Title: Neural Networks for Learnable and Scalable Influence Estimation of Instruction Fine-Tuning Data
Venue: NeurIPS 2025
Accepted: yes
Keywords: Influence Estimation

Data Valuation

Data Attribution
Abstract: Influence functions provide crucial insights into model training, but existing methods suffer from large computational costs and limited generalization. Particularly, recent works have proposed various metrics and algorithms to calculate the influence of data using language models, which do not scale well with large models and datasets. This is because of the expensive forward and backward passes required for computation, substantial memory requirements to store large models, and poor generalization of influence estimates to new data. In this paper, we explore the use of small neural networks -- which we refer to as the InfluenceNetwork -- to estimate influence values, achieving up to 99% cost reduction. Our evaluation demonstrates that influence values can be estimated with models just 0.0007% the size of full language models (we average across 1.5B-22B versions). We apply our algorithm of estimating influence values (called NN-CIFT: Neural Networks for effiCient Instruction Fine-Tuning) to the downstream task of subset selection for general instruction fine-tuning. In our study, we include four state-of-the-art influence functions and show no compromise in performance, despite large speedups, between NN-CIFT and the original influence functions. We provide an in-depth hyperparameter analyses of NN-CIFT. The code for our method can be found here: https://github.com/agarwalishika/NN-CIFT/tree/main.

Neural Networks for Learnable and Scalable Influence Estimation of Instruction Fine-Tuning Data

Abstract

Influence functions provide crucial insights into model training, but existing methods suffer from large computational costs and limited generalization. Particularly, recent works have proposed various metrics and algorithms to calculate the influence of data using language models, which do not scale well with large models and datasets. This is because of the expensive forward and backward passes required for computation, substantial memory requirements to store large models, and poor generalization of influence estimates to new data. In this paper, we explore the use of small neural networks - which we refer to as the InfluenceNetwork - to estimate influence values, achieving up to 99% cost reduction. Our evaluation demonstrates that influence values can be estimated with models just 0.0007% the size of full language models (we average across 1.5B-22B versions). We apply our algorithm of estimating influence values (called NN-CIFT : N eural N etworks for effi C ient I nstruction F ineT uning) to the downstream task of subset selection for general instruction fine-tuning. In our study, we include four state-of-the-art influence functions and show no compromise in performance, despite large speedups, between NN-CIFT and the original influence functions. We provide an in-depth hyperparameter analyses of NN-CIFT. The code for our method can be found here: https://github.com/agarwalishika/NN-CIFT.

1 Introduction

The strong instruction-following abilities of large language models (LLMs) can be attributed to instruction fine-tuning (IFT) [Zhang et al., 2024]. IFT builds on top of current language modeling capabilities and strengthens the instruction following abilities of models. Recent works have taken data efficient approaches for IFT. The goal is to select a small subset of samples on which to fine-tune a model Agarwal et al. [2025], Mirzasoleiman et al. [2020], Das and Khetan [2024], Xia et al. [2024], Renduchintala et al. [2024], Liu et al. [2024c] that emulates the full dataset.

Data efficient pipelines typically consist of two stages: (1) data valuation : designing functions to estimate the influence of data points, and (2) data selection : using influence estimates to choose a balanced set of influential data. Usually, data selection is cheaper than valuation - for instance, DELIFT (SE) 1 [Agarwal et al., 2025] computes the similarity of sentence embeddings between pairs of data (expensive) for valuation and selects representative data using a submodular function (cheap).

Formally, influence functions estimate the value of data. For instance, brute force influence functions use leave-one-out (LOO) training to measure impact by omitting each data point and evaluating performance Scanlon [1982]. More recent influence functions use LLMs to estimate influence. Table

Step 1: collect training data

Step 1: collect training data

Step 2: train/evaluate the InfluenceNetwork

m x n

Training data

Train InfluenceNetwork

𝐼𝑁𝜃

Evaluate on the rest of the

similarity matrix

Step 3: use similarity matrix for IFT

IFT datasets

𝐷𝐹, 𝐷𝑇

Random subsets

of

𝑢

of

𝐷𝐹

,

𝐷𝑇

N

Calculate influence matrix

with influence function

M x N

M

m

n

𝑠𝑖𝑚 𝑖, 𝑗

𝑖 ∈

, 𝑗 ∈

m

n

m x n

Influence values

Use data selection

to select

𝑣

samples

Obtain pruned IFT data

𝑆𝐹

⊂ 𝐷𝐹

|𝑆 𝐹

|

Fine-tune model

𝑀′

M x N

M x N

1 outlines the expenses of state-of-the-art (SOTA) influence functions, which comes from the large amount of forward and backward passes through highly parameterized models.

