It is always demanding to learn robust visual representation for various learning problems; however, this learning and maintenance process usually suffers from noise, incompleteness or knowledge domain mismatch. Thus, robust representation learning by removing noisy features or samples, complementing incomplete data, a…
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48 results for “knowledge flows”
Multilayer Network Analysis of the Drug Pipeline in the Global Pharmaceutical Industryphysics.soc-ph
Study reveals similarities in knowledge flows between pharmaceutical and AI industries.
problem Understanding the dynamics of drug pipelines in global pharmaceutical industry.
method Multilayer network analysis of drug pipeline, global supply chain, and ownership data.
result Proven similarities in knowledge flows between pharmaceutical and AI industries.
A zoo of deep nets is available these days for almost any given task, and it is increasingly unclear which net to start with when addressing a new task, or which net to use as an initialization for fine-tuning a new model. To address this issue, in this paper, we develop knowledge flow which moves 'knowledge' from mult…
In this paper we propose a novel index to quantify and measure the flow of information on macro and micro scales. We discuss the implications of this index for knowledge management fields and also as intellectual capital that can thus be utilized by entrepreneurs. We explore different function and human oriented metric…
Enhances generative model accuracy through knowledge transfer.
problem Improving generative model precision across different tasks.
method Introduces a novel framework for transfer learning using shared structures.
result Demonstrates enhanced performance in diffusion and normalizing flows models.
New flows model distributions on Riemannian manifolds without domain knowledge.
problem Limited modeling of distributions on Riemannian manifolds.
method Riemannian convex potential maps using optimal transport.
result These flows can model standard distributions on spheres and tori.
Unified geometric flows improve deep learning efficiency and simplify neural network topologies.
problem Improving deep learning performance and simplifying neural network structures.
method Proposes a thermodynamically coupled Ricci flow that dynamically adapts parameter space geometry to loss landscape topology, enabling automated singularity resolution and providing entanglement entropy bounds.
result Demonstrates 2.1× convergence acceleration and 63% topological simplification while maintaining complexity, outperforming Riemannian baselines by 15.2% in few-shot accuracy.
Illustrates Ricci flow for a general audience.
problem Explains Ricci flow to non-experts.
method Illustrative introduction without prerequisites.
result Provides a working definition and intuition for Ricci flow.
We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph…
ContextFlow++ improves generative models by conditioning on mixed-variable contexts.
problem Lack of effective methods for context conditioning in flow-based generative models.
method Proposes ContextFlow++ with additive conditioning and mixed-variable architecture.
result ContextFlow++ achieves higher performance metrics and faster training.
Paper explores curvature flows on spheres to prove inequalities.
problem Prove inequalities for convex domains on spheres.
method Designs locally constrained curvature flows to preserve quermassintegrals.
result Flow convergence to a round sphere would settle inequalities.
EMFs combine deep learning and probabilistic models for better density estimation.
problem Combining domain-specific knowledge with general-purpose deep learning.
method Alternating transformations with structured layers that embed domain-specific inductive biases.
result EMFs induce desirable properties like multimodality and hierarchical coupling.
Dynamics of veering triangulations: infinitesimal components of their flow graphs and applicationsmath.GT
Study on veering triangulations and their flow graphs, proving new applications.
problem Understanding the structure of veering triangulations and their flow graphs.
method Analyzing the infinitesimal components of the flow graph associated with veering triangulations.
result Infinitesimal components of veering triangulations' flow graphs have specific forms related to subsets called 'walls'.
Study infinite combinatorial Ricci flow on spherical surfaces.
problem Investigate infinite combinatorial Ricci flow with spherical background.
method Establish existence and convergence of solution for infinite cellular decompositions.
result Existence and convergence of solution for infinite combinatorial Ricci flow in spherical geometry.
The article analyzes the stability of a curve shortening flow for planar networks.
problem Stability analysis of anisotropic curve shortening flow for planar networks.
method Used Lojasiewicz-Simon gradient inequality to derive stability results.
result For initial data close to an energy minimizer, the flow exists globally and converges to a different energy minimum.
In this paper, we prove that any solution of Kähler-Ricci flow on a Fano compactification of semisimple complex Lie group, is of type II, if admits no Kähler-Einstein metrics. As an application, we found two Fano compactifications of and one Fano compactification of $\mathrm{Sp}_4(\m…
E-NFs generate molecules and their positions while preserving Euclidean symmetries.
problem Generating molecules with their positions while preserving Euclidean symmetries.
method Integrating E(n) graph neural networks into a differential equation to create an invertible equivariant function.
result E-NFs significantly outperform baselines and existing methods in log-likelihood for particle systems and molecules.
A new method speeds up sampling of Boltzmann distribution in high-dimensional systems.
problem High computational cost of obtaining Jacobian of flow-based models in high dimensions.
method Flow perturbation method that incorporates stochastic perturbations and reweighting.
result Achieves unbiased sampling of Boltzmann distribution with orders of magnitude speedup.
Flows on Graded Manifoldsmath.DG
The paper defines flows on -graded manifolds and proves unique maximal flows for vector fields.
problem Lack of a treatment for flows on -graded manifolds.
method Definition and proof of maximal flows for vector fields on -graded manifolds.
result Every vector field admits a unique maximal flow, with conditions for vector fields invariant under flows and commuting flows.
Paper introduces combinatorial Ricci flows on infinite disk triangulations.
problem Discrete Ricci flows on infinite triangulations of the open disk.
method Combinatorial Ricci flows (CRFs) in Euclidean and hyperbolic geometries.
result Existence and uniqueness of CRFs, convergence results, uniformization theorem.
