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.
The pullback approach to global Finsler geometry is adopted. Three classes of recurrence in Finsler geometry are introduced and investigated: simple recurrence, Ricci recurrence and concircular recurrence. Each of these classes consists of four types of recurrence. The interrelationships between the different types of …
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.
To generalize the notion of recurrent manifold, there are various recurrent like conditions in the literature. In this paper we present a recurrent like structure, namely, \textit{super generalized recurrent manifold}, which generalizes both the hyper generalized recurrent manifold and weakly generalized recurrent mani…
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.
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 object of the present paper is to obtain the characterization of a warped product semi-Riemannian manifold with a special type of recurrent like structure, called super generalized recurrent. As consequence of this result we also find out the necessary and sufficient conditions for a warped product manifold to sati…
The present paper deals with the proper existence of a generalized class of recurrent manifolds, namely, hyper-generalized recurrent manifolds. We have established the proper existence of various generalized notions of recurrent manifolds. For this purpose we have presented a metric and computed its curvature propertie…
Stable recurrent models perform similarly to unstable ones, proving useful for sequence tasks.
problem The lack of stability in recurrent neural networks hinders their practical application.
method Theoretical analysis and empirical testing of stable recurrent models.
result Stable recurrent models can be well approximated by feed-forward networks, performing similarly to unstable ones.
Interneurons improve learning in neural networks by accelerating convergence.
problem Rapid adaptation to changing input statistics in neural networks.
method Two mathematically tractable recurrent linear neural networks were compared: one with direct recurrent connections and the other with interneurons that mediate recurrent communication.
result The network with interneurons converges more quickly than the network with direct recurrent connections, scaling logarithmically with initialization spectrum.
Unified recurrent networks reveal differences in complexity levels of grammars.
problem Understanding the complexity and behavior of recurrent networks.
method Connecting recurrent networks with deterministic finite automata and formal grammars.
result Unified recurrent networks improve performance and match grammars from different complexity levels.
Study predicts colorectal polyp recurrence using medical records and statistical models.
problem Identifying patient characteristics influencing colorectal polyp recurrence.
method Natural language processing for extracting polyp characteristics, Kaplan-Meier curves, Cox proportional hazards modeling, random survival forest models.
result Polyp size, number, location, and patient smoking status significantly influence recurrence risk.
Enhanced speech emotion recognition using nonlinear recurrence dynamics.
problem Improving speech emotion recognition accuracy.
method Phase space reconstruction, Recurrence Plot, Recurrence Quantification Analysis, statistical functionals, feature fusion, Bidirectional Recurrent Neural Network.
result State-of-the-art performance on IEMOCAP with up to 10.7% improvement in accuracy.
It is proved that every concircularly recurrent manifold must be necessarily a recurrent manifold.
Examines special manifolds with specific properties.
problem Analyzing properties of (LCS)n-manifolds.
method Investigates semi-generalized recurrent, semi-generalized Ricci recurrent, and conformal Ricci soliton properties.
result Discovers new insights into the structure of (LCS)n-manifolds.
Recurrent-DBN models dynamic relational data with interpretable latent structures.
problem Interpreting dynamic relational data with hidden structures.
method Recurrent Dirichlet Belief Network framework with hierarchical latent structures and efficient inference strategy.
result Recurrent-DBN discovers interpretable latent structures and improves link prediction.
In this paper we adopt the pullback approach to global Finsler geometry. We investigate horizontally recurrent Finsler connections. We prove that for each scalar (π)1-form A, there exists a unique horizontally recurrent Finsler connection whose h-recurrence form is A. This result generalizes the existence and u…
Transformer models outperform recurrent ones in modeling hierarchical data.
problem Modeling hierarchical structure in data.
method Introducing Multiresolution Transformer Networks leveraging self-attention.
result Multiresolution Transformer Networks significantly outperform state-of-the-art models on query suggestion datasets.
Lipschitz RNNs improve stability and performance in various tasks.
problem Improving stability and performance of RNNs.
method Introduced a Lipschitz recurrent unit with a linear and Lipschitz nonlinear component for stability analysis.
result Lipschitz RNNs outperform existing units on benchmark tasks.
