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.
Survey on smooth function and form density in Riemannian Sobolev spaces.
Paper presents a new policy gradient theorem using weak derivatives for reinforcement learning.
Novel weak MLMC scheme for Lévy-driven SDEs, applied to financial derivatives pricing.
Weak correlations explain linear dynamics in deep learning models.
Characterizes when differential forms have weak exterior derivatives based on limiting behavior of integration over simplices.
We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic …
Paper develops proper, lower-bounded losses for weakly supervised classification.
Study the geometry of weak para-f-structures and subclasses.
Study on fourth order Lamm-Riviere system for biharmonic mappings in 4D.
We introduce the notion of weak commensurabilty of arithmetic subgroups and relate it to the length equivalence and isospectrality of locally symmetric spaces. We prove many strong consequences of weak commensurabilty and derive from these many interesting results about isolength and isospectral locally symmetric space…
Establishes equivalence between models of derived stacks.
Gradient estimates for solutions to a p-Laplacian equation on Riemannian manifolds.
Self-test loss functions improve data-driven modeling of weak-form operators and gradient flows.
Atiyah classes of DG manifolds of positive amplitude are invariant under weak equivalences.
We give a proof that Brakke's mean curvature flow under the unit density assumption is smooth almost everywhere in space-time. More generally, if the velocity is equal in a weak sense to its mean curvature plus some given α-Hölder continuous vector field, then we show C^{2,α} regularity almost everywhere.
We study weakened -structures on manifolds, generalizing classical results.
We obtain sharp quantitative Laplacian upper and lower estimates under no assumption on curvatures. As a result, we derive quantitative Laplacian, area and volume comparison theorems for tubes in Riemannian and Kähler manifolds under weak integral curvature assumptions. We also give some applications, such as a general…
The study explores the strengths and weaknesses of models that generalize from weak to strong supervision.
Weak base-point freeness leads to Kähler-Ricci flow diameter bounds.
Generative models enhance weak supervision for better image classification.
We study a geometric flow where the motion of a set is driven by the mean curvature of its boundary and the normal derivative of its capacity potential. We establish local well-posedness and propose two possible weak formulations that exist after singularities.
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …
We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved so…
Paper generalizes Andreev's theorem with obtuse angles.
New method estimates model performance bounds without ground truth labels.
The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibrati…
Stein variational gradient descent (SVGD) is a deterministic sampling algorithm that iteratively transports a set of particles to approximate given distributions, based on an efficient gradient-based update that guarantees to optimally decrease the KL divergence within a function space. This paper develops the first th…
We develop semistrict higher gauge theory from first principles. In particular, we describe the differential Deligne cohomology underlying semistrict principal 2-bundles with connective structures. Principal 2-bundles are obtained in terms of weak 2-functors from the Cech groupoid to weak Lie 2-groups. As is demonstrat…
Sparse-penalized deep neural networks improve performance in weakly dependent processes.
New deep learning architecture learns martingales efficiently.
New regularization method corrects over-shrinkage in small data regression.
Unified approach for learning with weak labels across various tasks.
Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuit…
In this paper, we develop an approach to recursively estimate the quadratic risk for matrix recovery problems regularized with spectral functions. Toward this end, in the spirit of the SURE theory, a key step is to compute the (weak) derivative and divergence of a solution with respect to the observations. As such a so…
New method improves IV estimation with many weak and invalid instruments.
We consider spaces of smooth immersed plane curves (modulo translations and/or rotations), equipped with reparameterization invariant weak Riemannian metrics involving second derivatives. This includes the full -metric without zero order terms. We find isometries (called -transforms) from some of these spaces i…
Formula derived for blow-up of quaternionic maps on Hyperkähler manifolds.
Efficient simulation scheme for rough Heston model reduces computational cost.
We introduce a notion of a weak Poisson structure on a manifold modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition (the differentials of elements of $\cA$ separate tangent vectors) and we postulate …
We extend martingale transport results to weak martingale transport.
We introduce cylindrical projections to simulate infinite-dimensional occupation flows of diffusions.
Paper proves mass theorems for nonnegative scalar curvature metrics.
We analyze the Standard & Poor's 500 stock market index from the last 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong super-diffusion together with short-time correlations, and the second one corresponds to we…
Derives estimate for Kähler-Ricci flows with weaker conditions.
Improved volatility models for option pricing with weak error rates.
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting with respect to any convex objective and introduce a new measure of weak learner p…
The paper explores new connections in non-symmetrical gravitational theory using weak metric structures.
This paper concerns the inverse mean curvature flow of convex hypersurfaces which are Lipschitz in general. After defining a weak solution, we study the evolution of the singularity by looking at the blow-up tangent cone around each singular point. We prove the cone also evolves by the inverse mean curvature flow and e…