Recurrent Neural Networks

Neural network models with latent recurrent processing, where identical layers are recursively applied to the latent state, have gained attention as promising models for performing reasoning tasks. A strength of such models is that they enable test-time scaling, where the models can enhance their performance in the test phase without additional training. Models such as the Hierarchical Reasoning Model (HRM) and Artificial Kuramoto Oscillatory Neurons (AKOrN) can facilitate deeper reasoning by increasing the number of recurrent steps, thereby enabling the completion of challenging tasks, including Sudoku, Maze solving, and AGI benchmarks. In this work, we introduce confidence-based voting (C-voting), a test-time scaling strategy designed for recurrent models with multiple latent candidate trajectories. Initializing the latent state with multiple candidates using random variables, C-voting selects the one maximizing the average of top-1 probabilities of the predictions, reflecting the model's confidence. Additionally, it yields 4.9% higher accuracy on Sudoku-hard than the energy-based voting strategy, which is specific to models with explicit energy functions. An essential advantage of C-voting is its applicability: it can be applied to recurrent models without requiring an explicit energy function. Finally, we introduce a simple attention-based recurrent model with randomized initial values named ItrSA++, and demonstrate that when combined with C-voting, it outperforms HRM on Sudoku-extreme (95.2% vs. 55.0%) and Maze (78.6% vs. 74.5%) tasks.

The IEC-61850 GOOSE protocol underpins time-critical communication in modern digital substations but lacks native security mechanisms, leaving it vulnerable to replay, masquerade, and data injection attacks. Intrusion detection in this setting is challenging due to strict latency constraints (sub-4ms) and limited availability of labeled attack data. This paper evaluates whether unsupervised temporal modeling can provide effective and deployable anomaly detection for GOOSE networks. Five models are compared on the ERENO IEC-61850 dataset: a supervised Random Forest baseline, a feedforward Autoencoder, and three recurrent sequence autoencoders (RNN, LSTM, and GRU). The supervised Random Forest achieves the highest detection performance (F1=0.9516) but fails to meet real-time constraints at 21.8ms per prediction. All four unsupervised models satisfy the 4ms requirement, with the GRU achieving the best accuracy to latency tradeoff among them (F1=0.8737 at 1.118ms). A cross-environment evaluation on an independent dataset shows that all models degrade under distribution shift. However, recurrent models retain substantially higher relative performance than the supervised baseline, suggesting that temporal sequence modeling generalizes better than fitting labeled attack distributions. Anomaly thresholds for the unsupervised models are selected on a held out validation partition to avoid test set leakage. These results support unsupervised temporal models as a practical choice for real-time GOOSE intrusion detection, particularly in environments where labeled training data may be unavailable or where large-scale deployment across diverse substations is required.

The selection of the optimal embryo for transfer is a critical yet challenging step in in vitro fertilization (IVF), primarily due to its reliance on the manual inspection of extensive time-lapse imaging data. A key obstacle in this process is predicting blastocyst formation from the limited number of daily images available. Many clinics also lack complete time-lapse systems, so full videos are often unavailable. In this study, we aimed to predict which embryos will develop into blastocysts using limited daily images from time-lapse recordings. We propose a novel hybrid model that combines DINOv2, a transformer-based vision model, with an enhanced long short-term memory (LSTM) network featuring a multi-head attention layer. DINOv2 extracts meaningful features from embryo images, and the LSTM model then uses these features to analyze embryo development over time and generate final predictions. We tested our model on a real dataset of 704 embryo videos. The model achieved 96.4% accuracy, surpassing existing methods. It also performs well with missing frames, making it valuable for many IVF laboratories with limited imaging systems. Our approach can assist embryologists in selecting better embryos more efficiently and with greater confidence.

Reasoning has become a central capability in large language models. Recent research has shown that reasoning performance can be improved by looping an LLM's layers in the latent dimension, resulting in looped reasoning language models. Despite promising results, few works have investigated how their internal dynamics differ from those of standard feedforward models. In this paper, we conduct a mechanistic analysis of the latent states in looped language models, focusing in particular on how the stages of inference observed in feedforward models compare to those observed in looped ones. To this end, we analyze cyclic recurrence and show that for many of the studied models each layer in the cycle converges to a distinct fixed point; consequently, the recurrent block follows a consistent cyclic trajectory in the latent space. We provide evidence that as these fixed points are reached, attention-head behavior stabilizes, leading to constant behavior across recurrences. Empirically, we discover that recurrent blocks learn stages of inference that closely mirror those of feedforward models, repeating these stages in depth with each iteration. We study how recurrent block size, input injection, and normalization influence the emergence and stability of these cyclic fixed points. We believe these findings help translate mechanistic insights into practical guidance for architectural design.

