Real NVP models improve image modeling with exact computations.
problem Unsupervised learning of probabilistic models.
method Real-valued non-volume preserving transformations.
result Exact log-likelihood computation, sampling, inference, interpretable latent space.
Researchers found unique exact Lagrangian fillings for a specific type of knot.
problem Tackling the uniqueness of exact Lagrangian fillings for Legendrian (2,n) torus knots. method Computed augmentations induced by exact Lagrangian fillings to distinguish them.
result Identified that these exact Lagrangian fillings are pairwise non-isotopic.
Exact Bayesian inference for discrete models using probability generating functions.
problem Discrete statistical models with infinite support and continuous priors.
method Probabilistic programming language with automatic differentiation and probability generating functions.
result Genfer tool provides exact solutions for a wide range of inference problems.
Algorithm finds smooth primitives for exact forms.
problem Computing smooth primitives for exact forms on manifolds.
method Diagram chasing in Čech-de Rham complex, explicit formulas.
result Explicit formulas for primitive families.
Study exact polynomials to compute Mahler measure and relate it to volume function.
problem Compute Mahler measure of exact polynomials.
method Define volume function on vanishing set, prove local extrema on 2D torus, derive Mahler measure formula.
result Prove Mahler measure of irreducible exact polynomials is greater than volume function amplitude.
Develops a new algorithm for computing exact Wasserstein distance efficiently.
problem High computational complexity of exact Wasserstein distance computation.
method Inexact Proximal Point Method (IPOT) with approximate projections to the probability simplex.
result Algorithm converges to exact Wasserstein distance with theoretical guarantees and robust regularization parameter selection.
Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.
Exact GPs trained on over a million points in under 2 hours.
problem Computational limitations of exact Gaussian processes for large datasets.
method Multi-GPU parallelization and linear conjugate gradients for kernel matrix multiplication.
result Exact GPs can be trained on over a million points in less than 2 hours.
Involutive bordered Floer homology computes 3-manifold invariants.
problem Computing involutive Heegaard Floer homology for 3-manifolds.
method Bordering technique to extend involutive HF-hat, algorithmic approach, mapping class group action computation.
result Involutive HF-hat satisfies a surgery exact triangle, computed for many knots.
Researchers compute exact decision boundaries of neural networks.
problem Finding exact decision boundaries of trained neural networks is intractable.
method Developed mathematical tools to investigate decision boundaries of trained deep models.
result Some simplifying assumptions about decision boundaries are unreliable.
Paper shows approximate Dirichlet domain works as well as exact one for tiling hyperbolic balls.
problem Empirical success of SnapPea's length spectrum algorithm despite using approximate data.
method Showed under certain conditions, approximate Dirichlet domain can perform equivalently to exact one.
result Empirical success of SnapPea's length spectrum algorithm explained.
Paper computes a specific term of knot homology for 3-braids.
problem Computing a specific term in knot homology for 3-braids.
method Used skein exact sequence and Xu's classification.
result Computed the second-to-top term of HFK for closed 3-braids.
Researchers create an exact entangling gate using braiding and measurement of Fibonacci anyons.
problem No known leakage-free entangling gate using braiding of Fibonacci anyons.
method Supplement braiding with measurement operations to produce an exact controlled rotation gate.
result Exact entangling gate on two qubits created using Fibonacci anyons and measurement.
Study corrects previous computation of Lagrangian topology in Calabi-Yau threefold.
problem Correcting a previous computation of the topology of a real Lagrangian in Schoen's Calabi-Yau threefold.
method Used two methods to compute mod 2 cohomology: Mayer-Vietoris calculation and an exact sequence.
result Agreement between the two methods confirms the topology of the real Lagrangian.
New algorithm finds nearest neighbors with less computation.
problem Finding nearest neighbors in high-dimensional data efficiently.
method Bandit-based Monte Carlo optimization for nearest neighbors.
result Algorithm identifies exact nearest neighbors with high probability.
Federated learning supports exact support recovery with minimal communication.
problem Learning the exact support of sparse linear regression in federated learning.
method One-shot communication algorithm for exact support recovery without optimization.
result Polynomial sample complexity and logarithmic number of clients required.
