# Flexible Online Representation Learning Based on Similarity Matching

arXiv: https://arxiv.org/abs/2606.01546 · HTML: https://mlsanity.com/paper/2606.01546/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 38 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Training Neural Networks with Local Error Signals](https://mlsanity.com/paper/1901.06656/) (2019)
- [The non-convex Burer-Monteiro approach works on smooth semidefinite programs](https://mlsanity.com/paper/1606.04970/) (2016)
- [Statistical-Computational Tradeoffs in Planted Problems and Submatrix Localization with a Growing Number of Clusters and Submatrices](https://mlsanity.com/paper/1402.1267/) (2014)
- [On semidefinite relaxations for the block model](https://mlsanity.com/paper/1406.5647/) (2014)
- [Neuroscience-inspired online unsupervised learning algorithms](https://mlsanity.com/paper/1908.01867/) (2019)
- [Robust and computationally feasible community detection in the presence of arbitrary outlier nodes](https://mlsanity.com/paper/1404.6000/) (2014)
- [Relax, no need to round: integrality of clustering formulations](https://mlsanity.com/paper/1408.4045/) (2014)
- [A biologically plausible neural network for multi-channel Canonical Correlation Analysis](https://mlsanity.com/paper/2010.00525/) (2020)
- [A Normative and Biologically Plausible Algorithm for Independent Component Analysis](https://mlsanity.com/paper/2111.08858/) (2021)
- [A Survey on Theoretical Advances of Community Detection in Networks](https://mlsanity.com/paper/1809.07691/) (2018)
- [A Hebbian/Anti-Hebbian Network for Online Sparse Dictionary Learning Derived from Symmetric Matrix Factorization](https://mlsanity.com/paper/1503.00690/) (2015)
- [A correlation game for unsupervised learning yields computational interpretations of Hebbian excitation, anti-Hebbian inhibition, and synapse elimination](https://mlsanity.com/paper/1704.00646/) (2017)

## Abstract (arXiv)

Sparse high-dimensional representations are conducive to uncovering nontrivial structures in unsupervised exploration of data. Such a representation can deal with the dense connectivity in graphs relevant to community detection problems. However, sparse high-dimensional representations are capable of doing more, including manifold tiling and feature learning. Conventional algorithms optimize in the space of computationally intractable completely positive matrices or relax the problem to the space of doubly nonnegative matrices that scale with sample size in a way rendering them impractical for large data sets. Some of these methods also impose a row sum constraint, such as double stochasticity. Row sum constraints have the added advantage of being shift-invariant, in the context of manifold tiling. Constraints on the row sum of output similarity matrices require nontrivial online learning rules. Addressing these needs, we propose a versatile online biologically plausible learning algorithm capable of learning sparse shift-invariant representations, useful for clustering, manifold tiling, or sparse coding, depending on the data structure.