Pure combinatorial models for BPL_n and Gauss map of a combinatorial manifold are described.
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48 results for “combinatorial model”
Combining models in appropriate ways to achieve high performance is commonly seen in machine learning fields today. Although a large amount of combinatorial models have been created, little attention is drawn to the commons in different models and their connections. A general modelling technique is thus worth studying …
This paper applies combinatorial testing to machine learning for robust model performance.
problem Identifying robust machine learning models using test and training sets.
method Adapting combinatorial interaction testing for machine learning, focusing on simple features.
result Combinatorial coverage can enhance model performance and robustness.
New method uses diffusion models for unsupervised combinatorial optimization.
problem Learning to sample from intractable discrete distributions without training data.
method Lifts the restriction of generative models needing exact sample likelihoods using a loss that bounds reverse KL divergence.
result Achieves new state-of-the-art results in data-free Combinatorial Optimization.
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global structure of the underlying graph. Examples include testing the graph connectivity…
Novel theory combines combinatorial and topological elements.
problem Understanding combinatorial phenomena at the intersection of topology.
method Synthesizes combinatorial and topological approaches with a new framing concept.
result Framed combinatorial spaces exhibit better behavior than classical spaces.
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly evaluations pose challenges for current techniques in discrete optimization and machine …
The paper introduces combinatorial Calabi flows to find hyperbolic metrics on surfaces with boundary.
problem Finding hyperbolic metrics on surfaces with totally geodesic boundaries of given lengths.
method Introducing combinatorial Calabi flows and proving their long time existence and global convergence.
result Proves the long time existence and global convergence of combinatorial Calabi flow on surfaces with boundary.
New combinatorial method for sparse PCA works beyond spiked identity model.
problem Sparse PCA under general covariance matrices.
method Combinatorial truncated power method with global convergence guarantee.
result First combinatorial sparse PCA method provably successful for general covariance matrices.
A new deep learning framework for topological data.
problem Developing models for data on complex topological domains.
method Introducing combinatorial complexes and developing attention-based CCNNs.
result CCNNs outperform existing models in tasks involving mesh shape analysis and graph learning.
Parameterized discrete uniformization theorems and curvature flows for polyhedral surfaces, IImath.GT
The paper develops algorithms for finding metrics with prescribed combinatorial curvature on polyhedral surfaces.
problem Finding metrics with prescribed combinatorial curvature on polyhedral surfaces.
method Discrete uniformization theorem, combinatorial α-Yamabe flow, combinatorial α-Calabi flow, edge flipping surgery.
result Longtime existence and convergence of combinatorial α-Yamabe flow and combinatorial α-Calabi flow with surgery.
The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.
problem Discrete conformal structures on polyhedral surfaces and their rigidity.
method Parameterized combinatorial curvature, combinatorial α-Ricci flow, and flow extension through singularities.
result Existence and convergence of combinatorial α-Ricci flow for solving the Yamabe problem.
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links. We then introduce a combinatorial notion of adjacency for bipartite graph links…
LGS-Net improves NCO performance on combinatorial optimization tasks.
problem NP-hard combinatorial optimization problems in logistics, manufacturing, and drug discovery.
method LGS-Net uses a latent space model that conditions on problem instances and introduces Latent Guided Sampling for efficient inference.
result Empirical results show state-of-the-art performance on benchmark routing tasks.
Low-rank combinatorial optimization and statistical learning by spatial photonic Ising machinecond-mat.dis-nn
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
problem Solving large-scale combinatorial optimization problems efficiently.
method Proposed a new computing model for SPIM that can handle low-rank interaction matrices.
result Demonstrated efficient learning, classification, and sampling of MNIST images using the model.
RL improves combinatorial optimization by automating heuristic search.
problem Hard combinatorial optimization problems with suboptimal solutions.
method Training RL agents to solve these problems.
result RL can outperform traditional algorithms in solving complex problems.
DeepCO uses deep learning for offline combinatorial optimization in warehouse operations.
problem Optimizing warehouse operation sequences in offline settings.
method DeepCO framework utilizing distribution regularized optimization for TSP.
result DeepCO reduces route length by 5.7% on average for TSP problems.
Paper tackles combinatorial reinforcement learning with preference feedback.
problem Modeling long-term user engagement in scenarios like recommender systems and online advertising.
method Assumes a contextual MNL preference model with linear mean utilities and approximates item values. Proposes MNL-VQL algorithm.
result Achieves nearly minimax-optimal regret for linear MDPs with preference feedback.