In this paper, we introduce NNCIFT : N eural N etworks for effi C ient I nstruction F ineT uning and explore how to train influence functions efficiently. We improve efficiency by using compact neural networks - which we coin as the InfluenceNetwork - that are 0.0077% the size of LLMs, to estimate influence. Figure 1 outlines our methodology with a pairwise influence function (more details about pairwise influence functions in Appendix C.1).

As depicted, NN-CIFT is a three-step algorithm. The neural network must be trained to estimate influence values effectively. Hence, we first use the influence function (with LLMs) to output influence values for a very small subset of data. This becomes our training data for the InfluenceNetwork. We find that a small neural network can sufficiently learn to

estimate influence with very few data (covered in Section 4).

Second, we train the InfluenceNetwork, and use it to estimate the influence values for the rest of the data points. Finally, we apply a data selection algorithm on the influence values. This helps to obtain a small subset of IFT data to enhance language models. After fine-tuning language models on the chosen subsets, we find that NN-CIFT achieves comparable performance to the original influence functions (covered in Section 5).

Our contributions and findings are listed as follows. NN-CIFT:

alleviates the cost of using expensive LLMs during data valuation by using smaller and cheaper neural networks, without affecting the performance on downstream tasks (Tables 4-6);

achieves competitive performance to previous data valuation methods, despite using only 0.25%-5% of the data. The average mean square error in influence values between NN-CIFT and the original influence functions is merely 0.067 (Figure 2);

is shown to be effective for new data points, circumventing the need to retrain an influence function for new data - previous works incur this cost (Figure 2).

reduces costs by 77-99% time during data valuation (Table 7).

Section 2 outlines the current state of research in data valuation and data selection. Section 3 explains the problem setting. Section 4 presents the main methodology for NN-CIFT and motivating results. Finally, Section 5 reports results on the downstream task of subset selection after the data valuation stage. In our evaluation, we find that using a small LLM with the original influence functions results in degraded performance. Our hyperparameter studies are in Appendix A.1, Figure 4 and Appendix A.2, Figure 8. We also show language model performance with smaller subsets of selected fine-tuning data in Appendix B. Lastly, the SOTA influence functions are detailed in Appendix C.

2 Related Works

2.1 Data Valuation

Wei et al. [2023] hint that different models extract different information from the same data. Hence, effective fine-tuning requires datasets to be specific to each model. Not all data points affect the model equally - models learn more from certain data points than others. Therefore, data valuation methods prune out such low-influence data for efficient fine-tuning [Xia et al., 2024, Agarwal et al., 2025]. Current research is divided into model-independent and model-dependent valuation metrics.

Model-independent methods, such as distance or clustering-based methods [Das and Khetan, 2024, Liu et al., 2024c, Renduchintala et al., 2024] are faster and less computationally expensive. Distancebased methods assign more "influence" to data points that are further from each other, optimizing for a diverse subset. Clustering-based methods assign more "influence" to data points that are representative (i.e., the centroids of clusters).

On the other hand, model-dependent methods - such as inference-based and gradient-based - are more resource intensive. Inference-based methods [Liu et al., 2024a, Agarwal et al., 2025] use model inference signals (e.g., token distributions) to evaluate the performance or confidence of models, and valuate data based on how performative/confident they are. Gradient based methods [Xia et al., 2024, Mirzasoleiman et al., 2020, Killamsetty et al., 2021, Koh and Liang, 2020], on the other hand, can assign higher influence to data points with (1) higher magnitudes of gradients, or (2) gradients that match domain-specific data (for domain-specific fine-tuning, for example).

While they are expensive to calculate, when paired with data selection algorithms, model-dependent data valuation metrics can be used to select subsets of data that are specific to a model's capabilities. Model-dependent data valuation metrics help to select data that will maximize a certain objective for each model, rendering fine-tuning more effective.

2.2 Data Selection

Data selection aims to prune redundant and noisy data samples from large datasets to produce a small, information-rich subset [Agarwal et al., 2025, Xia et al., 2024]. This subset should be representative of the larger dataset while performing comparably, if not better, than using the full dataset. Data selection methods usually have objectives for selecting data: (1) instruction tuning [Liu et al., 2024a], (2) task-specific fine-tuning [Liu et al., 2024c], (3) continual learning [Agarwal et al., 2025], (4) preference alignment [Liu et al., 2024b], etc. While certain objectives are subsets of others (e.g. (2) is subset of (1)), the data selected for each purpose may not necessarily overlap. For instance, (1) requires data that is representative of a particular dataset, whereas (2) focuses on samples that reflect

