We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we …
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48 results for “weak”
Tensoring -weak differentiable structures preserves their properties.
problem Tensorization of -weak differentiable structures.
method Proving the product of -weak charts is a -weak chart, and showing isometric embeddings.
result Tensorization of -weak differentiable structures is possible under certain conditions.
New structures defined for studying contact foliations and their geometry.
problem Understanding dynamics of contact foliations and their applications.
method Define and study weak nearly S- and weak nearly C-structures.
result Characterize weak nearly S- and weak nearly C- submanifolds in weak nearly Kähler manifolds.
The study examines conditions for weak nearly cosymplectic manifolds to split into products.
problem Understanding the curvature and topology of weak nearly cosymplectic manifolds.
method Analyzes the conditions for splitting and characterizes specific manifolds.
result Conditions for weak nearly cosymplectic manifolds to become Riemannian products are identified.
Subset selection improves weak supervision performance.
problem Optimizing the use of weakly-labeled data.
method Combining pretrained data representations with the cut statistic for subset selection.
result Subset selection improves weak supervision performance by up to 19%.
Defines weak geodesics on specific subsets of manifolds.
problem Characterizing geodesics on prox-regular subsets of Riemannian manifolds.
method Defining weak geodesics as continuous curves with weak regularities, and characterizing them as viscosity critical points of the energy functional.
result Characterizes weak geodesics on prox-regular subsets of Riemannian manifolds.
Study weak conjugacy in surface homeomorphisms.
problem Understanding weak conjugacy in homeomorphisms of surfaces.
method Exploring the group of homeomorphisms isotopic to the identity.
result New insights into weak conjugacy relations.
New model shows weak teachers can help strong students learn even with imperfect labels.
problem Improving strong student's performance with weak teacher's imperfect pseudolabels.
method Stylized overparameterized spiked covariance model with Gaussian covariates, proving two phases of generalization.
result Provable successful and random guessing phases of strong student's generalization.
Weak -Dirac manifoldsmath.DG
Introduces weak -Dirac structures in geometric settings.
problem Defining and analyzing new geometric structures.
method Introducing and studying weak -Dirac structures in .
result Weak -Dirac structures contain more information than -Lagrangian structures.
RAVEN improves weak-to-strong generalization under distribution shifts.
problem Weak models fail to supervise strong models effectively under distribution shifts.
method RAVEN dynamically learns optimal combinations of weak models and strong model parameters.
result RAVEN outperforms existing methods by over 30% on out-of-distribution tasks.
Study weak -K-contact manifolds, finding Einstein-type metrics and solitons.
problem Characterize and study geometric properties of weak -K-contact manifolds.
method Analyzing weak metric -structures, using Killing vector fields, and Jacobi operators.
result Einstein weak -K-contact manifolds are Ricci flat.
Study the geometry of weak para-f-structures and subclasses.
problem Understand the geometry of weak para-f-structures and their subclasses.
method Express covariant derivative of f, prove Killing characteristic vector fields, show foliations, and demonstrate rigidity.
result Prove that characteristic vector fields are Killing and ker f defines a totally geodesic foliation.
The study explores new metric structures on manifolds, linking them to Einstein metrics.
problem Characterizing and understanding weak K-contact manifolds and their properties.
method Analyzing weak K-contact manifolds and their properties, including the parallel Ricci tensor and generalized Ricci soliton structures.
result Sufficient conditions for weak K-contact manifolds with specific properties to be Einstein manifolds.
Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.
problem Characterizing Einstein metrics in weak β-Kenmotsu manifolds.
method Adapted -Ricci tensor to weak almost contact manifolds and studied its interaction with weak β-Kenmotsu structures.
result New characteristics of Einstein metrics obtained.
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
problem Characterize weak reducing pairs in critical Heegaard splittings.
method Analyze the properties of weak reducing pairs in critical Heegaard splittings.
result Provide a necessary condition for a Heegaard surface to be critical.
We study weakened -structures on manifolds, generalizing classical results.
problem Classical -structures and their properties on manifolds.
method Introduced and studied weakened -structures, subclasses, and their properties.
result Generalized known results on globally framed -manifolds.
