RNN-based Online Learning: An Efficient First-Order Optimization Algorithm with a Convergence Guarantee
N. Mert Vural, Selim F. Yilmaz, Fatih Ilhan, Suleyman S. Kozat
备注：
This paper was an early draft of the presented results. We have written and published another paper (arXiv:2005.08948) where we have improved the material in this paper. The published paper covers most of the material presented in this paper as well. Therefore, we remove this paper from Arxiv and kindly refer the interested readers to arXiv:2005.08948
We investigate online nonlinear regression with continually running recurrent neural network networks (RNNs), i.e., RNN-based online learning. For RNN-based online learning, we introduce an efficient first-order training algorithm that theoretically guarantees to converge to the optimum network parameters. Our algorithm is truly online such that it does not make any assumption on the learning environment to guarantee convergence. Through numerical simulations, we verify our theoretical results and illustrate significant performance improvements achieved by our algorithm with respect to the state-of-the-art RNN training methods.
Recurrent Neural Networks (RNNs) are widely used for online regression due to their ability to generalize nonlinear temporal dependencies. As an RNN model, Long-Short-Term-Memory Networks (LSTMs) are commonly preferred in practice, as these networks are capable of learning long-term dependencies while avoiding the vanishing gradient problem. However, due to their large number of parameters, training LSTMs requires considerably longer training time compared to simple RNNs (SRNNs). In this paper, we achieve the online regression performance of LSTMs with SRNNs efficiently. To this end, we introd…
This abstract explores an RNN-based approach to online handwritten recognition problem. Our method uses data from an accelerometer and a gyroscope mounted on a handheld pen-like device to train and run a character pre-diction model. We have built a dataset of timestamped gyroscope and accelerometer data gathered during the manual process of handwriting Latin characters, labeled with the character being written; in total, the dataset con-sists of 1500 gyroscope and accelerometer data sequenc-es for 8 characters of the Latin alphabet from 6 different people, and 20 characters, each 1500 samples …
University of Science and Technique of China（中国科学技术大学）
Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic network, which can be typically divided into two categories: a) topologically evolving graphs whose nodes and edges will increase (decrease) over time; b) temporal graphs whose edges contain time information. In order to handle the changing size of dynamic networks, RNNE adds virtual node, which is not connected to any other nodes, to the networks and replaces it w…
Mila（米拉）；Université de Montréal（蒙特利尔大学）；DeepMind（深度思维）
The recently proposed Unbiased Online Recurrent Optimization algorithm (UORO, arXiv:1702.05043) uses an unbiased approximation of RTRL to achieve fully online gradient-based learning in RNNs. In this work we analyze the variance of the gradient estimate computed by UORO, and propose several possible changes to the method which reduce this variance both in theory and practice. We also contribute significantly to the theoretical and intuitive understanding of UORO (and its existing variance reduction technique), and demonstrate a fundamental connection between its gradient estimate and the one t…
Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature set of the input sequence, known as the signature. This connection allows us to frame a RNN as a kernel method in a suitable reproducing kernel Hilbert space. As a consequence, we obtain theoretical guarantees on generalization and stability for a large class of recurrent networks. Our results are illustrated on simulated datasets.
Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
This study introduces PV-RNN, a novel variational RNN inspired by the predictive-coding ideas. The model learns to extract the probabilistic structures hidden in fluctuating temporal patterns by dynamically changing the stochasticity of its latent states. Its architecture attempts to address two major concerns of variational Bayes RNNs: how can latent variables learn meaningful representations and how can the inference model transfer future observations to the latent variables. PV-RNN does both by introducing adaptive vectors mirroring the training data, whose values can then be adapted differ…
Short-term traffic flow prediction is one of the crucial issues in intelligent transportation system, which is an important part of smart cities. Accurate predictions can enable both the drivers and the passengers to make better decisions about their travel route, departure time and travel origin selection, which can be helpful in traffic management. Multiple models and algorithms based on time series prediction and machine learning were applied to this issue and achieved acceptable results. Recently, the availability of sufficient data and computational power, motivates us to improve the pred…
Conventional hyperparameter optimization methods are computationally intensive and hard to generalize to scenarios that require dynamically adapting hyperparameters, such as life-long learning. Here, we propose an online hyperparameter optimization algorithm that is asymptotically exact and computationally tractable, both theoretically and practically. Our framework takes advantage of the analogy between hyperparameter optimization and parameter learning in recurrent neural networks (RNNs). It adapts a well-studied family of online learning algorithms for RNNs to tune hyperparameters and netwo…
In this paper, we propose a context-aware keyword spotting model employing a character-level recurrent neural network (RNN) for spoken term detection in continuous speech. The RNN is end-to-end trained with connectionist temporal classification (CTC) to generate the probabilities of character and word-boundary labels. There is no need for the phonetic transcription, senone modeling, or system dictionary in training and testing. Also, keywords can easily be added and modified by editing the text based keyword list without retraining the RNN. Moreover, the unidirectional RNN processes an infinit…
University of Southern California（南加州大学）；Disney Research（迪士尼研究院）
Spoken Language Understanding (SLU) typically comprises of an automatic speech recognition (ASR) followed by a natural language understanding (NLU) module. The two modules process signals in a blocking sequential fashion, i.e., the NLU often has to wait for the ASR to finish processing on an utterance basis, potentially leading to high latencies that render the spoken interaction less natural. In this paper, we propose recurrent neural network (RNN) based incremental processing towards the SLU task of intent detection. The proposed methodology offers lower latencies than a typical SLU system, …
Australian Centre for Field Robotics（澳大利亚野外机器人中心）；The University of Sydney（悉尼大学）
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many applications. In this paper, we formulate convex sets of RNNs with stability and robustness guarantees. The guarantees are derived using incremental quadratic constraints and can ensure global exponential stability of all solutions, and bounds on incremental $ \ell_2 $ gain (the Lipschitz constant of the learned sequence-to-sequence mapping). Using an implicit m…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Cambridge University（剑桥大学）
Recurrent neural networks (RNNs) are instrumental in modelling sequential and time-series data. Yet, when using RNNs to inform decision-making, predictions by themselves are not sufficient; we also need estimates of predictive uncertainty. Existing approaches for uncertainty quantification in RNNs are based predominantly on Bayesian methods; these are computationally prohibitive, and require major alterations to the RNN architecture and training. Capitalizing on ideas from classical jackknife resampling, we develop a frequentist alternative that: (a) does not interfere with model training or c…
This paper presents methods to accelerate recurrent neural network based language models (RNNLMs) for online speech recognition systems. Firstly, a lossy compression of the past hidden layer outputs (history vector) with caching is introduced in order to reduce the number of LM queries. Next, RNNLM computations are deployed in a CPU-GPU hybrid manner, which computes each layer of the model on a more advantageous platform. The added overhead by data exchanges between CPU and GPU is compensated through a frame-wise batching strategy. The performance of the proposed methods evaluated on LibriSpee…
