Unified framework extends adjoint Schrödinger bridge sampler to discrete spaces.
problem Challenges in learning discrete neural samplers due to gradients and combinatorial complexity.
method Introduces discrete ASBS, a unified framework that extends adjoint Schrödinger bridge sampler to discrete spaces.
result Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.
Adjoint sampler targets infinite-dimensional function spaces for efficient sampling.
problem Limited theory and algorithms for sampling infinite-dimensional function spaces.
method Adjoint Sampler for infinite-dimensional function spaces based on stochastic maximum principle.
result FAS achieves superior performance in synthetic and real systems.
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This is due to the mixed Lagrangian-Eulerian formulation of large-displacement FSI in…
Derives adjoint polynomials of torus knots in explicit form.
problem Understanding adjoint invariants of torus knots.
method Closed-form double sum expression derivation.
result Explicit double sum form of adjoint polynomials.
Corrected samplers reduce discretization error in discrete flow models without additional computational cost.
problem Discretization error in samplers for discrete flow models.
method Established non-asymptotic error bounds for samplers, proposed time-corrected and location-corrected samplers.
result Location-corrected sampler has lower complexity and better generation quality.
We describe a canonical form for linear differential operators that are formally self-adjoint or formally skew-adjoint.
New samplers improve MCMC efficiency in high dimensions.
problem Efficient sampling in high-dimensional problems.
method Affine invariant ensemble samplers, including derivative-free and derivative-based HMC.
result Affine invariant ensemble HMC outperforms standard HMC in high dimensions.
Proves formal self-adjointness of certain differential operators.
problem Verifying conjectures about differential operators.
method Proving formal self-adjointness through mathematical proof.
result Proves two conjectures about differential operators.
Study of adjoint orbits in simplest non-trivial Lie algebra case.
problem Geometric properties of adjoint orbits in sl(2,R). method Analysis of adjoint orbits, showing three possibilities: hyperboloids or cones.
result Just three possibilities for adjoint orbits: hyperboloids or cones.
Abstracts a construction of boundary triplets for self-adjoint elliptic problems.
problem Computing the index of families of self-adjoint elliptic boundary problems.
method Abstract axiomatic version of boundary triplets and their applications.
result Analytic proof of index theorem and computation of index differences.
New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.
problem The difficulty of sampling from heavy-tailed distributions using Gaussian versus stable oracles.
method Comparison of Gaussian and stable oracles for proximal samplers.
result Gaussian samplers have a fundamental barrier for high-accuracy guarantees in heavy-tailed sampling, while stable samplers excel.
SRO optimizes decisions against worst-case sampler induced by generative models.
problem Operational uncertainty shifts from explicit probability law to sampler induced by learned generators.
method SRO optimizes decisions against the worst-case sampler induced by perturbing the learned generator.
result Empirical worst-case objective provides high-probability upper certificate for true population objective.
The Gibbs sampler is a particularly popular Markov chain used for learning and inference problems in Graphical Models (GMs). These tasks are computationally intractable in general, and the Gibbs sampler often suffers from slow mixing. In this paper, we study the Swendsen-Wang dynamics which is a more sophisticated Mark…
Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians.
problem Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians. method Consider the sum of the adjoint Reidemeister torsions and prove integrality for twist knots and meridians.
result Prove integrality of genus-g indices with adjoint Reidemeister torsions for twist knots and meridians. Quantizes Stäckel integrable systems into self-adjoint operators.
problem Quantizing Stäckel integrable systems into self-adjoint operators.
method Constructs commutative self-adjoint operators from quadratic Hamiltonians in involution.
result Proves multiplicative separation of variables for Stäckel integrable systems.
We give explicit descriptions of the adjoint group of the Coxeter quandle QW associated with an arbitrary Coxeter group W. The adjoint group of QW turns out to be an intermediate group between W and the corresponding Artin group AW, and fits into a central extension of W by a finitely generated free abel…
Discrete diffusion samplers improve sampling from unnormalised densities.
problem Sampling from discrete unnormalised densities efficiently.
method Introduce off-policy training techniques and data-to-energy Schrödinger bridge training for discrete diffusion samplers.
result Improved performance on synthetic and new benchmarks.