Neural Quantum States based on autoregressive recurrent neural network (RNN) wave functions enable efficient sampling without Markov-chain autocorrelation, but standard RNN architectures are biased toward finite-length correlations and can fail on states with long-range dependencies. A common response is to adopt transformer-style self-attention, but this typically comes with substantially higher computational and memory overhead. Here we introduce dilated RNN wave functions, where recurrent units access distant sites through dilated connections, injecting an explicit long-range inductive bias while retaining a favorable $\mathcal{O}(N \log N)$ forward pass scaling. We show analytically that dilation changes the correlation geometry and can induce power-law correlation scaling in a simplified linearized and perturbative setting. Numerically, for the critical 1D transverse-field Ising model, dilated RNNs reproduce the expected power-law connected two-point correlations in contrast to the exponential decay typical of conventional RNN ansätze. We further show that the dilated RNN accurately approximates the one-dimensional Cluster state, a paradigmatic example with long-range conditional correlations that has previously been reported to be challenging for RNN-based wave functions. These results highlight dilation as a simple geometric mechanism for building correlation-aware autoregressive neural quantum states.

For applications on the extreme edge, minimal networks of only a few dozen artificial neurons for event detection and classification in discrete time signals would be highly desirable. Feed-forward networks, RNNs, and CNNs evolved through evolutionary algorithms can all be successful in this respect but pose the problem of allowing little systematicity in mutation and recombination if the standard direct genetic encoding of the weights is used (as for instance in the classic NEAT algorithm). We therefore introduce Echo Networks, a type of recurrent network that consists of the connection matrix only, with the source neurons of the synapses represented as rows, destination neurons as columns and weights as entries. There are no layers, and connections between neurons can be bidirectional but are technically all recurrent. Input and output can be arbitrarily assigned to any of the neurons and only use an additional (optional) function in their computational path, e.g., a sigmoid to obtain a binary classification output. We evaluated Echo Networks successfully on the classification of electrocardiography signals but see the most promising potential in their genome representation as a single matrix, allowing matrix computations and factorisations as mutation and recombination operators.

Context-dependent sequential decision making is commonly addressed either by providing context explicitly as an input or by increasing recurrent memory so that contextual information can be represented internally. We study a third alternative: realizing contextual dependence by intervening on a shared recurrent latent state, without enlarging recurrent dimensionality. To this end, we introduce an intervention-based recurrent architecture in which a recurrent core first constructs a shared pre-intervention latent state, and context then acts through an additive, context-indexed operator. We evaluate this idea on a context-switching sequential decision task under partial observability. We compare three model families: a label-assisted baseline with direct context access, a memory baseline with enlarged recurrent state, and the proposed intervention model, which uses no direct context input to the recurrent core and no memory growth. On the main benchmark, the intervention model performs strongly without additional recurrent dimensions. We also evaluate the models using the conditional mutual information (I(C;O | S)) as a theorem-motivated operational probe of contextual dependence at fixed latent state. For task-relevant phase-1 outcomes, the intervention model exhibits positive conditional contextual information. Together, these results suggest that intervention on a shared recurrent state provides a viable alternative to recurrent memory growth for contextual control in this setting.

Developmental approaches to neural architecture search grow functional networks from compact genomes through self-organisation, but the resulting networks operate with fixed post-growth weights. We characterise Hebbian and anti-Hebbian plasticity across 50,000 morphogenetically grown recurrent controllers (5M+ configurations on CartPole and Acrobot), then test whether co-evolutionary experiments -- where plasticity parameters are encoded in the genome and evolved alongside the developmental architecture -- recover these patterns independently. Our characterisation reveals that (1) anti-Hebbian plasticity significantly outperforms Hebbian for competent networks (Cohen's d = 0.53-0.64), (2) regret (fraction of oracle improvement lost under the best fixed setting) reaches 52-100%, and (3) plasticity's role shifts from fine-tuning to genuine adaptation under non-stationarity. Co-evolution independently discovers these patterns: on CartPole, 70% of runs evolve anti-Hebbian plasticity (p = 0.043); on Acrobot, evolution finds near-zero eta with mixed signs -- exactly matching the characterisation. A random-RNN control shows that anti-Hebbian dominance is generic to small recurrent networks, but the degree of topology-dependence is developmental-specific: regret is 2-6x higher for morphogenetically grown networks than for random graphs with matched topology statistics.

Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis proposes a new method of transfer learning for Recurrent Neural Networks (RNNs) based on time-warping. We prove that for a class of linear, first-order differential equations known as time lag models, an LSTM can approximate these systems with any desired accuracy, and the model can be time-warped while maintaining the approximation accuracy. The Time-Warping method of transfer learning is then evaluated in an applied problem on predicting fuel moisture content (FMC), an important concept in wildfire modeling. An RNN with LSTM recurrent layers is pretrained on fuels with a characteristic time scale of 10 hours, where there are large quantities of data available for training. The RNN is then modified with transfer learning to generate predictions for fuels with characteristic time scales of 1 hour, 100 hours, and 1000 hours. The Time-Warping method is evaluated against several known methods of transfer learning. The Time-Warping method produces predictions with an accuracy level comparable to the established methods, despite modifying only a small fraction of the parameters that the other methods modify.

The benefits of depth in feedforward neural networks are well known: composing multiple layers of linear transformations with nonlinear activations enables complex computations. While similar effects are expected in recurrent neural networks (RNNs), it remains unclear how depth interacts with recurrence to shape expressive power. Here, we formally show that depth increases RNNs' memory capacity efficiently with respect to the number of parameters, thus enhancing expressivity both by enabling more complex input transformations and improving the retention of past information. We broaden our analysis to 2RNNs, a generalization of RNNs with multiplicative interactions between inputs and hidden states. Unlike RNNs, which remain linear without nonlinear activations, 2RNNs perform polynomial transformations whose maximal degree grows with depth. We further show that multiplicative interactions cannot, in general, be replaced by layerwise nonlinearities. Finally, we validate these insights empirically on synthetic and real-world tasks.

We study out of distribution generalization in streaming tasks where models are trained on short sequences but must operate over much longer, unknown horizons under bounded memory. Our focus is on a persistent fast slow recurrent formulation in which a latent state is maintained across observations rather than reset at each stream step. For each incoming observation, the model performs multiple weight-shared latent updates with a recurrent core and then carries the resulting state forward to the next observation. This allows the model to maintain and refine a compact stream-level state without reprocessing a growing context. We evaluate this formulation across symbolic sequence prediction, supervised navigation, and partially observable reinforcement learning tasks. Across these settings, persistent latent recurrence improves OOD generalization over recurrent, state-space, and Transformer baselines. Through recurrent-core ablations, we identify architectural ingredients that are consistently associated with strong OOD performance, including state-dependent transitions and feature-wise nonlinear mixing. Together, these results highlight the value of revisiting persistent recurrence as an architectural bias for more generalizable sequence prediction.

Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet approximating the complete spatio-temporal trajectory is essential for mechanistic insight and understanding, model calibration, and operational decision-making. We introduce LAPIS-SHRED (LAtent Phase Inference from Short time sequence using SHallow REcurrent Decoders), a modular architecture that reconstructs and/or forecasts complete spatiotemporal dynamics from sparse sensor observations confined to short temporal windows. LAPIS-SHRED operates through a three-stage pipeline: (i) a SHRED model is pre-trained entirely on simulation data to map sensor time-histories into a structured latent space, (ii) a temporal sequence model, trained on simulation-derived latent trajectories, learns to propagate latent states forward or backward in time to span unobserved temporal regions from short observational time windows, and (iii) at deployment, only a short observation window of hyper-sparse sensor measurements from the true system is provided, from which the frozen SHRED model and the temporal model jointly reconstruct or forecast the complete spatiotemporal trajectory. The framework supports bidirectional inference, inherits data assimilation and multiscale reconstruction capabilities from its modular structure, and accommodates extreme observational constraints including single-frame terminal inputs. We evaluate LAPIS-SHRED on six experiments spanning complex spatio-temporal physics: turbulent flows, multiscale propulsion physics, volatile combustion transients, and satellite-derived environmental fields, highlighting a lightweight, modular architecture suited for operational settings where observation is constrained by physical or logistical limitations.

