Gated Recurrent Unit

Also known as GRU

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Latest papers

17 papers3 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Oct 9, 2026

The RNN Homunculus: Learning to Gate Long-Term Memory

Learning long-range dependencies with recurrent neural networks (RNNs) is difficult because of the vanishing gradient problem. Gated recurrent neural networks like GRUs and LSTMs address this problem and are commonly explained by their ability to create additive copy paths through time. This explanation is correct, but incomplete: useful RNN gate values must themselves be learned, which is typically done with another RNN. We study this gate-learning problem through carefully controlled sequence classification tasks. Our analysis shows that gated architectures struggle when all training samples require long-range memory and thus equally suffer from the vanishing gradient problem. We intervene by adding short-dependency samples which let gated models learn solutions that capture long-dependency samples, but also generalize across different class labels. When properly learned, gated RNNs match or even exceed the test accuracy of modern architectures like Mamba and xLSTM. Overall, our results highlight gate learning as a central part of learning long-range memory and show how training data can support this process by exposing the same task over shorter dependencies.

Zeyu Fan, Alexandru-Dragos Manolache, Jan van Gemert

Delft University of Technology, Mekelweg 5, 2628 CD Delft, The Netherlands

Long-Range Dependency Modeling Recurrent Neural Networks Sequence Modeling Gated Recurrent Unit Long Short-Term Memory Networks Deep Learning Optimization

Sep 30, 2026

Bounded Channel-Adaptive Spectral Learning for Forward-Consistent Inverse Flapping-Wing Aerodynamics

Flapping-wing vehicles regulate aerodynamic forces and moments through coordinated variations in stroke, deviation, and pitch motion. Because the resulting loads depend on both the instantaneous wing configuration and its preceding motion history, recovering suitable wing kinematics from a desired aerodynamic trajectory is a challenging inverse problem. Existing sequence models capture temporal dependencies, while spectral methods can exploit the periodic structure of flapping motion. However, unrestricted frequency-domain augmentation may interfere with temporal representations and produce inconsistent corrections across kinematic variables and prediction horizons. We propose the Bounded Channel-Adaptive Spectral Residual Gated Recurrent Unit (BCS-GRU), which retains recurrent temporal prediction as its primary representation and restricts spectral information to a controlled output-specific correction. We further introduce a causally aligned forward-consistency objective that evaluates predicted kinematics through a separately trained and frozen aerodynamic surrogate. Experiments under a unified episode-level protocol show that BCS-GRU improves inverse prediction over recurrent and adaptive-spectral baselines, with greater benefits at longer prediction horizons. Forward-consistent fine-tuning further improves surrogate-based aerodynamic consistency while maintaining mean kinematic accuracy. These results demonstrate that controlled spectral correction and forward-consistent learning provide an effective framework for history-aware inverse modelling of flapping-wing aerodynamics.

Haichuan Li

University of Turku

Gated Recurrent Unit Recurrent Neural Networks Spectral Methods Inverse Dynamics

Sep 25, 2026

BreathGRU: A Novel Semi-Supervised Bidirectional Gated Recurrent Unit Framework for Speech and Breath Segmentation for Respiratory Audio

Speech-breath segmentation is a fundamental preprocessing step in respiratory audio analysis, enabling applications such as respiratory acoustic biomarker extraction, lung function prediction and disease monitoring. Existing approaches, including threshold methods, Fourier Transform-based techniques, and unsupervised and pretrained voice activity detection (VAD) models, primarily focus on speech detection and often classify breathing events as non-speech or silence, limiting their applicability for precise breath detection. To address this limitation, we propose BreathGRU, a semi-supervised Bidirectional Gated Recurrent Unit (BiGRU) framework specifically designed for speech-breath segmentation. The proposed framework combines frame-level acoustic feature extraction with bidirectional recurrent modelling, pseudo-label refinement and duration-constrained Segmental Viterbi decoding to produce speech and breath segmentation. BreathGRU was evaluated against the existing approaches, using manually annotated recordings. Performance was assessed using event-based, time-based, overlap-based, duration-based and boundary-based segmentation metrics. Experiment results demonstrated that BreathGRU achieved the highest breath event recall (0.83), the lowest onset-localisation error (0.14s) and the highest Mean Match Intersection over Union (0.81), with competitive overall segmentation performance compared to large pretrained VAD models like Silero. Qualitative evaluation on manually annotated recordings further showed close agreement between BreathGRU and manual annotation, with better breath detection compared to Silero. These findings demonstrate that explicit breath event modelling provides advantages over general-purpose VAD models and establish BreathGRU as an effective speech-breath segmentation framework which can be applied for respiratory audio analysis and pulmonary healthcare applications.

