Proposes HypCSE for enhanced hierarchical clustering.
problem Challenges in existing hierarchical clustering methods.
method Hyperbolic Continuous Structural Entropy (HypCSE) neural networks.
result Superior performance on seven datasets.
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48 results for “continuous structure”
Study shows how to balance memory and learning efficiency in continual learning.
problem Balancing memory and learning efficiency in continual learning.
method Structural regularization with Hessian-based regularization.
result Structural regularization improves statistical performance at the cost of increased memory complexity.
Researchers examine various causal structures for spacetimes with continuous metrics.
problem Comparing causal structures for spacetimes with continuous but not necessarily smooth metrics.
method Examined three key properties: push-up lemma, openness of chronological futures, and existence of limit causal curves.
result Spacetimes with continuous metrics do not always satisfy all three key properties.
We classify hyperbolic monopoles with continuous symmetries and construct new examples.
problem Classifying and constructing hyperbolic monopoles with continuous symmetries.
method Developed a Structure Theorem and used representation theory to simplify the problem.
result Found constraints on structure groups and constructed novel spherically symmetric hyperbolic monopoles.
Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which represents a finite state continuous time Markov process whose transition model is…
The paper analyzes continuous optimization for DAG structure learning and its limitations.
problem The performance of continuous structure learning approaches is not consistent after data standardization.
method Analysis of continuous optimization for DAG structure learning, focusing on equal and non-equal noise variances.
result Continuous structure learning approaches may not perform well after data standardization, especially with non-equal noise variances.
Continual Learning is a learning paradigm where learning systems are trained with sequential or streaming tasks. Two notable directions among the recent advances in continual learning with neural networks are () variational Bayes based regularization by learning priors from previous tasks, and, () learning the s…
Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.
problem Understanding unique spacetime extensions across null boundaries in 1+1 dimensions.
method Analyzing the - and -structures of continuous spacetime extensions.
result Extensions can have the same -structure but different -structures.
In recent years, there is a growing interest in learning Bayesian networks with continuous variables. Learning the structure of such networks is a computationally expensive procedure, which limits most applications to parameter learning. This problem is even more acute when learning networks with hidden variables. We p…
CANDI solves the gap between continuous and discrete diffusion models for text generation.
problem Underperformance of continuous diffusion models in discrete data domains.
method Introduces token identifiability and a hybrid framework (CANDI) to decouple discrete and continuous corruption.
result CANDI successfully avoids temporal dissonance, enabling continuous diffusion benefits for discrete spaces.
The paper studies curves in Finsler-like spaces and their properties.
problem Investigating properties of curves in asymmetric metric spaces induced by Finsler structures.
method Analyzes three types of absolutely continuous curves in Finsler-like spaces and establishes the Lisini structure theorem.
result Characterizes the nature of absolutely continuous curves in terms of dynamical transference plans.
We quantify causal bias in continuous treatment settings.
problem Identifying and quantifying causal bias in continuous treatment scenarios.
method Developed a novel characterization of causal bias in structural causal models, proving conditions for zero bias and efficient estimation.
result Causal bias can be estimated efficiently under certain structural equation restrictions, allowing for causal regularization of predictive models.
Adaptive tensor modeling preserves continuity in multidimensional data.
problem Discretization of continuous multidimensional data loses important information.
method Functional Tucker decomposition (FTD) with RKHS modeling.
result FTD enables adaptive and expressive tensor modeling.
We are concerned with the global weak continuity of the Cartan structural system -- or equivalently, the Gauss--Codazzi--Ricci system -- on semi-Riemannian manifolds with lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over semi-Riemannian m…
The space of convex projective structures has been well studied with respect to the topological entropy. But, to better understand the geometry of the structure, we study the entropy of the Sinai-Ruelle-Bowen measure and show that it is a continuous function.
Proposes a new algorithm for learning continuous-time Bayesian network structures.
problem Lack of constraint-based algorithms for continuous-time Bayesian networks.
method Develops a constraint-based algorithm using statistical tests for conditional independence.
result The proposed algorithm is more accurate with variables having more than two values.