End-to-end OCR for historical newspapers remains challenging, as models must handle long text sequences, degraded print quality, and complex layouts. While Transformer-based recognizers dominate current research, their quadratic complexity limits efficient paragraph-level transcription and large-scale deployment. We investigate linear-time State-Space Models (SSMs), specifically Mamba, as a scalable alternative to Transformer-based sequence modeling for OCR. We present to our knowledge, the first OCR architecture based on SSMs, combining a CNN visual encoder with bi-directional and autoregressive Mamba sequence modeling, and conduct a large-scale benchmark comparing SSMs with Transformer- and BiLSTM-based recognizers. Multiple decoding strategies (CTC, autoregressive, and non-autoregressive) are evaluated under identical training conditions alongside strong neural baselines (VAN, DAN, DANIEL) and widely used off-the-shelf OCR engines (PERO-OCR, Tesseract OCR, TrOCR, Gemini). Experiments on historical newspapers from the Bibliotheque nationale du Luxembourg, with newly released >99% verified gold-standard annotations, and cross-dataset tests on Fraktur and Antiqua lines, show that all neural models achieve low error rates (~2% CER), making computational efficiency the main differentiator. Mamba-based models maintain competitive accuracy while halving inference time and exhibiting superior memory scaling (1.26x vs 2.30x growth at 1000 chars), reaching 6.07% CER at the severely degraded paragraph level compared to 5.24% for DAN, while remaining 2.05x faster. We release code, trained models, and standardized evaluation protocols to enable reproducible research and guide practitioners in large-scale cultural heritage OCR available at https://github.com/MarcoPerson/ssm-ocr-benchmark.

For three decades online recurrent learning has been assumed to require propagating a Jacobian tensor through the network's dynamics at $O(n^4)$ per step. We show it doesn't. Dropping the propagation entirely ($d=0$, $O(n^2)$ memory) matches full RTRL within CI on held-out BCI cross-session drift (TOST equivalent within $\pm 3$ pp at $n=20$, Adam, float64), and across vanilla-RNN synthetic cells (sine and Lorenz under Adam and SGD) and LSTM/sine under Adam. A decomposition $g_{RTRL} = g_{imm} + g_{past}$ explains why. On BCI, $g_{past}$ concentrates in a single direction (top-1 singular fraction 0.62-0.74 across four optimizers, vs 0.333 for $g_{imm}$), and the four-optimizer full-RTRL-vs-$d=0$ recovery gap tracks each optimizer's per-layer update-magnitude ratio $\|ΔW_{hh}\|/\|ΔW_{out}\|$ monotonically. A stationary (no-drift) control collapses both concentrations to ~0.6: the drift-specific signal is the differential, not $g_{past}$'s absolute rank-1 structure. The signature and the behavioral gap both collapse on LSTM, consistent with a mechanism specific to additive linear recurrence. On synthetic sine, $g_{imm}$ is redundant with $g_{past}$, which predicts the synthetic null. Full RTRL's one robust advantage is LARS (+17 to +27 pp), but $d=0$+LARS also fails to adapt independently; the gap is an optimizer$\times$method interaction, not a method-quality claim. We characterize the regime: $d=0$+Adam+float64 is robust; SGD, Adafactor, and float32 have specific fragilities documented in the paper. On the evaluated cells, the $1000\times$ memory saving at $n=1024$ ($O(n^2)$ vs $O(n^4)$) comes with no measured recovery cost.

Connectivity structure shapes neural computation, but inferring this structure from population recordings is degenerate: multiple connectivity structures can generate identical dynamics. Recent work uses low-rank recurrent neural networks (lrRNNs) to infer low-dimensional latent dynamics and connectivity from observed activity, enabling a mechanistic interpretation of the dynamics. However, standard approaches for training lrRNNs can recover spurious structures irrelevant to the underlying dynamics. We first characterize the identifiability of connectivity structures in lrRNNs and determine conditions under which a unique solution exists. To find such solutions, we develop an inference framework based on maximum entropy and continuous normalizing flows (CNFs), trained via flow matching. Instead of estimating a single connectivity matrix, our method learns a distribution over connection weights that is maximally unbiased over unidentifiable components while matching the observed dynamics. This approach captures complex yet necessary distributions such as heavy-tailed connectivity found in empirical data. We validate our method on synthetic datasets with connectivity structures that generate multistable attractors, limit cycles, and ring attractors, and demonstrate its applicability in recordings from rat frontal cortex during decision-making. Our framework shifts circuit inference from recovering connectivity to identifying which connectivity structures are computationally required, and which are artifacts of underconstrained inference.

The practical deployment of nonlinear model predictive control (NMPC) is often limited by online computation: solving a nonlinear program at high control rates can be expensive on embedded hardware, especially when models are complex or horizons are long. Learning-based NMPC approximations shift this computation offline but typically demand large expert datasets and costly training. We propose Sequential-AMPC, a sequential neural policy that generates MPC candidate control sequences by sharing parameters across the prediction horizon. For deployment, we wrap the policy in a safety-augmented online evaluation and fallback mechanism, yielding Safe Sequential-AMPC. Compared to a naive feedforward policy baseline across several benchmarks, Sequential-AMPC requires substantially fewer expert MPC rollouts and yields candidate sequences with higher feasibility rates and improved closed-loop safety. On high-dimensional systems, it also exhibits better learning dynamics and performance in fewer epochs while maintaining stable validation improvement where the feedforward baseline can stagnate.

