2-jets determine symmetries of parabolic geometries.
problem Determining symmetries of parabolic geometries.
method 2-jet determinacy for the symmetry algebra of parabolic geometries.
result Symmetry algebra is 1-jet determined at non-flat points and for various parabolic geometries.
Study on robust utility maximization with nonconcave utility functions under projective determinacy.
problem Investor's optimal investment strategy under model ambiguity and nonconcave utility.
method Projective functions of the path and sets of priors, upper-semicontinuous utility.
result Existence of optimal investment strategy under PD.
Paper establishes robust no-arbitrage conditions under projective determinacy.
problem Understanding financial models under Knightian uncertainty.
method Adopting a projective framework, treating all model components uniformly in terms of measurability.
result Establishes characterizations of robust no-arbitrage condition under PD.
Knot diagrams can have isomorphic homologies, challenging HOMFLY-PT theory.
problem Non-determinacy of HOMFLY-PT homology for knot diagrams.
method Expands on Abel's method [Abe17].
result Isomorphic homologies for non-deterministic knot diagrams.
A new framework CyGen models joint distributions using cyclic conditionals.
problem Modeling a joint distribution using only two conditional models without relying on an uninformative prior.
method Developed a general theory for operable equivalence criteria for compatibility and sufficient conditions for determinacy. Proposed CyGen framework and methods to achieve compatibility and determinacy.
result CyGen better fits data and captures more representative features compared to models using an uninformative prior.
Extended Blackwell approachability to quitting games, providing conditions for weak approachability.
problem Designing strategies for repeated games with quitting actions.
method Extending Blackwell approachability to generalized quitting games and providing geometric conditions.
result Characterization of weak approachability in quitting games, proving equivalence and full characterization.
Geometric regularisation improves statistical models by avoiding degeneracy loci.
problem Non-identifiability, singular information, and moment indeterminacy in statistical models.
method Develops the geometric regularisation of distribution-kernel pairs (T,φ) using Whitney, Thom, and Mather theorems. result Finite-dimensional weak transversality theorem for generic kernels, avoiding degeneracy strata of high codimension.
Intact-VAE estimates treatment effects with latent confounders.
problem Estimating treatment effects under unobserved confounding.
method Intact-VAE, a VAE variant, models latent confounders to identify treatment effects.
result Intact-VAE is a consistent estimator of treatment effects under certain settings.
Empower efficient representation of distributions through moment-preserving methods.
problem Representing high-dimensional probability measures efficiently and accurately.
method Empower efficient representation of distributions through moment-preserving methods.
result Empowers efficient and accurate representation of high-dimensional probability measures.
Develops a framework for distributional Granger causality
problem Identifying predictive dependence in time series beyond Gaussian settings
method Using finite collection of channel-specific restrictions
result Identifies distributional Granger non-causality through testable hypotheses
Study on homeomorphism groups of manifolds using set theory.
problem Relationship between set theory and homeomorphism groups of manifolds.
method First-order rigidity, type versus conjugacy, axiom of constructibility, projective determinacy.
result Under V=L, homeomorphism groups of manifolds are first-order rigid and conjugacy class is determined by type.
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 …
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.
Tensoring p-weak differentiable structures preserves their properties.
problem Tensorization of p-weak differentiable structures. method Proving the product of p-weak charts is a p-weak chart, and showing isometric embeddings. result Tensorization of p-weak differentiable structures is possible under certain conditions. 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.
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.
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.
Introduces weak (p,k)-Dirac structures in geometric settings.
problem Defining and analyzing new geometric structures.
method Introducing and studying weak (p,k)-Dirac structures in TM⊕ΛpT∗M. result Weak (p,k)-Dirac structures contain more information than (p,k)-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.
Paper defines weak representations and their equivalence to VB-groupoids.
problem Understanding representations of Lie groupoids and VB-groupoids.
method Introduces weak representations and shows equivalences between categories.
result Equivalence between 2-term representations up to homotopy and weak representations of G.
Study weak f-K-contact manifolds, finding Einstein-type metrics and solitons.
problem Characterize and study geometric properties of weak f-K-contact manifolds. method Analyzing weak metric f-structures, using Killing vector fields, and Jacobi operators. result Einstein weak f-K-contact manifolds are Ricci flat. Study shows comparison principle for weak solutions in narrow domains.
problem Weak solutions to degenerate quasilinear elliptic equations in unbounded tubular domains.
method Showed weak comparison principle holds under narrow conditions.
result Weak comparison principle holds in narrow tubular domains.
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.
Direct proof of weak compactness in Kähler Ricci flow.
problem Weak compactness in Kähler Ricci flow.
method Direct proof approach.
result Time-slice weak compactness on Fano manifolds.
Weak labels can significantly speed up learning for strong tasks.
problem Learning with limited strong labels.
method Using weak labels to accelerate learning of strong tasks.
result Weak labels can accelerate learning to O(icefrac1n) rate. Contractibility of unknot's weak reducing disks shown.
problem Contractibility of unknot's weak reducing disks in 3-bridge position.
method Analysis of weak reducing disks in 3-bridge position.
result Complex of weak reducing disks for the unknot in 3-bridge position is contractible.
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 f-structures on manifolds, generalizing classical results.
problem Classical f-structures and their properties on manifolds. method Introduced and studied weakened f-structures, subclasses, and their properties. result Generalized known results on globally framed f-manifolds. Paper strengthens splitting theorem using weak KAM theory.
problem Splitting theorem in warped product spaces.
method Weak KAM theory approach.
result Strengthened splitting theorem.
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.
Study weak Frenet frame for non-smooth curves with finite curvature and torsion.
problem Defining weak binormal and normal for non-smooth curves with finite total curvature and torsion.
method Piecewise linear methods and density argument applied to polygonal curves.
result Weak binormal and normal are rectifiable curves agreeing with total absolute torsion and vector product of tangent indicatrix and weak binormal.
Study several weak forms of a lemma on compact complex manifolds.
problem Understanding weak forms of a lemma on compact complex manifolds.
method Complete unified study of weak forms of the $\ddb-$Lemma.
result Unified understanding of various weak forms of the $\ddb-$Lemma.
Simplicial spheres have a weak Lefschetz property in characteristic 2.
problem Proving the weak Lefschetz property for simplicial spheres.
method Using bistellar moves to show the property is preserved.
result The weak Lefschetz property is preserved by bistellar moves for PL-spheres.
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.
Example shows disk surgeries can alter weak reducibility property.
problem Weak reducibility of compressing disks after surgery.
method Example of weak reducing disks and their surgeries.
result Weak reducibility property is not preserved by disk surgery.
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.
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 …
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.
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 …