Exact Gaussian Processes for massive datasets using non-stationary sparsity-discovering kernels.
problem High computational and storage costs for exact GPs in large datasets.
method Develop non-stationary kernels that allow the GP to discover sparse structure naturally.
result Exact Gaussian Processes scalable to over 5 million data points.
This paper explores the computational hardness of generating latent vectors for generative models.
problem Computational hardness of generating latent vectors for generative models.
method Established lower bounds for exact and approximate model inversion under strong exponential time hypothesis (SETH) and exponential time hypothesis (ETH).
result Lower bounds for computational complexity of exact and approximate model inversion.
Efficient MCMC inference in differentiable models for asymptotic exactness.
problem Efficient inference in differentiable generative models.
method Constrained Hamiltonian Monte Carlo on the manifold of inputs consistent with observed outputs.
result Asymptotically exact inference in various models.
Study on stable torsion length in groups, showing it vanishes in crystallographic groups and providing algorithms for computation.
problem Understanding the stable torsion length in groups, especially in crystallographic and free products of groups.
method Developed linear programming and exact algorithms to compute stable torsion length in free products of groups and finite groups.
result Showed that stable torsion length vanishes in crystallographic groups and provided exact computations for nontrivial examples.
W. Thurston suggested a method for computing hyperbolic volume of hyperbolic 3-manifolds, based on a triangulation of the manifold. The method was implemented by J. Weeks in the program SnapPea, which produces a decimal approximation as a result. For hyperbolic 2-bridge links, we give formulae that allow one to find th…
In this paper, using similar idea as in Fukaya-Oh's work ([9]), we devise a method to compute the Fukaya category of certain exact symplectic manifolds by reducing it to the corresponding Morse category of non-Hausdorff manifold as perturbation of the Lagrangian skeleton of the exact symplectic manifold.
We show a connection between a surgery exact sequence in knot Floer homology and the sequence derived in [18]. As a consequence of this relationship we see that the exact sequence in [18] also works with coherent orientations and admits refinements with respect to spinc-structures. As an application of this discussion,…
By means of a slight modification of the notion of GM-complexity, the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C^{28}, due to Lins, is used to obtain upper bounds for the comp…
SPPL simplifies probabilistic programming for exact inference.
problem Efficient exact inference in probabilistic models.
method SPPL translates probabilistic programs into sum-product expressions, leveraging new techniques for scalability.
result SPPL achieves up to 3500x speedups in exact inference.
PixelCNN models can achieve state-of-the-art results on CIFAR-10 with exact likelihood computation.
problem Dequantization gap in modeling discrete data like images.
method Introducing subset flows to allow exact computation of likelihoods for discrete data.
result PixelCNN models trained with exact likelihood computation achieve state-of-the-art results on CIFAR-10.
Paper explores limits of exact inference in structured prediction models.
problem Exact recovery of true labels in graph-based structured prediction models.
method Analyzes necessary and sufficient conditions for exact recovery using maximum likelihood estimation.
result Derives tight conditions for exact recovery, revealing a gap with computationally tractable methods.
GPU speeds up derivatives sensitivity computation for Heston model options.
problem Efficient computation of option Greeks under the Heston model.
method Implemented exact simulation and novel Milstein discretisation methods on GPU.
result GPU speeds up Greeks computation up to 200x compared to CPU methods.
Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average…
The article provides obstructions for exact submanifolds in symplectic applications.
problem Existence of exact submanifolds with specific homology classes.
method Study of formal deformations of the de Rham complex to compute obstructions.
result Symplectic manifolds like Kähler and Kodaira-Thurston admit no non-separating exact hypersurfaces.
Exact minibatch MH method improves scalability for large datasets.
problem Inexactness in minibatch MH methods causes inference errors.
method TunaMH proposes an exact minibatch MH method with a tunable batch size.
result TunaMH is asymptotically optimal in terms of batch size.
A new parallel BO method with exact gradients for multi-objective optimization.
problem Efficiently optimizing multiple objectives in a sample-efficient manner.
method Derive q-Expected Hypervolume Improvement (qEHVI) for parallel, constrained evaluation.
result qEHVI is computationally tractable and outperforms state-of-the-art methods.