Machine learning techniques, such as Transformers and Long Short-Term Memory (LSTM) networks, play a crucial role in Symbolic Music Generation (SMG). Existing literature indicates a difference between LSTMs and Transformers regarding their ability to model local melodic continuity versus maintaining global structural coherence. However, their specific properties within the context of SMG have not been systematically studied. This paper addresses this gap by providing a fine-grained comparative analysis of LSTMs versus Transformers for SMG, examining local and global properties in detail using 17 musical quality metrics on the Deutschl dataset. We find that LSTM networks excel at capturing local patterns but fail to preserve long-range dependencies, while Transformers model global structure effectively but tend to produce irregular phrasing. Based on this analysis and leveraging their respective strengths, we propose a Hybrid architecture combining a Transformer Encoder with an LSTM Decoder and evaluate it against both baselines. We evaluated 1,000 generated melodies from each of the three architectures on the Deutschl dataset. The results show that the hybrid method achieves better local and global continuity and coherence compared to the baselines. Our work highlights the key characteristics of these models and demonstrates how their properties can be leveraged to design superior models. We also supported the experiments with ablation studies and human perceptual evaluations, which statistically support the findings and provide robust validation for this work.

Inferring the connectivity of neural circuits from incomplete observations is a fundamental challenge in neuroscience. We present a covariance-based method for estimating the weight matrix of a recurrent neural network from sparse, partial measurements across multiple recording sessions. By accumulating pairwise covariance estimates across sessions where different subsets of neurons are observed, we reconstruct the full connectivity matrix without requiring simultaneous recording of all neurons. A Granger-causality refinement step enforces biological constraints via projected gradient descent. Through systematic experiments on synthetic networks modeling small brain circuits, we characterize a fundamental control-estimation tradeoff: stimulation aids identifiability but disrupts intrinsic dynamics, with the optimal level depending on measurement density. We discover that the ``incorrect'' linear approximation acts as implicit regularization -- outperforming the oracle estimator with known nonlinearity at all operating regimes -- and provide an exact characterization via the Stein--Price identity.

Real-time recurrent learning (RTRL) computes exact online gradients by propagating a Jacobian tensor forward through recurrent dynamics, but at O(n^4) cost per step. Prior work has sought structured approximations (rank-1 compression, graph-based sparsity, Kronecker factorization). We show that, in the continuous error signal regime, the recurrent Jacobian is massively redundant:propagating through a random 6% of paths (k=4 of n=64) recovers 84 +/- 6% of full RTRL's adaptation ability across five seeds, and the absolute count k=4 remains effective from n=64 to n=256 (6% to 1.6%, recovery 84 to 78%), meaning sparse RTRL becomes relatively cheaper as networks grow. In RNNs, the recovery is selection-invariant (even adversarial path selection works) and exhibits a step-function transition from zero to any nonzero propagation. Spectral analysis reveals the mechanism: the Jacobian is full-rank but near-isotropic (condition numbers 2.6-6.5), so any random subset provides a directionally representative gradient estimate. On chaotic dynamics (Lorenz attractor), sparse propagation is more numerically stable than full RTRL (CV 13% vs. 88%), as subsampling avoids amplifying pathological spectral modes. The redundancy extends to LSTMs (k=4 matches full RTRL) and to transformers via sparse gradient transport (50% head sparsity outperforms the dense reference; 33% is borderline), with higher thresholds reflecting head specialization rather than isotropy. On real primate neural data, sparse RTRL (k=4) adapts online to cross-session electrode drift (80 +/- 11% recovery, 5 seeds), where sparse propagation is again more stable than full RTRL. Without continuous error signal, Jacobian propagation accumulates numerical drift and degrades all RTRL variants, a scope condition for all forward-mode methods. Results hold with SGD (92 +/- 1% recovery), suggesting independence from optimizer choice.

