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 work connects symmetries and conserved quantities in machine learning.
Paper proposes COM-QEL to avoid overoptimistic solutions in offline optimization.
Theoretical proof shows COMs are a type of contrastive divergence model with improved sampling.
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…
This article uses Cartan-Kähler theory to construct local conservation laws from covariantly closed vector valued differential forms, objects that can be given, for example, by harmonic maps between two Riemannian manifolds. We apply the article's main result to construct conservation laws for covariant divergence free…
Conservation laws improve diffusion model training by optimizing likelihood.
In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of symmetry is just a relative integral invariant, a differential form which only upon integration over a cycle provides a conserved real number…
We consider the problem of estimating the set of all inputs that leads a system to some particular behavior. The system is modeled by an expensive-to-evaluate function, such as a computer experiment, and we are interested in its excursion set, i.e. the set of points where the function takes values above or below some p…
A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.
Simplified kernel ridge regression with a conservation law.
ECD algorithm speeds up non-convex optimization, offering quantum and stochastic enhancements.
Unified neural network framework for context-aware Gaussian overbounds in uncertainty propagation.
Companies try to maximize their profits by recovering returned products of highly uncertain quality and quantity. In this paper, a reverse logistics network for an Original Equipment Manufacturer (OEM) is presented. Returned products are selected for remanufacturing or scrapping, based on their quality and proportional…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that those objects can be naturally associated to systems with constraints -- we recall…
We associate an integrable generalized complex structure to each 2-dimensional symplectic Monge-Ampère equation of divergent type and, using the Gualtieri operator, we characterize the conservation laws and the generating function of such equation as generalized holomorphic objects.
Survey on conservation laws for geometric PDEs.
In an effort to better understand meaning from natural language texts, we explore methods aimed at organizing lexical objects into contexts. A number of these methods for organization fall into a family defined by word ordering. Unlike demographic or spatial partitions of data, these collocation models are of special i…
CQL learns conservative Q-functions to improve offline RL performance.
Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or i…
We propose a novel objective function for learning robust deep representations of data based on information theory. Data is projected into a feature-vector space such that the mutual information of all subsets of features relative to the supervising signal is maximized. This objective function gives rise to robust repr…
We propose a dynamical model for business cycle based on an optimal DI model. In the model there exists a conserved quantity, which corresponds to the total energy in a dynamical system. We found that the business cycle with the period 6 or 7 years is nicely reproduced, since the model predicts a periodic motion in the…
New neural network enforces mass conservation for better ice flow predictions.
Deep learning is built on the foundational guarantee that gradient descent on an objective function converges to local minima. Unfortunately, this guarantee fails in settings, such as generative adversarial nets, that exhibit multiple interacting losses. The behavior of gradient-based methods in games is not well under…
MC-LSTM extends LSTM to conserve mass in neural networks.
Proposes a conservative exploration method for RL agents.
New framework models non-conservative stochastic processes without energy conservation constraints.
Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
Study finds conserved quantities for two types of curves on conformal sphere.
Discover conservation laws from trajectories using a neural network.
New approach relaxes inductive biases of physics-inspired NNs for better performance.
Enhances HNNs for conservative systems with noisy data.
The article discusses conservation laws for polyharmonic maps and their applications.
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the action principle to define the conservation law for such general fields. By con…
LNNs learn Lagrangians without canonical coordinates, conserving energy and relativity.
Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.
I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservatio…
Offline RL policies should adapt to unknown aspects of the environment.
Zellner (1988) modeled statistical inference in terms of information processing and postulated the Information Conservation Principle (ICP) between the input and output of the information processing block, showing that this yielded Bayesian inference as the optimum information processing rule. Recently, Alemi (2019) re…
GP-MRO discovers robust mixed strategies for unknown objectives.
Non-trivial conservation law found for a specific system.
We derive conservation laws for Dirac-harmonic maps and their extensions to manifolds that have isometries, where we mostly focus on the spherical case. In addition, we discuss several geometric and analytic applications of the latter.
Safe exploration method for RL under disturbance ensures safety with probabilistic guarantees.
GeoHNN models physics laws for stable, accurate predictions.
INO learns physical models with momentum conservation laws.
Conservation law for weakly harmonic mappings in high dimensions.
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …
Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the Kelvin circulation theorem being a well-known special case. More generally, conserved…