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.
Survival MDN uses invertible functions to speed up survival analysis models.
A new framework solves complex optimization problems with continuous worst-case distributions.
A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be u…
By a result of John Ball (1981), a locally orientation preserving Sobolev map is almost everywhere globally invertible whenever its boundary values admit a homeomorphic extension. As shown here for any dimension, the conclusions of Ball's theorem and related results can be reached while completely avoiding the problem …
The paper studies global invertibility of maps on Finsler manifolds.
ISR creates analytical relationships from data via invertible maps.
Continuous time analysis of bubble formation in harmonic maps.
New model for simulating and inferring from inverse problems.
JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.
Maps from metrics to Ricci curvature are locally invertible near Einstein manifolds.
We establish a link between Fourier optics and a recent construction from the machine learning community termed the kernel mean map. Using the Fraunhofer approximation, it identifies the kernel with the squared Fourier transform of the aperture. This allows us to use results about the invertibility of the kernel mean m…
We study invertible generating pairs of fundamental groups of graph manifolds, that is, pairs of elements (g,h) for which the map g --> g^{-1}, h --> h^{-1} extends to an automorphism. We show in particular that a graph manifold is of Heegaard genus 2 if and only if its fundamental group has an invertible generating pa…
The paper explores how invertibility affects the complexity of encoder models in VAEs.
For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones wer…
Develops equivariant grid homology for strongly invertible knots.
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
iGNN tackles inverse graph prediction using invertible neural networks.
Study on equivariant Q-sliceness for strongly invertible knots.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
Electronic power inverters are capable of quickly delivering reactive power to maintain customer voltages within operating tolerances and to reduce system losses in distribution grids. This paper proposes a systematic and data-driven approach to determine reactive power inverter output as a function of local measuremen…
Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…
Normalizing flows attempt to model an arbitrary probability distribution through a set of invertible mappings. These transformations are required to achieve a tractable Jacobian determinant that can be used in high-dimensional scenarios. The first normalizing flow designs used coupling layer mappings built upon affine …
Method estimates parameters of complex nonlinear systems.
Incorporates matrix exponential into generative flows for improved performance.
Study on knots, genera, and algebraic concordance groups.
Paper presents a nearly invertible mapping between high-dimensional and lower-dimensional spheres.
While conformal transformations of the plane preserve Laplace's equation, Lorentz-conformal mappings preserve the wave equation. We discover how simple geometric objects, such as quadrilaterals and pairs of crossing curves, are transformed under nonlinear Lorentz-conformal mappings. Squares are transformed into curvili…
Featurization improves density ratio estimation for complex data.
Generative Adversarial Networks (GANs) play an increasingly important role in machine learning. However, there is one fundamental issue hindering their practical applications: the absence of capability for encoding real-world samples. The conventional way of addressing this issue is to learn an encoder for GAN via Vari…
SGNs use Hamiltonian mechanics for invertible deep generative modeling.
Method generates time-series attribution maps with identifiability guarantees.
Twisted spectral triples are a twisting of the notion of spectral triple aiming at dealing with some type III geometric situations. In the first part of the paper, we give a geometric construction of the index map of a twisted spectral triple in terms of -connections on finitely generated projective modules. This ma…
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for universal approximation using continuous-time deep residual networks, which can …
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditio…
E-NFs generate molecules and their positions while preserving Euclidean symmetries.
We present and discuss several old and new methods for mapping a circular disc to a square. In particular, we present analytical expressions for mapping each point (u,v) inside the circular disc to a point (x,y) inside a square region. Ideally, we want the mapping to be smooth and invertible. In addition, we put emphas…
Mathematical conditions and practical computations for adversarial robustness measures are established.
We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, using this, we obtain a version of the Hadamard integral condition for invertib…
Second-order estimator improves continuous-time policy evaluation.
OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz bounds of the nonlinear analysis map and we establish theoretical performance bo…
Sobolev maps on product spaces are split or approximately split.
We address representational challenges in normalizing flows, particularly depth and conditioning issues.
Index difference on surfaces of genus at least 3 is non-trivial.
Flip symmetry on knot diagrams affects Khovanov homology.
Momentum ResNets improve ResNets' memory efficiency.
A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory index map associated to the continuous extension to A of the principal-symbol map i…
Recommender systems play an essential role in the modern business world. They recommend favorable items like books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accura…