GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters

## Abstract

Abstract Sparse fine-tuning techniques adapt LLMs to downstream tasks by only tuning a sparse subset of model parameters. However, the effectiveness of sparse adaptation depends on optimally selecting the model parameters to be fine-tuned. In this work, we introduce a novel sparse fine-tuning technique named GaLLoP : G radient-based Sp a rse L earning on Lo w-Magnitude P arameters, which fine-tunes only those model parameters which have the largest gradient magnitudes on downstream tasks and the smallest pre-trained magnitudes, intuitively prioritizing parameters that are highly task-relevant, but minimally disruptive to pre-trained knowledge. Our experimentation with LLaMA3 8B and Gemma 2B as base models shows that GaLLoP consistently improves or matches the in-distribution as well as out-of-distribution performance obtained via the usage of other leading parameter-efficient fine-tuning techniques, including LoRA, DoRA, and SAFT. Our analysis demonstrates that GaLLoP mitigates catastrophic forgetting and memorization of task data, as important pre-trained parameters remain unchanged, and stabilizes performance relative to other fine-tuning techniques, robustly generalizing across most random seeds.

### 1 Introduction

Noting that pre-trained LLMs have a low intrinsic dimension (Aghajanyan et al., 2021a), efficient reparametrization of fine-tuning via a low-rank decomposition made techniques such as LoRA, DoRA, and their variants (Hu et al., 2022; yang Liu et al., 2024; Kopiczko et al., 2024) gain widespread popularity. However, such techniques are still susceptible to overfitting (Zhang et al., 2023; Wang et al., 2024) and hence, fine-tuning models using them can also result in the *memorization* of patterns in the training dataset(s) and the loss of pre-trained knowledge, i.e., *catastrophic forgetting* (McCloskey & Cohen, 1989). This can further impair their *generalizability*, i.e., their ability to perform well on tasks related to yet unseen during fine-tuning, not only for cases wherein the task data used for testing possesses the same distribution as the fine-tuning data and differs only in content (*In-Distribution* (ID)) but also for cases wherein the test data and the fine-tuning data possess different distributions altogether (*Out-of-Distribution* (OOD)) (Miller et al., 2021). Sparse Fine-Tuning (SpFT) techniques (Ansell et al., 2024; Nguyen et al., 2024) have recently emerged as promising alternatives to overcome these issues since they leverage the low intrinsic dimensionality of LLMs by directly fine-tuning only a small fraction of the original model parameters without introducing any additional parameters. However, the effectiveness of sparse adaptation crucially depends upon the selection criterion used to decide which parameters to update.

In this work, we introduce a novel SpFT technique named GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters. To enhance both ID as well as OOD generalizability, GaLLoP fine-tunes only a selected fraction of the model parameters which have the largest gradients on the downstream task (indicating strong ID task relevance (Nguyen et al., 2024)) and the smallest pre-trained magnitudes (preserving the pre-trained knowledge (Zhou et al., 2025; Ramesh et al., 2024) for OOD tasks).

Through experiments on eight datasets with LLaMA3 8B (Grattafiori et al., 2024) and Gemma 2B (Team et al., 2024) as base models, we show that fine-tuning models with GaLLoP consistently enhances both their ID and OOD generalizability by preventing catastrophic forgetting and memorization as compared to state-of-the-art (SOTA) PEFT and post-training model editing techniques. Furthermore, we show that GaLLoP demonstrates robustness to overtraining and stabilizes performance.

### 2 Related Work

#### 2.1 Parameter-Efficient Fine-Tuning (PEFT)

Given the large number of trainable parameters in LLMs, PEFT techniques facilitate the compute- and memory-efficient adaptation of LLMs to downstream tasks by only updating a small number of model parameters while keeping the rest frozen (Houlsby et al., 2019). They can be broadly classified into the following three categories:

Additive Fine-Tuning (AFT): Additional modules (adapter layers) are connected to or introduced into the original frozen LLM and these new modules (with a lower number of parameters than the original model) are then fine-tuned (Houlsby et al., 2019; Lin et al., 2020). However, their sequential processing introduces unwanted latency during training as well as inference (Hu et al., 2022).

Reparametrized Fine-Tuning (RFT): A low-rank decomposition-based reparametrization of the update matrix can be performed with almost the same effectiveness as the original full-rank representation (Hu et al., 2022). The fine-tuned parameters can then be merged with the pre-trained parameters prior to inference, doing away with any additional latency as in AFT. This category includes LoRA (Hu et al., 2022), the original RFT technique; DoRA, which fine-tunes magnitude and directional components separately to close LoRA’s performance gap with Full Fine-Tuning (FFT) (yang Liu et al., 2024); as well as other variants which either increase LoRA’s efficiency (Kopiczko et al., 2024; Valipour et al., 2023) or its expressivity (Huang et al., 2025; Hayou et al., 2024; Nikdan et al., 2024). However, in contrast to GaLLoP, these techniques are still susceptible to overfitting (Zhang et al., 2023; Wang et al., 2024; 2025) since all the newly introduced parameters are fine-tuned on the downstream task.

Sparse Fine-Tuning (SpFT): Only a selected fraction of the model parameters is fine-tuned on the downstream task to ensure high memory and compute efficiency. Diff pruning (Guo et al., 2021) and LT-SFT (Ansell et al., 2022) incorporate FFT phases, defeating the very purpose of SpFT. PaFi (Liao et al., 2023) selects the parameters with the smallest pre-trained magnitudes while FISH Mask (Sung et al., 2021), SIFT (Song et al., 2024), SAFT (Nguyen et al., 2024), SMT (He et al., 2025), and SpIEL (Ansell et al., 2024) select the parameters with the highest gradient magnitudes on a downstream task for fine-tuning. While FISH Mask, SIFT, SAFT, and SMT generate a *static* (fixed before fine-tuning) mask of the parameters to be fine-tuned via a single pass on the downstream task dataset, SpIEL iteratively generates *dynamic* masks by alternating between the updation, deletion, and growth of the candidate parameter set. To the best of our knowledge, GaLLoP is the only SpFT technique which incorporates dual parameter selection criteria: high task gradient magnitudes and low pre-trained magnitudes, which consistently improves generalizability and ensures stability.

#### 2.2 Post-Training Model Editing

Most fine-tuning techniques (except SAFT (Nguyen et al., 2024)) focus solely on improving ID accuracy on a target downstream dataset at the risk of OOD performance degradation (Miller et al., 2021; Taori et al., 2020). Consequently, weight-space modifications to a single fine-tuned model can serve as a robust and efficient alternative to complex modifications in fine-tuning. WiSE-FT (Weight-Space Ensembles for Fine-Tuning) (Wortsman et al., 2022) performs a linear ensembling of zero-shot and end-to-end fine-tuned model weights to combine robustness with target-specific accuracy. LiNeS (Layer-increasing Network Scaling) performs layer-wise parameter scaling by maintaining shallower layers close to their pre-trained values for preserving generality while allowing deeper layers to retain task-specific characteristics (Wang et al., 2025). However, the dependence of editing techniques on the fine-tuned model limits their own performance improvements (if any).

### 3 Motivation

Fine-tuning a model with our SpFT algorithm must not only minimize the model’s loss on the downstream task (for enhancing ID generalizability) but at the same time, also preserve the pre-trained knowledge stored in the model parameters (for enhancing OOD generalizability). The first criterion is straightforward to realize: since parameters with the largest gradients generally lead to fast convergence to the optimum on the downstream task, they must be selected for fine-tuning so as to minimize the loss on the downstream task (Nguyen et al., 2024). However, the second criterion does not directly follow from the first since parameters with high gradients on the downstream task can still be highly relevant for the pre-trained model and fine-tuning them can potentially lead to catastrophic forgetting (Aghajanyan et al., 2021b). While the model pruning literature regards parameters with the smallest pre-trained magnitudes as the least important (Han et al., 2015), fine-tuning them does not necessarily lead to the least impact on the pre-trained loss (Lee et al., 2019).

Therefore, we analyze the differences in ID and OOD performance upon fine-tuning only the top-$\rho\%$ of the model parameters based on whether they have a) the smallest or b) the largest pre-trained magnitudes. We consider eight reasoning datasets (Hu et al., 2023) and fine-tune Gemma 2B (Team et al., 2024) models, considering four different density levels. Models are fine-tuned on the training set of each of these datasets (*individually*) and their performance is evaluated on the corresponding dataset’s test set (unseen during fine-tuning yet possesses the training set’s distribution), which measures their ID accuracy, and the test sets of the remaining seven datasets (unseen during fine-tuning and possess distributions which differ from the training set’s distribution), which measures their OOD accuracy (averaged over the seven datasets). The averaged (over all possible ID and OOD task combinations) ID and OOD accuracies of these models are shown in [Figure 1](https://arxiv.org/html/2510.19778v1#S3.F1) (see [Appendix H](https://arxiv.org/html/2510.19778v1#A8) for further details).

Figure: Figure 1: Fine-tuning the top-$\rho\%$ of model parameters with the largest pre-trained magnitudes leads to no performance improvements over the non fine-tuned, vanilla model while fine-tuning the top-$\rho\%$ of model parameters with the smallest pre-trained magnitudes enhances the pre-trained knowledge, leading to significantly increased ID (left) and OOD (right) generalizability.
Refer to caption: x1.png

While fine-tuning the parameters with the largest pre-trained magnitudes leads to no performance improvements over the non fine-tuned, vanilla model (only 3-4% ID and OOD accuracies), fine-tuning the parameters with the smallest pre-trained magnitudes leads to increasingly high ID ($\approx$ 50 - 70% accuracy) and OOD ($\approx$ 30 - 40% accuracy) generalizability. These findings are also in agreement with recent studies (Zhou et al., 2025; Ramesh et al., 2024) and support our hypothesis that fine-tuning low-magnitude parameters enhances pre-trained knowledge.

### 4 Methodology

Motivated by the results discussed in [Section 3](https://arxiv.org/html/2510.19778v1#S3), we now present our SpFT algorithm, GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters. Given a density level $\rho$, GaLLoP fine-tunes the top-$\rho\%$ of the model parameters with the largest gradient magnitudes (to enhance ID generalizability) and the smallest pre-trained magnitudes (to enhance OOD generalizability). We now give a formal description of how GaLLoP works.

