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.
This paper describes how to define and work with differential equations in the abstract setting of tangent categories. The key notion is that of a curve object which is, for differential geometry, the structural analogue of a natural number object. A curve object is a preinitial object for dynamical systems; dynamical …
Develops scalable differentiable physics for complex object interactions.
Paper compares semi-supervised training for differentiable particle filters.
Shows flexible sheaves as fibrant objects for Gromov's h-principle.
New algebraic formalism for differential calculus in Diolic algebras.
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably…
Study improves sampling efficiency of diffusion models using RL and PDEs.
Algorithm improves vanilla option pricing accuracy during and before COVID-19.
BoTier optimizes experiments by balancing multiple objectives hierarchically.
A new parallel BO method with exact gradients for multi-objective optimization.
Advances M-polyfolds for complex geometry applications.
Variational approach to basic manifold structures.
An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue of the non-abelian Hodge theory in the context of -difference modu…
We provide a draft of a theory of geometric integration of rough differential forms which are generalizations of classical (smooth) differential forms to similar objects with very low regularity, for instance, involving Hölder continuous functions that may be nowhere differentiable. Borrowing ideas from the theory of r…
Abstract Lie algebroids generalize Lie algebroids to abstract categories.
Tangent categories provide an axiomatic framework for understanding various tangent bundles and differential operations that occur in differential geometry, algebraic geometry, abstract homotopy theory, and computer science. Previous work has shown that one can formulate and prove a wide variety of definitions and resu…
We refurbish our axiomatics of differential geometry introduced in [Mathematics for Applications,, 1 (2012), 171-182]. Then the notion of Euclideaness can naturally be formulated. The principal objective in this paper is to present an adaptation of our theory of differential forms developed in [International Journal of…
New method tackles rugged optimization landscapes in contact-rich scenarios.
We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space which corresponds to the pairing between the space of quadratic differentials an…
In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned with differential-geometric developments within the above axiomatic scheme, this…
We study the cross-entropy method (CEM) for the non-convex optimization of a continuous and parameterized objective function and introduce a differentiable variant that enables us to differentiate the output of CEM with respect to the objective function's parameters. In the machine learning setting this brings CEM insi…
The Lagrangian formalism on a arbitrary non-fibrating manifold is considered. The kinematical description of this generic situation is based on the concept of (higher-order) Grassmann manifolds which is the factorization of the regular velocity manifold to the action of the differential group. Here we introduce in this…
We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the gradient of a variational objective. We tackle the challenge by generalizing the repa…
Preserving differential privacy has been well studied under centralized setting. However, it's very challenging to preserve differential privacy under multiparty setting, especially for the vertically partitioned case. In this work, we propose a new framework for differential privacy preserving multiparty learning in t…
The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have emancipated microlinearity from within well-adapted models…
A new category of Lie algebras, called generalized Lie algebras, is presented such that classical Lie algebras and Lie-Rinehart algebras are objects of this new category. A new philosophy over generalized Lie algebroids theory is presented using the notion of generalized Lie algebra and examples of objects of the categ…
3D object detection improved using energy-based models.
The caloron correspondence is a tool that gives an equivalence between principal -bundles based over the manifold and principal -bundles on , where is the Fréchet Lie group of smooth loops in the Lie group . This thesis uses the caloron correspondence to construct certain differential f…
New method improves training stochastic neural networks with tighter guarantees.
A new variational method for SSMs improves inference efficiency.
This work analyzes the convergence rate of unrolling for optimizing quadratic objectives.
Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the per…
The thesis explores stability conditions and metrics in differential geometry.
Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some significant examples from mechanics and economics are presented.
Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they…
The paper analyzes and proposes methods for privately sharing individual privacy losses using per-instance differential privacy.
Improved set prediction model using multiset-equivariant operations and approximate implicit differentiation.
Integrates differential privacy and demographic parity in multi-class classification.
We develop a theory of Lie algebroids over differentiable stacks that extends the standard theory of Lie algebroids over manifolds. In particular we show that Lie algebroids satisfy descent for submersions, define the category of Lie algebroids over a differentiable stack, construct a cohomology theory for these object…
The purpose of this thesis is to study classical combinatorial objects, such as polytopes, polytopal complexes, and subspace arrangements, using tools that have been developed in combinatorial topology, especially those tools developed in connection with (discrete) differential geometry, geometric group theory and low-…
New method stabilizes private LASSO for high-dimensional data with diverse covariate scales.
Modeling interacting objects with latent Gaussian process ODEs.
The process of data mining with differential privacy produces results that are affected by two types of noise: sampling noise due to data collection and privacy noise that is designed to prevent the reconstruction of sensitive information. In this paper, we consider the problem of designing confidence intervals for the…
Groupoids provide a more appropriate framework for differential geometry than principal bundles. Synthetic differential geometry is the avant-garde branch of differential geometry, in which nilpotent infinitesimals are available in abundance. The principal objective in this paper is to show within our favorite framewor…
New method optimizes multiple objectives in A/B testing for AI and clinical trials.
AutoSimulate efficiently optimizes synthetic data generation.
We introduce multiplicative differential forms on Lie groupoids with values in VB-groupoids. Our main result gives a complete description of these objects in terms of infinitesimal data. By considering split VB-groupoids, we are able to present a Lie theory for differential forms on Lie groupoids with values in 2-term …
Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract setting for differential geometry by axiomatizing key aspects of the subject which all…