RotRNN uses rotations to simplify long sequence modelling.
problem Complex initialisation and normalisation schemes in linear recurrent models.
method RotRNN employs rotation matrices to simplify and normalise linear recurrent models.
result RotRNN achieves competitive performance on long sequence modelling datasets.
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.
Proposes a new model for better speech segmentation.
problem Improving speech segmentation accuracy.
method Integrates recurrent explicit duration variables into rSLDS and uses Pólya-gamma augmentation for inference.
result Demonstrates improved segmentation on various datasets.
Recurrent neural networks can learn complex transduction problems that require maintaining and actively exploiting a memory of their inputs. Such models traditionally consider memory and input-output functionalities indissolubly entangled. We introduce a novel recurrent architecture based on the conceptual separation b…
Linear recurrent networks explain reinforcement learning performance in partially observable settings.
problem Understanding why linear recurrent networks work in reinforcement learning with partial observability.
method Constructed and studied two linear filters for HMMs and action-controlled HMMs.
result Linear filters serve as sufficient statistics and reduce state ambiguity, explaining empirical reinforcement learning success.
Improved electricity price forecasting model combining linear and non-linear structures.
problem Day-ahead electricity price forecasting in energy systems.
method Recurrent neural networks with embedded linear structures.
result Approximately 11% higher accuracy than state-of-the-art models.
Study of recurrences in earthquakes, climate, financial time-series, etc. is crucial to better forecast disasters and limit their consequences. However, almost all the previous phenomenological studies involved only a long-ranged autocorrelation function, or disregarded the multi-scaling properties induced by potential…
A linear multi-factor model is one of the most important tools in equity portfolio management. The linear multi-factor models are widely used because they can be easily interpreted. However, financial markets are not linear and their accuracy is limited. Recently, deep learning methods were proposed to predict stock re…
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.
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.
For a knot K in S3, the sl2-colored Jones function JK(n) is a sequence of Laurent polynomials in the variable t, which is known to satisfy non-trivial linear recurrence relations. The operator corresponding to the minimal linear recurrence relation is called the recurrence polynomial of K. The AJ conject…
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.
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.
Study on memory effects in RNNs learning temporal data.
problem Understanding memory effects in RNNs for temporal data learning.
method Mathematical analysis of continuous-time linear RNNs, focusing on approximation and optimization dynamics.
result Long-term memory requires a large number of neurons and slows down training.
Study asymptotics of one part monotone Hurwitz numbers in high genus.
problem Asymptotic analysis of one part monotone Hurwitz numbers in high genus.
method Used a linear recurrence and a recent method to extract asymptotics.
result Obtained bivariate asymptotics for one part monotone Hurwitz numbers in high genus.
Traditional convolutional layers extract features from patches of data by applying a non-linearity on an affine function of the input. We propose a model that enhances this feature extraction process for the case of sequential data, by feeding patches of the data into a recurrent neural network and using the outputs or…
Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple ta…
Stability of recurrent models is closely linked with trainability, generalizability and in some applications, safety. Methods that train stable recurrent neural networks, however, do so at a significant cost to expressibility. We propose an implicit model structure that allows for a convex parametrization of stable mod…
We derive formulas for HOMFLY polynomials of torus links using braid groups and linear recurrences.
problem Calculating HOMFLY polynomials for torus links.
method Using braid groups and linear recurrences, derived from the skein relation.
result Explicit formulas for HOMFLY polynomials of torus links T(3,n) and T(−3,n) are derived. Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments that are each explained by simpler dynamic units. Building on switching linear dy…
The paper examines how NFT valuations correlate with market data and social trends.
problem Predicting NFT valuations based on market data and social trends.
method Utilizes public market data, NFT metadata, and social trends data; employs linear regression and recurrent neural networks.
result Identifies correlations between NFT valuations and various features.
Learning to solve sequential tasks with recurrent models requires the ability to memorize long sequences and to extract task-relevant features from them. In this paper, we study the memorization subtask from the point of view of the design and training of recurrent neural networks. We propose a new model, the Linear Me…
New approach improves linear-time attention for language models.
problem Challenges of quadratic attention in long-sequence modelling, especially for discrete data.
method Reinterpreting linear attention through latent probabilistic graphical models, introducing asymmetric structure and recurrent parameterisation.
result Our model achieves competitive performance and outperforms existing linear attention variants on language modelling benchmarks.
Generalizes memory and forecasting capacities for nonlinear recurrent networks with dependent inputs.
problem Understanding memory and forecasting capabilities in networks with dependent inputs.
method Formulated bounds for memory and forecasting capacities in terms of network size and input properties.
result Proved that memory capacity for linear recurrent networks with independent inputs is given by the rank of the controllability matrix.
Training recurrent neural networks (RNNs) is a hard problem due to degeneracies in the optimization landscape, a problem also known as vanishing/exploding gradients. Short of designing new RNN architectures, previous methods for dealing with this problem usually boil down to orthogonalization of the recurrent dynamics,…
This paper compares Transformers and RNNs in various tasks, showing size differences.
problem Comparing representational capabilities of Transformers and RNNs across tasks.
method Analysis of differences in tasks like index lookup, nearest neighbor, and string equality.
result Size differences in Transformers and RNNs for various tasks.
CRUs model irregular time series with continuous hidden states.
problem Handling irregular time intervals in sequential data.
method Continuous Recurrent Units (CRUs) that integrate hidden states via a linear stochastic differential equation.
result CRUs outperform methods based on neural ordinary differential equations in irregular time series interpolation.
