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.
The paper stabilizes invertible neural networks by using Gaussian mixture models.
problem Invertible neural networks can have exploding Lipschitz constants, leading to numerical errors.
method The authors use Gaussian mixture models to stabilize the latent distribution of invertible neural networks.
result Numerical simulations confirm that this modification improves sampling quality in multimodal applications.
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.
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.
INNs can approximate diverse functions despite layer restrictions.
problem Can INNs approximate sufficiently diverse functions?
method Developed a theoretical framework based on differential geometry to simplify the approximation problem of diffeomorphisms.
result INNs have the universal approximation property.
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.
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.
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.
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…
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…
JacNet learns Jacobians to enforce structure on derivatives for invertibility and Lipschitz functions.
problem Enforcing structure on derivatives of neural network mappings.
method Proposes using a neural network to directly learn the Jacobian of the input-output function, allowing control over derivative structure.
result Demonstrates learning invertible approximations to simple and 1-Lipschitz functions.
INVERT connects neural representations to human-understandable concepts.
problem Lack of understanding and statistical significance in existing explainability methods.
method Inverse Recognition (INVERT) approach that connects learned representations to human-understandable concepts.
result INVERT provides interpretable metrics and statistical significance for representation alignment.
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…
Studying the invertibility of deep neural networks (DNNs) provides a principled approach to better understand the behavior of these powerful models. Despite being a promising diagnostic tool, a consistent theory on their invertibility is still lacking. We derive a theoretically motivated approach to explore the preimag…
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.
This research reverses feature visualization in neural networks to optimize for specific feature objectives.
problem The invertibility of feature visualization in neural networks is not well understood.
method The approach involves optimizing for the feature objective that generates the input used in feature visualization, using the gradient of a specific objective function.
result A closed-form solution is found to minimize the gradient, providing an alternative view on network sensitivity.
Momentum ResNets improve ResNets' memory efficiency.
problem Memory inefficiency in deep residual neural networks (ResNets).
method Adding a momentum term to the forward rule of ResNets to make them invertible.
result Momentum ResNets can learn any linear mapping up to a multiplicative factor, improving memory efficiency.
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…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our method uses only a single loss and is easy to train. This is an improvement on t…
Survival MDN uses invertible functions to speed up survival analysis models.
problem Training neural ODEs for survival analysis is computationally expensive.
method Survival MDN applies an invertible positive function to MDN outputs.
result Survival MDN outperforms or matches other models on concordance, Brier score, and log-likelihood.
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.
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…
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…
New invertible transformations improve flow-based generative models.
problem Improving flow-based generative models for better performance.
method Proposed new invertible transformations and coupling layers.
result New coupling layers achieve better results in IDF.
A new method combines generative models and regularization to prevent forgetting in continual learning.
problem Catastrophic forgetting in neural networks when learning new tasks.
method Uses a normalizing flow as a generative model to keep past data embeddings and regularize them.
result Performs favorably compared to existing methods with constant memory overhead.
The paper provides non-asymptotic Edgeworth expansions for neural network outputs.
problem Approximating deviations of finite-width neural networks from their Gaussian limit.
method Multidimensional Edgeworth expansions of arbitrary order for neural network outputs.
result Established a bound on the total variation distance between neural network output and its Edgeworth approximation.
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.
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 …
AIKAE enhances IKAE for long-term time series forecasting.
problem Limitation of dimension conservation in IKAE models.
method Augmented with a non-invertible encoder network.
result AIKAE improves long-term forecasting accuracy.
Hydrogen atom confined in an inverted-Gaussian potential, with detailed numerical methods and results.
problem Studying hydrogen atom in a specific potential.
method Three numerical methods: Lagrange-mesh, fourth order finite differences, and finite element method.
result Accurate numerical results for hydrogen atom energies and eigenfunctions, improving previous literature.
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.
This paper proposes a new method to quantify uncertainty in reservoir characterization using invertible neural networks.
problem Quantifying uncertainty in reservoir characterization models.
method Training an invertible neural network to represent the posterior distribution of model parameters.
result The proposed method provides a more efficient and direct way to sample from the posterior distribution.
Paper proves CFlows can approximate any diffeomorphism and applies it in Bayesian optimization.
problem Proving the universality of CFlows in approximating diffeomorphisms.
method Deriving the universality of Para-CFlows through affine coupling layers and invertible linear transforms.
result Para-CFlows can approximate any diffeomorphism in C^k-norm.
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…
In this work we compute lower Lipschitz bounds of ℓp pooling operators for p=1,2,∞ as well as ℓp pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm tha…
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.
BayesFlow learns complex models using neural networks.
problem Estimating parameters in complex, non-likelihood models.
method Invertible neural networks for global Bayesian inference.
result Global probabilistic mapping from data to parameters.
Neural network estimates network models efficiently.
problem Estimating flexible ERGMs is challenging due to intractable normalizing constants.
method Trains a neural network on parameter-simulation pairs to invert and estimate parameters quickly and in parallel.
result The method performs well in practice and accommodates extra network statistics.
The Normalizing Flow (NF) models a general probability density by estimating an invertible transformation applied on samples drawn from a known distribution. We introduce a new type of NF, called Deep Diffeomorphic Normalizing Flow (DDNF). A diffeomorphic flow is an invertible function where both the function and its i…
A new method combines regularization and generative rehearsal for continual learning.
problem Catastrophic forgetting in neural networks over past tasks.
method Uses a normalizing flow to conditionally store past task data and regularize network embeddings.
result Performs favorably compared to state-of-the-art approaches with constant memory overhead.
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of param…
Time-frequency (TF) representations provide powerful and intuitive features for the analysis of time series such as audio. But still, generative modeling of audio in the TF domain is a subtle matter. Consequently, neural audio synthesis widely relies on directly modeling the waveform and previous attempts at unconditio…
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…
This paper proposes a new method to approximate posterior distributions using generative neural networks trained via scoring rule minimization.
problem Bayesian Likelihood-Free Inference for models with intractable likelihood.
method Approximate posterior with generative neural networks trained via scoring rule minimization, avoiding the instability of adversarial training.
result Scoring Rule minimization leads to better performance and uncertainty quantification compared to adversarial training.
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…
Framework for designing nonlinearities in neural networks with slope constraints.
problem Designing nonlinearities with specific properties for signal processing.
method Variational framework with regularization for slope constraints and optimization of adaptive splines.
result Adaptive nonuniform linear splines achieve global optimum in constrained optimization.
Kernelised flows improve density estimation and generation with fewer parameters.
problem Limited expressiveness of flow-based models due to invertibility constraints.
method Integrates kernels into normalising flows to enhance expressiveness and efficiency.
result Kernelised flows outperform neural network-based flows in parameter efficiency and low-data scenarios.
Invertible DenseNets improve model efficiency and performance.
problem Improving model efficiency and performance in neural networks.
method Enforcing invertibility in DenseNets by satisfying the Lipschitz constraint and proposing a learnable concatenation.
result i-DenseNets outperform Residual Flows in negative log-likelihood on various datasets.