Variational Autoencoder Training Using Sigma Points for Low-Variance Sampling
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Solution Overview
Problem
Training variational autoencoders (VAEs) for anomaly detection and sampling in high-dimensional spaces often results in high-variance gradient computations, leading to inefficient reconstruction and sampling capabilities.
Innovation Solution
The method employs sigma points, specifically mean-centered symmetric points, to determine a latent distribution in VAEs, reducing gradient variance and improving reconstruction abilities by using these points for training, rather than relying on the reparameterization trick.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If the reparameterization trick is used to simplify approximate posterior sampling in VAEs, then the gradient computation becomes more straightforward, but the sampling points may be very far from the mean in high-dimensional spaces, leading to high-variance policy gradient
Solution Approach 1:
The patent changes the sampling parameters by using sigma points with specific weighting schemes instead of standard random sampling. The sigma points are positioned at specific distances from the mean (e.g., sqrt(n) times the standard deviation) and assigned appropriate weights to reduce gradient variance while maintaining computational tractability.
Solution Approach 2:
The patent introduces sigma points as an intermediary between the mean and random samples. These sigma points serve as structured intermediate representations that capture the distribution characteristics more effectively than simple random samples, thereby reducing gradient variance without sacrificing computational simplicity.
2Device complexity
If single or few random samples are used in VAE setting, then the computation is simple, but the samples can be very far from the mean, especially in high dimensional spaces, leading to poor reconstruction ability
Solution Approach 1:
The patent modifies the sampling parameters by using multiple sigma points positioned at specific distances from the mean with appropriate weighting. This changes the distribution of sampling points to be more concentrated around the mean while still capturing the essential variability, thereby improving reconstruction precision without significantly increasing computational complexity.
Solution Approach 2:
The patent uses a moderate number of sigma points (more than single sampling but fewer than exhaustive sampling) to achieve sufficient reconstruction quality. This partial action approach provides a good trade-off between computational complexity and reconstruction precision, avoiding both oversampling and undersampling extremes.
3Manufacturing precision
If sigma points are used instead of reparameterization trick, then the reconstruction ability of VAE is improved and latent distribution is better modeled, but the gradient computation requires high-variance policy gradient
Solution Approach 1:
The patent resolves this contradiction by carefully selecting the parameters of sigma points, specifically their distance from the mean and their weighting coefficients. By optimizing these parameters, the patent achieves both improved reconstruction precision through better latent distribution modeling and reduced gradient variance through appropriate weighting schemes.
Solution Approach 2:
The patent incorporates feedback mechanisms in the training process where the gradient variance is monitored and the sigma point parameters are adjusted accordingly. This feedback loop allows the system to adapt the sigma point configuration to minimize gradient variance while maintaining reconstruction quality.
Data Source
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AI summary
Computer-implemented method for training a machine learning system (60), wherein the machine learning system (60) is configured for anomaly detection and/or sampling a trajectory for a traffic participant and/or sampling of sensor signals and/or for determining a value characterizing a likelihood of an input signal with respect to a training dataset, wherein training comprises: • Determining, by an encoder (61) of the machine learning system (60) and based on a training input signal (xi), a first intermediate representation (r1) characterizing a mean of a latent distribution of a latent space (l) and a second intermediate representation (r2) characterizing a variance and/or covariance of the latent distribution; • Determining, based on the first intermediate representation (r1) and the second intermediate representation (r2), a plurality of sigma points (σ) with respect to the latent distribution; • Determining an output signal (yi), wherein the output signal (yi) is determined by providing a randomly sampled sigma point (σ) of the plurality of sigma points (σ) to a decoder (62) of the machine learning system (60); • Adapting the machine learning system (60) based on a loss value, wherein the loss value characterizes a difference between the training input signal (xi) and the output signal (yi).