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.
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.
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.
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.
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.
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 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.
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…
We present a characterization, in terms of torsion-free generalized connections, for the integrability of various generalized structures (generalized almost complex structures, generalized almost hypercomplex structures, generalized almost Hermitian structures and generalized almost hyper-Hermitian structures) defined …
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…
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.
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…
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.
We study the problem of generating interesting endings for stories. Neural generative models have shown promising results for various text generation problems. Sequence to Sequence (Seq2Seq) models are typically trained to generate a single output sequence for a given input sequence. However, in the context of a story,…
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.
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…
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…
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.
Standard sequential generation methods assume a pre-specified generation order, such as text generation methods which generate words from left to right. In this work, we propose a framework for training models of text generation that operate in non-monotonic orders; the model directly learns good orders, without any ad…
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.
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…
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 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.
Generic groups satisfy a chain condition for subgroups.
problem Understanding subgroup structures in generic groups.
method Proving for fixed integers m,t,k in generic m-generator t-relator groups. result Generic groups satisfy the Ascending Chain Condition for k-generated subgroups. In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generaliz…
A new deep generative model uses BSDEs for high-dimensional data generation.
problem Generating high-dimensional complex data, especially images.
method Combines BSDEs with deep neural networks for training with MMD loss.
result BSDE-Gen effectively generates high-dimensional data with stochasticity.
Survey on combining causal models with deep generative models for improved explainability and fairness.
problem Deep generative models lack explainability, induce spurious correlations, and poor out-of-distribution extrapolation.
method Structural causal models (SCMs) combined with deep generative models to address shortcomings.
result Causal generative models offer robustness, fairness, and interpretability.
In unsupervised data generation tasks, besides the generation of a sample based on previous observations, one would often like to give hints to the model in order to bias the generation towards desirable metrics. We propose a method that combines Generative Adversarial Networks (GANs) and reinforcement learning (RL) in…
We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general rotational surfaces with plane meridian curves and give the complete classificat…
Unified approach unites GANs and diffusion models using particle methods.
problem Combining GANs and diffusion models for generative tasks.
method Proposes a unified framework where generator training is seen as a generalization of particle models.
result Demonstrates that GANs and diffusion models can be integrated within a unified framework.
New concept SB-generation helps classify transformation groups.
problem Classifying transformation groups through quasi-isometry invariants.
method Identifying SB-generated groups in specific transformation groups.
result SB-generation provides robust extension of finite generation.
Defines generalized Sasakian structures in contact geometry.
problem Understanding k-contact manifolds and CR manifolds.
method Introduced generalized Sasakian structures and proved their equivalence to Sasakian structures.
result k-contact manifolds are generalized Sasakian if and only if they are classically Sasakian.
We first make a little survey of the twistor theory for hypercomplex, generalized hypercomplex, quaternionic or generalized quaternionic manifolds. This last theory was iniated by Pantilie, who shows that any generalized almost quaternionic manifold equipped with an appropriate connection admit a twistor space with an …
Classifies and computes cohomologies of complex structures on Lie groups.
problem Classifying and computing cohomologies of complex structures on Lie groups.
method Complete classification and computation of invariant cohomologies for left invariant structures.
result Computed invariant cohomologies for various generalized complex and Kähler structures.
Class-conditional generative models are crucial tools for data generation from user-specified class labels. Existing approaches for class-conditional generative models require nontrivial modifications of backbone generative architectures to model conditional information fed into the model. This paper introduces a plug-…