Study finds almost contact structures in thermal QCD-like theories at intermediate coupling.
problem Understanding (Almost) Contact Structures in thermal QCD-like theories.
method Explicitly obtained (Almost) Contact Structures and SU(3) structures.
result Subspaces of C3S and AC3S are not mutually 'N-path connected' in the Infra-Red.
This paper analyzes microstructure dynamics in coupled markets using CFMMs.
problem Quantifying contributions of CFMMs to market dynamics in coupled markets.
method Examined constant function market makers (CFMMs) in coupled markets, focusing on basket inflation/deflation.
result CFMMs contribute significantly to basket inflation/deflation in coupled markets.
Study of M-theory dual of thermal QCD-like theories at intermediate coupling.
problem Missing top-down holographic dual for thermal QCD-like theories at intermediate 't Hooft coupling.
method Analysis of O(R4) corrections and O(lp6) corrections in the MQGP background. result Discovery of O(R4) corrections and G-structure classification of underlying geometries. We study the moduli space of torsion-free G2-structures on a fixed compact manifold, and define its associated universal intermediate Jacobian J. We define the Yukawa coupling and relate it to a natural pseudo-Kahler structure on J. We consider natural Chern-Simons type functionals, whose critical points give associati…
Survey of geometric flows from unified string theories.
problem None explicitly stated, but related to understanding geometric flows in string theories.
method Survey of geometric flows in various geometries (complex, almost-complex, symplectic) motivated by string theories.
result Intermediate flows between Ricci and Kähler-Ricci flows, often coupled to additional fields.
For many natural language processing (NLP) tasks the amount of annotated data is limited. This urges a need to apply semi-supervised learning techniques, such as transfer learning or meta-learning. In this work we tackle Named Entity Recognition (NER) task using Prototypical Network - a metric learning technique. It le…
Consider a multiperiod optimal transport problem where distributions μ0,…,μn are prescribed and a transport corresponds to a scalar martingale X with marginals Xt∼μt. We introduce particular couplings called left-monotone transports; they are characterized equivalently by a no-crossing property…
Zero-shot learning (ZSL) is a framework to classify images belonging to unseen classes based on solely semantic information about these unseen classes. In this paper, we propose a new ZSL algorithm using coupled dictionary learning. The core idea is that the visual features and the semantic attributes of an image can s…
Framework learns stochastic dynamics from endpoint and intermediate distributions using soft energy constraints.
problem Learning stochastic dynamics from endpoint and intermediate distributional observations.
method Formulates generation as a McKean-Vlasov control problem with soft energy constraints, solving it through FBSDE.
result Model learns coherent stochastic trajectories matching prescribed marginal laws.
Variational autoencoders (VAEs), that are built upon deep neural networks have emerged as popular generative models in computer vision. Most of the work towards improving variational autoencoders has focused mainly on making the approximations to the posterior flexible and accurate, leading to tremendous progress. Howe…
Study on rigidity with non-negative intermediate curvature on low-dimensional manifolds.
problem Extending non-existence theorem of positive scalar curvature to product manifolds.
method Introduced intermediate curvature and studied rigidity conditions.
result Rigidity when intermediate curvature is non-negative in low dimensions.
Preserves positive intermediate curvature on manifolds.
problem Obstructs positive intermediate curvature on partial tori.
method Shows smooth interpolation of metrics with positive intermediate curvature.
result Proves non-existence of certain manifolds with positive intermediate curvature.
The study connects manifold topology to metrics with positive intermediate curvature.
problem Understanding the relationship between manifold topology and metrics with positive intermediate curvature.
method Formulated a conjecture and proved it for specific dimensions and conditions.
result Closed, aspherical 6-manifolds cannot admit metrics with positive 4-intermediate curvature.
For a pair of points in a smooth closed convex planar curve γ, its mid-line is the line containing its mid-point and the intersection point of the corresponding pair of tangent lines. It is well known that the envelope of the mid-lines (EML) is formed by the union of three affine invariants sets: Affine Envelope Sy…
New rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
problem Understanding the structure of manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
method Recovering stronger topological rigidity results using higher intermediate Ricci curvatures and nontrivial fundamental groups.
result Stronger topological rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.
Highly accurate potential energy surfaces are of key interest for the detailed understanding and predictive modeling of chemical systems. In recent years, several new types of force fields, which are based on machine learning algorithms and fitted to ab initio reference calculations, have been introduced to meet this r…
Study on spaces of metrics with intermediate curvature bounds.
problem Understanding spaces of metrics with lower bounds on intermediate curvatures.
method Analyzing spaces of Riemannian metrics with specific curvature bounds on high-dimensional Spin-manifolds.
result Spaces of metrics with positive p-curvature and k-positive Ricci curvature have non-trivial homotopy groups.
