Stochastic reservoir computing is shown to be a universal approximator.
problem Theoretical justification for using stochastic reservoirs in machine learning.
method Investigated stochastic reservoir computing using probabilities of reservoir states as readout.
result Stochastic reservoir computers are universal approximating classes.
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.
We explore the hyperparameter space of reservoir computers used for forecasting of the chaotic Lorenz '63 attractor with Bayesian optimization. We use a new measure of reservoir performance, designed to emphasize learning the global climate of the forecasted system rather than short-term prediction. We find that optimi…
The paper analyzes the performance of delay-based reservoir computing using eigenvalue analysis.
problem Quantifying the performance of delay-based reservoir computing.
method Eigenvalue analysis of the dynamical system to predict reservoir computing performance.
result The performance of a reservoir computing system can be predicted by analyzing the small signal response and eigenvalue spectrum.
New insights on stability in reservoir computing for better performance.
problem Stability in reservoir computing networks.
method Using the recurrent kernel limit for large reservoir sizes.
result Quantitative characterization of stability and chaos frontier.
This paper provides a mathematical framework for time-delay reservoir computing.
problem Lack of rigorous mathematical foundations for reservoir computing properties.
method Control-theoretic framework, formal definitions of separation and fading memory, explicit lower bound derivation.
result Established formal definitions and connections to stability notions for time-delay systems.
New explanation of reservoir computing using random projections.
problem Understanding the randomness in reservoir computing.
method Constructing strongly universal reservoir systems as random projections of state-space systems.
result Approximation of any fading memory filters class by training a linear readout for each filter.
The paper introduces reservoir computing models for complex systems.
problem Modeling complex engineering systems using nonlinear autoregression.
method Introduces reservoir computing with output feedback as stationary and ergodic infinite-order nonlinear autoregressive models.
result Demonstrates versatility of classical and quantum reservoir computers in modeling synthetic and real data.
Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy and processing speed at benchmark tasks. However, these approaches require an e…
Reduced reservoir size for faster edge computing.
problem Efficiently reducing computational resources for reservoir computing.
method Concatenating past or drifting states of the reservoir to the output layer.
result Reduced reservoir size up to one tenth without significant error increase.
Reservoir computing's success depends on mapping different input time series to separable states.
problem Quantifying the ability of random linear reservoirs to map different input time series.
method Mathematical framework using spectral properties of the connectivity matrix.
result Separation capacity is fully characterized by the spectral properties of the connectivity matrix.
A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor, covariance and Kaplan-Yorke dimensions, are used to estimate the dimension of the res…
Study characterizes memory capacity of quantum reservoirs using transmon qubits.
problem Understanding the memory capacity of quantum reservoirs built with transmon qubits.
method Characterized memory capacity of quantum reservoirs using transmon qubits from IBM, focusing on NMSE and topology complexity.
result Found a peak in memory capacity for configurations with n-1 self-loops, suggesting optimal design for forecasting tasks.
Quantum reservoir computing improves volatility forecasting.
problem Forecasting realized volatility in finance.
method Quantum reservoir computing with Ising Hamiltonian and feature selection.
result Quantum reservoir computing outperforms benchmarks in volatility forecasting.
BNNs enhance reservoir computing by acting as generalization filters.
problem Understanding how BNNs integrate with reservoir computing.
method Optogenetics and calcium imaging to record BNNs, reservoir computing framework.
result BNNs improve reservoir computing performance through generalization.
We analyze the practices of reservoir computing in the framework of statistical learning theory. In particular, we derive finite sample upper bounds for the generalization error committed by specific families of reservoir computing systems when processing discrete-time inputs under various hypotheses on their dependenc…
New definitions of ESP for quantum reservoir computing handle non-stationary systems.
problem Traditional ESP does not apply to non-stationary systems.
method Introduce two new categories of ESP: non-stationary ESP and subset/subspace ESP.
result Demonstrates correspondence between non-stationary ESP and QRC with NARMA tasks.
Quantum reservoirs risk bounds are analyzed using Rademacher complexity.
problem Bounding generalization errors of quantum reservoirs.
method Using Rademacher complexity, specific bounds are derived for quantum reservoir classes.
result Risk bounds converge with increasing training samples and qubits.
ResCP uses reservoir computing to create efficient, scalable time series prediction intervals.
problem Building distribution-free prediction intervals for time series data with small sample sizes and changing distributions.
method Reservoir Conformal Prediction (ResCP) leverages reservoir computing to dynamically reweight conformity scores based on similarity among reservoir states.
result ResCP achieves asymptotic conditional coverage and is effective across diverse forecasting tasks.
New method combines long-memory reservoirs for accurate dengue forecasting from short data.
problem Accurate dengue forecasting from short, noisy, non-stationary, and nonlinear data.
method Fractional ESN and Wavelet ESN frameworks integrating long-term memory.
result fESN and wESN outperform baselines in multiple dengue datasets and forecasting horizons.
Deep learning speeds up pressure prediction in carbon storage reservoirs.
problem Accurately forecasting reservoir pressure in geologic carbon storage projects with sparse well data.
method Combining InSAR surface displacement data with deep learning and data assimilation techniques.
result Workflow can predict reservoir pressure with high efficiency and uncertainty quantification.
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.
Quantum Reservoir Computing classifies complex probability distributions and identifies volatility regimes.
problem Statistical and financial classification problems with heavy-tailed distributions and correlated time series.
method Implemented QRC in a superconducting quantum circuit with Josephson junctions.
result QRC outperforms classical methods in limited information scenarios.
