3-manifolds can be made parallelisable via surgery.
problem Making 3-manifolds parallelisable.
method Surgery presentation, refined by Kaplan, contact geometry.
result All closed, orientable 3-manifolds are parallelisable.
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48 results for “parallelisability”
We classify the simply-connected supersymmetric parallelisable backgrounds of heterotic supergravity. They are all given by parallelised Lie groups admitting a bi-invariant lorentzian metric. We find examples preserving 4, 8, 10, 12, 14 and 16 of the 16 supersymmetries.
Novel parallelization simplifies machine learning algorithms.
problem Adapting machine learning algorithms to growing data and needs.
method A novel parallelization scheme that applies to broad learning algorithms.
result Reduces runtime to polylogarithmic time on quasi-polynomially many units.
The study classifies complex parallelisable nilmanifolds with unobstructed deformations.
problem Characterizing complex parallelisable nilmanifolds with unobstructed deformations.
method Analyzing Lie algebras associated with nilmanifolds and their verbal ideals.
result There are finitely many complex homotopy types of unobstructed complex parallelisable nilmanifolds up to dimension 19, and infinitely many in dimension 20.
We show that the deformation space of complex parallelisable nilmanifolds can be described by polynomial equations but is almost never smooth. This is remarkable since these manifolds have trivial canonical bundle and are holomorphic symplectic in even dimension. We describe the Kuranishi space in detail in several exa…
We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different classes, some of them containing moduli. For each class we determine the amount of …
Bayesian Quadrature speeds up integration by selecting batches of points instead of single points.
problem Efficiently parallelizing Bayesian Quadrature for integration over non-negative integrands.
method Developed methods to select batches of points at each step, based on recent batch Bayesian Optimization.
result Significantly reduces computation time, especially for expensive integrands.
We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a frame algebra with constant coefficients. The consistent truncation then arises …
Auxiliary MCMC and particle Gibbs samplers for parallelisable inference in latent dynamical systemsstat.CO
New methods improve sampling from complex dynamical models.
problem Sampling from high-dimensional, non-linear latent dynamical models is computationally challenging.
method Introduce auxiliary MCMC and Particle Gibbs samplers with improved performance and parallelisation.
result Enhanced samplers maintain performance in high-dimensional latent spaces and support parallelisation.
Discovering causal relationships from data is the ultimate goal of many research areas. Constraint based causal exploration algorithms, such as PC, FCI, RFCI, PC-simple, IDA and Joint-IDA have achieved significant progress and have many applications. A common problem with these methods is the high computational complex…
G-algebroids: a unified framework for exceptional and generalised geometry, and Poisson-Lie dualitymath.DG
Unified framework for exceptional and generalised geometry, and Poisson-Lie duality.
problem Unified framework for exceptional and generalised geometry.
method Introducing G-algebroid, generalising Lie and Courant algebroids.
result Classification of 'exact' algebroids and compatibility with supergravity.
CAVIA improves meta-learning by adapting context parameters at test time.
problem Meta-learning overfits and requires complex parallelisation.
method CAVIA splits model into context and shared parameters, updating only the former.
result CAVIA outperforms MAML across regression, classification, and reinforcement learning.
We classify complex compact parallelizable manifolds which admit flat torsion free holomorphic affine connections. We exhibit complex compact manifolds admitting holomorphic affine connections, but no flat torsion free holomorphic affine connections.
Study of exceptional algebroids in relation to type IIB superstrings.
problem Understanding the structure of exceptional algebroids in type IIB superstring theory.
method Analyzing the local form of IIB-exact exceptional algebroids and deriving possible twists.
result A simple description of Leibniz parallelisable spaces and U-duality.
Efficient spatio-temporal Gaussian process inference method.
problem Scalable Gaussian process inference for multivariate, spatio-temporal data.
method Combines spatio-temporal filtering with natural gradient variational inference, resulting in a scalable non-conjugate GP method.
result Linear scaling with respect to time and logarithmic scaling with respect to time steps.
