Generalized Tensor-Based Parameter-Efficient Fine-Tuning via Lie Group Transformations
Bibliographic record
Abstract
Adapting pre-trained foundation models for diverse downstream tasks is a core practice in artificial intelligence. However, the wide range of tasks and high computational costs make full fine-tuning impractical. To overcome this, parameter-efficient fine-tuning (PEFT) methods like LoRA have emerged and are becoming a growing research focus. Despite the success of these methods, they are primarily designed for linear layers, focusing on two-dimensional matrices while largely ignoring higher-dimensional parameter spaces like convolutional kernels. Moreover, directly applying these methods to higher-dimensional parameter spaces often disrupts their structural relationships. Given the rapid advancements in matrix-based PEFT methods, rather than designing a specialized strategy, we propose a generalization that extends matrix-based PEFT methods to higher-dimensional parameter spaces without compromising their structural properties. Specifically, we treat parameters as elements of a Lie group, with updates modeled as perturbations in the corresponding Lie algebra. These perturbations are mapped back to the Lie group through the exponential map, ensuring smooth, consistent updates that preserve the inherent structure of the parameter space. Extensive experiments on computer vision and natural language processing validate the effectiveness and versatility of our approach, demonstrating clear improvements over existing methods.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".