BeamLoRA: Dynamic Fine-Tuning for LLMs

• BeamLoRA is a parameter-efficient fine-tuning framework that dynamically reallocates low-rank subspace contributions using a beam search–like approach.
• It introduces rank-wise importance scoring with a dynamic Top-P threshold to adaptively prune and expand model sub-solutions.
• Empirical results show BeamLoRA outperforms standard LoRA by optimizing computational resources for improved accuracy on various NLP tasks.

BeamLoRA is a parameter-efficient fine-tuning framework for LLMs that reinterprets the traditional Low-Rank Adaptation (LoRA) approach by introducing a dynamic “beam constraint” and intra-module rank adaptation. Instead of treating each rank within the low-rank update uniformly, BeamLoRA conceptualizes each rank as an independent sub-solution within a beam search–like scheme. The method adaptively prunes underperforming ranks and reallocates parameter capacity to promising ones, leading to superior fine-tuning accuracy with the same computational budget as standard LoRA. Empirical studies across multiple base models and datasets demonstrate consistent gains over baseline PEFT methods.

1. Motivation and Conceptual Foundations

BeamLoRA is prompted by the observation that, within conventional LoRA, the different rank components inserted into frozen pretrained weights contribute unequally to downstream task adaptation, and their importances evolve dynamically during fine-tuning. In standard LoRA, low-rank matrices $B \in \mathbb{R}^{d \times r}$ and $A \in \mathbb{R}^{r \times k}$ are inserted as $W_0 + BA$. Every rank (corresponding to paired columns in $B$ and rows in $A$) receives an identical parameter allocation, regardless of its actual contribution to the fine-tuning objective.

Analysis revealed not only variation but dynamic change in rank importance as fine-tuning progresses, implying that redundant or low-contribution ranks limit LoRA’s overall effectiveness. BeamLoRA formalizes this by treating each rank as an independent “sub-solution” within a beam, transforming the fine-tuning process into a combinatorial search over sub-solution quality and reallocation.

This reconceptualization distinguishes BeamLoRA from approaches like AdaLoRA or IncreLoRA, which primarily reallocate rank budgets across modules rather than within modules (Gu et al., 19 Feb 2025).

2. Technical Framework and Algorithmic Operations

2.1. Sub-solution Decomposition

For a frozen base weight $W_0 \in \mathbb{R}^{d \times k}$, LoRA rewrites the adaptation as

$W_0 + \sum_{i=1}^r (b_i a_i)$

where $(b_i, a_i)$ are the $i$th column of $B$ and the $i$th row of $A$ respectively. Each element $b_i a_i$ is identified as a possible sub-solution (hereinafter beam element).

2.2. Rank-wise Importance Scoring

BeamLoRA introduces a vector of learnable scores $s \in \mathbb{R}^r$, with normalized softmax values $s_i$: $s_i = \frac{\exp(s_i)}{\sum_{j=1}^r \exp(s_j)}$ During the forward pass, the update becomes

$y = W_0 x + B (s \odot (A x))$

where $\odot$ is elementwise multiplication. This enables dynamic weighting of each rank’s contribution based on learned significance during training.

2.3. Dynamic Pruning and Expansion

At fixed intervals (step interval $A_t$), BeamLoRA evaluates the $s_i$ scores:

• Pruning: Identify a set $I_p$ of the $K$ lowest-scoring ranks (determined via a dynamic Top-P threshold) and set the corresponding columns of $B$ and rows of $A$ to zero.
• Expansion: Simultaneously, take the $K$ highest-scoring ranks ($L_e$) and duplicate their parameters into the pruned slots (with historic optimizer state transfer to break symmetry).

This two-stage operation periodically reassigns parameter resources from low-utility to high-utility sub-solutions without increasing overall rank.

2.4. Dynamic Top-P Thresholding

Instead of fixing $K$, BeamLoRA uses a Top-P scheme whereby the proportion $P$ of operated ranks is scheduled (typically increasing gradually toward 1 with cosine annealing) as training converges. This matches the adaptation frequency to both optimization dynamics and the evolving sharpness of rank-wise importance.

3. Evaluation: Experimental Setup and Results

BeamLoRA was assessed on a suite of challenging domains:

• Mathematical reasoning: MetaMathQA (training), GSM8K and MATH (evaluation)
• Code generation: CodeFeedback (training), HumanEval, MBPP (evaluation)
• Commonsense reasoning: Benchmarks including BoolQ, PIQA, SIQA

Three foundation models were examined: LLaMA2-7B, Mistral-7B-v0.1, and LLaMA2-13B.

Empirically, BeamLoRA:

• Outperformed LoRA, DoRA, AdaLoRA, and IncreLoRA across tasks
• Achieved up to 1.57% higher accuracy than full fine-tuning while utilizing only 2.4% of the trainable parameters in code and math reasoning tasks
• Demonstrated through ablation that each mechanism—importance scoring, dynamic pruning/expansion, Top-P scheduling—contributes to observed gains
• Produced more balanced distributions of intra-module rank significance, validating the hypothesis of sub-solution inequality

4. Comparison to Baseline and Related Methods

Method	Dynamic Intra-Module Adaptation	Dynamic Cross-Module Adaptation	Key Innovations
LoRA	No	No	Standard PEFT
AdaLoRA	No	Yes	Cross-module rank adaption
IncreLoRA	No	Yes	Incremental module adaption
BeamLoRA	Yes	Partial	Dynamic beam constraint

BeamLoRA’s intra-module dynamic adaptation contrasts with AdaLoRA and IncreLoRA, where adaptation occurs between—but not within—modules. DoRA and vanilla LoRA do not address dynamic rank importance.

5. Design Implications and Limitations

BeamLoRA illustrates a paradigm in which parameter-efficient fine-tuning allocates resources at a finer-grained level, not only between but also within low-rank subspaces. This adaptivity enables models to allocate parameter space preferentially toward critical sub-solutions, yielding improved final task performance and potentially reduced overfitting or underfitting of unused capacity.

A limitation noted is that the mechanism depends on the existence of low-rank decomposition (LoRA’s $BA$ structure), so it is not directly applicable to full-matrix tunable models. Extending the principle of dynamic importance assessment, pruning, and expansion from low-rank (factorized) to full-parameter settings is identified as an open research problem. A plausible implication is the applicability of beam-style adaptive subunit exploration principles to other families of modular neural network adaptation techniques.

6. Broader Impact and Future Directions

BeamLoRA establishes that intra-module heterogeneity among adaptation subspaces can be monitored and leveraged for efficiency and accuracy. Its framework suggests future research into:

• Generalizations to other PEFT approaches and possibly non-factorized model updates
• Automated scheduling or learning of pruning/expansion intervals and Top-P parameters
• Extension to domains beyond LLMs, where model modularity and low-rank structure are present

This line of inquiry indicates that parameter-efficient methods need not uniformly treat all adaptive units, and that adaptivity within adaptation modules represents an effective lever for further gains.

7. Summary

BeamLoRA reframes LoRA’s static low-rank insertion as a beam search–like process over dynamically weighted sub-solutions. By pruning low-importance ranks and reallocating capacity to promising ones via learnable score vectors and periodic update rules, BeamLoRA achieves consistently superior fine-tuning outcomes on a range of large-scale NLP tasks. The method’s intra-module adaptivity and resource efficiency point toward a new class of fine-tuning strategies for large neural models (Gu et al., 19 Feb 2025).