Exploiting Presentative Feature Distributions for Parameter-Efficient Continual Learning of Large Language Models

Thank you for recognizing our work and taking the time to review our manuscript. Below is our response to address your concerns.

Q1: (Questions) How does the method disambiguate ...... layer-wise selection inherently mitigate this?

A1: Our method can effectively identify tasks with overlapping feature distributions. In cases where we have two identical tasks, the dynamic selection process will allocate selections evenly between them, similar to how each task would be trained independently. Furthermore, the layer-wise selection process offers additional mitigation against overlapping feature distributions. As evidenced by our visualizations in Figures 5–8, the model learns progressively from shallow to deep layers, and our method can capture and distinguish the nuances of feature overlaps.

Q2: (Questions) What is the maximum K tested? How ...... computation impact real-time inference?

A2: The parameter $K$ used for testing was consistent with that used during training. Specifically, in Tables 2, 10, and 14, we set $K$ to 1, while for the remainder of the experiments, $K$ was set to the total number of tasks. It is important to note that the values of $K$ during training and testing do not have to be identical. For simplicity, we chose to keep them the same.

During real-time inference, our method calculates the similarity between instances and the stored feature distributions and uses this similarity to select PEFT blocks. This process only adds a step for similarity computation compared to the original inference. Since quadratic similarity, dot-product similarity, and cosine similarity are easily implemented with matrix parallelization, the real-time inference time does not significantly change with different $K$.

As reflected in Figure 4, we present the results of quadratic similarity under different $K$. It can be observed that quadratic similarity maintains stable performance across various $K$ values. This stability arises because quadratic similarity is unbounded before normalization, leading to more extreme weights after normalization. Different values of $K$ prioritize the exclusion of irrelevant LoRA blocks, and these blocks inherently have low weights when using quadratic similarity.

Q3: (Questions) While similarity metrics are explained ...... enhance the quality of the paper.

A3: We agree that a stronger theoretical basis would enhance the quality of this paper. However, theoretical frameworks related to large models, particularly in high-dimensional spaces such as hidden layers and feature spaces, are still under development. All existing research lacks theoretical assurance. Fortunately, we can provide some theoretical support for our method.

Inspired by the studies on model merging[1], changes in model parameters are considered as directions that contain knowledge of specific tasks, referred to as task vectors. Since LoRA blocks are ultimately added to the original model parameters in our method, each LoRA blocks $A_k$ and $B_k$ can also be seen as task vectors, offering rationale for our dynamic selection.

For any given instance feature $\mathbf{W}^{l}h^{l}(x)$, it has undergone the same pre-trained parameters $\mathbf{W}^{l}$, thereby being a linear transformation applied uniformly across all instances. Given that related tasks require related knowledge, the final output space should be similar (e.g., vocabulary or patterns). Therefore, we establish a feature distribution $D^{l} _{k} = \mathbb{E} _{p(x^{k}, y^{k})} [\mathbf{W}^{l}h^{l}(x^{k})]$ for the transformed features, and select blocks based on the distance to these distributions.

[1] Gabriel Ilharco et al. Editing Models with Task Arithmetic. In NeurIPS, 2023.

Q4: (Questions) The fixed or limited tuning of hyperparameters ...... need further exploration.

A4: The temperature coefficient is an inherent hyperparameter of the softmax function, and the LoRA rank is inherent to LoRA fine-tuning. These two hyperparameters are not unique to our method. In Figure 4, we have discussed the specific hyperparameter $K$ associated with our method. To further validate the adaptability of our method across different hyperparameter settings, we have conducted additional experiments in the anonymous link https://anonymous.4open.science/r/ICML-2025-Rebuttal-10369/ICML_2025_Rebuttal.pdf (Table 20, 21 and 22).

In fact, the temperature coefficient and the parameter $K$ serve similar purposes, as they both adjust the scaling of weights. When the temperature $T$ approaches 0, it effectively corresponds to setting K to 1. Therefore, it is not necessary to simultaneously adjust multiple parameters externally, just choose one to adjust.

We agree that exploring adaptive hyperparameter tuning and systematic search is a promising area of research. This issue remains challenging, especially in large models, which have numerous hyperparameters that can be adjusted. We will make this challenging problem our future work.

