Neural Networks for Learnable and Scalable Influence Estimation of Instruction Fine-Tuning Data
Authors: Ishika Agarwal
Dilek Hakkani-Tür
Venue: NeurIPS 2025 poster ()
Keywords: Influence Estimation
Data Valuation
Data Attribution
Primary area: deep_learning
TL;DR: We replace expensive language models with cheap neural networks to estimate the value of data, thereby saving significant computations costs while maintaining performance.

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
Ishika Agarwal & Dilek Hakkani-Tür Department of Computer Science
UICC
Jirbana-Champati IL 61801, USA (ishikaa2, dilek))illinois edu
Abstract
Influence functions provide crucial insights into model training, but existing meth- ods suffer from large computational costs and limited generalization. Particularly, recent works have proposed various metrics and algorithms to calculate the influ- ence 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 use of small neural networks which we refer to as the InfluenceNetwookk to reduction. Our evaluation
data. In this paper, we explore the
estimate influence values, achieving up 99% demonstrates that influence values can be estimated with models just 0,000 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 eifiCient Instruction Fine- (unnnT to the downstream task of subset selection for general instruction fine-tuning. In our study, we include four state-of-the-we the-art influ- ence functions and show no compromise in performance, despite large speedups, between NN-CIFT and the original influence functions. We provide in in-depth hyperparameter analyses NN-CIFT. The code for our method can found here: https///ghhbbb.oomgggavviiiiaaaa
Introduction
The strong instruction-folloiing 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 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 balanced set of influential data. Usually, data selection is cheaper than valuation for instance, DELIFT (SE) [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
Short for "Sentence Embedding".
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Step 1: collect training data
datasets Dp, Dy
Random subsets of of Dy, Dr
Calculate influence matrix with influence function sim(t,)
MXN
Step 2: train/evaluate the Influenceeetwork
Training data
Train InfluenceNetwarkk Ni
Evaluate on the rest of the similarity matrix
MxN
Step 3: use similarity matrix for IFT
Influence values
Use data selection to select v samples
Obtain pruned data Dp
Fine-tune model
Ay
Figure Overview of NN-CIFT. The first step consists of using established influence functions to collect data for training the InfluenceNetwork. Next, the data from Step (1) is used to train the InfluenceNetwork and, subsequently, estimate the influence values for the rest of the data. Finally, the data selection algorithm corresponding to the original influence function is used select subset of IFT data to fine-tune model on.
1 outlines the expenses state-of of-the-arttttt (SOTA) influence functions, which comes from the large amount of forward and backward passes through highly parameterized models.
In this paper, we introduce NN-
CIFT: Neural Networks for effiCient Instruction Fine- Tuning and explore how to train influence functions effi ciently. improve efficiency by us- ing compact neural networks which we coin as InfluenceNettwork- that are 0.0077% the size of LLMs, to estimate influence. Figure 1 outlines our method- ology with pairwise influence function (more details about pairwise influence functions in Appendix C.1).
Method
Cost
Size
Pairwise
DELIFT [Agarwal et al., 2025) DELIFT (SE) [Agarwal et al., 2025]
O(MN) F O(MN)
7-8B
355M
LESS [Xia et al., 2024]
O(M + N)-
7-8B
NN-CIFT (ours)
O(MN) F
205K
Pointwise
Select|T [Liu al., 2024a]
O(M)
7-8B
NN-CIFT (ours)
O
205K
Table Approximating the computational complexity of data valuation in terms of the cost of forward passes (F) backward passes (B) through model. M |D5 and N |Dr], fine-tuning and target dataset respectively. we use for subset selection. See Appendix C. for more details. Size denotes the number of parameters of the corresponding model. Note: larger models have higher F and B.
As depicted, NN-CIFT is a three-step algorithm. The neural network must be trained to estimate influence values effec- tively. Hence, we first use the influence function (with LLMs) to output influence values for very small subset of data. This becomes our training data for the InfluenceNetwork. We find that small neural network can sufficiently learn to estimate influence with very few data (covered in Section 4).
Second, we train the Influeenceeetwor, and use to estimate the influence values for the rest of the data points Finally, we apply data selection algorithm on the influence values. This helps to obtain small subset of IFT data enhance language models. After fine-tuning language models on the chosen subsets, we find that NN-CIFT achieves comparable performance the original influence functions (covered in Section 5).

