Gradient descent on normalized networks reveals sparsity preferences.
problem Understanding the inductive bias of gradient descent on normalized neural nets.
method Analysis of gradient descent on weight-normalized smooth homogeneous neural nets, focusing on SWN and EWN.
result EWN causes weights to be updated in a way that prefers asymptotic relative sparsity.
Existence and uniqueness theorem for Ricci flow on weighted graphs proved.
problem Existence and uniqueness of solutions to Ricci flow equations on weighted graphs.
method Continuous time normalized Ricci flow approach.
result Existence and uniqueness theorem for solutions to Ricci flow on weighted graphs.
Study of Ricci flow on trees, focusing on edge weights and curvatures.
problem Understanding the evolution of metrics on trees under Ricci flow.
method Continuous-time Ricci flow based on Lin-Lu-Yau Ollivier Ricci curvature.
result Ricci flow converges to zero curvature on edge weights of positive normalized values in caterpillar trees.
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
EWFM trains continuous flows with only energy evaluations, improving sample quality with fewer computations.
problem Efficiently sampling from complex, high-dimensional Boltzmann distributions using only energy evaluations.
method Energy-Weighted Flow Matching (EWFM) using importance sampling and iterative/annealed training.
result Improved sample quality with up to 3 orders of magnitude fewer energy evaluations compared to existing methods.
Paper introduces VDE, a variance-reduced determinant estimator.
problem Estimating determinants with low variance and efficiency.
method Combines variational inference and spherical normalizing flows.
result VDE achieves zero variance in ideal cases, requiring only one sample.
Theoretical justification for deep networks' performance with regularization techniques.
problem Understanding the performance of deep networks trained with the square loss.
method Analysis of gradient flow and theoretical justification of regularization techniques.
result Convergence to solutions with smaller Frobenius norms leads to better classification error bounds.
Gradient Boosted Normalizing Flows improve flexibility of NFs without increasing complexity.
problem Improving flexibility of normalizing flows without increasing complexity.
method Gradient Boosting applied to normalizing flows to create a mixture model structure.
result GBNFs outperform non-boosted NFs and produce better results with simpler components.
Improved sampling efficiency for molecular systems using path gradients after Flow Matching.
problem Improving sampling efficiency for complex molecular systems.
method Hybrid approach combining Flow Matching and path gradients.
result Up to a threefold increase in sampling efficiency for molecular systems.
OT-Flow uses optimal transport to improve CNFs for faster and more accurate density estimation.
problem Computational challenges in continuous normalizing flows.
method OT-Flow leverages optimal transport to regularize CNFs and uses exact trace computation.
result OT-Flow achieves competitive performance with one-fourth the number of weights and significant speedups.
SNF combines stochastic and deterministic steps to sample complex distributions.
problem Sampling complex probability distributions efficiently.
method Stochastic Normalizing Flows (SNF) - sequence of invertible functions and stochastic blocks.
result SNFs improve efficiency and representational power over pure MCMC/LD.
Improves conditional distribution modeling with simpler training.
problem Analyzing inverse problems with invertible neural networks.
method Uses normalizing flows to maximize posterior likelihood, incorporating conditioning.
result Easier training and natural framework for conditional generation.
Sharp Minkowski inequality found for AdS-Melvin spacetime surfaces.
problem Proving a Minkowski-type inequality for surfaces in the AdS-Melvin space.
method Used weighted normal flow to prove inequality for general surfaces.
result Sharp Minkowski inequality holds for all surfaces in AdS-Melvin space.
A new method normalizes flow mixtures for better inference across different data types.
problem Inference failure across diverse posterior geometries in normalizing flows.
method Introduces a two-stage framework with a stable global weighting mechanism based on sEMA.
result Achieves consistent NLL improvements and stable weight trajectories over baselines.
