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.
Reduction principles for proper actions on smooth manifolds.
Variational reduction simplifies Lagrangian systems with scaling symmetries.
We discuss the use of Dirac structures to obtain a better understanding of the geometry of a class of optimal control problems and their reduction by symmetries. In particular we will show how to extend the reduction of Dirac structures recently proposed by Yoshimura and Marsden [Yo09] to describe the reduction of a cl…
New deep network derived from rate reduction principles, explaining features and efficiency.
PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives…
Study nonholonomic systems with collisions using variational principles.
Examines quantum mechanics equivalence with Newtonian geometry.
Dirac structures on tangent bundles provide a unified framework for Lagrange--Dirac dynamical systems.
Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) -dua…
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects generalizing Lie algebroids. This formulation of the PMP yields, in particular, a scheme comprising reductions of optimal control problems simil…
The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a small number of principal components to explain the variation found in a data set…
Ant colonies and boosting algorithms both reduce bias and variance through adaptive mechanisms.
This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classica…
Reduces constructing multiplicative connections to simpler tasks.
Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the sca…
New principle reduces load imbalance in LLM serving systems, saving up to 52% energy.
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is applied to the problem of curve matching in the plane, when the curves depend on more than one independent variable. This situation occurs in a…
We formulate a quantization commutes with reduction principle in the setting where the Lie group , the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and the zero set of a deformation vector field, associated to the momentum map and a…
Reduces survival analysis to common regression tasks.
Reduces proper actions to simpler core actions for analysis.
Maximizes coding rate difference for robust, discriminative features.
In this paper we show that the `quantization commutes with reduction' principle of Guillemin-Sternberg holds for the coadjoint orbits that parametrize the discrete series of a real connected semi-simple Lie group.
Develops a reduction theory for covariant field theories with gauge symmetries.
Derives stochastic and dissipative dynamics preserving Gibbs measure.
A framework for reducing PDEs by symmetry, preserving key structures.
New method reduces version space for CNNs, improving active learning performance.
Transformers reduce redundancy by focusing on invariant relational quantities.
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for…
ReduNet optimizes data compression by maximizing rate reduction in deep networks.
We prove injectivity and a support theorem for the X-ray transform on -step nilpotent Lie groups with many totally geodesic -dimensional flats. The result follows from a general reduction principle for manifolds with uniformly escaping geodesics.
We define an equivariant index of Spin-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to the quantisation commutes with reduction principle.
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
The paper examines how risk reduction and insurance choices interact under convex premium principles.
In this paper, we make a generalization of Routh's reduction method for Lagrangian systems with symmetry to the case where not any regularity condition is imposed on the Lagrangian. First, we show how implicit Lagrange-Routh equations can be obtained from the Hamilton-Pontryagin principle, by making use of an anholonom…
Dimension reduction is the process of embedding high-dimensional data into a lower dimensional space to facilitate its analysis. In the Euclidean setting, one fundamental technique for dimension reduction is to apply a random linear map to the data. This dimension reduction procedure succeeds when it preserves certain …
Typical dimensionality reduction methods focus on directly reducing the number of random variables while retaining maximal variations in the data. In this paper, we consider the dimensionality reduction in parameter spaces of binary multivariate distributions. We propose a general Confident-Information-First (CIF) prin…
Reduces complexity of financial contagion dynamics on networks.
This paper proposes a novel architecture, termed multiscale principle of relevant information (MPRI), to learn discriminative spectral-spatial features for hyperspectral image (HSI) classification. MPRI inherits the merits of the principle of relevant information (PRI) to effectively extract multiscale information embe…
ML reduces high-dimensional data to reveal its underlying structure.
Paper proposes a compression principle for neural networks using Bayesian optimization.
Bayesian framework reduces high-dimensional GP modeling costs.
ActiveCQ improves causal quantity estimation with active learning and Gaussian Processes.
HyperCR Einstein--Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the integrability. Simple examples of solutions including the hydrodynamic reductions …
Let be a smooth rational curve on a complex manifold . It is called ample if its normal bundle is positive. We assume that is covered by smooth holomorphic deformations of . The basic example of such a manifold is a twistor space of a hyperkahler or a 4-dimensional anti-selfdual Riemannian manifold (n…
Adaptive framework improves nonparametric dimensionality reduction.
This article continues a line of research aimed at solving an important problem of T. Kobayashi of the existence of compact Clifford-Klein forms of reductive homogeneous spaces. We contribute to this topic by showing that almost all symmetric spaces and 3-symmetric spaces do not admit solvable compact CliffordfKlein fo…
In this paper we introduce a generalisation of the notion of holonomy for connections over a bundle map on a principal fibre bundle. We prove that, as in the standard theory on principal connections, the holonomy groups are Lie subgroups of the structure group of the principle fibre bundle and we also derive a straight…
SPREV simplifies visualization of complex labeled datasets.