Training analysis method for generative adversarial network
By establishing an isolated point model to analyze the local stability and minimum values of the generated adversarial network, the difficulty of joint training of the generator and discriminator is solved, and the training effect of the generated adversarial network is optimized.
Patent Information
- Application Number
- PCT/CN2023/132901
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Priority Date
- 2023-10-31
- Filing Date
- 2023-11-21
- Publication Date
- 2025-07-10
AI Technical Summary
In the prior art, there are difficulties in joint training of discriminators and generators that generate adversarial networks, and there is a lack of effective theoretical basis for analysis and optimization.
By establishing an isolated point model, defining the real sample distribution, generating sample distribution, kernel discriminator and generator update methods, analyzing the local stability and minimum values in the training process of the generation adversarial network, and using the isolated point model to decouple and jointly update the training dynamics of the generator and discriminator.
The stability analysis of the generative adversarial network training process is realized, and local minimum values and approximate mode crashes are avoided, and the joint training effect of the generator and discriminator is optimized.
Smart Images
Figure CN2023132901_10072025_PF_FP_ABST
Abstract
Description
A training analysis method for generative adversarial networks
[0001] CROSS-REFERENCE TO RELATED APPLICATIONS
[0002] This application claims priority to Chinese patent application number 2023114392661, filed with the Chinese Patent Office on October 31, 2023, entitled "A Training and Analysis Method for Generative Adversarial Networks," the entire contents of which are incorporated by reference into this application. Technical Field
[0003] The present invention is applicable to the field of machine vision technology, and in particular relates to a training and analysis method for generating adversarial networks. Background Art
[0004] Generative Adversarial Networks (GANs) are the most widely used method for learning generative models for complex and structured data in an unsupervised manner. In fact, GANs have achieved incredible empirical success in numerous fields, including image generation, speech generation, and text generation. Models trained in this way have also become crucial in downstream applications. In the GAN approach, the generator is trained to output samples from the target dataset, known as real samples, while the discriminator's discriminative model is trained to distinguish between real and generated samples. The generator is trained in parallel to deceive the discriminator. However, correctly aligning the joint training of the discriminator and generator is one of the key challenges of GANs.
[0005] To address this problem, researchers have used a combination of sophisticated hyperparameter optimization and heuristics to solve this problem, but there is a lack of theoretical basis for analyzing and optimizing GAN training.
[0006] Therefore, a new training and analysis method for generative adversarial networks is urgently needed to solve the above problems.
[0007] Summary of the Invention
[0008] The present invention provides a training analysis method for a generative adversarial network, aiming to solve the difficult problem of adjusting the joint training of the discriminator and generator in a generative adversarial network.
[0009] The training analysis method comprises the following steps:
[0010] S1. Establish an outlier model and define the real sample distribution, generated sample distribution, kernel discriminator, kernel discriminator update method, generator update method, and outliers;
[0011] S2. Analyze the behavior near the real point in the real sample distribution using the isolated point model to determine whether the local area during the generative adversarial network training process is stable;
[0012] S3, analyzing erroneous local minima and approximate mode collapse during the training process of the generative adversarial network using the isolated point model;
[0013] S4. Analyzing what happens to the generated points isolated from the real points using the isolated point model;
[0014] S5. Analyze the effect of kernel width in the training of the generative adversarial network through the isolated point model.
[0015] Preferably, the calculation formula of the real sample distribution is as follows:
[0016] Among them, P r Indicates that N r represents the number of said real points, represents the true point, p i The probability of the true point.
[0017] Preferably, the calculation formula for generating the sample distribution is as follows:
[0018] Among them, P g represents the generating point, N g represents the number of the generation points, represents the generating point, p i The probability of generating the point.
[0019] Preferably, the updating method of the core discriminator satisfies the following calculation formula:
[0020] Among them, a(x) represents the basis function vector, θ represents the parameter vector, η d >0 indicates the step size of the discriminator and the regularization parameter λ>0.
