{"paper":{"title":"Beyond Perplexity: A Geometric and Spectral Study of Low-Rank Pre-Training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Low-rank pre-training methods reach geometrically distinct loss basins than full-rank training even at matched perplexity.","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Anna Rumshisky, Namrata Shivagunde, Sherin Muckatira, Vijeta Deshpande","submitted_at":"2026-05-13T15:11:37Z","abstract_excerpt":"Pre-training large language models is dominated by the memory cost of storing full-rank weights, gradients, and optimizer states. Low-rank pre-training has emerged to address this, and the space of methods has grown rapidly. A central question remains open: do low-rank methods produce models that generalize comparably to full-rank training, or does the rank constraint fundamentally alter the solutions reached? Existing comparisons rely almost entirely on validation perplexity from single-seed runs, often carried forward from prior literature. Yet perplexity is a poor proxy for solution quality"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. Full-rank training settles into a sharper basin than low-rank methods along random directions, while the reverse holds for the top-1 PCA direction.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the 16 metrics across 1-D loss landscape, interpolation, spectral structure, and activation similarity sufficiently characterize meaningful differences in solution quality, generalization, and downstream performance.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Low-rank pre-training methods converge to geometrically and spectrally distinct basins from full-rank training and from each other, even at similar validation perplexity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Low-rank pre-training methods reach geometrically distinct loss basins than full-rank training even at matched perplexity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"60bb05392f9d202279cbc3d85ee7309e1c5d2f0501b524da177fce0a21016081"},"source":{"id":"2605.13652","kind":"arxiv","version":1},"verdict":{"id":"f085b09f-888c-4faf-aa35-51a843a0f09e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:16:23.841652Z","strongest_claim":"We show that low-rank methods are not equivalent to full-rank training, nor to one another, even when validation perplexity is close. Full-rank training settles into a sharper basin than low-rank methods along random directions, while the reverse holds for the top-1 PCA direction.","one_line_summary":"Low-rank pre-training methods converge to geometrically and spectrally distinct basins from full-rank training and from each other, even at similar validation perplexity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the 16 metrics across 1-D loss landscape, interpolation, spectral structure, and activation similarity sufficiently characterize meaningful differences in solution quality, generalization, and downstream performance.","pith_extraction_headline":"Low-rank pre-training methods reach geometrically distinct loss basins than full-rank training even at matched perplexity."},"references":{"count":30,"sample":[{"doi":"","year":2023,"title":"A modern look at the relationship between sharpness and generaliza- tion","work_id":"f4cfd80b-20d4-4ee1-9cff-8db4420b01b6","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Understanding pre-training and fine-tuning from loss landscape perspectives","work_id":"eea59928-7026-41ae-92a7-e32519a2cd03","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Fira: Can we achieve full-rank training of llms under low-rank constraint?ArXiv, abs/2410.01623, 2024","work_id":"bc618a36-505b-4655-8771-ed9a465c53df","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"Linear mode connectivity and the lottery ticket hypothesis","work_id":"6d8c5789-2503-4bb7-ac1d-85f2d561f194","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"The language model evaluation harness, 07 2024","work_id":"9148854a-4b09-4c5d-b1a4-5ee9cccc772c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":30,"snapshot_sha256":"efb7cf3025648a1cb0c0cbee46227db8e907fb559456449435169a5a7d965018","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"10bee0cf672c63e78885db17e77a8090f4c3d7d443fd57aee1dcb8ea00c3794d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}