The paper solves conjectures related to strong openness and optimal L2 extension.
problem Strong openness of multiplier ideal sheaves and optimal L2 extension. method Solution of conjectures related to Demailly's strong openness and related conjectures.
result Optimal L2 extension implies Berndtsson's positivity of vector bundles. Paper generalizes complex Brunn-Minkowski theory and proves new extension theorems.
problem Complex Brunn-Minkowski theory and extension theorems.
method Hilbert bundle approach to complex Brunn-Minkowski theory.
result Generalizes Guan's sharp strong openness theorem and sharp Ohsawa-Takegoshi extension theorem.
The study describes Lefschetz-Bott fibrations on symplectic manifolds and their applications.
problem Understanding Lefschetz-Bott fibrations on symplectic manifolds.
method Explicit construction and analysis of Lefschetz-Bott fibrations over line bundles.
result Construction of strong symplectic fillings of symplectic manifolds.
Algorithm decides if knots satisfy a conjecture, linking Jones polynomial to surface complexity.
problem Deciding if knots satisfy the Strong Slope Conjecture based on Jones polynomial.
method Normal surface algorithm, relating Jones period to surface complexity.
result Established relation between Jones period and number of Jones surfaces.
In this article, we solve the strong openness conjecture on the multiplier ideal sheaves for the plurisubharmonic functions posed by Demailly. We prove two conjectures about the growth of the volumes of the sublevel sets of plurisubharmonic functions related to the complex singularity exponents and quasi-plurisubharmon…
This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
problem Classifying symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
method Using holomorphic curves and Lefschetz fibrations to classify fillings.
result Symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions can be classified up to deformation equivalence.
Penrose's conjecture links black holes and gravitational singularities.
problem Deterministic nature of General Relativity and black holes.
method Modern techniques in partial differential equations applied to gravitational collapse.
result Recent advances in understanding Strong Cosmic Censorship.
New findings show strong arbitrage is not possible over arbitrary time horizons.
problem Whether strong arbitrage is possible over arbitrary time horizons.
method Analyzing the total relative variation of an equity market.
result Strong arbitrage is not possible over arbitrary time horizons under the stated condition.
Paper proves weak unique continuation for harmonic functions on RCD spaces but finds counterexample for strong uniqueness.
problem Unique continuation of harmonic functions on RCD spaces, especially strong uniqueness.
method Establishes weak unique continuation theorem and provides counterexample for strong uniqueness.
result Found counterexample for strong unique continuation in RCD(K,N) spaces for N≥4 and K∈R.
Study of stochastic differential equations on non-compact manifolds, solving open problem on strong completeness.
problem Open problem on strong completeness of SDEs on non-compact spaces.
method Systematic study of stochastic differential equations, solving open problem on strong completeness.
result Existence of global smooth solution flow of SDEs on R^n, including substantial growth of coefficients.
New invariants measure entanglement of open curves in 3D space.
problem Characterizing the complexity of open curves in 3-space.
method Introducing linkoids and virtual knots, and new invariants.
result Strong invariants of linkoids independent of virtual closure.
We discuss a technique to construct Ricci-flat hermitian metrics on complements of (some) anticanonical divisors of almost homogeneous manifolds and discuss when this metric is complete and Kähler. This construction has a strong interplay with invariance groups of the same dimension as the manifold acting with an open …
This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follow…
New tools classify symplectic fillings of contact 3-manifolds.
problem Classifying symplectic fillings of contact 3-manifolds.
method Spinal open book decompositions and bordered Lefschetz fibrations.
result Symplectic fillings of contact 3-manifolds are deformation equivalent to complements of positive multisections in bordered Lefschetz fibrations.
Given two open books with equal pages we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the contact manifold associated to the open book with the same page and concatenated monod…
The study examines vector fields with integer singularities in 3D balls.
problem Characterizing the strong Lp-closure of vector fields with finitely many integer singularities. method Characterization and decomposition of vector fields with finitely many integer singularities.
result Decomposition theorem for elements in LZ1(B), revealing information about mass-minimizing currents. Proves common stellar subdivisions for all PL homeomorphic polyhedra.
problem Proving common stellar subdivisions for all PL homeomorphic polyhedra.
method Proved weighted strong factorization conjecture and iterated blowups.
result Every two PL homeomorphic polyhedra have a common stellar subdivision.