For triangulated surfaces, we introduce the combinatorial Calabi flow which is an analogue of smooth Calabi flow. We prove that the solution of combinatorial Calabi flow exists for all time. Moreover, the solution converges if and only if Thurston's circle packing exists. As a consequence, combinatorial Calabi flow pro…
When samples have internal structure, we often see a mismatch between the objective optimized during training and the model's goal during inference. For example, in sequence-to-sequence modeling we are interested in high-quality translated sentences, but training typically uses maximum likelihood at the word level. The…
Unified framework for gradient estimation in combinatorial spaces.
problem Scaling relaxed gradient estimators to large combinatorial distributions.
method Introducing stochastic softmax tricks within the perturbation model framework.
result Stochastic softmax tricks improve model performance and discover more latent structure.
Bayesian Optimization over High-Dimensional Combinatorial Spaces via Dictionary-based Embeddingscs.LG
Bayesian optimization for high-dimensional combinatorial spaces using embeddings.
problem Optimizing expensive functions over large, complex input spaces.
method Dictionary-based ordinal embeddings for high-dimensional combinatorial structures, using Gaussian process models.
result The proposed method outperforms state-of-the-art BO methods on diverse real-world benchmarks.
Fractional combinatorial flow improves surface conformal structures.
problem Improving discrete conformal structures on surfaces.
method Introducing a fractional combinatorial Calabi flow for discrete conformal structures on surfaces.
result Longtime existence and global convergence of the fractional combinatorial Calabi flow for various surface types.
With a compact PL manifold X we associate a category T(X). The objects of T(X) are all combinatorial manifolds of type X, and morphisms are combinatorial assemblies. We prove that the homotopy equivalence BT (X) \approx BPL(X) holds, where PL(X) is the simplicial group of PL-homeomorphisms. Thus the space BT(X) is a ca…
Combinatorial method computes Legendrian knot invariant.
problem Computing the Heegaard Floer contact invariant for Legendrian knots.
method Combining Plamenevskaya's combinatorial description with Heegaard Floer theory.
result Hat version of LOSS invariant can be computed combinatorially.
Paper uses RL to solve constrained combinatorial optimization problems.
problem Constrained combinatorial optimization problems.
method Extending NCO theory to CMDPs, using RL with penalty signals.
result Proposes a superior method for solving constrained problems.
Polynomial-time method solves complex combinatorial semi-bandits.
problem Optimal strategies for combinatorial semi-bandits with uncorrelated Gaussian rewards.
method Proposes a polynomial-time method to solve the Graves-Lai optimization problem for various combinatorial structures.
result First known approach to implement asymptotically optimal algorithms in polynomial time for combinatorial semi-bandits.
New combinatorial structure for hierarchically hyperbolic spaces.
problem Constructing new hierarchically hyperbolic spaces.
method Combinatorial hierarchical hyperbolicity criterion to construct and clarify HHS structures.
result HHSs admit a combinatorial structure, clarifying the application of the combinatorial HHS criterion.
Combinatorial curvature flows with surgery for inversive distance circle packings on surfacesmath.DG
New method finds metrics on surfaces with prescribed curvatures using circle packings and surgery.
problem Finding piecewise Euclidean metrics on surfaces with prescribed combinatorial curvatures.
method Combinatorial curvature flows with surgery for inversive distance circle packings.
result Longtime existence and global convergence of combinatorial curvature flows with surgery.
Bayesian optimization adapted for discrete spaces using random mappings.
problem Global optimization of expensive black-box functions with discrete variables.
method Embeds discrete space into a convex polytope, performs optimization in continuous space.
result Method outperforms existing methods in large combinatorial spaces.
This paper focuses on Bayesian Optimization (BO) for objectives on combinatorial search spaces, including ordinal and categorical variables. Despite the abundance of potential applications of Combinatorial BO, including chipset configuration search and neural architecture search, only a handful of methods have been pro…
New active learning method uses combinatorial coverage to improve data transfer and reduce bias.
problem Inability to transfer sampled data to new models and sampling bias issues.
method Data-centric active learning methods utilizing combinatorial coverage.
result Sampling data with coverage leads to better data transfer and competitive sampling bias.
