# Reservoir Subspace Injection for Online ICA under Top-n Whitening

arXiv: https://arxiv.org/abs/2603.02178 · HTML: https://mlsanity.com/paper/2603.02178/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Builds on (most cited first, 9 of 9)

- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA](https://mlsanity.com/paper/1605.06336/) (2016)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning](https://mlsanity.com/paper/2303.16535/) (2023)
- [Reservoir Computing meets Recurrent Kernels and Structured Transforms](https://mlsanity.com/paper/2006.07310/) (2020)
- [Independent Vector Analysis: Identification Conditions and Performance Bounds](https://mlsanity.com/paper/1303.7474/) (2013)
- [Signal-noise separation using unsupervised reservoir computing](https://mlsanity.com/paper/2404.04870/) (2024)
- [Echo State Networks as State-Space Models: A Systems Perspective](https://mlsanity.com/paper/2509.04422/) (2025)

## Abstract (arXiv)

Reservoir expansion can improve online independent component analysis (ICA) under nonlinear mixing, yet top-n whitening may discard injected features. We formalize this bottleneck as reservoir subspace injection (RSI): injected features help only if they enter the retained eigenspace without displacing passthrough directions. RSI diagnostics (IER, SSO, ρx) identify a failure mode in our top-n setting: stronger injection increases IER but crowds out passthrough energy (ρx: 1.00!rightarrow!0.77), degrading SI-SDR by up to 2.2,dB. A guarded RSI controller preserves passthrough retention and recovers mean performance to within 0.1,dB of baseline 1/N scaling. With passthrough preserved, RE-OICA improves over vanilla online ICA by +1.7,dB under nonlinear mixing and achieves positive SI-SDRsc on the tested super-Gaussian benchmark (+0.6,dB).