Proposes a new model for clustering multiplex networks with compositional data.
problem Clustering multiplex networks with multiple types of relations and compositional data.
method Multiplex Dirichlet stochastic block model for compositional networks.
result Validated through simulation and applied to international export data.
New kernels from neural networks show better performance than traditional methods.
problem Improving neural network performance on small datasets.
method Developed algebraic operations to create compositional kernels from neural network architectures.
result Compositional kernels achieve higher accuracy than neural tangent kernels and neural networks on small datasets.
Tangle blocks simplify knot theory by breaking down complex knots into manageable pieces.
problem Complex knot theory calculations are simplified by breaking down knots into tangle blocks.
method The approach involves expressing link polynomials as multilinear combinations of tangle blocks.
result Tangle blocks provide a powerful tool for understanding and calculating knot invariants.
The paper trains a neural network to compose music in a nonlinear, human-like manner.
problem Creating music in a non-chronological, revisiting manner.
method Trained a convolutional neural network with blocked Gibbs sampling to approximate human composition.
result Blocked Gibbs sampling improves sample quality and yields better results than ancestral sampling.
This study ranks feature-block importance in multiblock neural networks.
problem Understanding feature contributions in multiblock neural networks.
method Three methods: composite, knock-in, and knock-out strategies.
result Each strategy has its merits for specific application scenarios.
New algorithms solve nonconvex federated learning problems efficiently.
problem Nonconvex federated composite optimization in federated learning.
method FedDR and asyncFedDR algorithms combining Douglas-Rachford splitting, randomized block-coordinate strategies, and asynchronous implementation.
result Match communication complexity lower bound up to a constant factor.
Transformers learn to solve modular arithmetic tasks by in-context learning and skill composition.
problem Understanding how large language models generalize to unseen tasks in modular arithmetic.
method Pre-training on a set of modular arithmetic tasks and evaluating out-of-distribution performance.
result Transformers require two transformer blocks for out-of-distribution generalization, and deeper models exhibit transient out-of-distribution performance.
In this paper we develop a randomized block-coordinate descent method for minimizing the sum of a smooth and a simple nonsmooth block-separable convex function and prove that it obtains an ε-accurate solution with probability at least 1−ρ in at most O(εnlogρ1) iterations, where n is the numbe…
BL learns interpretable optimization structures from data.
problem Learning interpretable optimization structures from data.
method BL parameterizes a compositional utility function from intrinsically interpretable modular blocks.
result BL supports architectures from single to hierarchical compositions, modeling hierarchical optimization structures.
New framework models non-exchangeable networks with latent orders and graphons.
problem Modeling non-exchangeable network data with complex dependencies.
method Latent orders and graphon-based approach for adjacency matrix probabilities.
result Consistent estimation and clustering of latent network structure.
Two accelerated methods for linearly constrained convex programming are proposed, improving convergence rates.
problem Efficiently solving structured linearly constrained convex programming problems.
method Two accelerated methods: LALM and LADMM, for composite convex objectives.
result Accelerated methods achieve faster convergence rates compared to non-accelerated methods.
HCN discovers binary features in images without supervision.
problem Discovering and disentangling binary features in unlabeled images.
method Hierarchical compositional network with max-product message passing.
result HCN achieves classification similar to CNN but with binary features.
Proposes a new method to solve large-scale CSC minimization problems.
problem Composite self-concordant minimization problems in machine learning.
method Randomized block proximal damped Newton (RBPDN) method.
result RBPDN method significantly reduces computational cost per iteration.
Improved atomistic model predicts molecular properties using weighted skip-connections.
problem Understanding the relative importance of interactions in molecular property prediction.
method Extended SchNet architecture with weighted skip-connections to analyze molecule properties.
result Relative weighting of interaction blocks depends on molecule's chemical composition and configurational degrees of freedom.
Extends knot polynomial construction for braids with m strands.
problem Understanding structure of mysterious knot polynomials.
method Generalizes knot polynomials for arbitrary m-strand braids using R-matrices and mixing matrices.
result Explicit expressions for knot polynomials in sectors R^⊗3 → Q.
Edgeworth Accountant calculates privacy loss under differential privacy compositions efficiently.
problem Efficiently computing overall privacy loss under composition of private algorithms.
method Analytical approach using f-differential privacy framework and Edgeworth expansion. result Non-asymptotic (ε,δ)-differential privacy bounds with reduced computational cost. Dynamic batching enables efficient training of graph neural networks.
problem Efficient training and inference of graph neural networks with dynamic computation graphs.
method Dynamic batching technique and high-level library for compositional blocks.
result Concise and batch-wise parallel implementations of dynamic graph models.
Cosmos models scenes using neural encodings and symbolic attributes for compositional generalization.
problem Modeling scenes with high performance on unseen input scenes composed of known visual elements.
method Neurosymbolic grounding with neurosymbolic scene encodings and attention mechanisms.
result Establishes a new state-of-the-art for compositional generalization in world modeling.
Adversarial framework enforces fairness constraints on graph embeddings.
problem Fairness constraints in graph embeddings, especially age and gender.
method Adversarial framework for compositional fairness constraints.
result Framework allows for flexible combinations of fairness constraints.
