Paper proves unique Finsler connections for scalar forms.
problem Existence and uniqueness of Finsler connections.
method Pullback approach to global Finsler geometry, study of horizontally recurrent connections.
result Existence and uniqueness of horizontally recurrent Finsler connections for scalar forms.
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.
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.
VLN generates future video frames efficiently with lateral connections.
problem Efficiently generating future video frames.
method Neural encoder-decoder model with lateral connections, including recurrent and feedforward lateral connections.
result VLN achieves competitive results on the Moving MNIST dataset.
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.
The study connects Kleinian group divergence to random walk recurrence.
problem Understanding the recurrence of random walks on Schreier graphs of Kleinian groups.
method Connecting growth rates of orbits, volume, and Schreier graphs.
result Constructing Kleinian groups of divergence type.
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 …
This paper proposes structurally sparse RNNs to reduce computational and memory costs.
problem Heavy computational and memory burden in fully connected RNNs.
method Study structurally sparse RNNs, reducing recurrent operations and weights.
result Structurally sparse RNNs achieve competitive performance with reduced costs.
This paper investigates the role of sparsity in Reservoir Computing networks.
problem Designing efficient Recurrent Neural Networks (RNNs) with hidden recurrent layers.
method Empirical investigation of sparsity in input-reservoir connections and recurrent connections.
result Sparsity, particularly in input-reservoir connections, enhances the network's temporal memory and dimensionality.
Trains recurrent networks to perform complex tasks with fewer neurons and better robustness.
problem Training recurrent networks to handle temporally complex tasks efficiently.
method Introduces a target network to provide suitable dynamics for the task, modifying the full connectivity matrix.
result Trained networks perform tasks with fewer neurons and greater noise robustness.
Adaptive lateral connections improve visual action recognition.
problem Feedforward neural models lack feedback and lateral connections like the primate visual cortex.
method Dynamic weights in recurrent lateral connections, iteratively reintroduced input.
result Significant performance gains in visual action recognition without pretraining.
We prove quantitative recurrence and large deviations results for the Teichmuller geodesci flow on a connected component of a stratum of the moduli space Qg of holomorphic unit-area quadratic differentials on a compact genus g≥2 surface.
Paper connects WFA and 2-RNNs, offering a new learning algorithm.
problem Expressiveness and learning of recurrent neural networks.
method Spectral learning algorithm for linear 2-RNNs.
result Provable learning algorithm for linear 2-RNNs.
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multi…
RNNs guide clause selection in proof trees, improving inference accuracy.
problem Improving inference accuracy in proof trees.
method Recurrent Neural Networks (RNNs) encode literals to select clauses.
result RNNs outperform gradient boosted trees in clause selection.
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.
This work introduces a new model for complex stochastic processes.
problem Difficulties in representing non-stationary distributions with conventional models.
method Recurrent Autoregressive Flows using normalizing flows with recurrent neural connections.
result Demonstrates the effectiveness of the proposed model through experiments.
Recurrent CNNs improve image classification in low light conditions.
problem Poor performance of CNNs in noisy images.
method Added recurrent connections to CNN layers to enhance robustness.
result gruCNNs outperform cCNNs in low signal-to-noise ratio images.
Random walks on mapping class group lead to recurrent geodesics in quadratic differentials.
problem Understanding recurrence of geodesics in quadratic differentials.
method Analyzing random walks on mapping class group with specific properties.
result Recurrence of geodesics in the thick part of the principal stratum of quadratic differentials.
Tikhonov regularization improves LSTM network performance without dropout issues.
problem Improving LSTM network performance without dropout-induced memory loss.
method Derives a Tikhonov regularizer for LSTM networks, considering interactions between weights.
result Proposes a regularizer with three parameters for LSTM networks, maintaining stability during training.
The present paper is a continuation of a foregoing paper [Tensor, N. S., 69 (2008), 155-178]. The main aim is to establish \emph{an intrinsic investigation} of the conformal change of the most important special Finsler spaces, namely, Ch-recurrent, Cv-recurrent, C0-recurrent, C2-like, quasi-C-redu…
Optimal stock price prediction model using recurrent neural networks with RMSprop optimizer.
problem Stock price prediction using neural networks.
method Comparison of fully connected, convolutional, and recurrent architectures; inclusion of three optimization techniques.
result Single layer recurrent neural network with RMSprop optimizer produces optimal results with validation and test MAE of 0.0150 and 0.0148 respectively.
Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold M whose Brownian motion satisfies a certain recurrence property called ∗-recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, un…
Recurrent Neural Networks handle sequential data better than traditional networks.
problem Handling temporal context and gradient flow in training RNNs.
method Explains the structure and challenges of RNNs, including training complexities.
result RNNs improve performance in various sequential tasks.
Paper explores how neural codes can be derived from spike timing patterns.
problem Lack of computational models for spike timing information.
method Minimalistic abstraction of recurrent connections using information-theoretic techniques.
result Neural codes derived from polychronous groups meet benchmarks for linear classification and capacity.