Figure: (a) Phase 1
Refer to caption: x2.png

GaLLoP operates in two phases (see [Figure 2](https://arxiv.org/html/2510.19778v1#S4.F2)). Consider a model with a parameter vector $\bm{\theta}\in\mathbb{R}^{D}$ which needs to be fine-tuned on a dataset $\mathcal{D}={\{(\bm{x}_{n},\bm{y}_{n})\}}_{n=1}^{N}$, where, $\bm{x}_{n}\in\mathbb{R}^{P}$ and $\bm{y}_{n}\in\mathbb{R}^{Q}$. In the first phase, given a density level $\rho$, GaLLoP selects the learnable parameters using a dataset sample proportion $d_{s}$ (corresponding dataset sample size = $d_{s}N$). To do so, it proceeds by computing the gradient vector $\bm{g}$ of the net fine-tuning loss $\mathcal{L}(\bm{x}_{n},\bm{y}_{n};\bm{\theta})$ which is given by:

$$ $\displaystyle\bm{g}=\dfrac{1}{d_{s}N}\sum_{n=1}^{d_{s}N}\nabla_{\bm{\theta}}\mathcal{L}(\bm{x}_{n},\bm{y}_{n};\bm{\theta}).$ (1) $$

This allows us to enforce our first parameter selection criterion (high-magnitude gradients). In order to simultaneously enforce our second parameter selection criterion (low- (pre-trained) magnitude parameters), we compute a score vector $\bm{s}$ such that:

$$ $\displaystyle\bm{s}=\left(\dfrac{\text{abs}(\bm{g})}{\text{abs}(\bm{\theta})+\epsilon}\right),$ (2) $$

where, abs(.) computes the element-wise absolute value of a vector and a small value $\epsilon\approx 10^{-8}$ has been added to the denominator so as to prevent numerical overflows.

Subsequently, in order to select only the top-$\rho\%$ of all model parameters $\bm{\theta}$ for fine-tuning based on their corresponding scores $\bm{s}$, we compute a binary mask vector $\bm{m}$ such that, for a given parameter $\bm{\theta}_{i}$ with a score $\bm{s}_{i}$, the mask value $\bm{m}_{i}$ is given by:

$$ $\displaystyle\bm{m}_{i}=\begin{cases}1&\text{if }\bm{s}_{i}\geq s_{t},\\ 0&\text{otherwise.}\end{cases}$ (3) $$

where, the score threshold $s_{t}$ is computed as follows:

$$ $\displaystyle s_{t}=\mathtt{sorted}_{d}(\bm{s}_{0},\bm{s}_{1},\dots,\bm{s}_{\text{end}})[k]$ (4) $$

where, $k=\lfloor\rho D\rfloor$ and $\mathtt{sorted}_{d}(.)$ is the function used for sorting an array in the descending order.

Finally, in the second phase, GaLLoP only updates the selected, *unmasked*, parameters using mini-batch gradient descent while rendering the values of the remaining (unselected), *masked*, parameters unchanged by masking out their gradients during the update using $\bm{m}$. We give a practical implementation of GaLLoP in [Appendix A](https://arxiv.org/html/2510.19778v1#A1).

### 5 Experimental Settings

#### 5.1 Datasets

To examine the effectiveness of GaLLoP, we perform fine-tuning experiments on eight commonsense reasoning datasets with predefined training and test sets (Hu et al., 2023): ARC-c (Clark et al., 2018), ARC-e (Clark et al., 2018), BoolQ (Clark et al., 2019), HellaSwag (Zellers et al., 2019), OBQA (Mihaylov et al., 2018), PIQA (Bisk et al., 2020), SIQA (Sap et al., 2019), and WinoGrande (Sakaguchi et al., 2021). Further details are provided in [Appendix B](https://arxiv.org/html/2510.19778v1#A2).

For the purpose of experimentation, we consider all possible ID and OOD combinations involving these datasets by following a round-robin approach. Thus, for each experimental run, a model is fine-tuned on the training set of one of these eight datasets and then evaluated on its test set as well as the test sets of all the remaining seven datasets. Accordingly, eight different experimental runs are performed as part of an experiment for a given density level $\rho$ that is enforced during the fine-tuning of a model with a given algorithm. Performance evaluations on the test set of the dataset used for fine-tuning serve as a measure of ID generalizability while those on the test sets of the remaining datasets (not used for fine-tuning) serve as a measure of the OOD generalizability.

#### 5.2 Model Architectures

We perform our experiments with Gemma 2B (Team et al., 2024) (relatively small-sized) and LLaMA3 8B (Grattafiori et al., 2024) (relatively large-sized) as base models.

#### 5.3 Baselines

For a rigorous evaluation of performance, we compare GaLLoP with several SOTA fine-tuning algorithms for LLMs. We employ Full Fine-Tuning (FFT) as our fine-tuning baseline and the Zero-Shot (Vanilla) model performance as an overall, non fine-tuning (pre-trained) baseline. We also include LoRA (Hu et al., 2022) and DoRA (yang Liu et al., 2024) from the RFT category, SAFT (Nguyen et al., 2024) and SpIEL (Ansell et al., 2024) from the SpFT category, and WiSE-FT (Wortsman et al., 2022) and LiNeS (Wang et al., 2025) from the post-training model editing category.

#### 5.4 Evaluation Metrics

Since we consider all possible ID and OOD task combinations to ensure a robust evaluation, a fine-tuning experiment with an algorithm $\mathcal{A}$ and a density level $\rho$ on $N^{D}$ datasets involves $N^{D}$ experimental runs, such that, in each run $r$, fine-tuning is performed on a dataset $\mathcal{D}^{f_{r}}$. For a given experimental run $r$, we evaluate the ID and OOD performance of all the fine-tuned models using ID accuracy and OOD accuracy which are defined as follows:

$$ $\text{Accuracy}_{r}^{\text{ID}}=\text{accuracy($\mathcal{D}_{test}^{f_{r}}$)}\quad;\quad\text{Accuracy}_{r}^{\text{OOD}}=\dfrac{1}{N^{D}-1}\sum\limits_{\begin{subarray}{c}n=1\\ n\neq f_{r}\end{subarray}}^{N^{D}}\text{accuracy($\mathcal{D}_{test}^{n}$)},$ (5) $$

where, $\text{accuracy}(\mathcal{D}_{test})$ computes the percentage of correct responses generated by a fine-tuned model on the test set $\mathcal{D}_{test}$ of a dataset $\mathcal{D}$.

In addition to the standard accuracy metrics, we introduce two new metrics, the Forget Ratio and the Collapse Rate, which aim to quantify the extent of catastrophic forgetting and memorization incurred upon fine-tuning (respectively). For a given experimental run $r$, while fine-tuning leads to performance improvements on the (ID) downstream task, it may result in the degradation of zero-shot (vanilla) performance on the remaining OOD tasks due to the loss of pre-trained knowledge, i.e., catastrophic forgetting. Accordingly, we define the forget ratio as a measure of this relative drop in OOD performance such that:

$$ $\text{Forget Ratio}_{r}=\max\left(0,\dfrac{\text{Accuracy}_{\text{Vanilla},\,r}^{\text{OOD}}-\text{Accuracy}_{r}^{\text{OOD}}}{\text{Accuracy}_{\text{Vanilla},\,r}^{\text{OOD}}}\right),$ (6) $$

where, $\text{Accuracy}_{\text{Vanilla},\,r}^{\text{OOD}}$ refers to the accuracy of the zero-shot (vanilla) model on the OOD test sets for the $r\textsuperscript{th}$ experimental run. From the above equation, it follows that gains in OOD performance, relative to the performance of the vanilla model, lead to a 0% forget ratio as desired.

The collapse rate for a given experimental run $r$ measures the extent to which fine-tuning results in severe memorization of patterns present in $\mathcal{D}^{f_{r}}$. It is computed by determining the total number of OOD datasets, on the test sets of which, the accuracy drops to $\approx 0\%$ (indicative of a complete collapse) and is hence, defined as follows:

$$ $\text{Collapse Rate}_{r}=\sum\limits_{\begin{subarray}{c}n=1\\ n\neq{f_{r}}\end{subarray}}^{N^{D}}\mathbbm{1}[\lfloor\text{accuracy}({\mathcal{D}_{test}^{n}})\rfloor=0\%],$ (7) $$

where, $\mathbbm{1}[.]$ denotes the indicator function which evaluates to 1 when its argument is True and 0 otherwise.

For each fine-tuning algorithm $\mathcal{A}$ and density level $\rho$, the obtained performance and the extent of catastrophic forgetting and memorization incurred across the entire experiment consisting of $N^{D}$ experimental runs is given by the average of the aforementioned four metrics across all the runs.

#### 5.5 Implementation Details

We perform all our experiments using Torchtune (torchtune maintainers & contributors, 2024) and Huggingface’s PEFT library (Mangrulkar et al., 2022). We use NVIDIA RTX A6000 and/or NVIDIA RTX 6000 Ada GPUs with 48 GB of internal memory and perform mixed-precision (using the BF16 datatype), distributed fine-tuning of all our models (except SpIEL, which can be only run on a single GPU (Ansell et al., 2024)) using Fully Sharded Data Parallel (FSDP) (Zhao et al., 2023), activation checkpointing, and gradient accumulation. To ensure a fair comparison, we apply each fine-tuning algorithm across all the transformer layers and maintain the same density level ($\rho$) for a given experiment. We explore four density levels: {0.24%, 0.47%, 0.93%, 1.85%} for LLaMA3 8B, and {0.37%, 0.73%, 1.45%, 2.86%} for Gemma 2B which correspond to ranks {8, 16, 32, 64} used for reparametrized fine-tuning. Further details on the hyperparameters are given in [Appendix C](https://arxiv.org/html/2510.19778v1#A3).

### 6 Results and Discussion

#### 6.1 ID and OOD Accuracy

[Figure 3](https://arxiv.org/html/2510.19778v1#S6.F3) shows the averaged ID and OOD accuracies of models fine-tuned with GaLLoP against those of the vanilla models and models fine-tuned and/or edited with the competing algorithms (per-run ID and OOD accuracies are discussed in detail in [Section E.1](https://arxiv.org/html/2510.19778v1#A5.SS1) of [Appendix E](https://arxiv.org/html/2510.19778v1#A5)).

Figure: Figure 3: a) LLaMA3 8B models fine-tuned with GaLLoP form a dominant Pareto front for both ID and OOD performance (on average) over all the models fine-tuned and/or edited with the competing algorithms across all density levels. b) Gemma 2B models fine-tuned with GaLLoP attain consistently high and balanced ID and OOD performance (on average) across all density levels.
Refer to caption: x4.png

LLaMA3 8B and Gemma 2B models fine-tuned with GaLLoP attain high ID and OOD accuracies (on average) while maintaining relatively balanced ID and OOD performance across all the density levels. In fact, LLaMA3 8B models fine-tuned with GaLLoP form a dominant Pareto front for both ID and OOD performance over all the other fine-tuned and/or edited models. Models fine-tuned with GaLLoP consistently surpass those fine-tuned with SAFT with a high average margin of roughly 10% (for both ID and OOD performance), which only narrows down for the highest density level due to *high gradient dilution* and *low-magnitude dilution*. With the increase in the density level, parameters with a relatively higher pre-trained magnitude and lower gradient magnitude also fall into the ‘high gradient and low-magnitude’ category, resulting in an overlap between the set of parameters selected by SAFT and GaLLoP. Nevertheless, as is observed, GaLLoP is more efficient in its selection of parameters and would still form a performance upper bound over SAFT even as $\rho\rightarrow 100\%$ (asymptotic limit), particularly because it would still select a larger/at least as large a concentration of low-magnitude high gradient parameters than/as the latter.

