Traffic density adaptive vehicle trajectory prediction method

Abstract

This invention provides a traffic density-adaptive vehicle trajectory prediction method, comprising two basic steps: S1, traffic state prediction; S2, trajectory prediction considering traffic state adaptation. S1 includes two specific steps: traffic state variable representation and traffic state prediction using a temporal convolutional neural network. S2 includes trajectory prediction problem modeling, extraction of vehicle historical trajectory features, extraction of vehicle spatiotemporal features, representation of vehicle future trajectory features, acquisition of latent variables, and prediction of vehicle future trajectories. This invention achieves accurate prediction of vehicle trajectories under different traffic densities by real-time evaluation of traffic density and adjusting the parameters or structure of the trajectory prediction model according to different traffic densities. This invention achieves trajectory prediction through efficient feature extraction and attention mechanisms, maintaining the simplicity and efficiency of the model, simplifying computational complexity, and improving the accuracy and robustness of trajectory prediction under different traffic densities.

Description

Technical Field

[0001] This invention belongs to the field of intelligent transportation, and specifically relates to a vehicle trajectory prediction method that adapts to traffic density. Background Technology

[0002] Patent application CN118419065A discloses a method for predicting the trajectory of an autonomous vehicle based on a dual-crossing Transformer. This method includes the following steps:

[0003] S1, collect historical trajectory data and vehicle status data of the target vehicle and surrounding vehicles as input sequence X;

[0004] S2 captures the interaction between the target vehicle and surrounding vehicles, outputs the preliminary predicted trajectories of the target vehicle and surrounding vehicles, and evaluates individual uncertainty and cooperative uncertainty.

[0005] S3, measures the prediction performance using a loss function and updates and optimizes the parameters;

[0006] Specifically, S1 is:

[0007] Vehicle historical trajectory data acquisition, including historical trajectory points for the first three seconds, is collected once every ten frames per second, and the trajectory points are represented as (x, y);

[0008] Vehicle status data acquisition, including vehicle speed v and heading angle θ, is used to determine vehicle driving behavior and predict the trajectory of the target vehicle and surrounding vehicles by analyzing the trajectory, vehicle speed v and heading angle θ; historical trajectory data and vehicle status data are used as input sequence X.

[0009] S2 includes the following steps:

[0010] S201, perform position encoding on the input sequence X in S1;

[0011] S202 captures the interaction between the target vehicle and surrounding vehicles through a bidirectional cross-attention mechanism, obtains the interaction feature Attenbidir(fs,fg), and trains repeatedly.

[0012] S203, outputs the preliminary predicted trajectory of the target vehicle and its surrounding vehicles;

[0013] S204 assesses individual and collaborative uncertainties in the interaction feature Attenbidir(fs,fg).

[0014] The invention patent with authorization announcement number CN110304075B discloses a vehicle trajectory prediction method based on a hybrid dynamic Bayesian network and a Gaussian process. The method includes the following main steps:

[0015] Step 1: Construct a natural driving database;

[0016] A test set is established for the surrounding vehicle-related sequence information, road-related sequence information, and traffic-related sequence information collected by the perception system of autonomous vehicles, as well as a training set for calibrating driving intentions and driving characteristics based on the above information. The surrounding vehicle-related sequence information includes vehicle position, vehicle speed, vehicle acceleration, vehicle yaw rate, distance of the vehicle from both sides of the road, and the on / off status of the vehicle's left and right turn signals. The road-related sequence information includes road structural features and road signs. The traffic-related sequence information includes surrounding traffic signs and traffic light status. The test set includes a test set for a hybrid dynamic Bayesian network and a test set for a Gaussian process. The training set includes a training set for a hybrid dynamic Bayesian network and a training set for a Gaussian process.

[0017] Step 2: Using a hybrid dynamic Bayesian network, short-term predicted trajectories of surrounding vehicles are obtained, as well as estimated probabilities of driving intentions and driving characteristics.

[0018] Using driver information, vehicle model selection, and vehicle state information as hidden layer variables, and surrounding vehicle-related sequence information, road-related sequence information, and traffic-related sequence information collected by the autonomous vehicle perception system as observation layer variables, a hybrid dynamic Bayesian network model is constructed. The output of the hybrid dynamic Bayesian network is obtained through posterior probability inference: short-term trajectory prediction based on the vehicle model and the estimated probability of driving intention and driving characteristics. This output is used as the input for step 4.

