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.
Constructs coordinates to diagonalize Toda flow on matrices with simple spectrum.
The main purpose of this note is to prove that any basis of a nilpotent Lie algebra for which all diagonal left-invariant metrics have diagonal Ricci tensor necessarily produce quite a simple set of structural constants; namely, the bracket of any pair of elements of the basis must be a multiple of some of them and onl…
We discuss the Ricci flow on homogeneous 4-manifolds. After classifying these manifolds, we note that there are families of initial metrics such that we can diagonalize them and the Ricci flow preserves the diagonalization. We analyze the long time behavior of these families. We find that if a solution exists for all t…
Flexible VAEs using FIFs improve model likelihood on image datasets.
We show that a basis of a semisimple Lie algebra of compact type, for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being "nice". Namely, the bracket of any two basis elements is a multiple of another basis element. This extends the work of Laur…
Gradient methods work well on overparameterized diagonal linear networks.
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
Study shows mixing of flows on specific geometric spaces.
New proof shows coupling-based flows converge linearly to diagonalize data covariance.
Unified analysis of DLNs using DMFT reveals dynamics of loss convergence and generalization trade-offs.
Sharp results link DLN gradient flow to basis pursuit optimization and GHA phase transitions.
In this paper, we propose a new volume-preserving flow and show that it performs similarly to the linear general normalizing flow. The idea is to enrich a linear Inverse Autoregressive Flow by introducing multiple lower-triangular matrices with ones on the diagonal and combining them using a convex combination. In the …
In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and ass…
We find exact solutions describing Ricci flows of four dimensional pp-waves nonlinearly deformed by two/three dimensional solitons. Such solutions are parametrized by five dimensional metrics with generic off-diagonal terms and connections with nontrivial torsion which can be related, for instance, to antisymmetric ten…
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedr…
We investigate the existence of closed -structures which are solitons for the Laplacian flow on nilpotent Lie groups. We obtain that seven of the twelve Lie algebras admitting a closed -structure do admit a Laplacian soliton. Moreover, one of them admits a continuous family of Laplacian solitons which are pai…
The framework of normalizing flows provides a general strategy for flexible variational inference of posteriors over latent variables. We propose a new type of normalizing flow, inverse autoregressive flow (IAF), that, in contrast to earlier published flows, scales well to high-dimensional latent spaces. The proposed f…
Ancient solutions to Ricci flow on torus bundles have additional symmetries.
Gradients of neural networks can be computed efficiently for any architecture, but some applications require differential operators with higher time complexity. We describe a family of restricted neural network architectures that allow efficient computation of a family of differential operators involving dimension-wise…
Variational auto-encoders (VAE) are scalable and powerful generative models. However, the choice of the variational posterior determines tractability and flexibility of the VAE. Commonly, latent variables are modeled using the normal distribution with a diagonal covariance matrix. This results in computational efficien…
The group of real 4 by 4 upper triangular matrices with 1s on the diagonal has a left-invariant subRiemannian (or Carnot-Caratheodory) structure whose underlying distribution corresponds to the superdiagonal. We prove that the associated subRiemannian geodesic flow is not completely integrable. This provides the first …
The paper studies ergodicity of flows on subspaces, generalizing earlier work.
We study the family of holomorphic maps from the polydisk to the disk which restrict to the identity on the diagonal. In particular, we analyze the asymptotics of the orbit of such a map under the conjugation action of a unipotent subgroup of . We discuss an application our results to the stud…
The covariance of a stationary process is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic covariance moments, which rely on complex phases to capture non-Gaussian properties. The…
This paper solves matrix blind joint block diagonalization with noise.
Diagonalizes metrics of 3D Lorentzian manifolds.
Toda flow explained as a porous medium equation.
Study Ricci vector fields on 2D space with diagonal metrics.
Develops a novel stochastic algorithm for diagonal estimation of large matrices.
Combines techniques to remove tameness condition in Morse-Smale flows.
Improved phylogenetic inference with normalizing flows.
Octagon map accelerates diagonal changes algorithm.
Study finds symmetries in a special 3D space with a diagonal metric.
New diagonal knots found with non-torus structure.
We give a proof of Gaussian upper bound for the heat kernel coupled with the Ricci ow. Previous proofs by Lei Ni [5] use Harnack inequality and doubling volume property, also the recent proof by Zhang and Cao [6] uses Sobolev type inequality that is conserved along Ricci ow. We will use a horizontal coupling of curve […
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possib…
We use the bracket flow/algebraic soliton approach to study the Laplacian flow of -structures and its solitons in the homogeneous case. We prove that any homogeneous Laplacian soliton is equivalent to a semi-algebraic soliton (i.e.\ a -invariant -structure on a homogeneous space that flows by pull-ba…
Equal diagonal energies proven on Liouville surfaces.
Diagonal linear networks converge to lasso regularization path during training.
In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler, functions. There are constructed canonical almost symplectic connections for which the…
New diagonal move simplifies knots and links efficiently.
We show the non-positivity of the Einstein-Hilbert action for conformal flat Riemannian metrics. The action vanishes only when the metric is constant flat. This recovers an earlier result of Fathizadeh-Khalkhali in the setting of spectral triples on noncommutative four-torus. Furthermore, computations of the gradient f…
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem…
This paper analyzes implicit bias in Deep Linear Discriminant Analysis.
We consider Ricci flow on two classes of nilpotent Lie groups that generalize the three-dimensional Heisenberg group: the higher-dimensional classical Heisenberg groups, and the groups of real unitriangular matrices. Each group is known to admit a Ricci soliton, but we construct them \textit{explicitly} on each group. …
Study grid homology of diagonal knots, finding key terms related to prime factors and decompositions.
Study on stability of non-diagonal Einstein metrics on specific homogeneous spaces.