This paper analyzes the generalization risk of unrolled neural networks using Stein's Unbiased Risk Estimator.
problem Analyzing the generalization risk of unrolled neural networks and its relationship to network design and train sample size.
method Using Stein's Unbiased Risk Estimator (SURE), the paper analyzes the generalization risk with bias and variance components for recurrent unrolled networks, focusing on the degrees-of-freedom (DOF) component and the trace of the end-to-end network Jacobian.
result DOF is well-approximated by the weighted path sparsity of the network under incoherence conditions on the trained weights, and DOF increases with train sample size and converges to the generalization risk for both recurrent and non-recurrent schemes.
ENRNN uses eigenvalue normalization for short-term memory in RNNs.
problem Vanishing/exploding gradient problem and long-term dependency modeling.
method Eigenvalue normalization of recurrent matrix to simulate short-term memory.
result ENRNN outperforms existing RNN variants in experiments.
Bayesian units improve speech recognition with minimal parameters.
problem Improving speech recognition models with fewer parameters.
method Derived Bayesian recurrent units integrated into deep learning frameworks.
result Adding Bayesian units improves speech recognition performance.
Proposes a new Deep Recurrent Double Q-Learning model for Atari games.
problem Improving Deep Reinforcement Learning models for Atari games.
method Integrates Double Q-Learning and Recurrent Networks (LSTM, DRQN) for Atari games.
result Demonstrates improved performance in Atari games compared to existing models.
Bayesian approach improves neural network recurrence.
problem Improving neural network recurrence mechanisms.
method Introducing Bayesian recurrence relations and gates.
result Bayesian approach can perform as well as or better than conventional recurrent networks.
New method improves learning of long-term dependencies in recurrent models.
problem Improving learning of long-term dependencies in recurrent neural networks.
method Proves learnable gates in recurrent models provide quasi-invariance to time transformations and recovers part of LSTM architecture from axiomatic approach.
result New chrono initialization of gate biases greatly improves learning of long-term dependencies.
Recurrent neural networks improve time series forecasting accuracy.
problem Time series forecasting is challenging, especially for sequential data.
method A recurrent neural network framework for feature engineering, prediction, and evaluation is presented.
result The LSTM and GRU networks outperform traditional methods in forecasting accuracy.
RecNets use RNNs to process image channels in a compact, recurrent way.
problem Creating efficient neural network architectures for computer vision.
method Introducing RecNets with CRC layers that simulate recurrent processing of image channels.
result RecNets achieve superior size-accuracy trade-off compared to other compact models.
In this paper, we prove that evry 3-dimensional manifold M is a ?- recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ?-recurrent contact metric manifolds of constant curvature. This implies that there exists no ?-recurrent N(k)-contact metric manifold, which is neither symmetric nor…
Batch-normalized RHN improves gradient control in recurrent networks.
problem Gradient vanishing or exploding in recurrent networks.
method Batch normalization applied at each recurrence loop in RHN.
result Batch-normalized RHN converges faster and performs better.
Improved GRU model with weighted time-delay feedback for long-term dependencies.
problem Modeling long-term dependencies in sequential data.
method Introducing a gated recurrent unit (GRU) with a weighted time-delay feedback mechanism.
result τ-GRU outperforms state-of-the-art models on various tasks.
Study properties of Kenmotsu manifolds with a specific connection.
problem Properties of Kenmotsu manifolds with a semi-symmetric non-metric connection.
method Analysis of generalized recurrent, Ricci-recurrent, weakly symmetric, and weakly Ricci-symmetric properties.
result New findings on properties of Kenmotsu manifolds under semi-symmetric non-metric connection.
Scalable verifier for recurrent neural networks using polyhedral abstractions.
problem Certifying the correctness of recurrent neural networks.
method Combining sampling, optimization, and Fermat's theorem for polyhedral abstractions; gradient descent for refinement.
result Successfully verified challenging recurrent models in various domains.
Classification of specific pseudo-Riemannian manifolds.
problem Classifying conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds.
method Complete classification through mathematical analysis.
result Conformally flat generalized Ricci recurrent pseudo-Riemannian manifolds are either de Sitter or anti-de Sitter spacetimes.
The paper proves recurrence relations for heat kernels on hyperbolic and spherical spaces.
problem Understanding recurrence relations of heat kernels on different space forms.
method Direct proof and computation of recurrence relations for heat kernels on hyperbolic and spherical spaces.
result Computed diagonal of heat kernels for odd dimensional hyperbolic spaces and heat trace asymptotic expansions for odd dimensional spheres.