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Our contributions and findings are listed as follows. NN-CIFT:
1. alleviates the cost of using expensive LLMs during data valuation by using smaller and cheaper neural networks, without affecting the performance downstream tasks (Tables 4-6);
2. 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):
3. 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).
4. 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 presents the main methodology for NN-CIFT and motivating results. Finally, Section 5 reports results 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 detailed in Appendix C.
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 distance or clustering- based methods [Das and Khetan, 2024, Liu et al., 2024c, Renduchintala et al., 2024] are faster and less computationally expensive. Distance- based 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] model inference signals (e.g., token distributions) to evaluate the performance or confidence of models, and valuate data based on how performative/ccofiier 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 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 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-depended data valuation metries help to select data that will maximize certain objective for each model, rendering mee-tnnng 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) sask-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)
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 samples that reflect
3

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01
Proliing3 20
Nokizg
Squared
4200
600
20 training
15
Figure 2: MSE versus InfluenceNetwork training data size (u) plotted for 8 different training sizes, broken down by the quadrant. These results are for learning DELIFT influence values. Error rates on each quadrant correspond to losses across different sets: Q1 for training, Q2/Q3 for validation, and Q4 for testing. As shown, the InfluenceNetwork achieves MSE of merely 0.05% starting from 0.05 and always outperforms the baselines.
specific tasks like math reasoning, question answering, or summarization. Similarly, (3)'s samples specifically chosen to introduce new information to model without overriding repeating previously learned information.
Problem Formulation
Given a model M and fine-tuning data Dr, the goal is to select a small subset SF C Dr that maximizes the performance of M after fine-tuning M on Sx. SF is the optimal subset if it can be used to train model that is comparable to model trained on Dr. However, more recent works jointly optimize other objectives during subset selection. Examples of objectives include not only representation, but also task-specifi refinement and continual learning. For such joint optimization, the subset SF is aligned with another target domain dataset Dr. The choice of 'DT can guide the subset selection towards various objectives. For example, if the objective is representation or task-specific refinement, Sy will contain points from Dj= that are similar to D [Liu et al., 2024c, Xia et al., 2024, Das and Khetan, 2024]. Alternatively, if the objective is continual learning, SF will contain points from D, that would allow the model M to learn new information that is present in Dy Agarwal et al. [2025], Tiwari al. [2022].
As mentioned before, computing influence functions can be 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. 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 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 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,,)). 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 inffuence values, unlike previous work.
4 Learning Influence Estimation
This section describes in detail Steps and in Figure It outlines the structure and initial experimentation of the InfluenceNetwork.

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4.1 Defining the Influenne/Networ..
For estimating the influence values of data samples. we call our neural network the InfuuenceNerwork It is a 2-layer neural network with hidden size of 100 neurons, and an output size of neuron. For activation, we use ReLU between the layers. The function INg represents the neural network with parameters 0. As input, INo takes two data points and j and outputs the estimated influence of on j. Specifically, embeddings for and j are computed (denoted as emb() below) using the
BAAI General Embedding model Tbge-larges en-gee--eii... en-vi. v1.5, in particular) [Xiao et al., 2023] and are concatenated:
0 (No(t,) S 0 Σ (connctteemb(), emb (j)) - 1,
(1)
(2)
v(i,)) D x Dr
The bge-large-en-vl- model generates embeddings of size 1,024, which means the input has total length of 2,048. Hence, the InfluenceNetwork has exactly 204,900 parameters. For training, we use 20 epochs and learning rate 7) 0.0001.
note that NN-CIFT relies on an embedding model that often larger than the actual size of the InftuenceNetwork. However, choose not to include it in the cost for 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 offline cost.
4.2 Training the InfluenceNetwork.
Below an illustration 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, small fraction of influence values computed - we call this fraction u. We use u% of data from DD and u% of data from D7 to compute the training for the InftuenceNetwork. As mentioned above, this training set represented by Q1 in the illustration.