[0019] Step 3, establish Gaussian process functions under different driving intentions and driving characteristics; including the following steps:

[0020] Step 3.1, Setting the mean function and covariance function

[0021] With x as input, the expression for the Gaussian process function is as follows:

[0022] f(x)~GP(u(x),Σ(x,x'))

[0023] Among them, the mean function u(x) represents the vehicle trajectory trend under a certain driving intention, so the mean function can be used to represent the expected predicted trajectory; the covariance function Σ(x,x') represents both the variance of different inputs x themselves and the variance between (x,x'), so the covariance function can be used to represent the uncertainty corresponding to the expected predicted trajectory.

[0024] The mean function u(x) is set according to the vehicle trajectory under different driving intentions;

[0025] The covariance function Σ(x,x') in the noisy mean-square exponential form is defined as follows:

[0026]

[0027] Where, σ f Let σ be the signal standard deviation, l be the characteristic length, and σ be the signal standard deviation. n The standard deviation of the observed noise is given by δ, which is the Kronecker function.

[0028] Step 3.2, Learning the unknown parameters of the Gaussian process function

[0029] Based on the mean function u(x) and covariance function Σ(x,x') set in step 3.1, the unknown parameters involved are learned using the training set of the Gaussian process established in step 1. Based on the log marginal likelihood function and its partial derivative with respect to each unknown parameter, the parameter learning results are obtained using a gradient-based optimization algorithm, thereby establishing Gaussian process functions under different driving intentions and driving characteristics.

[0030] Step 4: Long-term trajectory prediction and uncertainty representation based on hybrid dynamic Bayesian networks and Gaussian processes;

[0031] Based on the estimated probabilities of driving intention and driving characteristics output by the hybrid dynamic Bayesian network in step 2, the corresponding driving intention and driving characteristics are determined using the maximum probability principle. Then, the corresponding Gaussian process function in step 3 is determined based on these driving intentions and characteristics. The short-term predicted trajectory based on the vehicle model output by the hybrid dynamic Bayesian network in step 2 is taken as the vehicle trajectory sequence information x1, and the predicted future trajectory is x2. Then, (x1, x2) follows a Gaussian distribution as follows:

[0032]

[0033] in, Represents the normal function;

[0034]

[0035] The mean functions corresponding to x1 and x2 are u1 and u2, respectively; the covariance matrix Σ is a symmetric matrix, i.e., Σ=ΣT, the covariance functions corresponding to x1 and x2 are Σ11 and Σ22, respectively, and the covariance functions between x1 and x2 are Σ12 and Σ21, and ∑12=∑21T; then the conditional probability P(x2|x1) of the possible future trajectory x2 of the vehicle under the known vehicle trajectory x1 follows the following Gaussian distribution expression:

[0036]

[0037] Where u2|1 and Σ2|1 are the mean function and covariance function corresponding to the variable x2|1, and the expression of (u2|1,Σ2|1) is derived from the following equation:

[0038] u 2|1 =u2+∑ 12 T Σ 11 -1 (x1-u1)

[0039] ∑ 2|1 =∑ 22 -∑ 12 T ∑ 11 -1 ∑ 12

[0040] Ultimately, we obtain the future trajectory of the vehicle in the long time domain and its uncertainty representation under the driving intention and driving characteristics determined by the maximum probability principle.

[0041] In summary, the technical solution disclosed in patent application CN118419065A improves the accuracy and robustness of vehicle trajectory prediction by acquiring historical vehicle trajectory data and vehicle status data, and conducting simulation training based on multiple vehicles in a vehicle-road cooperative environment. It fully considers the interaction between the target vehicle and surrounding vehicles. The technical solution disclosed in patent application CN110304075B combines vehicle models, abstract intentions, and data-driven approaches. Its MDBN and GP models are highly scalable and applicable to different driving scenarios. It considers both the short-term prediction characteristics under the vehicle's physical motion model and long-term trajectory prediction and uncertainty representation based on vehicle and driver information.