Connectionist temporal classification (CTC) based supervised sequence training of recurrent neural networks (RNNs) has shown great success in many machine learning areas including end-to-end speech and handwritten character recognition. For the CTC training, however, it is required to unroll (or unfold) the RNN by the length of an input sequence. This unrolling requires a lot of memory and hinders a small footprint implementation of online learning or adaptation. Furthermore, the length of training sequences is usually not uniform, which makes parallel training with multiple sequences ineffici…
We present Higher-Order Tensor RNN (HOT-RNN), a novel family of neural sequence architectures for multivariate forecasting in environments with nonlinear dynamics. Long-term forecasting in such systems is highly challenging, since there exist long-term temporal dependencies, higher-order correlations and sensitivity to error propagation. Our proposed recurrent architecture addresses these issues by learning the nonlinear dynamics directly using higher-order moments and higher-order state transition functions. Furthermore, we decompose the higher-order structure using the tensor-train decomposi…
Exploiting Symmetric Temporally Sparse BPTT for Efficient RNN Training
Institute of Neuroinformatics, University of Zurich and ETH Zurich（苏黎世大学和苏黎世联邦理工学院神经信息学研究所）；Department of Microelectronics, Delft University of Technology（代尔夫特理工大学微电子系）
KTH Royal Institute of Technology（瑞典皇家理工学院）；Watty AB；Purdue University（普渡大学）
This paper introduces Wisture, a new online machine learning solution for recognizing touch-less dynamic hand gestures on a smartphone. Wisture relies on the standard Wi-Fi Received Signal Strength (RSS) using a Long Short-Term Memory (LSTM) Recurrent Neural Network (RNN), thresholding filters and traffic induction. Unlike other Wi-Fi based gesture recognition methods, the proposed method does not require a modification of the smartphone hardware or the operating system, and performs the gesture recognition without interfering with the normal operation of other smartphone applications. We disc…
IBM Research – Zurich（IBM研究院苏黎世分部）；Graz University of Technology（格拉茨工业大学）；Institute of Theoretical Computer Science（理论计算机科学研究所）
Biological neural networks are equipped with an inherent capability to continuously adapt through online learning. This aspect remains in stark contrast to learning with error backpropagation through time (BPTT) applied to recurrent neural networks (RNNs), or recently to biologically-inspired spiking neural networks (SNNs). BPTT involves offline computation of the gradients due to the requirement to unroll the network through time. Online learning has recently regained the attention of the research community, focusing either on approaches that approximate BPTT or on biologically-plausible sche…
Click-through rate (CTR) prediction is a critical task in online advertising systems. Models like Deep Neural Networks (DNNs) are simple but stateless. They consider each target ad independently and cannot directly extract useful information contained in users' historical ad impressions and clicks. In contrast, models like Recurrent Neural Networks (RNNs) are stateful but complex. They model temporal dependency between users' sequential behaviors and can achieve improved prediction performance than DNNs. However, both the offline training and online prediction process of RNNs are much more com…
In this paper, we apply neural networks into digital marketing world for the purpose of better targeting the potential customers. To do so, we model the customer online behaviours using dedicated neural network architectures. Starting from user searched keywords in a search engine to the landing page and different following pages, until the user left the site, we model the whole visited journey with a Recurrent Neural Network (RNN), together with Convolution Neural Networks (CNN) that can take into account of the semantic meaning of user searched keywords and different visited page names. With…
We show how to take any two parameter-free online learning algorithms with different regret guarantees and obtain a single algorithm whose regret is the minimum of the two base algorithms. Our method is embarrassingly simple: just add the iterates. This trick can generate efficient algorithms that adapt to many norms simultaneously, as well as providing diagonal-style algorithms that still maintain dimension-free guarantees. We then proceed to show how a variant on this idea yields a black-box procedure for generating optimistic online learning algorithms. This yields the first optimistic regr…
Recurrent neural networks (RNNs) such as Long Short Term Memory (LSTM) networks have become popular in a variety of applications such as image processing, data classification, speech recognition, and as controllers in autonomous systems. In practical settings, there is often a need to deploy such RNNs on resource-constrained platforms such as mobile phones or embedded devices. As the memory footprint and energy consumption of such components become a bottleneck, there is interest in compressing and optimizing such networks using a range of heuristic techniques. However, these techniques do not…
PerVoice Spa（PerVoice公司）；Fondazione Bruno Kessler（布鲁诺·凯斯勒基金会）