The quadrants Q1 to Q4 represent the subset of influence values between combination of in-distribution (ID) data and out-of-distribution (OOD) data. ID and OOD data is de- termined by whether the InfluenceNetwork was trained the data (ID) or not (OOD):
Dy
Ql: Fully ID data from D, and Df
Q2: ID data from D>= and OOD data from Dy
Q1
Q2
Q3: OOD data from F and ID data from Dy
Q3
Q4
Q4: Fully OOD data from Dy and DD
4.3 Evaluating the InfluenceNNtworrk
To ensure our InfluenceNetwork 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:
Σ
(IFo(i,)) sim(i.j))²
D D
(L
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) Randomly generating number between and 1, and (2) only Predicting 0 influence. These results can be found in Figure 2.
5

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Q1 sid
Q2 sid
Q3 sid
Q4 std
0.01
0.0080
00000
0,0188
0.
0.05
0.0090
0.0011
0,0032
0.0032
0.0062
0,0088
0.0032
0.15
0.0062
0.0056
(1005)
0.0037
0,0020
0.25
0.0102
0.0096
0,0020
0.0020
0.30
0.0118
0.0112
0.0020
0.0020
0.40
0.0067
0.0053
0.0018
0.0018
Table 2: Variance of the InfluenceNetwork for varying u for DELIFT values.
Einbedding Model
Q1
Q2
Q3
Q4
BAAE/ wargge ml.v1..
0.051
0.084
0.074
0.084
Qwer/Qwen 3- Embedding-O -066B
0.087
inttloat/S5-msste mistrrl--7-insttus
0.026
0.083
0.084
0.083
Snowilake'snow llake aucti--emmed-------
0.077
0.087
0.087
0.088
Table Varying embedding models and their corresponding MSE values (averaged across runs)
between estimated influence values and ground truth influence values, with 5% selected data. These
results are for learning DELIFT influence values. As shown, NN-CIFT invariant to the embedding model selected, and is able to effectively estimate the influence values.
The InfluenceNetwork is able predict influence values with low rates. After just 0.05, it is consistently better than random influence values and predicting only O. The average MSE between the InfluenceNetwork's influence scores and DELIFT's influence scores is 0.072, 0.072, 0.062, 0.063 for QI 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 retrained estimate the influence of new data points that are collected after the training data. One thing to note is that although
0.05, with pairwise influence functions, we end up using only 0.25% of the data to train the InfluenceNetoork because we use 5% of D and 5% of Dr.
Finally, report the robustness of the InftuenceNetwork. In Table 2 reports the variance of the InflueenceNewwork 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 shows low variance across each quadrant and each u in the InfluenceNetwork scores. Table 3 shows that the InfluenceNetwork is invariant 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
Figure 3: Distribution of influence values across each of the methods on the Alpaca dataset. To clarify, "D F" is D, and "D "D is Dy. The x-axis spans the 15,000 examples from D, and the y-axis spans the 5,000 samples from Dy. SelectIT only has an x-axis.
We posit two reasons that contribute to the InfluenceNetwork' 's success: (1) most data points have the same influence, and (2) influence estimation is lossy task.
Firstly, we visualize the distribution of the influence values in Figure As shown, the most "different" influence values (the stark dark/light colors indicating low/high influence) are sparse. This

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Datasel
MixInstruct
Alpaca
MMLU
Method
ICL
QLoRA
ICL
QLoRA
ICL
QLoRA
Metric
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
Accuracy
Accuracy
Initial
28.53
74.05
2.94
34.42
78.54
3.00
24.85
72.45
2.26
34.29
80.82
70.7
70.8
Random
40.07
84,04
3,26
41.68
84.26
3.22
36,95
80.47
3.12
38.64
80.46
3.07
71.9
71.9
SelectIT
46.51
86.18
3.25
50.31
87.38
3.25
83.25
3.27
44.51
84.18
3.34
73.0
DisullPP12
41.26
80.33
3.20
44.86
84.72
3,23
39.18
80.99
2,99
41.72
81.50
3.14
72.0
72.7
85.13
72.9
L.SSS
48.21
86.19
3.34
51.24
86.07
3.37
43.34
84.19
3.38
73
84.04
3.32
75.6
76.7
DistilGPT2
42.18
78.34
3.23
48. 68.64
3,27
3.29
42.51
82.35
3.29
74.6
74.1
NN-CIFT
48.20
86.31
3.36
51.56
86.39
3.41
44.42
84.89
3.32
46.40
85.44
3.36
75.0
76.5
DELIFT (SE)
48.36
85.91
3,38
51.43
86,20
3,34
44,30
85.52
3,41
45.35
86.34
3.48
78.9
79.8
DisuiGPP2
47.21
84.24
3.28
49.37
84.24
3,29
43.551
85:45
3.41
44.89
79.81
3,36
75.4
76.1
NN CIFT
48.59
85.01
3.39
50.53
86.10
3.33
45.49
86.27
3.44
45.75
86.45
3.47
78.5
79.8
DELIFT
51.66
3.50
3.50
87.74
83.1
DistilGPT2
47.09
84.74
3.26
48.21
84.24
3,28
45.08
81.45
3.41
41.07
83.22
3.44
77.1
78.5
-N-CIFF
52.03
88.38
87.74
Full Data
54.43
92.55
3.40
59.47
94.12
3.58
48.53
91.21
3.63
48.29
90.82
3.66
80.5
81.6
Table 4: Results on the Llama-8B model with 0.3, 0.05. "+ NN-CIFT" indicates using NN-CIFT to estimate influence values computed from the corresponding method's influence function. "+ DistilGPT2" indicates using the DistilGPT2 model as the language model in the corresponding method's influence function. The average performance difference between NN-CIFT and the original influence function is merely 0.13%.