Study shows how a strong model can learn a task's feature while retaining other capabilities.
problem How to align superhuman AI systems using weak-to-strong generalization.
method Two-layer neural networks, reward-model learning, multi-step SGD, feature learning.
result The strong model efficiently learns task features while retaining general capabilities.
Study finds open data sets favor Western locales, impacting classifier performance.
problem Impact of biased open data sets on classifier performance in the developing world.
method Analysis of two large, publicly available image data sets and classifiers trained on them.
result Open data sets exhibit a bias towards Western locales, affecting classifier performance.
Bourgeois structures are tight in 5D and provide symplectic fillability obstructions.
problem Understanding the tightness and symplectic fillability of Bourgeois contact structures.
method Explicit construction and obstructions for symplectic fillings.
result Bourgeois structures are universally tight in 5D and provide obstructions in higher dimensions.
Open-FinLLMs tackle financial tasks with multimodal capabilities.
problem Financial LLMs lack multimodal capabilities and real-world applicability.
method Developed Open-FinLLMs, an open-source multimodal financial LLM suite.
result Open-FinLLMs outperform advanced financial and general LLMs in diverse tasks.
FastAdaBelief improves convergence rate of AdaBelief by exploiting strong convexity.
problem Improving convergence rate of AdaBelief without sacrificing generalization ability.
method Designing FastAdaBelief that adjusts step size considering strong convexity.
result Proves O(logT) regret bound for FastAdaBelief. Reduces bounded loss learning to binary classification.
problem Universal consistency of non-i.i.d. processes with bounded loss.
method Constructive reduction to binary classification.
result Any bounded loss output setting can be reduced to binary classification.
Strongly convex bodies can be approximated by smooth ones.
problem Approximating strongly convex bodies with smooth ones.
method Using C2 locally strongly convex bodies. result Smooth approximations of strongly convex bodies exist and can be controlled in terms of Hausdorff distance.
Study on continuity of solutions for complex Monge-Ampère equations with movable singularities.
problem Continuity of solutions with prescribed singularities for complex Monge-Ampère equations.
method Strong continuity methods with movable singularities, including Kähler-Einstein metrics.
result Sufficient conditions for strong continuity of solutions and openness results for Fano type equations.
New theory relaxes assumptions for optimal cooperative inference.
problem Achieving optimal cooperative inference under strong assumptions.
method Relaxing restrictive assumptions, demonstrating convergence, robustness, and stability.
result Generalized cooperative inference for any discrete joint distribution.
Proves Strong Cosmic Censorship conjecture for specific spacetimes.
problem Proving the Strong Cosmic Censorship conjecture for certain spacetimes.
method Analyzing curvature invariants and expansion-normalised variables.
result Proven for orthogonal Bianchi class B perfect fluids and vacuum spacetimes.
HEAR benchmark evaluates audio representations for diverse tasks.
problem Developing a general-purpose audio representation for various tasks.
method Evaluated 29 models across 19 tasks using 16 datasets.
result No single audio representation performs holistically.
We prove that dynamical coherence is an open and closed property in the space of partially hyperbolic diffeomorphisms of T3 isotopic to Anosov. Moreover, we prove that strong partially hyperbolic diffeomorphisms of T3 are either dynamically coherent or have an invariant two-dimensional torus whi…
SAdam improves Adam's performance for strongly convex functions.
problem Improving Adam's performance for strongly convex functions.
method Developed SAdam, a variant of Adam, which exploits strong convexity.
result Achieves a data-dependent O(logT) regret bound for strongly convex functions. Meena is a chatbot trained on social media data, achieving human-like conversation quality.
problem Creating a chatbot that can have human-like conversations in an open-domain setting.
method End-to-end training of a 2.6B parameter neural network on social media data, using perplexity and a human evaluation metric (SSA) to assess quality.
result Meena achieves a high human-like conversation quality (79% SSA) when compared to existing chatbots.
TAMD prevents degeneracy in finite mixtures, offering strong guarantees but modest practical improvements.
problem Degeneracy in maximum likelihood estimation of finite mixtures.
method Transcendental regularization with analytic barrier functions.
result Strong theoretical guarantees (identifiability, consistency, robustness) but modest practical improvements.
Novel approach to universal online learning for bounded losses, closing open problems.
problem Characterizing processes for universal online learning under non-i.i.d. conditions.
method Characterization of processes admitting strong and weak universal learning, introduction of optimistically universal learning rule.
result Introduction of a novel 1NN algorithm that is optimistically universal for bounded losses.