Sania Fatima Sayed, John W. Holloway, Reyer Zwiggelaar +1

Department of Computer Science, Aberystwyth University, Aberystwyth, United Kingdom, UK SY23 3DB · Human Development and Health, Faculty of Medicine, University of Southampton, United Kingdom, SO16 6YD

Gated Recurrent Unit Speech Processing Recurrent Neural Networks

Sep 3, 2026

Neural-Network Maxent: a general extension with learned nonlinearity, applied to time-series for Desert Locust distribution modelling

Species Distribution Modelling (SDM) is essential for understanding how environmental conditions shape biodiversity, particularly for destructive pests such as the Desert Locust (Schistocerca gregaria), whose breeding dynamics are tightly coupled to rapidly evolving environmental conditions. Maxent has become the dominant method for presence-only data, but its reliance on a linear combination of hand chosen feature transforms limits its ability to capture the nonlinear, temporal relationships common in ecological monitoring, where covariates such as precipitation, soil moisture, and vegetation indices evolve meaningfully over time. Standard implementations flatten time-series covariates into independent features, discarding sequential structure that carries critical signal. We introduce RNN Maxent, an extension of the Maxent framework that replaces the fixed feature dictionary with a neural network, specifically a Gated Recurrent Unit (GRU), trained end to end via backpropagation. The approach preserves Maxent's presence only statistical foundations, background normalization, and probability calibration, differing only in that the nonlinearity is learned from data rather than fixed in advance. We apply RNN Maxent to map suitable habitat for the Desert Locust using 50 day environmental time series derived from ERA5 Land, MODIS, and Sentinel 3, maintaining a 7 day gap between covariates and presence records to yield forecasting behavior. Compared against standard Maxent, RNN Maxent improves performance across metrics (ROC AUC 0.862 std 0.036 vs. 0.792; F1 0.671 std 0.056 vs. 0.590).

Alessandro Grassi, Edoardo Kimani Bellotto, Wassim El Azami +2

SISTEMA GmbH, Vienna, Austria · Beyond EO, Paris, France

Gated Recurrent Unit Recurrent Neural Networks

Aug 19, 2026

DevGRU: Depth-guided Visual Navigation using a Collision-aware Recurrent Model

Existing visual navigation models often aim to develop foundation models that can generalize robot navigation across diverse platforms. However, many of these models are prone to collisions when deployed in complex indoor environments, particularly in structured layouts and narrow passages. To address this problem, we propose a depth image- and point-goal-conditioned navigation system, DevGRU. The proposed system employs an action predictor (AP) that generates collision-aware future trajectories, enabling effective avoidance of immediate obstacles. In conjunction with a collision predictor, the AP further compensates for errors accumulated in the goal pose estimation and proactively mitigates future deviations. To evaluate our method, we conducted experiments across nine different scenes and three state-of-the-art approaches - ViNT, NoMaD, and NavDP - as well as four additional variants of ViNT and NoMaD. In terms of navigation performance, DevGRU significantly outperforms ViNT and NoMaD by a large margin. In addition, the proposed model has a relatively small number of trainable parameters, resulting in the fastest inference time among the baselines, particularly outperforming NavDP by 7x in model size and 17x in inference time.