Optical ESNs enable flexible, efficient machine learning with reduced energy.
problem Implementing universal computational capabilities in machine learning.
method Optical implementation of ESNs leveraging stimulated Brillouin scattering.
result Efficient, scalable, and memory-capable optical reservoir computing.
Deep Echo State Networks (DeepESNs) recently extended the applicability of Reservoir Computing (RC) methods towards the field of deep learning. In this paper we study the impact of constrained reservoir topologies in the architectural design of deep reservoirs, through numerical experiments on several RC benchmarks. Th…
The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for temporal information processing, i.e., processing of input sequences to produce …
New reservoir computing approach handles infinite-dimensional systems.
problem Approximating and generalizing complex input/output systems.
method Randomly generated echo state networks with neural networks.
result Proves universal approximation properties for new class of systems.
Quantum reservoir computing needs coherence influx for effective information processing.
problem Understanding and optimizing quantum reservoir computing.
method Theoretical and numerical analysis of quantum systems, focusing on coherence influx and spectral radius of Pauli transfer matrix.
result Coherence influx is essential for realizing nonstationary echo state property in quantum reservoir computing.
Reservoir Computing (RC) refers to a Recurrent Neural Networks (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here we focus on the sequence lear…
Next-gen reservoir computers fail to predict complex processes, highlighting need for better architectures.
problem Predicting complex, non-Markovian processes with recurrent neural networks.
method Lower bound from Fano's inequality and analysis of large probabilistic state machines.
result Next-generation reservoir computers have an error probability at least 60% higher than optimal for highly non-Markovian processes.
EuSN uses Euler discretization for stable, non-dissipative reservoir computing.
problem Designing stable and efficient reservoir computing models.
method Forward Euler discretization and antisymmetric recurrent matrices.
result EuSN outperforms standard RC models in long-term memory tasks and time-series classification.
Ring-reservoir networks simplify graph embeddings efficiently.
problem Efficient graph embeddings using deep neural networks.
method Progressive simplification of Reservoir Computing models to ring topology.
result Ring-reservoir networks show consistent advantages in predictive performance.
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
problem Predicting and capturing long-term behaviors of stochastic dynamical systems.
method Data-driven framework combining Reservoir Computing and Normalizing Flow, integrating error modeling and both approaches virtues.
result Successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors.
We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the Bayesian evidential learning approach and exploits learning the direct relation bet…
Quantum systems with scrambling improve temporal information processing, but scaling requires exponential overhead.
problem Scalability and memory retention of quantum reservoirs in temporal information processing.
method Examined a quantum reservoir processing framework with scrambling reservoirs modeled by high-order unitary designs, analyzed in noiseless and noisy settings.
result Memory retention improves exponentially with reservoir size but worsens with reservoir iterations, requiring exponential shot overhead for scaling.
This paper presents a stochastic logic time delay reservoir design. The reservoir is analyzed using a number of metrics, such as kernel quality, generalization rank, performance on simple benchmarks, and is also compared to a deterministic design. A novel re-seeding method is introduced to reduce the adverse effects of…
Echo state networks are computationally lightweight reservoir models inspired by the random projections observed in cortical circuitry. As interest in reservoir computing has grown, networks have become deeper and more intricate. While these networks are increasingly applied to nontrivial forecasting tasks, there is a …
Predicting unobserved bifurcations in time series with unsupervised parameter extraction.
problem Predicting system behavior with unknown parameters from time series data.
method Reservoir computing framework for unsupervised extraction of slowly varying system parameters.
result Model predicts unknown bifurcations not present in training data.
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created wh…
Feedback improves ESN performance by 30-60% across various tasks.
problem Reducing computational complexity in ESNs for complex sequential data processing.
method State feedback to modify the internal reservoir state of ESNs.
result Feedback significantly improves ESN performance, reducing error by 30-60%.
Next-gen reservoir computing models dynamical systems from time-series data.
problem Modeling dynamical systems from time-series data.
method Pseudorandom nonlinear projection of time-delay embedded inputs.
result Models remain stable over long rollouts and generalize beyond training data.
Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing…
A new Latent Diffusion Model generates realistic reservoir facies.
problem Creating accurate reservoir facies from limited measurements.
method Proposes a Latent Diffusion Model for conditional facies generation.
result Significantly outperforms GAN-based alternatives in fidelity and realism.
Reservoir subspace injection improves online ICA by preserving injected features.
problem Discarding injected features in top-n whitening can degrade performance. method Formalized reservoir subspace injection (RSI) and developed diagnostics (IER, SSO, ρ_x) to identify and mitigate the failure mode.
result RSI controller preserves passthrough retention, improving performance by up to 2.2 dB.
NGRC shows numerical instabilities with short lags and high-degree polynomials.
problem Numerical instabilities in NGRC feature matrix.
method Combining numerical linear algebra and dynamical systems theory, we study feature matrix conditioning. We evaluate different numerical algorithms for solving the regularized least-squares problem.
result SVD-based training achieves accurate forecasts without regularization, preferable for short lags and high-degree polynomials.
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
Echo State Networks (ESN) are a class of Recurrent Neural Networks (RNN) that has gained substantial popularity due to their effectiveness, ease of use and potential for compact hardware implementation. An ESN contains the three network layers input, reservoir and readout where the reservoir is the truly recurrent netw…
New method uses randomised signatures for generating financial time series data.
problem Generating synthetic financial time series data accurately.
method Introduced a Wasserstein-type distance based on discrete-time randomised signatures.
result Demonstrated universal approximation for randomised signatures on continuous functions.