Dataset
MixInstruct
Alpaca
MMLU
Method
ICL
QLeRA
ICL
QLoRA
ICL
QLORA
Metric
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
ROUGE
BGE
Accuracy
Accuracy
32
2.06
2.09
71.79
70.9
Random
28.33
72.41
2.37
29.93
75.78
2.50
26.54
72.71
2.66
28.10
73.00
2.78
68.9
71,9
SelectlT'
40.64
DistiGPP2
40.33
71 71.49
2.11
43.26
74.14
2.38
29.65
75.32
2.62
31.66
74,20
2.67
69.9
70.8
NN-CIFT
41.59
71.36
2.58
76.82
2.78
32,90
77.12
LESS
45.33
78.68
3.03
46.03
81.04
3.05
38.43
78.83
2.98
41.68
81.83
3.09
74.0
75.6
DistilGPT2
43.15
74.69
2.42
42.87
75,80
2.46
34.76
75.26
2.86
37.66
78.57
3.06
66.7
69.3
NN-CIFF
46.32
78.84
3.05
47.84
80.48
3.03
39.59
78.75
2.89
42.06
81.06
3.08
74.1
74,9
DEL IIT (SF)
46.68
81.01
3.12
48 48.42
83.67
3.15
42,52
81.21
3.12
43.83
84.35
3.26
74.0
75.1
DistilGPT2
45.89
79.77
3.07
46.07
80.40
3.10
41.15
79.42
2.96
42.32
82.63
75.0
75.4
NN-CIFT
46.81
81.23
3,14
48.64
82.76
3,16
42.72
80.86
3.16
42.75
84,52
3.27
75.2
75.5
DELIFT
48.85
83.89
3.25
50.90
85.64
3.27
83.60
3.28
46.33
87.87
77.4
79.4
DistiiGPT2
43.69
77.83
3.D4
45.61
79.76
3.06
40.25
77.10
2.96
43.37
79.88
2.96
74.6
75.4
NN-CIFT
48.97
83.57
3.25
49.71
3.29
85.49
3.29
87.14
77.5
79.3
Full Data
49.31
86.25
3.48
52.55
89.58
3.51
49.31
89.39
3.45
50.95
90.23
3.66
73.7
74.6
Table 5: Results on the Qwen2.5 with 0.3, u 0.05. "+ NN-CIFT" indicates using NN-CIFT to estimate influence values computed from the corresponding method's influence function. "+ DistilGPT2" indicates using the DistilGPT2 model as the language model in the corresponding method's influence function. The average performance difference between NN-CIFT and the original influence function is merely 0.24%.
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 singular, sealar value. Furthermore, the scalar values are constrained to small range (see Equation 1), reducing the margin of error. Putting these two reasons together, we can see why a neural network can replace language model during influence estimation without any significant effect on performance.