MixerFlow combines MLP-Mixer with normalizing flows for efficient image modeling.
problem Efficiently modeling complex image densities using generative models.
method Proposes MixerFlow, a novel architecture based on MLP-Mixer for normalizing flows.
result Demonstrates improved density estimation and better scaling with higher image resolutions.
FTIP uses normalizing flows to improve posterior inference in function space.
problem Challenges in posterior inference with implicit-process priors.
method FTIP uses normalizing flows to define a richer variational distribution over combination weights.
result FTIP captures asymmetric and multimodal posterior structure better than Gaussian coefficient approximations.
A new method improves flow matching by dynamically weighting density estimates.
problem High-dimensional integration inefficiency in flow matching.
method Density-weighted Dynamic Stein operators.
result Significant improvement in vector field smoothness and sampling efficiency.
Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove bot…
Extends VAEs to handle complex Bayesian network structures.
problem Handling complex dependency structures in Bayesian networks.
method Extends VAEs with graphical residual flows to model arbitrary dependency structures.
result Demonstrates improved performance on synthetic datasets.
Normalizing Flows improve prediction interval efficiency in CP.
problem Inefficient prediction intervals in CP due to non-uniform error distribution.
method Train a Normalizing Flow to optimize the distance metric between errors and inputs.
result Optimized prediction intervals are more efficient and valid.
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Enhanced latent spaces improve collider simulation precision.
problem Improving the precision of collider physics simulations.
method Machine learning techniques including reweighting, pre-processing, and latent space refinement.
result Sub-percent precision across various phase spaces achieved.
Theoretical work on mode collapse in variational inference models.
problem Mode collapse in variational inference models, where models focus on a few modes instead of all possible ones.
method Theoretical investigation of mode collapse in Gaussian mixture models, identifying key low-dimensional statistics and equations governing their evolution.
result Mode collapse is present even in favorable scenarios, driven by mean alignment and vanishing weight mechanisms.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
This paper introduces a new method to train normalizing flows using precision-recall divergences.
problem Training generative models with mode dropping and low-quality samples.
method Introduces PR-divergences and proposes a novel generative model to minimize precision-recall trade-offs.
result Normalizing flows can be trained to achieve specific precision-recall trade-offs using PR-divergences.
The paper introduces a new type of Ricci flow on graphs to study their curvature.
problem Understanding the curvature of graphs and their convergence properties.
method Proposes a weighted Forman and Lin-Lu-Yau Ricci flow on graphs and proves the existence and uniqueness of solutions.
result The normalized curvature flow on trees converges to a constant curvature metric.
Maximum likelihood training improves the performance of score-based diffusion models.
problem Training score-based diffusion models with maximum likelihood.
method Trained by minimizing a weighted combination of score matching losses, with a specific weighting scheme that bounds negative log-likelihood.
result Maximum likelihood training improves the log-likelihood of score-based diffusion models across multiple datasets.
Paper advances black-box VI using flows and Monte-Carlo methods.
problem Improving automatic posterior inference in black-box VI.
method Combines normalizing flows, Monte-Carlo methods, and optimization considerations.
result Significant improvement in state-of-the-art variational inference.
The paper studies matrix normalization and graph balancing using a new functional and gradient descent.
problem Matrix normalization and graph balancing.
method A new functional called the non-normal energy, and gradient descent.
result Gradient descent of the non-normal energy converges to balanced graphs and preserves spectra and realness of weights.
The paper connects Ricci flow and harmonic spinors, proving new inequalities.
problem Understanding the behavior of harmonic spinors under Ricci flow.
method Introduced a weighted monopole equations and used Perelman's entropy.
result Ricci flow is the gradient flow of energy related to harmonic spinors.
NoFAS combines variational inference and adaptive surrogate models for efficient inference of computationally expensive models.
problem Efficient inference of parameters from data with computationally expensive models.
method Variational inference with normalizing flow and adaptive surrogate model training.
result NoFAS reduces computational cost without sacrificing inferential accuracy.
