Theoretical work shows integrating coherent reasoning improves LLM performance and error correction.
problem Improving reasoning and error correction in large language models (LLMs) with few-shot prompting.
method Theoretical analysis and sensitivity experiments on transformer behavior with coherent reasoning and corrupted demonstrations.
result The transformer gains better error correction ability and more accurate predictions when coherent reasoning is integrated.
A new method uses denoising diffusion models to improve seismic data interpolation.
problem Improving the accuracy of seismic data interpolation to enhance imaging and interpretation.
method The approach combines denoising diffusion probabilistic models with coherence-corrected resampling strategies.
result The proposed method achieves superior performance and generalization to various missing patterns and noise levels.
Method guarantees coherent factuality for language model outputs in reasoning tasks.
problem Ensuring correctness of language model outputs in reasoning tasks.
method Developed a conformal-prediction-based method applied to subgraphs within a deducibility graph.
result Achieved coherent factuality across target coverage levels, 90% on stricter definition.
Paper proves noise-tolerant SSC using greedy methods under coherence conditions.
problem Proving noise-tolerant SSC using greedy methods under coherence conditions.
method Derives coherence-based sufficient conditions for correct neighbor identification using MP/OMP in the presence of bounded noise.
result MP/OMP succeed in identifying correct neighbors under certain noise levels, leading to higher clustering accuracy.
This work analyzes label embedding for large multiclass classification problems.
problem Label embedding for large multiclass classification problems.
method Analysis of label embedding in extreme multiclass classification, presenting an excess risk bound and showing a trade-off between computational and statistical efficiency.
result The statistical penalty for label embedding vanishes with sufficiently low coherence under the Massart noise condition.
Generative model improves wind field downscaling from coarse climate models.
problem Limited spatial resolution and biases in GCMs for wind energy studies.
method SerpentFlow for domain alignment and conditional fine-scale learning.
result Improved spatial coherence, inter-variable consistency, robustness under climate change.
In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence on…
This paper concerns orientability of moduli spaces of Spin(7)-instantons on compact 8-manifolds X with Spin(7)-structure for the Lie groups SU(m) and U(m), and of moduli spaces of coherent sheaves on Calabi-Yau 4-folds. Such orientations are needed to define enumerative invariants 'counting' Spin(7) instantons, o…
This paper studies the convergence behaviour of dictionary learning via the Iterative Thresholding and K-residual Means (ITKrM) algorithm. On one hand it is proved that ITKrM is a contraction under much more relaxed conditions than previously necessary. On the other hand it is shown that there seem to exist stable fixe…
Cohesion uses deep Koopman operators to generate long-range forecasts of chaotic dynamics.
problem Challenges in data-driven emulation of chaotic dynamics, especially long-range skill decay.
method Generative modeling with coherent priors estimated using reduced-order models.
result Superior long-range forecasting skill on chaotic systems, including climate dynamics.
Lagrangian data assimilation is a complex problem in oceanic and atmospheric modeling. Tracking drifters in large-scale geophysical flows can involve uncertainty in drifter location, complex inertial effects, and other factors which make comparing them to simulated Lagrangian trajectories from numerical models extremel…
This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters. They claimed that averages are inaccurate if they are incorrect or drift-outs. F…
Paper uses deep Q-network to correct eye movement artifacts in OCT volumes.
problem Unsupervised correction of inter-frame misalignments in OCT volumes due to eye movement artifacts.
method Dueling deep Q-network trained to maximize reward signals based on intensity-based image similarity metrics.
result Average normalized mutual information and correlation coefficient of 0.985 and 0.914, respectively.
Study shows class imbalance and temporal coherence impact solar flare analysis.
problem Class imbalance and temporal coherence in rare-event analysis.
method Experiments on SWAN-SF dataset, including data and model manipulations.
result Temporal coherence invalidates randomness assumption, impacting sampling practices.
The study analyzes and mitigates errors in PC-based causal discovery methods.
problem Errors in PC-based causal discovery methods can lead to incorrect graphs.
method The study introduces coherency scores to detect assumption violations and small sample errors in PC-based methods.
result The coherency scores can detect errors that other methods cannot, bridging between global and local error detection.
Defines coherent manifolds and their quantum applications.
problem Understanding quantum spaces and coherent states.
method Generalizes quantum field theory and Schrödinger equation solutions.
result Solves Schrödinger equation on coherent manifolds.
CoRe method improves time series forecasting coherency without strict constraints.
problem Noisy hierarchical time series data that doesn't perfectly adhere to aggregation constraints.
method Coherency Regularization using neural networks.
result Improved forecast accuracy and coherence, especially in noisy data scenarios.