CRB tackles rising rewards in combinatorial online learning.
problem Rising rewards in combinatorial online learning.
method CRB framework and CRUCB algorithm.
result Empirical and theoretical validation of CRUCB's effectiveness.
Combinatorial Ricci flow finds hyperbolic metrics on 3-manifolds.
problem Finding complete hyperbolic metrics on cusped 3-manifolds.
method Analogue of surface and compact 3-manifold flows, minimizing co-volume, extending through singularities.
result Existence of complete hyperbolic metric is equivalent to flow convergence.
In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial…
Topic models have emerged as fundamental tools in unsupervised machine learning. Most modern topic modeling algorithms take a probabilistic view and derive inference algorithms based on Latent Dirichlet Allocation (LDA) or its variants. In contrast, we study topic modeling as a combinatorial optimization problem, and p…
A connected combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. A connected combinatorial 2-manifold is called weakly regular if it has a vertex-transitive automorphism group. Clearly, a weakly regular combinatorial 2-manifold is degree-regular and a degree-regular combinator…
We study combinatorial modulus on boundaries of hyperbolic Coxeter groups. We give new examples of hyperbolic groups whose boundary satisfies a combinatorial version of the Loewner property, and prove Cannon's conjecture for Coxeter groups. We also establish some connections with l^p cohomology.
The paper establishes a discrete uniformization theorem for surfaces with piecewise hyperbolic metrics.
problem Finding decorated piecewise hyperbolic metrics with prescribed combinatorial curvature.
method Introduced combinatorial α-Ricci flow with surgery to handle potential singularities and prove longtime existence and convergence.
result Existence of decorated piecewise hyperbolic metrics with prescribed combinatorial α-curvature.
New Ising models improve consensus clustering on specialized hardware.
problem Consensus clustering optimization problems.
method Formulated consensus clustering as Ising models and evaluated on specialized hardware.
result Our Ising models outperform existing techniques on consensus clustering.
Proves a conjecture for 3D Artin groups using new combinatorial curvature.
problem Proving the conjecture for Artin groups of dimension 3.
method Introduces new combinatorial non-positive curvature.
result Proves the conjecture for Artin groups of dimension 3.
Study on combinatorial -systoles on surfaces, showing growth in intersection numbers.
problem Understanding the intersection numbers of closed curves on surfaces.
method Analyzing combinatorial -systoles on punctured tori and pairs of pants.
result The maximal intersection number of combinatorial -systoles grows like and approaches infinity as increases.
The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.
problem Finding piecewise constant curvature metrics on surfaces with prescribed combinatorial curvatures.
method Combinatorial curvature flows, including Ricci flow and Calabi flow, are applied to deform Glickenstein's discrete conformal structures.
result The solution of the combinatorial Ricci flow can be uniquely extended and converges exponentially fast for any initial value under certain conditions.
Algorithm BGLM-OFU minimizes regret in combinatorial causal bandits with binary models.
problem Minimizing expected regret in combinatorial causal bandits with binary generalized linear models.
method BGLM-OFU algorithm based on maximum likelihood estimation for Markovian BGLMs, and causal inference techniques for linear models with hidden variables.
result Achieves regret for binary generalized linear models.
New combinatorial model for Milnor fibration using oriented matroids.
problem Understanding the homotopy type of Milnor fibers of complexified real arrangements.
method Introducing a poset quasi-fibration based on a subdivision of the Salvetti complex and an oriented matroid.
result Homotopy type of Milnor fiber depends only on the combinatorial structure of the oriented matroid.
Master-slave architecture tackles combinatorial multi-armed bandits with diversity constraints.
problem Solving top- combinatorial multi-armed bandits with non-linear feedback and diversity constraints.
method Master-slave architecture with six slave models, teacher learning, and policy co-training.
result Significantly outperforms existing algorithms in synthetic and real datasets.
Study counterfactuals in combinatorial choice using a representative agent model.
problem Analyzing decision-making from aggregated binary polytope data.
method Nonparametric approach based on a representative agent model, solving polynomial and mixed-integer convex programs.
result Developed a method for counterfactual prediction that works even under model misspecification.
Combinatorial definition of bordered Floer theory for torus-boundary manifolds.
problem Defining Floer homology for manifolds with torus boundaries.
method Combinatorial definition with coefficients.
result Recovery of combinatorial Heegaard Floer homology.