Recently, a fully supervised speaker diarization approach was proposed (UIS-RNN) which models speakers using multiple instances of a parameter-sharing recurrent neural network. In this paper we propose qualitative modifications to the model that significantly improve the learning efficiency and the overall diarization performance. In particular, we introduce a novel loss function, we called Sample Mean Loss and we present a better modelling of the speaker turn behaviour, by devising an analytical expression to compute the probability of a new speaker joining the conversation. In addition, we d…
We consider the decision-making framework of online convex optimization with a very large number of experts. This setting is ubiquitous in contextual and reinforcement learning problems, where the size of the policy class renders enumeration and search within the policy class infeasible. Instead, we consider generalizing the methodology of online boosting. We define a weak learning algorithm as a mechanism that guarantees multiplicatively approximate regret against a base class of experts. In this access model, we give an efficient boosting algorithm that guarantees near-optimal regret against…
Hasselt University（哈塞尔特大学）；Tilburg University（蒂尔堡大学）；Warsaw University of Technology（华沙理工大学）；Universidad de Talca（塔尔卡大学）
Forecasting windmill time series is often the basis of other processes such as anomaly detection, health monitoring, or maintenance scheduling. The amount of data generated on windmill farms makes online learning the most viable strategy to follow. Such settings require retraining the model each time a new batch of data is available. However, update the model with the new information is often very expensive to perform using traditional Recurrent Neural Networks (RNNs). In this paper, we use Long Short-term Cognitive Networks (LSTCNs) to forecast windmill time series in online settings. These r…
Models for sequential data such as the recurrent neural network (RNN) often implicitly model a sequence as having a fixed time interval between observations and do not account for group-level effects when multiple sequences are observed. We propose a model for grouped sequential data based on the RNN that accounts for varying time intervals between observations in a sequence by learning a group-level base parameter to which each sequence can revert. Our approach is motivated by the mixed membership framework, and we show how it can be used for dynamic topic modeling in which the distribution o…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low complexity per iteration andreasonable memory footprint. In contrast to previous online matrix factorization methods, our approach relies on low-dimensional statistics from past iterates to control the extra variance introduced by subsampling. We present a convergence analysis that guarantees us to reach a stationary point of the problem. Large speed-ups can be ob…
Carnegie Mellon University（卡内基梅隆大学）；University of California, Irvine（加利福尼亚大学欧文分校）
In this paper, we resolve many of the key algorithmic questions regarding robustness, memory efficiency, and differential privacy of tensor decomposition. We propose simple variants of the tensor power method which enjoy these strong properties. We present the first guarantees for online tensor power method which has a linear memory requirement. Moreover, we present a noise calibrated tensor power method with efficient privacy guarantees. At the heart of all these guarantees lies a careful perturbation analysis derived in this paper which improves up on the existing results significantly.
Australian Artificial Intelligence Institute（澳大利亚人工智能研究所）；University of Technology Sydney（悉尼科技大学）
As a powerful Bayesian non-parameterized algorithm, the Gaussian process (GP) has performed a significant role in Bayesian optimization and signal processing. GPs have also advanced online decision-making systems because their posterior distribution has a closed-form solution. However, its training and inference process requires all historic data to be stored and the GP model to be trained from scratch. For those reasons, several online GP algorithms, such as O-SGPR and O-SVGP, have been specifically designed for streaming settings. In this paper, we present a new theoretical framework for onl…
Most existing matching algorithms are one-off algorithms, i.e., they usually measure the distance between the two image feature representation vectors for only one time. In contrast, human's vision system achieves this task, i.e., image matching, by recursively looking at specific/related parts of both images and then making the final judgement. Towards this end, we propose a novel loopy recurrent neural network (Loopy RNN), which is capable of aggregating relationship information of two input images in a progressive/iterative manner and outputting the consolidated matching score in the final …
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Google Research（谷歌研究院）；Tel Aviv University（特拉维夫大学）
