A nonlinear equalization method and device based on liquid time constant neural network

Abstract

The application discloses a liquid time constant neural network-based nonlinear equalization method and device, relates to the field of optical fiber communication and sensing technology, and discloses the liquid time constant neural network-based nonlinear equalization method, which comprises the following steps: determining a training set according to a sampled signal sequence; calculating the loss of each input in the training set according to a liquid time constant neural network; the liquid time constant neural network can enable a single element of a hidden state to identify input features reaching each time point; updating liquid time constant neural network parameters based on the loss and a gradient descent method to train a neural network model; and obtaining an equalization result of a signal according to the trained neural network model. The equalization method disclosed by the application has a good equalization effect and can obtain a lower equalization signal bit error rate.

Description

Technical Field

[0001] This application relates to the field of optical fiber communication technology, specifically to a nonlinear equalization method and apparatus based on a liquid time constant neural network. Background Technology

[0002] Nonlinear effects in optical transmission systems and optical access networks significantly impact signal transmission performance and signal quality. Traditional nonlinear equalization algorithms are highly complex, rely heavily on link information, are difficult to implement, and have significant limitations in application.

[0003] While existing machine learning-based nonlinear equilibrium algorithms can achieve performance similar to traditional algorithms with lower complexity, LSTM (Long Short-Term Memory) is a type of recurrent neural network specifically designed to address the long-term dependency problem inherent in general RNNs (Recurrent Neural Networks).

[0004] However, due to the relatively outdated LSTM network mechanism, its equalization method has a relatively low accuracy rate and cannot meet current needs. Summary of the Invention

[0005] This application provides a nonlinear equalization method and apparatus based on a liquid time constant neural network, which has a better equalization effect and can obtain a lower bit error rate of the equalized signal.

[0006] In a first aspect, embodiments of this application provide a nonlinear equalization method based on a liquid time constant neural network, the nonlinear equalization method based on a liquid time constant neural network comprising:

[0007] The training set is determined based on the sampled signal sequence;

[0008] The loss for each input in the training set is calculated based on a liquid time constant neural network, which has a varying liquid time constant, enabling individual elements of the hidden state to identify input features arriving at each time point.

[0009] Based on loss and gradient descent methods, the parameters of the liquid time constant neural network are updated to train the neural network model;

[0010] The signal equalization result is obtained based on the trained neural network model.

[0011] In conjunction with the first aspect, in one implementation, the step of calculating the loss for each input in the training set based on a liquid time constant neural network, wherein the liquid time constant neural network has a varying liquid time constant, enabling individual elements of the hidden state to identify input features arriving at each time point, includes:

[0012] According to the formula: Iteratively calculate the hidden state x of the next neuron t+Δt , where x(t) is the hidden state of the current neuron, f(.) is the activation function of the neural network, I(t) is the time-dependent neural network input sequence in the training set, θ is the parameter set, and A is the bias vector;

[0013] Determine the final hidden state x of the last god general element through iterative computation;

[0014] According to the formula: Calculate the predicted value Among them W out For the output weights, b out For output bias;

[0015] According to the formula: Calculate the loss for each input in the training set, where y j (t) represents the actual value of the sampled signal sequence, L total Let T be the loss function and T be the length of the training set.

[0016] In conjunction with the first aspect, in one implementation, updating the liquid time constant neural network parameters based on loss and gradient descent to train the neural network model includes:

[0017] According to the formula: Calculate gradient

[0018] According to the formula: θ'=θ-αL total (θ), update parameter θ, where α is the learning rate.

[0019] In conjunction with the first aspect, in one implementation, the training set is divided into multiple batches, and the updated liquid time constant neural network parameters of the previous batch are passed to the next batch for iterative calculation until the liquid time constant neural network parameters of all batches are updated to obtain a trained neural network model.

[0020] In conjunction with the first aspect, in one implementation, the L total This is the mean squared error loss function or the cross-entropy loss function.

[0021] Secondly, embodiments of this application provide a nonlinear equalization device based on a liquid time constant neural network, characterized in that the nonlinear equalization device based on the liquid time constant neural network comprises:

[0022] The sampling module determines the training set based on the sampled signal sequence;

[0023] The calculation module calculates the loss for each input in the training set based on a liquid time constant neural network, which has a varying liquid time constant, enabling individual elements of the hidden state to identify the input features arriving at each time point.

[0024] The training module, based on loss and gradient descent, updates the parameters of the liquid time constant neural network to train the neural network model;

[0025] The equalization module obtains the signal equalization result based on the trained neural network model.

