arXiv research

CoRe method improves time series forecasting coherency without strict constraints.

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …

Defines coherent manifolds and their quantum applications.

Generates coherent storybooks from plain text using diffusion models.

New metric $m$-coherence measures gradient alignment during training, revealing surprising memorization patterns.

Generates music with coherent rhythm, chords, and melody using LSTM models.

A group is coherent if all its finitely generated subgroups are finitely presented. In this article we provide a criterion for positively determining the coherence of a group. This criterion is based upon the notion of the perimeter of a map between two finite 2-complexes which is introduced here. In the groups to whic…

Model criticism tool evaluates text coherence and structure in generated long-form text.

Project aims to improve coherence in language generation models.

Extends coherence results to one-relator products of locally indicable groups.

This paper generalizes L2 cohomology theory for complex manifolds.

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space…

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training …

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze t…

New coherence parameter for GNNs with Fourier measurements improves signal recovery.

The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this as…

For arbitrary quantizable compact Kaehler manifolds, relations between the geometry given by the coherent states based on the manifold and the algebraic (projective) geometry realised via the coherent state mapping into projective space, are studied. Polar divisors, formulas relating the scalar products of coherent vec…

Uniform negative immersions prove coherence of one-relator groups.

This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category of coherent sheaves equivariant under an action of an algebraic …

The paper defines and analyzes coherent and squeezed states on manifolds and their quantization.

The Wiener chaos approach to interest rate modelling arises from the observation that the pricing kernel admits a representation in terms of the conditional variance of a square-integrable random variable, which in turn admits a chaos expansion. When the expansion coefficients factorise into multiple copies of a single…

Let M be a K3 surface or an even-dimensional compact torus. We show that the category of coherent sheaves on M is independent from the choice of the complex structure, if this complex structure is generic.

The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.

New $L_\infty$ liftings derived from Chern-Simons classes for coherent sheaves.

GenInSAR uses CNNs to filter InSAR phase and estimate coherence without supervision.

Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.

The paper explores non-convex risk measures and their characterizations.

TOAD-GAN generates coherent game levels from a single example.

The paper establishes a connection between different risk measures and their risk contributions.

On certain manifolds, the phase which appears in the scalar product of two coherent state vectors is twice the symplectic area of the geodesic triangle determined by the corresponding points on the manifold and the origin of the system of coordinates. This result is proved for compact Hermitian symmetric spaces using t…

The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert space and a simple geometric interpretation of Calabi's diastasis follows.

We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.

Optimal hashing embeddings reduce linear least squares solving time.

We show that any one-relator group $G=F/\langle\langle w\rangle\rangle$ with torsion is coherent -- i.e., that every finitely generated subgroup of $G$ is finitely presented -- answering a 1974 question of Baumslag in this case.

The paper develops residue currents for cohesive modules and proves a generalized Poincaré-Lelong formula.

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equati…

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio cannot be optimized under any coherent measure on that sample, and the risk measure …

This paper studies non-asymptotic model selection for the general case of arbitrary design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence---termed as the wor…

Paper constructs Chern character for coherent sheaves.

The paper constructs minimal coherent filling pairs on surfaces.

Text documents are structured on multiple levels of detail: individual words are related by syntax, but larger units of text are related by discourse structure. Existing language models generally fail to account for discourse structure, but it is crucial if we are to have language models that reward coherence and gener…

We prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always contains a rank 2 free group.

Paper defines dynamical coherence for flows and proves it under specific conditions.

Develops equivariant Chern characters for coherent sheaves with group actions.

We illustrate relationships between classical kernel-based dimensionality reduction techniques and eigendecompositions of empirical estimates of reproducing kernel Hilbert space (RKHS) operators associated with dynamical systems. In particular, we show that kernel canonical correlation analysis (CCA) can be interpreted…

In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains invisible when only the traditional analysis is employed. We define estimators which c…

We study a space of coherent risk measures M_phi obtained as certain expansions of coherent elementary basis measures. In this space, the concept of ``Risk Aversion Function'' phi naturally arises as the spectral representation of each risk measure in a space of functions of confidence level probabilities. We give nece…

Enhances multimodal generation with Normalizing Flows and correlation analysis.