Q1

Q2

Q3

Q4

0.30

Predicting o

InfluenceNetwork

0.250

Predicting o

InfluenceNetwork

0.35

Predicting o

InfluenceNetwork

0.24

Predicting 0

InfluenceNetwork

rror

Random

0.225

Random

0.30

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0.22

Random

出

0.25

0.20

Squared

0.200

0.25

0.18

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0.175

0.20

0.16

Mean

0.15

0.150 -

0.125

0.15

0.14

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M

0.10

0.100

0.10 -

0.10

0.075

0.08

0.00

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InfluenceNetwork training size(u)

specific tasks like math reasoning, question answering, or summarization. Similarly, (3)'s samples are specifically chosen to introduce new information to a model without overriding or repeating previously learned information.

3 Problem Formulation

Given a model M and fine-tuning data D F , the goal is to select a small subset S F ⊂ D F that maximizes the performance of M after fine-tuning M on S F . S F is the optimal subset if it can be used to train a model that is comparable to a model trained on D F . However, more recent works jointly optimize other objectives during subset selection. Examples of objectives include not only representation, but also task-specific refinement and continual learning. For such joint optimization, the subset S F is aligned with another target domain dataset D T . The choice of D T can guide the subset selection towards various objectives. For example, if the objective is representation or task-specific refinement, S F will contain points from D F that are similar to D T [Liu et al., 2024c, Xia et al., 2024, Das and Khetan, 2024]. Alternatively, if the objective is continual learning, S F will contain points from D F that would allow the model M to learn new information that is present in D T Agarwal et al. [2025], Tiwari et al. [2022].

As mentioned before, computing influence functions can be a very expensive process. There are two kinds of influence functions: pairwise and pointwise - both require forward/backward passes through language models, but the costs slightly differ. Pairwise influence functions compute the influence between every pair of points in a dataset. We study three SOTA pairwise functions, whose formulations are details in Appendix C.1. This paper also studies one pointwise influence functions that simply compute the influence of each data point individually, formally outlined in Appendix C.2. While pointwise influence functions are more efficient than pairwise, they are not as performant during subset selection Xia et al. [2024], Agarwal et al. [2025].

3.1 Our motivation

Overall, our aim is to reduce the total number of forward or back propagations through models with millions and billions of parameters by replacing a large portion with forward propagations through small neural networks with (merely) hundreds of thousands of parameters. Pairwise influence functions calculate the similarity between two data points (denoted as sim ( i, j ) ). Because influence values are usually not learned, they need to be recomputed for any data beyond the training data. In other words, as data is constantly being collected, influence values for new data must be recomputed. However, NN-CIFT is learned. Hence, our method does not require any extra computation to estimate influence values , unlike previous work.

4 Learning Influence Estimation

This section describes in detail Steps 1 and 2 in Figure 1. It outlines the structure and initial experimentation of the InfluenceNetwork.

4.1 Defining the InfluenceNetwork.

For estimating the influence values of data samples, we call our neural network the InfluenceNetwork . It is a 2-layer neural network with a hidden size of 100 neurons, and an output size of 1 neuron. For activation, we use ReLU in between the layers. The function IN θ represents the neural network with parameters θ . As input, IN θ takes two data points i and j and outputs the estimated influence of i on j . Specifically, embeddings for i and j are computed (denoted as emb () below) using the BAAI General Embedding model ( bge-large-en-v1.5 , in particular) [Xiao et al., 2023] and are concatenated:

The bge-large-en-v1.5 model generates embeddings of size 1,024, which means the input has a total length of 2,048. Hence, the InfluenceNetwork has exactly 204,900 parameters. For training, we use 20 epochs and a learning rate η = 0 . 0001 .

We note that NN-CIFT relies on an embedding model that is often larger than the actual size of the InfluenceNetwork. However, we choose not to include it in the cost for a few reasons: (1) our method does not rely on the underlying embedding model, (2) NLP pipelines generally use embedding models to store, retrieve, cluster, and/or visualize data and hence, is an offline cost.

4.2 Training the InfluenceNetwork.

Below is an illustration of the quadratic similarity matrix that is computed during the data valuation stages. Previous influence compute the entire matrix for data valuation - we only use Q1.

Using the predefined influence functions in Appendix C, a small fraction of influence values are computed - we call this fraction u . We use u %of data from D F and u %of data from D T to compute the training set for the InfluenceNetwork. As mentioned above, this training set is represented by Q1 in the illustration.