[0026] In conjunction with the second aspect, in one implementation, the calculation module calculates the loss for each input in the training set based on a liquid time constant neural network, wherein the liquid time constant neural network has a varying liquid time constant, enabling individual elements of the hidden state to identify input features arriving at each time point, including:

[0027] According to the formula: Iteratively calculate the hidden state x of the next neuron t+Δt , where x(t) is the hidden state of the current neuron, f(.) is the activation function of the neural network, I(t) is the time-dependent neural network input sequence in the training set, θ is the parameter set, and A is the bias vector;

[0028] Determine the final hidden state x of the last god general element through iterative computation;

[0029] According to the formula: Calculate the predicted value Among them W out For the output weights, b out For output bias;

[0030] According to the formula: Calculate the loss for each input in the training set, where y j (t) represents the actual value of the sampled signal sequence, L total Let T be the loss function and T be the length of the training set.

[0031] In conjunction with the second aspect, in one implementation, the calculation module updates the parameters of the liquid time constant neural network based on loss and gradient descent methods to train the neural network model, including:

[0032] According to the formula: Calculate gradient

[0033] According to the formula: θ'=θ-αL total (θ), update parameter θ, where α is the learning rate.

[0034] In conjunction with the second aspect, in one implementation, the training module is used to:

[0035] The training set is divided into multiple batches. The updated liquid time constant neural network parameters from the previous batch are passed to the next batch for iterative calculation until the liquid time constant neural network parameters of all batches are updated, so as to obtain the trained neural network model.

[0036] In conjunction with the second aspect, in one implementation, the calculation module calculates the loss for each input using a mean squared error loss function or a cross-entropy loss function.

[0037] The beneficial effects of the technical solutions provided in this application include at least the following:

[0038] The nonlinear equalization method based on a liquid time constant neural network in this application determines a training set based on a sampled signal sequence; calculates the loss for each input in the training set based on the liquid time constant neural network, wherein the liquid time constant neural network has a changing liquid time constant, enabling individual elements of the hidden state to identify the input features arriving at each time point; updates the parameters of the liquid time constant neural network based on the loss and gradient descent method to train the neural network model; and obtains the signal equalization result based on the trained neural network model.

[0039] Instead of declaring the dynamics of the learned system through implicit nonlinearity, this application constructs a network of linear first-order dynamic systems tuned by nonlinear interconnect gates. The resulting model represents a dynamic system with varying (i.e., liquid) time constants coupled to its implicit states, and its output is computed by a numerical differential equation solver. These neural networks exhibit stable and bounded behavior, produce excellent expressiveness in the family of neural differential equations, and improve the performance of time series prediction tasks. This results in better equalization and a lower bit error rate in the obtained equalized signal. Attached Figure Description

[0040] Figure 1 This is a flowchart illustrating an embodiment of the nonlinear equilibrium method based on a liquid time constant neural network according to this application.

[0041] Figure 2 This is a functional module diagram of an embodiment of the nonlinear equalization device based on a liquid time constant neural network according to this application. Detailed Implementation

[0042] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0043] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0044] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0045] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0046] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0047] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0048] In a first aspect, embodiments of this application provide a nonlinear equilibrium method based on a liquid time constant neural network.

[0049] In one embodiment, reference is made to Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the nonlinear equalization method based on a liquid time constant neural network according to this application. Figure 1 As shown, the nonlinear equalization method based on a liquid time constant neural network includes:

[0050] S1. Determine the training set based on the sampled signal sequence;

[0051] Specifically, in this embodiment, the training set I is obtained by partitioning the sampled signal sequence y. For example, for the sampled signal sequence y = [1,2,3,4,5,6,7,8], y(t,t=3) = 4 and y(t,t=4) = 5. If the number of taps is 3, then I(t,t=3) = [1,2,3,4] and I(t,t=4) = [2,3,4,5], and so on, thus determining the training set.

[0052] S2. Calculate the loss for each input in the training set based on the liquid time constant neural network, wherein the liquid time constant neural network has a varying liquid time constant, which enables the individual elements of the hidden state to identify the input features arriving at each time point;

[0053] It is worth noting that, compared with LSTM networks under the same input and computational complexity, the present application achieves better equalization performance, i.e., a lower bit error rate. This is because the hidden state flow of the optimized CT-RNN in this application is replaced by a substitution formula declared by a linear ordinary differential equation:

[0054]

[0055] After conversion, it can also be expressed as:

[0056]

[0057] Where x(t) is the hidden state of the current neuron, f(.) is the neural network activation function, I(t) is the time-dependent neural network input sequence in the training set, θ is the parameter set, and A is the bias vector. θ is a parameter set that includes the time constant τ, weight γ, cyclic weight γr, and bias μ, which is existing technology and will not be elaborated in detail in this embodiment.

