# A Letter on Convergence of In-Parameter-Linear Nonlinear Neural Architectures with Gradient Learnings

arXiv: https://arxiv.org/abs/2111.12877 · HTML: https://mlsanity.com/paper/2111.12877/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 25 Nov 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [An Approach to Stable Gradient Descent Adaptation of Higher-Order Neural Units](https://mlsanity.com/paper/1606.07149/) (2016)

## Built on by (most cited first, 1 of 1)

- [Learning Entropy Signature for Image Representation and Classification](https://mlsanity.com/paper/2606.22634/) (2026)

## Abstract (arXiv)

This letter summarizes and proves the concept of bounded-input bounded-state (BIBS) stability for weight convergence of a broad family of in-parameter-linear nonlinear neural architectures as it generally applies to a broad family of incremental gradient learning algorithms. A practical BIBS convergence condition results from the derived proofs for every individual learning point or batches for real-time applications.