MetaTT: A Global Tensor-Train Adapter for Parameter-Efficient Fine-Tuning

Low-Rank Adaptation (LoRA) is a popular parameter-efficient fine-tuning (PEFT) method that restricts weight updates to low-rank adapters, introducing a fixed low-rank inductive bias by optimizing in a low-dimensional subspace. In this work, we question whether a fixed-rank constraint is the most effective inductive bias for parameter-efficient fine-tuning. We introduce Learnable Rank LoRA (LR-LoRA), a PEFT method in which the adapter rank is learned during the training process. Instead of prescribing a uniform rank for all adapter layers, LR-LoRA allows the optimizer to determine the appropriate rank for each layer. Using this approach, we find substantial layer-wise variation in the learned ranks, with the attention and MLP layers in the transformer models exhibiting systematically different rank preferences. Across a range of language understanding and commonsense reasoning benchmarks, LR-LoRA achieves state-of-the-art performance in most settings and consistently outperforms strong PEFT baselines, demonstrating that a learnable rank provides a more flexible and effective inductive bias than fixed-rank adaptations.

Parameter-efficient fine-tuning (PEFT) methods face a tradeoff between adapter size and expressivity: ultra-low-parameter adapters are confined to fixed low-rank subspaces, capping performance even with extended training. We propose BoostLoRA, a gradient-boosting framework that overcomes this limit by iteratively training and merging minimal adapters on the examples the current model gets wrong. A ROTATE SVD basis strategy assigns each round to an orthogonal subspace, so cumulative effective rank grows linearly with the number of rounds while each adapter remains ultra-low-rank. After merging, adapters are discarded, leaving zero inference overhead. On Qwen2.5-3B, BoostLoRA reaches 89.1% on GSM8K and 68.8% on MATH-500, surpassing both the best single-shot ultra-low parameter adapter (TinyLoRA) and full fine-tuning; on code generation it reaches 57.2% on MBPP and 80.4% on HumanEval while full fine-tuning drops below the zero-shot baseline. We also demonstrate cross-architecture transfer on protein binding classification with ESM2-650M and cross-entropy training. BoostLoRA is, to our knowledge, the first PEFT method whose effective rank grows with training, separating per-round parameter cost from total representational capacity.

Full fine-tuning remains a strong way to adapt pretrained LLMs, but it updates all weights and can be expensive. LoRA reduces the number of trainable parameters, but it does not directly answer which pretrained components should be trained and which can be frozen during adaptation. We introduce TopoTuner, a topology-guided fine-tuning framework for selective freezing of attention projection matrices. \method treats each projection matrix as a row cloud and uses Wasserstein distances between persistence diagrams to measure how its topology changes during fine-tuning. TopoTuner learns a reusable freezing profile from a source dataset and transfers it to efficiently fine-tune models on out-of-domain datasets, evaluating whether task-specific topological drift generalizes across question answering and sentiment analysis tasks. Across LLaMA-3.1-8B, Mistral-7B-v0.3, and Qwen3-8B-Base, TopoTuner is competitive with full fine-tuning while training only 1-2% of the model parameters, and outperforms LoRA in 7 out of 9 model-dataset settings, which can change up to 39.57% of the projection parameters. Along with minimized updates, TopoTuner reduces training time by 20.4% relative to full fine-tuning and 5.5% relative to LoRA on average. TopoTuner opens a new direction for reusable freezing profiles, where fine-tuning behavior learned on one dataset can be shared across multiple tasks.