The paper proves the existence of isotropic complete solutions for generalized Hamilton-Jacobi equations.
problem Existence of isotropic complete solutions for generalized Hamilton-Jacobi equations.
method Analyzes symplectic manifolds, Hamiltonian vector fields, and fibrations to prove the existence of isotropic complete solutions.
result Proves the existence of isotropic complete solutions around almost every point of the manifold.
In this paper we develope, in a geometric framework, a Hamilton-Jacobi Theory for general dynamical systems. Such a theory contains the classical theory for Hamiltonian systems on a cotangent bundle and recent developments in the framework of general symplectic, Poisson and almost-Poisson manifolds (including some appr…
New theory extends Hamilton-Jacobi for contact systems, ensuring integrability.
problem Integrability of contact Hamiltonian systems.
method Developed a Hamilton-Jacobi theory for fibered phase spaces, applied to contact systems, studied HJE solutions.
result Complete pseudo-isotropic solutions ensure integrability by quadratures for contact systems.
Study of Hamilton-Jacobi Theory with symmetries and integrability by quadratures.
problem Hamilton-Jacobi equation in systems with symmetries.
method Constructing complete solutions and solving reconstruction equations.
result Explicit expressions for exponential curves in Lie groups, valid for all elements in the Lie algebra.
Paper defines generalized braids and proves their subgroup status.
problem Understanding the structure of generalized braids and knots.
method Defined generalized braid theories and computed their generating sets.
result Quasitoric normal generalized braids form a subgroup of normal generalized braid group.
Defines a new Poisson structure for generalized Sasakian spaces.
problem No specific problem stated; focuses on new structure definition.
method Defines a canonical Poisson structure on generalized contact metric spaces.
result Shows distinction between generalized Sasakian and coKähler structures.
Characterizes integrability of generalized structures on Courant algebroids.
problem Integrability of generalized structures on Courant algebroids.
method Characterization via torsion-free generalized connections and Dirac generating operators.
result Criterion for integrability of generalized almost Hermitian structures and hyper-Hermitian structures.
Improved image generation through iterative flow matching to reduce hallucinations.
problem Hallucinations in image generation models.
method Iterative flow matching to refine and correct paths in generative models.
result Enhanced generative modeling with reduced unrealistic images.
Plug-and-play multimodal controller improves class-conditional image generation.
problem Generating class-conditional images from user-specified labels.
method Introduces a `multimodal controller` to generate multimodal data without additional learning parameters.
result Multimodal controlled generative models produce higher quality class-conditional images and novel modalities.
Framework generates personalized insulin treatment strategies using deep models.
problem Developing optimal personalized treatment strategies for diabetes patients.
method Combines deep generative time series models with decision theory.
result Demonstrated improved personalized insulin treatment strategies for diabetes patients.
The study addresses exposure bias in generative models, proposing unconditional generation as a solution.
problem Exposure bias in autoregressive generative models using ground-truth contexts at training and generated ones at test.
method Combining latent variable modeling with reinforcement learning exploration, the study proposes unconditional generation as a benchmark for generalization.
result The model demonstrates improved generalization capability on language modeling and variational sentence auto-encoding tasks.
Survey on deep models for graph generation.
problem Improving fidelity of generated graphs.
method Taxonomy and comparison of deep generative models.
result Advances in deep generative models for graph generation.
OptiGAN uses GAN and RL to optimize sequence generation for specific goals.
problem Challenging in sequence generation tasks to generate sequences with specific desired goals.
method Integrates GAN and RL to optimize desired goal scores using policy gradients.
result Achieves higher desired scores in text and real-valued sequence generation.
Improves deep generative models to generate images of any size.
problem Fixed-sized output images from deep generative models.
method Integrates spatial noise vectors into fully convolutional neural networks.
result Theoretical interpretation of infinite spatial generation using spatial stochastic processes.
Develops a unified theory of Yang-Mills and GR using generalized principal bundles.
problem Combining Yang-Mills theories and General Relativity into a single framework.
method Using generalized principal bundle theory, the authors develop a new approach to field theories.
result Recover General Relativity within the framework of generalized principal connections.