Unified analysis for deterministic samplers in diffusion models.
problem Challenges in analyzing deterministic samplers for diffusion models.
method Unified convergence analysis framework.
result Achieved polynomial iteration complexity for DDIM-type samplers.
Paper analyzes double twist knots using adjoint hyperbolic torsion polynomial.
problem Determining the genus and fibering of double twist knots.
method Uses adjoint hyperbolic torsion polynomial to analyze double twist knots.
result The adjoint hyperbolic torsion polynomial determines the genus and fibering of double twist knots.
Derives adjoint formulas for matrix operations and applies them to specific cases.
problem Computing adjoints for matrix operations and specific matrix types.
method Derives adjoint formulas for matrix operations and applies them to specific cases.
result Closed-form expressions for adjoints in specific matrix types.
This paper analyzes MaskGIT sampler and introduces a moment sampler for faster masked diffusion sampling.
problem Efficiently sampling from masked diffusion models.
method Theoretical analysis of MaskGIT sampler, introduction of moment sampler, and two innovations for improving choose-then-sample efficiency.
result The moment sampler is an asymptotically equivalent, more interpretable alternative to MaskGIT.
PTSD improves neural samplers by combining diffusion models and PT, enhancing efficiency.
problem Efficiency and correlation issues in neural samplers compared to PT.
method Sequential training of diffusion models across temperatures, combining high-temperature models for approximate lower-temperature samples.
result Significantly improved target evaluation efficiency, outperforming diffusion-based samplers.
Explicit formula for Reidemeister torsion of two-bridge knots.
problem Calculating Reidemeister torsion for two-bridge knots.
method Provided an explicit formula and proved vanishing identities.
result Adjoint Reidemeister torsion satisfies vanishing identities.
This paper introduces a neural sampler for scalable sampling from complex distributions.
problem Efficiently sampling from high-dimensional un-normalized distributions.
method Neural implicit sampler trained with KL and Fisher divergence methods.
result The neural sampler generates large batches of samples with low computational costs.
By now it is well established that the quantum dimensions of descendants of the adjoint representation can be described in a universal form, independent of a particular family of simple Lie algebras. The Rosso-Jones formula then implies a universal description of the adjoint knot polynomials for torus knots, which in p…
The paper explores self-adjointness of Laplace-Beltrami operator on special geometric manifolds.
problem Characterizing self-adjoint extensions of the Laplace-Beltrami operator on α-Grushin manifolds. method Introducing an exotic calculus of pseudodifferential operators adapted to the geometry of the singularity.
result Criterion for essential self-adjointness and determination of several self-adjoint extensions.
Study extends Vogel's universality to torus knots in adjoint representation.
problem Applying Vogel's universality to knot invariants in adjoint representation theory.
method Extending Vogel's parameters to include torus knots T[m,n] and focusing on T[4,n] with odd n. result Unified description of adjoint invariants for torus knots T[4,n] with odd n. Two parallel samplers enhance image quality in limited denoising steps.
problem Limited denoising steps in diffusion models reduce image quality.
method Two parallel samplers denoise at successive times, integrating their information.
result Two parallel samplers improve image quality compared to a single sampler.
For large scale on-line inference problems the update strategy is critical for performance. We derive an adaptive scan Gibbs sampler that optimizes the update frequency by selecting an optimum mini-batch size. We demonstrate performance of our adaptive batch-size Gibbs sampler by comparing it against the collapsed Gibb…
New PDMP samplers tackle variable selection in models.
problem Jointly explore model space and parameter space.
method Develop reversible jump PDMP samplers.
result New samplers mix better and are more efficient.
Extends adjoint representation concept to higher Lie groupoids.
problem Defining adjoint representation for higher Lie groupoids.
method Generalizes standard construction to higher Lie groupoids using simplicial vector bundles.
result Adjoint representation up to homotopy is well-defined and unique.
