Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (αReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks (d |V|). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.

Scaling laws have profoundly shaped our understanding of model performance in computer vision and natural language processing, yet their application to general audio representation learning remains underexplored. A key challenge lies in the multifactorial nature of general audio representation-representation quality is jointly influenced by variables such as audio length, embedding dimensionality, model depth, model architecture, data volume, etc., many of which are difficult to isolate or express analytically. In this work, we present a systematic study of scaling laws for general audio representations by utilizing embedding effective rank (RankMe) as a unifying metric that encapsulates the impact of diverse variables on representation quality. RankMe enables a label-free, information-theoretic quantification of audio embeddings, allowing us to examine scaling behaviors across a wide hyper-parameter space, including model size, training data volume, computational budget, architectural configurations, etc. Our empirical findings reveal a consistent power-law relationship between RankMe and representation quality, suggesting that embedding effective rank serves as a reliable proxy for assessing and predicting model performance in audio representation learning. This work not only validates the applicability of classical scaling principles to the general audio domain but also offers a theoretically grounded and empirically robust framework for guiding future model scaling strategies in audio foundation models.

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay ($α$-ReQ). With OLMo (1B-7B) and Pythia (160M-12B) models, we uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining. The initial "warmup" phase exhibits rapid representational collapse. This is followed by an "entropy-seeking" phase, where the manifold's dimensionality expands substantially, coinciding with peak n-gram memorization. Subsequently, a "compression-seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, a transition marked with significant improvement in downstream task performance. We show these phases can emerge from a fundamental interplay of cross-entropy optimization under skewed token frequencies and representational bottlenecks ($d \ll |V|$). Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data, improving in-distribution performance while degrading out-of-distribution robustness. Conversely, RLVR induces "compression-seeking", enhancing reward alignment but reducing generation diversity.

Driven by the recent advances in deep learning methods and, in particular, by the development of modern self-supervised learning algorithms, increased interest and efforts have been devoted to build foundation models (FMs) for medical images. In this work, we present our scalable training pipeline for large pathology imaging data, and a comprehensive analysis of various hyperparameter choices and training techniques for building pathology FMs. We release and make publicly available the first batch of our pathology FMs (https://github.com/kaiko-ai/towards_large_pathology_fms) trained on open-access TCGA whole slide images, a commonly used collection of pathology images. The experimental evaluation shows that our models reach state-of-the-art performance on various patch-level downstream tasks, ranging from breast cancer subtyping to colorectal nuclear segmentation. Finally, to unify the evaluation approaches used in the field and to simplify future comparisons of different FMs, we present an open-source framework (https://github.com/kaiko-ai/eva) designed for the consistent evaluation of pathology FMs across various downstream tasks.

Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. A key obstacle to using JE methods, however, is the inherent challenge of evaluating learned representations without access to a downstream task, and an annotated dataset. Without efficient and reliable evaluation, it is difficult to iterate on architectural and training choices for JE methods. In this paper, we introduce LiDAR (Linear Discriminant Analysis Rank), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance rank by discriminating between informative and uninformative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task -- a measure that intuitively captures the information content as it pertains to solving the SSL task. We empirically demonstrate that LiDAR significantly surpasses naive rank based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of assessing the quality of representations within JE architectures, which we hope facilitates broader adoption of these powerful techniques in various domains.

Unsupervised learning has recently significantly gained in popularity, especially with deep learning-based approaches. Despite numerous successes and approaching supervised-level performance on a variety of academic benchmarks, it is still hard to train and evaluate SSL models in practice due to the unsupervised nature of the problem. Even with networks trained in a supervised fashion, it is often unclear whether they will perform well when transferred to another domain. Past works are generally limited to assessing the amount of information contained in embeddings, which is most relevant for self-supervised learning of deep neural networks. This works chooses to follow a different approach: can we quantify how easy it is to linearly separate the data in a stable way? We survey the literature and uncover three methods that could be potentially used for evaluating quality of representations. We also introduce one novel method based on recent advances in understanding the high-dimensional geometric structure of self-supervised learning. We conduct extensive experiments and study the properties of these metrics and ones introduced in the previous work. Our results suggest that while there is no free lunch, there are metrics that can robustly estimate embedding quality in an unsupervised way.

Joint-Embedding Self Supervised Learning (JE-SSL) has seen a rapid development, with the emergence of many method variations but only few principled guidelines that would help practitioners to successfully deploy them. The main reason for that pitfall comes from JE-SSL's core principle of not employing any input reconstruction therefore lacking visual cues of unsuccessful training. Adding non informative loss values to that, it becomes difficult to deploy SSL on a new dataset for which no labels can help to judge the quality of the learned representation. In this study, we develop a simple unsupervised criterion that is indicative of the quality of the learned JE-SSL representations: their effective rank. Albeit simple and computationally friendly, this method -- coined RankMe -- allows one to assess the performance of JE-SSL representations, even on different downstream datasets, without requiring any labels. A further benefit of RankMe is that it does not have any training or hyper-parameters to tune. Through thorough empirical experiments involving hundreds of training episodes, we demonstrate how RankMe can be used for hyperparameter selection with nearly no reduction in final performance compared to the current selection method that involve a dataset's labels. We hope that RankMe will facilitate the deployment of JE-SSL towards domains that do not have the opportunity to rely on labels for representations' quality assessment.