Road network spatio-temporal state uncertainty calculation method based on graph convolution model

Abstract

The application discloses a kind of based on graph convolution model's road network traffic space-time state uncertainty calculation method, comprising: collecting historical traffic space-time data;Based on DCRNN model, road network traffic state point prediction model is constructed;Establish the loss function method of describing accidental uncertainty, and using historical traffic space-time data, based on the MC-Dropout of bayesian framework, traffic state uncertainty training is carried out to road network traffic state point prediction model, and the trained road network traffic state interval range prediction model is obtained;The traffic state in the predicted time range is obtained by inputing the traffic space-time data to be predicted into the trained road network traffic state interval range prediction model.The application is more in-depth and effective to quantify the uncertainty of traffic state by combining deep learning technology and bayesian framework, to provide more flexible and comprehensive decision support for traffic management and dispatch.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of traffic prediction, in particular to a road network traffic spatio-temporal state uncertainty calculation method under a graph convolution model framework. BACKGROUND

[0002] With the continuous improvement of traffic information collection technology, the acquisition of real-time traffic data has become more convenient and accurate, making it possible to predict real-time traffic conditions. This technological progress provides a large amount of real-time or near real-time data for traffic management and prediction, greatly promoting the development of traffic flow prediction models. However, traditional point prediction methods, although they can predict the traffic flow at a certain time in the future, cannot effectively measure the volatility and uncertainty of traffic flow. The volatility of traffic flow is mainly caused by various unpredictable factors, such as sudden events, weather changes, and holiday effects. These factors cause the traffic flow state to have a high degree of uncertainty, and a single point prediction value cannot provide enough information to describe this uncertainty.

[0003] Therefore, how to provide a road network traffic spatio-temporal state uncertainty calculation method based on a graph convolution model that can predict the possible range of changes in future traffic conditions is a technical problem that needs to be solved by those skilled in the art. SUMMARY

[0004] The present application provides a road network traffic spatio-temporal state uncertainty calculation method based on a graph convolution model, which uses a graph convolution model as a spatio-temporal prediction framework to establish a method for calculating the uncertainty of road network traffic spatio-temporal state, more directly quantifying the traffic fluctuations caused by uncertain factors, and supporting more effective management and guidance of traffic flow.

[0005] The road network traffic spatio-temporal state uncertainty calculation method based on a graph convolution model provided by the present application comprises the following steps:

[0006] S1: Collecting historical traffic spatio-temporal data, including road network traffic spatial data and traffic state time series data under the road network traffic space;

[0007] S2: Constructing a road network traffic state point prediction model based on a DCRNN model, using historical traffic state time series data and road network traffic spatial data as input, and road network traffic state spatio-temporal prediction point values and the variance of the prediction point values as output;

[0008] S3: Establishing a loss function method to describe accidental uncertainty, and using the historical traffic spatio-temporal data, training the road network traffic state point prediction model for traffic state uncertainty based on a Bayesian framework MC-Dropout, to obtain a trained road network traffic state interval range prediction model;

[0009] S4: inputting the traffic spatio-temporal data to be predicted into the trained road network traffic state interval range prediction model to obtain the predicted traffic state in the time range.

[0010] Preferably, the road network structure data in S1 comprises road connection information, road length, and actual distance between roads; and the traffic state time series data under the road network structure comprises road traffic volume and road section average speed at uniform time intervals.

[0011] Preferably, the road network traffic spatial data in S1 further comprises a spatial correlation matrix constructed according to the actual spatial distance between two road sections, for representing the weight between the two road sections.

[0012] Preferably, S2 comprises a step of modeling time characteristics:

[0013] The traffic state time series data is processed by using GRU to capture dynamic changes over time, and the final hidden state is output by setting update gate, reset gate, and candidate hidden state.

[0014] Preferably, S2 comprises a step of modeling spatial characteristics:

[0015] The road network traffic spatial data is processed by using the diffusion convolution method to capture the spatial dependence relationship between nodes.