[0021] Preferably, the updating method of the generator satisfies the following calculation formula:
[0022] in, An update expression representing the parameters of the generator.
[0023] Preferably, in step S2, whether the local stability of the generative adversarial network training process is determined by determining whether the corresponding dynamic equilibrium point in the isolated area of the real point is locally stable.
[0024] Preferably, the local stability of the dynamic equilibrium point is determined based on the mass difference between the true probability of the isolated area of the true point and the total probability of the generated points in the isolated area. The mass difference is calculated as follows:
[0025] Among them, Δ i represents the mass difference of the dynamic equilibrium point corresponding to the i-th real point, p i represents the true probability;
[0026] When Δ i >0, the dynamic equilibrium point is locally stable;
[0027] When Δ i <0 and |N i When |≥1, the dynamic equilibrium point is locally unstable;
[0028] When |N i |=1 and When , the dynamic equilibrium point is locally stable;
[0029] When |N i |=1 and When , the dynamic equilibrium point is locally unstable; where, represents the probability of the generated point, μ represents the proportional coefficient, k1, k2, k3, k4 represent the weight coefficients, N i Represents the number of real points.
[0030] The beneficial effects of the present invention are that, by establishing an isolated point model and defining the real sample distribution, the generated sample distribution, the kernel discriminator, the update method of the kernel discriminator, the update method of the generator and the isolated points; the behavior near the real point in the real sample distribution is analyzed by the isolated point model to determine whether the local stability in the training process of the generative adversarial network is determined; the erroneous local minima and approximate mode collapse in the training process of the generative adversarial network are analyzed by the isolated point model; the situation that will occur when the generated point is isolated from the real point is analyzed by the isolated point model; the role of the kernel width in the training of the generative adversarial network is analyzed by the isolated point model. The isolated point model can be used to decouple the training dynamics of the kernel in the generative adversarial network that jointly updates the generator and the discriminator, analyze its stable local balance and bad local minima, and analyze the important role of the kernel width in the joint training of the generative adversarial network. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] The present invention will be described in detail below with reference to the accompanying drawings. The above and other aspects of the present invention will become clearer and easier to understand through the detailed description made with reference to the following drawings. In the accompanying drawings:
[0032] FIG1 is a flowchart of a training and analysis method for a generative adversarial network provided by an embodiment of the present invention;
[0033] FIG2 is a schematic diagram of an outlier model of a training and analysis method for a generative adversarial network provided in an embodiment of the present invention. DETAILED DESCRIPTION
[0034] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0035] 1 and 2 , the present invention provides a training and analysis method for a generative adversarial network, the training and analysis method comprising the following steps:
[0036] S1. Establish an isolated point model and define the real sample distribution, the generated sample distribution, the kernel discriminator, the update method of the kernel discriminator, the update method of the generator, and the isolated points;
[0037] In this embodiment of the present invention, it is assumed that the real sample distribution P r and generate sample distribution P g In the discrete set R d On, we have:
[0038] Where N r and N g is the number of real points and generated points, and are the real point and the generated point respectively, p i and is their probability, assuming fixed.
[0039] The linear parameterization of the kernel discriminator is as follows: f(x,θ)=a(x) T θ(2)
[0040] Where a(x) is the basis function vector and θ is the parameter vector.
[0041] The update formula of the discriminator is as follows:
[0042] Where η d >0 is the step size of the discriminator and the regularization parameter λ>0.
[0043] Generator update: Assume that the generator distribution P in formula (1) g Directly parameterized by point locations, To update with the minimum loss, we have:
[0044] in, An update expression representing the parameters of the generator.
[0045] Definition of isolated points: Assume that the distance between real samples is far enough, so each sample x i There is a non-empty isolated neighborhood V around i . K(x,x′)=0for all x∈V i and x′∈V j for all i≠j (5)
[0046] S2. Analyze the behavior near the real point in the real sample distribution using the isolated point model to determine whether the local area during the generative adversarial network training process is stable;
[0047] In an embodiment of the present invention, whether the local stability of the generative adversarial network training process is determined by whether the corresponding dynamic equilibrium point in the isolated area of the real point is locally stable.