We consider online algorithms under both the competitive ratio criteria and the regret minimization one. Our main goal is to build a unified methodology that would be able to guarantee both criteria simultaneously. For a general class of online algorithms, namely any Metrical Task System (MTS), we show that one can simultaneously guarantee the best known competitive ratio and a natural regret bound. For the paging problem we further show an efficient online algorithm (polynomial in the number of pages) with this guarantee. To this end, we extend an existing regret minimization algorithm (speci…
There is a growing interest in the speech community in developing Recurrent Neural Network Transducer (RNN-T) models for automatic speech recognition (ASR) applications. RNN-T is trained with a loss function that does not enforce temporal alignment of the training transcripts and audio. As a result, RNN-T models built with uni-directional long short term memory (LSTM) encoders tend to wait for longer spans of input audio, before streaming already decoded ASR tokens. In this work, we propose a modification to the RNN-T loss function and develop Alignment Restricted RNN-T (Ar-RNN-T) models, whic…
Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究所）；Leiden University（莱顿大学）
We consider online learning algorithms that guarantee worst-case regret rates in adversarial environments (so they can be deployed safely and will perform robustly), yet adapt optimally to favorable stochastic environments (so they will perform well in a variety of settings of practical importance). We quantify the friendliness of stochastic environments by means of the well-known Bernstein (a.k.a. generalized Tsybakov margin) condition. For two recent algorithms (Squint for the Hedge setting and MetaGrad for online convex optimization) we show that the particular form of their data-dependent …
We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints , which arise, for example, in online display advertising problems. We propose an on-line primal-dual algorithm for which we obtain dynamic cumulative regret guarantees. They depend on the convexity and the smoothness of the non-additive penalty, as well as terms capturing the smoothness with which the residuals of the non-stationary and long-term constraint…
Center for Neural Science（神经科学中心）；New York University（纽约大学）；Facebook AI Research（Facebook人工智能研究院）；Center for Data Science（数据科学中心）
We present a framework for compactly summarizing many recent results in efficient and/or biologically plausible online training of recurrent neural networks (RNN). The framework organizes algorithms according to several criteria: (a) past vs. future facing, (b) tensor structure, (c) stochastic vs. deterministic, and (d) closed form vs. numerical. These axes reveal latent conceptual connections among several recent advances in online learning. Furthermore, we provide novel mathematical intuitions for their degree of success. Testing various algorithms on two synthetic tasks shows that performan…
Unintentional falls can cause severe injuries and even death, especially if no immediate assistance is given. The aim of Fall Detection Systems (FDSs) is to detect an occurring fall. This information can be used to trigger the necessary assistance in case of injury. This can be done by using either ambient-based sensors, e.g. cameras, or wearable devices. The aim of this work is to study the technical aspects of FDSs based on wearable devices and artificial intelligence techniques, in particular Deep Learning (DL), to implement an effective algorithm for on-line fall detection. The proposed cl…
We study the problem of estimating an unknown parameter in a distributed and online manner. Existing work on distributed online learning typically either focuses on asymptotic analysis, or provides bounds on regret. However, these results may not directly translate into bounds on the error of the learned model after a finite number of time-steps. In this paper, we propose a distributed online estimation algorithm which enables each agent in a network to improve its estimation accuracy by communicating with neighbors. We provide non-asymptotic bounds on the estimation error, leveraging the stat…
Brown University（布朗大学）；Harvard Medical School（哈佛医学院）
Intracortical brain computer interfaces (iBCIs) using linear Kalman decoders have enabled individuals with paralysis to control a computer cursor for continuous point-and-click typing on a virtual keyboard, browsing the internet, and using familiar tablet apps. However, further advances are needed to deliver iBCI-enabled cursor control approaching able-bodied performance. Motivated by recent evidence that nonlinear recurrent neural networks (RNNs) can provide higher performance iBCI cursor control in nonhuman primates (NHPs), we evaluated decoding of intended cursor velocity from human motor c…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；UCLA Vision Lab（加州大学洛杉矶分校视觉实验室）；Robotics and Mechanisms Laboratory（机器人与机械实验室）；Laboratory for Embedded Machines and Ubiquitous Robots（嵌入式机器与普适机器人实验室）
In this paper, we propose an online path planning architecture that extends the model predictive control (MPC) formulation to consider future location uncertainties for safer navigation through cluttered environments. Our algorithm combines an object detection pipeline with a recurrent neural network (RNN) which infers the covariance of state estimates through each step of our MPC's finite time horizon. The RNN model is trained on a dataset that comprises of robot and landmark poses generated from camera images and inertial measurement unit (IMU) readings via a state-of-the-art visual-inertial…