While models fine-tuned with SpIEL show high ID accuracies, they perform poorly on OOD tasks with a huge average gap ($\gtrapprox 30\%$) in their own ID and OOD accuracies (on average), which widens with the increase in the density level. Contrary to the other SpFT methods, SpIEL iteratively selects parameters, potentially updating a much larger number of parameters overall. Hence, it leads to increasingly high overfitting on the in-domain distribution with the increase in the density level. Models fine-tuned with RFT techniques also exhibit high levels of overfitting since all the newly introduced trainable parameters are fine-tuned on the training set. Further, while the ID and OOD accuracies obtained via RFT are greater than those obtained via GaLLoP for Gemma 2B for the first two density levels, these gains are only confined to certain datasets and not to others due to catastrophic forgetting and memorization, as we show subsequently in [Section 6.2](https://arxiv.org/html/2510.19778v1#S6.SS2) and [Section 6.3](https://arxiv.org/html/2510.19778v1#S6.SS3).

Moreover, the performance of FFTed models is highly dependent on their zero-shot performance. While FFT works quite well for the small Gemma 2B model by yielding high performance levels comparable to those yielded by GaLLoP, it completely fails for the 4X larger LLaMA3 8B model. Overtraining, i.e., considerably higher pre-training (6T pre-training tokens for Gemma 2B (Team et al., 2024) versus 15T pre-training tokens for LLaMA3 8B (Grattafiori et al., 2024)), makes models much more sensitive to parameter updates, leading to severe catastrophic forgetting and losses in OOD as well as ID generalizability (Kumar et al., 2022; Springer et al., 2025). In fact, this is also the reason why the performance gap between GaLLoP and the competing algorithms decreases for Gemma 2B as compared to LLaMA3 8B. However, GaLLoP exhibits superior performance in both pre-training regimes which implies that it is robust to overtraining, a pre-training regime wherein the competing algorithms simply fail. Finally, the fine-tuned performance dependence and meagre performance improvements (*if any*) yielded by WiSE-FT and LiNeS defeats the very purpose of these post-training model editing techniques which were developed with an aim to provide higher robustness to generalization while avoiding the complexities of fine-tuning.

#### 6.2 Catastrophic Forgetting

[Figure 4](https://arxiv.org/html/2510.19778v1#S6.F4) shows the averaged forget ratios of models fine-tuned with GaLLoP against those fine-tuned and/or edited with the competing algorithms (per-run forget ratios are discussed in [Section E.2](https://arxiv.org/html/2510.19778v1#A5.SS2) of [Appendix E](https://arxiv.org/html/2510.19778v1#A5)). In an ideal scenario, the forget ratio must be zero since fine-tuning a model must not lead to any loss in the pre-trained knowledge stored in the model.

Figure: Figure 4: Models fine-tuned with GaLLoP show 0% forget ratios across all density levels.
Refer to caption: x6.png

LLaMA3 8B and Gemma 2B models fine-tuned with GaLLoP do not undergo catastrophic forgetting since they consistently show 0% forget ratios. In contrast, all the competing algorithms show high forget ratios which may even take on increasingly high values with the increase in the density level due to overfitting. In general, for all competing algorithms, fine-tuned Gemma 2B models show significantly decreased forget ratios as compared to their LLaMA3 8B counterparts. While this does happen because of overtraining, there are, in actuality, *two sides* of the same coin. While lesser pre-training of Gemma 2B (as compared to LLaMA3 8B) lowers the sensitivity of updates to its parameters and allows fine-tuning it to be more stable and performant (which decreases the risk of catastrophic forgetting) (Springer et al., 2025), it also leads to the decreased and (here) near-zero, vanilla (zero-shot) performance of the former as compared to the latter, in the first place itself (see [Figure 15](https://arxiv.org/html/2510.19778v1#A5.F15) in [Appendix E](https://arxiv.org/html/2510.19778v1#A5)). Since forget ratios are defined relative to vanilla performance ([Equation 6](https://arxiv.org/html/2510.19778v1#S5.E6)), even though the OOD performance of certain fine-tuned Gemma 2B models is quite low, it never goes below that of their vanilla counterpart, which leads to all of them attaining a 0% forget ratio. Nevertheless, these fine-tuning algorithms may lead to a more severe phenomenon which impairs generalizability: *memorization*. This forms the subject of our subsequent discussion.

#### 6.3 Memorization

[Figure 5](https://arxiv.org/html/2510.19778v1#S6.F5) shows the total collapse rates of models fine-tuned with GaLLoP against those fine-tuned and/or edited with the competing algorithms. In an ideal scenario, the collapse rate must be zero since fine-tuning a model must not lead to the memorization of any kind of patterns present in the dataset used for fine-tuning it.

Figure: Figure 5: Models fine-tuned with GaLLoP show 0% collapse rates across all density levels.
Refer to caption: x8.png

LLaMA3 8B and Gemma 2B models fine-tuned with GaLLoP and SAFT exhibit 0% collapse rates across all density levels. Combined with the dominant ID as well as OOD performance and 0% forget ratios exhibited by models fine-tuned with GaLLoP over those fine-tuned with SAFT (see [Figure 3](https://arxiv.org/html/2510.19778v1#S6.F3) and [Figure 4](https://arxiv.org/html/2510.19778v1#S6.F4)), it is clear that fine-tuning models with GaLLoP allows for the attainment of high yet balanced generalizability.

For the other algorithms, fine-tuned LLaMA3 8B models show higher collapse rates than their Gemma 2B counterparts due to overtraining. Furthermore, while memorization inevitably occurs due to overfitting, it can manifest in different ways. Throughout our experiments, the most dominant form of memorization observed by us is that of the memorization of the response format of the dataset used for fine-tuning. With the increase in the density level, this kind of memorization leads to models fine-tuned with these algorithms increasingly failing on an OOD task which does not share the same response format as the ID task. Another, more severe form of memorization seems to be more pervasive since it affects the performance of fine-tuned LLaMA3 8B models across all the datasets (ID as well as OOD) irrespective of whether they share response formats or not: memorization of the most frequently occurring words/phrases in the fine-tuning dataset. This leads to the generation of repetitive sequences as answers and consequently, degrades their intelligibility. Since we find that repetition is only restricted to RFT and does not occur on performing SpFT, we attribute its occurrence to the fact that the former class of algorithms restrict fine-tuning to be performed on newly introduced parameters, tied to specific positions in the model, which leads to *concerted overfitting* while the latter class of algorithms allow for much more flexibility in fine-tuning via a position-independent selection of parameters to be fine-tuned and lead to *scattered (unstructured) learning*. Finally, LLaMA3 8B models fine-tuned with SpIEL and FFT (and hence, even those edited with WiSE-FT and LiNeS) occasionally undergo the worst form of memorization: generation of the EOS token. In fact, not only FFT but also SpIEL (as explained earlier in [Section 6.1](https://arxiv.org/html/2510.19778v1#S6.SS1)) fine-tunes a much larger number of parameters than the other algorithms and hence, both of them are more prone to lead to instability in the learning dynamics in the overtrained regime which can lead to such a detrimental form of memorization. We discuss all these interesting cases in more detail with representative samples of LLM-generated responses in [Appendix F](https://arxiv.org/html/2510.19778v1#A6).

#### 6.4 Stability

[Figure 6](https://arxiv.org/html/2510.19778v1#S6.F6) shows the boxplots of ID and OOD performance for LLaMA3 8B models fine-tuned with GaLLoP against models fine-tuned with the competing algorithms across 20 different random seeds. We deliberately choose the PIQA dataset here because the FFTed LLaMA3 8B model attains the lowest ID and OOD performance on this dataset (see [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8) in [Appendix E](https://arxiv.org/html/2510.19778v1#A5)). Moreover, we only consider the highest $\rho$ ($=1.85\%$) so as to rigorously analyze performance stability in the overtrained regime with the largest examined number of update-sensitive parameters. Note that we do not consider editing techniques here since their stability is inherently dependent upon the stability of the fine-tuned model (see [Section 6.1](https://arxiv.org/html/2510.19778v1#S6.SS1)). More details are given in [Appendix G](https://arxiv.org/html/2510.19778v1#A7).

Figure: Figure 6: LLaMA3 8B models fine-tuned with GaLLoP are the most stable and consistently attain the highest ID and OOD accuracies across 20 different random seeds upon fine-tuning on the PIQA dataset with the highest density level ($\rho=1.85\%$).
Refer to caption: x10.png

Models fine-tuned with GaLLoP consistently attain the highest median ID and OOD accuracies with the least interquartile ranges. Furthermore, the difference between the farthest outlier and median performance is amongst the lowest for GaLLoP and never falls below the lowest performance level of SAFT. Hence, fine-tuning with GaLLoP leads to the highest performance stability. In contrast, models fine-tuned with competing algorithms show high performance instability and lower median accuracies, with instability being the highest on performing RFT or FFT (Dodge et al., 2020; Mosbach et al., 2021). Directly leveraging low intrinsic dimensionality by infusing sparsity (as in SpFT) effectively regularizes fine-tuning as compared to reparametrization (as in RFT) which does not constrain updates to the newly introduced low-rank matrices and hence, leads to instability.

### 7 Conclusion

In this work, we have thus developed a novel SpFT technique named GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters which enhances the ID as well as the OOD generalizability of models, prevents catastrophic forgetting and memorization, ensures robustness to overtraining, and stabilizes performance. Nevertheless, as is the case for other SpFT techniques, GaLLoP leads to unstructured sparsity. Accelerating unstructured fine-tuning poses a challenge for current hardware that is optimized for performing dense and/or structured computations (Hooker, 2021; Nguyen et al., 2024). An interesting direction for future work could therefore be to perform densification of this unstructured sparsity by following an aggregation scheme (He et al., 2025) so as to make it more structured (only) for fine-tuning and further increase the memory and compute efficiency of GaLLoP.

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## Appendix

### Appendix A Practical Implementation of GaLLoP

Following the method outlined in [Section 4](https://arxiv.org/html/2510.19778v1#S4), in practice, since we fine-tune LLMs with billions of parameters, sorting the corresponding set of billions of scores in order to compute the score threshold $s_{t}$ (see [Equation 4](https://arxiv.org/html/2510.19778v1#S4.E4)) is computationally inefficient. Therefore, we perform layer-wise uniform random sampling of the scores and utilize only a small proportion $s$ of the total number of scores in order to compute $s_{t}$.

Accordingly, we now use a more specific, layer-wise notation for the model to be fine-tuned.

