This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse -structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing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 …
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48 results for “coherence requirements”
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…
Machine learning predicts quantum advantage in noisy quantum walks.
problem Finding optimal graph types and coherence requirements for quantum advantage.
method Convolutional neural network trained on simulated examples of quantum walks on cycle graphs.
result Machine learning can predict quantum advantage for a wide range of decoherence parameters.
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.
Coherent structure coloring: identification of coherent structures from sparse data using graph theoryphysics.flu-dyn
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…
New proof of Grauert's theorem using differential geometry.
problem Proper holomorphic morphisms and coherence of higher direct images.
method Differential-geometric proof, antiholomorphic superconnection, Hironaka's desingularization.
result New proof of Grauert's theorem in both smooth and singular cases.
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.
New method for exact matrix completion with reduced observation complexity.
problem Exact recovery of matrices with high coherence.
method Adaptive sampling method and relation to sparsest vector of column and row spaces.
result Exact recovery of -coherent column space matrices with much smaller observation complexity.
The paper analyzes risk measures and optimal reserve allocation strategies.
problem Risk measures and optimal reserve allocation across multiple lines of business.
method Formalizes expected maximum deficit, introduces implicitly bounded risk measures, and proposes capital allocation approaches.
result Theoretical results on static and dynamic coherence, convexity, and exact optimizations of aggregate minimum reserves.
New coherence parameter for GNNs with Fourier measurements improves signal recovery.
problem Characterizing generative compressed sensing with Fourier measurements.
method Subspace counting arguments and high-dimensional probability theory.
result First known restricted isometry guarantee for generative compressed sensing with subsampled isometries.
Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called "Standard Formula" or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator permi…
Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper provides the first working method for coherent matrix completion under the standard …
Optimal hashing embeddings reduce linear least squares solving time.
problem Efficiently solving large-scale linear least squares problems.
method Optimal hashing sketching matrices for linear least squares.
result Ski-LLS outperforms state-of-the-art solvers on various problem types.
Diffusion models learn hierarchical composition rules from data.
problem How many samples do generative models need to learn hierarchical composition rules?
method Theoretical and empirical investigation of diffusion models on probabilistic context-free grammars.
result Diffusion models learn hierarchical composition rules with sample complexity scaling polynomially with context size.
High-fidelity quantum simulations demonstrated on short-coherence hardware.
problem Short coherence times limit the depth of quantum algorithms.
method Fixed State Variational Fast Forwarding (fsVFF) algorithm.
result Simulations of 600 time steps possible, 150x longer than previous methods.
We examine a condition on a simply connected 2-complex X ensuring that groups acting properly on X are coherent. This extends earlier work on 2-complexes with negative sectional curvature which covers the case that G acts freely. Our extension of these results involves a generalization of the notion of sectional curvat…
Proposes a new algorithm for efficient probabilistic reconciliation of forecasts.
problem Ensuring coherence in forecasts for hierarchical time series.
method Bottom-Up Importance Sampling algorithm for any type of forecast distribution.
result Significant improvement over base probabilistic forecasts in experiments.
A new neural topic model using optimal transport improves document representation and topic coherence.
problem Challenges in achieving good document representation and coherent/diverse topics in existing NTMs.
method Proposes a neural topic model via optimal transport, learning topic distribution by minimising OT distance to document word distributions.
result Significantly outperforms state-of-the-art NTMs on discovering coherent and diverse topics.
Faster, context-aware topic modeling approach unveiled.
problem Slow and heavy preprocessing in topic modeling.
method Conceptualizes topics as independent axes, decomposes embeddings using ICA.
result 4.5x faster than BERTopic on average, with diverse and coherent topics.
We examine the problem of dynamic reserving for risk in multiple currencies under a general coherent risk measure. The reserver requires to hedge risk in a time-consistent manner by trading in baskets of currencies. We show that reserving portfolios in multiple currencies are time-consistent when (and only…
Coherent manifoldsmath-ph
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 …
Risk-averse model uncertainty framework for safe reinforcement learning.
problem Safe decision making in uncertain environments.
method Risk-averse perspective towards model uncertainty using coherent distortion risk measures; equivalent to distributionally robust safe reinforcement learning problems; efficient, model-free implementation.
result Demonstrates robust performance and safety across perturbed test environments.
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.
Meta-analysis improves personalized treatment rules across multiple sites.
problem Lack of generalizability in learning individualized treatment rules across different medical sites.
method Developed a method for individual-level meta-analysis of ITRs, borrowing sign-coherency information between sites.
result Jointly learned site-specific ITRs with improved generalizability.
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.
ConvNP improves SP prediction with translation equivariance and coherent samples.
problem Predicting stationary stochastic processes with coherent samples.
method Convolutional Neural Processes (ConvNP) with a new maximum-likelihood objective.
result ConvNP outperforms standard NPs and demonstrates strong generalization on various tasks.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their indisputable success, CNNs are not mathematically validated as to how and what …
Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-foldshep-th
Let X be a Calabi-Yau 3-fold, T=D^b(coh(X)) the derived category of coherent sheaves on X, and Stab(T) the complex manifold of Bridgeland stability conditions Z on T. It is conjectured that one can define rational numbers J^a(Z) for Z in Stab(T) and a in the numerical Grothendieck group K(T) generalizing Donaldson-Thom…
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.
Star-shaped Risk Measuresecon.TH
Paper characterizes star-shaped risk measures and their properties.
problem Characterizing risk measures in the presence of liquidity risk and competitive delegation.
method Characterization of star-shaped risk measures, study of their properties.
result Star-shaped risk measures include all practically used risk measures.
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 for .
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 -coherence measures gradient alignment during training, revealing surprising memorization patterns.
problem Measuring and understanding the alignment of per-example gradients during training.
method Introducing -coherence as a metric to study gradient alignment, showing its advantages over existing metrics.
result Training with random labels leads to high -coherence, indicating common patterns even when generalization is not possible.
Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloringphysics.flu-dyn
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…
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.
The clustering of data into physically meaningful subsets often requires assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the under…
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 cumbersome hypothesis for Viro patchworking of real algebraic curves is the convexity of the given subdivision. It is an open question in general to know whether the convexity is necessary. In the case of trigonal curves we interpret Viro method in terms of dessins d'enfants. Gluing the dessins d'enfants in a coheren…
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.
Deep generative model for healthcare data identifies coherent substructures and mutational clusters.
problem Analytical challenges in healthcare data, including sparsity, missingness, and small sample sizes.
method Proposes a deep generative Bayesian model with collapsed Gibbs sampling for multinomial count data.
result Identifies coherent substructures and biologically meaningful mutational clusters in cancer data.
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…