[0016] Preferably, the DCRNN model captures the structural information of the road network traffic spatial data by using bilateral random walk in the diffusion convolution step, comprising:

[0017] The traffic network graph G=(V, E) is constructed by using the spatial correlation matrix, where V represents a road section set, and E represents an edge set representing the correlation relationship between road sections;

[0018]

[0019] wherein H represents the output matrix of the aggregated input feature X after the diffusion process, K represents the diffusion step number, X represents the input feature matrix including the traffic state data of each node, the diffusion operator D is used to capture the information propagation and influence relationship between nodes, and Θ k represents the weight matrix to be learned in the diffusion convolution model. By learning the parameters of the weight matrix, the model adaptively adjusts the internal calculation so that the output result is as close to the real traffic flow as possible.

[0020] Preferably, the method for establishing the loss function describing the accidental uncertainty in S3 comprises:

[0021] The conditional variance function σ(x i ) 2where N is the number of input data x i , and 0 is the model parameter, y i and represent the true value and the predicted value of the model respectively, x i is the input traffic state data, and a loss function is established as follows:

[0022]

[0023] Preferably, the S4 comprises:

[0024] The cognitive uncertainty of the output is estimated by sampling from the posterior distribution using Dropout; the total prediction variance and the total prediction interval are obtained by the following expressions:

[0025]

[0026] where T is the number of MC-Dropout samplings, represents the predicted value obtained by the t-th sampling, u(y) and l(y) represent the upper and lower bounds of the prediction interval respectively, and z α / 2 is the critical value corresponding to the confidence level (1-a) % in the standard normal distribution.

[0027] The method for calculating the spatio-temporal state uncertainty of a road network traffic based on a graph convolution model has the following beneficial effects compared with the prior art:

[0028] The prediction interval is used to represent the possible variation range of the future traffic state, which helps to more comprehensively understand the uncertainty of the traffic flow. The prediction interval not only gives the predicted value, but also provides information about the credibility of the prediction result, and the possible maximum and minimum traffic flow is represented by the upper and lower bounds, thereby providing more flexible and comprehensive decision support for traffic management and scheduling. This method based on the prediction interval can more effectively cope with the uncertainty and risk in traffic management, and improve the adaptability and response speed of the traffic system. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of the provided drawings.

[0030] Figure 1 The flowchart of the method for calculating the spatio-temporal state uncertainty of a road network traffic based on a graph convolution model is provided for the embodiments of the present application.

[0031] Figure 2The schematic diagram of the prediction result of a certain road section detector interval is provided for the embodiments of the present application. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the present application.

[0033] As Figure 1 shown, the present application provides a road network traffic space-time state uncertainty calculation method based on a graph convolution model, including the following steps:

[0034] S1: collecting historical traffic space-time data, including road network traffic spatial data and traffic state time series data under the road network traffic spatial data;

[0035] S2: constructing a road network traffic state point prediction model based on a DCRNN model, taking the historical traffic state time series data and the road network traffic spatial data as inputs, and taking the road network traffic state space-time prediction point value and the variance of the prediction point value as outputs;

[0036] S3: establishing a loss function method for describing accidental uncertainty, and training the road network traffic state point prediction model for traffic state uncertainty based on a Bayesian framework MC-Dropout using the historical traffic space-time data, to obtain a trained road network traffic state interval range prediction model;

[0037] S4: inputting the to-be-predicted traffic space-time data into the trained road network traffic state interval range prediction model to obtain the predicted traffic state in the time range.

[0038] In one embodiment, the road network structure data in S1 includes road connection information, road length and actual distance between roads; and the traffic state time series data under the road network structure includes road traffic volume and road section average speed at uniform time intervals.

[0039] In this embodiment, the detector is used to detect the road traffic volume, and data is collected at a specified time interval (for example, 5 minutes) to obtain time series information at uniform intervals.

[0040] In one embodiment, the road network traffic spatial data in S1 further includes: the spatial structure information of the road section is represented by the longitude and latitude of the midpoint of the road section, the actual spatial distance d(v i ,v j ) between two road sections is calculated, and a spatial correlation matrix is constructed therefrom to represent the weight A ijto describe the relevance between road segments in the road network.