In real-time speech recognition applications, the latency is an important issue. We have developed a character-level incremental speech recognition (ISR) system that responds quickly even during the speech, where the hypotheses are gradually improved while the speaking proceeds. The algorithm employs a speech-to-character unidirectional recurrent neural network (RNN), which is end-to-end trained with connectionist temporal classification (CTC), and an RNN-based character-level language model (LM). The output values of the CTC-trained RNN are character-level probabilities, which are processed b…
The University of Tokyo（东京大学）；Japan Atomic Energy Commission（日本原子能委员会）；National Institutes for Quantum and Radiological Science and Technology（日本量子科学技术研究开发机构）
During lung radiotherapy, the position of infrared reflective objects on the chest can be recorded to estimate the tumor location. However, radiotherapy systems have a latency inherent to robot control limitations that impedes the radiation delivery precision. Prediction with online learning of recurrent neural networks (RNN) allows for adaptation to non-stationary respiratory signals, but classical methods such as RTRL and truncated BPTT are respectively slow and biased. This study investigates the capabilities of unbiased online recurrent optimization (UORO) to forecast respiratory motion an…
Bocconi University（博科尼大学）；Politecnico di Milano（米兰理工大学）；Columbia University（哥伦比亚大学）
We study online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$ resource constraints. By casting the learning process over a suitably defined space of strategy mixtures, we recover strong duality on a Lagrangian relaxation of the underlying optimization problem, even for general settings with non-convex reward and resource-consumption functions. Then, we provide the first best-of-many-worlds type framework for this setting, with no-regret guarantees under stochastic, adversarial, and non-stationary inputs. Our framework …
We propose a novel nonparametric online predictor for discrete labels conditioned on multivariate continuous features. The predictor is based on a feature space discretization induced by a full-fledged k-d tree with randomly picked directions and a recursive Bayesian distribution, which allows to automatically learn the most relevant feature scales characterizing the conditional distribution. We prove its pointwise universality, i.e., it achieves a normalized log loss performance asymptotically as good as the true conditional entropy of the labels given the features. The time complexity to pro…
Online Time Series Forecasting with Theoretical Guarantees
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Guangdong University of Technology（广东技术大学）；Johns Hopkins University（约翰霍普金斯大学）；University of California San Diego（加州大学圣地亚哥分校）
Real-time respiratory motion forecasting with online learning of recurrent neural networks for accurate targeting in externally guided radiotherapy
The University of Tokyo（东京大学）；Japan Atomic Energy Commission（日本原子能委员会）；National Institutes for Quantum and Radiological Science and Technology（量子与辐射科学和技术国家研究所）
This article describes an efficient training method for online streaming attention-based encoder-decoder (AED) automatic speech recognition (ASR) systems. AED models have achieved competitive performance in offline scenarios by jointly optimizing all components. They have recently been extended to an online streaming framework via models such as monotonic chunkwise attention (MoChA). However, the elaborate attention calculation process is not robust for long-form speech utterances. Moreover, the sequence-level training objective and time-restricted streaming encoder cause a nonnegligible delay…
In this paper we provide provable regret guarantees for an online meta-learning receding horizon control algorithm in an iterative control setting. We consider the setting where, in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and there are affine control input constraints. By analysing conditions under which sub-linear regret is achievable, we prove that the meta-learning online receding horizon controller achieves an average of the dynamic regret for t…
The University of Texas at Austin（得克萨斯大学奥斯汀分校）；Radboud University（拉德堡德大学）；Albert-Ludwigs-Universität Freiburg（阿尔伯特-路德维希大学弗莱堡分校）；Concept Engineering GmbH（康赛普特工程有限公司）
We study strategy synthesis for partially observable Markov decision processes (POMDPs). The particular problem is to determine strategies that provably adhere to (probabilistic) temporal logic constraints. This problem is computationally intractable and theoretically hard. We propose a novel method that combines techniques from machine learning and formal verification. First, we train a recurrent neural network (RNN) to encode POMDP strategies. The RNN accounts for memory-based decisions without the need to expand the full belief space of a POMDP. Secondly, we restrict the RNN-based strategy …
