Invertible neural networks with masked convolutions improve classification and generative models.
problem Building robust invertible neural networks for better model interpretability and generative tasks.
method Combining masked convolutions and iterative inversion methods to create invertible architectures.
result Invertible neural networks achieve competitive performance in classification and generative tasks.
Glow uses invertible 1x1 convolutions to improve image generation and manipulation.
problem Efficient and realistic image generation and manipulation.
method Invertible 1x1 convolutions in generative flows.
result Significant improvement in log-likelihood and realistic image synthesis.
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.
Improved generative models using flexible convolutions.
problem Generating high-quality images efficiently.
method Generalized 1 x 1 convolutions to d x d convolutions, chaining autoregressive and periodic convolutions.
result Flexible d x d convolutions significantly improve generative flow models' performance.
Incorporates matrix exponential into generative flows for improved performance.
problem Improving generative flow models for better density estimation.
method Integrates matrix exponential into generative flows, proposing new layers and modifying network architecture.
result The proposed model achieves great performance on density estimation.
Woodbury transformations improve deep generative models with efficient invertibility and determinant calculation.
problem Efficiently invertible and determinant-calculable functions for deep generative models.
method Introducing Woodbury transformations that leverage matrix identities for efficient invertibility and determinant calculation.
result Woodbury transformations enable high-dimensional interactions, efficient sampling, and likelihood evaluation, outperforming other flow architectures.
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…
Finet uses FBN for efficient, lightweight neural networks.
problem Building efficient neural networks with limited computational resources.
method Introduces Fine-grained Batch Normalization (FBN) and a novel light-weight network (Finet) that combines FBN with standard convolution.
result Finet achieves state-of-the-art performance on ImageNet classification with reduced computational complexity.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
problem Building efficient invertible layers for complex probability distributions.
method Proposes butterfly layers for invertible linear layers, leveraging their ability to capture complex structures.
result ButterflyFlow achieves strong density estimation and significantly better log-likelihoods on various datasets.
Residual neural networks don't help overcome sampling complexity issues.
problem Learning invertible residual neural networks from samples is hard due to the curse of dimensionality.
method Investigated invertible residual neural networks and their sampling complexity.
result Invertible residual neural networks still suffer from the curse of dimensionality in sampling complexity.
Here, we present a novel approach to solve the problem of reconstructing perceived stimuli from brain responses by combining probabilistic inference with deep learning. Our approach first inverts the linear transformation from latent features to brain responses with maximum a posteriori estimation and then inverts the …
iGNN tackles inverse graph prediction using invertible neural networks.
problem Inverse graph prediction problem in data analysis and machine learning.
method Developed invertible graph neural network (iGNN) to solve inverse prediction problem on graphs.
result iGNN model allows efficient generation from output labels and forward prediction.
The paper explores how invertibility affects the complexity of encoder models in VAEs.
problem The complexity of the encoder model in VAEs when the generative map is invertible.
method Formalizes the concept of strong invertibility and analyzes the complexity of the encoder model.
result Strongly invertible generative maps allow for simpler encoder models, while non-invertible maps require exponentially larger encoders.
This research studies affine invariance in continuous-domain convolutional neural networks.
problem Recognizing patterns and features under affine transformations in continuous domains.
method Introduces a new criterion for assessing affine invariance, embeds images into the affine Lie group, and analyzes convolution over this group.
result Extends the scope of geometrical transformations that deep-learning pipelines can handle.
Convolutional neural networks learn phase-dependent frequency representations.
problem Capturing phase dependence in frequency representations for better signal analysis.
method Convolutional neural networks learn filters with different phases, which rectify to phase-dependent descriptors.
result Phase harmonics correlations can compressively represent signals with sparse wavelet coefficients.
It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network …
Flowification enriches neural networks with an inverse pass and likelihood monitoring.
problem Neural networks lack an inverse pass and likelihood monitoring, limiting their generative capabilities.
method Introduce flowification, enriching neural networks with a stochastic inverse pass and likelihood monitoring.
result Certain neural network architectures can be enriched to fall under the generalized notion of a normalizing flow.
