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.
A frame independent formulation of analytical mechanics in the Newtonian space-time is presented. The differential geometry of affine values i.e., the differential geometry in which affine bundles replace vector bundles and sections of one dimensional affine bundles replace functions on manifolds, is used. Lagrangian a…
Main ideas of the differential geometry on affine bundles are presented. Affine counterparts of Lie algebroid and Poisson structures are introduced and discussed. The developed concepts are applied in a frame-independent formulation of the time-dependent and the Newtonian mechanics.
Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by physical mechanisms that give rise to dependences between observables. Mechanisms, howe…
The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize the…
In the present paper we discuss an independent on the Grothendieck-Sato isomorphism approach to the Riemann-Roch-Hirzebruch formula for an arbitrary differential operator. Instead of the Grothendieck-Sato isomorphism, we use the Topological Quantum Mechanics (more or less equivalent to the well-known constructions with…
A common assumption in causal modeling posits that the data is generated by a set of independent mechanisms, and algorithms should aim to recover this structure. Standard unsupervised learning, however, is often concerned with training a single model to capture the overall distribution or aspects thereof. Inspired by c…
We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit fo…
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and unifies various geometrical approaches to mechanics in the Lagrangian and Hamilt…
Based on ideas of W. M. Tulczyjew, a geometric framework for a frame-independent formulation of different problems in analytical mechanics is developed. In this approach affine bundles replace vector bundles of the standard description and functions are replaced by sections of certain affine line bundles called AV-bund…
The Galilean group is the group of symmetries of Newtonian mechanics, with Lie a lgebra $\gal(n)$. We find algebraically independent generators for the center of the universal enveloping algebra of $\gal(n)$ using coadjoint orbits.
In this paper, we focus on developing a novel mechanism to preserve differential privacy in deep neural networks, such that: (1) The privacy budget consumption is totally independent of the number of training steps; (2) It has the ability to adaptively inject noise into features based on the contribution of each to the…
VAEs improve representation learning by inverting the data-generating process through self-consistency.
problem VAEs struggle to invert the data-generating process, yet often succeed in representation learning.
method Studied VAEs in the limit of near-deterministic decoders, proving self-consistency and showing ELBO convergence to a regularized log-likelihood.
result VAEs can perform independent mechanism analysis (IMA), recovering true latent factors under specific conditions.
We propose a method to classify the causal relationship between two discrete variables given only the joint distribution of the variables, acknowledging that the method is subject to an inherent baseline error. We assume that the causal system is acyclicity, but we do allow for hidden common causes. Our algorithm presu…
Researchers develop methods for causal inference with imperfect instrumental variables.
problem Quantifying cause and effect relationships with imperfect instrumental variables.
method Established a quantitative relationship between violations of instrumental inequalities and minimal measurement dependence, providing adapted inequalities valid in the presence of relaxed measurement dependence.
result Adapted inequalities for average causal effect in instrumental scenarios with binary outcomes, addressing violations of instrumental inequalities.
It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper, we develop a framework for causal discovery from such data…
Writing the article-Time independent pricing of options in range bound markets; the question in the title came naturally to my mind. It is stated, in the above article, that in certain market conditions the stock price is subjected to an equation that exactly matches a time independent Schrodinger equation. The time in…
New bounds for KANs trained with DP-SGD, addressing correlated noise.
problem Risk bounds for Kolmogorov-Arnold Networks trained by DP-SGD with correlated noise.
method Established new optimization and population risk analysis for KANs trained with DP-SGD, addressing correlated noise.
result First optimization and population risk analysis of correlated-noise mechanisms for DP training in non-convex settings, including neural networks.
Information Geometric Causal Inference (IGCI) is a new approach to distinguish between cause and effect for two variables. It is based on an independence assumption between input distribution and causal mechanism that can be phrased in terms of orthogonality in information space. We describe two intuitive reinterpretat…
This paper tackles time series imputation by identifying and modeling different missing mechanisms.
problem Different types of missing mechanisms (MAR, MNAR) in time series data.
method Proposes a framework for time series imputation by analyzing data generation processes and modeling latent variables via variational inference and normalizing flow.
result Establishes identifiability results for latent variables under nonlinear independent component analysis, showing that latent variables are identifiable.
The usual formulations of time-dependent mechanics start from a given splitting Y=R×M of the coordinate bundle Y→R. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a splitting is broken under reference frame transformations and time-dependent canonical …