# Recurrent Neural Networks

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arXiv Nov 6, 2026
Recurrent state estimation gets a convergence guarantee: one gain drives the error exponentially into any small neighborhood
Recurrent models for state estimation previously had empirical success but no formal convergence or robustness guarantees. This work treats a recurrent network as a discretization of continuous latent dynamics and requires the latent flow to contract, proving that a smooth injective map embeds the true physical state into latent space; raising a single scalar gain κ drives the estimation error exponentially fast into an arbitrarily small neighborhood of zero, at the cost of decoder capacity growing polynomially in κ. On a real mobile-robot pose-estimation task, the provably contracting model outperforms a vanilla GRU and trains more stably.
Recurrent models for state estimation previously had empirical success but no formal convergence or robustness guarantees. This work treats a recurrent network as a discretization of continuous latent dynamics and requires the latent flow to contract, proving that a smooth injective map embeds the true physical state into latent space; raising a single scalar gain κ drives the estimation error exponentially fast into an arbitrarily small neighborhood of zero, at the cost of decoder capacity growing polynomially in κ. On a real mobile-robot pose-estimation task, the provably contracting model outperforms a vanilla GRU and trains more stably.
Centre National de la Recherche Scientifique
Vincent Andrieu（First author）
State Estimation Contracting GRU Nonlinear KKL Observers Recurrent Neural Networks Neural Ordinary Differential Equations
arXiv Nov 10, 2026
CURRENT fills in both space and time for aortic 4D flow MRI with one recurrent network, sharpening relative pressure estimates
A team at the University of Zurich and ETH Zurich built CURRENT, a recurrent neural network that performs spatial, temporal and spatiotemporal super-resolution of aortic 4D flow MRI within one architecture. On synthetic data its spatial super-resolution directional error was 0.072±0.037 versus 0.097±0.053 for 4DFlowNet, and its temporal directional error was 0.062±0.031 versus 0.064±0.031 for T4DFlowNet. Joint spatiotemporal super-resolution gave relative pressure estimates closer to the high-resolution reference than either direction alone, and the model, trained only on synthetic data, showed promising generalization to in vivo acquisitions.
A team at the University of Zurich and ETH Zurich built CURRENT, a recurrent neural network that performs spatial, temporal and spatiotemporal super-resolution of aortic 4D flow MRI within one architecture. On synthetic data its spatial super-resolution directional error was 0.072±0.037 versus 0.097±0.053 for 4DFlowNet, and its temporal directional error was 0.062±0.031 versus 0.064±0.031 for T4DFlowNet. Joint spatiotemporal super-resolution gave relative pressure estimates closer to the high-resolution reference than either direction alone, and the model, trained only on synthetic data, showed promising generalization to in vivo acquisitions.
ETH Zurich
Luuk Jacobs（First author, Corresponding author）
CURRENT 4D Flow MRI Image Super-Resolution Recurrent Neural Networks
arXiv Nov 5, 2026
Neural circuits that grow while working: trained at just three developmental snapshots, a controller keeps visuomotor behavior at untrained ages
A recurrent neural controller must keep behaving while neurons are born, move, and change their intrinsic time constants during development; controllers optimized only on the initial or the mature substrate generally failed at other ages. The study feeds developmental time into a compact connectivity generator and optimizes the same generator at three, five, or fifteen developmental snapshots, testing it on two geometrically distinct substrates and two visuomotor tasks. Optimization at only three snapshots was often enough to keep performance high and consistent at trained and untrained ages, while the generated connectomes changed substantially with age and did not converge on a single sparsity or weight trajectory.
A recurrent neural controller must keep behaving while neurons are born, move, and change their intrinsic time constants during development; controllers optimized only on the initial or the mature substrate generally failed at other ages. The study feeds developmental time into a compact connectivity generator and optimizes the same generator at three, five, or fifteen developmental snapshots, testing it on two geometrically distinct substrates and two visuomotor tasks. Optimization at only three snapshots was often enough to keep performance high and consistent at trained and untrained ages, while the generated connectomes changed substantially with age and did not converge on a single sparsity or weight trajectory.
Duke University
Christof Fehrman（First author）
Developmental Neuroevolution HyperNEAT Compositional Pattern Producing Networks Time-Varying Connectomes Recurrent Neural Networks
arXiv Oct 12, 2026
RWKV fades on long horizons: alternating in attention blocks lets a 36M model match a 1B forecaster on GIFT long-horizon MASE