Consider a deep neural network model with $L$ layers in total (1 input layer of width $p$, $L-2$ hidden layers of width $k$, and 1 output layer of width $q$), represented by $\bm{y}=F_{\{\bm{\Theta^{l}}\}_{l=1}^{L}}(\bm{x})$, such that the parameter matrices $\bm{\Theta}^{l}$ possess the following set of dimensions:

$$ $\displaystyle\bm{\Theta}^{1}$ $\displaystyle\in\mathbb{R}^{p\times k}$ $\displaystyle\bm{\Theta}^{l}$ $\displaystyle\in\mathbb{R}^{k\times k}\quad\forall\quad l\in\{2,\dots,L-1\}$ $\displaystyle\bm{\Theta}^{L}$ $\displaystyle\in\mathbb{R}^{k\times q}$ $$

This model is to be fine-tuned on a dataset $\mathcal{D}={\{(\bm{x}_{n},\bm{y}_{n})\}}_{n=1}^{N}$, where, $\bm{x}_{n}\in\mathbb{R}^{P}$ and $\bm{y}_{n}\in\mathbb{R}^{Q}$.

In line with this notation, [Equation 1](https://arxiv.org/html/2510.19778v1#S4.E1), [Equation 2](https://arxiv.org/html/2510.19778v1#S4.E2), and [Equation 3](https://arxiv.org/html/2510.19778v1#S4.E3) can be re-written as follows:

$$ $\displaystyle\bm{G}^{l}$ $\displaystyle=\dfrac{1}{d_{s}N}\sum_{n=1}^{d_{s}N}\nabla_{\bm{\Theta}^{l}}\mathcal{L}(\bm{x}_{n},\bm{y}_{n};\{\bm{\Theta}^{l}\}_{l=1}^{L}),$ (8) $\displaystyle\bm{S}^{l}$ $\displaystyle=\left(\dfrac{\text{abs}(\bm{G}^{l})}{\text{abs}(\bm{\Theta}^{l})+\epsilon}\right),$ (9) $\displaystyle\bm{M}_{ij}^{l}$ $\displaystyle=\begin{cases}1&\text{if }\bm{S}_{ij}^{l}\geq s_{t},\\ 0&\text{otherwise,}\end{cases}$ (10) $$

where, abs(.) computes the element-wise absolute value of a matrix.

Now, on performing the layer-wise uniform random sampling of scores (with a small proportion $s$ of the total number of scores), since the full set of scores is still required for the computation of the binary mask (note that an element-wise comparison: $\mathcal{O}({D})$, is much less compute intensive than sorting: $\mathcal{O}({D\log{D}})$, for large $D$), we modify [Equation 8](https://arxiv.org/html/2510.19778v1#A1.E8), [Equation 9](https://arxiv.org/html/2510.19778v1#A1.E9), and [Equation 10](https://arxiv.org/html/2510.19778v1#A1.E10) such that for each layer $l$, $\bm{G}^{l}$, $\bm{S}^{l}$, and $\bm{M}^{l}$ respectively become:

$$ $\displaystyle\bm{G}^{l}$ $\displaystyle=\left(\dfrac{\dfrac{1}{d_{s}N}\sum\limits_{n=1}^{d_{s}N}\text{abs}(\nabla_{\bm{\Theta}^{l}}\mathcal{L}(\bm{x}_{n},\bm{y}_{n};\{\bm{\Theta}^{l}\}_{l=1}^{L}))}{\text{abs}(\bm{\Theta}^{l})+\epsilon}\right),$ (11) $\displaystyle\bm{S}^{l}$ $\displaystyle\overset{{s}}{\sim}\mathcal{U}\left(\bm{G}^{l}\right),$ (12) $\displaystyle\bm{M}^{l}$ $\displaystyle=\begin{cases}1&\text{if }\bm{G}^{l}\geq s_{t},\\ 0&\text{otherwise.}\end{cases}$ (13) $$

Moreover, since we now modify the gradients *in place* using [Equation 11](https://arxiv.org/html/2510.19778v1#A1.E11) and instead of storing all the $D$ scores (as in [Equation 2](https://arxiv.org/html/2510.19778v1#S4.E2)), we now store only $s\%$ of them (as in [Equation 12](https://arxiv.org/html/2510.19778v1#A1.E12)), we now save on $(100-s)\%$ of the memory as well.

Throughout our experiments (see [Figure 7](https://arxiv.org/html/2510.19778v1#A1.F7) for representative cases), we observe that with a dataset sample proportion ($d_{s}$) of 0.5, sampling only $s=10\%$ of the scores to compute $s_{t}$ allows us to obtain the required $\rho\%$ of the parameters above the threshold which are to be selected for fine-tuning, i.e., the effective density level $\rho_{eff}$ matches the required density level $\rho$. This drastically reduces the compute and memory requirements of GaLLoP and hence, makes it highly efficient.

An algorithmic implementation of GaLLoP is given in [Algorithm 1](https://arxiv.org/html/2510.19778v1#algorithm1).

Figure: Figure 7: Representative experiments show that sampling only $s=10\%$ of the scores allows us to attain a stable effective density level $\rho_{eff}$ which matches the required density level $\rho$ while drastically reducing the memory and compute requirements of GaLLoP.
Refer to caption: x11.png

Figure: Algorithm 1 GaLLoP

### Appendix B Datasets

A detailed overview of the eight commonsense reasoning datasets which have been used throughout our experiments is as follows:

- •
ARC-c: The AI2 Reasoning Challenge (ARC) dataset consists of natural, grade-school level science questions, authored for standardized tests taken by humans. ARC-c is the Challenge Set of this question bank, containing only those questions which have been incorrectly answered by both a retrieval-based and a word co-occurrence algorithm. Hence, high performance on this dataset requires AI models to possess advanced reasoning capabilities (Clark et al., 2018).
- •
ARC-e: The Easy Set of the ARC dataset which consists of the questions remaining in the ARC dataset post the formation of the Challenge Set (Clark et al., 2018).
- •
BoolQ: A dataset of naturally occurring, True/False (boolean) questions which have been formed from queries directed to the Google search engine. It requires AI models to utilize complex, non-factoid information for solving them (Clark et al., 2019). Note that the version of the BoolQ dataset used by us – which is created by Hu et al. (2023) – does not include the (context) passages alongside the questions at all.
- •
HellaSwag: The Harder Endings, Longer contexts, and Low-shot Activities for Situations With Adversarial Generations dataset tests the robustness of AI models towards commonsense Natural Language Inference (NLI). It comprises questions formed from the ActivityNet captions dataset (Krishna et al., 2017) and the online WikiHow manuals with challenging, incorrect answer options obtained via Adversarial Filtering (Zellers et al., 2019).
- •
OBQA: The OpenBookQA dataset tests the multi-hop reasoning ability of AI models in answering questions based on elementary-level science facts and commonsense knowledge. Note that the version of the OBQA dataset used by us – which is created by Hu et al. (2023) – does not include the (open book) scientific facts alongside the questions at all (Mihaylov et al., 2018).
- •
PIQA: The Physical Interaction: Question Answering dataset tests the physical commonsense of AI models by requiring knowledge of the physical properties of objects used in day-to-day life by humans to answer the ‘how-to’ questions contained in it. Syntactically and topically similar semantic perturbations or alternative solutions have been introduced by annotators to counteract the possibility of spurious biases assisting AI models in achieving high performance (Bisk et al., 2020).
- •
SIQA: The Social Intelligence Question Answering dataset tests the social and emotional intelligence of AI models with regards to everyday situations. Some incorrect answer options are obtained via question-switching around the same context so as to minimize the occurrence of stylistic artifacts arising from the cognitive biases of human annotators which could otherwise be exploited by an AI model for obtaining high performance (Sap et al., 2019).
- •
WinoGrande: This large-scale fill-in-the-blank dataset tests pronoun resolution-based commonsense reasoning capabilities of AI models and is unsolvable upon their complete reliance on embedding associations. Systematic algorithmic bias reduction is performed via AfLite, a lightweight and improved Adversarial Filtering algorithm (Sakaguchi et al., 2021).

The sizes of the training and test splits of each of these datasets as well as their response formats are provided in [Table 1](https://arxiv.org/html/2510.19778v1#A2.T1).

**Table 1: Details of all the datasets (Hu et al., 2023) used across all our experiments.**
| Dataset | Training Set Size | Test Set Size | Response Format |
| --- | --- | --- | --- |
| ARC-c | 1119 | 1172 | the correct answer is answer$\langle\text{ID}\rangle$ |
| ID = {1,2,3,4} |  |  |  |
| ARC-e | 2251 | 2376 | the correct answer is answer$\langle\text{ID}\rangle$ |
| ID = {1,2,3,4} |  |  |  |
| BoolQ | 9427 | 3270 | the correct answer is $\langle\text{BOOL}\rangle$ |
| BOOL = {true/false} |  |  |  |
| HellaSwag | 39905 | 10042 | the correct answer is ending$\langle\text{ID}\rangle$ |
| ID = {1,2,3,4} |  |  |  |
| OBQA | 4957 | 500 | the correct answer is answer$\langle\text{ID}\rangle$ |
| ID = {1,2,3,4} |  |  |  |
| PIQA | 16113 | 1837 | the correct answer is solution$\langle\text{ID}\rangle$ |
| ID = {1,2} |  |  |  |
| SIQA | 33410 | 1954 | the correct answer is answer$\langle\text{ID}\rangle$ |
| ID = {1,2,3} |  |  |  |
| WinoGrande | 63238 | 1267 | the correct answer is option$\langle\text{ID}\rangle$ |
| ID = {1,2} |  |  |  |

### Appendix C Hyperparameters for Fine-Tuning Algorithms

We fix the maximum input sequence length to 512 in all our experiments and utilize the chunked cross-entropy loss for fine-tuning, so as to save memory by upcasting only a single chunk (token) at a time from BF16 to FP32 while computing the loss. We perform early stopping in order to select the best fine-tuned model checkpoint across the three epochs, based on the ID accuracy on the test-dev set (here, the ID test set serves as the test-dev set for a given experimental run). We set $\alpha=0.5$ for WiSE-FT and $\alpha=\beta=0.5$ for LiNeS following the overall recommendations of their authors (Wortsman et al., 2022; Wang et al., 2025). The specific hyperparameters are as follows:

#### C.1 GaLLoP and SAFT

[Table 2](https://arxiv.org/html/2510.19778v1#A3.T2) shows the hyperparameter configurations employed upon performing fine-tuning with GaLLoP and SAFT. We use a low learning rate of 2e-5 in order to prevent divergences during fine-tuning.