[0042] However, the technical solutions disclosed in invention patent applications CN118419065A and CN110304075B also have certain defects, specifically in the following two aspects:

[0043] First, while both invention patent applications CN118419065A and CN110304075B consider vehicle-to-vehicle interactions, they do not explicitly address how to adapt trajectory prediction to different traffic densities. Changes in traffic density significantly impact vehicle-to-vehicle interaction patterns and the accuracy of trajectory prediction, especially in high-density areas where vehicle-to-vehicle interactions are more complex.

[0044] Second, while the bidirectional cross-attention mechanism used in invention patent CN118419065A can capture complex interaction relationships, it also increases the computational complexity and training time of the model. The model in invention patent CN110304075B, which combines MDBN and GP, also has high computational complexity, especially in autonomous driving systems with high real-time requirements, where the computation process is particularly complex. Summary of the Invention

[0045] The purpose of this invention is to overcome the first and second defects of the prior art.

[0046] To achieve the above objectives, the present invention employs the following technical solution:

[0047] A traffic density-adaptive vehicle trajectory prediction method includes the following two basic steps:

[0048] S1, Traffic Condition Prediction;

[0049] S2, trajectory prediction considering traffic conditions adaptively;

[0050] S1 includes the following specific steps:

[0051] S101, traffic state variable representation, the trajectory of all vehicles is represented by a three-dimensional one-hot vector S, where 001 represents no congestion, 010 represents congestion, and 100 represents moderate congestion;

[0052] S102 uses a temporal convolutional neural network for traffic state prediction;

[0053] S2 includes the following specific steps:

[0054] S201, Trajectory Prediction Problem Modeling, considering the future trajectories of N vehicles in an adaptive prediction scenario based on traffic conditions, defining the input trajectory as X = X1, X2, ..., X... N The model predicts the future trajectory as follows For each vehicle i, the input trajectory is the past t. h The vehicle position at each time step is represented as...

[0055] S202 is a conditional coding prediction network based on a self-attention mechanism, which includes vehicle historical trajectory feature extraction, vehicle spatiotemporal feature extraction, vehicle future trajectory feature representation, latent variable acquisition, and vehicle future trajectory prediction.

[0056] Based on the above technical solutions, the present invention can employ the following technical means to better or more specifically solve the technical problems to be solved by the present invention:

[0057] When executing step S102, the given filter F = (f1, f2, ..., f k The sequence X = (x1, x2, ..., x) k ), then in x t The causal convolution at the location is The value of time t depends only on the values ​​of the current and previous levels.

[0058] Furthermore, during step S102, the dilated convolution allows the convolution input to have interval sampling, and the sampling rate is controlled by the dilation, with the dilation size d, then in x t The causal convolution at the location is

[0059] Furthermore, when performing step S102, the input of the temporal convolutional neural network is historical traffic flow, and the output is traffic flow for a future period of time.

[0060] Furthermore, during step S202, a graph is used to represent the entire scene, where each vehicle is represented by a node, and each node is represented by an LSTM with 4 hidden dimensions, which represents the vehicle at the observed t. h Location information and traffic status information within a time step are encoded into node historical codes. As shown below:

[0061]

[0062] In the formula, This indicates the vehicle's position and status information at time step t. θ represents the hidden state of the LSTM, and θ represents the network parameters of the LSTM.

[0063] Furthermore, during step S202, edges are added based on the distance between the vehicle and its neighboring vehicles. Each edge is represented as an LSTM, and the edge history encoding of the vehicle is output. As shown below:

[0064]

[0065] In the formula, This represents the edge encoding between the vehicle and its neighboring vehicles at time step t-1, where φ is a parameter of the LSTM.

[0066] Furthermore, the node history encoding, edge history encoding, and traffic state are concatenated to obtain the vehicle's node representation vector e. i As shown below:

[0067]

[0068] Furthermore, during step S202, the Transformer model is used to extract temporal and spatial features using a multi-head attention mechanism, as shown below:

[0069]

[0070] In the formula, Q is the query matrix, K is the key matrix, V is the value matrix, and K is the value matrix. T d is the transpose of the value matrix K. k is the dimension of the key vector.

