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LIT-658: Knowledge is a Region in Weight Space for Fine-tuned Language Models

3 min read

Properties4
StatusActive — read in full 2026-10-03 (NOTE-515); worth reading as the paper that turns linear connectivity between fine-tuned models into a claim about regions. RoBERTa-base models fine-tuned on the same dataset, the same task, or any of 12 GLUE/SuperGLUE datasets cluster in weight space by cosine of their task vectors, and the convex hull of each group performs as well as or better than the fine-tuned members: sampled hull points beat the members in 88% of comparisons on MNLI. Linear extrapolation past the members fails quickly, so the fine-tuned models sit near the edge of a small basin. Averaging the region (its centroid) is a better start for further fine-tuning than the pretrained model on 9 of 12 datasets. One pretrained model, classification only, English only.
Tagsloss-landscapes, anthology-candidate
Cited as “paper” byNOTE-515 — Knowledge is a Region in Weight Space for Fine-tuned Language Models
Cited as “source” byTHEORY-105 — For RoBERTa-base fine-tuned on English classification data, with loss measured by a linear probe refitted on the frozen encoder, points sampled from the convex hull of models fine-tuned on one dataset, one task family or twelve GLUE and SuperGLUE datasets lost no more than any model fine-tuned elsewhere and beat the group's own members in 88% to 96.7% of comparisons, and the centroid of the general-level models was a better starting point for BitFit than the pretrained model, THEORY-115 — Linear connectivity from a shared, already-stable start holds only when the objectives the runs optimise share structure, and breaks as that structure is removed, THEORY-828 — Fine-tuning from one pretrained model typically lands near the edge of a task-specific low-loss region in weight space that contains the convex hull of the fine-tuned models, and averaging their weights, as model soups and stochastic weight averaging do, works by moving inward

Graph View

Almog Gueta, Elad Venezian, Colin Raffel, Noam Slonim, Yoav Katz and Leshem Choshen (2023), arXiv preprint — ARXIV-2302.04863

Key takeaways

  • Fine-tuning moves a model in a direction set by the data. With task vectors (fine-tuned minus pretrained weights) compared by cosine, 280 models fine-tuned on 12 datasets with 20 seeds each cluster by dataset with 98% accuracy, and models from three task families cluster by family with 90% (§4). Clusters follow the kind of data and not its amount (§4.1, App. C). Euclidean distance did not give clear clusters, which the authors put down to weight-norm growth during training (§2.3).
  • The space between fine-tuned models is as good as the models, or better. Lines between pairs (§5.1) and samples from the convex hull of a group (§5.2) keep low loss on the group’s data, and often lower loss than the endpoints: on MNLI every hull sample beats every model fine-tuned on another dataset, and hull samples beat the MNLI-fine-tuned models in 88% of comparisons. Loss is compared through a “generalized loss”, a linear probe refitted on the frozen encoder for each target dataset (§3).
  • The region is small and its walls are steep. Extrapolating along the same lines past the endpoints raises the loss quickly (§6, App. G), so the fine-tuned models lie near the edge of a basin with a flat floor. Starting further fine-tuning from the region’s centroid beats starting from the pretrained model on 9 of 12 datasets (§7, Table 2).

Standing in the record

Filed with the owner’s batch on mode connectivity and model merging, under the loss-landscapes topic that ADR-027 added for it. The anthology could hold it as model merging; this record holds it for what it says about the shape of the solution set, so it carries the anthology-candidate flag.

It generalises the shared-start linear connectivity of Frankle et al. (LIT-654), whom it cites for the dependence of linear paths on a shared origin, from a line between two runs to a convex region spanned by many fine-tuning runs from one pretrained model. The paper credits Entezari et al. (LIT-652) for the linear connectivity of same-dataset fine-tuning (§1), which is not the setting that paper studies: it conjectures linear connectivity modulo permutation for networks trained from different random initialisations. See the reading. It reads Mirzadeh et al. (LIT-651) as the multitask precedent, and Benton et al. (LIT-656) as the precedent for low-loss volumes rather than lines. No relation is declared: none of these is a design it builds on or a result it measures.

Its §8 offers the region picture as an explanation of weight averaging in practice: model soups (ANTH-LIT-675) average models from one dataset region, and robust fine-tuning by interpolation (ANTH-LIT-674) moves within the region of the pretrained model. TIES-Merging (LIT-675), by an overlapping author group, cites it among the works showing that separately trained weights can be interpolated without a rise in loss (its §2). Its region claim is the one a THEORY would rest on; see the report on theory candidates.

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