This work characterizes global quotient stacks---smooth stacks associated to a finite group acting a manifold---among smooth quotient stacks , where is a smooth manifold equipped with a smooth proper action by a Lie group . The characterization is described in terms of the action of the connected componen…
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48 results for “toric DM stack”
Quantum Kirwan maps between K-theories of G-varieties and GIT quotients.
problem Constructing maps between K-theories of G-varieties and their GIT quotients.
method Formal construction of maps in quantum K-theory, using equivariant and non-equivariant quantum K-theory.
result Presentation of quantum K-theory for smooth proper toric DM stacks.
Computes infinitesimal automorphisms for -valued Higgs bundles, leading to DM stacks.
problem Computing infinitesimal automorphisms for Higgs bundles.
method Extending known results, using obstruction theory.
result Shows moduli stack of stable Higgs bundles is a DM stack.
In this paper we will describe an approach to mirror symmetry for appropriate 1-dimensional DM stacks of arithmetic genus , called tcnc curves, which was developed by the author with Treumann and Zaslow in arXiv:1103.2462 . This involves introducing a conjectural sheaf-theoretic model for the Fukaya category …
Given a smooth projective toric variety of complex dimension , Fang-Liu-Treumann-Zaslow \cite{FLTZ} showed that there is a quasi-embedding of the differential graded (dg) derived category of coherent sheaves into the dg derived category of constructible sheaves on a torus . Recently, K…
Let be a separated, -shifted symplectic derived -scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension , and the underlying complex analytic topological space. We prove that …
Real-world large-scale datasets usually contain noisy labels and are imbalanced. Therefore, we propose derivative manipulation (DM), a novel and general example weighting approach for training robust deep models under these adverse conditions. DM has two main merits. First, loss function and example weighting are commo…
Improved DMs with DP-SGD for generating private images.
problem Low privacy of DMs and lack of good privacy-utility tradeoff.
method Adopt LDMs with DP-SGD on attention modules of LDMs.
result Generates high-quality DP images with reduced parameters.
New BGs use diffusion models to improve sampling from complex distributions.
problem Sampling from complex, multi-modal distributions is challenging.
method Combines diffusion models with annealed Monte Carlo for improved sampling.
result Second-order denoising kernels can improve performance in high-dimensional spaces.
DM improves self-supervised transfer learning by matching target distributions.
problem Improving self-supervised transfer learning performance.
method Distribution Matching (DM) method that drives representation distribution towards a predefined reference distribution.
result DM outperforms existing methods on target classification tasks.
A new method uses DMs as priors for imaging problems, offering more accurate reconstructions.
problem Accurate probabilistic imaging for complex inverse problems.
method Markov chain Monte Carlo algorithm using DMs as plug-and-play priors for solving Bayesian inverse problems.
result Offers more accurate reconstructions and posterior estimation compared to existing methods.
Bayesian optimization learns DM preferences for multi-outcome experiments.
problem Optimizing expensive experiments with unknown utility functions and multiple outcomes.
method Alternates preference learning and Bayesian optimization, using pairwise comparisons.
result Preference exploration strategies improve Bayesian optimization performance.
SciRE-Solver accelerates DMs sampling by recursively calculating the score function derivative.
problem Slow iterative process of diffusion models due to estimating the score function derivative.
method Recursive Difference (RD) method combined with truncated Taylor expansion of score-integrand.
result SciRE-Solver achieves state-of-the-art FIDs with significantly fewer score function evaluations.
In Divide & Recombine (D&R), big data are divided into subsets, each analytic method is applied to subsets, and the outputs are recombined. This enables deep analysis and practical computational performance. An innovate D\&R procedure is proposed to compute likelihood functions of data-model (DM) parameters for big dat…
DM framework improves robustness and efficiency in latent-mixture models.
problem Efficient and robust inference in latent-mixture models.
method Divergence-minimization framework with monotonic convergence and robustness guarantees.
result DM yields consistent and asymptotically normal estimators under correct specification.