The quadrants Q1 to Q4 represent the subset of influence values between a combination of in-distribution (ID) data and out-of-distribution (OOD) data. ID and OOD data is determined by whether the InfluenceNetwork was trained on the data (ID) or not (OOD):

Q1: Fully ID data from D F and D T

Q2: ID data from D F and OOD data from D T

Q3: OOD data from D F and ID data from D T

Q4: Fully OOD data from D F and D T

4.3 Evaluating the InfluenceNetwork.

To ensure our InfluenceNetwork is able to output influence values correctly, we compute the average mean squared error (MSE) between the ground truth influence values (from Appendix C) and the predicted influence values:

We separate the evaluation between the four quadrants of data to study the performance with ID and OOD data.

To train the InfluenceNetwork, we use DELIFT's influence values on the MixInstruct dataset [Jiang et al., 2023] to train our InfluenceNetwork (more dataset details in Section 5). We report the results from InfluenceNetwork and two other baselines: (1) Random ly generating a number between 0 and 1, and (2) only Predicting 0 influence. These results can be found in Figure 2.

Q1

Q2

Q3

Q4

D

F

D

T

The InfluenceNetwork is able to predict influence values with low error rates. After just u = 0 . 05 , it is consistently better than random influence values and predicting only 0. The average MSE between the InfluenceNetwork's influence scores and DELIFT's influence scores is 0.072, 0.072, 0.062, 0.063 for Q1 to Q4, respectively (averaging to 0.067). Furthermore, the error rate stays consistent across all four quadrants, showing that NN-CIFT does not need to be retrained to estimate the influence of new data points that are collected after the training data. One thing to note is that although u = 0 . 05 , with pairwise influence functions, we end up using only 0.25% of the data to train the InfluenceNetwork because we use 5% of D F and 5% of D T .

Finally, we report the robustness of the InfluenceNetwork. In Table 2 reports the variance of the InfluenceNetwork after five runs. We assume the original influence values are given and static, and therefore, do not measure the variance of the individual influence functions. Table 2 shows low variance across each quadrant and each u in the InfluenceNetwork scores. Table 3 shows that the InfluenceNetwork is invariant to the choice of the embedding model. As the MSE between the predicted influence values and ground truth influence values remains small, we posit the downstream performance of NN-CIFT will be maintained no matter the choice of embedding model.

4.4 Interpretive Analysis

DELIFT

DELIFT (SE)

LESS

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- 0.8

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D

D

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We posit two reasons that contribute to the InfluenceNetwork's success: (1) most data points have the same influence, and (2) influence estimation is a lossy task.

Firstly, we visualize the distribution of the influence values in Figure 3. As shown, the most "different" influence values (the stark dark/light colors indicating low/high influence) are sparse. This

indicates that the neural network simply has to learn to estimate the extremes , and can achieve good performance for the rest of the values. Second, we notice that influence estimation is an incredibly lossy task . It involves compressing high-dimensional text representations to a singular, scalar value. Furthermore, the scalar values are constrained to a small range (see Equation 1), reducing the margin of error. Putting these two reasons together, we can see why a neural network can replace a language model during influence estimation without any significant effect on performance.

5 Subset Selection Evaluation

Motivated by the results in Figure 2, we apply the InfluenceNetwork to the downstream task of subset selection: can we achieve the same performance when using the InfluenceNetwork instead of the original influence function ? Thus, this section corresponds to Step 3 in Figure 1.

Datasets and models. We use MixInstruct, [Taori et al., 2023], Alpaca [Taori et al., 2023], and MMLU [Hendrycks et al., 2021] to evaluate NN-CIFT. These are instruction-tuning, preference alignment, and knowledge-based benchmarks where we use 15k for training, 5k for validation, and 5k for testing. We evaluate using three models: meta-llama/Llama-3.1-8B [Grattafiori et al., 2024], Qwen/Qwen2.5-1.5B [Qwen et al., 2025], and mistralai/Mistral-Small-Instruct2409 (22.2B) [Jiang et al.]. Note, we use Llama-8b, Qwen2.5 and Mistral as shorthand for the rest of the experimental section.

Metrics. To evaluate the instruction following capabilities of our fine-tuned model M ′ , we employ a variety of metrics to capture the similarity between ground truth answers and predicted answers from M ′ : (1) ROUGE [Lin, 2004]: n -gram word overlap (specifically, rouge-1), (2) BGE: semantic similarity of embeddings using bge-large-en-v1.5 , and (3) LAJ: an LLM-as-a-Judge, namely the prometheus-7b-v2.0 model [Kim et al., 2023]. Prometheus' grading rubric is borrowed from Agarwal et al. [2025] in Appendix B. Next, to evaluate the costs of each method, we use time (in seconds) took on 2 Nvidia A40 GPUs. However, for MMLU, we use classification accuracy.

