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.
CF-INNs can approximate any invertible function, resolving a long-standing problem.
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…
INNs can approximate diverse functions despite layer restrictions.
JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.
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 …
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 …
Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is c…
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…
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…
Residual neural networks don't help overcome sampling complexity issues.
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
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…
SGNs use Hamiltonian mechanics for invertible deep generative modeling.
iGNN tackles inverse graph prediction using invertible neural networks.
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
A new base distribution for normalizing flows allows modeling complex distributions without sacrificing invertibility.
The paper explores how invertibility affects the complexity of encoder models in VAEs.
Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable modelers to capture effects that are difficult to characterize analytically or su…
We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-Factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases…
Inferring the latent variable generating a given test sample is a challenging problem in Generative Adversarial Networks (GANs). In this paper, we propose InvGAN - a novel framework for solving the inference problem in GANs, which involves training an encoder network capable of inverting a pre-trained generator network…
Monotonic neural networks have recently been proposed as a way to define invertible transformations. These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous probability distributions. Architectures that ensure monotonicity typically enfor…
This paper presents a simulator-assisted training method (SimVAE) for variational autoencoders (VAE) that leads to a disentangled and interpretable latent space. Training SimVAE is a two-step process in which first a deep generator network(decoder) is trained to approximate the simulator. During this step, the simulato…
The Gumbel-Softmax is a continuous distribution over the simplex that is often used as a relaxation of discrete distributions. Because it can be readily interpreted and easily reparameterized, it enjoys widespread use. We propose a modular and more flexible family of reparameterizable distributions where Gaussian noise…
While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing the target posterior as a product of subposteriors, running MCMC for each of them …
Paper develops polynomial approximations for complex probability densities.
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formal…
Inference amortization methods share information across multiple posterior-inference problems, allowing each to be carried out more efficiently. Generally, they require the inversion of the dependency structure in the generative model, as the modeller must learn a mapping from observations to distributions approximatin…
MsIGN tackles high-dimensional Bayesian inference using multiscale structure.
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently proposed extended variational inference (EVI) framework is adopted to derive an a…
Study on estimating invertible functions with minimax analysis.
The paper provides non-asymptotic Edgeworth expansions for neural network outputs.
Local invertibility of higher order tensor transforms on compact manifolds.
Study of strongly invertible Legendrian links in contact 3-space.
A new method for aligning multiple distributions efficiently.
Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.
Dirac operator invertibility proven for specific manifolds.
This paper proposes a new method to approximate posterior distributions using generative neural networks trained via scoring rule minimization.
Table of symmetric diagrams for knots up to 10 crossings.
ISR creates analytical relationships from data via invertible maps.
Local invertibility of ray transforms on convex manifolds.
This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
Develops equivariant grid homology for strongly invertible knots.
Improved sampling quality with RBM-Flow and D-Flow models.
New findings on knot genera using advanced techniques.
Defines knot signature invariant using G-signature theorem.
Paper shows invertibility of tensor X-ray transform on certain manifolds.
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…