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

Expectation Error Bounds for Transfer Learning in Linear Regression and Linear Neural Networks | Signal Canvas | ScienceToStartup

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Proof freshness: stale
Proof status: unverified
Display score: 2/10
Last proof check: 2026-03-31
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 3
Source count: 3
Coverage: 50%

This page is showing the last landed evidence receipt and score bundle because the latest proof data is outside the freshness window.

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Evidence Receipt

Route status: building

Claims: 8

References: 3

Proof: Verification pending

Freshness state: computing

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

PDF: https://arxiv.org/pdf/2603.28739v1

Source count: 3

Coverage: 50%

Last proof check: 2026-03-31T20:24:29.868Z

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Not build-ready: Expectation Error Bounds for Transfer Learning in Linear Regression and Linear Neural Networks

/buildability/expectation-error-bounds-for-transfer-learning-in-linear-regression-and-linear-neural-networks

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

Verdict

Ignore

Verdict is Ignore because current viability and proof state do not clear the buildability gate.

Preparing verified analysis

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Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
For linear regression, we derive exact closed-form expressions for the expected generalization error with bias-variance decomposition
Implicationpartial
Explicitly stated in the abstract and detailed in the analysis excerpt with a specific formula provided.
Verificationpartial
partial
Evidencepartial
yielding necessary and sufficient conditions for auxiliary tasks to improve generalization on the main task.
Implicationpartial
Directly stated in the abstract as a key contribution and elaborated in the analysis.
Verificationpartial
partial
Evidencepartial
We also derive globally optimal task weights as outputs of solvable optimization programs, with consistency guarantees for empirical estimates.
Implicationpartial
Explicitly claimed in the abstract and highlighted as a contribution.
Verificationpartial
partial
Evidencepartial
yielding the first non-vacuous sufficient condition for beneficial auxiliary learning in this setting
Implicationpartial
Explicitly stated in the abstract and analysis as a key novel contribution.
Verificationpartial
partial
Evidencepartial
We achieve this by proving a new column-wise low-rank perturbation bound for random matrices, which improves upon existing bounds by preserving fine-grained column structures.
Implicationpartial
Explicitly stated as a technical contribution in the abstract and analysis, with a comparison table provided.
Verificationpartial
partial
Evidencepartial
showing that auxiliary learning can be understood as a bias-variance trade-off.
Implicationpartial
Directly stated in the analysis with a specific decomposition formula provided.
Verificationpartial
partial
Evidencepartial
Our bound reveals two driving factors: low-rank truncation loss as σ_{q+1}(W^*Λ) and a tunable signal-to-noise ratio r.
Implicationpartial
Strongly supported by the analysis excerpt discussing the bound's driving factors and their role in achieving improvement.
Verificationpartial
partial
Evidencepartial
which, however, does not indicate whether incorporating auxiliary data is beneficial.
Implicationpartial
Implied from the analysis comparing prior work, which derived bounds or asymptotic limits but not explicit beneficial conditions.
Verificationpartial
partial

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

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