New inequality for refined knot invariants in a specific space.
problem General adjunction inequality for refined s-invariants does not hold. method Introduced an adjunction inequality for a specific spatial refinement in kCP2. result An adjunction inequality holds for the s-version of the Sq1-refinement in kCP2. Refines Khovanov homology using stable homotopy theory.
problem Khovanov homology needs refinement.
method Stable homotopy refinement approach.
result Stable homotopy refinement of Khovanov homology constructed.
We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…
Refines neural network predictions using background knowledge for improved accuracy.
problem Compensate for lack of labeled data in neural networks.
method Introduces differentiable refinement functions and Iterative Local Refinement (ILR) algorithm to refine predictions efficiently and accurately.
result ILR finds competitive results in MNIST addition task and refines predictions on complex SAT formulas.
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.
Refines Khovanov homology for knots with involution.
problem Detecting mutations in knots with an involution.
method Introduces a triply-graded theory with two filtrations.
result Shows the refinement can detect mutation.
In a previous paper we constructed a spectrum-level refinement of Khovanov homology. This refinement induces stable cohomology operations on Khovanov homology. In this paper we show that these cohomology operations commute with cobordism maps on Khovanov homology. As a consequence we obtain a refinement of Rasmussen's …
New homotopy refinements for tangle invariants defined.
problem Stable homotopy refinements for tangle invariants.
method Defined stable homotopy refinements of Khovanov's arc algebras and tangle invariants.
result Stable homotopy refinements of Khovanov's arc algebras and tangle invariants defined.
New homotopy refinements for tangle invariants.
problem Stable homotopy refinements for tangle invariants.
method Refined Khovanov and Chen-Khovanov spectra.
result Induces refinements of platform algebras and invariants.
Refined 3D index uses surgery and gradings to distinguish 3-manifolds.
problem Distinguishing 3-manifolds and gauge theories phases.
method Dehn surgery presentation, ideal triangulation, and enhanced flavor symmetries.
result Invariance of refined index under various transformations.
The paper refines large N duality for knots using M-theory and string theory.
problem Understanding refined Chern-Simons invariants of knots.
method Formulating large N duality in refined Chern-Simons theory with torus knots, studying refined BPS states in M-theory, and relating to Type IIA string theory.
result The duality predicts graded dimensions of cohomology groups of moduli spaces of M2-M5 bound states associated to torus knots in the resolved conifold.
Refines deep generative models to improve data density precision.
problem Achieving precise representation of data probability density in deep models.
method Iterated generative modeling to refine latent space, addressing topological obstructions.
result Latent Space Refinement (LaSeR) protocol improves generative model precision.
Established a stable cohomotopy refinement for Pin(2) monopole invariants.
problem Refining monopole invariants for Pin(2) structures.
method Adapted Bauer-Furuta's Seiberg-Witten refinement method to Pin(2) monopole invariants.
result Connected sum formula for the refined invariants.
Refined 1-cocycle for knots helps quantify isotopies.
problem Quantify knot isotopies using refined tangle equations.
method Refined combinatorial 1-cocycle for regular isotopies of knots.
result Refined tangle equations provide quantitative knot information.
Braverman and Kappeler introduced a refinement of the Ray-Singer analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold. We study this notion and improve the Braverman-Kappeler theorem comparing the refined analytic torsion with Farber-Turaev refinement of the combinatorial torsion. …
EGR refines and assesses protein complex structures.
problem Improving the accuracy of protein complex 3D structures for drug discovery.
method E(3)-equivariant graph neural network (GNN) for multi-task refinement and assessment.
result EGR achieves state-of-the-art performance in refining and assessing protein complexes.
A novel framework refines diffusion models iteratively for better downstream reward optimization.
problem Optimizing reward functions during inference of diffusion models.
method Iterative refinement process with noising and reward-guided denoising steps.
result Superior empirical performance in protein and DNA design.
A new framework forecasts implied volatility surfaces by separating learning and refinement stages.
problem Forecasting implied volatility surfaces is challenging due to stochastic future surfaces and static no-arbitrage constraints.
method Decoupled generative refinement framework using a conditional diffusion model and SAAM for surface refinement.
result The framework improves forecasting accuracy and reduces static no-arbitrage violations.
Formula conjectured for refined SU(3) Vafa-Witten invariants of surfaces.
problem Calculating refined SU(3) Vafa-Witten invariants for smooth surfaces.
method Proved modularity transformation and used Mochizuki's formula and Maulik-Thomas's definition.
result Conjectured formula satisfies refined S-duality and verified in examples.
Study uses AI to refine loan assessments, improving credit default predictions.
problem Improving credit default prediction accuracy using AI-refined text.
method Comparative analysis of human-written and AI-refined loan assessments using deep learning techniques.
result AI-refined texts significantly enhance credit default predictions, especially when combined with structured data.
Let E be a flat complex vector bundle over a closed oriented odd dimensional manifold M endowed with a flat connection ∇. The refined analytic torsion for (M,E) was defined and studied by Braverman and Kappeler. Recently Mathai and Wu defined and studied the analytic torsion for the twisted de Rham complex…
The refined analytic torsion, defined by M. Braverman and T. Kappeler on closed manifolds, can be viewed as a refinement of the Ray-Singer torsion, since it is a canonical choice of an element with Ray-Singer norm one, in case of unitary representations. The complex phase of the refinement is given by the rho-invariant…
Refined BN-S model improves crude oil hedging with machine learning.
problem Finding optimal hedging strategy for commodity markets.
method Implemented a refined Barndorff-Nielsen and Shephard model with machine learning algorithms.
result The refined model performs better than the classical BN-S model.