[0058] In other words, the neural network not only determines the derivative of the hidden state x(t), but also uses it as a variable time constant (τ) that depends on the input. sys =τ / (1+τf(x(t),I(t),t,θ)) is used to learn the system (the time constant is a parameter characterizing the speed and coupling sensitivity of the ordinary differential equation). This property allows a single element of the hidden state to identify the input features arriving at each time point in a dedicated dynamic system.

[0059] Specifically, step S2 includes:

[0060] S21. According to the formula: Iteratively calculate the hidden state x of the next neuron t+Δt ;

[0061] S22. Determine the final hidden state x of the last god general element after iterative calculation;

[0062] S23. According to the formula: Calculate the predicted value Among them W out For the output weights, b out For output bias;

[0063] S24. According to the formula: Calculate the loss for each input in the training set, where y j (t) represents the actual value of the sampled signal sequence, L total Let T be the loss function and T be the length of the training set.

[0064] S3. Based on loss and gradient descent, update the parameters of the liquid time constant neural network to train the neural network model;

[0065] After step S2, the loss for each input in the training set can be obtained, and then the parameters of the liquid time constant neural network can be updated.

[0066] Specifically, step S3 includes:

[0067] S31. According to the formula: Calculate gradient

[0068] S32. According to the formula: θ'=θ-αL total (θ), update parameter θ, where α is the learning rate.

[0069] In practical implementation, in order to obtain a better neural network model, the training set can be divided into multiple batches. The updated liquid time constant neural network parameters of the previous batch are passed to the next batch for iterative calculation until the liquid time constant neural network parameters of all batches are updated, so as to obtain a trained neural network model.

[0070] S4. Obtain the signal equalization result based on the trained neural network model.

[0071] It is understandable that by processing the collected signals that were not used in training and then inputting them into a neural network, an equalization result can be obtained.

[0072] In summary, the nonlinear equalization method based on a liquid time constant neural network in this application determines a training set based on the sampled signal sequence; calculates the loss for each input in the training set based on the liquid time constant neural network, wherein the liquid time constant neural network has a changing liquid time constant, enabling individual elements of the hidden state to identify the input features arriving at each time point; updates the parameters of the liquid time constant neural network based on the loss and gradient descent method to train the neural network model; and obtains the signal equalization result based on the trained neural network model.

[0073] Instead of declaring the dynamics of the learned system through implicit nonlinearity, this application constructs a network of linear first-order dynamic systems tuned by nonlinear interconnect gates. The resulting model represents a dynamic system with varying (i.e., liquid) time constants coupled to its implicit states, and its output is computed by a numerical differential equation solver. These neural networks exhibit stable and bounded behavior, produce excellent expressiveness in the family of neural differential equations, and improve the performance of time series prediction tasks. This results in better equalization and a lower bit error rate in the obtained equalized signal.

[0074] Secondly, embodiments of this application also provide a nonlinear equalization device based on a liquid time constant neural network.

[0075] In one embodiment, reference is made to Figure 2 , Figure 2 This is a functional module diagram of an embodiment of the nonlinear equalization device based on a liquid time constant neural network according to this application. Figure 2 As shown, the nonlinear equalization device based on a liquid time constant neural network includes:

[0076] The sampling module determines the training set based on the sampled signal sequence;

[0077] The calculation module calculates the loss for each input in the training set based on a liquid time constant neural network, which has a varying liquid time constant, enabling individual elements of the hidden state to identify the input features arriving at each time point.

[0078] The training module, based on loss and gradient descent, updates the parameters of the liquid time constant neural network to train the neural network model;

[0079] The equalization module obtains the signal equalization result based on the trained neural network model.

[0080] Further, in one embodiment, the calculation module calculates the loss for each input in the training set based on a liquid time constant neural network, wherein the liquid time constant neural network has a varying liquid time constant, enabling individual elements of the hidden state to identify input features arriving at each time point, including:

[0081] According to the formula: Iteratively calculate the hidden state x of the next neuron t+Δt , where x(t) is the hidden state of the current neuron, f(.) is the activation function of the neural network, I(t) is the time-dependent neural network input sequence in the training set, θ is the parameter set, and A is the bias vector;

[0082] Determine the final hidden state x of the last god general element through iterative computation;

[0083] According to the formula: Calculate the predicted value Among them W out For the output weights, b out For output bias;

[0084] According to the formula: Calculate the loss for each input in the training set, where y j (t) represents the actual value of the sampled signal sequence, L total Let T be the loss function and T be the length of the training set.

[0085] Furthermore, in one embodiment, the calculation module updates the parameters of the liquid time constant neural network based on loss and gradient descent methods to train the neural network model, including:

[0086] According to the formula: Calculate gradient

[0087] According to the formula: θ'=θ-αL total (θ), update parameter θ, where α is the learning rate.

