Algorithm samples composite logconcave densities efficiently.
problem Sampling from composite logconcave densities efficiently.
method Uses a restricted Gaussian oracle and gradient queries.
result Achieves strong total variation distance guarantees.
New algorithms sample structured logconcave families with improved efficiency.
problem Sampling structured logconcave families to high accuracy.
method Reduction framework inspired by proximal point methods, combined with restricted Gaussian oracles.
result Improved bounds for sampling structured distributions, matching or surpassing state-of-the-art results.
Improves sampling, rounding, and integration of logconcave functions.
problem Sampling, rounding, and integration of logconcave functions.
method Algorithmic diffusion approach.
result First complexity improvements in nearly two decades for general logconcave functions.
Unified complexity bound for sampling logconcave distributions
problem Sampling arbitrary logconcave distributions
method In-and-Out algorithm with exponential lifting
result Nearly tight convergence rate
Faster algorithm for sampling logconcave densities in high dimensions.
problem Cubic barrier in sampling logconcave densities from a cold start.
method Two key ingredients: weaker distance sampling and refined log-Sobolev inequality.
result First sub-cubic sampling algorithms for isotropic position.
New method improves sampling from logconcave distributions truncated on polytopes.
problem Sampling from logconcave distributions with polytope constraints.
method Regularized Dikin walks, using Lewis weights.
result Improved mixing time guarantees for various distributions and polytopes.
Improved Metropolized HMC runtime for logconcave distributions.
problem Improving the runtime of Metropolized HMC for logconcave sampling.
method Gradient norm concentration and new mixing time analysis techniques.
result Metropolized HMC mixes in O~(κd) iterations, improving runtime by a factor of (κ/d)1/2. We study Hamiltonian Monte Carlo (HMC) for sampling from a strongly logconcave density proportional to e−f where f:Rd→R is μ-strongly convex and L-smooth (the condition number is κ=L/μ). We show that the relaxation time (inverse of the spectral gap) of ideal HMC is O(κ), improving…
Polynomial-time algorithm learns high-dimensional halfspaces without labels.
problem Learning high-dimensional halfspaces with margins in polynomial time.
method Contrastive moments and polynomial-time algorithm.
result Establishes the unique and efficient identifiability of the hidden halfspace.
Sampling logconcave functions arising in statistics and machine learning has been a subject of intensive study. Recent developments include analyses for Langevin dynamics and Hamiltonian Monte Carlo (HMC). While both approaches have dimension-independent bounds for the underlying continuous processes under s…
New schemes improve error estimates for sampling from non-log-concave distributions.
problem Improving sampling from non-log-concave distributions with super-linear drift growth.
method Developed tamed Euler and randomized Euler schemes with error estimates.
result Near-optimal error bounds for sampling and optimization problems.
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic analysis results are established in the L1-Wasserstein distance for the behavio…
In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order 2. Using this interpretation and techniques borrowed from convex optimization, we give a …
New Langevin algorithm works well even for rough distributions.
problem Sampling from non-smooth distributions.
method Simple Langevin algorithm without smoothness assumptions.
result Algorithm performs well even with discontinuous gradients.
MALA mixes efficiently under smoothness and isoperimetry assumptions.
problem Sampling from target densities efficiently.
method Metropolis-Adjusted Langevin algorithm (MALA) with smoothness and isoperimetry assumptions.
result MALA mixes in $O\left(\frac{(LΥ)^{\frac12}}{ψ_μ^2} \log\left(\frac{1}ε
ight)
ight)$ iterations.
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Study on deep neural networks using branching processes and Mehler's formula.
problem Understanding the mathematical role of activation functions in compositional neural networks.
method Connection between compositional kernels and branching processes via Mehler's formula; new random features algorithm.
result Explicit formulas for eigenvalues of compositional kernels quantify complexity.
We establish conditions for compositional generalization in machine learning.
problem Achieving compositional generalization in machine learning models.
method We reformulate compositionality as a property of the data-generating process and derive mild conditions on the training distribution and model architecture.
result Our theoretical framework enables compositional generalization under mild conditions.
This paper proves hyperbolicity of virtual knot compositions.
problem Proving hyperbolicity of virtual knot compositions.
method Exploring the composition of hyperbolic virtual knots.
result Strong lower bounds on the volume of compositions.
Develops methods for causal inference in compositional data using instrumental variables.
problem Interpreting summary statistics like diversity indices as causal effects in compositional data.
method Statistical data transformations and regression techniques tailored for compositional data.
result Advantages and limitations of the proposed methods demonstrated on synthetic and real microbiome data.
In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on composite fibred manifolds. In particular, we get the horizontal splitting of the vertic…
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
Model predicts composite structures assembly quality with input uncertainty.
problem Accurate prediction of dimensional deviations and residual stress in composite structures assembly.
method Neural Network Gaussian Process considering input uncertainty.
result NNGPIU model outperforms other methods for nonsmooth, nonlinear responses.
New algorithm reduces complexity for optimizing complex machine learning tasks.
problem Optimizing complex machine learning objectives like reinforcement learning and portfolio management.
method Developed SARAH-Compositional algorithm using Stochastic Recursive Gradient Descent.
result Achieved optimal IFO complexity bounds for stochastic compositional optimization.
This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
problem Statistical issues with standard financial ratios at industry level.
method Compositional data analysis techniques for financial ratios.
result Improved analysis of financial ratios using compositional data methods.