Kyung Min Han, Eunsom Kim, Young J. Kim

Gated Recurrent Unit Robot Navigation Robot Collision Avoidance Recurrent Neural Networks

Jul 15, 2026

A Comparative Analysis of Machine Learning Models for Long and Short-Term Forecasting of the Egyptian Stock Market: A Focus on EGX30

This study concentrates on predicting stock prices in the Egyptian market, focusing on the EGX30, an influential financial hub in the Middle East. While most research focuses on global stocks, there's a growing need to understand stock trends in developing countries like Egypt. The study compares different machine learning models for forecasting EGX30 trends, covering short and long-term predictions. Using historical EGX30 data, including metrics like root mean squared error, Mean Absolute Percentage Error, and coefficient of determination, models like K-Nearest Neighbours, random forest, extreme gradient boosting, long short-term memory networks, and gated recurrent unit networks were evaluated. The goal is to determine the most effective models for EGX30 prediction, considering Egypt's unique market dynamics. Insights from this study aid investors in making informed decisions. Results show that the Gated Recurrent Unit (GRU) outperformed the other models in the one-week, one-month, and two-months while the eXtreme Gradient Boosting (XGBoost) model outperformed others in the one-day predictions, highlighting their usefulness in predictive analysis for financial markets. The study also showed the importance of using the ensemble techniques, especially in the long-term predictions which proved better results reaching 5 times the GRU in the two-month predictions. Additionally, the study notes the surprisingly good performance of K-Nearest Neighbours (KNN) on long-term predictions, suggesting its enduring relevance and potential for future applications in the fintech domains.

Muhammed Walid, Ahmed El-Naeimy, Hosam Moubarak +1

Cyber Physical Lab, Department of Computer Science & Engineering · Egypt-Japan University Of Science and Technology, Alexandria, Egypt · Accounting Department +1

Gated Recurrent Unit Long-Term Time Series Forecasting Recurrent Neural Networks Financial Time Series

Jul 13, 2026

Dzongkha Next Word Prediction System

Dzongkha, being the national language of Bhutan, is a common and widely spoken language in the country. Official documents, scriptures and other literature products are written in Dzongkha in order to retain the cultural value. However, documenting Dzongkha writing is a challenging and time-consuming process, largely due to the complexity of the script, the need for multiple keystrokes per syllable, and the limited availability of efficient typing tools. An immediate system that can predict and display a list of probable words for Dzongkha is the solution for this problem. The project is mainly aimed to make Dzongkha typing as convenient as possible by reducing the number of keystrokes. Our dataset is acquired from DCDD and has a total of 100000 sentences, 1331282 words and 28344 unique words. The data preprocessing was done by removing all the alphanumeric characters, tokenization, generating N-gram sequences and padding. Three models selected for training are LSTM, Bi-LSTM and GRU. The training process included fine-tuning of the model's hyperparameters. GRU being lightweight and able to handle larger datasets performed best with 74.03% accuracy and also solved the problem of overfitting.

Prerna Chhetri, Tenzin Yoezer, Phuntsho Wangmo +1

Information Technology Department, College of Science and Technology, Royal University of Bhutan

Gated Recurrent Unit Next-Token Prediction Language Modeling Low-Resource Language Processing Text Generation

Jun 25, 2026

Towards Explainable Adjudicative Variance: Quantifying Judicial Discretion via Gated Multi-Task Learning

