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.
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48 results for “compositional coherence”
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.
This paper extends compositional data analysis using graph signal processing.
problem Traditional log-ratios between all variables are not suitable for specific variable relationships.
method Linking compositional data analysis with graph signal processing, it considers only selected log-ratios.
result The approach retains desirable properties of scale invariance and compositional coherence.
Enhances neural forecasting for hierarchically organized time series data.
problem Probabilistic coherent forecasting of time series data across different levels of aggregation.
method Proposes a coherent multivariate mixture output for neural forecasting architectures, optimizing with a composite likelihood objective.
result 13.2% average accuracy improvements on most datasets compared to state-of-the-art baselines.
DeepCoDA provides personalized interpretability for complex health data.
problem Interpreting complex health data, especially compositional data, is challenging.
method DeepCoDA framework for high-dimensional compositional data, personalized interpretability through patient-specific weights.
result DeepCoDA maintains state-of-the-art performance and provides coherent, personalized interpretations.
A big challenge in algorithmic composition is to devise a model that is both easily trainable and able to reproduce the long-range temporal dependencies typical of music. Here we investigate how artificial neural networks can be trained on a large corpus of melodies and turned into automated music composers able to gen…
The intuition of risk is based on two main concepts: loss and variability. In this paper, we present a composition of risk and deviation measures, which contemplate these two concepts. Based on the proposed Limitedness axiom, we prove that this resulting composition, based on properties of the two components, is a cohe…
BacHMMachine harmonizes Baroque chorales using theory-driven principles and Hidden Markov Models.
problem Algorithmic harmonization of Baroque chorales.
method Theory-driven approach guided by music composition principles, combined with data-driven learning of key and chord transitions.
result BacHMMachine generates musically coherent harmonizations with reduced computational burden and greater interpretability.
Music Transformercs.LG
Music relies heavily on repetition to build structure and meaning. Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure. The Transformer (Vaswani et al., 2017), a sequence model based on self-attention, has achieved compelling …
This paper compares two different frameworks recently introduced in the literature for measuring risk in a multi-period setting. The first corresponds to applying a single coherent risk measure to the cumulative future costs, while the second involves applying a composition of one-step coherent risk mappings. We summar…
Describes explaining neurons in deep representations using compositional logical concepts.
problem Interpreting neuron behavior in deep neural networks.
method Identifying compositional logical concepts that closely approximate neuron behavior.
result Compositional explanations provide insights into model performance and allow for adversarial example creation.
Generates coherent 3D scenes from monocular videos without supervision.
problem Lack of 3D scene modeling in video generation models.
method Trains a model to generate 3D scenes with moving objects and a background from monocular videos.
result Trained model generates coherent 3D scenes with multiple moving objects and a background.
New methods for predicting compositional data using conformal prediction.
problem No well-established methods for constructing valid prediction sets in compositional data.
method Investigated three conformal prediction-based approaches for Dirichlet regression models.
result HDR approximation approach is robust in terms of coverage, while grid discretization reduces overcoverage.
Bayesian model predicts evolving guest origin markets in tourism.
problem Forecasting the changing composition of guest origin markets in tourism.
method Developed and applied Bayesian Dirichlet autoregressive moving average (BDARMA) models to Airbnb booking data.
result BDARMA models achieve lower forecast error and competitive performance in guest origin market shares.
Bayesian models predict evolving guest origin markets in tourism.
problem Forecasting the changing composition of guest origin markets in tourism.
method Developed and applied Bayesian Dirichlet autoregressive moving average (BDARMA) models to Airbnb booking data.
result BDARMA models outperform standard benchmarks in forecasting guest origin market shares.
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.
Bayesian ARMA model with directional shifts captures structural breaks in compositional time series.
problem Structural breaks in compositional time series due to external shocks or policy changes.
method Developed a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism.
result The model captures structural breaks through interpretable parameters and produces coherent probabilistic forecasts.
A great number of deep learning based models have been recently proposed for automatic music composition. Among these models, the Transformer stands out as a prominent approach for generating expressive classical piano performance with a coherent structure of up to one minute. The model is powerful in that it learns ab…
Differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy in the past decade. This privacy definition and its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition of private algorithms or in analyzing important primi…
LLM generates coherent macroeconomic stress scenarios for portfolio risk assessment.
problem Macro-financial stress testing and portfolio risk assessment using traditional methods.
method Hybrid prompt-RAG pipeline combining structured prompting and retrieval of country fundamentals and news.
result LLM-generated scenarios yield stable tail-risk amplification with limited sensitivity to retrieval choices.
The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such r…
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 …
Mackey showed that for a compact Lie group , the pair has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of invariant polarizations on . The …
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.
Dynamic risk measures follow law invariance principles over time.
problem Tackles dynamic risk measurement principles.
method Shows equivalence between adapted law invariance and recursive one-step conditional-law representation for time-consistent risk measures.
result Identifies adapted law invariance as the dynamic counterpart of ordinary law invariance.
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.
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 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 …
A natural one-parameter family of Kähler quantizations of the cotangent bundle of a compact Lie group , taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the…
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…
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.
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-…
Researchers often summarize their work in the form of posters. Posters provide a coherent and efficient way to convey core ideas from scientific papers. Generating a good scientific poster, however, is a complex and time consuming cognitive task, since such posters need to be readable, informative, and visually aesthet…
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…
Coherent states and geometrymath.DG
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…
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…
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
problem Tackling the indistinguishability of spectral line profiles under scalar summaries.
method Introduces a geometric representation of line profiles using rough path theory, mapping profiles to a common velocity grid and defining descriptors from path properties.
result Compact descriptors separate morphologies with similar scalar summaries, revealing ordered line structures.
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…