What does this research mean for the field?

In the joint proportional limit where both depth and width diverge at a constant ratio, linear neural networks converge to a non-Gaussian distribution characterized as a nontrivial mixture of Gaussian processes that retains correlations between outputs. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To characterize the asymptotic distribution of deep linear neural networks with random parameters when depth and width simultaneously grow to infinity at a fixed ratio.

September 5, 2026Stochastics and DynamicsOpen Access

Proportional infinite-width infinite-depth limit for deep linear neural networks

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Authors

FBFederico BassettiPolitecnico di Milano LLLucia LadelliPolitecnico di Milano PRPietro RotondoUniversity of Parma

Discussion

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Implication

Theoretical analysis reveals a non-Gaussian mixture limit in deep linear neural networks scaled proportionally in depth and width, indicating preserved output correlations and feature dependencies.

Key Points

To characterize the asymptotic distribution of deep linear neural networks with random parameters when depth and width simultaneously grow to infinity at a fixed ratio.
Analyzed linear neural networks with random parameters under a proportional scaling regime where depth and width diverge with a constant ratio.
Evaluated output correlations and process limits relative to conventional fixed-depth infinite-width neural network Gaussian process models.
Demonstrated that proportional scaling of depth and width breaks the standard Gaussian collapse, preserving output correlations and feature dependencies.
Explicitly characterized the limiting distribution of the full linear network process as a nontrivial mixture of Gaussian processes.

Cite This Study

Bassetti et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd3726b95aff0620eaa98 https://doi.org/10.1142/s021949372650022x

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September 5, 2026Stochastics and DynamicsOpen Access

Proportional infinite-width infinite-depth limit for deep linear neural networks

View Full Paper

Ask AI

Bookmark

Authors

FBFederico BassettiPolitecnico di Milano LLLucia LadelliPolitecnico di Milano PRPietro RotondoUniversity of Parma

Discussion

Member takes

Implication

Theoretical analysis reveals a non-Gaussian mixture limit in deep linear neural networks scaled proportionally in depth and width, indicating preserved output correlations and feature dependencies.

Key Points

To characterize the asymptotic distribution of deep linear neural networks with random parameters when depth and width simultaneously grow to infinity at a fixed ratio.
Analyzed linear neural networks with random parameters under a proportional scaling regime where depth and width diverge with a constant ratio.
Evaluated output correlations and process limits relative to conventional fixed-depth infinite-width neural network Gaussian process models.
Demonstrated that proportional scaling of depth and width breaks the standard Gaussian collapse, preserving output correlations and feature dependencies.
Explicitly characterized the limiting distribution of the full linear network process as a nontrivial mixture of Gaussian processes.

Cite This Study

Bassetti et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd3726b95aff0620eaa98 https://doi.org/10.1142/s021949372650022x

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