Legal outcome prediction must disentangle objective case facts from adjudicative context. Merit-based rulings rely on factual evidence while technical disposals may hinge on judicial discretion. We propose a Judge-Aware Gated Multi-Task Learning architecture that explicitly models this distinction. We introduce a fine-grained outcome taxonomy to supervise the encoder, enforcing a structural regularization that disentangles distinct semantic pathways. This granular legal curriculum enables our Gated Fusion mechanism to dynamically modulate reliance on judge identity. We evaluate our approach on 13,937 UK Employment Tribunal decisions. We benchmark our design against supervised fine-tuning (SFT) of a Gemma-4 26B-A4B backbone, in which judge identity and the taxonomy are injected as prompt tokens or autoregressive output targets. The two contextual signals compose only weakly when forced through a single autoregressive channel. In contrast, coupling a LoRA-adapted Gemma-4 encoder with our gated architecture defines a new state of the art on this benchmark while requiring an order of magnitude fewer trainable parameters than the generative SFT baselines, with gains concentrated on the most ambiguous and rarest outcome classes. Beyond accuracy, the architecture is interpretable; learned judge embeddings and calibration profiles localize the cases where adjudicative context drives the prediction. These results indicate that, for identity-conditioned classification of legal outcomes, the choice of conditioning interface dominates scale: differentiable structured composition yields more accurate, more parameter-efficient models than prompt-based composition over a substantially larger backbone.

Stanisław Sójka, Felix Steffek, Matthias Grabmair

School of Computation, Information, and Technology, Technical University of Munich, Germany · Faculty of Law, University of Cambridge

Gated Recurrent Unit Legal NLP AI-Assisted Decision Making Legal Judgment Prediction Interpretable ML Multi-Task Learning+1

Jun 19, 2026

LK Jam: System Architecture and Implementation of a Real-Time Human-AI Interactive Music Generation System using Role-Aware GRU

As artificial intelligence advances into the era of Embodied AI, live musical interaction urgently needs to break free from the limitations of offline, unidirectional generation, achieving a "virtual synergy" capable of low-latency, dynamic interplay. To address this, this technical report presents LK_Jam, a real-time, bidirectional human-computer interactive music generation system based on a lightweight Gated Recurrent Unit (GRU) and a high-performance audio host architecture. In the algorithmic representation layer, this system abandons the computationally expensive fixed time-grid. Instead, it constructs a multi-dimensional sparse event stream integrating time-shifts, continuous harmonic embeddings, and role-aware encoding, enabling the model to accurately capture turn-taking logic and micro-timing in a single-step inference. In the engineering implementation layer, this paper builds a strict multithreaded lock-free communication bridge using C++ and the JUCE framework, incorporating the RTNeural inference engine designed specifically for real-time audio. By utilizing compile-time network topology solidification and a zero-allocation (allocation-free) mechanism, the end-to-end overhead of autoregressive decoding is strictly locked at

O(1)

complexity, structurally mitigating the risk of audio thread dropouts in DAW plugin environments. Furthermore, this study designs a three-stage progressive training strategy, achieving a leap from basic chord harmonization to expert-level interaction. Preliminary observations and architectural analysis demonstrate that while ensuring musical coherence and interactive role-play, the proposed system successfully challenges extreme real-time engineering constraints, offering a highly robust and deployable technical paradigm for next-generation AI co-performers in live music.

Yakun Liu, Zhiyu Jin, Dong Liu +1

Yakun Liu, Dong Liu, and Hai Luan are with the Shenyang Conservatory of Music. · Z. Jin is an independent collaborator.

Gated Recurrent Unit Music Generation Autoregressive Generation Human-AI Co-Creation

Jun 15, 2026

From Compression to Deployment: Real-Time and Energy-Efficient FastGRNN on Ultra-Constrained Microcontrollers