Proves metrics with positive intermediate Ricci curvature on complex manifolds.
problem Establishing metrics with positive intermediate Ricci curvature on complex manifolds.
method Canonical variation and surgery techniques.
result Existence of metrics with positive intermediate Ricci curvature on various examples.
Extends Perelman's theorem to positive intermediate curvature conditions.
problem Positive intermediate curvature conditions and their implications.
method Generalization of Perelman's gluing theorem to positive intermediate curvature conditions.
result Observer moduli space can have non-trivial higher homotopy groups.
The study proves that certain manifolds with boundary cannot have metrics with positive intermediate curvatures.
problem Proving the nonexistence of metrics with positive intermediate curvatures on manifolds with boundary.
method Curvature obstruction theorems for manifolds with boundary.
result Topologically nontrivial compact manifolds with boundary cannot have metrics of positive m-intermediate curvature if the boundary is m-convex. Study finds metrics with positive intermediate Ricci curvature on specific low-dimensional manifolds.
problem Existence of invariant metrics with positive intermediate Ricci curvature on low-dimensional cohomogeneity one manifolds.
method Construction of invariant metrics with positive intermediate Ricci curvature on specific manifolds.
result Invariant metrics with positive 4th-intermediate Ricci curvature exist but not for 3rd-intermediate Ricci curvature on certain manifolds.
Sharp dimension constraints for positive intermediate curvature metrics are established.
problem Proving sharp dimension constraints for metrics with positive intermediate curvature.
method Constructing counterexamples and extending rigidity results.
result Sharp dimension constraints for positive intermediate curvature metrics are established.
This paper introduces a novel approach to measuring privacy risks in deep computer vision models based on intermediate outputs.
problem The exposure of intermediate results in hidden layers of deep computer vision models poses significant privacy concerns.
method The approach leverages Degrees of Freedom (DoF) to evaluate the amount of information retained in each layer and combines this with the rank of the Jacobian matrix to assess sensitivity to input variations.
result The proposed framework provides deeper insights into privacy risks associated with intermediate representations without requiring adversarial attack simulations.
Constructs explicit solutions to Spin(7)-structures gradient flow.
problem Finding explicit solutions to Spin(7)-structures gradient flow.
method Expressed Spin(7)-torsion tensor and gradient flow in terms of torsion forms; used these formulae to find solutions.
result Found explicit solutions including a shrinking soliton on SU(3) and another on a T7-bundle over S1. The paper proves manifold splitting theorems with nonnegative intermediate curvature.
problem Proving rigidity results for manifolds with nonnegative intermediate curvatures.
method New recursion theorem for spectral intermediate curvatures and cylindrical splitting theorems.
result Smooth metrics with uniformly positive intermediate curvature constructed.
A new method solves American put options with high accuracy and speed.
problem Solving American put options with high accuracy and speed.
method Adaptive fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme.
result The method provides a more accurate solution and better performance in terms of computational speed.
A framework to explain decoder-only sequence classification models using intermediate predictions.
problem Explaining predictions of decoder-only sequence classification models.
method Progressive Inference framework with Single Pass-Progressive Inference and Multi Pass-Progressive Inference methods.
result Significantly better attributions compared to prior work on text classification tasks.
Polyhedral semantics for intermediate logics; Nerve Criterion ensures completeness.
problem Characterize polyhedrally-complete intermediate logics.
method Developed Nerve Criterion to characterize polyhedrally-complete logics combinatorially.
result Nerve Criterion provides a necessary and sufficient condition for polyhedrally-completeness.
We use a local argument to prove if an r-dimensional torus acts isometrically and effectively on a connected n-dimensional manifold which has positive kth-intermediate Ricci curvature at some point, then r≤⌊2n+k⌋. This symmetry rank bound generalizes those established by Gr…
We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.
Knowledge distillation (KD) is a popular method for reducing the computational overhead of deep network inference, in which the output of a teacher model is used to train a smaller, faster student model. Hint training (i.e., FitNets) extends KD by regressing a student model's intermediate representation to a teacher mo…
A cost-effective framework for gradual domain adaptation using multifidelity.
problem Degrading prediction performance due to large domain distance.
method Combines multifidelity and active domain adaptation.
result Improves prediction performance with reduced sample cost.
Given a completely arbitrary surface, whether or not it has bounded curvature, or even whether or not it is complete, there exists an instantaneously complete Ricci flow evolution of that surface that exists for a specific amount of time [GT11]. In the case that the underlying Riemann surface supports a hyperbolic metr…
Gradual domain adaptation improves model transfer between domains with intermediate training.
problem Challenges in unsupervised domain adaptation when distribution shifts are large.
method Gradual self-training using intermediate domains along the Wasserstein geodesic.
result GOAT framework generates intermediate domains for improved adaptation.