[0048] Around a real point x i Isolated region V i :
[0049] From the above formula, we can see that V i All generated points in are close to the real points.
[0050] The mass difference of the probability is defined as:
[0051] Δ i Represents the true probability p in the region i The mass difference from the total probability of generating points in this area.
[0052] The fixed isolated area is expressed as follows:
[0053] There is only one Make It is region V i The dynamic equilibrium point of GAN in . If the parameter k i ,λ, is fixed, and for sufficiently small step sizes it has the following representation:
[0054] (a) When Δ i >0, the dynamic equilibrium point is locally stable;
[0055] (b) When Δ i<0 and |N i When |≥1, the dynamic equilibrium point is locally unstable;
[0056] (c) When |N i |=1 and When , the dynamic equilibrium point is locally stable;
[0057] (d) When |N i |=1 and When , the dynamic equilibrium point is locally unstable; where, represents the probability of the generated point, μ represents the proportional coefficient, k1, k2, k3, k4 represent the weight coefficients, N i Represents the number of real points.
[0058] In (c) and (d) is the point mass of a single generated point in an isolated region. In case (a), when Δ i >0, the generated point will converge locally to the real point, that is, the real point mass exceeds the total generated mass, and the generated point will converge to the real point. i =0,|N i When |=1 (there is a single generated point), the generated point and the true point have the same quality, and the generated point will converge to the true point. These convergence cases are shown in Figure 2, as shown by v1 (Δ1=0) and V3 (Δ3>0). In contrast, case (b) shows that Δ i <0 (i.e. the probability of generation exceeds the true probability), the generated mass cannot stay stably at the true point. As shown in V2 in Figure 2, the generated point and the true point repel each other. Among them, the outer circle represents the isolated area, and the disk at the center of the circle represents the true point. That is, there are 8 generated points with a mass of
[0059] S3, analyzing erroneous local minima and approximate mode collapse during the training process of the generative adversarial network using the isolated point model;
[0060] In the embodiment of the present invention, in FIG2, when Δ i When < 0, the generated points may stay close to the true points, a phenomenon known as approximate mode collapse.
[0061] Theorem 2: Assume |N i |>1, there are multiple generating points in the region. There is a constant c>0, which is related to the kernel width σ and N max It is irrelevant, it is just a function of d. If |N i |≤N max , the system has a local stable equilibrium
[0062] The theorem states that under certain conditions, even if the generated mass exceeds the true mass, the generated points may fall into a local minimum, as shown by V2 in Figure 2. For very small kernel width σ, generated points with arbitrarily high mass accumulate at a single true point. This phenomenon is called approximate mode collapse.
[0063] S4. Analyzing what happens to the generated points isolated from the real points using the isolated point model;
[0064] In the embodiment of the present invention, it is assumed that a single generating point Its trajectory satisfy:
[0065] In this case, Away from other generated points and true points, the kernel can be considered as zero.
[0066] Theorem 3: It shows that an isolated generating point can enter a trajectory. The generating point is Unit vector μ∈R d is small enough, and the velocity v0>0, then:
[0067] This generated isolated point will continue to simply move linearly in the direction pushed by its own kernel. As shown in Figure 2, the generated point in the upper right corner moves along a straight line to the right.
[0068] S5. Analyze the effect of kernel width in the training of the generative adversarial network through the isolated point model.
[0069] In the embodiment of the present invention, a key parameter of any distance-based kernel is its kernel width. If the kernel width σ is very large, when When it is close to x0, the loss will have a small gradient, that is, the generated point is close to the real point. If the kernel width σ is very small, when When far away from x0, the loss will also have a small gradient, that is, the generated point is far away from the true point. The following insights can be drawn from the isolated point model: the two failure mechanisms of approximate mode collapse in step S3 and divergence problem in step S4 can be prevented by a wider kernel width.
