IFS with average shadowing property ensure chain recurrence and have specific examples.
problem Analyzing the average shadowing property in IFS.
method Examining uniformly contracting, conjugacy, and product IFS; proving chain recurrence; introducing examples.
result IFS with average shadowing property ensure chain recurrence.
Proposes a new RNN for language generation capturing long-range dependencies.
problem Capturing long-range word dependencies and sentence order in text corpora.
method Recurrent Hierarchical Topic-Guided RNN with dynamic deep topic model.
result Outperforms larger-context RNN-based language models and learns interpretable topics.
Gradual training and gradient clipping improve RNN performance.
problem RNNs are hard to train and prone to overfitting.
method Formulated RNN as a Markov chain, gradually trained, and used layer-wise gradient clipping.
result Improvements in language modeling tasks.
A new GARCH model uses a two-dimensional Markov chain to capture long memory in volatility.
problem Capturing long-term volatility persistence in financial data.
method A GARCH-type model with state-dependent decay of past shocks using a two-dimensional Markov chain.
result The model successfully captures substantial volatility persistence and outperforms forecasts using only a two-dimensional state.
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many finite recurrent communicating classes and define our language model as the invarian…
This paper compares HMC and RNN expressivity using SRT.
problem Comparing expressivity of HMC and RNN models.
method Embed HMC and RNN in a GUM, use SRT to compare structured covariance series.
result Conditions for realizing covariance series by GUM, HMC, or RNN.
Model learns collective and individual dynamics in time series data.
problem Lack of models capturing system-level collective behavior in individual time series.
method Hierarchical switching-state model with latent system-level and entity-level Markov chains.
result Model improves interpretability and forecasting accuracy compared to larger models.
Study uses ML to reconstruct stock market sentiment from trading data.
problem Reconstructing underlying sentiment states from stock price behavior.
method Applied Hidden Markov Models and Recurrent Neural Networks.
result Recovered sentiment states from observed stock price behavior.
The paper proves properties of robust diffeomorphisms and their invariant sets.
problem Investigating robust diffeomorphisms and their invariant sets.
method Demonstrates the robust inverse shadowing property on chain recurrent and transitive sets.
result Proves that invariant sets are hyperbolic under robust inverse shadowing.
Analyzes convex structures in Teichmüller space unit tangent spheres.
problem Characterize faces and extreme points of unit tangent spheres in Teichmüller space.
method Analyzes Finsler infinitesimal balls of Thurston metric, characterizes faces, exposed faces, and extreme points.
result Characterizes faces and extreme points of unit tangent spheres in Teichmüller space.
The paper develops new inequalities for Markov chain sums, linking them to mixing time.
problem Establishing concentration inequalities for Markov chain sums.
method Developed novel concentration inequalities for geometrically ergodic Markov chains, linking bounds to mixing time constants.
result Explicit bounds for additive functionals of Markov chains, linked to Rosenthal inequality constants and mixing properties.
The paper proposes a novel model to forecast patent citations using multi-attention recurrent networks.
problem Forecasting forward citations to patents to discover emerging technologies.
method The approach employs a sequence-to-sequence model with an attention-of-attention mechanism to capture dependencies in multiple time sequences.
result The proposed model outperforms state-of-the-art models in forward citation forecasting.
We show that for a C1 residual subset of diffeomorphisms far away from tangency, every non-trivial chain recurrent class that is accumulated by sources ia a homoclinic class contains periodic points with index 1 and it's the Hausdorff limit of a family of sources.
This paper tackles data-efficient nonlinear control in Hamiltonian systems using symplectic geometry.
problem Data-efficient nonlinear control in Hamiltonian systems.
method Combines symplectic geometry, recurrence on energy level sets, and chain policies to solve target reachability problems.
result Data requirements depend on geometric and recurrence properties of the Hamiltonian, not the state dimension.
New HMC method handles features in POS tagging, outperforming MEMM.
problem HMC struggles with arbitrary features in POS tagging.
method Introduced Entropic Forward-Backward (EFB) probabilities to compute HMC restorations.
result EFB-based HMC outperforms MEMM in POS tagging.
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key …
New method for fMRI missing value imputation improves robustness.
problem High frequency of missing values in fMRI data.
method Spatial and time-dependent regularization with a novel recurrent layer.
result Improved robustness against state-of-the-art alternatives.