7

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Datasel
MixInstruct
Alpaca
MMLU
Method
ICL
QLoRA
ICL
QLoRA
ICL
QLORA
Metric
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
ROUGE
BGE
LAJ
Accuracy
Accuracy
Initial
32.31
74.27
2.18
35.16
78.13
2.21
37.44
78.65
2.41
37.81
78.69
2.43
71.9
72.3
Random
35.83
80.62
2.98
37.13
81.57
3.01
40.44
82.75
2.48
40.19
81.15
2.46
71.3
72.3
SelectIT
40.64
84,99
3.17
45,97
86.31
3,20
82.00
2.54
43.06
83.59
73.6
75.8
DisuitOP12
39.84
80.48
3,02
41.81
81.21
3,03
40.74
81.44
2.37
40.36
81.85
2.53
73.5
73.8
40.33
3.19
82.18
43.45
82.86
75.4
L.SSS
48.33
85.78
3,30
49.93
IIntruutt--- Llama-Sh, Qwen2.5 and Mistral as shorthand for the rest of 87.42 42
3.37
44. 14
85,80
3.04
47.13
87.
3.05
75.4
76.6
DistilGPT2
45.22
82.80
3.23
44.53
84.56
3,31
80.23
2.68
42.65
84,29
74.5
74.4
NN-CIFT
48.75
86.15
3.33
51,93
86.57
3.41
44.43
85.79
3.07
47.90
88.01
3.04
75.2
77.3
DELIFT (SE)
48.84
88.10
3,42
48.85
88.16
3,44
45,13
87.34
3.35
48.47
89.19
3.42
76.7
77.1
DisuiGPP2
46.25
86.22
3.39
46.29
87.67
3.41
44.84
86.00
3,25
46.86
86,93
3,38
75.7
77.7
CIFT
48.81
88.77
3.41
49.14
88.33
3.44
46.01
86.43
3.36
47.99
88.03
3.41
76.8
77.4
DELIFT
3,56
3.40
78.2
80.4
DistilGPT2
46.55
88.81
3.41
47.78
89.34
3.46
45.31
83.69
3.23
44.78
85.08
3.31
75.3
76.9
-N-CIFF
53.53
90.82
3.55
88.97
52.48
92.03
78.4
80.9
Full Data
52,30
91.32
3.60
54.83
91.57
3.69
50.61
90.77
3.41
54.51
90.70
3.58
79.1
81.2
Table 6: Results on the Mistral model with v 0.3, 0.05. "+ NN-CIFT" indicates using NN-CIFT to estimate influence values computed from the corresponding method's influence function. "+ DistilGPT2" indicates using the DistilGPT2 model as the language model in the corresponding method's influence function. The average performance difference between NN-CIFT and the original influence function is merely 0.12%.
Subset Selection Evaluation
Motivated by the results in Figure 2, we apply the InfluenceNetwork 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 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 iirruction-tuning, preference alignment, and knowledge-base based benchmarks where we use 15k for training, 5k for validation, and 5k for testing. We evaluate using three models: meta-llama/LLama-> 3.1-88 [Grattafiori al., 2024], twen/Quen2 5.....51..55 1B [Qwen et al., 2025), and mistralai/Miiiiao 2409 (22.2B) [Jiang et al.). Note, the experimental section.
Metries. To evaluate the instruction following capabilities of our fine-tuned model M', employ a variety of metrics to capture the similarity between ground truth answers and predicted answers from M': (1) ROUGE [Lin, 2004]: 7-gram word overlap (specifically, rouge-1), (2) BGE: semantic en-v1. 5, and (3) LAJ: an ILM-as-a-Judge namely the prometheus 7aas--b--e v2-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.
similarity of embeddings using agg-large-ar aarge-en-vl.
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 0.0. This is the base model's performance on the dataset. Next, we use a small language model DistilGPT2 ddistilbert/distiilgtt) [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 = 1.0. i... the model's performance when the full dataset used.
Setup. We use 0.05 for training the InfluenceNetwork. We also use small fraction of Dy 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 OLoRA [Dettmers et al., 2023] on M, or (2) in-context learning (ICL) examples. To elaborate the ICL set up, choose the top-5 most semantically similar
8

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samples from the chosen subset to add in-context. To measure semantic similarity, we again use bge-large-en-vz 5. Table 4-6 reports results for each model on all three datasets with 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 0.00096-0.0 0.00% 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 '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 Select]T). This is because the model-dependent methods experience significant performance gains when the data valuation model the same as the fine-tuning model. We note that our evaluation's '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 funetions and NN-CIFT is only O. 16%%. 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.