[0070] The beneficial effects of the present invention are that, by establishing an isolated point model and defining the real sample distribution, the generated sample distribution, the kernel discriminator, the update method of the kernel discriminator, the update method of the generator and the isolated points; the behavior near the real point in the real sample distribution is analyzed by the isolated point model to determine whether the local stability in the training process of the generative adversarial network is determined; the erroneous local minima and approximate mode collapse in the training process of the generative adversarial network are analyzed by the isolated point model; the situation that will occur when the generated point is isolated from the real point is analyzed by the isolated point model; the role of the kernel width in the training of the generative adversarial network is analyzed by the isolated point model. The isolated point model can be used to decouple the training dynamics of the kernel in the generative adversarial network that jointly updates the generator and the discriminator, analyze its stable local balance and bad local minima, and analyze the important role of the kernel width in the joint training of the generative adversarial network.
[0071] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.
[0072] The embodiments of the present invention are described above in conjunction with the accompanying drawings. What is disclosed is only a preferred embodiment of the present invention. However, the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms and equivalent changes without departing from the scope of protection of the purpose of the present invention and the claims, which are all within the protection of the present invention.
Claims
1. A training analysis method for a generative adversarial network, characterized in that, The training analysis method includes the following steps: S1. Establish an outlier model, and define the true sample distribution, the generated sample distribution, the kernel discriminator, the update method of the kernel discriminator, the update method of the generator, and the outlier; S2. Analyze the behavior near the true points in the true sample distribution through the outlier model to determine whether the local part in the training process of the generative adversarial network is stable; S3. Analyze the false local minima and approximate mode collapse in the training process of the generative adversarial network through the outlier model; S4. Analyze what will happen to the generated points isolated from the true points through the outlier model; S5. Analyze the role of the kernel width in the training of the generative adversarial network through the outlier model.
2. The training analysis method of the generative adversarial network according to claim 1, characterized in that The calculation formula for the true sample distribution is as follows: Among them, P r represents the distribution of true points, N r represents the number of the true points, Denote the true point, p i The probability of the true point.
3. The training analysis method of the generative adversarial network according to claim 2, characterized in that The calculation formula for generating the sample distribution is as follows: Among them, P g represents the distribution of the generated points, N g represents the number of the generated points, Denote the generation point, p i The probability of the generation point.
4. The training analysis method of the generative adversarial network according to claim 3, wherein The update method of the nuclear discriminator satisfies the following calculation formula: where \(a(x)\) represents the basis function vector, \(\theta\) represents the parameter vector, \(\eta\) d > 0 represents the step size of the discriminator, and the regularization parameter \(\lambda>0\).
5. The training analysis method of the generative adversarial network according to claim 4, characterized in that, The update method of the generator satisfies the following calculation formula: Among them, The update expression representing the parameters of the generator.
6. The training analysis method of the generative adversarial network according to claim 5, characterized in that, In step S2, it is determined whether the local part in the training process of the generative adversarial network is stable by whether the corresponding dynamic equilibrium point in the outlier region of the true points is locally stable.
7. The training analysis method of the generative adversarial network according to claim 6, characterized in that, The local stability of the dynamic equilibrium point is determined according to the magnitude of the mass difference between the true probability in the isolated region of the true point and the total probability of the generated points in the isolated region. The calculation formula for the mass difference is as follows: Among them, Δ i represents the mass difference of the dynamic equilibrium point corresponding to the i-th said true point, p i represents the true probability; When Δ i > 0, the local dynamic equilibrium point is stable; When Δ i < 0 and |N i | ≥ 1, the local dynamic equilibrium point is unstable; When |N i | = 1 and When, the dynamic equilibrium point is locally stable; When |N i | = 1 and When, the local dynamic equilibrium point is unstable; where, represents the probability of the generation point, μ represents the proportionality coefficient, k1, k2, k3, k4 represent the weight coefficients, and N i represents the number of the true points.