The dominant trajectory of modern machine learning has been to scale up: larger models, larger accelerators, larger memory budgets. Yet a multi-year global semiconductor supply constraint and the growing energy and carbon cost of always-online inference expose the fragility of this trajectory and motivate the opposite direction: refactoring AI and ML algorithms to fit the small, ubiquitous microcontrollers already in mass production in wearables, sensors, and edge appliances. We present an end-to-end open-source reproduction of FastGRNN, a compact gated recurrent cell, deployed on two bare-metal targets: the 8-bit Arduino (ATmega328P) and the 16-bit MSP430 (no hardware multiplier; 16 KB Flash; 512 B SRAM). Our compression pipeline combines low-rank weight factorization, iterative hard-thresholding sparsity, and per-tensor Q15 post-training quantization with explicit activation calibration. The deployed model occupies 566 bytes of weights and achieves macro F1 = 0.918 (seed 0; five-seed Q15 mean 0.853+-0.107) on the HAPT test set. It matches a PyTorch reference at 100% prediction agreement across 3,399 test windows (MCU seed 0; 99.91-100% C-equivalent across five seeds). Both platforms sustain real-time 50 Hz streaming inference (9.21 ms per sample on Arduino; 13 ms on MSP430), where a 256-entry sigmoid/tanh look-up table delivers a 30.5x speedup on the multiplier-less MSP430. Four contributions extend the original FastGRNN paper: (i) cross-platform bit-equivalent deterministic inference; (ii) characterization of recurrent warm-up latency (median 74 samples, 1.48 s; worst-case 125 samples, 2.50 s over 100 test windows); (iii) a deployable look-up-table recipe for multiplier-less embedded targets; and (iv) hardware energy characterization showing 17.7 mW active inference power, <0.09 mW idle power, and 96.7% energy reduction with the LUT.

Emre Can Kizilates

Independent Researcher, Izmir, Turkey

Gated Recurrent Unit Efficient Neural Network Inference Recurrent Neural Networks Neural Network Compression On-Device Inference

May 11, 2026

A Random-Matrix Criterion for Initializing Gated Recurrent Neural Networks

Proper weight initialization prior to training has historically been one of the key factors that helped kick off the deep learning revolution. Initialization is even more crucial in "reservoir computing", where the weights of a readout layer are learned linearly while the reservoir weights are fixed and largely determine the richness, stability and memory of the resulting dynamics. In the infinite-width limit it has been shown that meaningful initializations are those sitting at an effective critical point of the randomly initialized model. The phase transition is controlled by the weight variance

g^2

and separates an ordered phase from a chaotic one where information progressively degrades. Here we derive a simple criterion to estimate the critical

g_c

for a broad class of recurrent architectures and we show that it closely tracks the gain at which a gated-RNN reservoir achieves peak performance on a chaotic forecasting task. Finally, we argue that our criterion can serve as a design principle for future initialization schemes.

Tommaso Fioratti, Riccardo Marcaccioli, Francesco Casola

Capital Fund Management, 75007 Paris, France · Institute of Mathematics, EPFL, 1015 Lausanne, Switzerland

Gated Recurrent Unit Neural Network Initialization Recurrent Neural Networks Reservoir Computing

May 9, 2026

C2L-Net: A Data-Driven Model for State-of-Charge Estimation of Lithium-Ion Batteries During Discharge

Accurate state-of-charge (SOC) estimation is critical for the safe and efficient operation of lithium-ion batteries in battery management systems (BMS). Although data-driven approaches can effectively capture nonlinear battery dynamics, many existing methods rely on long historical input sequences, resulting in high computational cost and introducing padding-induced positional bias at the beginning of drive cycles. To address these limitations, we propose C2L-Net, a novel context-to-latest data-driven framework for realistic online SOC estimation using only a short historical window (20 s). Unlike existing short-receptive-field or long-history models, the proposed framework explicitly separates contextual encoding from latest-measurement updating, enabling both efficient temporal modeling and rapid adaptation to dynamic battery states. The proposed model incorporates a chunk-based feature extraction mechanism that combines Theta Attention Pooling with a Fourier-based Seasonality Basis to capture local temporal patterns while reducing sequence length. A causal context encoder, integrating a gated recurrent unit (GRU) with Causal Cosine Attention, models temporal dependencies without information leakage. Furthermore, a latest-measurement decoder, inspired by recursive filtering, updates the contextual state using the most recent measurement, enhancing responsiveness to dynamic operating conditions. Extensive experiments on a public lithium-ion battery drive-cycle dataset under multiple fixed-temperature conditions demonstrate that the proposed method achieves state-of-the-art or competitive accuracy while significantly improving computational efficiency. In particular, C2L-Net achieves up to 60 times faster inference and requires fewer parameters than recent data-driven baselines, while maintaining robust performance across unseen driving profiles.