We are grateful for the time and effort you have dedicated to reviewing our work. We provide point-by-point responses to address your concerns.

Q1: (Weaknesses) The empirical evidence is evident but ...... like cosine similarity.

A1: Due to word limit and the repeated mention of this weakness, we kindly ask you to refer to the responses for Q3 of Reviewer D8DQ and Q3 of Reviewer 54sH.

Q2: (Weaknesses) The hyperparameter sensitivity is not discussed ...... of this coefficient in the experiments.

A2: The temperature coefficient $T$ is an inherent hyperparameter of the softmax function. Following previous studies (SAPT, Zhao et al.), we fix this coefficient to 1.0. We add additional experiments concerning the impact of the temperature coefficient in the anonymous link https://anonymous.4open.science/r/ICML-2025-Rebuttal-10369/ICML_2025_Rebuttal.pdf (Table 17 and 18).

In fact, the temperature coefficient and the $K$ have similar usage, as they both adjust the scaling of weights. When the $T$ methodes 0, it effectively corresponds to setting $K$ to 1. Therefore, it is not necessary to simultaneously adjust multiple parameters externally. We can only adjust one of them.

Q3: (Weaknesses and Questions) In the ...... compare the actual memory usage or training time with O-LoRA?

A3: We explicitly discussed the memory usage of our method in Lines 380-384 of the manuscript. To further clarify, we provide a detailed comparison across different methods in the anonymous link https://anonymous.4open.science/r/ICML-2025-Rebuttal-10369/ICML_2025_Rebuttal.pdf (Table 19).

(Memory) While our method stores additional feature distributions compared with O-LoRA, these distributions are represented as lightweight vectors. Even when stored across all layers, they introduce only 0.262M additional parameters. As shown in Figure 3, retaining feature distributions for only a subset of layers achieves strong CL performance while further reducing memory overhead.

(Training Time) SAPT and our method incur only a small increase in lightweight computations during training. However, the parameters added by SAPT require gradient updates and replay data, resulting in slower training speed for SAPT. In contrast, O-LoRA necessitates calculating the square difference between LoRA parameters during loss computation, which introduces substantial computational overhead and leads to the slowest training speed.

There is no rank reduction during the combination process (illustrated in Figure 2). The feature distributions $D^{l} _{k} = \mathbb{E} _{p(x^{k}, y^{k})} [\mathbf{W}^{l}h^{l}(x^{k})]$ are derived from pre-trained model features and are independent of the LoRA blocks. This allows our method to seamlessly combine LoRA blocks of different ranks into a unified model.

Q4: (Questions) The authors define “information leakage” ...... Could authors clarify the technique novelty compared to O-LoRA?

A4: O-LoRA avoids catastrophic forgetting by ensuring that the parameters of new tasks are orthogonal to those of existing tasks. However, when new tasks overlap or conflict with learned tasks, this constraint can limit the learning performance. As a result, O-LoRA cannot perform as well as state-of-the-art continual learning methods, although it prevents IL as well as our method.

Our method treats each LoRA block as a repository of knowledge, dynamically selecting them as needed. Although our method preserves the presentative feature distributions, these distributions are high-dimensional and beyond human comprehension, similar to the LoRA parameters. Moreover, presentative feature distributions represent averaged information across populations and cannot reconstruct individual information. Therefore, our approach achieves superior continual learning performance while effectively avoiding information leakage.

Q5: (Questions) In Table 2, the AP result ...... Could the authors clarify the reason for this discrepancy?

A5: To ensure a fair comparison, we implemented previous CL methods using the open-source framework of SAPT. These adjustments led to improved performance for most methods compared with their original reports. Our experiments are based on the SAPT framework, which explains the lack of significant differences in SAPT results as reported. It's important to note that SAPT did not provide detailed instructions for reproducing O-LoRA. Our settings may differ due to two key hyperparameters in O-LoRA: we consistently set $\lambda_{1}$ to 0.5 and $\lambda_{2}$ to 0, retaining all LoRA layers without merging them—factors that significantly impact results. Additionally, discussions on the O-LoRA GitHub indicate that the number of GPUs used can influence results, with an error margin exceeding 8%. Our experiments utilized 8 A100 GPUs, while SAPT used 4 A800 GPUs. We provide the code to reproduce the O-LoRA results in the anonymous link https://anonymous.4open.science/r/ICML-2025-Rebuttal-10369/ICML_2025_Rebuttal.pdf.