Baselines. Besides the influence functions DELIFT, DELIFT (SE), LESS, and SelectIT, we include three other baselines: Initial, DistilGPT2, and Full Data. Initial is the setting where v = 0 . 0 . This is the base model's performance on the dataset. Next, we use a small language model DistilGPT2 ( distilbert/distilgpt2 ) [Sanh et al., 2020] which has 88.2M parameters as the underlying language/embedding model in the influence functions. Finally, Full Data is the setting where v = 1 . 0 , i.e., the model's performance when the full dataset is used.

Setup. We use u = 0 . 05 for training the InfluenceNetwork. We also use a small fraction of D F to fine-tune the language model - we call this fraction v . We evaluate with v = 0 . 3 . Our evaluation framework includes two different settings to fine-tune the language model: using the selected subset of data points as (1) PEFT data for QLoRA [Dettmers et al., 2023] on M , or (2) in-context learning (ICL) examples. To elaborate on the ICL set up, we choose the top-5 most semantically similar

samples from the chosen subset to add in-context. To measure semantic similarity, we again use bge-large-en-v1.5 . Table 4-6 reports results for each model on all three datasets with v = 0 . 3 ; Table 7 reports the cost in time for each method. All tables report the results for one run.

5.1 Analysis

Table 7 reports the costs for each method, in seconds. It shows that data valuation can be performed at 77-99% faster than the original influence functions. This is because the number of parameters in NN-CIFT is 0.00096-0.013% the size of the language model in the original influence function. Also, when using the DistilGPT2 model, which is near 1% the size of the language model, the costs are reduced by 54-91%. While these results are promising, the results on the downstream task of subset selection clearly differentiate NN-CIFT and the DistilGPT2 baseline. Despite the significant speedups, NN-CIFT shows no compromise to performance , as shown in Tables 4-6.

To begin, the pairwise functions outperform the pointwise function (SelectIT) because they are able to capture more fine-grained effects of the data point on a model's learning. Next, DELIFT and DELIFT (SE) are able to outperform LESS because the theoretical guarantees of using submodular functions yields improved empirical performance. Finally, DELIFT uses model dependent information, tailoring the subset to the model's weaknesses, allowing it to outperform DELIFT (SE).

Keeping these in mind, NN-CIFT is able to achieve performance comparable to the original data valuation methods, even across models and datasets . DistilGPT2 shows performance degradations, especially in the model-dependent methods (DELIFT, LESS, and SelectIT). This is because the model-dependent methods experience significant performance gains when the data valuation model is the same as the fine-tuning model. We note that our evaluation's focus is that NN-CIFT works as well as the original influence functions, and not the comparison of performance between them.

The absolute average performance difference across metrics between the original influence functions and NN-CIFT is only 0.16% 2 . Because the neural network is able to estimate the influence values with great accuracy, the selected subsets of data would be mostly the same between the original influence function and NN-CIFT. Hence, the performance difference of 0.16% can be attributed as the variability in the language model's performance between two runs. Additionally, this trend is consistent across datasets and models, which shows the wide applicability of our method.

6 Conclusion

In this paper, we introduce NN-CIFT: N eural N etworks for effi C ient I nstruction F ineT uning to distill highly parameterized models used in modern influence functions into small neural networks. We empirically show the effectiveness of our InfluenceNetwork design through low prediction error rates, and competitive performance on the downstream task of subset selection for IFT. We use four different influence functions to test with NN-CIFT; our experimentation shows that NN-CIFT can lower costs for expensive data valuation, is adaptive to all kinds of influence functions (model-dependent or -independent; pairwise or pointwise), and does not require retraining for new data. Future work will focus on two things: applicability and more targeted modeling. To improve applicability, incorporate more fine-tuning stage objectives such as task-specific dataset selection or continual learning. To target the modeling, we can shift from learning influence between data points to estimating influence between data and a model parameters. Finally, we leave to future work to generalize to distributional shifts within the data (although, the training is lightweight enough that retraining would suffice for now).

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A Hyperparameter Studies

Q1

Q2

Q3

Q4

0.225

InfluenceNetwork

Predicting 0

0.225

Predicting 0

InfluenceNetwork

0.225

Predicting 0

InfluenceNetwork

0.225

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InfluenceNetwork

0.200

Random

0.200

Random

0.200

Random

0.200

Random

LLJ 0.175

S

M

0.150

0.175

0.150

0.175

0.150

0.175

0.150

/era

O0.125

0.125

0.125

0.125

0.100

0.100

0.100

0.100

0.075

0.075

0.075

0.075

0.050

0.050

0.050

0.050

le7

5

0

1e7

5

0

1e7

5

InfluenceNetworksize（# ofparams)

A.1 Hyperparameter Study #1: InfluenceNetwork sizes

We vary the number of layers and dimensions of each layer. For simplicity, we plot the number of parameters in the InfluenceNetwork versus the MSE. The results can be found in Figure 4. This figure shows that small InfluenceNetwork's perform comparatively well as larger InfluenceNetwork's.