**Table 2: Hyperparameter configurations of GaLLoP and SAFT used while fine-tuning LLaMA3 8B and Gemma 2B models. * indicates that Effective Batch Size = (Per-GPU Batch Size $\times$ Gradient Accumulation Steps $\times$ No. of GPUs).**
| Hyperparameters | LLaMA3 8B | Gemma 2B |
| --- | --- | --- |
| Dataset Sample Proportion $d_{s}$ | 0.5 |  |
| Score Sample Proportion $s$ | 0.1 |  |
| Optimizer | Fused AdamW ($\beta_{1}$ = 0.9; $\beta_{1}$ = 0.999) |  |
| Weight Decay | 0 |  |
| Learning Rate | 2e-5 |  |
| Learning Rate Scheduler | Cosine |  |
| Warmup Steps | 100 |  |
| Effective Batch Size* | 16 |  |
| Per-GPU Batch Size | 4 |  |
| Gradient Accumulation Steps | 1 | 2 |
| No. of GPUs | 4 | 2 |
| Epochs | 3 |  |

#### C.2 SpIEL

[Table 3](https://arxiv.org/html/2510.19778v1#A3.T3) shows the hyperparameter configurations employed upon performing fine-tuning with SpIEL. Most of these are in line with those mentioned in (Ansell et al., 2024). However, unlike Ansell et al. (2024) and just like with GaLLoP and SAFT, we find that a lower learning rate works better since it prevents divergences during fine-tuning. Moreover, during the course of our experiments, we find that adding weight decay upon fine-tuning with SpIEL does not help. Upon exploring the addition of weight decay from amongst the following four values: {0, 3, 10, 30} (same as those examined by Ansell et al. (2024)) while fine-tuning LLaMA3 8B, we find that adding any amount of weight decay leads to a comparable/slightly-lowered performance with/than a zero weight decay. Hence, we do not use weight decay while fine-tuning models using SpIEL.

**Table 3: Hyperparameter configurations of SpIEL used while fine-tuning LLaMA3 8B and Gemma 2B models. * indicates that Effective Batch Size = (Per-GPU Batch Size $\times$ Gradient Accumulation Steps $\times$ No. of GPUs).**
| Hyperparameters | LLaMA3 8B | Gemma 2B |
| --- | --- | --- |
| Optimizer | AdamW ($\beta_{1}$ = 0.9; $\beta_{1}$ = 0.999) |  |
| Weight Decay | 0 |  |
| Learning Rate | 2e-5 |  |
| Learning Rate Scheduler | Linear |  |
| Warmup Ratio | 0.03 |  |
| Effective Batch Size | 16 |  |
| Per-GPU Batch Size | 16 |  |
| Gradient Accumulation Steps | 1 |  |
| No. of GPUs | 1 |  |
| Epochs | 3 |  |

#### C.3 FFT

[Table 4](https://arxiv.org/html/2510.19778v1#A3.T4) shows the hyperparameter configurations employed upon performing fine-tuning with FFT. Just like with GaLLoP and SAFT, we use a low learning rate of 2e-5 in order to prevent divergences during fine-tuning.

**Table 4: Hyperparameter configurations of FFT used while fine-tuning LLaMA3 8B and Gemma 2B models. * indicates that Effective Batch Size = (Per-GPU Batch Size $\times$ Gradient Accumulation Steps $\times$ No. of GPUs).**
| Hyperparameters | LLaMA3 8B | Gemma 2B |
| --- | --- | --- |
| Optimizer | Fused AdamW ($\beta_{1}$ = 0.9; $\beta_{1}$ = 0.999) |  |
| Weight Decay | 0 |  |
| Learning Rate | 2e-5 |  |
| Learning Rate Scheduler | Cosine |  |
| Warmup Steps | 100 |  |
| Effective Batch Size | 16 |  |
| Per-GPU Batch Size | 4 |  |
| Gradient Accumulation Steps | 1 |  |
| No. of GPUs | 4 |  |
| Epochs | 3 |  |

#### C.4 LoRA and DoRA

[Table 5](https://arxiv.org/html/2510.19778v1#A3.T5) and [Table 6](https://arxiv.org/html/2510.19778v1#A3.T6) show the hyperparameter configurations employed upon performing fine-tuning with LoRA and DoRA (respectively). Most of these are in line with those mentioned in (yang Liu et al., 2024). Unlike GaLLoP and SAFT, we observe that a low learning rate of 2e-5 slows down learning and results in decreased ID and OOD performance for both LoRA and DoRA. Hence, we use the learning rates of 3e-4 and 1e-4 suggested by yang Liu et al. (2024) for faster (and divergence-free) learning and better performance for LoRA and DoRA (respectively). Moreover, during the course of our experiments, we find that adding dropout upon fine-tuning with LoRA and DoRA does not help. Upon exploring the addition of dropout from amongst the following four values: {0, 0.05, 0.10, 0.20} while fine-tuning Gemma 2B, we find that adding any amount of dropout leads to a comparable/slightly-lowered performance with/than the case when no dropout is used. Hence, we do not use dropout while fine-tuning models using LoRA and DoRA.

**Table 5: Hyperparameter configurations of LoRA used while fine-tuning LLaMA3 8B and Gemma 2B models. * indicates that Effective Batch Size = (Per-GPU Batch Size $\times$ Gradient Accumulation Steps $\times$ No. of GPUs).**
| Hyperparameters | LLaMA3 8B | Gemma 2B |
| --- | --- | --- |
| Optimizer | Fused AdamW ($\beta_{1}$ = 0.9; $\beta_{1}$ = 0.999) |  |
| Weight Decay | 0.01 |  |
| Learning Rate | 3e-4 |  |
| Learning Rate Scheduler | Cosine |  |
| Warmup Steps | 100 |  |
| Effective Batch Size* | 16 |  |
| Per-GPU Batch Size | 4 |  |
| Gradient Accumulation Steps | 1 | 2 |
| No. of GPUs | 4 | 2 |
| Epochs | 3 |  |
| Target Modules | q_proj, k_proj, v_proj, up_proj, down_proj |  |

**Table 6: Hyperparameter configurations of DoRA used while fine-tuning LLaMA3 8B and Gemma 2B models. * indicates that Effective Batch Size = (Per-GPU Batch Size $\times$ Gradient Accumulation Steps $\times$ No. of GPUs).**
| Hyperparameters | LLaMA3 8B | Gemma 2B |
| --- | --- | --- |
| Optimizer | Fused AdamW ($\beta_{1}$ = 0.9; $\beta_{1}$ = 0.999) |  |
| Weight Decay | 0.01 |  |
| Learning Rate | 1e-4 |  |
| Learning Rate Scheduler | Cosine |  |
| Warmup Steps | 100 |  |
| Effective Batch Size* | 16 |  |
| Per-GPU Batch Size | 4 |  |
| Gradient Accumulation Steps | 1 | 2 |
| No. of GPUs | 4 | 2 |
| Epochs | 3 |  |
| Target Modules | q_proj, k_proj, v_proj, up_proj, down_proj |  |

### Appendix D Hyperparameters for Decoding

The values of the hyperparameters used for decoding the LLM-generated outputs are provided in [Table 7](https://arxiv.org/html/2510.19778v1#A4.T7) and have been taken *as-is* from (Hu et al., 2023) so as to maintain consistency with prior work.

**Table 7: Hyperparameters for decoding the output generated by the fine-tuned models into text. Values have been taken as-is from (Hu et al., 2023).**
| Hyperparameters | Values |
| --- | --- |
| Temperature $T$ | 0.1 |
| $k$ (as in top-$k$) | 40 |
| $p$ (as in top-$p$) | 0.75 |
| Number of Beams (as in Beam Search) | 4 |

### Appendix E Per-Run Results of our Experiments

#### E.1 ID and OOD Accuracy

For LLaMA3 8B, models fine-tuned on the ARC-c and ARC-e datasets using GaLLoP form a dominant Pareto front for both ID as well as OOD performance over models fine-tuned and/or edited on the same datasets using the other algorithms (respectively; see [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8) and [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8)). While models fine-tuned on the HellaSwag, OBQA, PIQA, and WinoGrande datasets using SpIEL outperform those fine-tuned on the same datasets using GaLLoP by a slight margin on the ID test sets, models fine-tuned with GaLLoP form a dominant Pareto front on the corresponding OOD test sets on which the models fine-tuned with SpIEL perform quite poorly and with a performance drop that widens as we approach the higher density levels (respectively; see [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8), [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8), [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8), and [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8)). On the SIQA dataset, the model fine-tuned with SAFT is quite competitive and has an almost similar/comparable level of performance with the model fine-tuned with GaLLoP (see [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8)).

Figure: Figure 8: LLaMA3 8B models fine-tuned with GaLLoP attain the most stable and highest/high levels of ID and OOD performance across all density levels when fine-tuning is performed on a) ARC-c, b) ARC-e, c) HellaSwag, d) OBQA, e) PIQA, f) WinoGrande, g) SIQA, and h) BoolQ (except OOD).
Refer to caption: x13.png

Figure: Figure 9: While Gemma 2B models fine-tuned on a) ARC-c and b) ARC-e with GaLLoP attain stable and high levels of ID and OOD performance across all density levels, Gemma 2B models fine-tuned on the same datasets with DoRA attain the highest levels of ID and OOD performance across all density levels owing to the two training sets possessing the smallest sizes.
Refer to caption: x21.png

Figure: Figure 10: While Gemma 2B models fine-tuned on a) OBQA, b) BoolQ, and c) PIQA with GaLLoP attain stable and high levels of ID and OOD performance across all density levels, Gemma 2B models fine-tuned with LoRA and DoRA tend to overfit on their moderately-large sized training sets and show drastic ID and/or OOD performance drops.
Refer to caption: x23.png

Figure: Figure 11: While Gemma 2B models fine-tuned on a) SIQA, b) HellaSwag, and c) WinoGrande with GaLLoP attain the most stable and the highest/high levels of ID and OOD performance across all density levels, Gemma 2B models fine-tuned with LoRA or DoRA tend to overfit on their moderately-large/large sized training sets and show drastic ID and/or OOD performance drops.
Refer to caption: x26.png