Khoa Tran, T. Nguyen-Thoi, Vin Nguyen-Thai +3

Data Science Laboratory, Faculty of Information Technology, Ton Duc Thang University, Ho Chi Minh City, Vietnam. · Laboratory for Applied and Industrial Mathematics, Institute for Computational Science and Artificial Intelligence, Van Lang University, Ho Chi Minh City, 70000, Viet Nam. · Faculty of Mechanical, Electrical, and Computer Engineering, Van Lang School of Technology, Van Lang University, Ho Chi Minh City, 70000, Viet Nam. +6

Gated Recurrent Unit Causal Attention Lithium-Ion Batteries

May 3, 2026

Learn-To-Learn on Arbitrary Textual Conditioning: A Hypernetwork-Driven Meta-Gated LLM

Conventional LLMs may suffer from corpus heterogeneity and subtle condition changes. While finetuning can create the catastrophe forgetting issue, application of meta-learning on LLMs is also limited due to its complexity and scalability. In this paper, we activate the meta-signal of

β

within the SwiGLU blocks, resulting in a meta-gating mechanism that adaptively adjusts the nonlinearity of FFN. A hypernetwork is employed which dynamically produces

β

on textual conditions, providing meta-controllability on LLMs. By testing on different condition types such as task, domain, persona, and style, our method outperforms finetuning and meta-learning baselines, and can generalize reasonably on unseen tasks, condition types, or instructions. Our code can be found in https://github.com/AaronJi/MeGan.

Luo Ji, Qi Qin, Ningyuan Xi +3

Geely AI Lab, Geely Auto Group, Zhejiang, China · Peking University, Beijing, China

Gated Recurrent Unit Meta-Learning LLM Fine-Tuning

Apr 28, 2026

Learning-Based Dynamics Modeling and Robust Control for Tendon-Driven Continuum Robots

Tendon-Driven Continuum Robots (TDCRs) pose significant modeling and control challenges due to complex nonlinearities, such as frictional hysteresis and transmission compliance. This paper proposes a differentiable learning framework that integrates high-fidelity dynamics modeling with robust neural control. We develop a GRU-based dynamics model featuring bidirectional multi-channel connectivity and residual prediction to effectively suppress compounding errors during long-horizon auto-regressive prediction. By treating this model as a gradient bridge, an end-to-end neural control policy is optimized through backpropagation, allowing it to implicitly internalize compensation for intricate nonlinearities. Experimental validation on a physical three-section TDCR demonstrates that our framework achieves accurate tracking and superior robustness against unseen payloads, outperforming Jacobian-based methods by eliminating self-excited oscillations. For implementation details and source code, please refer to https://github.com/ZiqingZou/ContinuumControl.

Ziqing Zou, Ke Qiu, Fei Wang +3

Department of Control Science and Engineering, Zhejiang University, Hangzhou, China

Gated Recurrent Unit Robot Trajectory Tracking Robot Dynamics Learning Recurrent Neural Networks Robust Control Continuum Robot Control+2

Mar 2, 2026

Real-Time Thermal-Inertial Odometry on Embedded Hardware for High-Speed GPS-Denied Flight

We present a real-time monocular thermal-inertial odometry system designed for high-velocity, GPS-denied flight on embedded hardware. The system fuses measurements from a FLIR Boson+ 640 longwave infrared camera, a high-rate IMU, a laser range finder, a barometer, and a magnetometer within a fixed-lag factor graph. To sustain reliable feature tracks under motion blur, low contrast, and rapid viewpoint changes, we employ a lightweight thermal-optimized front-end with multi-stage feature filtering. Laser range finder measurements provide per-feature depth priors that stabilize scale during weakly observable motion. High-rate inertial data is first pre-filtered using a Chebyshev Type II infinite impulse response (IIR) filter and then preintegrated, improving robustness to airframe vibrations during aggressive maneuvers. To address barometric altitude errors induced at high airspeeds, we train an uncertainty-aware gated recurrent unit (GRU) network that models the temporal dynamics of static pressure distortion, outperforming polynomial and multi-layer perceptron (MLP) baselines. Integrated on an NVIDIA Jetson Xavier NX, the complete system supports closed-loop quadrotor flight at 30 m/s with drift under 2% over kilometer-scale trajectories. These contributions expand the operational envelope of thermal-inertial navigation, enabling reliable high-speed flight in visually degraded and GPS-denied environments.