Study challenges neural models in compositional learning tasks.
problem Challenges in neural models for compositional and relational learning.
method Introduced ConceptWorld environment for generating images from compositional concepts, tested various neural architectures.
result Neural models struggle with longer compositional chains and substitutivity tests.
SCL discovers compositional structures in analogical reasoning tasks.
problem Discovering compositional structures in analogical reasoning tasks like Raven's Progressive Matrices.
method Proposes Scattering Compositional Learner (SCL) that composes neural networks in sequence.
result Achieves state-of-the-art performance on RPM datasets with significant improvements.
Composite neural network improves PM2.5 prediction.
problem Improving PM2.5 prediction accuracy.
method Composite neural network framework with pre-trained models.
result Composite neural network outperforms individual models and new components added.
New filters match advanced composition for adaptive privacy, with practical constants.
problem Limitations of existing adaptive composition methods.
method Constructed new filters and odometers that match advanced composition rates, including constants.
result Achieved fully adaptive privacy with practical filters and odometers.
Paper develops momentum schemes with variance reduction for non-convex composition optimization.
problem Lack of convergence guarantee and efficient momentum design in existing algorithms.
method Develops various momentum schemes with SPIDER-based variance reduction.
result Achieves near-optimal sample complexity and linear convergence rate.
Extends knockoff filter for composite null hypotheses in variable selection.
problem Handling composite null hypotheses in variable selection.
method Developed two methods for composite inference with knockoffs: S-OLS and FRPP.
result Proposed heuristic variants of S-OLS outperforming BH procedure for composite nulls.
Model estimates foreign exchange reserve compositions of undisclosed central banks.
problem Limited information on central bank reserve compositions hinders analysis.
method Hidden Markov Model relating portfolio valuation to exchange rates.
result China's reserve composition likely matches global average, while Singapore holds fewer US dollars.
In this paper we study n-composition series of affine manifolds. One composition series are classified using gerbe theory. It is natural to think that n-composition series must be classified using n-gerbe theory. In the last section of this, we propose a notion of abelian n-gerbe theory
Study on when RLVR can learn compositional problems.
problem Understanding when RLVR can learn compositional problems.
method Theoretical analysis of task-advantage ratio to characterize learnability.
result Identified conditions for learnability of compositional problems.
This work proves composite neural networks outperform their components under certain conditions.
problem Understanding the performance of composite neural networks.
method Theoretical investigation of a composite neural network combining pre-trained models.
result A composite neural network, with high probability, performs better than any of its pre-trained components.
Tree-SMU enables strong compositional generalization in neural networks.
problem Zero-shot generalization to novel compositions of concepts.
method Tree Stack Memory Units (Tree-SMU) with Stack Memory Units (SMU).
result Tree-SMU achieves strong empirical results on mathematical reasoning benchmarks.
A new geometry-preserving method for interpreting compositional data.
problem Statistical challenges in high-dimensional compositional data.
method Geometry-preserving framework for dimension reduction of compositional data.
result Identification of a central compositional subspace for compositional predictors.
RICH models scenes as hierarchical tree to learn and generate complex compositions.
problem Learning compositional structures between parts and objects in natural scenes.
method RICH uses a latent scene graph to organize entities into a tree structure and employs a top-down inference approach.
result RICH learns and generates complex scene hierarchies from unlabeled data.
Using quilted Floer cohomology and relative quilt invariants, we define a composition functor for categories of Lagrangian correspondences in monotone and exact symplectic Floer theory. We show that this functor agrees with geometric composition in the case that the composition is smooth and embedded. As a consequence …
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
New samplers improve compositional generation with diffusion models.
problem Improving compositional generation with diffusion models.
method Score-based interpretation, energy-based parameterization, Metropolis-corrected samplers.
result New samplers enable successful compositional generation across various tasks.
NeSS combines neural and symbolic approaches for better compositional generalization.
problem Lack of compositional generalization in deep learning models.
method NeSS uses a neural network to generate traces, executed by a symbolic stack machine with sequence manipulation.
result Achieves 100% generalization performance across multiple domains.
The paper studies tunnel and bridge numbers of composite genus 2 spatial graphs.
problem Understanding the tunnel and bridge numbers of composite genus 2 spatial graphs.
method Analyzes connected sum and trivalent vertex sum operations on genus 2 spatial graphs, proving bounds for tunnel and bridge numbers.
result Sharp bounds for the tunnel number of composite genus 2 spatial graphs, including lower bounds for bridge numbers.
I consider how to influence CycleGAN, image-to-image translation, by using additional constraints from a neural network trained on art composition attributes. I show how I trained the the Art Composition Attributes Network (ACAN) by incorporating domain knowledge based on the rules of art evaluation and the result of a…
Paper analyzes stability and generalization of SCO algorithms.
problem Understanding how SCO algorithms perform on unseen data.
method Algorithmic stability analysis in statistical learning theory.
result Derives dimension-independent excess risk bounds for SCGD and SCSC.
New sparse GP model learns compositional kernels efficiently.
problem Learning accurate Gaussian Process models with complex kernel structures.
method MultiSVGP model with Horseshoe prior for kernel selection.
result Our model provides better fit and faster computation for large-scale data.
C-ADAM is a new adaptive solver for complex nested problems.
problem Solving compositional problems involving nested expected values.
method Adaptive solver for non-linear functional nesting of expected values.
result C-ADAM converges to a stationary point in O(δ−2.25).