For Gemma 2B, since pre-training has been performed on a much less number of tokens (= 6T) as compared to LLaMA3 8B (= 15T), there is a significantly lower risk of fine-tuning sensitivity due to overtraining (Springer et al., 2025). Hence, Gemma 2B models fine-tuned with some of the competing PEFT algorithms (LoRA, DoRA, SpIEL) and even FFT (and hence, WiSE-FT and LiNeS) perform much better than their LLaMA3 8B counterparts. However, these models still perform quite poorly when it comes to OOD tasks and display high performance drops as we approach the higher density levels. These drops in performance are not only present for the OOD tasks (LoRA, DoRA, and SpIEL) but are also present for the ID tasks (LoRA and DoRA). Moreover, an important trend is noticeable across all these datasets: overfitting across all the density levels with the increase in the size of the dataset used for fine-tuning. While models fine-tuned with LoRA and DoRA attain higher accuracies as compared to models fine-tuned with GaLLoP on both ID and OOD tasks upon utilizing small datasets (ARC-c and ARC-e; models fine-tuned with LoRA already start exhibiting large OOD performance drops upon increasing the density level for fine-tuning on ARC-e) for fine-tuning (see [Figure 9](https://arxiv.org/html/2510.19778v1#A5.F9)), they tend to overfit and break down with drastic OOD performance drops along with even moderately-high/high ID performance drops for higher density levels as move towards utilizing moderately-large sized datasets (OBQA, BoolQ, PIQA, SIQA, HellaSwag; see [Figure 10](https://arxiv.org/html/2510.19778v1#A5.F10), [Figure 11](https://arxiv.org/html/2510.19778v1#A5.F11), and [Figure 11](https://arxiv.org/html/2510.19778v1#A5.F11)) and completely break down on both the ID and OOD tasks upon fine-tuning on WinoGrande, the largest dataset (see [Figure 11](https://arxiv.org/html/2510.19778v1#A5.F11)). In contrast, models fine-tuned with GaLLoP demonstrate high and stable performance across all density levels and upon fine-tuning on all the datasets (*individually*) with sizes spread across the spectrum, and form a dominant Pareto front over all the other fine-tuned models when fine-tuning is performed on WinoGrande, the largest dataset (see [Figure 9](https://arxiv.org/html/2510.19778v1#A5.F9), [Figure 10](https://arxiv.org/html/2510.19778v1#A5.F10), and [Figure 11](https://arxiv.org/html/2510.19778v1#A5.F11)). This shows that fine-tuning with GaLLoP makes models the most robust to overfitting. Finally, on shifting our focus to models fine-tuned with SAFT, we can clearly see that on average (across all datasets: see [Figure 3](https://arxiv.org/html/2510.19778v1#S6.F3)) as well as individually, across seven out of the eight datasets (see [Figure 9](https://arxiv.org/html/2510.19778v1#A5.F9), [Figure 10](https://arxiv.org/html/2510.19778v1#A5.F10), [Figure 10](https://arxiv.org/html/2510.19778v1#A5.F10), and [Figure 11](https://arxiv.org/html/2510.19778v1#A5.F11)), models fine-tuned with GaLLoP form a dominant Pareto front over models fine-tuned with SAFT.

Finally, for both LLaMA3 8B and Gemma 2B, an important case to note is that of fine-tuning on the BoolQ dataset. While the LLaMA3 8B (except for the highest density level) and Gemma 2B models fine-tuned with GaLLoP consistently outperform the models fine-tuned with SAFT on the ID (BoolQ) test set, the models fine-tuned with SAFT consistently outperform (except for the first two density levels for LLaMA3 8B) the models fine-tuned with GaLLoP on the corresponding OOD test sets (see [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8) and [Figure 10](https://arxiv.org/html/2510.19778v1#A5.F10)). This might potentially be due to the heavily skewed distribution of the correct responses for BoolQ in its own test set (‘True’: 62.171%; ‘False’: 37.829%) which is in consonance with the correct response distribution in its training set (‘True’: 62.304%; ‘False’: 37.686%); ‘True’ is roughly about twice as frequent as ‘False’ for BoolQ. On analyzing the generated responses, we find that models fine-tuned with GaLLoP consistently try to learn what characterizes a ‘False’ response whereas models fine-tuned with SAFT *undesirably* generate ‘True’ as the most frequent response, *albeit incorrectly* (their ID accuracies are generally lower than those of the models fine-tuned with GaLLoP), possibly due to the near-perfect memorization of ‘True’ as the correct response. For LLaMA3 8B, fine-tuning with GaLLoP leads to a huge drop in the prediction rate of ‘True’ (from 66.391% for $\rho$ = 0.93% to 47.073% for $\rho$ = 1.85%) while fine-tuning with SAFT leads to a fairly constant and high prediction rate of ‘True’ (80.764% for $\rho$ = 0.93% and 80.367% for $\rho$ = 1.85%). For Gemma 2B, such a trend can be seen across all density levels in [Figure 12](https://arxiv.org/html/2510.19778v1#A5.F12).

Figure: Figure 12: Gemma 2B models fine-tuned with GaLLoP on the highly skewed BoolQ dataset increasingly learn what characterizes a ‘False’ response while those fine-tuned with SAFT frequently generate ‘True’ as the response potentially due to the memorization of the dominant correct response in BoolQ.
Refer to caption: x29.png

While memorizing and frequently generating ‘True’ allows models fine-tuned with SAFT to easily attain a constant, moderate/moderately-low level OOD accuracy, learning what makes a response ‘False’ seems to require harder effort on the part of models fine-tuned with GaLLoP and they increasingly start to respond with something different than the response format for the OOD tasks: either they generate the answer in words rather than the corresponding option number, or generate an explanation to the answer, or even generate the question itself, or etc. We leave the further examination of this phenomenon for future work.

#### E.2 Catastrophic Forgetting

The per-run forget ratios are shown in [Figure 14](https://arxiv.org/html/2510.19778v1#A5.F14) for fine-tuned and/or edited LLaMA3 8B models and in [Figure 13](https://arxiv.org/html/2510.19778v1#A5.F13) for fine-tuned and/or edited Gemma 2B models.

The fact that fine-tuning LLaMA3 8B models with the runners-up algorithm SAFT results in instability with sudden and high rises/falls in ID and/or OOD performance on all datasets (except BoolQ; see [Figure 8](https://arxiv.org/html/2510.19778v1#A5.F8)) and moderately-high catastrophic forgetting for $\rho=0.47\%$ on the largest dataset (WinoGrande) (see [Figure 14](https://arxiv.org/html/2510.19778v1#A5.F14)) while fine-tuning them with GaLLoP does not — reveals the benefits of GaLLoP’s dual parameter selection criterion. Restricting the selection of high gradient parameters to those with the smallest pre-trained magnitudes leads to increased stability, relatively balanced ID as well as OOD performance, and prevents catastrophic forgetting across all datasets even in the overtrained regime.

Interestingly, upon fine-tuning Gemma 2B models individually on four datasets (ARC-c, ARC-e, OBQA, and SIQA), no catastrophic forgetting occurs (and hence those plots are not shown here). While this follows, *in part*, from the explanation provided in [Section 6.2](https://arxiv.org/html/2510.19778v1#S6.SS2), why this specifically happens for only these four datasets is discussed in detail in the next appendix on memorization ([Appendix F](https://arxiv.org/html/2510.19778v1#A6)).

Finally, as a follow-up to the discussion on the near-zero, vanilla (zero-shot) performance of Gemma 2B as compared to the relatively higher vanilla (zero-shot) performance of LLaMA3 8B (see [Section 6.2](https://arxiv.org/html/2510.19778v1#S6.SS2)), we analyze the responses of the vanilla Gemma 2B and LLaMA3 8B models. Consequently, we observe that while the vanilla LLaMA3 8B model does respond with an answer/answers adhering to the response format (on most datasets), the vanilla Gemma 2B model, in most cases, does not respect the response format while responding or simply repeats the entire question or repeats all the answer choices verbatim from the question used for prompting it. A representative example of the responses generated by both the vanilla models is shown in [Figure 15](https://arxiv.org/html/2510.19778v1#A5.F15).

Figure: Figure 13: Gemma 2B models fine-tuned with GaLLoP show a 0% forget ratio across all density levels when fine-tuning is performed on a) BoolQ, b) HellaSwag, c) PIQA, and d) WinoGrande.
Refer to caption: x30.png

Figure: Figure 14: LLaMA3 8B models fine-tuned with GaLLoP show a 0% forget ratio across all density levels when fine-tuning is performed on a) ARC-c, b) ARC-e, c) HellaSwag, d) OBQA, e) PIQA, f) WinoGrande, g) SIQA, and h) BoolQ.
Refer to caption: x34.png

Figure: Figure 15: The vanilla LLaMA3 8B model generates an answer when prompted with a question from the PIQA dataset while the vanilla Gemma 2B model generates both answers without respecting the answer format when prompted with the same question.

### Appendix F Memorization

Collapse rates and forget ratios do not always reveal the same information; rather, they actually reveal *complementary* information. For instance, even though the LLaMA3 8B models fine-tuned with DoRA possess high forget ratios varying between 10-20% (see [Figure 4](https://arxiv.org/html/2510.19778v1#S6.F4)), they do not undergo extremely high memorization and hence, showcase low collapse rates (see  [Figure 5](https://arxiv.org/html/2510.19778v1#S6.F5)). Additionally, while Gemma 2B models fine-tuned with SpIEL (for the first three density levels) and FFT possess 0% forget ratios (see [Figure 4](https://arxiv.org/html/2510.19778v1#S6.F4)), they do undergo memorization (see [Figure 5](https://arxiv.org/html/2510.19778v1#S6.F5)). Decrease in the extent of memorization on fine-tuning LLaMA3 8B models with DoRA as compared to fine-tuning them with LoRA is likely due to the former’s fine-grained (magnitude and directional) reparametrized update of the overtrained parameter matrix which imparts higher learning capabilities than the latter. Nevertheless, since DoRA is still an RFT technique, all the trainable parameters introduced by it are fine-tuned on the training set which then leads to catastrophic forgetting and moderate levels of memorization. 0% forget ratios versus high collapse rates of Gemma 2B models fine-tuned with SpIEL and FFT follows from our previous discussion on the performance of the vanilla Gemma 2B model (see [Section 6.2](https://arxiv.org/html/2510.19778v1#S6.SS2)). Near-zero performance of the vanilla Gemma 2B model along with the near-zero performance of the same model fine-tuned with SpIEL and FFT yields a 0% forget ratio in line with [Equation 6](https://arxiv.org/html/2510.19778v1#S5.E6). However, an analysis of the responses generated by both of them (vanilla and fine-tuned) reveal striking differences between them with the latter consistently responding with an EOS token (as discussed in [Section 6.3](https://arxiv.org/html/2510.19778v1#S6.SS3)).

When models memorize the response formats of the dataset used for fine-tuning (see [Table 1](https://arxiv.org/html/2510.19778v1#A2.T1) in [Appendix B](https://arxiv.org/html/2510.19778v1#A2) for response formats), it means that while a model fine-tuned on the training set of any one of the following datasets: ARC-c, ARC-e, OBQA, and SIQA (which share the same response format), is increasingly likely to perform well on the test sets of the remaining three OOD datasets (note that this is also the reason why forget ratios equal zero on these datasets for the fine-tuned Gemma 2B models: see [Section E.2](https://arxiv.org/html/2510.19778v1#A5.SS2)), models fine-tuned on any one of the following datasets: BoolQ, HellaSwag, PIQA, and WinoGrande (which possess response formats completely orthogonal to the other datasets), increasingly fail on the test sets of all the corresponding seven OOD datasets.