A.2 Hyperparameter study #2: Trade-off between u and v

We perform a hyperparameter study between u and v on MixInstruct using DELIFT's influence function (Equation 4). We perform a grid search where u = v = { 0 , 0 . 01 , 0 . 05 , 0 . 1 , 0 . 15 , 0 . 20 , 0 . 25 , 0 . 3 , 0 . 4 , 0 . 5 , 0 . 6 , 0 . 7 , 0 . 8 } , amounting to 169 experiments. Figure 8 shows the results using the BGE metric from each of these experiments. As shown, the two figures in each row follow the same general trend, showcasing that NN-CIFT can effectively replace the expensive influence function estimation .

As expected, we notice a few trends. (1) QLoRA generally has better performance than ICL. This is because finetuning has more impact on the model than simply adding examples to the prompt (i.e., prompt engineering). (2) The bottom right tends to be darker as fewer IFT data lead to insufficient training. (3) Larger IFT subsets, especially in the ICL setting, lead to poorer performance. During ICL, the top-5 semantically similar samples are chosen from the subset to add as in-context examples. However, semantic similarity does not always translate to performance enhancement as these samples can be harmful to the model's performance. Finally, a follow-up to (3), the highest performance regions tend to be around v = 0 . 2 -0 . 4 . Appendix B contains results on smaller subsets of IFT data ( v = 0 . 1 and 0 . 2 ).

DELIFT (ICL)

0.90

NN-CIFT + DELIFT (ICL)

0.90

0.7 -

0.8

0.89

8'0

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0.4 -

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opad

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Perfo

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0.85

0.2

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0.2

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0.1

0.83

0.1

0.83

T'0

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.82

0.2

0.3

0.6

8'0

0.82

DELIFT (QLoRA)

NN-CIFT + DELIFT (QLoRA)

0.91

0.7

0.8

0.90

0.7

8'0

0.90

0.6

0.5

0.88

0.6

0.5

0.89

0.88

0.4

0.86

sopad

0.4

0.87

ero

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0.3

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0.2

a2

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0.1

0.82

0.1

0.84

0.1 0.2

0.3

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0.8

0.1

0.4

0.5

0.6

0.83

B Evaluation on Smaller Subsets

Tables 9 and 11 report extra results for the Phi-3 model on v = 0 . 1 and v = 0 . 2 , respectively. Similarly, Tables 10 and 12 report results for Llama-8B on v = 0 . 1 and v = 0 . 2 , respectively. With Tables ?? and 4 in the main text, these results show an increasing trend in performance with a higher subset of IFT data (i.e., higher v ). They also show similar trends where NN-CIFT performs similarly to the original influence function.

C Influence Functions

Following the problem formulation, we formally define the influence functions we used throughout our evaluation.

C.1 Pairwise Influence Functions

DELIFT [Agarwal et al., 2025] is a model-dependent, inference-based metric. Samples ( i x , i y ) ∈ D F are used as in-context examples for evaluating ( j x , j y ) ∈ D T , and those with improved model performance are chosen to represent D T . This can be calculated by comparing the performance with and without ( i x , i y ) as an in-context example (where D ( · , · ) ∈ [0 , 1] is a function to measure distance

between two probability distributions, and f ( q | θ ) is a language model with parameters θ and input query q ):

After data valuation, the data selection stage consists of using submodular functions [Bilmes, 2022]. In particular, we use the Facility Location submodular function. It takes as input a similarity kernel that will optimize the maximum similarity between the chosen subset and the overall dataset while also minimizing the size of the chosen subset. To minimize the subset size, the Facility Location and submodular functions, in general - employ a diminishing gains property. This property states that samples added to a smaller subset have more value than samples added to a larger subset. Hence, we rely on our influence function to capture the informativeness of samples, and submodular functions to choose a set of representative samples, resulting in a small, information-rich subset on which to fine-tune a model.

DELIFT (SE) [Agarwal et al., 2025] is a model-independent metric, and chooses samples from D F which are semantically closest to the samples from D T . Semantic distance is calculated by the cosine distance between embeddings of samples:

, where emb ( q ) is an embedding model with input data q . Similar to DELIFT, DELIFT (SE) also uses the Facility Location function to select a small, information-rich subset of samples.

