Iterative Embedding Normalization for Accurate Cross-Lingual Alignment
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Solution Overview
Problem
Existing preprocessing techniques for cross-embedding alignment, such as mean centering, length normalization, and principle component analysis, result in suboptimal performance by altering distances between embedding vectors, affecting the accuracy of cross-lingual word embeddings.
Innovation Solution
Applying mean centering, spectral normalization, and length normalization iteratively to embedding sets, involving singular value decomposition and substitution of singular values, to maintain consistent distance metrics across embedding sets.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If mean centering is applied to embedding vectors, then the embedding alignment is improved, but the Euclidean distance between pairs of points changes
Solution Approach 1:
The patent applies mean centering as a preprocessing transformation that changes the parameter space of embedding vectors by subtracting the mean vector from all vectors. This parameter change improves alignment accuracy while the patent acknowledges it alters Euclidean distances, which is why subsequent normalization techniques are applied to compensate.
2Measurement precision
If length normalization is applied to embedding vectors, then the cosine distance between pairs of points is improved, but the Euclidean distance between pairs of points changes
Solution Approach 1:
The patent applies length normalization (L2 normalization) that changes the magnitude parameter of embedding vectors to unit length. This improves cosine distance measurements for semantic similarity while necessarily altering Euclidean distances, which is why the patent combines multiple preprocessing techniques and uses configurable weighting.
3Device complexity
If PCA removal is applied to embedding vectors, then the top principal component is reduced, but the transformation is overly blunt and reduces performance
Solution Approach 1:
The patent avoids excessive dimensionality reduction by not applying full PCA removal. Instead, it uses gentler preprocessing techniques (mean centering, length normalization) that partially transform the embedding space without completely removing important variance, thereby maintaining alignment accuracy while still reducing complexity.
4Measurement precision
If multiple preprocessing techniques are applied iteratively, then the cross-embedding alignment performance is improved, but the computational complexity increases
Solution Approach 1:
The patent applies preprocessing techniques iteratively in periodic cycles (mean centering, then length normalization, then Procrustes alignment, repeated multiple times). This periodic application of transformations progressively improves alignment accuracy while the fixed number of iterations controls computational complexity.
Data Source
AI summary
Provided is a method for normalizing embeddings for cross-embedding alignment. The method may include applying mean centering to the at least one embedding set, applying spectral normalization to the at least one embedding set, and/or applying length normalization to the at least one embedding set. Spectral normalization may include decomposing the at least one embedding set, determining an average singular value of the at least one embedding set, determining a respective substitute singular value for each respective singular value of a diagonal matrix, and/or replacing the at least one embedding set with a product of the at least one embedding set, a right singular vector, and an inverse of the substitute diagonal matrix. The mean centering, spectral normalization, and/or length normalization may be iteratively repeated for a configurable number of iterations. A system and computer program product are also disclosed.