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 …
Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.
problem Identifying and visualizing coherence among multiple time series.
method Fast spectral similarity based on cosine similarity metrics of Fourier-transformed signals and sparse time-frequency wavelet coherence.
result Scalable real-time system for low-latency inference and monitoring of inter-signal relationships.
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.
Paper constructs Chern character for coherent sheaves.
problem Chern character for coherent sheaves with values in Bott-Chern cohomology.
method Based on Block's fundamental construction, constructs Chern character.
result Proves Riemann-Roch-Grothendieck formula for coherent sheaves.
The paper constructs minimal coherent filling pairs on surfaces.
problem Finding minimal intersecting coherent filling pairs on surfaces.
method Geometric procedure starting from a torus filling pair.
result Construction of minimal intersecting coherent filling pairs on Sg for g≥3. 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 …
Paper defines dynamical coherence for flows and proves it under specific conditions.
problem Understanding the dynamics of partially hyperbolic flows.
method Introduces dynamical coherence and proves it for flows with a specific foliation.
result Dynamical coherence proved for flows with a particular foliation.
Develops equivariant Chern characters for coherent sheaves with group actions.
problem Computing Chern characters for coherent sheaves on manifolds with group actions.
method Introduces equivariant Chern characters and proves Riemann-Roch-Grothendieck theorem in Bott-Chern cohomology.
result Establishes a Riemann-Roch-Grothendieck theorem for coherent sheaves with finite group actions.
New metric m-coherence measures gradient alignment during training, revealing surprising memorization patterns.
problem Measuring and understanding the alignment of per-example gradients during training.
method Introducing m-coherence as a metric to study gradient alignment, showing its advantages over existing metrics. result Training with random labels leads to high m-coherence, indicating common patterns even when generalization is not possible. 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…
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…
Generates coherent storybooks from plain text using diffusion models.
problem Ensuring coherency in a sequence of images for storytelling applications.
method Combines pre-trained LLM and text-guided Latent Diffusion Model for zero-shot generation.
result Outperforms state-of-the-art image editing baselines in generating coherent storybooks.
Extends coherence results to one-relator products of locally indicable groups.
problem Coherence in one-relator products of locally indicable groups.
method Developed new methods to extend results of Helfer, Wise, Louder, Wilton, and Brodsky.
result New proof of a theorem by Brodsky.
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of matrix entries in the context of these low-rank approximations and other sampling-…
A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.
Develops non-standard analysis for coherent risk estimation.
problem Estimating coherent risk measures in financial contexts.
method Non-standard analysis, hyperfinite representations, discrete Kusuoka formulae, plug-in asymptotics.
result Uniform almost sure consistency and asymptotic normality of spectral plug-in estimators.
We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coh…
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus a…
Paper improves video categorization using temporal coherence.
problem Video categorization in multiple modalities.
method Temporal coherence-based regularization for multimodal models.
result Models with temporal coherence outperform state-of-the-art.
CNNs improve InSAR coherence classification.
problem Improving demarcation of InSAR imagery regions based on coherence.
method Convolutional Neural Networks (CNNs) for preprocessing and classification.
result CNNs reduce misclassifications in incoherent regions and outperform established methods.
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…
Paper benchmarks adversarial robustness methods on image classification.
problem Vulnerability of deep neural networks to adversarial examples.
method Established a comprehensive benchmark with robustness curves.
result Found important findings on adversarial attack and defense methods.
For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.
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…
Recently, neural approaches to coherence modeling have achieved state-of-the-art results in several evaluation tasks. However, we show that most of these models often fail on harder tasks with more realistic application scenarios. In particular, the existing models underperform on tasks that require the model to be sen…
New method produces coherent forecasts for long-range data.
problem Inaccurate and non-coherent forecasts on long-horizon data.
method Probabilistic forecasting with KL-divergence for coherent aggregates.
result Improves forecast performance across base levels and aggregates.
This is a large audience version of our previous work (see math.AG/0301146) in which we prove the existence of an (exact) equivalence between the category of coherent analytic sheaves and the category of ∂ˉ-coherent sheaves. We also include here the complete proof of our main Theorem.
The study examines Kähler structures on coadjoint orbits of Lie groups using coherent and squeezed states.
problem Does the coadjoint orbits of Lie groups support a Kähler structure?
method Examined three Lie groups: Weyl-Heisenberg, SU(2), and SU(1,1). Used coherent and squeezed states to explore Kähler structures.
result Coherent states provide Kähler embeddings, while squeezed states only symplectic embeddings.
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…
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 …