[0071] Furthermore, during step S202, the vehicle's future trajectory Y i Encoding is performed using a bidirectional LSTM with 64 hidden units, where the node future encoding is as follows:

[0072]

[0073] Furthermore, during step S202, the training process uses node representation vectors, node future encodings, and the vehicle category C. i To estimate the distribution parameters of the 32-dimensional latent variable z, as shown below:

[0074]

[0075] In the formula, This is a 2D CNN with 10 layers. The kernel sizes for each layer are {5, 5, 5, 5, 5, 3, 3, 3, 3, 3}. The first 5 layers use a stride of 2 for convolutional operations, while the last 5 layers use a stride of 1. It is made by g i Parameterized classification distribution captures patterns of agent trajector ...ies associated with each traffic state;

[0076] After obtaining the distribution parameters of the 32-dimensional latent variable z, a 128-dimensional multilayer perceptron decoder is used to generate 16 component parameters for the Gaussian mixture model. Then, the future trajectory is sampled for each vehicle i from the Gaussian mixture model, as shown below:

[0077]

[0078] Compared with the prior art, and especially with the prior art described in invention patent applications CN118419065A and CN110304075B, the present invention has the following beneficial effects:

[0079] First, the present invention fully considers the changes in traffic density during the trajectory prediction process. It evaluates the traffic density in real time through the traffic state prediction step and adjusts the parameters or structure of the trajectory prediction model according to different traffic densities, thereby achieving more accurate prediction of vehicle trajectories under different traffic densities.

[0080] Second, this invention achieves trajectory prediction through efficient feature extraction and attention mechanisms, while maintaining the simplicity and efficiency of the model. It not only simplifies the computational complexity but also improves the accuracy and robustness of trajectory prediction under different traffic densities. Attached Figure Description

[0081] Figure 1 This is a flowchart of an embodiment of the present invention;

[0082] Figure 2 This is a schematic diagram illustrating the working principle of step S202 in this embodiment. Detailed Implementation

[0083] To facilitate a thorough understanding of the technical solution of the present invention by those skilled in the art, an embodiment of the present invention is described below in conjunction with the accompanying drawings.

[0084] like Figure 1 As shown, a traffic density adaptive vehicle trajectory prediction method includes the following two basic steps:

[0085] S1, Traffic Condition Prediction;

[0086] S2, trajectory prediction considering traffic conditions adaptively;

[0087] S1 includes the following specific steps:

[0088] S101 represents the traffic state variables, which indicate traffic flow on the lanes and provide future information for the trajectory prediction model. Traffic states provide spatiotemporal information about adjacent vehicles and their future movements. Possible traffic states include congested, uncongested, and moderate. The trajectories of all vehicles are represented using a three-dimensional one-hot vector S, where 001 represents uncongested, 010 represents congested, and 100 represents moderate.

[0089] S102 uses a Temporal Convolutional Neural Network (TCN) for traffic state prediction. TCNs, derived from Convolutional Neural Networks (CNNs), directly leverage the powerful capabilities of convolutions to extract features across time steps. Therefore, TCNs exhibit better performance than LSTM and GRUs in many sequence-related tasks. A TCN primarily consists of causal convolutions for processing sequences, dilated convolutions for storing historical data, and residual modules.

[0090] It should also be noted that causal convolution is a strictly time-constrained model, where the value of time t depends only on the values ​​of the current and previous layers. This invention provides a filter F = (f1, f2, ..., f...). k The sequence X = (x1, x2, ..., x) k ), then in x t The causal convolution at the location is

[0091] In implementing the technical solution of this invention, dilated convolution allows for interval sampling of the convolution input, and the sampling rate is controlled by dilation. The higher the layer, the larger the dilation size d, which causes the effective window size to grow exponentially with the number of layers. Assume the filter F = (f1, f2, ..., f...). k The sequence X = (x1, x2, ..., x) k ), then in x t The causal convolution at the location is

[0092] In this embodiment, the input to the TCN network is historical traffic flow, and the output is traffic flow for a future period. This invention uses the TCN output for subsequent trajectory prediction research, adaptively predicting vehicle trajectories based on traffic conditions.

[0093] S2 includes the following specific steps:

[0094] S201, Trajectory Prediction Problem Modeling, considering the future trajectories of N vehicles in an adaptive prediction scenario based on traffic conditions, defining the input trajectory as X = X1, X2, ..., X... N The model predicts the future trajectory as follows For each vehicle i, the input trajectory is the past t. h The vehicle position at each time step is represented as... The objective is to predict the future t f The position of each time step, i.e.