[0041] The specific calculation method of the two-point spatial correlation matrix is determined by the following expression:

[0042]

[0043] A ij is the weight value between the two road segments i and j, and the weight value size shows the size of the space between the two points. d(v i ,v j ) is the actual spatial distance between the two road segments, σ 2 represents the variance parameter of the Gaussian kernel, which affects the speed at which the correlation between the two road segments v i and v j decreases as the distance increases.

[0044] In one embodiment, the traffic state prediction model based on diffusion graph convolution established in S2 can be divided into modeling of time characteristics and modeling of space characteristics. The steps of modeling the time characteristics are:

[0045] The GRU (Gated Recurrent Unit) is used to process the traffic state time series data to capture the dynamic changes over time. By setting the update gate, reset gate and candidate hidden state, the final hidden state is output.

[0046] In specific implementation, it is assumed that the input time series is {x1,x2,...,x T}, where x T represents the input feature at the Tth time step.

[0047] At each time step, the GRU updates the hidden state h t in the following manner:

[0048] z t =σ(W z x t +U z h t-1 +b z )

[0049] r t =σ(W r x t +U r h t-1 +b r )

[0050]

[0051] where z t , r t , These represent the update gate, reset gate, and candidate hidden state, respectively. The final hidden state can be used as the output or further passed to subsequent layers. Through the above process, DCRNN can capture the dynamic changes and long-term and short-term dependencies of time series data.

[0052] In one embodiment, the traffic state prediction model based on diffusion graph convolution established in S2 can be divided into modeling of temporal features and modeling of spatial features. The steps for modeling spatial features are as follows:

[0053] The diffusion convolution method is used to process network traffic spatial data and capture the spatial dependencies between nodes.

[0054] In one embodiment, the DCRNN model captures structural information of road network traffic spatial data through bilateral random walks during the diffusing convolution step, including:

[0055] The transportation network is represented as a graph G = (V, E), where V is the set of nodes and E is the set of edges, representing the relationships between roads, i.e., the spatial incidence matrix. The spatial incidence matrix A of the graph... ij Calculated from S1.

[0056] Diffusion convolution captures graph structure information through a diffusion process (random walk):

[0057]

[0058] Where H represents the output matrix of the aggregated input features X after the diffusion process, K represents the number of diffusion steps, X represents the input feature matrix, specifically the traffic state data of each node, and the diffusion operator D is used to capture the information propagation and influence relationships between nodes. k This represents the weight matrix that needs to be learned in the diffusion convolution model. By learning the parameters of the weight matrix, the model adaptively adjusts its internal calculations to make the output result as close as possible to the real traffic flow.

[0059] In one embodiment, DCRNN employs an encoder-decoder architecture to process spatiotemporal sequence data. First, the encoder processes the input sequence and converts it into a hidden state vector. Then, the decoder generates a prediction sequence based on the hidden state vector generated by the encoder. Specifically, this includes:

[0060] Encoder stage:

[0061] First, during the training phase, DCRNN receives historical traffic spatiotemporal data as input, which includes traffic flow data from multiple traffic monitoring points at different times.

[0062] In the encoder, convolutional layers are used to extract local spatial features. This helps capture the correlation between different location traffic monitoring points.

[0063] The diffusion layer utilizes graph structure (road network structure in the traffic network) to propagate information. This step allows longer-range spatial dependencies to be considered.

[0064] Then, GRU layers are used to process time series data, capturing dynamic features over time, effectively capturing long and short-term dependencies through its gating mechanisms (including update gate and reset gate). This helps the model understand patterns and trends in time series.

[0065] The last GRU hidden state of the encoder serves as the context vector, containing important information about all input sequences.

[0066] Decoder stage:

[0067] The decoder uses the context vector generated by the encoder as the initial state to generate future traffic flow sequences through GRU layers.

[0068] At each time step, the decoder generates the next time step's prediction value based on the current hidden state and previous output.

[0069] The final output layer converts the decoder's hidden state into a predicted spatio-temporal sequence, resulting in future traffic flow prediction results.

[0070] In one embodiment, the step of training the road network traffic state point prediction model for traffic state uncertainty based on the Bayesian framework MC-Dropout in S3 includes:

[0071] 1. Initialize the DCRNN model based on the Bayesian framework MC-Dropout

[0072] Initialize the CDRNN model to ensure that a Dropout layer is included in each RNN layer, convolutional layer, or fully connected layer. The Dropout layer will remain active during the training and testing phases to introduce uncertainty into the model.

