Study abelian varieties' Weil-Petersson metric asymptotics.
problem Asymptotic behavior of Weil-Petersson metric on abelian varieties.
method Linking asymptotic with multi-scale collapsing limits of parametrized flat tori.
result Refined description of Weil-Petersson metric on abelian varieties.
New measures quantify diversity of latent representations using metric space magnitude.
problem Evaluating the diversity of latent representations in machine learning models.
method Developed magnitude-based measures for latent representations, stable under data perturbations.
result Demonstrated superior performance across various domains and tasks.
Novel neural network solves PDEs with multi-scale resolution.
problem Solving time-dependent PDEs with varying spatial and temporal scales.
method Multi-scale message passing neural network with temporal and spatial gating modules.
result Outperforms baselines on PDEs with diverse scales.
This study presents a new lossy image compression method that utilizes the multi-scale features of natural images. Our model consists of two networks: multi-scale lossy autoencoder and parallel multi-scale lossless coder. The multi-scale lossy autoencoder extracts the multi-scale image features to quantized variables a…
Polynomial-time algorithm learns ReLU networks without assumptions.
problem Learning linear combinations of ReLU activations with Gaussian inputs.
method Random contractions of moment tensors and multi-scale analysis.
result First polynomial-time algorithm without additional assumptions.
Paper introduces multi-scale methods to improve CATE estimation from EO data.
problem Challenges in balancing fine-grained and contextual information in EO-based causal inference.
method Multi-Scale Representation Concatenation, combining Vision Transformer and Causal Forests.
result Multi-scale approach captures effect heterogeneity better than single-scale models.
Boosting theory explains why multi-scale GNNs work.
problem Over-smoothing in graph neural networks.
method Gradient boosting and transductive learning analysis.
result Test error bound decreases with more node aggregations.
In this paper, we propose the idea of radial scaling in frequency domain and activation functions with compact support to produce a multi-scale DNN (MscaleDNN), which will have the multi-scale capability in approximating high frequency and high dimensional functions and speeding up the solution of high dimensional PDEs…
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
problem Applying spectral clustering to multi-scale data where clusters vary in size and density.
method CAST integrates reachability similarity with distance-based similarity to derive a coefficient matrix, then applies trace Lasso regularization.
result CAST provides excellent performance and robustness across various multi-scale data test cases.
The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and the communities are observed to have a hierarchical structure referred to as mult…
Framework for multi-scale clustering using phase transitions.
problem Clustering datasets with multi-scale structures.
method Cascade of phase transitions in simulated annealing of Expectation-Maximisation algorithm with weighted local covariance.
result Approximation of the number and size of clusters at different scales.
We explore the use of Vector Quantized Variational AutoEncoder (VQ-VAE) models for large scale image generation. To this end, we scale and enhance the autoregressive priors used in VQ-VAE to generate synthetic samples of much higher coherence and fidelity than possible before. We use simple feed-forward encoder and dec…
We construct a compactification of the moduli spaces of abelian differentials on Riemann surfaces with prescribed zeroes and poles. This compactification, called the moduli space of multi-scale differentials, is a complex orbifold with normal crossing boundary. Locally, our compactification can be described as the norm…
EvoMSN tackles time series forecasting under distribution shifts by evolving multi-scale normalization.
problem Accurate long-term time series forecasting under complex distribution shifts.
method EvoMSN framework with multi-scale statistics prediction and adaptive ensembling for collaborative updating.
result Improves forecasting performance of five mainstream methods on benchmark datasets.
New PINN architectures learn high-frequency features using Fourier features.
problem PINNs struggle with high-frequency or multi-scale features.
method Employ spatio-temporal and multi-scale random Fourier features.
result Effective PINN models for multi-scale PDEs.
Proposes OC4Seq for detecting anomalies in discrete event sequences.
problem Challenges in detecting anomalies in discrete event sequences, including data imbalance, discrete events, and sequential nature.
method Integrates anomaly detection with recurrent neural networks (RNNs) to embed sequences into latent spaces and designs a multi-scale RNN framework to capture multi-scale sequential patterns.
result OC4Seq consistently outperforms various baselines on three benchmark datasets.
