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.

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