The paper explains how continuous language models can produce discrete, interpretable meanings.
problem Semantic collapse in continuous systems of large language models.
method Formalizing large language models as Continuous State Machines (CSMs) and analyzing the associated transfer operator.
result The leading eigenfunctions of the transfer operator induce a finite number of invariant meaning basins, explaining how continuous computation can produce discrete, interpretable semantics.
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.
Proposes a new convolutional neural network for non-grid data.
problem Limited applicability of standard CNNs to non-grid structured data.
method Introduces Parametric Continuous Convolution (PCC) with learnable kernel functions.
result Significant improvement in point cloud segmentation and lidar motion estimation.
The paper proposes a method to learn the structure of continuous-action games with non-parametric utilities using a limited number of samples.
problem Learning the exact structure of continuous-action games with non-parametric utility functions.
method An regularized method that encourages sparsity of the Fourier transform coefficients of the utility functions, accessed via a few Nash equilibria and their noisy utilities.
result The method recovers the exact structure of the utility functions and the game structure with provable theoretical guarantees.
Topic models are probabilistic models for discovering topical themes in collections of documents. In real world applications, these models provide us with the means of organizing what would otherwise be unstructured collections. They can help us cluster a huge collection into different topics or find a subset of the co…
New algorithm for context bandits with continuous actions.
problem Efficient decision-making with unknown action structures.
method Reduction-style algorithm combining supervised learning.
result Proven to work in general and validated with experiments.
Flow based models such as Real NVP are an extremely powerful approach to density estimation. However, existing flow based models are restricted to transforming continuous densities over a continuous input space into similarly continuous distributions over continuous latent variables. This makes them poorly suited for m…
Constructs continuous families of minimal surfaces and holomorphic immersions.
problem Creating continuous families of minimal surfaces and holomorphic immersions.
method Continuous family of complex structures and conformal minimal immersions.
result Continuous families of proper -conformal minimal immersions and holomorphic null immersions.
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self…
It is well-known that the class of piecewise smooth curves together with a smooth Riemannian metric induces a metric space structure on a manifold. However, little is known about the minimal regularity needed to analyze curves and particularly to study length-minimizing curves where neither classical techniques such as…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a…
Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelstat.ML
Proposes a new model to identify unknown counterfactual outcomes for continuous variables.
problem Counterfactual inference for continuous outcomes with strong assumptions.
method Curvature Sensitivity Model to relax assumptions and provide informative bounds.
result Demonstrates effectiveness of the Curvature Sensitivity Model in identifying counterfactual outcomes.
The study examines non-continuous Riemannian metrics on manifolds and their infinitesimal properties.
problem Investigating non-continuous Riemannian metrics and their infinitesimal structure.
method Constructing examples of metric measure spaces with discontinuous metrics.
result Examples show failure of infinitesimal Hilbertian or quasi-Riemannian properties.
Continuity of roots of hyperbolic polynomials with smooth coefficients.
problem Continuity of the solution map for hyperbolic polynomials.
method Proving continuity of the solution map from hyperbolic polynomials of degree d with C^d coefficients to their increasingly ordered roots.
result Continuity of the solution map for hyperbolic polynomials with C^d coefficients.
Survey on discovering causal relationships from data.
problem Discover causal relationships from data.
method Modern, continuous optimization methods for structure learning.
result Survey of methods and resources for structure discovery.
On the continuity of bendingmath.GT
We examine the dependence of the deformation obtained by bending quasi-Fuchsian structures on the bending lamination. We show that when we consider bending quasi-Fuchsian structures on a closed surface, the conditions obtained by Epstein and Marden to relate weak convergence of arbitrary laminations to the convergence …
Regulated curves on Banach manifolds with continuous projections and regulated derivatives are studied.
problem Regulated curves on Banach manifolds with continuous projections and regulated derivatives.
method Building a Banach manifold structure on the set of such curves.
result Existence of a 'local addition' on such a manifold for any Banach manifold.
