arXiv research

We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space $X$ is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the …

Paper proposes a perfect-fit model for CDO tranches.

This is an exposition of results on the existence problem of $π_1$-injective immersed and embedded surfaces in graph-manifolds, and also of nonpositively curved metrics on graph-manifolds, obtained by different authors. The results are represented from a unified point of view based on the notion of compatible cohomolog…

Reduces Poisson manifolds with Hamiltonian Lie algebroids.

We define spin-c prequantization of a symplectic manifold to be a spin-c structure and a connection which are compatible with the symplectic form. We describe the cutting of an S^1-equivariant spin-c prequantization. The cutting process involves a choice of a spin-c prequantization for the complex plane. We prove that …

We show that a model of chain complex of the free loop space of a $C^\infty$-manifold, which is proposed in arxiv:1404.0153, admits an action of a certain dg operad. This is a chain level structure under the Chas-Sullivan BV structure on loop space homology. Our dg operad is a variant of the cacti operad, and we introd…

New framework tackles bi-level optimization without LLS condition.

A new GNN framework for graphs with heterophily.

The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce the $\textit{inflation technique}$ for tackling this problem. An inflation of a…

Maps self-duality in little disks operad to framed manifolds.

Notions of compatible and almost compatible pseudo-Riemannian metrics, which are motivated by the theory of compatible (local and nonlocal) Poisson structures of hydrodynamic type and generalize the notion of flat pencil of metrics, are introduced and studied.

We devise an algorithm which allows one to count the number of Killing vectors for a Lorentzian manifold of dimension 3. Our algorithm relies on the principal traces of powers of the Ricci tensor and branches intricately according to the values of differential invariants arising from the compatibility conditions of the…

Defines compatibility between Jacobi structures and pseudo-Riemannian metrics on Jacobi algebroids.

We show in this paper that the correspondence between $2$-term representations up to homotopy and $\mathcal{VB}$-algebroids, established by Gracia-Saz and Mehta, holds also at the level of morphisms. This correspondence is hence an equivalence of categories. As an application, we study foliations and distributions on a…

Study rigidity of Hamiltonians near a minimum in symplectic and magnetic settings.

The paper characterizes compatible linear connections on 3D Finsler manifolds.

Cross-modal hashing has been receiving increasing interests for its low storage cost and fast query speed in multi-modal data retrievals. However, most existing hashing methods are based on hand-crafted or raw level features of objects, which may not be optimally compatible with the coding process. Besides, these hashi…

Framework controls uncertainty in LLMs without labels or probabilities.

The paper proposes reusable network components by making them compatible across tasks.

Geometric deformations preserve post-Lie algebra structure in regularity structures.

New algorithm for learning preferences in decentralized matching markets reduces regret to logarithmic levels.

Though neural network models demonstrate impressive performance, we do not understand exactly how these black-box models make individual predictions. This drawback has led to substantial research devoted to understand these models in areas such as robustness, interpretability, and generalization ability. In this paper,…

The paper studies properties of group relations induced by compatible coarse structures.

Derdzinski and Shen's theorem on the restrictions posed by a Codazzi tensor on the Riemann tensor holds more generally when a Riemann-compatible tensor exists. Several properties are shown to remain valid in this broader setting. Riemann compatibility is equivalent to the Bianchi identity of the new "Codazzi deviation …

Compatibility equations adapted to magnetic geometry.

The causal compatibility question asks whether a given causal structure graph -- possibly involving latent variables -- constitutes a genuinely plausible causal explanation for a given probability distribution over the graph's observed variables. Algorithms predicated on merely necessary constraints for causal compatib…

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additi…

Overparameterized deep networks have the capacity to memorize training data with zero \emph{training error}. Even after memorization, the \emph{training loss} continues to approach zero, making the model overconfident and the test performance degraded. Since existing regularizers do not directly aim to avoid zero train…

Study extends null distance concept to Lorentzian length spaces for spacetime analysis.

New methods reveal compatible liquid crystal phases in 3D.

We disprove the generalized Chern-Hamilton conjecture on the existence of critical compatible metrics on contact $3$-manifolds. More precisely, we show that a contact $3$-manifold $(M,α)$ admits a critical compatible metric for the Chern-Hamilton energy functional if and only if it is Sasakian or its associated Reeb fl…

We present a new approach to harmonic analysis that is trained to segment music into a sequence of chord spans tagged with chord labels. Formulated as a semi-Markov Conditional Random Field (semi-CRF), this joint segmentation and labeling approach enables the use of a rich set of segment-level features, such as segment…

A linear connection on a Finsler manifold is called compatible to the metric if its parallel transports preserve the Finslerian length of tangent vectors. Generalized Berwald manifolds are Finsler manifolds equipped with a compatible linear connection. Since the compatibility to the Finslerian metric does not imply the…

Some general properties of compatible Poisson brackets of hydrodynamic type are discussed, in particular: (1) an invariant differential-geometric criterion of the compatibility based on the Nijenhuis tensor; (2) the Lax pair with a spectral parameter governing compatible Poisson brackets in the diagonalizable case; (3)…

The construction of gauge theories beyond the realm of Lie groups and algebras leads one to consider Lie groupoids and algebroids equipped with additional geometrical structures which, for gauge invariance of the construction, need to satisfy particular compatibility conditions. This paper analyzes these compatibilitie…

We show that well known structures on Lie algebroids can be viewed as Nijenhuis tensors or pairs of compatible tensors on Courant algebroids. We study compatibility and construct hierarchies of these structures.

New proof for unique semi-symmetric compatible linear connection on Finsler manifolds.

Defines odd Khovanov homology via categorification of q-Schur algebra.

A local Riemann-Hilbert correspondence for tame meromorphic connections on a curve compatible with a parahoric level structure will be established. Special cases include logarithmic connections on G-bundles and on parabolic G-bundles, where G is a complex reductive group. The corresponding Betti data involves pairs (M,…

New method improves compatibility of risk stratification models without sacrificing accuracy.

Given the Riemann, or the Weyl, or a generalized curvature tensor K, a symmetric tensor $b_{ij}$ is named `compatible' with the curvature tensor if $b_i{}^m K_{jklm} + b_j{}^m K_{kilm} + b_k{}^m K_{ijlm} = 0$. Amongst showing known and new properties, we prove that they form a special Jordan algebra, i.e. the symmetriz…

The study examines backward compatibility issues in ML systems, especially with noisy data.

Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are impose…

We will introduce two notions of compatibility bettwen pseudo-Riemannian metric and Poisson structure using the notion of contravariant connection introduced by Fernandes R. L., we will study some proprities of manifold endowed with such compatible structures an we will give some examples.

In the literature different concepts of compatibility between a projective structure and a conformal structure on a differentiable manifold are used. In particular compatibility in the sense of Weyl geometry is slightly more general than compatibility in the Riemannian sense. An often cited paper [Ehlers-Pirani-Schild:…

Extends ONNX for quantized neural networks with new formats and operators.

A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.

AI systems are being deployed to support human decision making in high-stakes domains. In many cases, the human and AI form a team, in which the human makes decisions after reviewing the AI's inferences. A successful partnership requires that the human develops insights into the performance of the AI system, including …