We give sufficient conditions for a measured length space (X,d,m) to admit local and global Poincare inequalities. We first introduce a condition DM on (X,d,m), defined in terms of transport of measures. We show that DM, along with a doubling condition on m, implies a scale-invariant local Poincare inequality. We show …
Paper shows DMS as an EM algorithm with improved convergence.
problem Improving the convergence of DMS algorithm.
method Shows DMS as a generalized EM algorithm and provides new proofs.
result Demonstrates global convergence and linear convergence of DMS.
DM approximates submanifolds with error bounds.
problem Understanding the accuracy of Diffusion Maps in embedding submanifolds.
method Deriving geometric properties and deriving bounds on embedding errors.
result Error bounds for DM embeddings and tangent spaces.
DM uses semigroup property to tune diffusion time for better data analysis.
problem Difficulty in tuning diffusion time for optimal data analysis.
method Proposes a semigroup criterion to select diffusion time.
result Effective and robust method for picking diffusion time.
Paper optimizes diffusion models for denoising tasks with theoretical guarantees.
problem Lack of theoretical understanding of MSE optimality in diffusion models.
method Inspired by MSE-optimal CME, proposes a novel denoising strategy for diffusion models.
result Demonstrates polynomial-time convergence to the CME under mild conditions.
Bringing transparency to black-box decision making systems (DMS) has been a topic of increasing research interest in recent years. Traditional active and passive approaches to make these systems transparent are often limited by scalability and/or feasibility issues. In this paper, we propose a new notion of black-box D…
EVODiff optimizes DM inference by reducing conditional entropy, improving image generation.
problem Slow and inaccurate inference in diffusion models.
method Entropy-aware variance optimization for efficient inference.
result Significant improvement in image generation quality and efficiency.
Sensitivity Estimation for Dark Matter Subhalos in Synthetic Gaia DR2 using Deep Learningastro-ph.GA
Paper uses machine learning to detect dark matter subhalos in simulated Gaia DR2 data.
problem Detecting dark matter subhalos in simulated Gaia DR2 data.
method Proposed anomaly detection and classification-based approaches.
result Anomaly detection algorithm is sensitive to DM subhalos, but classification-based approach is not.
Machine learning models predict DM performance for AO systems.
problem Designing high-performance AO systems with large-scale DMs.
method Simulated FE model, neural network estimation, VARX input models, steady-state control.
result Estimated models reproduce DM input-output behavior and predict steady-state performance.
With the growing prevalence of smart grid technology, short-term load forecasting (STLF) becomes particularly important in power system operations. There is a large collection of methods developed for STLF, but selecting a suitable method under varying conditions is still challenging. This paper develops a novel reinfo…
New method uses diffusion models for inverse problems without approximations.
problem Solving complex inverse problems in high dimensions.
method Ensemble-based algorithm using diffusion models without approximations.
result Empirically validated method gives more accurate reconstructions.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
Improved RL training for DMs reduces mode collapse and preserves diversity.
problem Mode collapse and training instability in RL fine-tuned diffusion models.
method Dynamic hierarchical RL training with sliding-window parameter regularisation.
result Models trained with HRF achieve better preservation of diversity in downstream tasks.
New method improves language model fine-tuning without forgetting.
problem Fine-tuning language models to match specific distributions without forgetting.
method Combines Distribution Matching and Reinforcement Learning techniques.
result Adding a baseline improves constraint satisfaction, stability, and efficiency.
WS diffusion models handle anisotropic Gaussian noise better than conventional methods.
problem Handling anisotropic Gaussian noise in imaging inverse problems.
method Whitened Score (WS) diffusion models based on stochastic differential equations.
result WS DMs outperform conventional DMs on anisotropic Gaussian noise.
Bayesian optimization with preference learning identifies preferred solutions in multi-objective problems.
problem Optimizing multiple criteria with decision maker preferences in expensive functions.
method Bayesian optimization with interactive preference learning and active acquisition function.
result Identifies the most preferred solution with reduced interaction cost.