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c >= rank(A) columns depend on the right singular vector matrix of A. For a Monte-…
Proves exact triangle linking knot instanton Floer homology to surgeries.
problem Relating knot instanton Floer homology to surgeries.
method Proves an exact triangle using integer coefficients.
result Poincaré Homology Sphere is not an instanton L-space with integer coefficients.
Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.
problem Computational challenges in high-dimensional ℓ1 penalized quantile regression. method Pathwise coordinate descent algorithm to solve exact coordinatewise minimum of the nonsmooth loss function.
result Algorithm runs faster than existing alternatives and maintains estimation accuracy.
Extends cobordism groups of immersions to projections with new results.
problem Understanding cobordism groups of projected immersions.
method Classifying space construction by Szűcs and Terpai, Salomonsen's exact sequence.
result Obtains results on cobordism groups in small and large codimensional cases.
Exact solution for sparse-reward MDPs with minimal state space dependence.
problem Finding optimal policies for MDPs with sparse rewards and large state spaces.
method Proposes an algorithm with time complexity O(∣R∣3imes∣A∣2) and memory complexity O(∣R∣imes∣A∣) for exact computation. result Exact policy computation without state space dependency for sparse-reward MDPs.
This work extends knot homology theory to links, proving exact triangles and categorifying link signatures.
problem Extending knot homology theory to links and proving exact triangles.
method Equivariant singular instanton Floer theory, circle-equivariant Morse-Floer theory, cobordism constructions.
result Established unoriented skein exact triangles and categorified link signatures.
This paper computes exact posterior distributions of mixture weights in hierarchical Bayesian models.
problem Uncertainty in class membership or data-generating processes in heterogeneous data.
method Exact marginalization of mixture weights using dynamic programming and FFT for two components, and joint dynamic program for K >= 3 components.
result Exact posterior distributions of mixture weights are finite mixtures of Beta distributions, providing credible intervals and per-observation local false-discovery rates.
TERA method speeds up derivative Gaussian processes in high dimensions.
problem High-dimensional function evaluations and gradient computations are computationally expensive.
method TERA uses exact gradient reduction to decouple n and d from the computational cost. result TERA achieves state-of-the-art predictive accuracy with orders of magnitude faster computation.
Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalizat…
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an m-by-n nonnegative matrix X and a factorization rank r, find, if possible, an m-by-r nonnegative matrix W and an r-by-n nonnegative matrix H such that X=WH. In this paper, we propose two heuristics for exac…
New kernel enables exact GP analysis of massive datasets.
problem Limited scalability and flexibility of traditional GPs for large data sets.
method Explicitly derived nonstationary kernel for large-scale GP analysis.
result Novel kernel outperforms existing methods in synthetic and real-world applications.
Exact causal network discovery is polynomial for sparse networks.
problem Finding the optimal causal Bayesian network from data is computationally hard.
method Pruning the search space using network properties, combined with dynamic programming and shortest-path searches.
result Exact discovery is polynomial for sparse causal Bayesian networks.
We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that saddle cobordisms can be computed in terms of maps in a decorated skein exact triangle that extends the oriented skein exact triangle in knot…
Researchers found a new exact solution for pricing Aunt Michaela options using modified Black-Scholes equation.
problem Pricing Aunt Michaela options with a specific maturity condition.
method Computed a new exact series solution of a modified Black-Scholes equation using Maple.
result The modified Black-Scholes equation with Aunt Michaela option is exactly solvable using associated Laguerre polynomials or Whittaker M functions.
TDS provides exact samples for conditional distributions in diffusion models.
problem Lack of exact sampling methods for diffusion models.
method Sequential Monte Carlo (SMC) algorithm with twisting technique.
result TDS offers more accurate approximations with fewer particles compared to heuristics.
Graph-based active learning improves with a new algorithm that balances exploration and exploitation.
problem Graph-based active learning algorithms based on expected error minimization (EEM) often use approximations due to computational hardness, leading to suboptimal performance.
method Proposes TSA (Two-Step Approximation) algorithm that efficiently balances exploration and exploitation with similar computational complexity.
result Empirically shows that balancing exploration and exploitation improves performance in both toy and real-world datasets.