Transformers are highly parallel but are limited to computations in the TC$^0$ complexity class, excluding tasks such as entity tracking and code execution that provably require greater expressive power. Motivated by this limitation, we revisit non-linear Recurrent Neural Networks (RNNs) for language modeling and introduce Matrix-to-Matrix RNN (M$^2$RNN): an architecture with matrix-valued hidden states and expressive non-linear state transitions. We demonstrate that the language modeling performance of non-linear RNNs is limited by their state size, and show how the state size expansion mechanism enables efficient use of tensor cores. Empirically, M$^2$RNN achieves perfect state tracking generalization at sequence lengths not seen during training. These benefits also translate to large-scale language modeling. In hybrid settings that interleave recurrent layers with attention, Hybrid M$^2$RNN outperforms equivalent Gated DeltaNet hybrids by $0.4$-$0.5$ perplexity points on a 7B MoE model, while using $3\times$ smaller state sizes for the recurrent layers. Notably, replacing even a single recurrent layer with M$^2$RNN in an existing hybrid architecture yields accuracy gains comparable to Hybrid M$^2$RNN with minimal impact on training throughput. Further, the Hybrid Gated DeltaNet models with a single M$^2$RNN layer also achieve superior long-context generalization, outperforming state-of-the-art hybrid linear attention architectures by up to $8$ points on LongBench. Together, these results establish non-linear RNN layers as a compelling building block for efficient and scalable language models.

Effective urban traffic monitoring is essential for improving mobility, enhancing safety, and supporting sustainable cities. Distributed Acoustic Sensing (DAS) enables large-scale traffic observation by transforming existing fiber-optic infrastructure into dense arrays of vibration sensors. However, modeling the high-resolution spatio-temporal structure of DAS data for reliable traffic event recognition remains challenging. This study presents a real-world DAS-based traffic monitoring experiment conducted in Granada, Spain, where vehicles cross a fiber deployed perpendicular to the roadway. Recurrent neural networks (RNNs) are employed to model intra- and inter-event temporal dependencies. Spatial and temporal attention mechanisms are systematically integrated within the RNN architecture to analyze their impact on recognition performance, parameter efficiency, and interpretability. Results show that an appropriate and complementary placement of attention modules improves the balance between accuracy and model complexity. Attention heatmaps provide physically meaningful interpretations of classification decisions by highlighting informative spatial locations and temporal segments. Furthermore, the proposed SA-bi-TA configuration demonstrates spatial transferability, successfully recognizing traffic events at sensing locations different from those used during training, with only moderate performance degradation. These findings support the development of scalable and interpretable DAS-based traffic monitoring systems capable of operating under heterogeneous urban sensing conditions.

Magnetohydrodynamic (MHD) effects play a key role in the design and operation of nuclear fusion systems, where electrically conducting fluids (such as liquid metals or molten salts in reactor blankets) interact with magnetic fields of varying intensity and orientation, which affect the resulting flow. The numerical resolution of MHD models involves highly nonlinear multiphysics systems of equations and can become computationally expensive, particularly in multi-query, parametric, or real-time contexts. This work investigates a fully data-driven framework for MHD state reconstruction that combines dimensionality reduction via Singular Value Decomposition (SVD) with the SHallow REcurrent Decoder (SHRED), a neural network architecture designed to recover the full spatio-temporal state from sparse time-series measurements of a limited number of observables. The methodology is applied to a parametric MHD test case involving compressible lead-lithium flow in a stepped channel subjected to thermal gradients and magnetic fields spanning a broad range of intensities. To improve efficiency, the full-order dataset is first compressed using SVD, yielding a reduced representation used as reference truth for training. Only temperature measurements from three sensors are provided as input, while the network reconstructs the full fields of velocity, pressure, and temperature. To assess robustness with respect to sensor placement, thirty randomly generated sensor configurations are tested in ensemble mode. Results show that SHRED accurately reconstructs the full MHD state even for magnetic field intensities not included in the training set. These findings demonstrate the potential of SHRED as a computationally efficient surrogate modeling strategy for fusion-relevant multiphysics problems, enabling low-cost state estimation with possible applications in real-time monitoring and control.

Residual connections are central to modern deep neural networks, enabling stable optimization and efficient information flow across depth. In this work, we propose SCORE (Skip-Connection ODE Recurrent Embedding), a discrete recurrent alternative to classical layer stacking. Instead of composing multiple independent layers, SCORE iteratively applies a single shared neural block using an ODE (Ordinary Differential Equation)-inspired contractive update: ht+1 = (1 - dt) * ht + dt * F(ht) This formulation can be interpreted as a depth-by-iteration refinement process, where the step size dt explicitly controls stability and update magnitude. Unlike continuous Neural ODE approaches, SCORE uses a fixed number of discrete iterations and standard backpropagation without requiring ODE solvers or adjoint methods. We evaluate SCORE across graph neural networks (ESOL molecular solubility), multilayer perceptrons, and Transformer-based language models (nanoGPT). Across architectures, SCORE generally improves convergence speed and often accelerates training. SCORE is reducing parameter count through shared weights. In practice, simple Euler integration provides the best trade-off between computational cost and performance, while higher-order integrators yield marginal gains at increased compute. These results suggest that controlled recurrent depth with contractive residual updates offers a lightweight and effective alternative to classical stacking in deep neural networks.

