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.
New invertible transformations improve flow-based generative models.
Study of strongly invertible Legendrian links in contact 3-space.
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple …
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…
By using parity arguments we prove that free knots are, generally, not invertible.
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…
We propose a new way of constructing invertible neural networks by combining simple building blocks with a novel set of composition rules. This leads to a rich set of invertible architectures, including those similar to ResNets. Inversion is achieved with a locally convergent iterative procedure that is parallelizable …
ISR creates analytical relationships from data via invertible maps.
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…
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…
This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.
CF-INNs can approximate any invertible function, resolving a long-standing problem.
Incorporates matrix exponential into generative flows for improved performance.
The paper explores how invertibility affects the complexity of encoder models in VAEs.
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…
SGNs use Hamiltonian mechanics for invertible deep generative modeling.
Study on estimating invertible functions with minimax analysis.
New model for simulating and inferring from inverse problems.
iGNN tackles inverse graph prediction using invertible neural networks.
Neural ODEs and i-ResNet are recently proposed methods for enforcing invertibility of residual neural models. Having a generic technique for constructing invertible models can open new avenues for advances in learning systems, but so far the question of whether Neural ODEs and i-ResNets can model any continuous inverti…
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
Local invertibility of higher order tensor transforms on compact manifolds.
Study on equivariant Q-sliceness for strongly invertible knots.
INNs can approximate diverse functions despite layer restrictions.
We prove that for cobordant closed spin manifolds of dimension the associated spaces of metrics with invertible Dirac operator are homotopy equivalent. This is the spinorial counterpart of a similar result on positive scalar curvature of Chernysh/Walsh and generalizes the surgery result of Ammann-Dahl-Humbert…
This paper focuses on a novel generative approach for 3D point clouds that makes use of invertible flow-based models. The main idea of the method is to treat a point cloud as a probability density in 3D space that is modeled using a cloud-specific neural network. To capture the similarity between point clouds we rely o…
Residual neural networks don't help overcome sampling complexity issues.
New CycleGAN uses invertible generator for faster, less resource-intensive CT denoising.
Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.
Proves invertibility of layer potentials for generalized Stokes operators on smooth domains.
Dirac operator invertibility proven for specific manifolds.
Distribution grids are currently challenged by frequent voltage excursions induced by intermittent solar generation. Smart inverters have been advocated as a fast-responding means to regulate voltage and minimize ohmic losses. Since optimal inverter coordination may be computationally challenging and preset local contr…
Table of symmetric diagrams for knots up to 10 crossings.
In this manuscript, we investigate deep invertible networks for EEG-based brain signal decoding and find them to generate realistic EEG signals as well as classify novel signals above chance. Further ideas for their regularization towards better decoding accuracies are discussed.
Local invertibility of ray transforms on convex manifolds.
A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based models are slow to invert, making either density estimation or sample generation sl…
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
Develops equivariant grid homology for strongly invertible knots.
New findings on knot genera using advanced techniques.
A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choic…
Defines knot signature invariant using G-signature theorem.
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…
As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…
Paper shows invertibility of tensor X-ray transform on certain manifolds.
Deep neural networks are vulnerable to adversarial attacks and hard to interpret because of their black-box nature. The recently proposed invertible network is able to accurately reconstruct the inputs to a layer from its outputs, thus has the potential to unravel the black-box model. An invertible network classifier c…
IZF uses flow-based models to overcome ZSL limitations.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. Th…