Meta-CoTGAN improves adversarial text generation by preventing mode collapse.
problem Mode collapse in adversarial text generation.
method Meta-Cooperative Training Paradigm with a language model.
result Meta-CoTGAN effectively slows down mode collapse and improves generation quality and diversity.
Generative models can still learn from contaminated data, but with limitations.
problem How much contamination can generative models tolerate?
method Characterized robustness under contaminated enumerations, proving generation is achievable for all countable collections if contamination fraction converges to zero.
result Generation under contamination is achievable for all countable collections if contamination fraction converges to zero, but dense generation is strictly less robust.
Generative models use EOT cost for better image generation.
problem Developing models to learn implicit distributions for image generation.
method Two models: one-shot optimization with EOT cost and adversarial game with EOT cost.
result Improved image generation performance on MNSIT.
Generative AI tasks analyzed for text, images, audio, video, code, and molecules.
problem What is the core question when using generative AI?
method Survey of generative model families, probabilistic framework, game-theoretic setup, post-training modifications, socially responsible considerations.
result Generative AI is a distinct machine learning task with connections to prediction, compression, and decision-making.
New method learns text generation orders without pre-specification.
problem Generating text in arbitrary orders without manual specification.
method Generates text in non-monotonic orders using a binary tree structure and imitation learning.
result Models can generate text without pre-specifying an order, achieving competitive performance.
Defines Kahler angle for a broader context.
problem Generalizing results about Kahler angle.
method Provides a general definition of Kahler angle.
result Generalized results about Kahler angle.
Established a generalized Boothby-Wang theorem in contact geometry.
problem Generalized contact structures and their properties.
method Courant reduction methods and construction of principal bundles.
result Induced symplectic foliation on leaf space under certain conditions.
The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry à la Hitchin). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the…
This research proves guarantees on sequence models' generalization to longer and novel sequences.
problem Generalization to longer sequences and novel token combinations in sequence models.
method Provable guarantees on length and compositional generalization for various sequence models.
result Limited capacity models achieve both length and compositional generalization with diverse training distributions.
SHADOWCAST generates graphs with user-specified attributes.
problem Controlling graph generation with understandable structures.
method Conditional generative adversarial network guided by Markov model.
result Competitive performance in generating desired graphs.
In this paper we define the notion of a generalized coKähler structure and prove that the product M1×M2 of generalized contact metric manifolds (Mi,Φi,E±,i,Gi), i=1,2, where M1×M2 is endowed with the product generalized complex structure induced from Φ1 and Φ2, is gener…
Paper analyzes and improves GANs' generalization and stability.
problem Poor generalization of GANs' discriminators in practical settings.
method Proposes a zero-centered gradient penalty to improve discriminator's generalization.
result Improves GANs' generalization and convergence through the proposed penalty.
In this communication, we describe some interrelations between generalized q-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the entropy. We show that this identity can be extended to generalized versions of en…
We define the generalized connected sum for generic closed plane curves, generalizing the strange sum defined by Arnold, and completely describe how the Arnold invariants J± and St behave under the generalized connected sums.
Proposes models to generate more interesting story endings.
problem Generating diverse and interesting story endings for a given context.
method Trains models to focus on keyphrases and promotes non-generic words.
result Models generate more diverse and interesting story endings.
A new method generates graphs with hierarchical structures.
problem Generating graphs with natural hierarchical structures.
method Recursively generates community structures at multiple resolutions, parallel generation of all sub-structures.
result Improves generative performance on multiple graph datasets.
The paper extends symplectic techniques to generalized complex geometry.
problem Creating stable generalized complex structures on high-dimensional manifolds.
method Introducing generalized Luttinger surgery and generalized Gluck twist.
result Produced stable generalized complex structures with non-homotopy-equivalent components.