Equivalent bicategories constructed from action Lie groupoids.
problem Equivalence of bicategories constructed from action Lie groupoids.
method Localizing at equivariant weak equivalences, surjective submersive equivariant weak equivalences, and all weak equivalences.
result Weak equivalences between action Lie groupoids are isomorphic to compositions of nice forms of equivariant weak equivalences.
We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous notation for polygonal curves, where the polarity property is exploited, and then m…
Classifies compact spaces by shape, finite spaces by weak homotopy.
problem Classifying compact Hausdorff spaces and finite topological spaces.
method Constructs a category that classifies spaces by shape and weak homotopy.
result Classifies compact spaces by shape, finite spaces by weak homotopy.
Optimal algorithm converts weak to strong learner with less data.
problem Constructing a strong learner from a weak learner with minimal data.
method New algorithm that uses less training data than AdaBoost.
result Optimal sample complexity for converting weak to strong learner.
Formalizes weak and strong verification for LLMs, controlling errors without assumptions.
problem Balancing cost and reliability in reasoning with LLMs.
method Formalizes weak-strong verification policies, introduces metrics, develops online algorithm.
result Optimal policies admit a two-threshold structure, and calibration and sharpness govern value of weak verifiers.
In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…
Random feature models can outperform a weak teacher with early stopping.
problem Generalization from a weak to a strong model in random feature networks.
method Random feature models, early stopping, proving weak-to-strong generalization.
result Random feature models can outperform a weak teacher with early stopping.
In this paper, I introduce weak representations of a Lie groupoid . I also show that there is an equivalence of categories between the categories of 2-term representations up to homotopy and weak representations of . Furthermore, I show that any VB-groupoid is isomorphic to an action groupoid associated to a weak…
A new method for weakly supervised learning that improves model accuracy.
problem Training machine learning models with precise labels is expensive; weak supervision provides a low-cost alternative.
method Data consistent weak supervision algorithm that searches over classifiers to find plausible labelings, considering features of the training data and estimating labels for low/no coverage data.
result Empirically, the method significantly outperforms state-of-the-art weak supervision methods on text and image classification tasks.
Paper introduces methods for more reliable probabilistic predictions with confidence intervals.
problem Inaccurate labeling of datasets due to unreliable probabilistic predictions from weak labeling functions.
method Proposes a methodology to provide confidence intervals for label probabilities using uncertainty sets of distributions.
result Improves reliability of probabilistic predictions and provides confidence intervals for label probabilities.
We detail the construction of a weak Poisson bracket over a submanifold of a smooth manifold M with respect to a local foliation of this submanifold. Such a bracket satisfies a weak type Jacobi identity but may be viewed as a usual Poisson bracket on the space of leaves of the foliation. We then lift this weak Poisson …
Functorial maps and weak parities are equivalent descriptions of rules of substitution virtual crossings for classical in diagrams of a knot in a way compatible with Reidemeister moves. We introduce the notion of maximal weak parity and describe it for knots in a given closed oriented surface. This weak parity defines …
Convergence of the financial value of weak information for a sequence of discrete-time marketsmath.PR
Study shows financial value of weak information converges in discrete vs continuous markets.
problem Analyzing financial value of weak information in discrete vs continuous markets.
method Defined minimal probability measure and financial value of weak information, then showed convergence.
result Financial value of weak information converges in discrete vs continuous markets.
Weak diffusion priors can still perform well in inverse problems.
problem Using mismatched or low-fidelity diffusion priors in inverse problems.
method Extensive experiments and theoretical analysis combining Bayesian-consistency theory and local-correlation analysis.
result Weak priors succeed when measurements are highly informative, and they fail in other regimes.
New research shows label refinement and weak training have limitations for aligning LLMs.
problem Limitations of refinement methods for aligning large language models.
method Analyzed probabilistic assumptions and alternative approaches to label refinement and weak training.
result Label refinement and weak training suffer from irreducible error, leaving a performance gap.
The paper finds the Finsler structure of Apollonian weak metric on unit disc.
problem Understanding the Finsler structure of Apollonian weak metric on the unit disc.
method Analyzing the deformation of hyperbolic Poincaré metric by a closed 1-form.
result The Apollonian weak-Finsler structure has bounded below -curvature and flag curvature satisfying .
Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.
problem Defining and studying weak dual pairs in Dirac-Jacobi structures.
method Adopting omni-Lie algebroid approach, proving equivalence and leaf correspondence theorems.
result Existence of self-dual pairs and alternative proof of normal form theorem.
The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.
problem Classifying knot projections based on weak homotopy equivalence.
method Defining weak (1, 2, 3) homotopy and using it to find an invariant.
result There are an infinite number of weak (1, 2, 3) homotopy equivalence classes of knot projections.
Study --Ricci solitons on weak Kenmotsu -manifolds.
problem Characterize --Ricci solitons on weak Kenmotsu -manifolds.
method Adapted -Ricci tensor to weak metric -manifolds, studied the interaction with weak -Kenmotsu structure.
result Obtained new characteristics of -Einstein metrics.
The paper proves properties of curves in Riemannian manifolds.
problem Characterizing curves in Riemannian manifolds.
method Analyzing locally minimizing and weak geodesics.
result Locally minimizing curves are weak geodesics under certain conditions.
This paper proves that one-relator groups have a weak Z-structure.
problem The existence of weak Z-structures for all groups of type F.
method Analyzing the geometric properties of one-relator groups and their boundaries.
result Torsion-free one-relator groups have a weak Z-structure.
Proves weak convergence equals mean convergence in GGC.
problem Proving convergence in GGC distributions.
method Using generalized gamma convolution (GGC) and expected utility maximization.
result Weak convergence implies mean convergence in GGC.
The Capabilities and Limitations of Weak-to-Strong Generalization: Generalization and Calibrationcs.LG
The study explores the strengths and weaknesses of models that generalize from weak to strong supervision.
problem Understanding the limitations and capabilities of models that generalize from weak to strong supervision.
method Theoretical analysis and experimental validation in both classification and regression settings.
result Theoretical bounds reveal the importance of strong generalization and calibration of the weak model and a careful balance in the training process.
ASTRA uses unlabeled data and weak rules to train deep models effectively.
problem Learning with weak supervision rules is challenging due to their heuristic and noisy nature.
method ASTRA framework that considers contextualized representations and pseudo-labels for unlabeled data, and a rule attention network to aggregate labels.
result Significant improvements over state-of-the-art baselines on text classification benchmarks.
Proves existence and uniqueness of weak solutions for specific equations.
problem Existence and uniqueness of solutions for generalized Monge-Ampère and deformed Hermitian-Yang-Mills equations.
method Combines viscosity-theoretic and pluripotential-theoretic techniques.
result Existence and uniqueness of weak solutions in boundary cases.
Paper proves uniqueness of weak solutions for Plateau flow.
problem Proving uniqueness of weak solutions for Plateau flow.
method Used natural energy condition and alternative methods from Struwe.
result Proves uniqueness of weak solutions under natural condition.
Extends weak continuity of Yang-Mills connections to a broader class.
problem Weak compactness of -Yang-Mills connections.
method Compensation compactness argument applied to Yang-Mills fields.
result Weak continuity result extended to -Yang-Mills connections.
Combines foundation models with weak supervision to improve NLP and video tasks.
problem Leveraging weak supervision with foundation models without labeled data.
method Liger, a combination of foundation model embeddings and weak supervision techniques.
result Liger outperforms existing weak supervision methods by 14.1 points on benchmark NLP and video tasks.
Sharp bounds on weak convergence rate for rough volatility models.
problem Understanding the convergence rate in discretizing rough volatility models.
method Analyzing general and linear models to derive bounds.
result Sharper bound of \(H + 1/2\) for linear models.
Study approximates weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
problem Approximating weak error for specific stochastic models with rough and Gaussian mean-reverting volatility.
method Used Euler type scheme with integrated kernels to study weak convergence rate.
result Obtained weak convergence rate of for discretised rough Ornstein-Uhlenbeck process and stochastic rough volatility model.
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
Every weak Perron number is realized as a stretch factor of a homeomorphism on a surface.
problem Finding stretch factors for weak Perron numbers.
method Constructing an end-periodic homeomorphism on a surface.
result Every weak Perron number is an end-periodic stretch factor.