Conclusion
In this paper, we introduce NN-CIFT: Neural Networks for eiei Instruction Fine- Lame-Tuning 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 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 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 lightweight enough that retraining would suffice for now).
References
I. Agarwal, K. Killamsetty, L. Popa, and M. Danilevsky. DELIFT: Data efficient language model instruction fine-tuning. The Thirteenth International Conference on Learning Representations, 2025. URL https: htt.://pes/pppoeeeeeeeeeeee////r net:/forum/.d-FPttooeeee
'The average performance difference is calculated by taking the absolute difference in performance, dividing it by the original performance, and then averaging this ratio across all settings (datasets, methods, metrics, baselines).

---

Model
Phi-3
Llama-8B
Dataset
MixInstruct
Alpaca
MixInstruct
Alpaca
Initial
Random
12.4
12.3
12.9
12.3
SelectIT
7,047
6,594
6,671
6,470
DistilGPT2 + SelectIT
144
139
144
139
NN-CIFT' + SelectIT
65
63
64
63
LESS
12,338
11,217
10,843
14,819
DistilGPT2 + LESS
1,291
1,278
1,291
1,278
NN-CIFT' + LESS
78
75
74
84
DELIFT (SE)
216
218
218
219
DistilGPT2 + (ELIFT(SE)
98
99
98
99
NN-CIFT + DELIFT (SE)
48
48
48
DELIFT
67,379
68,117
68,076
65,711
DELIFT NN-CIFT + DELIFT
DistilGPT2 + DELIFT
8,058
7,790
8,058
7,790
215
217
217
211
Full Data
Table 7: Costs (in seconds) of data valuation. Specifically: Random: chooses random subset of points. SelectIT: calculates the ranking scores for each data point according to Appendix C.2. LESS: computes the cosine similarity between pairs of projected gradients for D> and DT, according to Equation 6. DELIFT (SE): computes the distance between each pair of embeddings (i,j)
Dr.j Dr. according to Equation 5. DELIFT: computes the inference-based utility metric for each pair of embeddings (i.j), according to Equation 4. NN-CIFT: Steps and 2 in Figure 1. Note, the costs of DistilGPT2 are the same across both models because they use the same data valuation.
Bilmes. Submodularity in machine learning and artificial intelligence, 2022. URL https: // //arxiv..ao.//////////////aa org/ wtw.//222..o. 00132..
D. Das and V. Khetan. Deft: Data efficient fine-tuning for pre-trained language models via unsuper- vised core-set selection, 2024. URL http::://aaiii.or////aaaaaa httpg//abb/3111117/7. 16776.
T. Dettmers, A. Pagnoni, A. Holtzman, and L. Zettlemoyer. Qlora: Efficient finetuning of quantized Ilms, 2023. URL. https::t//// /ttpas://////v////aeeeaeeasmmav/ attaaaaivvvv..../aaa abs /305/ 2305. 14314.
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A Hyperparameter Studies
tediiing
427
C25
Prediting
nandan
6000
Infuencclleteerrk size params!
Figure 4: MSE versus InfluenceNetwwrkk sizes (measured by the number of parameters). We try 1-5 layers with 46 different combinations of hidden layer sizes from (5, 10, 20, 50, 100, 200, 500, 1000, 2000, 3000, 4000, 5000).
A.1 Hyperparameter Study #1: InftuenceNetwork 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 This figure shows that small InfluenceNetworkk perform comparatively well as larger InfluenceNetworkss
A.2 Hyperparameter study #2: Trade-off between and
We perform a hyperparameter study between u and v on MixInstruct using DELIFT's influ- function (Equation 4). We perform grid search where u. 0.1,0.15, 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 metrie from each of these experiments. As shown, the figures in each row follow the same general trend, showcasing that NN-CIFT can effectively replace the expensive influence function estimation.
{0, 0.01, 0.05,
expected, we notice a few trends. (I) QLoRA generally has better perfor- mance than ICL. This because fine- tuning has more impact 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 train- ing. (3) Larger IFT subsets, especially in the ICL setting, lead poorer perfor- mance. During ICI., the top-5 seman- tically similar samples are chosen from the subset to add as in-context examples, However, semantic similarity does al- ways translate to performance enhance- ment these samples can be harmful to the model's performance. Finally, a follow-up to (3), the highest performance regions tend to be around 0.2 0.4. Appendix B contains results on smaller subsets of IFT data (v 0.1 and 0.2).