Decomposes smooth manifolds into algebraic submanifolds.
problem Understanding the structure of smooth manifolds induced by continuous selections.
method Generic continuous selection of smooth functions provides stratification of the manifold.
result Stratification leads to local topological structure with nondegenerate critical points.
The paper tackles fast rates in structured prediction problems.
problem Structured prediction problems with discrete outputs.
method Introducing continuous surrogate problems and leveraging their convergence rates for discrete problems.
result Super fast rates, including exponential rates, for excess risk in structured prediction problems.
Transfer learning for bandits with latent Lipschitz continuity.
problem Learning to transfer structural information from prior tasks to new tasks.
method Proposes a framework to estimate Lipschitz constant from prior tasks and apply it to new tasks.
result Regret bound close to oracle algorithm with full knowledge of Lipschitz constant under mild assumptions.
Equivalences of Smooth and Continuous Principal Bundles with Infinite-Dimensional Structure Groupmath.DG
Let K be a a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth principal K-bundles over M which are continuously equivalent are also smoothly eq…
This paper tackles continuous domain generalization, improving model performance across unseen domains.
problem Existing domain generalization approaches fail to capture the complex, multidimensional nature of real-world variation.
method Introduces Continuous Domain Generalization (CDG), a principled framework grounded in geometric and algebraic theories. Proposes a Neural Lie Transport Operator (NeuralLio) for structure-preserving parameter transitions and a gating mechanism for robust generalization.
result Demonstrates significant improvement in generalization accuracy and robustness across various datasets.
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of…
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined by G1 gluing data in terms of rational functions are analyzed further. A general…
Continuous-depth Evoformer reduces protein folding prediction time and resource usage.
problem Efficient protein structure prediction with reduced computational costs.
method Continuous-depth formulation of Evoformer using Neural Ordinary Differential Equations (Neural ODEs).
result The continuous-time Evoformer achieves constant memory cost and improved efficiency.
New CTBNs with clocks allow for non-exponential survival times.
problem Modeling phenomena with non-exponential survival times in continuous time.
method Introduced node-wise clocks to construct graph-coupled semi-Markov chains, enabling non-exponential survival times without auxiliary states.
result Parameter and structure inference algorithms provided, demonstrating advantages over current CTBN extensions.
Continuous-time Bayesian networks (CTBNs) constitute a general and powerful framework for modeling continuous-time stochastic processes on networks. This makes them particularly attractive for learning the directed structures among interacting entities. However, if the available data is incomplete, one needs to simulat…
Unsupervised framework captures acquisition variability in structural connectomes.
problem Acquisition differences across sites, scanners, and protocols complicate structural connectome analysis.
method An unsupervised framework using architectural annealing to balance discrete and continuous latent variables.
result Architectural annealing produces stronger site learning than baseline models.
A new method learns quantization boundaries in continuous space using tessellation.
problem Mapping between discrete and continuous distributions is difficult.
method Constructs normalizing flows on convex polytopes with exact likelihood evaluations.
result Improves likelihood evaluation and quantization learning across various data modalities.
Cryo-electron microscopy (cryo-EM) is a powerful technique for determining the structure of proteins and other macromolecular complexes at near-atomic resolution. In single particle cryo-EM, the central problem is to reconstruct the three-dimensional structure of a macromolecule from noisy and randomly orien…
Proposes a value-based method for continuous control without an actor.
problem Computational infeasibility of evaluating Q-values in continuous action spaces.
method Structurally maximizable Q-functions, actor-free approach.
result Performance and sample efficiency comparable to actor-critic methods.
DFMs enable flow-based models for multimodal discrete and continuous data.
problem Combining discrete and continuous data for generative models.
method Discrete Flow Models (DFMs) using Continuous Time Markov Chains.
result DFMs achieve state-of-the-art co-design performance for protein structure and sequence generation.