Improved physics-integrated generative models with noise robustness and fidelity.
problem Enhancing generative models to produce outputs that comply with physical laws and improve generalization.
method Integrating variational autoencoder with planar normalizing flow and attention mechanisms to learn latent posterior distributions and mitigate noise.
result Significant improvement in reconstruction quality and robustness against noise.
Active researches are currently being performed to incorporate the wealth of scientific knowledge into data-driven approaches (e.g., neural networks) in order to improve the latter's effectiveness. In this study, the Theory-guided Neural Network (TgNN) is proposed for deep learning of subsurface flow. In the TgNN, as s…
Flow-based data sets are necessary for evaluating network-based intrusion detection systems (NIDS). In this work, we propose a novel methodology for generating realistic flow-based network traffic. Our approach is based on Generative Adversarial Networks (GANs) which achieve good results for image generation. A major c…
We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a priori knowledge of the number of classes or the relationships between classes. Th…
Coupled Flow Matchingstat.ML
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
New method compares geometric and standard cup products.
problem Reconciling partially defined and fully defined cochain products.
method Vector field flow through cubulation to compare products.
result Explicit cochain level comparison between intersection and cup products.
Molecular graph generation is a fundamental problem for drug discovery and has been attracting growing attention. The problem is challenging since it requires not only generating chemically valid molecular structures but also optimizing their chemical properties in the meantime. Inspired by the recent progress in deep …
New method finds ideal circle patterns on spheres.
problem Finding ideal circle patterns on spheres with prescribed curvatures.
method Combinatorial Calabi flow in spherical geometry.
result Existence and convergence of the flow for ideal circle patterns.
Shrinkers are special solutions of mean curvature flow (MCF) that evolve by rescaling and model the singularities. While there are infinitely many in each dimension, [CM1] showed that the only generic are round cylinders $\SS^k\times \RR^{n-k}$. We prove here that round cylinders are rigid in a very strong sense. Namel…
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the co…
Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, con…
The paper studies parallel spinor flows on 3D Cauchy hypersurfaces and provides initial data characterizations.
problem Characterizing parallel spinors on Ricci flat Lorentzian four-manifolds.
method Evolution flow defined by parallel spinors, proving preservation of constraints, solving left-invariant flows.
result Initial data characterization of parallel spinors on Ricci flat Lorentzian four-manifolds.
An outsider's overview of Anosov flows in 3D.
problem Understanding Anosov flows in 3D and their interactions.
method Overview and discussion of main results and questions.
result Highlighting the interaction with topology and symplectic geometry.
Machine Learning for Fluid Mechanicsphysics.flu-dyn
The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the…
Hadamard Wirtinger Flow recovers sparse signals from fewer measurements.
problem Reconstructing sparse signals from magnitude-only measurements.
method Gradient descent with Hadamard parametrization (HWF).
result A single step of HWF recovers support from samples.
Recently, practical applications for passenger flow prediction have brought many benefits to urban transportation development. With the development of urbanization, a real-world demand from transportation managers is to construct a new metro station in one city area that never planned before. Authorities are interested…
Causal normalizing flows recover causal models from observational data.
problem Recovering causal models from observational data.
method Use autoregressive normalizing flows and analyze design choices.
result Causal normalizing flows can capture causal data-generating processes.
We investigate Liouville theorems and dimension estimates for the space of exponentially growing holomorphic functions on complete Kähler manifolds. While our work is motivated by the study of gradient Ricci solitons in the theory of Ricci flow, the most general results we prove here do not require any knowledge of cur…
Graphical normalizing flows use Bayesian networks to improve normalizing flows' interpretability and performance.
problem Improving the interpretability and performance of normalizing flows.
method Revisiting normalizing flows as probabilistic graphical models, proposing graphical normalizing flows with either prescribed or learnable graph structures.
result Graphical conditioners lead to competitive white box density estimators.
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth and invertible transformation that maps a simple distribution to the desired ma…
Domain adaptation leverages the knowledge in one domain - the source domain - to improve learning efficiency in another domain - the target domain. Existing heterogeneous domain adaptation research is relatively well-progressed, but only in situations where the target domain contains at least a few labeled instances. I…
Two fundamental problems in unsupervised learning are efficient inference for latent-variable models and robust density estimation based on large amounts of unlabeled data. Algorithms for the two tasks, such as normalizing flows and generative adversarial networks (GANs), are often developed independently. In this pape…
Flow Annealing Posterior Sampling unifies stochastic-process regression and PDE inverse problems.
problem Function-space posterior sampling for stochastic processes and inverse problems.
method Flow Annealing Posterior Sampling (FAPS) using pretrained function-space flow-matching priors.
result Coherent posterior samples with accurate uncertainty quantification.
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
Proposes TgNN-LD to improve neural network effectiveness and efficiency.
problem Limits in maintaining tradeoff between data and domain knowledge.
method Converts loss function to constrained form with PDEs, ECs, and EK as constraints, incorporating Lagrangian variables for equitable tradeoff.
result Improves prediction accuracy and conserves resources.
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 -divergence with .
result FAB learns Boltzmann distribution of alanine dipeptide without MD samples.
Frugal Flows learn complex data and infer marginal causal effects.
problem Challenges in estimating marginal causal effects from complex data.
method Frugal Flows use normalizing flows to flexibly learn data and infer causal quantities.
result Frugal Flows can generate synthetic data that closely matches real-world data and exactly parameterize causal quantities.
Improved KL bounds and Wasserstein guarantees for diffusion flow matching under minimal conditions.
problem Theoretical convergence properties of Brownian motion based diffusion flow matching.
method Refined analysis under Kullback-Leibler and 2-Wasserstein distances.
result State-of-the-art scaling in KL convergence bounds under minimal conditions.