New model identifies microbial subcommunities robustly, accounting for cross-sample heterogeneity.
problem Inference in LDA is sensitive to the number of subcommunities and often creates artificial ones.
method Incorporates logistic-tree normal (LTN) model into LDA to account for cross-sample heterogeneity.
result Restores robustness of inference and identifies meaningful subcommunities.
A new model clusters network nodes based on relative edge weights.
problem Clustering networks ignores node capacities, leading to biased results.
method Proposes a Dirichlet stochastic block model for composition-weighted networks.
result Validated on simulated and real-world networks, showing improved clustering accuracy.
Researchers develop methods to construct Lagrangian cobordisms between Legendrian knots.
problem Understanding the relationship between Legendrian knots through Lagrangian cobordisms.
method Combinatorial and geometric methods, including Heegaard Floer Homology and contact surgery.
result Construction of nondecomposable Lagrangian cobordisms between Legendrian knots.
A framework for designing and evaluating new GCN variants.
problem Designing and evaluating new graph convolutional network (GCN) variants.
method Propose a framework to compose networks using building blocks of GCN.
result Several newly composed variants are useful alternatives and competitive with original GCNs.
SlicStan improves Stan's usability and efficiency.
problem Stan's block syntax sacrifices usability for scalability.
method Formalized Stan, introduced SlicStan with compositional syntax and flexible functions.
result SlicStan facilitates better code reuse and abstraction.
CoLA automates efficient numerical linear algebra for complex matrix structures.
problem Efficiently solving large-scale linear algebra problems with complex matrix structures.
method Combining linear operator abstraction with compositional dispatch rules.
result Automatic and efficient numerical algorithms for various linear algebra operations.
Inertial methods solve non-convex non-smooth optimization problems efficiently.
problem Non-convex non-smooth optimization problems.
method Inertial block proximal methods for solving these problems.
result The methods converge globally under certain conditions and perform well in applications like NMF.
Unified tensor model disentangles object appearance factors.
problem Representing hierarchical intrinsic and extrinsic causal factors of object appearance.
method Compositional hierarchical tensor factorization.
result Interpretable object representation robust to occlusion and reduced training data requirements.
Proposes a new framework for learning image augmentations to improve classification performance.
problem Improving classification performance with a given class of predictors.
method Transformed Risk Minimization (TRM) framework that optimizes both predictive models and data transformations.
result Performance of TRM with SCALE algorithm compares favorably to prior methods on CIFAR10/100.
Symbol calculus extended for foliations' transverse geometry.
problem Understanding index theory of transversely elliptic operators on foliations.
method Constructing Getzler rescaling calculus and Block-Fox calculus of asymptotic operators.
result Composition of AΨDOs is again an AΨDO, with a leading symbol formula. Proposes a method to learn dynamic models for systems with variable number of objects.
problem Efficiently modeling systems with a variable number of objects.
method Uses graph neural networks and block-wise linear transition matrices to learn compositional Koopman operators.
result The method adapts to new environments and produces better control signals.
This paper precisely estimates transformer derivatives for explicit learning guarantees.
problem Computing fully-explicit generalization bounds for transformers with precise higher-order derivative estimates.
method Analyzes and estimates all higher-order derivatives of transformers with multiple attention heads and layer normalization.
result Obtains explicit pathwise generalization bounds for transformers learning from non-i.i.d. samples.
A deep probabilistic model analyzes DNA-encoded library data for efficient screening.
problem Complex data from DNA-encoded library experiments mask underlying signals.
method Compositional deep probabilistic model of DEL data, modeling latent reactions between synthons.
result DEL-Compose model demonstrates strong performance and valuable insights.
Seq2Tens uses tensors to efficiently represent sequences, improving performance on time series and video tasks.
problem Challenges in analyzing sequential data due to complex dependencies and non-commutativity.
method Uses tensor algebra to capture dependencies and low-rank tensor projections to manage computational complexity.
result State-of-the-art performance on multivariate time series classification and video generation benchmarks.
This paper tackles exact recovery of clusters in a stochastic Ising model on a SBM graph.
problem Recovering clusters in a stochastic Ising model on a SBM graph.
method Proposes a Stochastic Ising Block Model (SIBM) and establishes a sharp threshold for exact recovery.
result Sharp threshold m∗ for exact recovery of clusters in SIBM, with O(n) time complexity for m≥m∗. Invertible neural networks with masked convolutions improve classification and generative models.
problem Building robust invertible neural networks for better model interpretability and generative tasks.
method Combining masked convolutions and iterative inversion methods to create invertible architectures.
result Invertible neural networks achieve competitive performance in classification and generative tasks.
Sharp stability threshold found for deep residual architectures.
problem Ensuring stable training and inference in deep residual networks.
method Sublinear-growth principle and optimal-control analysis.
result Stable training condition: input-magnitude exponent q ≤ 1.
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.
Uses art composition attributes to guide CycleGAN image translation.
problem Improving image-to-image translation quality.
method Trained ACAN on art composition attributes to influence CycleGAN.
result CycleGAN translations improved with ACAN constraints.
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.
This text explores strategies for learning discrete latent structures in neural networks.
problem Learning discrete latent structures in neural networks is challenging.
method Continuous relaxation, surrogate gradients, and probabilistic estimation.
result Many latent structure learning strategies use the same fundamental building blocks but apply them differently.
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.