Paper tackles leverage effect estimation from noisy data.
problem Estimating leverage effect from high-frequency data with microstructure noise.
method Holistic multi-scale framework operating directly on leverage effect, using Subsampling-and-Averaging Leverage Effect (SALE) and Multi-Scale Leverage Effect (MSLE) estimators.
result Holistic multi-scale framework achieves substantial efficiency gains over existing benchmarks.
New method improves robustness of large models without sacrificing accuracy.
problem Improving robustness of large pre-trained models without accuracy loss.
method Multi-scale diffusion denoised smoothing, selectively applying smoothing at multiple noise scales.
result Strong certified robustness at high noise levels with accuracy close to non-smoothed classifiers.
Deep generative modeling using flows has gained popularity owing to the tractable exact log-likelihood estimation with efficient training and synthesis process. However, flow models suffer from the challenge of having high dimensional latent space, the same in dimension as the input space. An effective solution to the …
DRFormer uses dynamic tokenization and multi-scale transformer to forecast long time series.
problem Forecasting long-term time series data across diverse scales.
method Dynamic tokenizer, multi-scale transformer, dynamic sparse learning, rotary position encoding.
result DRFormer outperforms existing methods in forecasting accuracy.
We construct a new map from a convex function to a distribution on its domain, with the property that this distribution is a multi-scale exploration of the function. We use this map to solve a decade-old open problem in adversarial bandit convex optimization by showing that the minimax regret for this problem is $\tild…
CrossAD detects anomalies in time series data by considering cross-scale associations and cross-window modeling.
problem Anomaly detection in time series data is challenging due to varying patterns at different scales and fixed window sizes.
method CrossAD incorporates cross-scale reconstruction and a query library to capture dynamic cross-scale associations and comprehensive context.
result CrossAD achieves state-of-the-art performance in anomaly detection across multiple real-world datasets.
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a possible explanation for the complex dynamics of markets' returns. Scaling and m…
Novel framework for systemic risk analysis in financial markets.
problem Systemic risk in financial markets.
method Multi-scale network dynamics, transfer entropy networks, agent-based modeling, wavelet decomposition, Model Context Protocol (MCP).
result Multi-scale approach reveals hidden systemic risk patterns.
Space2Vec learns multi-scale spatial representations from grid cell insights.
problem Encoding spatial features with varying scales from GIS data.
method Proposes Space2Vec, a multi-scale representation learning model using grid cell insights.
result Space2Vec outperforms baselines in predicting POI types and image classification with geo-locations.
MCFNet recovers spatial detail and fuses it with semantic information for real-time segmentation.
problem Recovering spatial detail information and fusing it with semantic information in real-time.
method Proposes a new architecture (MCFNet) with feature refinement and fusion modules, and a gating unit.
result Achieves competitive performance with high speed (75.5% mIOU, 151.3 FPS on Cityscapes).
Federated learning improves CRC grading accuracy and privacy.
problem Inter-observer variability and data privacy in CRC grading.
method Multi-scale federated learning framework integrating ResNetRS50.
result Framework achieves 83.5% accuracy, outperforming centralized models.
Langevin Dynamics speeds up mixing time with manifold hypothesis and multi-scale approach.
problem Langevin Dynamics struggles in high dimensions and nonconvex landscapes.
method Utilizes manifold hypothesis to reduce mixing time and employs multi-scale approach to improve image generation quality.
result Mixing time depends on intrinsic dimension rather than ambient dimension, significantly reducing computational complexity.
Locally adaptive clustering for tree delineation.
problem Tree delineation from distance data.
method Locally adaptive hierarchical cluster termination.
result Multi-scale alternative to conventional termination criteria.
This study improves uncertainty estimation in FWI using SVGD with annealing and PCA.
problem Uncertainty quantification in FWI solutions.
method Annealed Stein Variational Gradient Descent (SVGD) combined with multi-scale strategy and PCA.
result Improved uncertainty estimation in FWI solutions.
Improves speaker verification for variable-duration utterances using a feature pyramid module.
problem Improving robustness for variable-duration utterances in speaker verification.
method Integrates a feature pyramid module into multi-scale aggregation to enhance speaker-discriminative information from multiple layers.
result Improves performance for both short and long utterances compared to state-of-the-art approaches.
Model for directed synthesis of audio textures using multi-scale RNNs.
problem Challenges in modeling complex audio textures with traditional methods.
method Combining multi-scale RNNs with a conditioning strategy for user-directed synthesis.
result Demonstrated improved performance on various audio texture datasets.