While repetition of the most frequently occurring words/phrases in the fine-tuning dataset is partly due to the maximum likelihood-based fine-tuning objective (Welleck et al., 2020b), and might also arise due to an unfortunate set of parameters selected for combined deterministic beam-search (Graves, 2012) and random (top-$k$ (Fan et al., 2018) and top-$p$ (Holtzman et al., 2020)) sampling (Shaham & Levy, 2022; Welleck et al., 2020a; Borec et al., 2024) which makes the repetition-encouraging nature dominant during decoding (this is solely because of the parameter values defined by Hu et al. (2023) and enlisted in [Table 7](https://arxiv.org/html/2510.19778v1#A4.T7) in [Appendix D](https://arxiv.org/html/2510.19778v1#A4)), its occurrence seems to also depend upon the type of fine-tuning employed since it only occurs on performing RFT and not SpFT. Following the discussion in [Section 6.3](https://arxiv.org/html/2510.19778v1#S6.SS3), *concerted overfitting*, along with the detrimental effects of maximum likelihood-based fine-tuning, only gets exacerberated in the overtrained regime (Springer et al., 2025) which is why this is only observed for LLaMA3 8B (and not Gemma 2B) models.

While the generation of the EOS token might partly be due to the dominant effect of beam search (over random sampling) in the overtrained regime which consequently might cause high probablities to be assigned to the shortest hypotheses with just the EOS token (Stahlberg & Byrne, 2019), the fact that it only occurs upon fine-tuning LLaMA3 8B models with SpIEL and FFT must also be noted and hence, we attribute it to the tendency of these algorithms to cause instability in the learning dynamics in the overtrained regime.

Representative samples of responses generated by such models, showcasing all the aforementioned forms of memorization, against those generated by models fine-tuned with GaLLoP and SAFT can be seen in [Figure 16](https://arxiv.org/html/2510.19778v1#A6.F16), [Figure 17](https://arxiv.org/html/2510.19778v1#A6.F17), [Figure 18](https://arxiv.org/html/2510.19778v1#A6.F18), and [Figure 19](https://arxiv.org/html/2510.19778v1#A6.F19).

Figure: Figure 16: Gemma 2B models fine-tuned on WinoGrande with GaLLoP, SAFT, SpIEL, FFT and/or edited with WiSE-FT and LiNeS respect ARC-e’s response format whereas those fine-tuned with LoRA and DoRA do not.

Figure: Figure 17: Gemma 2B models fine-tuned on SIQA with GaLLoP and SAFT respect HellaSwag’s response format whereas those fine-tuned and/or edited with the other competing algorithms do not.

Figure: Figure 18: LLaMA3 8B models fine-tuned on ARC-c with GaLLoP, SAFT, FFT and/or edited with WiSE-FT and LiNeS respect OBQA’s response format whereas those fine-tuned with LoRA, DoRA, and SpIEL either generate repetitive text or do not respond (except with the EOS token; $<\text{EOS}>$).

Figure: Figure 19: LLaMA3 8B models fine-tuned on PIQA with GaLLoP and SAFT respect BoolQ’s response format whereas those fine-tuned and/or edited with the other competing algorithms either do not respect the response format and/or generate repetitive text or do not respond (except with the EOS token; $<\text{EOS}>$).

### Appendix G Variability in Forget Ratios and Collapse Rates

[Figure 20](https://arxiv.org/html/2510.19778v1#A7.F20) and [Figure 20](https://arxiv.org/html/2510.19778v1#A7.F20) show the boxplots of forget ratios and collapse rates (respectively) for LLaMA3 8B models fine-tuned with GaLLoP against models fine-tuned with the competing algorithms across 20 different random seeds.

Models fine-tuned with GaLLoP and SAFT consistently attain 0% forget ratios and 0% collapse rates. In contrast, models fine-tuned with SpIEL consistently attain high forget ratios (80 - 100%) and high collapse rates mostly equivalent to a complete failure on all the seven OOD datasets. The extent of variability in their forget ratios and collapse rates is also quite high and never allows them to perform on par/even close to models fine-tuned with GaLLoP on OOD tasks. These observations can possibly be owed to SpIEL’s dynamic parameter selection: variability in random seeds can lead to changes in the candidate parameter set and hence, different sets of parameters being considered for updates at each reselection stage. Models fine-tuned with the RFT techniques also possess high forget ratios and high collapse rates (LoRA and FFT) and/or with high variance in their values (LoRA, DoRA, and FFT) owing to an absence of regularization during fine-tuning.

Figure: Figure 20: LLaMA3 8B models fine-tuned with GaLLoP consistently attain a) 0% forget ratios and b) 0% collapse rates across 20 different random seeds upon fine-tuning on the PIQA dataset with the highest density level ($\rho=1.85\%$).
Refer to caption: x42.png

### Appendix H Ablations on Parameter Selection Criteria

To investigate whether GaLLoP’s dual parameter selection criterion (parameters with high gradients and low-magnitudes) potentially leads to performance benefits over selecting parameters satisfying only one of these two criteria, we conduct an ablation study on Gemma 2B models. [Figure 21](https://arxiv.org/html/2510.19778v1#A8.F21) shows the results of this study with the corresponding averaged ID and OOD accuracies which are reported for all the four density levels. The per-run performance results are shown in [Figure 22](https://arxiv.org/html/2510.19778v1#A8.F22).

Figure: Figure 21: Gemma 2B models fine-tuned with GaLLoP form a dominant Pareto front for both ID and OOD performance (on average) over models fine-tuned by selecting parameters on the basis of either parameter or gradient magnitudes.
Refer to caption: x44.png

Fine-tuning with GaLLoP allows for the attainment of the highest ID and OOD accuracies: both on average and across all the datasets (except OOD accuracies obtained upon fine-tuning on BoolQ: see [Figure 22](https://arxiv.org/html/2510.19778v1#A8.F22) and [Section E.1](https://arxiv.org/html/2510.19778v1#A5.SS1) in [Appendix E](https://arxiv.org/html/2510.19778v1#A5) for an explanation). Further, as can also be seen from [Figure 21](https://arxiv.org/html/2510.19778v1#A8.F21) and as discussed in [Section 3](https://arxiv.org/html/2510.19778v1#S3), fine-tuning high-magnitude parameters leads to no improvements over the performance of the non fine-tuned, vanilla counterpart. In contrast to this, fine-tuning low-magnitude parameters allows models to perform quite well on both ID and OOD tasks. In fact, except for the OOD performance obtained upon fine-tuning with BoolQ (see [Figure 22](https://arxiv.org/html/2510.19778v1#A8.F22); the explanation from [Section E.1](https://arxiv.org/html/2510.19778v1#A5.SS1) in [Appendix E](https://arxiv.org/html/2510.19778v1#A5) applies here as well, *albeit* with lesser OOD performance metrics than the model fine-tuned with GaLLoP), ID and OOD performance levels obtained on fine-tuning low-magnitude parameters interpolate between the corresponding performance levels obtained on fine-tuning parameters with high gradients (as in SAFT; generally forms the lower bound) and fine-tuning low-magnitude parameters with high gradients (as in GaLLoP; forms the upper bound): see [Figure 22](https://arxiv.org/html/2510.19778v1#A8.F22).

Moreover, with increasing density levels, performance obtained on fine-tuning low magnitude parameters generally overtakes that obtained on fine-tuning parameters with high gradients (as in SAFT) and finally, saturates at a performance level comparable to that obtained on fine-tuning with GaLLoP. This illustrates how GaLLoP potentially operates in different density regimes to yield the most superior performance: while the high gradient parameter selection criterion might dominate at lower density levels, the low-magnitude parameter selection criterion becomes increasingly dominant as the density level increases.

Further, as mentioned earlier (see [Section 6.1](https://arxiv.org/html/2510.19778v1#S6.SS1)), *low-magnitude dilution* kicks in as we move closer towards the highest density level because of which we observe a somewhat saturation and convergence in the performance attained by models fine-tuned with GaLLoP and those fine-tuned by selecting parameters with low-magnitudes. This trend of saturation is also reflected in models fine-tuned with SAFT which suggests that *high gradient dilution* starts to set in at that point as well. Effectively, in the asymptotic limit ($\rho\rightarrow 100\%$), as what can also be expected theoretically, the performance of models fine-tuned with static SpFT algorithms such as GaLLoP and SAFT, and models fine-tuned by selecting parameters with low-magnitudes, will converge to the performance of models fine-tuned with the dense FFT algorithm. This hypothesis is also supported by several previous studies wherein it was found that FFT predominantly updates a small fraction of low magnitude parameters for downstream task(s) and utilization of SpFT should be able to recover FFT performance (Chen et al., 2020; Prasanna et al., 2020; Jaiswal et al., 2023; Ramesh et al., 2024). Nevertheless, as can be seen from our experiments, by combining the strengths of high gradients and low-magnitudes, fine-tuning with GaLLoP is expected to continue forming a performance upper bound over other static SpFT algorithms.

Figure: Figure 22: Gemma 2B models fine-tuned with GaLLoP form a dominant Pareto front for both ID and OOD performance over models fine-tuned by selecting parameters on the basis of either parameter or gradient magnitudes when fine-tuning is performed on a) ARC-c, b) ARC-e, c) PIQA, d) SIQA, e) HellaSwag, f) WinoGrande, g) OBQA, and h) BoolQ (except OOD).
Refer to caption: x45.png

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 2
presentation: 2
questions: Fig 3: It is very surprising that OOD performance improves over Vanilla - this is the opposite of forgetting, as it means that fine-tuning on one dataset improves performance on 7 others when doing e.g. LoRA or other such. How is this possible ? It seems to go against what other papers in forgetting show - that fine-tuning on a dataset improves ID but degrades OOD.
soundness: 1
strengths: The paper is clearly written.
summary: Summary: This paper proposes a method to mitigate forgetting, by choosing whether to update a particular parameter based on a score that is its ( ( gradient_magnitude ) / ( magnitude + epsilon) ) - the top "k" highest scoring ones are updated in that iteration and others are not.  

Evaluation of forgetting is done by taking 8 datasets, fine-tuning on one ("IID") and measuring performance on the others ("OOD") - and averaging this over round-robin selection of IID/OOD.
weaknesses: (A) comparisons: Mitigating catastrophic forgetting is a rich field and this paper is missing comparisons against several state of the art methods, for example:
(1) https://arxiv.org/abs/1612.00796 (classic method, works very well on modern LLMs as well)
(2) https://arxiv.org/abs/2407.20999 (another method that selects individual parameters - based on a different logic - to update, instead of updating all parameters)
(3) https://icml.cc/virtual/2025/poster/46655 ( more recent paper and method, contains overview of preceeding)

Indeed this method is only compared against other methods that update fewer parameters, but if the main aim is mitigating catastrophic forgetting then a much more robust comparison against other approaches like the three above, and also others, is needed. 

