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.
Paper solves NGCA for discrete distributions using LLL method.
New algorithm recovers high-dimensional linear regression vectors without sparsity assumptions.
Reduces learning periodic neural networks to lattice problems, proving hardness under cryptographic assumptions.
Polynomial-time algorithm for inferring high-dimensional linear regression from a single sample.
The asymptotic lattices and their transformations are studied within the line geometry approach. It is shown that the discrete asymptotic nets are represented by isotropic congruences in the Plucker quadric. On the basis of the Lelieuvre-type representation of asymptotic lattices and of the discrete analog of the Mouta…
SLR tackles sparse linear regression problems, showing hardness for efficient algorithms.
Polynomial-time algorithm finds planted hypercube vectors in Gaussian mixtures.
New framework compares two stochastic learning dynamics in games.
The paper constructs a star product on a symplectically reduced phase space for a lattice gauge model.
In this paper we prove that every H-type Lie algebra possesses a basis with respect to which the structure constants are integers. Existence of such an integral basis implies via the Mal'cev criterion that all simply connected H-type Lie groups contain cocompact lattices. Since the Campbell-Hausdorff formula is very si…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least squares optimization problem in any constant dimension. Next, in an average-case…
The lattice cohomology of a plumbed 3--manifold associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of , and in the comparison of the topological properties with analytic ones when is realized as complex analytic singularity link. By defini…
Kronecker trend filtering improves lattice data smoothing.
Let G be a lattice in PSL(2,C). The pro-normal topology on G is defined by taking all cosets of non-trivial normal subgroups as a basis. This topology is finer than the pro-finite topology, but it is not discrete. We prove that every finitely generated subgroup H<G is closed in the pro-normal topology. As a corollary w…
Group lattices (Cayley digraphs) of a discrete group are in natural correspondence with differential calculi on the group. On such a differential calculus geometric structures can be introduced following general recipes of noncommutative differential geometry. Despite of the non-commutativity between functions and (gen…
We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such trans…
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric properties of the lattice we give the algebro-geometric construction of the BQL ephasizing the role of Prym varieties and the corres…
In this paper we investigate flows on discrete curves in $\C^2$, $\CP^1$, and $\C$. A novel interpretation of the one dimensional Toda lattice hierarchy and reductions thereof as flows on discrete curves will be given.
In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal basis in the space of quantum states, but also give a lattice structure to this…
The paper proves a conjecture about the dimensions of centralizer algebras related to quantum super-algebras.
Introduces a continuous version of LWE problem.
Paper improves distributed mean estimation and variance reduction without relying on input norm.
Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.
The paper introduces a method to decorrelate circular coordinates using lattice reduction.
The main aim of this paper is the description of a large class of lattices in some nilpotent Lie groups, sometimes filiformes, carrying a flat left invariant linear connection anf often a left invariant symplectic form. As a consequence we obtain an infinity of, non homeomorphic, compact affine or symplectic manifolds.…
Let be a connected reductive affine algebraic group defined over , and let be a cocompact lattice in . We prove that any invariant bundle on is semistable.
Classifies actions of tori on manifolds up to diffeomorphisms.
The paper proves existence of solutions for mean field equations on compact Riemann surfaces.
We present a family of complete acyclic Morse matchings on the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. In a future paper we will utilize these matchings to classify every subcomplex whose reduced homology groups are concentra…
We study representations of lattices of PU(m,1) into PU(n,1). We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m-space to complex hyperbolic n-space. This allows us to give a differential geometric proof of rigidity …
New algorithm reduces autocorrelation in HMC for lattice field theories.
We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.
Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and the resulting basis is called continuum directions. With a presence of binary sup…
Data-driven method solves multiscale elliptic PDEs with random coefficients.
Adaptive neural networks learn functional data bases for improved performance.
Improves MARS for nonparametric multivariate regression with dimension reduction.
Paper develops a two-population model to assess longevity basis risk.
In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving 3 distinct masses. A proof is devised, though it cannot be accounted as a derivation; rather it certifies that an Ansatz found by PSLQ sati…
Clock theorem extended to knotoids and linkoids.
This work ensures stability in POD basis interpolation for pMOR in hyperelasticity.
American put options are among the most frequently traded single stock options, and their calibration is computationally challenging since no closed-form expression is available. Due to the higher flexibility in comparison to European options, the mathematical model involves additional constraints, and a variational in…
The paper explores polysymplectic structures and their reductions in field theories.
Lossy compression of statistical data using quantum annealing.
Geometrically represents path integral reduction Jacobian for interacting systems.
New basis for quantum gl_N invariants derived from Macdonald polynomials.
A model order reduction framework reduces financial risk analysis models efficiently.
BasisVAE combines VAE and clustering for tabular data analysis.
Three LF training criteria improve neural network acoustic models without cross-entropy pre-training.