A new method for generating sets and graphs without requiring exchangeability.
problem Generating exchangeable distributions for sets and graphs is challenging.
method Top-n creation, a differentiable generation mechanism that selects relevant points from a latent vector.
result Top-n method outperforms i.i.d. generation in various tasks.
DeepWeightFlow generates diverse neural network weights efficiently.
problem Generating complete neural network weights efficiently and accurately.
method Flow Matching in weight space with Git Re-Basin and TransFusion.
result DeepWeightFlow generates high-accuracy neural networks without fine-tuning.
Generative concept representations improve deep learning by handling uncertainty and integrating learning and reasoning.
problem Discriminative deep learning struggles with uncertainty and lacks integration of learning and reasoning.
method Probabilistic and generative deep learning, variational autoencoders, and generative adversarial networks.
result Generative concept representations enhance deep learning by addressing these limitations.
Style generators can invertibly generate images, useful for image enhancement and animation.
problem Generating all possible images and maintaining invertibility are challenging for GANs.
method Proposed style generators are invertible and can generate all possible images.
result Style generators outperform other GANs and Deep Image Prior as image priors.
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving several characterizations of invertibility in the algebra of generalized functions we define the notions of generalized pseudo-Riemannian met…
It is known that the scalar curvature arises as the moment map in Kahler geometry. In pursuit of this analogy, we introduce the notion of a moment map in generalized Kahler geometry which gives the definition of a generalized scalar curvature on a generalized Kahler manifold. From the viewpoint of the moment map, we ob…
We characterize language generation with stability and breadth, proving impossibility results.
problem Characterizing and proving impossibility results for language generation with stability and breadth.
method Analysis of existing notions of breadth and stability, proving lower bounds.
result Proven impossibility of generating with higher perplexity or lower hallucination rate for stable generators.
This is an expository paper, which provides a first introduction to geometric structures on TM⊕T∗M. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal, almost) contact and generalized Sasakian structures. A few of these properties are n…
Rate GENERIC extends thermodynamics principles to non-equilibrium systems.
problem Understanding non-equilibrium thermodynamics and its relation to equilibrium thermodynamics.
method Developed a geometrical framework for rate GENERIC, extending Onsager's variational principle.
result Rate GENERIC structure provides a new perspective on thermodynamics in non-equilibrium systems.
QGAA learns latent quantum states, reducing errors in quantum data generation.
problem Learning latent representations for quantum data generation.
method Quantum Generative Adversarial Autoencoder (QGAA) combining QAE and QGAN.
result Average errors in energies for H2 and LiH are 0.02 Ha and 0.06 Ha respectively, demonstrating QGAA's potential.
Sharpness minimization algorithms don't solely improve generalization.
problem Why do overparameterized neural networks generalize?
method Theoretical and empirical investigation of two-layer ReLU networks.
result Sharpness minimization algorithms do not always lead to better generalization.
The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
The notion of a generalized Lie bialgebroid (a generalization of the notion of a Lie bialgebroid) is introduced in such a way that a Jacobi manifold has associated a canonical generalized Lie bialgebroid. As a kind of converse, we prove that a Jacobi structure can be defined on the base space of a generalized Lie bialg…
The study shows manifolds with special generic maps also have nice multisections.
problem Characterizing manifolds with special generic maps and multisections.
method Analyzing manifolds with special generic maps and their properties, and showing how these maps restrict the differentiable structures of spheres and manifolds.
result Manifolds admitting special generic maps also admit nice generalized multisections.
Generative model creates detailed 3D shapes from text descriptions.
problem Creating high-resolution 3D models from natural language descriptions.
method Two-step process: first generating low-resolution shapes, then high-resolution shapes using Conditional Wasserstein GAN framework.
result Improved method generates 3D shapes more faithful to natural language.
The paper proposes a method to incorporate prior knowledge into generative models using a regularizer.
problem Learning generative models with prior domain knowledge is costly and often impractical.
method Formulate a regularizer that makes generative model marginals follow prescribed feature relations.
result The method effectively incorporates prior knowledge into generative models without requiring specific model architectures.