New knot theory module shows torsion-ness in number theory.
problem Torsion-ness of Selmer modules in Galois representations.
method Introducing adjoint homological Selmer module for SL2-representations of knot groups. result Finitely generated torsion-ness of the new Selmer module.
The Bouncy Particle Sampler is a novel rejection-free non-reversible sampler for differentiable probability distributions over continuous variables. We generalize the algorithm to piecewise differentiable distributions and apply it to generic binary distributions using a piecewise differentiable augmentation. We illust…
Neural network MCMC sampler maximizes proposal entropy for efficient sampling.
problem Inefficient sampling from complex probability distributions.
method Proposes a neural network MCMC sampler that maximizes proposal entropy.
result Significantly higher efficiency in various sampling tasks.
Develops new bounds for deterministic samplers in diffusion models.
problem Analyzing deterministic samplers in diffusion generative models.
method Operational interpretation of deterministic sampling; restoration and degradation steps.
result First polynomial convergence bounds for DDIM-type samplers.
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of ana…
Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have bottlenecks, sometimes termed "local maxima", and thus samplers often return suboptima…
PDMP samplers improve Bayesian PDE coefficient inference.
problem Efficient Bayesian inference in non-linear inverse problems with expensive likelihoods.
method Piecewise deterministic Markov process (PDMP) with surrogate-assisted thinning.
result PDMP samplers achieve higher accuracy and efficiency than traditional methods.
The paper evaluates samplers on multi-modal targets, focusing on mode separation and recovery.
problem Handling multi-modality in sampling.
method Synthetic experimental setting focusing on mode relative importance recovery.
result Illustrates the challenges and potential of samplers in multi-modality.
The study confirms essential self-adjointness for certain differential operators on manifolds.
problem Essential self-adjointness of differential operators on closed manifolds.
method Analyzing the Hamiltonian flow of the symbol of differential operators.
result The conjecture that certain differential operators are essentially self-adjoint if their Hamiltonian flow is complete.
We present a new data-driven benchmark system to evaluate the performance of new MCMC samplers. Taking inspiration from the COCO benchmark in optimization, we view this task as having critical importance to machine learning and statistics given the rate at which new samplers are proposed. The common hand-crafted exampl…
Paper proves index theorem for self-adjoint elliptic boundary problems.
problem Proving index theorem for self-adjoint elliptic boundary problems.
method Topological and pseudo-differential methods, generalized Atiyah-Singer approach.
result Removed technical assumption to prove index theorem.
With the rapidly growing scales of statistical problems, subset based communication-free parallel MCMC methods are a promising future for large scale Bayesian analysis. In this article, we propose a new Weierstrass sampler for parallel MCMC based on independent subsets. The new sampler approximates the full data poster…
Single-step samplers generate high-quality samples efficiently.
problem Sampling from unnormalized distributions is computationally expensive.
method Developed consistent diffusion samplers that generate samples in a single step.
result Single-step samplers produce high-fidelity samples with less than 1% of traditional samplers' evaluations.
BNEM improves Boltzmann sampler efficiency.
problem Generating IID samples from Boltzmann distributions efficiently.
method Bootstrapped Noised Energy Matching (NEM) combined with diffusion-based learning and bootstrapping.
result BNEM achieves state-of-the-art performance with improved robustness.
LSD distills high-quality samplers for DDMs with fewer steps.
problem Inefficient sampling in DDMs leads to low quality and high computational cost.
method LSD employs a distillation approach to train fast samplers with learnable coefficients and time schedules.
result LSD+ achieves higher sampling quality with fewer steps compared to existing samplers.
New sampler reduces MCMC complexity for Bayesian variable selection.
problem High-dimensional Bayesian variable selection with high computation complexity.
method Variable-complexity subset weighted-Tempered Gibbs Sampler (wTGS) with Rao-Blackwellized estimator.
result Variances of Rao-Blackwellized estimator are smaller than those of subset wTGS.