Tracing the Representation Geometry of Language Models from Pretraining to Post-training
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918149224398848 |
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| author | Li, Melody Zixuan Agrawal, Kumar Krishna Ghosh, Arna Teru, Komal Kumar Santoro, Adam Lajoie, Guillaume Richards, Blake A. |
| author_facet | Li, Melody Zixuan Agrawal, Kumar Krishna Ghosh, Arna Teru, Komal Kumar Santoro, Adam Lajoie, Guillaume Richards, Blake A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tracing the Representation Geometry of Language Models from Pretraining to Post-training Li, Melody Zixuan Agrawal, Kumar Krishna Ghosh, Arna Teru, Komal Kumar Santoro, Adam Lajoie, Guillaume Richards, Blake A. Machine Learning Artificial Intelligence Computation and Language 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. |
| title | Tracing the Representation Geometry of Language Models from Pretraining to Post-training |
| topic | Machine Learning Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2509.23024 |