HART alternates Transformer and RWKV blocks so prediction positions can retrieve history directly, beating pure RWKV at medium and long horizons on GIFT-Eval and TIME-Benchmark and matching Toto-2.0-1B's long-horizon MASE on GIFT with 36M parameters.
Huawei Technologies (China)Shantou University Guangdong University of Technology Université Paris Cité
Qingwen Lin（First author）
Hybrid Attention-RWKV Time-Series Foundation Model Placeholder Idling Decay Non-Autoregressive Multi-Step Forecasting Time-Series Foundation Model Recurrent Neural Networks
arXiv Oct 14, 2026
Gated RNNs stall on who learns the gates: mixing short-dependency samples into training lets GRU and LSTM catch Mamba and xLSTM
The long-range memory bottleneck in gated recurrent networks is traced to the gates themselves having to be learned by the same recurrent computation, and adding short-dependency samples to training brings GRU and LSTM long-dependency test accuracy from near chance back to roughly ninety percent or higher, matching or exceeding Mamba and xLSTM.
Delft University of Technology
Zeyu Fan（First author）
Gate Learning in Gated RNNs Vanishing Gradient Problem Recurrent Neural Networks Temporal XOR Sequence Classification Short-Dependency Training Samples
Journal of Neural Engineering Oct 16, 2026
Cross-region neural dynamics stop being drowned by local activity: shared dynamics come first, and nonlinearity gets a location
Models of cross-region neural dynamics have largely stayed linear, while each region's recorded activity mixes local dynamics with dynamics shared across regions. CroP-DYNO sets learning directly on predicting target-population activity from source activity, so shared dynamics are extracted first, and it lets each model component be specified as linear or nonlinear. On macaque S1–M1 and rat CA1–CA3 data it predicts target activity better than a non-prioritized nonlinear model and a prioritized linear model, and it localizes nonlinear structure and yields interaction strengths consistent with known circuit anatomy.
Models of cross-region neural dynamics have largely stayed linear, while each region's recorded activity mixes local dynamics with dynamics shared across regions. CroP-DYNO sets learning directly on predicting target-population activity from source activity, so shared dynamics are extracted first, and it lets each model component be specified as linear or nonlinear. On macaque S1–M1 and rat CA1–CA3 data it predicts target activity better than a non-prioritized nonlinear model and a prioritized linear model, and it localizes nonlinear structure and yields interaction strengths consistent with known circuit anatomy.
University of Southern California
Trisha Jha（First author）Maryam M Shanechi（Corresponding author）
CroP-DYNO Cross-region neural interaction modeling Recurrent Neural Networks
arXiv Oct 9, 2026
SpatialRNN replaces direct neuron-to-neuron links with a PDE medium, holding near-100% copy-task accuracy with 6.8k parameters while HORNNs degrade to about 13%
The authors introduce SpatialRNN, in which recurrent neuron-to-neuron communication is replaced by a spatially evolving medium governed by discretized PDEs, and prove that the medium state equals a convolution over the entire history of hidden states, i.e. a structured infinite-order RNN with a fixed parameter count; constructive conditions confine gradient modes to circles of prescribed radii, yielding better long-horizon performance than other recurrent models with fewer parameters.
The authors introduce SpatialRNN, in which recurrent neuron-to-neuron communication is replaced by a spatially evolving medium governed by discretized PDEs, and prove that the medium state equals a convolution over the entire history of hidden states, i.e. a structured infinite-order RNN with a fixed parameter count; constructive conditions confine gradient modes to circles of prescribed radii, yielding better long-horizon performance than other recurrent models with fewer parameters.
Northwestern University University of California San Diego Massachusetts Institute of Technology
Aleix Salvador-Pomarol（First author）
SpatialRNN Spatial Computing Recurrent Neural Networks Long-Range Dependency Modeling Vanishing Gradient Problem

You’re all caught up

Recurrent state estimation gets a convergence guarantee: one gain drives the error exponentially into any small neighborhood

CURRENT fills in both space and time for aortic 4D flow MRI with one recurrent network, sharpening relative pressure estimates

Neural circuits that grow while working: trained at just three developmental snapshots, a controller keeps visuomotor behavior at untrained ages

RWKV fades on long horizons: alternating in attention blocks lets a 36M model match a 1B forecaster on GIFT long-horizon MASE

Gated RNNs stall on who learns the gates: mixing short-dependency samples into training lets GRU and LSTM catch Mamba and xLSTM

Cross-region neural dynamics stop being drowned by local activity: shared dynamics come first, and nonlinearity gets a location

SpatialRNN replaces direct neuron-to-neuron links with a PDE medium, holding near-100% copy-task accuracy with 6.8k parameters while HORNNs degrade to about 13%