Parallelized Bayesian quadrature improves sample efficiency and inference.
problem Efficient Bayesian inference and model evidence calculation.
method Batch Bayesian quadrature with kernel recombination for parallel sampling.
result Empirically, outperforms state-of-the-art methods in various datasets.
A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Liftingcs.LG
SOBER framework optimizes Bayesian optimization tasks efficiently.
problem Challenges in parallel Bayesian optimization.
method Probabilistic Lifting with Kernel Quadrature.
result Versatile and flexible batch Bayesian optimization.
For let be a -connected closed manifold. If mod assume further that is -parallelisable. Then there is a homotopy sphere such that admits a Ricci positive metric. This follows from a new description of these manifolds as the boundarie…
Improved text-conditioned regression using LLMs and diffusion-based neural processes.
problem Major error cascades and computational inefficiency in LLMs for short sequences.
method Combining LLM predictive densities with a diffusion-based neural process.
result Better-calibrated predictions and locally consistent trajectories.
We design a randomised parallel version of Adaboost based on previous studies on parallel coordinate descent. The algorithm uses the fact that the logarithm of the exponential loss is a function with coordinate-wise Lipschitz continuous gradient, in order to define the step lengths. We provide the proof of convergence …
Study on geometrically formal metrics on complex manifolds.
problem Existence and properties of geometrically formal metrics on complex manifolds.
method Topological and cohomological obstructions, detailed analysis for specific manifolds, and metric constructions.
result Existence and non-existence conditions for geometrically formal metrics on various complex manifolds.
I will discuss the emergence of lorentzian symmetric spaces as supersymmetric supergravity backgrounds. I will focus on supergravity theories in dimension 11, 10, and 6, and will concentrate on the determination of the so-called maximally supersymmetric backgrounds, for which a classification exists up to local isometr…
The study of quasi-Kähler Chern-flat almost Hermitian manifolds is strictly related to the study of anti-bi-invariant almost complex Lie algebras. In the present paper we show that quasi-Kähler Chern-flat almost Hermitian structures on compact manifolds are in correspondence to complex parallelisable Hermitian structur…
New method merges MCMC samples without distributional assumptions.
problem Efficiently merging MCMC samples from disjoint subsets.
method Diffusion generative modelling for density approximation.
result Outperforms existing methods on high-dimensional problems.
We show that after forming a connected sum with a homotopy sphere, all (2j-1)-connected 2j-parallelisable manifolds in dimension 4j+1, j > 0, can be equipped with Riemannian metrics of 2-positive Ricci curvature. The condition of 2-positive Ricci curvature is defined to mean that the sum of the two smallest eigenvalues…
We propose a practical and scalable Gaussian process model for large-scale nonlinear probabilistic regression. Our mixture-of-experts model is conceptually simple and hierarchically recombines computations for an overall approximation of a full Gaussian process. Closed-form and distributed computations allow for effici…
The paper constructs infinitely many stably diffeomorphic but non-homotopy equivalent manifolds.
problem Realising modified surgery obstructions for stably diffeomorphic manifolds.
method Proving a realisation result for subsets of Kreck's modified surgery monoid.
result Infinitely many stably diffeomorphic but non-homotopy equivalent manifolds.
For large matrix factorisation problems, we develop a distributed Markov Chain Monte Carlo (MCMC) method based on stochastic gradient Langevin dynamics (SGLD) that we call Parallel SGLD (PSGLD). PSGLD has very favourable scaling properties with increasing data size and is comparable in terms of computational requiremen…
Study of quantum Riemannian geometries over binary field, finding many non-flat examples.
problem Classifying parallelizable quantum Riemannian geometries over .
method Classification of geometries up to dimension 3, characterizing quantum Laplacian eigenvectors.
result Found many non-flat quantum Riemannian geometries over .
To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP approximations, the rBCM is conceptually simple and does not rely on inducing or …
The paper constructs multiple manifolds with similar properties.
problem Finding multiple distinct manifolds with stable diffeomorphism.
method Constructing pairwise homotopically inequivalent manifolds.
result Each constructed manifold is stably diffeomorphic to one another.
