholonomic frames and possessing, in general, nontrivial torsion and nonmetricity. The formalism of nonlinear connections is elaborated for (pseudo) Riemannian and Einstein-C…
We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general relativity). There are constructed and analyzed three classes of solutions of Ricci …
In a number of physically important cases, the nonholonomically (nonintegrable) constrained Ricci flows can be modelled by exact solutions of Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We develop two geometric methods for constructing such solutions: The first approach applies the form…