Improved inference and learning in directed belief networks through iterative refinement of the approximate posterior.
problem Limited capacity of recognition networks constrains the representational power and increases variance of Monte Carlo estimates.
method Iterative refinement procedure to enhance the approximate posterior of the recognition network.
result Training with the refined posterior is competitive with state-of-the-art methods and improves effective sample size and gradient estimates.
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the underlying data distribution setting where connections to maximal marginal diver…
Refined invariants for 4D 2-handlebodies, linking quantum groups and cohomology.
problem Constructing and studying new invariants for 4D 2-handlebodies.
method Defining invariants for pairs (W,ω), using unimodular ribbon Hopf coalgebras. result Decomposition formulas for original invariants in terms of refined ones.
We construct a canonical element, called the refined analytic torsion, of the determinant line of the cohomology of a closed oriented odd-dimensional manifold M with coefficients in a flat complex vector bundle E. We compute the Ray-Singer norm of the refined analytic torsion. In particular, if there exists a flat Herm…
Quantifies scalar curvature under C0 convergence, proving a refined version in all dimensions.
problem Proving a refined quantitative bound for scalar curvature under C0 convergence. method Established the refined quantitative bound in all dimensions using smoothing techniques.
result Established the refined quantitative bound for scalar curvature in all dimensions.
Inspired by the work of Boris Vertman on refined analytic torsion for manifolds with boundary, in this paper we extend the construction of the Cappell-Miller analytic torsion to manifolds with boundary. We also compare it with the refined analytic torsion on manifolds with boundary. As a byproduct of the gluing formula…
Improved graph embedding through refined linear transformation and community recovery.
problem Identifying meaningful latent communities in graph data.
method Refined graph encoder embedding via linear transformation, self-training, and latent community recovery.
result Improved vertex embedding and better decision boundaries for vertex classification.
We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action. We give an explicit solution of the theory, in terms of a one-parameter refi…
A bicategory approach to differential cohomology is presented. Based on the axioms of Bunke-Schick, a symmetric monoidal groupoid is associated to differential refinements of cohomology theories. It is proven that such differential refinements are unique up to equivalence of the corresponding symmetric monoidal groupoi…
This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an…
Refined theorem on linear perturbations with applications in singularity theory and optimization.
problem Linear perturbations and their implications in singularity theory and optimization.
method New perspective of Hausdorff measures for refined transversality theorem.
result Applications in singularity theory and optimization.
We prove a refined Kato inequality for closed and coclosed differential (p,q) forms on a Kahler manifold.
Graph neural networks refine speaker embeddings for better session-level diarization.
problem Local speaker distinction in meeting sessions using deep embeddings.
method Graph Neural Networks (GNNs) refine speaker embeddings using session-level structural information.
result Spectral clustering on refined embeddings outperforms original embeddings significantly.
IterefinE combines KG refinement with embeddings to improve KG quality.
problem Noisy Knowledge Graphs lead to poor performance in downstream tasks.
method Iterative KG refinement using embeddings and inference rules.
result Improved KG refinement leading to higher F1 scores.
For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation. This new invariant can be viewed as an analytic counterpart of the refined combina…
Proposes a new Hodge conjecture in Bott-Chern cohomology.
problem Hodge conjecture in Bott-Chern cohomology.
method Characterization of real holomorphic chains, atomic section theory, refined Bott-Chern classes.
result Proof of a new Hodge conjecture in Bott-Chern cohomology.
We establish refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator. Our main result is a general expression which gives the value of the constants appearing in the refined inequalities. These consta…
Improved anti-cancer drug sensitivity prediction using REFINED CNN ensemble learning.
problem Challenges in predicting anti-cancer drug sensitivity for individual cell lines.
method Using REFINED CNN, which represents high-dimensional vectors as compact 2D images with spatial correlations, and building ensembles of these models.
result Ensemble approaches significantly improve drug sensitivity prediction performance compared to single models.
AURA: Adaptive Uncertainty-aware Refinement for LLM-as-a-Judge Auditing
problem Auditing LLM-as-a-Judge decisions
method Adaptive uncertainty-aware refinement
result Human-consistent signal learning and evidence propagation
In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without boundary. We now derive a gluing formula for our construction, which can be viewed as…
We work in the reduced SU(N,K) modular category as constructed recently by Blanchet. We define spin type and cohomological refinements of the Turaev-Viro invariants of closed oriented 3-manifolds and give a formula relating them to Blanchet's invariants. Roberts' definition of the Turaev-Viro state sum is exploited. Fu…
Refines Kronheimer-Mrowka's invariant for 4-manifolds with specific boundary conditions.
problem Constructing a refined invariant for 4-manifolds with contact boundaries.
method Uses Kronheimer-Mrowka's invariant and Furuta's finite dimensional approximation.
result Refined invariant for 4-manifolds with H1(X,∂X;R)=0. Method retrieves similar fashion items from images and text, enabling style refinement.
problem Lack of intuitive, interactive refinement in search engines for fashion items.
method Joint visual-textual embedding training, Mini-Batch Match Retrieval, attribute extraction.
result Improved performance in multimodal style search, demonstrated through benchmark.
Automated refinement of sensor labels improves process mining models in smart homes.
problem Finding precise labels for sensor events in smart home data.
method Automated generation of event label refinements based on time attributes.
result Automatically refined labels lead to more insightful process models.
Refines Hurwitz numbers with a two-parameter theory.
problem Understanding polynomial structure and tropicalization of b-Hurwitz numbers. method Introducing CJT-refinement of symmetric functions on Fock space.
result Derives tropicalization of b-Hurwitz numbers and solves an open problem.