Flexible Online Representation Learning Based on Similarity Matching

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.

Unlocking the Potential of Similarity Matching: Scalability, Supervision and Pre-training

While effective, the backpropagation (BP) algorithm exhibits limitations in terms of biological plausibility, computational cost, and suitability for online learning. As a result, there has been a growing interest in developing alternative biologically plausible learning approaches that rely on local learning rules. This study focuses on the primarily unsupervised similarity matching (SM) framework, which aligns with observed mechanisms in biological systems and offers online, localized, and biologically plausible algorithms. i) To scale SM to large datasets, we propose an implementation of Convolutional Nonnegative SM using PyTorch. ii) We introduce a localized supervised SM objective reminiscent of canonical correlation analysis, facilitating stacking SM layers. iii) We leverage the PyTorch implementation for pre-training architectures such as LeNet and compare the evaluation of features against BP-trained models. This work combines biologically plausible algorithms with computational efficiency opening multiple avenues for further explorations.