New counterexamples found to cosmic censor conjecture in 4D.
problem Cosmic censor conjecture in 4D physics.
method Constructing non-globally hyperbolic Lorentzian 4-manifolds using exotic and self-dual spaces.
result Found physical counterexamples to the strong cosmic censor conjecture.
Investigates time-inconsistent portfolio selection under MMV preferences.
problem Time-inconsistent optimal strategies for MMV preferences.
method Nash equilibrium controls for MMV and MV preferences, solving FBSDE and HJB equations.
result MMV optimal strategies lead to higher investment amounts than MV strategies, narrowing over time.
We propose localization techniques for computing Gromov-Witten invariants of maps from Riemann surfaces with boundaries into a Calabi-Yau, with the boundaries mapped to a Lagrangian submanifold. The computations can be expressed in terms of Gromov-Witten invariants of one-pointed maps. In genus zero, an equivariant ver…
New RL algorithm gives tighter bounds without domain knowledge.
problem Improving worst-case performance bounds in reinforcement learning.
method Derives algorithm for finite horizon discrete MDPs with analysis yielding state-of-the-art worst-case regret bounds.
result Substantially tighter bounds for environments with small environmental norm, no prior knowledge required.
The Familiarity Hypothesis explains deep open set methods' success in detecting novel objects.
problem Detecting novel objects in open set recognition problems.
method Logits-based detection of absence of familiar features.
result Familiarity-based detection fails in scenarios with both novel and familiar objects.
Let P be a knot in a solid torus, K a knot in 3-space and P(K) the satellite knot of K with pattern P. This defines an operator on the set of knot types and induces a satellite operator P:C--> C on the set of smooth concordance classes of knots. There has been considerable interest in whether certain such functions are…
The study proves a strong parametric h-principle for minimal surfaces.
problem Proving a parametric h-principle for minimal surfaces.
method Using a parametric h-principle due to Forstneric and Larusson.
result The space of complete nonflat conformal minimal immersions has the same homotopy type as the space of continuous maps.
Epoch-GDA achieves optimal convergence rate for SCSC min-max problems.
problem Solving stochastic min-max problems with strong convexity and strong concavity.
method Epoch-wise stochastic gradient descent ascent method (Epoch-GDA) without additional assumptions.
result Achieves the optimal rate of O(1/T) for the duality gap of general SCSC min-max problems. New example solves topological dynamics problem.
problem Embedding compact metric space into cubical shift.
method Borsuk-Ulam theorem, p-adic completions, equivariant Sullivan conjecture.
result Existence of a compact metric space not embeddable into a cubical shift.
MAPIE provides uncertainty quantification for ML models.
problem Estimating uncertainties in ML model predictions.
method Conformal prediction methods for single-output regression and multi-class classification.
result Strong theoretical guarantees on marginal coverages.
Limits of manifolds with Kato bound on Ricci curvature are rectifiable.
problem Understanding limits of manifolds with specific curvature bounds.
method Proving rectifiability of limits of manifolds with Kato bound on Ricci curvature.
result Rectifiability of limits of manifolds with Kato bound on Ricci curvature.
Solves the gauge problem for Ricci flow cylinders, proving strong rigidity.
problem Recognizing metrics in different coordinates and diffeomorphisms.
method Solves a nonlinear system of PDEs to produce a diffeomorphism fixing a gauge.
result Strong rigidity of cylinders in Ricci flow, proving all tangent flows are cylinders.
Many key algorithms in 3-manifold topology involve the enumeration of normal surfaces, which is based upon the double description method for finding the vertices of a convex polytope. Typically we are only interested in a small subset of these vertices, thus opening the way for substantial optimization. Here we give an…
Develops a method to plan exploration that learns strong policies with fewer samples.
problem Lack of efficient exploration in reinforcement learning for real-world tasks.
method Plans an action sequence that maximizes information gain about the optimal trajectory.
result 2x fewer samples than exploration baselines and 200x fewer than model-free methods.
Defines a distance function on a manifold using symplectic embeddings and recovers the metric.
problem Recovering a Riemannian metric from symplectic embeddings in cotangent bundles.
method Defines a distance-like function ρW using symplectic embeddings and recovers the metric when W is the unit disc-cotangent bundle. result The distance function ρW recovers the Riemannian metric when W is the unit disc-cotangent bundle.