[0095] S202, a conditional coding prediction network based on a self-attention mechanism, includes:

[0096] (1) Extraction of vehicle historical trajectory features

[0097] See Figure 2 In this embodiment, a single graph is used to represent the entire scene, with each vehicle represented by a node. Each node is represented by an LSTM (Long Short-Term Memory) network with four hidden dimensions, storing the observations of vehicle i at time t. h Location information and traffic status information within a time step are encoded into node historical codes. The process can be represented as:

[0098]

[0099] in, This indicates the position and status information of vehicle i at time step t. θ represents the hidden state of the LSTM, and θ represents the network parameters of the LSTM.

[0100] Compared to GRU networks, LSTM is better suited for capturing long-term dependencies, which is crucial in traffic scenarios. LSTM strikes a good balance between model complexity and performance. In this embodiment, interactions between agents are encoded using edges. Edges are added only when the distance between neighboring vehicles is within a certain range (this range, or the interaction range between adjacent vehicles, can be dynamically adjusted based on vehicle speed and driving environment; for example, it can be set to 30-50 meters in a low-speed urban environment and 70-100 meters in a highway environment). Each edge represents an LSTM, outputting the edge history encoding for vehicle i. The process can be described as follows:

[0101]

[0102] In the formula, φ represents the edge encoding of vehicle i and vehicle j (vehicle j is the vehicle adjacent to vehicle i) at time step t-1, and φ is the parameter of LSTM.

[0103] Traffic conditions help understand how many neighboring vehicles are approaching or leaving a vehicle. Adding traffic conditions helps generate future trajectories similar to the current traffic conditions. The node history encoding, edge history encoding, and traffic conditions are concatenated to obtain the node representation vector e for vehicle i. i As shown below:

[0104]

[0105] (2) Vehicle spatiotemporal feature extraction

[0106] The future trajectory of a vehicle is influenced by the interaction of time and space. This method utilizes...

[0107] Transformer extracts spatiotemporal features. The core of Transformer is its attention mechanism, which consists of a query vector Q, a key vector K, and a value vector V. Through Q, K, and V, the historical embedding features are mapped to a high-dimensional space. Attention coefficients are calculated using Q and K to extract heterogeneous interaction relationships. In this method, a multi-head attention mechanism is used to extract temporal and spatial features, as shown below:

[0108]

[0109] In the above formula, the scaling dot product attention mechanism calculates similarity through dot product processing of Q and K. A scaling factor sqrt(d) (used to calculate the square root of d) is used to avoid the difficulty in learning caused by excessive variance in the inner product of Q and K. The softmax function is applied to obtain the weights of the value. Q, K, and V are historical encoded features obtained through fully connected layers. Through the multi-head attention mechanism, the Transformer model can jointly attend to information from different subspaces at different locations, obtaining the estimated spatiotemporal feature representation of the vehicle.

[0110] (3) Representation of vehicle future trajectory features

[0111] In a conditional variational autoencoder, the latent variable z learns the mean and variance of the underlying input trajectory distribution, which requires acquiring the vehicle's historical and future trajectories. Therefore, the vehicle's future trajectory Y... i Encoding is performed using a bidirectional LSTM with 64 hidden units, where the node future encoding is as follows:

[0112]

[0113] The node future encoding is computed only during training. At test time, the node representation is used to estimate the distribution of latent variables.

[0114] (4) Conditional latent distribution (obtaining latent variables)

[0115] The training process uses node representation vector e i Node future coding And connected vehicles category C i To estimate the distribution parameters of the 32-dimensional latent variable z, as shown below:

[0116]

[0117] In the formula, This is a 2D CNN with 10 layers. The kernel sizes for each layer are {5, 5, 5, 5, 3, 3, 3, 3, 3}. The first 5 layers use larger 5×5 kernels to capture broader spatial features, while the last 5 layers use smaller 3×3 kernels to further refine features and capture finer details. Furthermore, the first 5 convolutional operations use a stride of 2 to quickly reduce the spatial dimensionality of the feature maps, while the last 5 convolutional operations use a stride of 1 to extract more abstract features while preserving spatial information. Distribution It is made by g i Parameterized classification distribution captures patterns of agent trajector ...ies associated with each traffic state.

