arXiv research

This work merges 3-anchored bundles into 3-Lie algebroids.

A pre-Lie algebroid is an anchored bundle provided with an almost Lie bracket such that the anchor is compatible with the Lie bracket of vector fields. We firstly show how most geometrical structures intensively studied in the framework of Lie algebroid can easily be extended in the pre-Lie algebroid context. The princ…

Universal construction for Lie algebroids from anchored bundles with connections.

First, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

Under appropriate assumptions, we generalize the concept of linear almost Poisson struc- tures, almost Lie algebroids, almost differentials in the framework of Banach anchored bundles and the relation between these objects. We then obtain an adapted formalism for mechanical systems which is illustrated by the evolution…

This paper is devoted to the framework of direct limit of anchored Banach bundles over a convenient manifold which is a direct limit of Banach manifold. In particular we give a criterion of integrability for distributions on such convenient manifolds which are locally direct limits of particular sequences of Banach anc…

We introduce the category of generalized Courant algebroids and show that it admits a free object on any anchored vector bundle. The free Courant algebroid is built from two components: the generalized Courant algebroid associated to a symmetric Leibniz algebroid and the free symmetric Leibniz algebroid on an anchored …

Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessary null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension of the bundle and the new anchor allows a Lie algebroid bracket. A cohomo…

We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new in…

We express any Courant algebroid bracket by means of a metric connection, and construct a Courant algebroid structure on any orthogonal Whitney sum $E\oplus C$ where E is a given Courant algebroid and C is a flat, pseudo- Euclidean vector bundle. Then, we establish the general expression of the bracket of a transitive …

We give numerous examples of almost Lie algebroids arising as Dirac structures in pre-Courant algebroids, e.g. from twisted Poisson structures, as well as from twisted actions of a Lie algebra. We moreover define a cohomology for them, motivated by a Q-structure, that is trivial for (bundles of) Lie algebras but charac…

Adaptive anchor methods improve multi-modal learning by balancing intra-modal and inter-modal information.

In this note we prove that, for a vector bundle $E$ over a manifold $M$, a Dorfman bracket on $TM\oplus E^*$ anchored by $\operatorname{pr}_{TM}$ and with $E$ a vector bundle over $M$, is equivalent to a lift from $Γ(TM\oplus E^*)$ to linear sections of $TE\oplus T^*E\to E$, that intertwines the given Dorfman bracket w…

Interactive topic models with user-defined anchor words.

Private anchors affect how information is communicated and can improve or distort transmission.

A new method selects anchor words for better topic discovery in text corpora.

Anchors explain text model decisions by highlighting key words.

A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a compl…

LargeMvC-Net improves scalability of multi-view clustering.

Anchoring is a term used in psychology to describe the common human tendency to rely too heavily (anchor) on one piece of information when making decisions. A trading algorithm inspired by biological motors, introduced by L. Gil\cite{Gil}, is suggested as a testing ground for anchoring in financial markets. An exact so…

Δ-UQ uses anchoring to estimate uncertainty in models.

Paper explores anchoring for vision models, improving generalization and safety.

The main purpose of this note is the study of the total space of a holomorphic Lie algebroid $E$. The paper is structured in three parts. In the first section we briefly introduce basic notions on holomorphic Lie algebroids. The local expressions are written and the complexified holomorphic bundle is introduced. The se…

The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent space,and the reversal diffeomorphism. We show that the constructions which yie…

Language is dynamic, constantly evolving and adapting with respect to time, domain or topic. The adaptability of language is an active research area, where researchers discover social, cultural and domain-specific changes in language using distributional tools such as word embeddings. In this paper, we introduce the gl…

Horizontal endomorphisms, almost complex structures, vertical, horizontal and complete lifts on prolongation of a Lie algebroid are considered. Then using exact sequences, semisprays are constructed. Moreover, important geometrical objects such as classical distinguished connections, torsions and partial curvatures are…

A method to learn transition matrices without anchor points improves classifier performance.

This work is motivated by a result of Drinfeld on Poisson homogeneous spaces. For each Poisson manifold $P$ with a Poisson action by a Poisson Lie group $G$, we describe a Lie algebroid structure on the direct sum vector bundle $P \times {\frak g} \oplus T^*P$, where ${\frak g}$ is the Lie algebra of $G$. It is built o…

Market stability depends on a fundamental value anchor, not price crashes.

A new noise model for preferential Bayesian optimization using user anchors.

We generalize the notion of a Lie algebroid over infinite jet bundle by replacing the variational anchor with an N-tuple of differential operators whose images in the Lie algebra of evolutionary vector fields of the jet space are subject to collective commutation closure. The linear space of such operators becomes an a…

In this article, we continue the classification of finite type Gauss map surfaces in the Euclidean 3-space E3 with respect to the first fundamental form by studying a subclass of tubes, namely the anchor rings. We show that anchor rings are of infinite type Gauss map.

A new method resolves non-identifiability in reward modeling using anchor labels.

Anchor PCA improves robustness in multi-domain PCA.

New method improves continual learning by anchoring past knowledge.

Paper proposes an alternative to anchor points for learning with noisy labels.

A new method for efficient inference in sequential latent-variable models.

Anchor-TS uses median anchoring to improve online decision-making from offline data with distribution shift.

In topic modeling, many algorithms that guarantee identifiability of the topics have been developed under the premise that there exist anchor words -- i.e., words that only appear (with positive probability) in one topic. Follow-up work has resorted to three or higher-order statistics of the data corpus to relax the an…

Study improves predictive models for ICU data across hospitals.

ADA augments data using AR replicas for robust regression.

Develops a new framework for temporal anchoring in deep embedding spaces.

FALL improves local model training with anchor regularization.

New method shows spectral clustering is consistent with theoretical guarantees.

Task-assisted domain adaptation improves performance on synthetic-to-real image tasks.

Novel ternary structures reveal new interpretations of linear connections.

MultiPath predicts multi-modal future trajectories for better motion planning.

A framework visualizes embedding spaces of neural survival analysis models using anchor directions.