[0073] 2. Training phase

[0074] During the training phase, the Dropout layer randomly turns off a portion of the neurons, which helps prevent overfitting and introduces uncertainty into the model during training. The training process is as follows:

[0075] The historical traffic spatio-temporal data is fed into the DCRNN model as an input sequence.

[0076] Convolutional layers are applied to extract local spatial features, and Dropout layers are used after the convolutional layers. Diffusion layers are used to propagate graph structure information, capturing spatial dependencies in the traffic network. GRU layers are applied to handle time series data, capturing dynamic features over time, and Dropout layers are used after each GRU layer. The loss function is used to calculate the discrepancy between the model's predictions and the actual labels.

[0077] The network weights are updated using the backpropagation algorithm to minimize the loss function. Through continuous iteration, the model parameters are optimized.

[0078] 3. Inference phase (MC-Dropout)

[0079] In the inference phase, the key of MC-Dropout lies in running the model multiple times and collecting the prediction results. The steps are as follows:

[0080] For a given input sequence, the CDRNN model is repeatedly run multiple times (e.g., T times), each time using a different Dropout mask.

[0081] The outputs of each run are collected, and the average of these outputs is calculated as the final prediction. The purpose of this step is to approximate Bayesian inference through multiple sampling.

[0082] The variance or standard deviation of the output is calculated as a measure of uncertainty to assess the model's prediction uncertainty for a particular input. A larger variance indicates higher uncertainty, and vice versa. In one embodiment, the epistemic uncertainty reflects the noise in the data itself, which is usually introduced during data generation or collection. The loss function method in S3 establishes a description of epistemic uncertainty, which includes:

[0083] By using the conditional variance function σ(x i ) 2 to model the variance of the output noise, where N is the number of input data x i , θ is the model parameter, y i and represent the true value and the model's predicted value, respectively, and x i is the input traffic state data, the loss function is established as:

[0084]

[0085] Using this loss function to train and optimize the model, the model's predicted value and the variance of the predicted value are obtained, the latter can represent the variability of the output prediction due to the different characteristics of the input data, and thus can be used to quantify the model's epistemic uncertainty.

[0086] In one embodiment, the cognitive uncertainty is caused by the prediction model, which is derived from the incompleteness of the model itself or the limited understanding of the data; the MC-Dropout method based on the Bayesian framework represents the parameter values of the model as probabilities under a distribution, and obtains the posterior probability of the parameters by combining the prior probability and the statistical data with the Bayesian theorem. S4 comprises the following specific steps:

[0087] The cognitive uncertainty of the output is estimated by sampling from the posterior distribution using Dropout; the total prediction variance and the total prediction interval are obtained by the following expressions:

[0088]

[0089] wherein T is the sampling number of MC-Dropout, represents the prediction value obtained by the t-th sampling, u(y) and l(y) represent the upper and lower bounds of the prediction interval, and z α / 2 is the critical value corresponding to the confidence level (1-α) % in the standard normal distribution.

[0090] The application will be described in detail below with reference to specific implementation examples:

[0091] This implementation takes 100 detector nodes within a certain range of a city as an example, each detector records the traffic flow at an interval of every 5 minutes within a month, and the traffic flow of all detectors is predicted. The steps required for this embodiment are described in detail:

[0092] S1: Detect the road traffic volume using the detector, collect data at a specified time interval (5 min), and obtain time series information at uniform intervals; collect road segment information, the spatial structure information of the road segment is represented by the longitude and latitude of the midpoint of the road segment, the actual spatial distance d(v i ,v j ) between two road segments is calculated, and the spatial correlation matrix is constructed based on the actual spatial distance;

[0093] A ij is the weight value between i and j, the weight value size shows the size of the space between the two points, d(v i ,v j ) is the actual spatial distance between two road segments, σ 2 represents the variance parameter of the Gaussian kernel, which affects the speed at which the correlation between two road segments v i and v j decreases as the distance increases. The specific calculation method of the two-point spatial correlation matrix is determined by the following expression:

[0094]

[0095] S2: The step 2 establishes a point prediction model based on diffusion graph convolution, which can be divided into modeling of time characteristics and modeling of space characteristics;

[0096] For time characteristic modeling: a GRU with 3 layers and 128 neurons is used to capture the dynamic changes of time series, and the sequence length is set to 12, assuming that the input time series is {x1, x2, …, xT}, where xi represents the input feature of the i-th time step; 12 i For time characteristic modeling: a GRU with 3 layers and 128 neurons is used to capture the dynamic changes of time series, and the sequence length is set to 12, assuming that the input time series is {x1, x2, …, xT}, where xi represents the input feature of the i-th time step;

[0097] At each time step, the GRU updates the hidden state h t , which is updated as follows:

[0098] z t =σ(W z x t +U z h t-1 +b z )

[0099] r t =σ(W r x t +U r h t-1 +b r )

[0100]

[0101] where z t , r t , represent the update gate, the reset gate and the candidate hidden state, respectively. The final hidden state can be used as output or further passed to subsequent layers. Through the above process, the DCRNN can capture the dynamic changes and long and short term dependencies of time series data;

[0102] For space characteristic modeling, a graph convolution method is used, specifically, a method called diffusion convolution is used to capture the spatial dependence between nodes;

[0103] The traffic network is represented as a graph G = (V, E), where V is the set of nodes and E is the set of edges (representing the relationship between roads. The adjacency matrix space correlation matrix A ij is calculated by step 1. Diffusion convolution captures graph structure information through bilateral random walk, where K represents the number of diffusion steps, X is the input feature matrix, X is the input feature matrix, the diffusion operator D is used to capture the information propagation and mutual influence between nodes, and Θ k is the weight matrix to be learned: ​

[0104]

[0105] An encoder-decoder architecture is used to process spatio-temporal sequence data. The encoder and decoder each contain a diffusion convolution recurrent layer with 3 layers and 128 neurons. The input sequence X is first processed using the encoder to convert it into a hidden state vector input , which is used to generate the predicted sequence Y by the decoder pred ;

[0106] S3: The variance of the output noise is modeled using the conditional variance function σ(x i ) 2 , where N is the number of input data 100, θ is the model parameter, y i and represent the true value and the predicted value of the model respectively, and the loss function is established:

[0107]

[0108] Using this loss function, the model is trained and optimized, and the predicted value and the variance of the predicted value σ(x i ) 2 are obtained.

[0109] S4: Set the Dropout rate to 0.2 in the test phase, and sample the trained model parameters 50 times to obtain the mean and standard deviation of the 50 prediction results.

[0110] The prediction mean, total prediction variance, and total prediction interval are obtained from the following expressions:

[0111]

[0112] where T is the number of MC-Dropout samples 50, represents the predicted value obtained by the t-th sampling, u(y) and l(y) represent the upper and lower bounds of the prediction interval, and z α / 2 is the critical value corresponding to the 95% confidence level in the standard normal distribution.

[0113] Figure 2 The three graphs in the middle show the effects of different uncertainties in the traffic flow prediction task. Specifically, each graph shows the actual traffic flow (blue solid line), predicted value (red solid line), confidence interval, and other related information for a certain node (Node 35). The following is a supplementary explanation of the three graphs:

[0114] The first graph shows the actual traffic flow, the predicted value and the predicted epistemic uncertainty. The comparison between the predicted value (red solid line) and the actual value (blue solid line) shows the prediction effect of the model, and the green shaded part represents the range of the predicted epistemic uncertainty, reflecting the incompleteness of the model itself or the limited understanding of the data;

[0115] The second graph shows the actual traffic flow, the predicted value and the predicted aleatory uncertainty. The comparison between the predicted value (red solid line) and the actual value (blue solid line) shows the prediction effect of the model, and the green shaded part represents the range of the predicted aleatory uncertainty, reflecting the influence of the noise of the data itself on the prediction;

[0116] The third graph shows the actual traffic flow, the predicted value and the total prediction interval. The comparison between the predicted value (red solid line) and the actual value (blue solid line) shows the prediction effect of the model, and the total prediction interval, which is the sum of the aleatory uncertainty and the epistemic uncertainty, contains the aleatory uncertainty and the epistemic uncertainty of the above two graphs and is the widest interval on the outside; it is the interval prediction result at a confidence level of 95%.