In dimensions congruent to 1 modulo 4, we prove that the cotangent bundle of an exotic sphere which does not bound a parallelisable manifold is not symplectomorphic to the cotangent bundle of the standard sphere. More precisely, we prove that such an exotic sphere cannot embed as a Lagrangian in the cotangent bundle of…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…
Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they do not represent topological 3-manifolds. In this paper we show how …
DRO-NPE improves neural posterior estimation by reducing overconfidence and overfitting.
problem Overconfident and unreliable posteriors in simulation-based inference with limited simulation budgets.
method Distributionally robust approach using Wasserstein ambiguity set and KL-based metrics.
result Consistently improves coverage and calibration across benchmark tasks.
This research reinterprets Lie and Cartan's work on geometric structures using Lie groupoids.
problem Revisiting Lie and Cartan's geometric structures from a modern perspective.
method Encoding geometric structures into principal -bundles with a transversally parallelisable foliation.
result Developed a notion of flatness for Lie groupoids encompassing various geometric structures.
In this paper, we discuss software design issues related to the development of parallel computational intelligence algorithms on multi-core CPUs, using the new Java 8 functional programming features. In particular, we focus on probabilistic graphical models (PGMs) and present the parallelisation of a collection of algo…
The paper parallelizes MCMC using random forests for big data Bayesian computation.
problem Efficiently computing Bayesian models in large datasets.
method Embed random forests into divide-and-conquer MCMC framework, using scaled subposteriors as proposal distributions.
result The approach works well across various model types, including misspecified models.
With the wealth of high-throughput sequencing data generated by recent large-scale consortia, predictive gene expression modelling has become an important tool for integrative analysis of transcriptomic and epigenetic data. However, sequencing data-sets are characteristically large, and previously modelling frameworks …
New algorithm improves Bayesian inference for complex models.
problem Poor performance of existing Bayesian approaches for simulators.
method Posterior bootstrap and maximum mean discrepancy estimators.
result Strong robustness and parallelizability of the new algorithm.
Study of Monge-Ampère volumes on hermitian manifolds, focusing on plurisigned metrics.
problem Behavior of Monge-Ampère volumes under hermitian variations.
method Analysis of hermitian forms and cohomology, studying boundedness and positivity.
result Existence and non-existence of plurisigned hermitian metrics on specific manifolds.
Study of exceptional algebroids in type IIA string theory.
problem Understanding the structure of algebroids in type IIA string theory.
method Warped compactifications and analysis of local moduli space.
result Local classification of algebroids reveals new scalar deformations and twists.
Parallel Gaussian process surrogate for noisy likelihood evaluations in Bayesian inference.
problem Bayesian inference with limited noisy log-likelihood evaluations from complex models.
method Hierarchical Gaussian process surrogate model for log-likelihood, batch-sequential design strategies.
result Robust, highly parallelizable, and sample-efficient method.
SurvLIMEpy is a Python package for computing feature importance in survival analysis.
problem Computing feature importance in survival analysis models.
method Parallelized implementation of the SurvLIME algorithm for various survival models.
result SurvLIMEpy accurately captures feature importance in survival analysis models.
SIMD operations boost Bayesian computations up to 6x faster.
problem Expensive Bayesian computations are computationally intensive and parallelizable.
method Demonstrated the utility of SIMD operations for Bayesian applications using standard libraries.
result Up to 6x improvement in floating point arithmetic performance.
A new method speeds up distributed learning while maintaining robustness.
problem Efficient and robust distributed machine learning in high dimensions.
method Multi-Bulyan for gradient aggregation in distributed learning.
result Multi-Bulyan achieves Byzantine resilience and near-averaging speed with linear complexity in .
A new algorithm speeds up solving complex spin system problems.
problem Finding the lowest energy state in Ising models, which is hard and important.
method Mean-field Annealing from a Random State (MARS) algorithm, combining SA and MFA.
result MARS solves large Ising spin systems and maximum cut problems efficiently.
Quasi-Monte Carlo speeds up option Greeks calculation on GPUs.
problem Efficiently calculating option Greeks for risk management.
method Quasi-Monte Carlo (QMC) combined with GPU acceleration for pathwise sensitivity calculation.
result Increased computational speed and efficiency in estimating option Greeks.