LESS [Xia et al., 2024] is model-dependent, gradient-based metric. Here, gradients between samples in D F and D T are matched by cosine similarity, and those that match the highest are chosen to represent D T (where ∇ ( q ; θ ) is the gradient of data point q from a model with parameters θ ):

During the data selection stage, the topk matching gradients are chosen to be part of the subset. One thing to notice is that the above equation implies a quadratic computation while Table 1 in the main text denotes a linear computation - this is because the gradients for each data point only need to be computed once, while the cosine similarity can be computed many times inexpensively.

C.2 Pointwise Influence Functions

Finally, SelectIT Liu et al. [2024a] is another model-dependent metric that uses performance signals for data valuation, but incurs linear cost as it uses a model's uncertainty to rank data samples. Still, as mentioned in Table 1 from the main text, the linear time operations are forward propagations through LLMs.

SelectIT ranks data points based on their token-level, sentence-level, and model-level uncertainty expressed via token distribution. The token-level uncertainty is represented as the maximum probability of a token during next-token prediction. The sentence-level uncertainty is computed based on the token-level uncertainties of all the tokens in a sentence, for each prompt in a pool of prompts. Finally, the model-level uncertainty is calculated by taking a weighted average of the sentence-level uncertainty scores for multiple model sizes (the weights are determined by model size). This three-stage process provides a ranking process - thus, during data selection, the points with the topk scores are chosen.

D License

All the code of this project is under the Apache 2.0 License. The datasets MixInstruct and Alpaca are under the MIT and Creative Commons Attribution Non Commercial 4.0 International Licenses, respectively. The code for the baselines are under the MIT and Apache 2.0 Licenses. Our use of existing artifact(s) is consistent with their intended use. The artifacts are all in English, and do not contain data with personally identifiable information.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method named NN-CIFT, which is used to efficiently estimate the influence of data in Instruction Fine-Tuning through a small Influence Network. Traditional influence function calculations are costly, especially in large datasets, and are not scalable. NN-CIFT alleviates this problem by calculating the influence values of a small amount of training data using the original influence function, training a small neural network using this data, and using this neural network to estimate the influence values of the remaining data.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nA Significant reduction in time cost was achieved on multiple influence functions. The proposed method applies to various downstream tasks. A smaller model achieves excellent results, where the scale of Influence Network is only 0.0007% of that of LLM, but its average MSE is only 0.067, maintaining a good estimation capability. Extensive experiments are conducted on three models and three tasks to verify the effectiveness. \n\nWeaknesses:\n\n1. The reliance on the embedding model is not included in the cost analysis. Although the author explains that the cost of the Embedding model is not included, it is indispensable in training/inference, and this cost still needs to be considered in deployment.\n2. Although the learning process of NN-CIFT is effective, it lacks an in-depth theoretical explanation of why simple neural networks can generalize impact estimation. It only explains from the perspective of the sparsity of the empirical distribution, which is somewhat intuitive.\n3.The innovation lies in engineering optimization. Although this method has practical value, it is more inclined towards accelerating optimization at the engineering scope rather than fundamentally advancing the theory of influence functions.\n\nQUESTIONS:\n1. How strongly bound is Influence Network to embedded models? If the embedding model is changed, can the estimation ability and downstream performance of NN-CIFT still be maintained?\n2. Why choose a single-layered MLP? Have you ever tried deeper networks? This might improve the quality of the impact estimation.\n3. Can Influence Network be trained on one task and directly used under another task/data distribution?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

comments: SUMMARY:
The paper proposes the use of a small surrogate model to directly predict the influence between pairs of training points.  The surrogate model is trained using the "actual" influence between a subset of the original training data.  Experiments show that filtering and re-training using "actual" influence and those predicted by the surrogate model gives comparable results, while reducing computation by between 75% to 99%.

STRENGTHS AND WEAKNESSES:
Strengths
- the idea is straightforward, fills a missing gap in the literature, and extensive empirical results across different influence functions and tasks show the benefit of the surrogate model.
- the method can reduce computational cost, potentially adding only minimal complexity

Weaknesses
- it would be useful to justify the choice of the particular BAAI embedding - why was it chosen, and does it generally work regardless of the underlying influence function being approximated?
- it will be useful to give guidance on when the proposed method should or should not be used - does it work better for some influence functions than others?

QUESTIONS:
- how sensitive is the training of the surrogate model to hyperparameters?  if its training can be plug-and-chug, it can be a lot easier to use, but if there needs to be experimentation, then the human engineering time will dominate that of the potential computational savings
- can the method be viewed as denoising noisy influence estimates?