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation structure between the observation and state innovation vectors and we extend the…
In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distribu…
We present a method for feature interpretation that makes use of recent advances in autoregressive density estimation models to invert model representations. We train generative inversion models to express a distribution over input features conditioned on intermediate model representations. Insights into the invariance…
Paper aims to find joint representation between vocal tract geometry and speech sound acoustics.
problem Finding a joint latent representation between articulatory and acoustic domains for vowel sounds.
method Invertible neural network models, convolutional autoencoder, normalizing flows, semi-supervised learning.
result Satisfactory performance in articulatory-to-acoustic and acoustic-to-articulatory mapping.
Paper investigates Lipschitz constants of self-attention modules in neural networks.
problem Lipschitz constants of self-attention modules in neural networks.
method Proved standard dot-product self-attention is not Lipschitz for unbounded input domain. Proposed L2 self-attention that is Lipschitz. Derived upper bound on L2 self-attention's Lipschitz constant.
result Proved standard self-attention is not Lipschitz for unbounded input domain and proposed an alternative L2 self-attention that is Lipschitz.
Study on estimating invertible functions with minimax analysis.
problem Minimizing risk of estimating invertible functions on a plane.
method Introduce two types of L2-risks, derive lower and upper rates for minimax values, develop an asymptotically almost everywhere invertible estimator. result Invertibility does not reduce the complexity of the estimation problem in terms of the rate.
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be o…
We address representational challenges in normalizing flows, particularly depth and conditioning issues.
problem Challenges in training normalizing flows, including vanishing/exploding gradients and poor conditioning.
method Analyzes representational aspects of depth and conditioning in normalizing flows, proving theoretical bounds and investigating phenomena.
result Proves that shallow affine coupling networks are universal approximators in Wasserstein distance if ill-conditioning is allowed.
Local invertibility of higher order tensor transforms on compact manifolds.
problem Invertibility of higher order tensor transforms on compact manifolds.
method Local invertibility of transverse and mixed ray transforms of tensors on compact Riemannian manifolds.
result Local invertibility of transverse and mixed ray transforms of tensors for specific dimensions.
Study of strongly invertible Legendrian links in contact 3-space.
problem Characterizing and understanding strongly invertible Legendrian links.
method Equivariant analogs of basic results for strongly invertible and Legendrian links.
result Existence of maximal equivariant Thurston-Bennequin number for strongly invertible links.
Invertible ResNets enable classification, density estimation, and generation.
problem Enforcing invertibility in ResNets without architectural changes.
method Simple normalization during training to make ResNets invertible.
result Invertible ResNets achieve competitive performance with single architecture.
Study on invariant Seifert surfaces for strongly invertible knots, showing large gaps in genus.
problem Understanding gaps in genus between strongly invertible knots and their invariant Seifert surfaces.
method Analysis of invariant Seifert surfaces and proof of genus gaps, with variants of Edmonds' theorem.
result Gap between equivariant genus and usual genus can be arbitrarily large for strongly invertible knots.
Dirac operator invertibility proven for specific manifolds.
problem Invertibility of twisted Dirac operator on manifolds.
method Closed connected spin manifold with non-negative scalar curvature, flat Hilbert module bundle.
result Dirac operator is invertible under given conditions.
Invertible networks help explain decisions and identify important features.
problem Interpreting and explaining the decisions of black-box neural networks.
method Two-stage approach: invertible transformation to feature space and linear classifier. Determining decision boundaries and feature importance using local linear models.
result Ability to explain decisions and identify important features in neural networks.
Table of symmetric diagrams for knots up to 10 crossings.
problem Finding symmetric diagrams for strongly invertible knots.
method Compilation of symmetric diagrams for knots up to 10 crossings.
result Similarity of transversal diagrams to symmetric union diagrams for strongly invertible knots.
Global invertibility proven for orientation-preserving maps without homeomorphic extension.
problem Global invertibility of orientation-preserving Sobolev maps.
method Avoiding homeomorphic extension, study of strictly orientation-preserving maps.
result Global invertibility can be achieved without homeomorphic extension.