Lyapunov 1-forms on orbifolds help understand flows on compact spaces.
problem Understanding flows on orbifolds using Lyapunov 1-forms.
method Introducing Lyapunov 1-forms, using asymptotic cycles and chain-recurrent sets.
result Existence of a Lyapunov 1-form in a prescribed cohomology class for compact orbifolds.
New Markov chains defined on simplicial complexes for understanding their topology.
problem Understanding the topology of simplicial complexes and hypergraphs.
method Defining new Markov chains on simplicial complexes and studying their properties.
result The generator of the new Markov chain is the upper Laplacian, and the Markov chain is positive recurrent.
Method measures weight similarity in neural networks using normalization and statistical inference.
problem Quantifying weight similarity in non-convex neural networks.
method Chain normalization rule and hypothesis-training-testing statistical inference.
result Weights of identical neural networks converge to similar local solutions.
Non-normal RNNs outperform orthogonal ones in sequential tasks.
problem Vanishing/exploding gradients in RNNs training.
method Investigate non-normal RNNs with non-normal recurrent connectivity matrix.
result Non-normal RNNs outperform orthogonal ones in various benchmarks.
A basic RNN model with bounded solutions and fast dynamics.
problem Time-series regression and gradient vanishing/exploding issues.
method State space viewpoint, CLM, CoV, gradient descent, co-state dynamics.
result Successfully performs regression tracking of time-series with quantified gradient issues.
RTRL optimizes long sequences without truncation, converging to loss minima.
problem Inaccuracies in TBPTT for long sequences.
method Online optimization with exact gradient calculation.
result RTRL converges to loss minima for a class of RNNs.
Develops a deep generative model for radar target recognition using HRRP data.
problem Automatic target recognition in radar systems using high-resolution range profiles.
method Recurrent gamma belief network (rGBN) with hybrid stochastic-gradient MCMC and variational inference.
result Efficient and accurate classification with interpretable latent structure.
Enhances sequence labeling with embedded-state latent CRFs.
problem Complex non-local constraints between sequence labels.
method Integrates multiple hidden states with low-rank log-potential scoring matrices.
result Model outperforms baseline CRF+RNN models with global constraints.
This paper detects multi-stage Feint Attacks using Bi-RNN and few-shot learning.
problem Detecting multi-stage Feint Attacks due to lack of professional datasets and semantic relationships.
method Fuzzy clustering for attack chain mining, few-shot deep learning, Bi-RNN for feature extraction.
result Accurately detected Feint Attacks using Bi-RNN and few-shot learning.
A new proof shows how Markov chains converge to their target distribution.
problem Proving convergence of Markov chains to their invariant distribution.
method Asymptotic equivalence criterion for Lebesgue decompositions.
result The criterion is both sufficient and necessary for convergence.
Proposes a new CG interpretation of neural networks for better theoretical analysis.
problem Lack of theoretical analysis in neural networks interpretation.
method Interprets neural networks as chain graphs and feed-forward as approximate inference.
result Provides novel theoretical support and insights for various neural network techniques.
Study analyzes stock order transitions during US-China trade war using Markov chains.
problem Understanding order dynamics during extreme macroeconomic events.
method First-order time-homogeneous discrete-time Markov chain model.
result Active participation by different traders during high volatility days, influencing market outcomes.
Paper proves CLT for quantile SGD with constant learning rate.
problem Quantile estimation via SGD with non-smooth, non-strongly convex loss.
method Viewed as a Markov chain, derived stationary distribution, analyzed MGF, proved CLT.
result Centered and standardized stationary distribution converges to Gaussian as ηightarrow0. Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal circuits, typically without a simultaneous record of neuronal spiking activity. H…
New approach to time functions on spacetimes using attractors.
problem Existence of time functions on Lorentzian manifolds.
method Developed a new approach based on Conley's work on Lyapunov functions for dynamical systems.
result Recover Hawking's result on stably causal spacetimes and extend it to a more general case.
Proposes a method to learn a transition operator for generating samples.
problem Learning a transition operator for generating samples efficiently and biologically plausibly.
method Directly learns a stochastic transition operator via variational methods, encouraging it to 'walk back' quickly to data points.
result The learned transition operator generates high-quality samples and matches the data distribution well beyond the length of individual training trajectories.