The paper introduces and analyzes pseudo generalized Ricci-recurrent spacetimes in modified gravity.
problem Characterizing and analyzing pseudo generalized Ricci-recurrent spacetimes in modified gravity.
method Introducing and characterizing pseudo generalized Ricci-recurrent spacetimes, proving their properties, and studying their impact under modified gravity scenarios.
result Pseudo generalized Ricci-recurrent spacetimes represent specific spacetime types under modified gravity scenarios.
Energy markets and the associated energy futures markets play a crucial role in global economies. We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times τ between consecutive volatilities exceeding a gi…
Stochastic models fail to outperform standard recurrent networks in sequence modeling.
problem Discrepancy in performance between stochastic and standard recurrent models in sequence modeling.
method Re-examine roles of latent variables, remove restriction on fully factorized output distribution, compare auto-regressive models.
result Standard recurrent models consistently outperform stochastic models in sequence modeling.
The study examines entropy and pressure at infinity in negatively curved manifolds, linking them to strong positive recurrence.
problem Investigating strong positive recurrence in negatively curved manifolds.
method Defining and comparing entropy and pressure at infinity through different measures.
result Strong positive recurrence potentials admit finite Gibbs measures.
Develops a method for causal inference in recurrent event data with terminal failure.
problem Causal inference in recurrent event data with a terminal event.
method Multiply robust estimation framework for causal inference.
result Proposes an estimator for the expected number of recurrent events and failure survival function.
In this paper, we show that there is no phi-recurrent Sasakian manifold. Then we prove that the only flat 3-dimensional manifolds are phi-recurrent (k, m)-contact metric manifolds.
Study compares LSTM, Transformer, and Mamba for bladder cancer recurrence analysis.
problem Complex time-dependent data in bladder cancer recurrence analysis.
method Evaluation of LSTM, Transformer, and Mamba models using Cox proportional hazards model.
result LSTM-Cox model outperforms Transformer-Cox and Mamba-Cox models in prediction accuracy.
This work optimizes reservoir computing models by linking recurrence and non-linear dynamics.
problem Understanding how recurrence and non-linear dynamics in cortical networks contribute to their function.
method Transformed time-continuous, recurrent dynamics into an effective feed-forward structure of linear and non-linear temporal kernels.
result Optimal time-series classifiers can be built from random reservoir networks, demonstrating significant performance gains.
Paper presents FPGA implementation for efficient recurrent neural networks.
problem Implementing recurrent neural networks on FPGAs for low latency.
method Developed hls4ml framework to implement LSTM and GRU layers.
result Demonstrated effective designs for both small and large models.
A new recurrent unit alleviates vanishing gradients for long-term dependencies.
problem Vanishing gradients in recurrent neural networks make long-term dependencies hard to model.
method Proposes a new NRU architecture that avoids saturating activation functions and gates.
result Demonstrates superior performance across various tasks with and without long-term dependencies.
New framework shows C∗-simplicity for groups without certain subalgebras.
problem Characterizing C∗-simplicity of groups. method Introducing confined subalgebras and Uniformly Recurrent States.
result A countable discrete group is C∗-simple if it has no non-trivial amenable confined subalgebras. A hybrid CNN with shared parameters learns to incorporate recurrent structures.
problem Designing efficient recurrent neural networks.
method Parameter sharing scheme combining CNN and recurrent layers.
result Substantial parameter savings with competitive accuracy.
The article introduces pseudo generalized Ricci-recurrent spacetimes and their applications in modified gravity.
problem Characterizing and understanding pseudo generalized Ricci-recurrent spacetimes.
method Introduced and characterized pseudo generalized Ricci-recurrent spacetimes, provided examples, and studied their implications in modified gravity.
result Pseudo generalized Ricci-recurrent spacetimes represent perfect fluid spacetimes and can model dark energy epochs or static spacetimes.
SnAp approximates RTRL for online training of sparse recurrent networks.
problem Training large sparse recurrent networks online is computationally expensive.
method Sparse n-step Approximation (SnAp) of the RTRL influence matrix.
result SnAp with n=2 remains tractable for highly sparse networks and outperforms backpropagation through time.