[0117] The above describes in detail the method for calculating the road network traffic space-time state uncertainty based on the graph convolution model provided by the present application, and the principles and implementation manners of the present application are described by using specific examples in the present application; the above description of the examples is only used to help understand the method of the present application and its core idea; meanwhile, for those skilled in the art, the specific implementation manners and application ranges will be changed according to the idea of the present application, and in summary, the content of the specification should not be understood as a limitation of the present application.

[0118] In this document, the term "only" is used to distinguish one entity or operation from another entity or operation, but does not necessarily require or imply any such actual relationship or order between the entities or operations. Moreover, the terms "include", "contain" or any other variants thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or device. Without more limitations, the element defined by the statement "including a" does not exclude the presence of another identical element in the process, method, article or device including the element.

Claims

1. A method for computing spatio-temporal state uncertainty of road network traffic based on a graph convolution model, characterized in that: The method comprises the following steps: S1: collecting historical traffic spatio-temporal data, including road network traffic spatial data and traffic state time series data under the road network traffic spatial data; S2: constructing a road network traffic state point prediction model based on a DCRNN model, taking the historical traffic state time series data and the road network traffic spatial data as input, and taking the road network traffic state spatio-temporal prediction point value and the variance of the prediction point value as output; the S2 comprises the following steps of modeling spatial features: The road network traffic spatial data is processed by using a diffusion convolution method to capture the spatial dependence relationship between nodes; The DCRNN model captures the structural information of the road network traffic spatial data by using double-sided random walk in the diffusion convolution step, comprising: A traffic network graph G=(V, E) is constructed by using a spatial correlation matrix, wherein V represents a road segment set, and E represents an edge set representing the correlation relationship between road segments; Wherein, H represents the output matrix of the aggregation input feature X after the diffusion process, K represents the diffusion step number, X represents the input feature matrix including the traffic state data of each node, and D represents the diffusion operator k For capturing the information propagation and influence relationship between nodes, Θ k Indicates the weight matrix to be learned in the diffusion convolution model, and by learning the parameters of the weight matrix, the model adaptively adjusts the internal calculation so that the output result is as close to the real traffic flow as possible; S3: establishing a loss function method for describing accidental uncertainty, and training the road network traffic state point prediction model based on the MC-Dropout of the Bayesian framework according to the historical traffic spatio-temporal data, to obtain a trained road network traffic state interval range prediction model; the loss function method for describing accidental uncertainty in the S3 comprises: The variance of the output noise is modeled by using a conditional variance function σ(x i ) 2 , where N is the number of input data x i in a batch, θ is a model parameter, y i and represent the true value and the predicted value of the model respectively, x i is the input traffic state data, and a loss function is established: S4: inputting the to-be-predicted traffic spatio-temporal data into the trained road network traffic state interval range prediction model to obtain the predicted traffic state in the time range; the S4 comprises: Dropout is applied to sample from the posterior distribution to estimate the cognitive uncertainty of the output; the total prediction variance and the total prediction interval are obtained by the following expression: where T is the number of samples of MC-Dropout, represents the prediction value obtained in the tth sample, u(y) and l(y) represent the upper and lower bounds of the prediction interval, respectively, and z α / 2 is the critical value corresponding to the confidence level (1 - a) % in the standard normal distribution.

2. The method of claim 1, wherein, The road network structure data in the S1 comprises road connection information, road length and actual distance between roads; the traffic state time series data under the road network structure comprises road traffic volume and road segment average speed at uniform time intervals.

3. The method of claim 1, wherein, The road network traffic spatial data in the S1 further comprises a spatial correlation matrix constructed according to the actual spatial distance between two road segments, for representing the weight between the two road segments.

4. The method of claim 1, wherein, The S2 comprises the following steps of modeling time features: The traffic state time series data is processed by using GRU to capture the dynamic change in time, and the final hidden state is output by setting the update gate, the reset gate and the candidate hidden state.

Images