Table 8: Hyperparameter study for and v on MixInstruct with DELIFT's influence function. Lighter colors indicate better BGE performance.
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Dataset
MixInstruct
Alpuca
Method
ICL
QLoRA
ICL
QoRRA
Metric
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
Initial
37.87
78.92
2.98
36.36
82.55
3.02
25.79
67.82
2.56
27.29
71.57
2.62
Random
37.51
78.01
3.05
35.55
82.13
3.04
24.33
67.37
2.84
29.34
70.86
3.06
SelectT
33.20
3.12
37.00
3.13
24.48
67.48
2.86
30.06
68.06
NN-CIFT + Selectff
33.55
72.15
3.07
35.38
72.45
3.18
26.41
65.57
2.81
28.78
67.83
2.99
LESS
32.57
72.07
3.05
34.61
72.82
3.18
26.15
69.83
2.81
28.53
67.17
2.99
NN-CIFT + LESS
33.19
72.94
3.02
35.42
72.03
3.18
24.63
70. 11
2.84
27.63
67.41
2.51
DELIFT (SE)
35.71
78.09
3.22
39.63
78.36
3.28
29.17
70.69
3.01
30.60
71,50
3.14
NN-CIFT DELIFT (SF)
36.34
78.76
3.33
72.28
30.23
71.01
DELIFT
36.45
78.11
3.23
39.83
78.83
3.29
30.15
74.01
3.18
37.81
78.49
3.31
NN-CIFT DELIFT
36.17
78.16
3.22
38.08
78.25
3.28
31,95
74.84
3.26
37.26
78.36
3.28
58.65
39.29
78.85
Table 9: Results on the Phi-3 model with v = 0.1, = 0.05. NN-CIFT + Method and DistilGPT2 + Method follow the same definitions as in Table ??. The average performance difference between NN-CIFT and the original influence function is merely 1.91%.
Dataset
MixInstruct
Alpuca
Method
ICL
QLoRA
ICL
QLORA
Metric
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
Initial
28.53
74.05
2.94
34.42
78.54
3.00
24.85
72.45
2.26
34.29
80.82
3.03
Random
35.67
76.30
3.18
37.20
80.63
3.19
30.82
75.38
2.82
36.95
80.48
3.05
Selectf
36.53
3.20
2.84
NN CIFT + Seleciff
NN-CIFT
35,57
78.86
3.17
37.20
80.56
3.21
30.52
74,86
2.88
37.20
80.55
3.13
LESS
35.31
77.07
3.19
37.46
80.86
3.23
31.31
75.07
2.71
37.45
80.85
3.23
NN-CIFT + LESS
35.16
78.11
3.16
37.93
81,36
3.20
32.16
76.
2.75
37.93
81.35
3.21
DELIPT (SF)
35.13
77.71
3.12
36.78
79.69
3.15
30.14
73.71
2.61
36.80
79.69
3.15
NN-CIFT DELIFT (SE)
35.12
78.69
3.13
37.33
80.34
3.08
31.12
74.69
2.62
37.33
80.34
DELIFT
37.82
80.55
3.18
37.61
82.63
3.20
31.82
75.62
2.83
37.61
80.55
3.29
NN-CIFT DELIFT
37.52
81.02
3.15
37.88
82.01
3.19
31.55
75.04
2.79
37.88
81.16
3.29
54.43
48.29
Table 10: Results on the Llama-8b model with v = 0.1, u = 0.05. NN-CIFT + Method and DistilGPT2 Method follow the same definitions as in Table ??. The average performance difference between NN-CIFT and the original influence function is merely 1.14%.
B Evaluation on Smaller Subsets
Tables 9 and 11 report extra results for the Phi-3 model Similarly, Tables 10 and 12 report results for Llama-8B on v = 0.1 and v = 0.2, respectively. With Tables ?? and in the main text, these results show an increasing trend in performance with higher subset of IFT data (i.e., higher v). They also show similar trends where NN-CIFT performs similarly the original influence function.
0.1 and 0.2, respectively.
C Influence Functions
Following the problem formulation, formally define the influence functions we used throughout our evaluation.