[0118] (5) Future trajectory prediction

[0119] After obtaining the distribution parameters of the 32-dimensional latent variable z, a 128-dimensional multilayer perceptron (MLP) decoder is used to generate 16 component parameters for the Gaussian mixture model. Then, future trajectories are sampled for each vehicle i from the Gaussian mixture model (GMM):

[0120]

[0121] Vehicle dynamics characteristics are combined to obtain future trajectories. Because it is difficult to predict the exact dynamics of different vehicles in laneless traffic, linear dynamics are used for all types of vehicles.

Claims

1. A traffic density-adaptive vehicle trajectory prediction method, characterized in that, It includes the following two basic steps: S1, Traffic Condition Prediction; S2, trajectory prediction considering traffic conditions adaptively; S1 includes the following specific steps: S101, traffic state variable representation, the trajectory of all vehicles is represented by a three-dimensional one-hot vector S, where 001 represents no congestion, 010 represents congestion, and 100 represents moderate congestion; S102 uses a temporal convolutional neural network for traffic state prediction; S2 includes the following specific steps: S201, Trajectory Prediction Problem Modeling, considering the future trajectories of N vehicles in an adaptive prediction scenario based on traffic conditions, defining the input trajectory as X = X1, X2, ..., X... N The model predicts the future trajectory as follows For each vehicle i, the input trajectory is the past t. h The vehicle position at each time step is represented as... S202 is a conditional coding prediction network based on a self-attention mechanism, which includes vehicle historical trajectory feature extraction, vehicle spatiotemporal feature extraction, vehicle future trajectory feature representation, latent variable acquisition, and vehicle future trajectory prediction. When executing step S102, the given filter F = (f1, f2, ..., f k The sequence X = (x1, x2, ..., x) k ), then in x t The causal convolution at the location is The value of time t depends only on the values ​​of the current and previous levels; In step S202, a graph is used to represent the entire scene, where each vehicle is represented by a node, and each node is represented by an LSTM with 4 hidden dimensions. The observed time t is then used to visualize the vehicle. h Location information and traffic status information within a time step are encoded into node historical codes. As shown below: In the formula, This indicates the vehicle's position and status information at time step t. θ represents the hidden state of the LSTM, and θ represents the network parameters of the LSTM. Edges are added based on the distance between a vehicle and its neighboring vehicles. Each edge is represented as an LSTM, and the edge history encoding of the vehicle is output. As shown below: In the formula, This represents the edge encoding between a vehicle and its neighboring vehicles at time step t-1. These are the parameters of the LSTM; By concatenating the node history encoding, edge history encoding, and traffic state, we can obtain the vehicle's node representation vector e. i As shown below: When performing step S202, the training process uses node representation vectors, node future encodings, and the vehicle category C. i To estimate the distribution parameters of the 32-dimensional latent variable z, as shown below: In the formula, This is a 2D CNN with 10 layers. The kernel sizes for each layer are {5, 5, 5, 5, 5, 3, 3, 3, 3, 3}. The first 5 layers use a stride of 2 for convolutional operations, while the last 5 layers use a stride of 1. It is made by g i Parameterized classification distribution captures patterns of agent trajector ...ies associated with each traffic state; After obtaining the distribution parameters of the 32-dimensional latent variable z, a 128-dimensional multilayer perceptron decoder is used to generate 16 component parameters for the Gaussian mixture model. Then, the future trajectory is sampled for each vehicle i from the Gaussian mixture model, as shown below:

2. The traffic density adaptive vehicle trajectory prediction method as described in claim 1, characterized in that: When performing step S102, dilated convolution allows the convolution input to have interval sampling, and the sampling rate is controlled by dilation. The dilation size d then... t The causal convolution at the location is 3. The traffic density adaptive vehicle trajectory prediction method as described in claim 2, characterized in that: When performing step S102, the input of the temporal convolutional neural network is historical traffic flow, and the output is traffic flow for a future period of time.

4. The traffic density adaptive vehicle trajectory prediction method as described in claim 1, characterized in that: In step S202, the Transformer model is used to extract temporal and spatial features using a multi-head attention mechanism, as shown below: In the formula, Q is the query matrix, K is the key matrix, V is the value matrix, and K is the value matrix. T d is the transpose of the value matrix K. k is the dimension of the key vector.

5. The traffic density adaptive vehicle trajectory prediction method as described in claim 1, characterized in that: During step S202, the vehicle's future trajectory Y i Encoding is performed using a bidirectional LSTM with 64 hidden units, where the node future encoding is as follows:

Images