Neural HMM with AGA captures multi-scale dynamics in financial markets.
problem Capturing multi-scale temporal dynamics in financial markets.
method Parallel multi-resolution encoders, adaptive gating, and multi-head attention.
result Outperforms fixed-resolution baselines in predicting price movements and liquidity shocks.
Improved recurrent neural networks learn long-term dependencies through multi-scale memory.
problem Capturing long-term dependencies in recurrent neural networks.
method Incremental training of a modular RNN architecture with multi-scale hidden states.
result Incremental training and multi-scale memory enhance RNNs' ability to learn long-term dependencies.
Paper proposes MSSDDPG for better financial trading strategies.
problem Extracting accurate features from noisy, non-stationary financial time series.
method Multi-scale stroke deep deterministic policy gradient reinforcement learning model (MSSDDPG).
result MSSDDPG outperforms other strategies in China's CSI 300 and SSE Composite.
SHAKE-GNN scales GNNs for large graphs with multi-scale representations.
problem Scaling Graph Neural Networks (GNNs) to large graphs.
method SHAKE-GNN uses a hierarchy of Kirchhoff Forests for stochastic multi-resolution graph decompositions.
result SHAKE-GNN achieves competitive performance on large-scale graph classification benchmarks.
New method disentangles sources of different timescales in planetary seismic data.
problem Unsupervised source separation of multi-scale seismic data from planetary missions.
method Wavelet scattering spectra for multi-scale clustering and variational autoencoder for source separation.
result Disentangles sources with different timescales in InSight mission seismic data.
We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than classification. Contrasted to more standard vector quantization methods, such as K-mea…
Recently, neural network based approaches have achieved significant improvement for solving large, complex, graph-structured problems. However, their bottlenecks still need to be addressed, and the advantages of multi-scale information and deep architectures have not been sufficiently exploited. In this paper, we theor…
Preformer improves Transformer for long-term time series forecasting.
problem Transformer's quadratic complexity and lack of context-awareness for long-term forecasting.
method Introduces Multi-Scale Segment-Correlation mechanism for efficient time series segmentation and context-aware attention.
result Preformer outperforms other Transformer-based methods in long-term time series forecasting.
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of granularity to capture diverse types of local information for subsequent machine lea…
Proposes a deep multi-scale neural network for EEG signal representation learning.
problem Capturing multi-frequency properties in EEG signals for better brain-computer interface.
method A novel deep multi-scale neural network that discovers feature representations in multiple frequency/time ranges and extracts spatial relationships.
result Improved performance in various active/passive BCI datasets compared to state-of-the-art methods.
Study explores fairness in financial deep learning through multi-scale trust quantification.
problem Ensuring fairness in financial deep learning models, especially under regulatory compliance.
method Conducts multi-scale trust quantification on a deep neural network for credit card default prediction.
result Demonstrates the feasibility and utility of multi-scale trust quantification for financial deep learning fairness.
This paper tackles denoising of complex measures using optimal transport and curvature analysis.
problem Denoising of complex, possibly non-log-concave measures.
method Score function and optimal transport theory to revert Langevin diffusion chains.
result The difficulty of denoising depends on the curvature complexity of the initial measure at specific SNR scales.
The multi-scale, mutli-physics nature of fusion plasmas makes predicting plasma events challenging. Recent advances in deep convolutional neural network architectures (CNN) utilizing dilated convolutions enable accurate predictions on sequences which have long-range, multi-scale characteristics, such as the time-series…
This work bridges two views of feature learning in neural networks.
problem The relationship between kernel scale changes and data-adaptive feature learning in neural networks remains unresolved.
method Using statistical mechanics, the work derives analytical expressions for network output statistics across scaling regimes.
result Kernel adaptation can be reduced to an effective kernel rescaling, but multi-scale adaptive approach provides richer insights.
Hybrid approach improves crude oil price forecasting using multi-scale data.
problem Forecasting crude oil prices with multi-scale data.
method Hybrid approach combining K-means, KPCA, and KELM.
result Hybrid approach outperforms traditional methods in both level and directional forecasting accuracy.
A multi-scale model predicts atomic-scale properties using both local and long-range information.
problem Inability of machine-learning schemes to capture long-range physical effects.
method Combines local and non-local information in a multipole expansion framework.
result Demonstrates the ability to model electrostatics, polarization, and dispersion.