New approach predicts stock price synchronization using RNNs and LSTMs.
problem Forecasting synchronization of stock prices in the Indian market.
method Utilizing recurrence plots and CRQA for non-linear analysis, RNNs and LSTMs for prediction.
result Accuracy of 0.98 and F1 score of 0.83 in predicting stock price synchronization.
Nonlinear RNNs' memory capacity varies widely, making it impractical.
problem The usefulness of memory capacity as a metric for linear RNNs is questioned.
method Analysis of random nonlinear RNNs with varying input scales.
result Memory capacity of nonlinear RNNs is arbitrary and impractical.
The paper develops a convex parameterization for robust RNNs ensuring stability and robustness.
problem Lack of stability and robustness guarantees in RNNs for sequence-to-sequence mapping applications.
method Formulated convex sets of RNNs with stability and robustness guarantees using incremental quadratic constraints.
result The proposed model structure ensures global exponential stability and bounds on incremental ℓ2 gain. 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.
Low dimensional representations of words allow accurate NLP models to be trained on limited annotated data. While most representations ignore words' local context, a natural way to induce context-dependent representations is to perform inference in a probabilistic latent-variable sequence model. Given the recent succes…
Study compares MoE and RNN models for stock price prediction across volatility profiles.
problem Improving stock price prediction accuracy across different volatility levels.
method Dynamic Mixture of Experts model combining RNN and linear models, adjusting weights through a gating network.
result MoE model outperforms individual models in reducing prediction errors.
A new framework for efficient sequence maps using Bayesian filtering and covariance.
problem Designing efficient recurrent sequence maps from explicit memory assumptions.
method Design-model framework, exact Bayesian filtering, query-dependent readout, linear-Gaussian instantiation.
result Improved robustness and retrieval performance across various benchmarks.
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, exist…
Central Pattern Generators (CPGs) are biological neural circuits capable of producing coordinated rhythmic outputs in the absence of rhythmic input. As a result, they are responsible for most rhythmic motion in living organisms. This rhythmic control is broadly applicable to fields such as locomotive robotics and medic…
Develops a tensor network framework to reduce RNN complexity for high-dimensional sequence modeling.
problem Exponential parameter growth in RNNs for large multidimensional data.
method Embeds a multi-linear graph filter in a tensor network architecture to approximate RNN hidden states.
result Demonstrates superior performance and reduced complexity compared to traditional RNNs.
Linear RNNs exhibit a bias towards shorter memory due to initialization variance.
problem Understanding the performance limitations of RNNs, especially linear ones.
method Kernel regime analysis to show equivalence to 1D-convolutional networks and analyze weightings.
result Linear RNNs with random initialization have a bias towards shorter memory periods.
We analyze generalization in deep learning models using random matrix theory.
problem Understanding the generalization error in deep learning models with random feature representations.
method Applying Random Matrix Theory to derive asymptotic generalization error formulas for various architectures.
result Linear ESNs are equivalent to ridge regression with exponentially time-weighted input covariance, revealing an inductive bias towards recent inputs.
SKOLR uses linear RNNs to approximate Koopman operators for time-series forecasting.
problem Nonlinear dynamical system analysis and time-series forecasting with infinite-dimensional Koopman operators.
method Established a connection between Koopman operator approximation and linear RNNs, integrating learnable spectral decomposition and MLP.
result SKOLR delivers exceptional performance in various forecasting benchmarks and dynamical systems.
Recently, studies on deep Reservoir Computing (RC) highlighted the role of layering in deep recurrent neural networks (RNNs). In this paper, the use of linear recurrent units allows us to bring more evidence on the intrinsic hierarchical temporal representation in deep RNNs through frequency analysis applied to the sta…
New differential geometry perspective on orthogonal RNNs.
problem Mitigating exploding and vanishing gradients in RNNs.
method Using tools from differential geometry, parameterizing vector fields via directional derivatives of scalar functions.
result Our approach achieves comparable or better results on benchmark tasks.
Vanishing long-term gradients are a major issue in training standard recurrent neural networks (RNNs), which can be alleviated by long short-term memory (LSTM) models with memory cells. However, the extra parameters associated with the memory cells mean an LSTM layer has four times as many parameters as an RNN with the…
Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.
problem Understanding the algebraic, geometric, and topological properties of grid cells.
method Investigating recurrent neural network models of grid cells, focusing on Lie group and Lie algebra representations, conformal isometry, and hexagon periodic patterns.
result Conformal isometry leads to hexagon periodic patterns in grid cell responses and accurate path integration.
New types of semi-Riemannian manifolds with linear curvature conditions identified.
problem Identifying new types of semi-Riemannian manifolds with linear curvature conditions.
method Analyzing semi-Riemannian manifolds that satisfy linear differential conditions on the curvature.
result Existence of new families of semi-Riemannian manifolds, including those with recurrent curvature and symmetric spaces.
A new approach learns to represent context for nonstationary bandits.
problem Nonstationary contextual bandits where patterns change over time.
method Combines recurrent neural networks with contextual linear bandit algorithm.
result Consistently outperforms handcrafted historical contexts and other methods.
In this paper, we unravel a fundamental connection between weighted finite automata~(WFAs) and second-order recurrent neural networks~(2-RNNs): in the case of sequences of discrete symbols, WFAs and 2-RNNs with linear activation functions are expressively equivalent. Motivated by this result, we build upon a recent ext…
Recurrence Plot (RP) and Recurrence Quantification Analysis RQA) are signal numerical analysis methodologies able to work with non linear dynamical systems and non stationarity. Moreover they well evidence changes in the states of a dynamical system. It is shown that RP and RQA detect the critical regime in financial i…