A Comparative Study of Label-free Representation Quality Metrics in Deep Learning

We present a comparative study of label-free metrics for assessing the quality of representations in deep neural networks to understand their reliability under a wide variety of configurations. We group existing label-free metrics into three families based on their construction and analytically establish connections between metrics within the same family. We then characterise the sensitivity of spectral metrics through controlled synthetic experiments. Finally, all label-free metrics are evaluated against downstream task accuracy across a diverse set of 260 vision models on six datasets spanning generic object classification, fine-grained object classification, scene recognition and geospatial task, stratifying results by architecture class and training objective. We find that intrinsic dimensionality (ID) is the most reliable predictor among the metrics considered. However, the reliability of all metrics, including ID, is moderated by architecture class and training objective. Our results provide a clearer understanding of what label-free representation quality metrics measure, when they are reliable, and how to interpret them in practice.

What Makes a Good Layer? Assessing the Layer-Wise Intrinsic Properties of Music Foundation Models

Music foundation models are commonly used as frozen audio feature extractors, yet selecting which layer to extract from remains largely heuristic. Current practice defaults to fixed depths or multi-layer fusion, with limited understanding of why certain layers transfer better across downstream tasks or how representation quality varies with depth and pre-training paradigm. We conduct a systematic layer-wise analysis of 12 music foundation models spanning three pre-training paradigms (masked modeling, autoregressive modeling, and contrastive learning), characterizing their hidden representations through intrinsic geometric and transformation-based properties. Correlating label-free representation-quality metrics with layer-wise performance across 15 downstream tasks, we find that several metrics track layer quality for genre classification, emotion recognition, automatic tagging, and beat tracking, albeit with varying strength across tasks and pre-training paradigms. However, all metrics fail on tonal tasks such as key estimation and chord recognition, indicating that no single property serves as a general proxy for representation quality across music information retrieval tasks. To address this gap, we introduce a pitch-transposition equivariance measure that captures properties missed by these standard metrics, providing a consistent indicator of tonal quality across model families. Finally, we show that intrinsic metrics can serve as effective proxies for layer selection, matching or outperforming trainable multi-layer fusion methods, particularly in limited-data settings.

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.

Complexity of Linear Regions in Self-supervised Deep ReLU Networks

There has been growing interest in studying the complexity of Rectified Linear Unit (ReLU) based activation networks. Recent work investigates the evolution of the number of piecewise-linear partitions (linear regions) that are formed during training. However, current research is limited to examining the complexity of models trained in a supervised way. Self-Supervised Learning (SSL) differs in that it directly optimises the representation space using a loss function to enhance the model's performance across multiple downstream tasks. This study investigates the local distribution of linear regions produced by SSL models. We demonstrate that the evolution of linear regions correlates with the representation quality by utilising SplineCam to extract two-dimensional polytopes near the data distribution. We track the number, area, eccentricity, and boundaries of regions throughout training. The study compares supervised, contrastive, and self-distillation methods over two standard benchmark datasets, MNIST and FashionMNIST. The analysis of the experimental results shows that self-supervised methods create substantially fewer regions to achieve comparable accuracy to supervised models. Contrastive methods rapidly expand regions over time, whereas self-distillation methods tend to consolidate by merging neighbouring regions. Lastly, we can detect representation collapse early within the geometric space of linear regions. Our analysis suggests that polytopal metrics can serve as reliable indicators of representation quality and model performance.