(B) reasoning: what is the intuition behind this method ? Eg Fig 1 shows that fine-tuning the lowest magnitude weights gives gains, but what about updating a randomly chosen subset of  weights ? 

(C) Novelty: there are many methods that choose only a subset of parameters to update based on values, gradients or a combination thereof; this paper is yet another in that line (albeit with a slightly variant selection logic). The novelty from an ideas perspective is low.

---

confidence: 4
contribution: 2
initial_rating: 2
presentation: 2
questions: 1. The paper assumes that gradient magnitude represents parameter sensitivity and that small-magnitude parameters correspond to more “adjustable” knowledge, but both claims lack theoretical or empirical justification. Could the authors provide supporting evidence such as theoretical relation between $\|\|g\|\|$, Fisher Information, or Hessian-based parameter sensitivity and analyses showing that parameter magnitude indeed aligns with knowledge stability or adaptability in pre-trained models?
2. The ID/OOD setup in this paper is based on cross-dataset evaluation within commonsense reasoning tasks, rather than across distinct domains. Could the authors clarify why this configuration should be regarded as out-of-distribution generalization rather than merely cross-task transfer? Additionally, have the authors examined whether GaLLoP’s advantages persist under more conventional domain-shift OOD settings?
3. Experimental coverage is limited to two baselines of different scales and a single task. Do the authors plan to test on other architectures or modalities to demonstrate general applicability of the proposed criterion?
soundness: 2
strengths: 1. Simple and straightforward design : The proposed scoring criterion is conceptually clear and easy to implement without architectural modification or additional modules.

2. Parameter-efficient fine-tuning : Only a small fraction of parameters (around <2%) are updated, yielding memory-efficient adaptation with no extra trainable layers.

3. Empirical stability : The method shows zero collapse or forgetting ratios across multiple seeds and densities, indicating robustness to optimization noise.
summary: This paper proposes GaLLoP, a sparse fine-tuning method that selects a subset of parameters to update based on the ratio between their gradient magnitude and pretrained weight magnitude. The key idea is that parameters with large gradients (task-relevant) and small pretrained magnitudes (less tied to prior knowledge) can be fine-tuned to improve in-domain (ID) performance while mitigating catastrophic forgetting on out-of-domain (OOD) tasks. Experiments on eight commonsense reasoning datasets show that GaLLoP achieves comparable or better ID/OOD accuracy compared to existing sparse fine-tuning baselines such as SAFT and SpIEL.
weaknesses: 1. Lack of theoretical justification : The claim that gradient magnitude directly represents parameter sensitivity is overstated. Without a connection to curvature-based measures such as the Fisher Information Matrix or Hessian spectrum, it is unclear whether $\|\|g\|\|$ accurately captures parameter importance.

2. Unverified assumption about parameter magnitude : The interpretation that low-magnitude parameters encode less critical or “more adjustable” knowledge is speculative and not theoretically demonstrated. The connection between parameter norm and the nature of stored knowledge seems vague.

3. Non-typical ID/OOD setup : The so-called OOD evaluation is defined only as cross-dataset testing within a single commonsense reasoning benchmark family. This does not constitute a true domain-shift scenario and thus limits claims about generalization.

4. Limited experimental scope : Despite involving eight datasets, the experiments are confined to the commonsense reasoning domain, and only two model scales (Gemma-2B, LLaMA3-8B) are tested. Broader evaluation on diverse task types (e.g., reasoning, factual QA, math) or architectures would strengthen the argument.

5. Marginal gains over baselines : On Gemma-2B, GaLLoP performs nearly identically to SAFT; even on LLaMA3-8B, the reported improvement is modest (see Fig. 8 in Appendix E). The performance advantage appears minor and inconsistent, suggesting that the proposed selection rule may not offer substantial benefits over existing sparse fine-tuning methods.

---

confidence: 3
contribution: 3
initial_rating: 6
presentation: 3
questions: 1) How does the method perform on already sparse LLM models? Such models are increasingly becoming more popular. A small experiment on applying the proposed algorithm to some sparse LLM may provide valuable insight.
 2) What is the effect of running the proposed method over multiple tasks in a sequence. The effect of overfitting and catastrophic forgetting would be more evident.
3) Authors may delve deeper into studying the set of parameters chosen for fine-tuning using the first and the second criteria (namely, low magnitude, and high gradient) respectively. What is the percentage intersection of these sets of parameters?
4) A summary table comparing the performance of the proposed approach with SOTA in terms of accuracy/forgetfullness/density may be reported in the main paper itself.
soundness: 3
strengths: 1) The paper proposes a simple, intuitive, but effective strategy for sparse fine tuning.
2) The strategy is well motivated by related experiments.
3) Exhaustive experimental results are presented to demonstrate the efficacy of the proposed technique.
4) An improvement in out-of-distribution tasks is shown.
summary: The paper presents a method for sparse fine tuning that attempts to avoid catastrophic forgetting while avoiding over fitting on newer tasks. Both in-distribution and out-of-distribution performance is shown to improve. The technique chooses a small subset of parameters that are fine tuned based on two criteria - (i) magnitude of the parameter in the pretrained model, (ii) and gradient of the parameter while fine tuning. A small data set sample is used for fine tuning to estimate the later value. The idea is simple but is well motivated by experimental results. Empirical results demonstrate the superiority of the proposed technique over related SpFT techniques.
weaknesses: 1) The idea is only experimentally demonstrated to work well. Theoretical justifications are missing. There are a number of view points and observations in literature about the choice of parameters while fine tuning. The role of magnitude of a parameter in determining its importance is not unanimously agreed upon. Similarly, gradient value while backpropagating on a small batch of data might be too noisy as a signal to score parameter importance. LoRA and related low-dimension projection techniques techniques looks at spectral properties of the parameter matrix rather than the magnitude and gradients. Other approaches like the ones based on expander graphs consider network connectivity rather than parameter weights. Authors may discuss/support the proposed algorithm in more "theoretical" term.
2) The efficacy of the proposed technique in a continual learning scenario is not discussed. Magnitude and gradient based parameter selection may either be erroneous or yield a low sparsification ratio when performed in sequence of rounds on multiple tasks. Experiments need to be presented to counter this claim. Such a scenario was mentioned as a motivation in the introduction. 
3) Because of the rather dynamic and unstructured nature of the proposed parameter selection technique the method may not align well with hardware acceleration thus defeating the benefits of sparse fine tuning.

---

confidence: 4
contribution: 2
initial_rating: 4
presentation: 2
questions: See Weaknesses above.
soundness: 2
strengths: 1. The paper’s core idea—selecting a sparse set of parameters that are simultaneously high-gradient and low-magnitude—creatively fuses two complementary signals to target updates that help in-domain learning without erasing pre-trained knowledge, and it is implemented in a clean two-phase procedure.  It also contributes two evaluation diagnostics, forget ratio and collapse rate, that formalize catastrophic forgetting and severe memorization in a way that is easy to compute and compare across methods.  

2. The empirical study is broad and careful: eight commonsense datasets, two model families, and strong baselines spanning full fine-tuning, parameter-efficient methods, and editing techniques.  Results consistently show a dominant ID/OOD Pareto front for GaLLoP, with particularly strong averages on LLaMA-3 8B and balance on Gemma-2B. Reproducibility is helped by explicit algorithmic pseudocode and detailed hyperparameters.

3. The exposition is easy to follow

4. Addressing the ever-present tension between adaptation and retention, the method delivers strong OOD gains while curbing overfitting that plagues several popular baselines—an outcome that matters for reliable deployment of fine-tuned LLMs.  Because GaLLoP is simple, model-agnostic, and efficient, it lowers the barrier to adopting sparse fine-tuning in practice.
summary: GaLLoP is a sparse fine-tuning method that updates only parameters that are simultaneously highly task-relevant (large gradients) and minimally disruptive to pre-trained knowledge (small magnitudes), boosting both in- and out-of-distribution generalization.
It runs in two phases—score-and-select a small subset using gradient accumulation over a data slice, then fine-tune only those while masking the rest—and is model-agnostic. Across LLaMA-3 8B and Gemma-2B on eight commonsense datasets, it typically forms a dominant ID/OOD Pareto front and shows strong stability across seeds compared to LoRA, DoRA, SAFT, SpIEL, WiSE-FT, LiNeS, and FFT.
The paper also introduces diagnostics for catastrophic forgetting and memorization, finds near-zero values for GaLLoP, and notes a limitation: its unstructured sparsity is less hardware-efficient, motivating future work on structured densification.
weaknesses: 1. The core scoring rule combines gradient size with (inverse) weight magnitude, but closely adjacent ideas already exist: SAFT selects by large gradients alone; Pruning and finetuning selects the smallest pre-trained weights; SNIP scores parameters using a gradient–weight product at (re)initialization; Movement Pruning selects by the magnitude of weight updates during fine-tuning; and dynamic sparse training like RigL periodically regrows weights based on gradient signals. A strong way to sharpen the contribution would be to add head-to-head ablations against these concrete criteria on exactly the same LLM setup and to explain theoretically why the ratio used here should dominate the product used in SNIP under typical LLM curvature/noise regimes. 

2. OOD is instantiated in an eight-dataset round-robin within the same commonsense QA family. That’s a convenient stress test but not a true distribution shift across modalities or task formats. To strengthen claims about generalization, evaluate on qualitatively different targets (instruction following, long-form QA/summarization, math/code, safety and refusal behavior) and on established OOD suites (e.g., CLIP-style ImageNet variants or robustness benchmarks) to mirror SAFT’s cross-domain evaluations. 

3. The paper argues that layer-wise score sampling cuts sort/memory costs and claims the method is “highly efficient,” but provides no end-to-end wall-clock, peak-memory, or throughput numbers (selection phase and training phase) versus LoRA/DoRA/SAFT. 

4. Sensitivity and design choices need deeper ablations - Important parameters (global vs layer-wise thresholds, effect of ϵ, optimizer interactions like weight decay, gradient-accumulation window length) are fixed or only lightly discussed.

5. LoRA/DoRA/SAFT/SpIEL/WiSE-FT/LiNeS are useful, but widely used PEFT baselines such as IA³ and BitFit are absent; including them (and tuning LoRA ranks under an iso-FLOPs or iso-trainable-parameter protocol) would make the comparison more complete. Also disclose and equalize the number of backpropagated layers and gradient-checkpointing settings, which materially affect wall-clock and stability. 

Papers:
[1]: https://arxiv.org/abs/2407.03036? "SAFT: Towards Out-of-Distribution Generalization in Fine-Tuning"
[2]: https://proceedings.mlr.press/v119/evci20a/evci20a.pdf "Rigging the Lottery: Making All Tickets Winners"
[3]: https://arxiv.org/abs/1810.02340 "SNIP: Single-shot Network Pruning based on Connection Sensitivity"


Decision: Reject