Study shows Gromov's Betti number bound fails for certain intermediate Ricci curvatures.
problem Gromov's Betti number bound for sectional curvature bounded below does not hold for intermediate Ricci curvatures.
method Established a surgery result for Riemannian metrics with Rick>0 and showed failure of Gromov's bound for specific ranges of k. result Gromov's Betti number bound fails for Rick>0 when ⌊n/2floor+2≤k≤n−1. Study analyzes financial intermediation costs in decentralized lending protocols.
problem Understanding the cost of financial intermediation in decentralized lending protocols.
method Analysis of publicly available data on rates, supply, borrow activity, and accounts.
result Ex-post margins are 1% and lower for stablecoin markets.
Intermediate logic of all convex polyhedra is axiomatized.
problem Defining and axiomatizing intermediate logic for convex polyhedra.
method Using Jankov-Fine formulas, classical polyhedral geometry, and p-morphic images to establish completeness.
result A finite axiomatisation of PL for all convex polyhedra.
Study estimates heterogeneous principal causal effects with binary treatments and intermediate variables.
problem Estimating subgroup effects within strata defined by potential values of an intermediate variable.
method Proposes a framework for estimating and forming confidence intervals for heterogeneous principal causal effects under principal ignorability assumption. Develops several estimators with varying robustness properties.
result Established large-sample theory and analyzed bias contributions of each approach.
Log-Sobolev inequality proven for submanifolds in specific types of manifolds.
problem Proving Log-Sobolev inequality for submanifolds in asymptotic non-negative intermediate Ricci curvature manifolds.
method Extending previous results, proving inequality for submanifolds in specific types of manifolds.
result Sharp Log-Sobolev inequality proven for submanifolds in complete non-compact Riemannian manifolds with asymptotic non-negative intermediate Ricci curvature and Euclidean volume growth.
Optimizes transport on submanifolds for curvature inequalities.
problem Proving Michael-Simon-Sobolev inequalities in manifolds with intermediate Ricci curvature bounds.
method Generalizes optimal transport theory to submanifolds and applies to curvature inequalities.
result Proves a variant of the Michael-Simon-Sobolev inequality in manifolds with nonnegative intermediate Ricci curvatures.
Extends metric properties over surgeries to higher codimensions.
problem Extending metrics of positive scalar curvature over surgeries in higher codimensions.
method Generalizes Gromov-Lawson, Schoen-Yau, and Walsh's construction to (p,n)-intermediate scalar curvature. result Shows infinitely many path components for certain metrics on (4n−1)-manifolds. Learning, taking into account full distribution of the data, referred to as generative, is not feasible with deep neural networks (DNNs) because they model only the conditional distribution of the outputs given the inputs. Current solutions are either based on joint probability models facing difficult estimation proble…
Proves positive Euler characteristic for certain manifolds with positive second intermediate Ricci curvature.
problem Hopf's conjecture on positive sectional curvature and its failure under relaxed conditions.
method Non-trivial extension of the Four Periodicity Theorem to higher degrees.
result Proves positive Euler characteristic for specific manifolds with positive second intermediate Ricci curvature.
Study improves understanding of Ricci curvature in manifolds.
problem Understanding Ricci curvature in manifolds with specific assumptions.
method Exploring m-intermediate Ricci curvature and proving comparison theorems.
result Stable weighted slicing in manifolds with non-negative m-intermediate Ricci curvature has almost non-negative Ricci curvature.
The paper establishes general results in Lorentzian optimal transport theory.
problem Establishing strong duality and optimality conditions in Lorentzian optimal transport.
method Providing non-trivial assumptions on measures, characterizing optimality, and proving regularity results.
result Regularity results for c-convex functions and (weak) Kantorovich potentials do not extend to the Lorentzian setting, but under suitable assumptions, they are locally semconvex. It is well known that (stochastic) gradient descent has an implicit bias towards flat minima. In deep neural network training, this mechanism serves to screen out minima. However, the precise effect that this has on the trained network is not yet fully understood. In this paper, we characterize the flat minima in linea…
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm framework, named Hierarchical Measure Group and Approximate System (HMGAS), nickn…
Study manifolds with positive intermediate Ricci curvature and large symmetry rank.
problem Closed, simply connected manifolds with positive 2nd-intermediate Ricci curvature and large symmetry rank.
method New tools for studying isometric actions on closed manifolds with positive kth-intermediate Ricci curvature, including isotropy rank lemma, symmetry rank bound, and connectedness principle.
result Even dimensional manifolds with large symmetry rank must have trivial odd degree integral cohomology and are either spheres or complex projective spaces.