RFM improves CNFs by adding a boundary constraint term and matching velocity fields.
problem Flow matching on constrained domains leads to unnatural samples.
method RFM adds a boundary constraint term and matches velocity fields in a simulation-free manner.
result RFM achieves comparable or better results on standard image benchmarks and produces high-quality samples.
Study of curve evolution in 2D space forms converging to a circle.
problem Understanding curve evolution in 2D space forms.
method Inverse curvature flow with normal speed defined by weighted inverse curvature and support function.
result Solutions exist for all time and converge exponentially to a standard round geodesic circle.
New method trains normalizing flows using entropy-regularized transport.
problem Training continuous normalizing flows efficiently.
method Formulates flows as gradients of scalar potentials, training only these potentials.
result Trains normalizing flows without explicit flow computation during training.
Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single…
Probabilistic Autoencoder learns latent space weights' distribution.
problem Nonlinear model reconstruction error and sample quality.
method Normalizing flow for latent space weights' probability distribution.
result PAE achieves small reconstruction errors, high sample quality, and good performance.
Preconditioned NFs speed up sampling from complex posterior distributions in inverse problems.
problem Sampling from posterior distributions of inverse problems with expensive forward operators.
method Preconditioning a conditional normalizing flow (NF) to speed up training.
result Significant speed-ups achieved compared to training NFs from scratch.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
PL-MCMC samples from normalizing flows' conditional distributions.
problem Sampling from complex conditional distributions learned by normalizing flows.
method Metropolis-Hastings implementation of PL-MCMC.
result PL-MCMC asymptotically samples from exact conditional distributions.
Ricci-Filtration enhances retrieval-augmented generation rerankers for query-answer tasks by using discrete Ricci flow on graphs.
problem Improving retrieval-augmented generation rerankers for query-answer tasks.
method Discrete Ricci flow on graphs to evaluate structural importance of chunks.
result Ricci-Filtration outperforms baseline methods in accuracy, precision, recall, and F1 scores.
Fractal Flow enhances normalizing flows with interpretable latent space and hierarchical modeling.
problem High-dimensional density estimation and generative modeling challenges.
method Integrates topic modeling (LDA) and fractal strategy into normalizing flows.
result Achieves latent clustering, controllable generation, and superior estimation accuracy.
Flow AIS Bootstrap improves flow training by generating samples in hard-to-reach regions.
problem Training flows with high variance and mode-seeking behavior.
method Augment flows with AIS and minimize α-divergence with α=2. result FAB learns Boltzmann distribution of alanine dipeptide without MD samples.
DIF extends NF with stochastic discrete latent variables for better density estimation.
problem Improving density estimation with discontinuities and fine details.
method Discretely indexed flows as an extension of Normalizing Flows with stochastic latent variables.
result DIF inherit good computational behavior of NF and can capture distributions with discontinuities.
Ricci flow stabilizes hyperbolic 3-manifolds near the hyperbolic metric.
problem Stability of Ricci flow on hyperbolic 3-manifolds.
method Normalized Ricci-DeTurck flow with exponential convergence to the hyperbolic metric.
result Normalized Ricci-DeTurck flow converges exponentially to the hyperbolic metric.
i-flow uses normalizing flows for high-dimensional integration and sampling.
problem High-dimensional integration in science and statistics.
method Normalizing flows for bijective mappings between distributions.
result i-flow outperforms other algorithms for high-dimensional correlated integrals.
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.
This paper establishes risk convergence and asymptotic weight matrix alignment --- a form of implicit regularization --- of gradient flow and gradient descent when applied to deep linear networks on linearly separable data. In more detail, for gradient flow applied to strictly decreasing loss functions (with similar re…
SurVAE Flows combine VAEs and flows using surjective transformations.
problem Combining the strengths of VAEs and flows to model complex densities.
method Modular framework of composable deterministic and stochastic transformations.
result Exact likelihood computation and lower bound on likelihood.