Paper uses algebraic signatures to identify probabilistic structures in empirical data.
problem Identifying probabilistic structure from observed binomials in empirical probability tensors.
method Treating vanishing binomials as algebraic signatures, matching signatures to identify models without parameter estimation.
result The method successfully identified rank-one structures in real language data, revealing interpretable sets of words.
Proposes a new method for optimizing designs based on uncertain preferences.
problem Optimizing designs with uncertain and time-consuming preferences.
method Bayesian optimization with preference learning for multi-attribute optimization.
result Produces a menu of designs and attributes for the DM to choose from.
New method improves DMs for solving inverse problems by maximizing conditional mutual information.
problem Efficiently solving noisy linear inverse problems without additional task-specific training.
method Maximizing conditional mutual information between reconstructed signal and measurement.
result Significantly improves the quality of generated images in inverse problems.
Bayesian approach improves rain field reconstruction using CMLs and DMs.
problem Challenges in accurately reconstructing ground-level rainfall from CML path-integrated measurements.
method Bayesian inverse problem with Diffusion Models as priors.
result Improved performance in rainfall estimation compared to existing methods.
By employing the differential structure recently developed by N. Gigli, we first give a notion of functions of bounded variation () in terms of suitable vector fields on a complete and separable metric measure space equipped with a non-negative Radon measure finite on bounded sets. Then, we e…
We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…
Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
problem Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
method Filtration approach to prove the conjecture.
result Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.
Toric hyperk{ä}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperk{ä}her manifolds as GIT quotients, we first establish geometrical criteria for the semi-stable po…
DPDMs use DP-SGD to generate private synthetic data.
problem Generating private synthetic data from sensitive datasets.
method Introduced DP-SGD for DMs, investigated DM parameterization and sampling, proposed noise multiplicity.
result Achieved state-of-the-art performance in image generation benchmarks.
Constructs scalar-flat Kähler metrics on toric symplectic manifolds.
problem Creating scalar-flat Kähler metrics on toric symplectic manifolds.
method Explicit construction and alternative construction with conical singularity.
result Explicit construction of scalar-flat Kähler metrics on toric symplectic manifolds.
Uniqueness of Kähler Ricci shrinkers proven on toric orbifolds.
problem Proving uniqueness of Kähler Ricci shrinkers on toric orbifolds.
method Extending results from toric manifolds to toric orbifolds.
result Uniqueness of Kähler Ricci shrinkers on toric orbifolds established.
This paper provides a new method to construct -symplectic toric manifolds from toric manifolds.
problem Classifying and constructing -symplectic toric manifolds.
method A new method to construct -symplectic toric manifolds from toric manifolds.
result This new method allows for the decomposition of -symplectic toric manifolds into toric manifolds.
Toric Quasifoldsmath.SG
Toric quasifolds extend toric geometry to non-rational polytopes.
problem Extending toric geometry to non-rational polytopes.
method Introduced toric quasifolds to solve symplectic extension problem.
result Illustrated toric quasifolds and their atlases.
Cylindrical contact homology linked to Ehrhart polynomials and Chen-Ruan cohomology.
problem Contact invariants of Q-Gorenstein toric contact manifolds.
method Relationships between cylindrical contact homology and Ehrhart polynomials, Chen-Ruan cohomology.
result Cylindrical contact homology invariants linked to Ehrhart polynomials and Chen-Ruan cohomology.
These are course notes on the application of SDEs to options pricing. The author was partially supported by NSF grant DMS-0739195.
Toric Vaisman Manifoldsmath.DG
Vaisman manifolds are strongly related to Kähler and Sasaki geometry. In this paper we introduce toric Vaisman structures and show that this relationship still holds in the toric context. It is known that the so-called minimal covering of a Vaisman manifold is the Riemannian cone over a Sasaki manifold. We show that if…
On Lagrangian Tori in math.SG
Classifies toric fibers in .
problem Identify Hamiltonian isotopy of toric fibers.
method Comprehensive classification of toric fibers in FOOO's construction.
result Determines Hamiltonian isotopy of toric fibers.