Thank you so much for your valuable comments! We provide point-by-point responses to address your concerns.

Q1: (Methods and References) Similar methods have already been proposed ...... e.g. Feature Adaptation (Iscen et al., 2020).

A1: Thank you for pointing out these relevant studies, and we will incorporate them into our related work. They indeed utilize feature representations for incremental learning. However, our method is significantly different from theirs.

Firstly, we focus on LLMs and aim to make them to continually learn (fine-tune) in dynamic environments, such as distribution shifts or integrating new knowledge. In contrast, iCaRL and Feature Adaptation primarily address classification tasks, where the goal is to increase the number of classes that the model can recognize, which is fundamentally different from our goal.

Secondly, iCaRL utilizes the distance between the output features and the centers of each class. In our selection module, we utilize distances between pre-trained features and task center from each layer. The sources of features and the targets of selection are different.

Additionally, Feature Adaptation preserves features extracted by different feature extractors and embeds them to the same space. In contrast, we directly utilize the feature from frozen pre-trained LLMs. Moreover, we do not claim to be the first to use feature distributions as a surrogate for training data. Our goal is to employ these distributions to avoid information leakage.

Q2: (Experiments) The effectiveness of different modules have not be sufficiently demonstrated by e.g. ablation studies.

A2: Our method first leverages pre-trained LLMs to encode tasks into presentative feature distributions, and then calculate the similarity between instances and the presentative feature distributions to dynamically select proper PEFT blocks. In other words, presentative feature distribution and dynamic selection are connected modules of our method that must work in sequence. Removing any module from our method would make it meaningless.

Q3: (Weaknesses and Questions) The authors mentioned that IL ...... and how CL can be applied to these scenarios?

A3: In most cases, model weights (instead of training data) are commonly shared (e.g., open-source ecosystem DeepSeek, Qwen and Mistral). In such situations, CL through data replay is not feasible. Enterprises and research institutions often fine-tune models for specialized tasks with training data that contains proprietary information, such as medical assistants and fraud detection systems. This data often includes user interactions, which cannot be shared due to privacy regulations. This presents challenges for CL, such as adapting models to evolving regulations or updating fraud detection systems to counter new threats, especially when these models must integrate prior knowledge. In these scenarios, effective CL without IL is crucial.

Q4: (Questions) Does your method support sparse activation like MoE ...... (since all LoRAs contribute to the final output).

A4: Of course, as our method is based on parameter isolation techniques, it inherently supports selective activation similar to MoE. In fact, we have already implemented this method. As demonstrated in Figure 4, we present the performance variation curve using Top-$k$ activation, which only activates the $k$ closest LoRA modules. We recommend selecting a smaller $k$ to achieve more stable results.

Q5: (Questions) What’s the difference between cosine similarity ...... you propose in Section 3.3?

A5: Cosine similarity $\text{Cos}(A, B) = \frac{A \cdot B}{||A|| ||B||}$ and dot product similarity $\text{Dot}(A, B) = \frac{A \cdot B}{\sqrt{d}}$ are both mathematical methods to measure the similarity degree between two vectors. Their primary difference lies in the normalization scale ($||A|| ||B||$ for cosine similarity and $\sqrt{d}$ for dot product similarity). We also conducted experiments using cosine similarity. Since dot product similarity is commonly used in the attention calculation, we reported its results in our manuscript. You can find the experiments of cosine similarity through the anonymous link https://anonymous.4open.science/r/ICML-2025-Rebuttal-10369/ICML_2025_Rebuttal.pdf (Table 15 and 16).

Q6: (Questions) In the zero-shot ...... why would SAPT-LoRA without IL perform better than the one with IL?

A6: We have indeed observed this phenomenon. It might be due to data replay causing the model to overfit, which results in reduced generalization capabilities. Since the replay data in SAPT is synthetic, it primarily emphasizes the prompt and structure of the problem. As a result, in a zero-shot setting, it is likely to overlook the knowledge required to select the LoRA blocks.