Self-supervised local learning rules learn the hidden hierarchical structure of high-dimensional data

The brain learns abstract representations of high-dimensional sensory input, but the plasticity rules that enable such learning are unknown. We study biologically plausible algorithms on the Random Hierarchy Model (RHM), an artificial dataset designed to investigate how deep neural networks learn the intrinsic hierarchical structure of high-dimensional data. We focus on two types of local learning rules that avoid both a long convergence time and the use of a symmetric error network. The first type uses direct feedback signals to approximate error propagation from the output layer. The second type uses layerwise self-supervised contrastive or non-contrastive loss functions that do not explicitly approximate errors at the output layer. We show that all rules of the first type fail to solve the tasks of the RHM and trace this failure back to input-specific nonlinearities (`masking') that are implemented in full backpropagation and are essential for learning complex tasks. However, algorithms of the second type are able to learn the hierarchical hidden structure of the RHM tasks and are as data-efficient as supervised backpropagation training, while being compatible with known rules of synaptic plasticity in cortex.

Can Local Learning Match Self-Supervised Backpropagation?

While end-to-end self-supervised learning with backpropagation (global BP-SSL) has become central for training modern AI systems, theories of local self-supervised learning (local-SSL) have struggled to build functional representations in deep neural networks. To establish a link between global and local rules, we first develop a theory for deep linear networks: we identify conditions for local-SSL algorithms (like Forward-forward or CLAPP) to implement exactly the same weight update as a global BP-SSL. Starting from the theoretical insights, we then develop novel variants of local-SSL algorithms to approximate global BP-SSL in deep non-linear convolutional neural networks. Variants that improve the similarity between gradient updates of local-SSL with those of global BP-SSL also show better performance on image datasets (CIFAR-10, STL-10, and Tiny ImageNet). The best local-SSL rule with the CLAPP loss function matches the performance of a comparable global BP-SSL with InfoNCE or CPC-like loss functions, and improves upon state-of-the-art for local SSL on these benchmarks.