Study analyzes price change patterns across different market capitalizations using Markov chains.
problem Understanding price dynamics in limit order markets across various market capitalizations.
method Discrete-time Markov chain analysis of intraday price changes in NASDAQ100 tick data.
result Systematic patterns in price inertia and stability across market capitalizations are identified.
RNNs struggle with in-context retrieval, while Transformers excel.
problem In-context retrieval capability of RNNs.
method Theoretical analysis and experimental techniques (CoT, RAG, Transformer layer).
result Enhancing RNNs with techniques improves their in-context retrieval capability, closing the representation gap with Transformers.
Study on different types of recurrence in Finsler geometry.
problem Understanding various recurrence patterns in Finsler geometry.
method Adopted pullback approach to investigate three classes of recurrence: simple, Ricci, and concircular.
result Introduce and investigate four types of each class of recurrence, highlighting interrelationships and a new concept of generalized concircular recurrence.
Analyzes the asymptotic bias of stochastic gradient search algorithms.
problem Understanding the long-term behavior of stochastic gradient search algorithms.
method Dynamic system theory and differential geometry to derive bounds on asymptotic bias.
result Tight bounds on the asymptotic bias of stochastic gradient search algorithms are derived.
Investigates new types of recurrence in Finsler geometry.
problem None explicitly stated in the abstract.
method Study of hyper-generalized recurrence and generalized conharmonic recurrence in Finsler geometry.
result Properties of hyper-generalized recurrence and generalized conharmonic recurrence are studied and their relations to other Finsler recurrences are explored.
Paper introduces super generalized recurrent manifold for manifold study.
problem Generalizing recurrent manifold concepts.
method Presented a new structure, super generalized recurrent manifold.
result Geometric properties of super generalized recurrent manifold studied.
Study on biharmonic hypersurfaces with specific recurrent operators in Euclidean space.
problem Characterizing biharmonic hypersurfaces with recurrent operators.
method Analysis of various recurrent operators and their impact on biharmonic hypersurfaces.
result Some well-known recurrent operators play a significant role in making biharmonic hypersurfaces minimal.
Characterizes a new type of warped product manifold with recurrent properties.
problem Characterizing a new type of warped product manifold with specific recurrent properties.
method Using semi-Riemannian manifolds and special types of recurrent structures.
result Characterizes a warped product super generalized recurrent manifold.
Simple conformally recurrent spaces are identified as pp-waves.
problem Characterizing conformally recurrent space-times.
method Analyzing dimension n>3 space-times.
result Simple conformally recurrent space-times are conformally recurrent pp-waves.
Deep models predict intraday electricity prices accurately.
problem Accurately forecasting intraday electricity prices.
method Two deep time series probabilistic models using ESNs with stochastic disturbances and copulas.
result Deep distributional models provide accurate short-term probabilistic price forecasts.
Two special Finsler spaces have been introduced and investigated, namely Rh-recurrent Finsler space and consircularly recurrent Finsler space. The defining properties of these spaces are formulated in terms of the first curvature tensor of Cartan connection. The following three results constitute the main object of …
The paper proves the existence of a new class of manifolds with specific curvature properties.
problem Proving the existence of a generalized class of recurrent manifolds.
method Presented a metric and computed curvature properties to establish the existence of various generalized notions of recurrent manifolds.
result Obtained the existence of a new class of semi-Riemannian manifolds with specific curvature properties.
Paper forecasts financial trading durations using a new point process model.
problem Forecasting limit order book durations in high-frequency financial data.
method Self-exciting flexible residual point process incorporating empirical distributional features.
result The model achieves strong predictive performance compared to alternative approaches.
Meta-learning optimizes SG-MCMC dynamics for efficient Bayesian modeling.
problem Lack of tailored SG-MCMC schemes for specific models.
method Meta-learning algorithm for automating SG-MCMC sampler design.
result Learned sampler generalizes and outperforms hand-designed ones.
Mathematical methods characterize RNNs' asymptotics as hidden units and data grow.
problem Characterize recurrent neural networks' behavior as hidden units and data grow.
method Developed mathematical methods to analyze RNNs' convergence to an infinite-dimensional ODE coupled with a fixed point of a random algebraic equation.
result RNNs converge to an infinite-dimensional ODE coupled with a fixed point of a random algebraic equation.