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.
Defines linear weightings for vector bundles and explores their applications.
Study of -vector cones in cluster algebras from weighted orbifolds.
The strength of association between a pair of data vectors is represented by a nonnegative real number, called matching weight. For dimensionality reduction, we consider a linear transformation of data vectors, and define a matching error as the weighted sum of squared distances between transformed vectors with respect…
Novel metric space magnitude and weighting vectors improve machine learning tasks.
The note answers a question about Betti numbers for 1D Euclidean space.
Paper develops a weighted linearization approach for vector fields.
This paper optimizes binary linear classifiers by tuning their weight vectors.
Proves conditions for weighted Hermite-Einstein metrics on vector bundles.
This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vec…
New method uses weighting vectors for efficient boundary and outlier detection.
Three new efficient algorithms project vectors onto weighted l1 ball.
In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that these groups contain the compactly supported diffeomorphisms. We finally show that …
In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4. In the case of formal Hamiltonian vector fields on R^2, we computed the relative Gel'fand-Kalinin-Fuks cohomology groups of weight <20 in the paper by Mikami-Nakae-Kodama. The main strategy…
The study of quotient structures in multi-graded bundles, including double vector bundles.
The study counts periodic orbits on smooth manifolds, adding ghost orbits for completeness.
This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Candès et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In particular, the margin required for each training vector is set independently, defining a n…
Develops theory of weightings for Lie groupoids and algebroids.
Proves weight polytope matches with energy vectors in toric varieties.
Introduces VB-structures for geometric objects on manifolds.
In this paper we study the problem of learning Rectified Linear Units (ReLUs) which are functions of the form with denoting the weight vector. We study this problem in the high-dimensional regime where the number of observations are fewer than the dimension of the weight vector. We assume that the we…
In "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations", arXiv:0910.3414, (October 2009) by D.Kotschick and S.Morita, the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields without constant vector fields on 2n-plane were characterized b…
The study examines stable regions in weighted manifolds with boundary properties.
A new term weighting scheme TF-IDFC-RF outperforms others in sentiment analysis.
We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an - cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from com…
We show that from an even degree symplectic NQ-manifold, whose homological vector field Q preserves the symplectic form, one can construct a weight system for tri-valent graphs with values in the Q-cohomology ring, satisfying the IHX relation. Likewise, given a representation of the homological vector field, one can co…
We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle , over a Riemannian manifold , when is endowed with a metric connection. The tangent bundle of admits a canonical decomposition and t…
Constructing transitive nilpotent Lie algebras from dilations and analyzing their prolongations.
We consider the problem of learning Relational Logistic Regression (RLR). Unlike standard logistic regression, the features of RLRs are first-order formulae with associated weight vectors instead of scalar weights. We turn the problem of learning RLR to learning these vector-weighted formulae and develop a learning alg…
We propose -graph embedding for robustly learning feature vectors from data vectors and noisy link weights. A newly introduced empirical moment -score reduces the influence of contamination and robustly measures the difference between the underlying correct expected weights of links and the specified generative m…
The autoencoder is an effective unsupervised learning model which is widely used in deep learning. It is well known that an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principa…
A weight system on graph homology was constructed by Rozansky and Witten using a compact hyperkähler manifold. A variation of this construction utilizing holomorphic vector bundles over the manifold gives a weight system on chord diagrams. We investigate these weights from the hyperkähler geometry point of view.
Graded bundles are a particularly nice class of graded manifolds and represent a natural generalisation of vector bundles. By exploiting the formalism of supermanifolds to describe Lie algebroids we define the notion of a weighted -connection on a graded bundle. In a natural sense weighted -connections are adapte…
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian metrics which do not have positive sectional curvature but support a vector field…
In representation learning (RL), how to make the learned representations easy to interpret and less overfitted to training data are two important but challenging issues. To address these problems, we study a new type of regulariza- tion approach that encourages the supports of weight vectors in RL models to have small …
New method preserves privacy by aggregating feature-vectors with weighted sums, ensuring label differential privacy.
Most of the information is stored as text, so text mining is regarded as having high commercial potential. Aiming at the semantic constraint problem of classification methods based on sparse representation, we propose a weighted recurrent neural network (W-RNN), which can fully extract text serialization semantic infor…
Post-training quantization method using multiple low-precision points achieves higher precision for critical weights.
Recent work on mode connectivity in the loss landscape of deep neural networks has demonstrated that the locus of (sub-)optimal weight vectors lies on continuous paths. In this work, we train a neural network that serves as a hypernetwork, mapping a latent vector into high-performance (low-loss) weight vectors, general…
Paper establishes identifiability conditions for a model with two latent vectors and auxiliary data.
Forecast dam inflow using sea surface feature weights.
OTSS learns personalized decision weights from logged decisions and outputs.
This study reveals the critical role of scale vectors in large language models, improving optimization and expressivity.
Paper refines Alesker-Bernig-Schuster theorem, proving Hodge-Riemann relations for Euclidean balls.
Gradient flow on softmax attention minimizes nuclear norm of weight matrices.
The paper proposes a method to improve forecast combination accuracy using portfolio theory.
We introduce and study the Wilson loops in a general 3D topological field theories (TFTs), and show that the expectation value of Wilson loops also gives knot invariants as in Chern-Simons theory. We study the TFTs within the Batalin-Vilkovisky (BV) and Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) framework, and the…
In this paper, we prove that a noncompact complete hypersurface with finite weighted volume, weighted mean curvature vector bounded in norm, and isometrically immersed in a complete weighted manifold is proper. In addition, we obtain an estimate for -stability index of a constant weighted mean curvature hypersurface…
Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional sparse data, however, the method suffers from slow convergence and high variance…