Tracing the Representation Geometry of Language Models from Pretraining to Post-training

• URL: http://arxiv.org/abs/2509.23024v1
• Date: Sat, 27 Sep 2025 00:46:29 GMT
• Title: Tracing the Representation Geometry of Language Models from Pretraining to Post-training
• Authors: Melody Zixuan Li, Kumar Krishna Agrawal, Arna Ghosh, Komal Kumar Teru, Adam Santoro, Guillaume Lajoie, Blake A. Richards,
• Abstract summary: We take a spectral approach to investigate the geometry of learned representations across pretraining and post-training.<n>We uncover a consistent non-monotonic sequence of three geometric phases during autoregressive pretraining.<n>Post-training further transforms geometry: SFT and DPO drive "entropy-seeking" dynamics to integrate specific instructional or preferential data.
• Score: 22.18942718274405
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 ($\alpha$-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.

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