Lipschitz verification of neural networks through training

Lipschitz verification of neural networks through training | Signal Canvas | ScienceToStartup

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Canonical route: /signal-canvas/lipschitz-verification-of-neural-networks-through-training

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Proof freshness: stale
Proof status: unverified
Display score: 3/10
Last proof check: 2026-03-31
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 68
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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Canonical ID lipschitz-verification-of-neural-networks-through-training | Route /signal-canvas/lipschitz-verification-of-neural-networks-through-training

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source_context

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Evidence Receipt

Route status: building

Claims: 8

References: 68

Proof: Verification pending

Freshness state: computing

Source paper: Lipschitz verification of neural networks through training

PDF: https://arxiv.org/pdf/2603.28113v1

Source count: 3

Coverage: 50%

Last proof check: 2026-03-31T20:24:35.845Z

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Not build-ready: Lipschitz verification of neural networks through training

/buildability/lipschitz-verification-of-neural-networks-through-training

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Subject: Lipschitz verification of neural networks through training

Verdict

Ignore

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

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Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
We show that directly penalizing the trivial bound during training forces it to become tight, thereby effectively regularizing the true Lipschitz constant.
Implicationpartial
Explicitly stated in the abstract as the core proposed method.
Verificationpartial
partial
Evidencepartial
we train robust networks on MNIST with Lipschitz bounds that are small (orders of magnitude lower than comparable works)
Implicationpartial
Directly stated in the abstract with a specific comparison to other works.
Verificationpartial
partial
Evidencepartial
and tight (within 10% of the ground truth).
Implicationpartial
Explicitly stated in the abstract with a precise numeric figure.
Verificationpartial
partial
Evidencepartial
not only the trivial bound, but also any Lipschitz bound which ignores the biases cannot help but impute to the biases their worst-case values, and is therefore liable to up to Ω(d) conservatism per layer on ReLU and tanh networks, and infinite conservatism on sinusoidal networks.
Implicationpartial
Strongly supported by a theoretical remark in the analysis, citing prior work.
Verificationpartial
partial
Evidencepartial
We mitigate this issue by using a specific polyactivation... This immediately rules out the adversarial biasing in Theorem 3.5... Now the LASL unit becomes x↦Acos(Wx)+Bsin(Wx)
Implicationpartial
Directly stated as a key architectural mitigation introduced by the paper.
Verificationpartial
partial
Evidencepartial
A network with ill-conditioned weight matrices can be less Lipschitz than it appears. This occurs when a neural network contains ill-conditioned subnetworks that cancel out.
Implicationpartial
Directly stated as a key structural obstruction to a tight trivial bound.
Verificationpartial
partial
Evidencepartial
In this toy example, minimizing the trivial Lipschitz bound over unconstrained degrees of freedom on a level set of the loss function recovers the ground truth Lipschitz constant.
Implicationpartial
Stated as a theoretical result (equivalence) in a toy example, forming the basis for the proposed penalty.
Verificationpartial
partial
Evidencepartial
The adversarial robustness against PGD attacks is comparable (±1% at each attack radius) to that of Xu & Sivaranjani (2025)’s MNIST network trained using a sophisticated local Jacobian penalty heuristic.
Implicationpartial
Directly stated with a precise numeric comparison to a specific prior method.
Verificationpartial
partial

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