Expectation Error Bounds for Transfer Learning in Linear Regression and Linear Neural Networks

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• For linear regression, the paper derives exact closed-form expressions for the expected generalization error with bias-variance decomposition.result 95%
• The paper provides necessary and sufficient conditions for auxiliary tasks to improve generalization on the main task in linear regression.result 90%
• For linear regression, globally optimal task weights can be derived as outputs of solvable optimization programs, with consistency guarantees for empirical estimates.method 90%
• For under-parameterized linear neural networks, the paper establishes the first non-vacuous sufficient condition for beneficial auxiliary learning.result 95%
• The paper proves a new column-wise low-rank perturbation bound for random matrices that improves upon existing bounds by preserving fine-grained column structures.technical 90%
• In linear regression, auxiliary learning can be understood as a bias-variance trade-off, where the error decomposes into variance, bias, and noise terms.result 85%
• For linear neural networks, the generalization error bound reveals that beneficial auxiliary learning depends on reducing low-rank truncation loss and increasing a tunable signal-to-noise ratio.result 80%
• Previous work on linear neural networks for transfer learning did not provide conditions indicating whether incorporating auxiliary data is beneficial.limitation 75%

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