Animal brains flexibly and efficiently achieve many behavioral tasks with a single neural network. A core goal in modern neuroscience is to map the mechanisms of the brain's flexibility onto the dynamics underlying neural populations. However, identifying task-specific dynamical rules from limited, noisy, and high-dimensional experimental neural recordings remains a major challenge, as experimental data often provide only partial access to brain states and dynamical mechanisms. While recurrent neural networks (RNNs) directly constrained neural data have been effective in inferring underlying dynamical mechanisms, they are typically limited to single-task domains and struggle to generalize across behavioral conditions. Here, we introduce JEDI, a hierarchical model that captures neural dynamics across tasks and contexts by learning a shared embedding space over RNN weights. This model recapitulates individual samples of neural dynamics while scaling to arbitrarily large and complex datasets, uncovering shared structure across conditions in a single, unified model. Using simulated RNN datasets, we demonstrate that JEDI accurately learns robust, generalizable, condition-specific embeddings. By reverse-engineering the weights learned by JEDI, we show that it recovers ground truth fixed point structures and unveils key features of the underlying neural dynamics in the eigenspectra. Finally, we apply JEDI to motor cortex recordings during monkey reaching to extract mechanistic insight into the neural dynamics of motor control. Our work shows that joint learning of contextual embeddings and recurrent weights provides scalable and generalizable inference of brain dynamics from recordings alone.

Music source separation is the task of isolating the instrumental tracks from a music song. Despite its spectacular recent progress, the trend towards more complex architectures and training protocols exacerbates reproducibility issues. The band-split recurrent neural networks (BSRNN) model is promising in this regard, since it yields close to state-of-the-art results on public datasets, and requires reasonable resources for training. Unfortunately, it is not straightforward to reproduce since its full code is not available. In this paper, we attempt to replicate BSRNN as closely as possible to the original paper through extensive experiments, which allows us to conduct a critical reflection on this reproducibility issue. Our contributions are three-fold. First, this study yields several insights on the model design and training pipeline, which sheds light on potential future improvements. In particular, since we were unsuccessful in reproducing the original results, we explore additional variants that ultimately yield an optimized BSRNN model, whose performance largely improves that of the original. Second, we discuss reproducibility issues from both methodological and practical perspectives. We notably underline how substantial time and energy costs could have been saved upon availability of the full pipeline. Third, our code and pre-trained models are released publicly to foster reproducible research. We hope that this study will contribute to spread awareness on the importance of reproducible research in the music separation community, and help promoting more transparent and sustainable practices.

Accurate and interpretable mortality risk prediction in intensive care units (ICUs) remains a critical challenge due to the irregular temporal structure of electronic health records (EHRs), the complexity of longitudinal disease trajectories, and the lack of clinically grounded explanations in many data-driven models. To address these challenges, we propose TA-RNN-Medical-Hybrid, a time-aware and knowledge-enriched deep learning framework that jointly models longitudinal clinical sequences and irregular temporal dynamics through explicit continuous-time encoding, along with standardized medical concept representations. The proposed framework extends time-aware recurrent modeling by integrating explicit continuous-time embeddings that operate independently of visit indexing, SNOMED-based disease representations, and a hierarchical dual-level attention mechanism that captures both visit-level temporal importance and feature/concept-level clinical relevance. This design enables accurate mortality risk estimation while providing transparent and clinically meaningful explanations aligned with established medical knowledge. We evaluate the proposed approach on the MIMIC-III critical care dataset and compare it against strong time-aware and sequential baselines. Experimental results demonstrate that TA-RNN-Medical-Hybrid consistently improves predictive performance in terms of AUC, accuracy, and recall-oriented F$_2$-score. Moreover, qualitative analysis shows that the model effectively decomposes mortality risk across time and clinical concepts, yielding interpretable insights into disease severity, chronicity, and temporal progression. Overall, the proposed framework bridges the gap between predictive accuracy and clinical interpretability, offering a scalable and transparent solution for high-stakes ICU decision support systems.