HINT improves invertible neural networks for better density estimation and Bayesian inference.
problem Sparse Jacobians limit expressiveness in invertible neural architectures.
method Recursive hierarchical coupling within subsets of variables leads to dense, triangular Jacobian.
result HINT allows efficient sampling from joint and posterior distributions using a single network.
ISR creates analytical relationships from data via invertible maps.
problem Creating analytical relationships from datasets.
method Combines INNs and EQL, using invertible maps and sparsity promoting regularization.
result ISR can serve as a normalizing flow for density estimation and solve inverse problems.
Local invertibility of ray transforms on convex manifolds.
problem Invertibility of ray transforms on compact Riemannian manifolds with strictly convex boundary.
method Local invertibility results for transverse and mixed ray transforms of 1 and 1+1 tensors.
result Local invertibility of ray transforms near boundary points, leading to global results.
Deep invertible networks decode EEG signals better than chance.
problem Decoding brain signals from EEG data.
method Deep invertible networks for generating and classifying brain signals.
result Deep invertible networks generate realistic EEG signals and classify novel signals above chance.
This work tackles exploding inverses in INNs, revealing and mitigating their numerical non-invertibility.
problem Exploding inverses in INNs cause numerical non-invertibility, leading to failures in various tasks.
method Derived bi-Lipschitz properties of INN building blocks, proposed regularizers for local invertibility, and stable INN designs for global invertibility.
result Bi-Lipschitz properties and stable INN designs are crucial for addressing numerical non-invertibility.
Neural ODEs and i-ResNets can't approximate all continuous invertible functions.
problem Neural ODEs and i-ResNets' limitations in approximating continuous invertible functions.
method Proving the approximation capabilities of Neural ODEs and i-ResNets.
result Neural ODEs and i-ResNets can approximate homeomorphisms on a p-dimensional Euclidean space.
CF-INNs can approximate any invertible function, resolving a long-standing problem.
problem Whether CF-INNs can approximate any invertible function.
method Demonstrated CF-INNs are universal approximators for invertible functions by showing a convenient criterion.
result CF-INNs are universal approximators for invertible functions.
This work presents a novel approach to train invertible linear layers by adding rank-one perturbations.
problem Training invertible linear layers during optimization with gradient-based methods is challenging.
method Train rank-one perturbations and add them to weight matrices infrequently, keeping track of inverses and determinants.
result Invertible linear layers improve mixing and mode separation in normalizing flows.
Spaces of metrics with invertible Dirac operator are homotopy equivalent for cobordant manifolds.
problem Proving homotopy equivalence of spaces of metrics with invertible Dirac operator.
method Using cobordism theory and properties of Dirac operators.
result Spaces of metrics with invertible Dirac operator are homotopy equivalent for cobordant manifolds.
Develops equivariant grid homology for strongly invertible knots.
problem Invariants of strongly invertible knots.
method Equivariant grid diagrams and mapping cones.
result Equivariant unknotting numbers and genus bounds.
New findings on knot genera using advanced techniques.
problem Understanding the 4-genus of knots, especially strongly invertible and periodic ones.
method Innovative concordance group invariants, Donaldson's theorem, and g-signature.
result Many new examples showing the equivariant 4-genus is larger than the 4-genus.
Defines knot signature invariant using G-signature theorem.
problem No specific problem stated; focuses on knot theory.
method Uses G-signature theorem to define knot invariant.
result Defines an invariant for strongly invertible knots.
A CNN-based method improves DTI of the human heart, compensating for motion.
problem Signal loss due to heart motion in DTI.
method Invertible Wavelet Scattering using CNN.
result Effective motion compensation and improved fiber structures.
Paper shows invertibility of tensor X-ray transform on certain manifolds.
problem Invertibility of tensor X-ray transform on asymptotically conic manifolds.
method Used 1-cusp pseudodifferential operator algebra and modified solenoidal gauge condition.
result Invertibility of tensor X-ray transform up to natural obstruction.
Deep convolutional networks have become a popular tool for image generation and restoration. Generally, their excellent performance is imputed to their ability to learn realistic image priors from a large number of example images. In this paper, we show that, on the contrary, the structure of a generator network is suf…