[0088] Furthermore, in one embodiment, the training module is used for:

[0089] The training set is divided into multiple batches. The updated liquid time constant neural network parameters from the previous batch are passed to the next batch for iterative calculation until the liquid time constant neural network parameters of all batches are updated, so as to obtain the trained neural network model.

[0090] Furthermore, in one embodiment, the calculation module calculates the loss for each input using a mean squared error loss function or a cross-entropy loss function.

[0091] The functions of each module in the nonlinear equalization device based on the liquid time constant neural network mentioned above correspond to the steps in the embodiment of the nonlinear equalization method based on the liquid time constant neural network mentioned above, and their functions and implementation processes will not be described in detail here.

[0092] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A nonlinear equalization method based on a liquid time constant neural network, characterized in that, The nonlinear equalization method based on a liquid time constant neural network includes: The training set is determined based on the sampled signal sequence; The loss for each input in the training set is calculated based on a liquid time constant neural network, which has a varying liquid time constant, enabling individual elements of the hidden state to identify input features arriving at each time point. Based on loss and gradient descent methods, the parameters of the liquid time constant neural network are updated to train the neural network model; The signal equalization result is obtained based on the trained neural network model; The loss for each input in the training set is calculated based on a liquid time constant neural network, wherein the liquid time constant neural network has a varying liquid time constant, enabling individual elements in the hidden state to identify input features arriving at each time point, including: According to the formula: Iteratively calculate the hidden state of the next neuron. ,in, This represents the current hidden state of the neuron. For neural network activation functions, To train a neural network with time-dependent input sequences, For parameter set, It is a paranoia vector; Determine the final hidden state of the last god general in the iterative computation. ; According to the formula: Calculate the predicted value ,in To output weights, For output bias; According to the formula: The loss for each input in the training set, where The actual values ​​of the sampled signal sequence, For loss function, This is the length of the training set.

2. The nonlinear equalization method based on a liquid time constant neural network as described in claim 1, characterized in that, The method of updating the liquid time constant neural network parameters based on loss and gradient descent to train the neural network model includes: According to the formula: Calculate the gradient ; According to the formula: Update parameters ,in This is the learning rate.

3. The nonlinear equalization method based on a liquid time constant neural network as described in claim 2, characterized in that: The training set is divided into multiple batches. The updated liquid time constant neural network parameters from the previous batch are passed to the next batch for iterative calculation until the liquid time constant neural network parameters of all batches are updated, so as to obtain the trained neural network model.

4. The nonlinear equalization method based on a liquid time constant neural network as described in claim 1, characterized in that: The This is the mean squared error loss function or the cross-entropy loss function.

5. A nonlinear equalization device based on a liquid time constant neural network, characterized in that, The nonlinear equalization device based on a liquid time constant neural network includes: The sampling module determines the training set based on the sampled signal sequence; The calculation module calculates the loss for each input in the training set based on a liquid time constant neural network, which has a varying liquid time constant, enabling individual elements of the hidden state to identify the input features arriving at each time point. The training module, based on loss and gradient descent, updates the parameters of the liquid time constant neural network to train the neural network model; The equalization module obtains the signal equalization result based on the trained neural network model; The calculation module calculates the loss for each input in the training set based on a liquid time constant neural network. This liquid time constant neural network has a varying liquid time constant, enabling individual elements in the hidden state to identify input features arriving at each time point, including: According to the formula: Iteratively calculate the hidden state of the next neuron. ,in, This represents the current hidden state of the neuron. For neural network activation functions, To train a neural network with time-dependent input sequences, For parameter set, It is a paranoia vector; Determine the final hidden state of the last god general in the iterative computation. ; According to the formula: Calculate the predicted value ,in To output weights, For output bias; According to the formula: The loss for each input in the training set, where The actual values ​​of the sampled signal sequence, For loss function, This is the length of the training set.

6. The nonlinear equalization device based on a liquid time constant neural network as described in claim 5, characterized in that, The calculation module updates the parameters of the liquid time constant neural network based on loss and gradient descent methods to train the neural network model, including: According to the formula: Calculate the gradient ; According to the formula: Update parameters ,in This is the learning rate.

7. The nonlinear equalization device based on a liquid time constant neural network as described in claim 6, characterized in that, The training module is used for: The training set is divided into multiple batches. The updated liquid time constant neural network parameters from the previous batch are passed to the next batch for iterative calculation until the liquid time constant neural network parameters of all batches are updated, so as to obtain the trained neural network model.

8. The nonlinear equalization device based on a liquid time constant neural network as described in claim 5, characterized in that: The calculation module calculates the loss for each input using either the mean squared error loss function or the cross-entropy loss function.

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