Radial Basis Function Networks as Projection Heads in Self-Supervised Learning

Self-supervised learning (SSL) typically relies on a backbone encoder followed by a small multilayer perceptron (MLP) projection head, which is conventionally discarded after training, while backbone quality is assessed via costly linear probing on labeled data. We argue that this approach including discarding the projector is rather computationally wasteful. Instead, we propose replacing the MLP head with a radial basis function network (RBFN), whose interpretable center and shape parameters can be exploited to judge representation quality without labels or a separate classifier. To this end, we introduce Scale-Normalized Separation (SNS), a novel label-free quality metric derived solely from the kernel centers and shapes learned during training. Across five canonical SSL architectures (MoCo, SimCLR, BYOL, SwAV and SimSiam) and four image classification datasets, we show that RBFN projection heads are competitive drop-in replacements for standard MLP projectors. We recommend constructing them with three RBF layers activated by the Gaussian radial basis function. Moreover, SNS exhibits strong to very strong positive correlation with established logistic regression metrics, demonstrating that a trained RBFN projector can act as a reliable proxy for backbone representation quality. We additionally publish a novel PyTorch compatible image classification dataset based on Google's Open Images V7 to facilitate reproducible research into representation learning.

Improving Nonlinear Projection Heads using Pretrained Autoencoder Embeddings

This empirical study aims at improving the effectiveness of the standard 2-layer MLP projection head $g(\cdot)$ featured in the SimCLR framework through the use of pretrained autoencoder embeddings. Given a contrastive learning task with a largely unlabeled image classification dataset, we first train a shallow autoencoder architecture and extract its compressed representations contained in the encoder's embedding layer. After freezing the weights within this pretrained layer, we use it as a drop-in replacement for the input layer of SimCLR's default projector. Additionally, we also apply further architectural changes to the projector by decreasing its width and changing its activation function. The different projection heads are then used to contrastively train and evaluate a feature extractor $f(\cdot)$ following the SimCLR protocol, while also examining the performance impact of Z-score normalized datasets. Our experiments indicate that using a pretrained autoencoder embedding in the projector can not only increase classification accuracy by up to 2.9% or 1.7% on average but can also significantly decrease the dimensionality of the projection space. Our results also suggest, that using the sigmoid and tanh activation functions within the projector can outperform ReLU in terms of peak and average classification accuracy. When applying our presented projectors, then not applying Z-score normalization to datasets often increases peak performance. In contrast, the default projection head can benefit more from normalization. All experiments involving our pretrained projectors are conducted with frozen embeddings, since our test results indicate an advantage compared to using their non-frozen counterparts.