Imitation Learning (IL) enables robots to acquire manipulation skills from expert demonstrations. Diffusion Policy (DP) models multi-modal expert behaviors but degrades when naively increasing stacked observation horizons, limiting long-horizon manipulation. We propose Self-Evolving Gated Attention (SEGA), a temporal module that maintains a time-evolving latent state via gated attention, enabling efficient recurrent updates that accumulate long-term context into a compact latent representation while filtering irrelevant temporal information. Integrating SEGA into DP yields Self-Evolving Diffusion Policy (SeedPolicy), which resolves the temporal modeling bottleneck and extends the effective temporal horizon with moderate overhead. On the RoboTwin 2.0 benchmark with 50 manipulation tasks, SeedPolicy outperforms DP and other IL baselines. Averaged across both CNN and Transformer backbones, SeedPolicy achieves 36.8% relative improvement in clean settings and 169% relative improvement in randomized challenging settings over the DP. Compared to vision-language-action models such as RDT with 1.2B parameters, SeedPolicy achieves stronger performance in the clean setting with one to two orders of magnitude fewer parameters, demonstrating strong efficiency. These results establish SeedPolicy as a state-of-the-art imitation learning method for long-horizon robotic manipulation. Code is available at: https://github.com/Youqiang-Gui/SeedPolicy.

The community is increasingly exploring linear RNNs (LRNNs) as language models, motivated by their expressive power and parallelizability. While prior work establishes the expressivity benefits of LRNNs over transformers, it is unclear what makes LRNNs -- but not traditional, nonlinear RNNs -- as easy to parallelize in practice as transformers. We answer this question by providing a tight connection between types of RNNs and standard complexity classes. We show that LRNNs can be viewed as log-depth (bounded fan-in) arithmetic circuits, which represents only a slight depth overhead relative to log-depth boolean circuits that transformers admit. Furthermore, we show that nonlinear RNNs can solve $\mathsf{L}$-complete problems (and even $\mathsf{P}$-complete ones, under polynomial precision), revealing a fundamental barrier to parallelizing them as efficiently as transformers. Our theory also identifies fine-grained expressivity differences between recent popular LRNN variants: permutation-diagonal LRNNs are $\mathsf{NC}^1$-complete whereas diagonal-plus-low-rank LRNNs are more expressive ($\mathsf{PNC}^1$-complete). We provide further insight by associating each type of RNN with a corresponding automata-theoretic model that it can simulate. Together, our results reveal fundamental tradeoffs between nonlinear RNNs and different variants of LRNNs, providing a foundation for designing LLM architectures that achieve an optimal balance between expressivity and parallelism.

Reasoning problems such as Sudoku and ARC-AGI remain challenging for neural networks. The structured problem solving architecture family of Recurrent Reasoning Models (RRMs), including Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM), offer a compact alternative to large language models, but currently handle symbol symmetries only implicitly via costly data augmentation. We introduce Symbol-Equivariant Recurrent Reasoning Models (SE-RRMs), which enforce permutation equivariance at the architectural level through symbol-equivariant layers, guaranteeing identical solutions under symbol or color permutations. SE-RRMs outperform prior RRMs on 9x9 Sudoku and generalize from just training on 9x9 to smaller 4x4 and larger 16x16 and 25x25 instances, to which existing RRMs cannot extrapolate. On ARC-AGI-1 and ARC-AGI-2, SE-RRMs achieve competitive performance with substantially less data augmentation and only 2 million parameters, demonstrating that explicitly encoding symmetry improves the robustness and scalability of neural reasoning. Code is available at https://github.com/ml-jku/SE-RRM.

Accurate Remaining Useful Life (RUL) prediction is a key requirement for effective Prognostics and Health Management (PHM) in safety-critical systems such as aero-engines. Existing deep learning approaches, particularly LSTM-based models, often struggle to generalize across varying operating conditions and are sensitive to noise in multivariate sensor data. To address these challenges, we propose a novel Bidirectional Residual Corrected LSTM (Bi-cLSTM) model for robust RUL estimation. The proposed architecture combines bidirectional temporal modeling with an adaptive residual correction mechanism to iteratively refine sequence representations. In addition, we introduce a condition-aware preprocessing pipeline incorporating regime-based normalization, feature selection, and exponential smoothing to improve robustness under complex operating environments. Extensive experiments on all four subsets of the NASA C-MAPSS dataset demonstrate that the proposed Bi-cLSTM consistently outperforms LSTM-based baselines and achieves competitive state-of-the-art performance, particularly in challenging multi-condition scenarios. These results highlight the effectiveness of combining bidirectional temporal learning with residual correction for reliable RUL prediction.