Dual neural network architecture improves accuracy and interpretability.
problem Improving neural network interpretability and accuracy.
method Stacked recurrent and feedforward layers, binary activation function.
result Binary activation leads to simpler, more interpretable models with higher accuracy.
A second-order differential identity for the Riemann tensor is obtained, on a manifold with symmetric connection. Several old and some new differential identities for the Riemann and Ricci tensors descend from it. Applications to manifolds with Recurrent or Symmetric structures are discussed. The new structure of K-rec…
New methods improve Reservoir Computing for chaotic time series prediction.
problem Chaotic time series prediction in Reservoir Computing.
method Established Recurrent Kernel limit, introduced Structured Reservoir Computing.
result Structured Reservoir Computing is faster and more memory-efficient.
The AJ conjecture is verified for certain connected sums of torus knots.
problem Verifying the AJ conjecture for specific connected sums of torus knots.
method Analyzing recurrence polynomials and their factorization properties.
result The AJ conjecture requires a modification for certain connected sums of torus knots.
Improved sentiment analysis explanations using LRP for RNNs.
problem Creating understandable explanations for recurrent neural network predictions.
method Extending Layer-wise Relevance Propagation (LRP) to recurrent neural networks (RNNs), specifically to multiplicative connections in LSTMs and GRUs.
result Better explanation quality for sentiment analysis tasks using LRP compared to gradient-based methods.
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We sugge…
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…
AntisymmetricRNN improves RNN trainability without extra computation.
problem Difficulty in learning long-term dependencies in RNNs.
method Connecting RNNs to ordinary differential equations and proposing AntisymmetricRNN.
result AntisymmetricRNN captures long-term dependencies more predictably and efficiently.
RNNs trained on spatial tasks develop grid-like spatial representations.
problem Understanding the neural code for spatial navigation in the brain.
method Training recurrent neural networks to perform spatial localization tasks.
result Grid-like spatial response patterns emerge in trained RNNs, similar to EC grid cells.
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.
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections and estimate system parameters of a recurrent network, given a sequence of node …
Deep RNNs reveal interesting insights about short-term memory dynamics.
problem Understanding the short-term memory capabilities of deep RNNs.
method Investigation of state dynamics in successive levels of deep RNNs.
result Higher layers in a hierarchically organized RNN architecture exhibit longer memory spans.
Mathematical study of learning long-term integration in linear RNNs.
problem How do linear recurrent neural networks learn to integrate over long timescales?
method Analytical study of linear RNNs trained to integrate white noise and damped oscillatory filters.
result Learning dynamics are described by low-dimensional effective equations for outlier eigenvalues.
The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold (M,g) is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of (M,g). We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their…
RNNs are reinterpreted as kernel methods using neural ODEs.
problem Improving generalization and stability of RNNs.
method Connecting RNNs to neural ODEs and reproducing kernel Hilbert spaces.
result RNNs can be viewed as linear functions of a specific feature set.
Paper uses RNN to predict SaaS user lifetime value.
problem Predicting user lifetime value in SaaS applications.
method Recurrent Neural Network with multi-cell architecture, accounting for cohort, age-in-system, and contemporaneous information.
result Significantly improved prediction accuracy compared to existing models.
Efficient deep GNNs achieve state-of-the-art performance without training.
problem Efficiency issue in deep graph neural networks.
method Representing graphs as fixed points of dynamical systems and using small, sparse, untrained recurrent networks.
result Small deep GNNs without training can achieve or improve state-of-the-art performance.
Proposes a new RNN structure to improve expressivity without sacrificing stability.
problem Exploding and vanishing gradient problems in RNNs and reduced expressivity.
method Introduces a non-normal RNN structure using Schur decomposition and splitting.
result Enhances expressivity while maintaining stability and training speed.
Integrates momentum into RNNs to improve training.
problem Vanishing gradient in RNNs during training.
method Established connection between RNN dynamics and GD, integrated momentum.
result MomentumRNNs alleviate vanishing gradient issue and improve convergence.
The paper improves RBP for stable and efficient training of recurrent neural networks.
problem Stability issues in RBP for training recurrent neural networks.
method Proposed two variants of RBP: CG-RBP and Neumann-RBP, and compared them with BPTT and TBPTT.
result Neumann-RBP is more efficient in terms of memory usage compared to TBPTT.
Differentiable plasticity enables efficient lifelong learning in neural networks.
problem Building agents that can learn from experience quickly and efficiently.
method Optimized plastic connections in recurrent neural networks using gradient descent.
result Plastic neural networks can learn and reconstruct novel images and solve meta-learning tasks.
High-order RNNs reduce speech recognition errors.
problem Vanishing gradients in RNNs.
method High-order RNNs with multiple connections from previous time steps.
result HORNNs reduce WER by 4.2% and 6.3% over RNNs.
Trellis networks improve sequence modeling performance.
problem Sequence modeling challenges.
method Temporal convolutional network with weight tying and direct input injection.
result Trellis networks outperform state-of-the-art methods on benchmarks.