Austin Stone, Mark Petersen, Cammy Peterson

Brigham Young University, Provo, UT 84602 USA.

Gated Recurrent Unit Inertial Odometry UAV Navigation GNSS-Denied Localization

Feb 23, 2026

DReX: An Explainable Deep Learning-based Multimodal Recommendation Framework

Multimodal recommender systems leverage diverse data sources, such as user interactions, content features, and contextual information, to address challenges like cold-start and data sparsity. However, existing methods often suffer from one or more key limitations: processing different modalities in isolation, requiring complete multimodal data for each interaction during training, or independent learning of user and item representations. These factors contribute to increased complexity and potential misalignment between user and item embeddings. To address these challenges, we propose DReX, a unified multimodal recommendation framework that incrementally refines user and item representations by leveraging interaction-level features from multimodal feedback. Our model employs gated recurrent units to selectively integrate these fine-grained features into global representations. This incremental update mechanism provides three key advantages: (1) simultaneous modeling of both nuanced interaction details and broader preference patterns, (2) eliminates the need for separate user and item feature extraction processes, leading to enhanced alignment in their learned representation, and (3) inherent robustness to varying or missing modalities. We evaluate the performance of the proposed approach on three real-world datasets containing reviews and ratings as interaction modalities. By considering review text as a modality, our approach automatically generates interpretable keyword profiles for both users and items, which supplement the recommendation process with interpretable preference indicators. Experiment results demonstrate that our approach outperforms state-of-the-art methods across all evaluated datasets.

Adamya Shyam, Venkateswara Rao Kagita, Bharti Rana +1

University of Delhi, Delhi, India · National Institute of Technology, Warangal, India

Gated Recurrent Unit Multimodal Recommendation Explainable Recommendation Multimodal Model Interpretability

Dec 5, 2025

Learnability Window in Gated Recurrent Neural Networks

We develop a statistical theory of temporal learnability in recurrent neural networks, quantifying the maximal temporal horizon

\mathcal{H}_N

over which gradient-based learning can recover lag-dependent structure at finite sample size

N

. The theory is built on the effective learning rate envelope

f(\ell)

, a function that captures how gating mechanisms and adaptive optimizers jointly shape the coupling between state-space dynamics and parameter updates during Backpropagation Through Time. Under heavy-tailed (

α

-stable) fluctuations, where empirical averages concentrate at rate

N^{-1/κ_α}

with

κ_α= α/(α-1)

, the interplay between envelope decay and statistical concentration yields explicit scaling laws for the growth of

\mathcal{H}_N

: logarithmic, polynomial, and exponential temporal learning regimes emerge according to the decay law of

f(\ell)

. These results identify envelope decay as the key determinant of temporal learnability. Slower attenuation of

f(\ell)

enlarges

\mathcal{H}_N

, while heavy-tailed fluctuations compress it by weakening statistical concentration. Moreover, envelope geometry outweighs dataset size: slowing the envelope's decay enlarges

\mathcal{H}_N

more than adding data, so more complex architectures that realize slower-decaying envelopes can be more data-efficient than simpler ones. Experiments across multiple gated architectures and optimizers corroborate these structural predictions.

Lorenzo Livi

OPIT – Open Institute of Technology

Gated Recurrent Unit Recurrent Neural Networks Neural Network Training Dynamics Statistical Learning Theory