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes using small neural networks—referred to as the InfluenceNetwork—to estimate influence values, thereby reducing the computational cost of calculating influence functions.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe idea is interesting, and this paper is easy to follow.\n\n\nWeaknesses:\n\nThe comparison with baselines is currently insufficient to convincingly demonstrate the advantages of the proposed method. In particular, several existing approaches have been specifically designed to relax the computational burden of influence function estimation, such as the method introduced in [1], which leverages stochastic approximations to reduce the overhead. Including such methods in the empirical comparison would provide a more comprehensive and fair assessment of the proposed approach’s relative efficiency and accuracy.\n\nMoreover, the paper does not clearly report the training time of the model or provide sufficient details to estimate it reliably. Without a clear accounting of the total computational cost—including both model training and influence estimation—it becomes challenging to evaluate the claimed gains in time efficiency. These limitations make it difficult for readers to assess the practical benefits of the proposed method, especially in real-world scenarios where computational resources are constrained.\n\nTo strengthen the contribution, the authors should include relevant baselines that target efficiency improvements and report precise runtime metrics for both training and inference stages.\n\n[1]  Tracing model outputs to the training data.\n\nQUESTIONS:\nThis paper is overall very interesting and presents a promising direction with potentially impactful contributions. The proposed method is well-motivated and addresses an important problem. However, as noted in the weaknesses, the evaluation of efficiency remains incomplete. The current comparison lacks key baselines that are specifically designed to improve the computational efficiency of influence estimation. Additionally, important details such as training time and overall computational overhead are either missing or insufficiently discussed. A more thorough and transparent analysis of efficiency—both in terms of runtime and resource usage—would significantly strengthen the empirical validation of the proposed approach and better support the claimed advantages.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-08"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces a novel algorithm for estimating the relative importance of data samples for LLM finetuning. This algorithm NN-CIFT (Neural Networks for Efficient Instruction Fine-Tuning) trains a 2-layer “Influence Network” on vector embeddings to then select a subset of samples from a given dataset. The Influence Network learns to predict a pairwise “influence” value i.e. similarity score between two data points. Their approach leads to good quality and speed performance over competitive alternative approaches.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n* The paper is well written and the results are novel. This seems like a promising approach for efficient dataset selection for finetuning.\n* The authors show results across multiple finetuning datasets and multiple models (and model sizes from 1.5B - 22B). This is very important for showing how their approach generalizes across conditions\n* The authors do rigorous benchmarking with multiple metrics (e.g. ROUGE, vector embeddings, LLM-as-a-Judge)\n\nWeaknesses:\n* As a ML practitioner, I am interested in the question of how to get to equal quality with fewer data samples during finetuning. This approach seems capable of answering this question, however the results in Tables 3-6 don’t address this directly. Rather, they just show that NN-CIFT is slightly better than alternative approaches/methods, and that it can achieve similar performance to SelectIT, LESS, DELIFT and DELIFT (SE) 77-99% of the time (which is impressive).\n\nQUESTIONS:\nQ1: Line 30: The authors state the DELIFT (SE) compares the similarity of sentence embeddings between pairs of data, and that this is computationally expensive. Is this a minor comment, or something deeper? Please explain.\n\nQ2: When you write “‘+NN-CIFT’ indicates using NN-CIFT to estimate influence values computed from the corresponding method’s influence function”, does this mean that in the example of “DELIFT+NN-CIFT,” DELIFT was used in “Step 1” on a very small subset of data, and then this subset was used to train the NN-CIFT influence network?\n\nQ3: A lot of the same data points from Table 4 and Table 5 were calculated in the original DELIFT paper (e.g. DELIFT (SE) baseline ICL ROUGE score for MixInstruct). Were these values recalculated in your paper? It seems that the values are not necessarily identical.\n\nQ4: The cost estimates in Table 1 don’t include the initial step of using the full sized LLMs to output influence values of a very small subset of data. Can you address this? Also, how small are these subsets? Have you explored the effects of dataset size in this first step?\n\nQ5: In Appendix Figure 4, it is surprising that there are no scaling trends as you increase model size. Why doesn’t MSE decrease appreciably as the model size increases? Can you address this in the paper? It seems like there should be a relationship between influence network size and training data size (as in Figure 2 of the main text). Maybe this has to do with model capacity?\n\nLIMITATIONS:\nYes, the authors have addressed the limitations of their work.\n\nVery minor comments:\n* It would be very helpful to bold and underline top values in Tables 3-5. It is hard to inspect by eye where NN-CIFT leads to strong improvements across the board\n* Line 34: “outlines the expenses” → maybe “efficiency considerations” instead?\n* Line 24, line 134 and elsewhere: the brackets around citations are missing\n* Line 421 in Appendix: “InfluenceNetwork’s” → Influence Networks\n* Line 453 in Appendix: “Tables ??”", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-11"}