C.1 Pairwise Influence Functions
DELIFT [Agarwal et al., 2025] a model-dependent, inference-based metric. Samples (iur, iny E Dj= are used as in-context examples for evaluating Jy) E 'D,, and those with improved model performance are chosen to represent Dy. This can be calculated by comparing the performance with and without (iz, ły) an in-context example (where D(,, -) e [0, 1] is function to measure distance
14

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Dataset
MixInstruct
Alpuca
Method
ICL
QLoRA
ICL
QLORA
Metric
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
Initial
37.87
78.92
2.98
36.36
82.55
3.02
25.79
67.82
2.56
27.29
71.57
2.62
Random
37,91
78.96
3.06
38.89
81,88
3.05
29.95
76.35
3.12
30.27
76.21
3.15
SeleetT
35.39
78.14
3.02
37.71
78.26
3.06
30.31
74.26
3.13
37.10
77.66
NN-CIFT + Selecttf
35.71
78.23
3.04
37.36
78.24
3.05
31.03
75.79
3.09
36.67
77.98
3.04
LESS
37.61
79.55
3.07
37.43
78.93
3.09
32.57
74.07
3.02
34.61
76.68
3,08
NN-CIFT + LESS
37.87
77.96
3.04
38.96
78.93
3.08
33.20
74.94
3.05
35.42
78.02
3.09
DELIFT (SE)
39.56
81,25
3.17
39.77
82.74
3.15
34.06
77.31
3.23
39.48
80.95
3.25
NN-CIFT DELIFT (SF)
39.62
3.16
39.14
3.14
76.67
38.89
80.80
DELIFT
45.55
82.32
3.36
43.74
82.35
3.50
35.02
77.89
3,40
39.32
80.89
3.35
NN-CIFT DELIFT
46.44
82.47
3.38
43.76
82.72
3.52
34.44
77.39
3.36
38.30
80.32
3.31
58.65
3.51
39.29
78.85
Table 1I: Results on the Llama-8b model with e = 0.2, u 0.05.
NN-CIFT + Method and
DistilGPT2 Method follow the same definitions as in Table ??. The average performance difference between NN-CIFT and the original influence function is merely 1.08%.
Dataset
MixInstruct
Alpaca
Method
ICL.
QLoRA
ICL
QLoRA
Metric
ROUGE
BGE
LAJ
ROUGE
BGB
LAJ
ROUGE
BGB
LAJ
ROUGE
BGE
LAJ
Initial
28.53
3,00
72.45
80.82 79.77
Random
39.55
82,79
3.25
39.05
82.64
3.26
31.49
76.96
3.06
41.67
3.14
SelectT
39.20
82.84
3.29
40.44
82.55
3.30
35,98
81,82
2.95
42.62
83.17
3.21
NN-CIFT + Seleatf
40.02
82.63
3.23
39.92
82.22
3.29
38.84
84.09
3.03
44.62
84.63
3.23
LESS
40.33
82,17
3.26
40.34
82.87
3.26
36.11
79.82
3.06
43.48
82,94
3.32
NN-CIFT + LESS
43.69
82.67
3.27
40.21
82,89
3.26
37,00
80,38
3.07
43.48
82.80
3.34
DELIFT (SE)
44.57
82.63
3.31
45.97
83.87
3.33
38:52
82,37
3.18
45.73
83.33
3.35
NN-CIFT DELIFT
45.03
3,40
45,20
82.79
DELIFT
45.55
83.69
3.37
48.21
86.81
3.36
39.16
82.30
3.26
45.24
83.38
3.39
NN-CIFT + DELIFT
46.40
84.73
3.34
47.81
86.83
3.31
40.16
82.37
3.28
45.67
83.49
3.41
54.43
3.40
3.58
48.29
90.82
Table 12: Results on the Llama-8b model with 0.2, 0.05.
NN-CIFT + Method and DistilGPT2 + Method follow the same definitions as in Table ??. The average performance difference between NN-CIFT and the original influence function is merely 1.26%.
between two probability distributions, and f(](f) is language model with parameters and input query q):
sim(i. DDj. f(e,, (yiriyy)a10))
D(jy, f(zl0))
(4)
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 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 larger subset. Hence, we rely on our influence function to capture the informativeness of samples, and submodular functions to choose set of representative samples, resulting in small, information-rich subset on which to fine-tune model.
DELIFT (SE) [Agarwal et al., 2025] is model-independent metric, and chooses samples from Dj which are semantically closest the samples from Dy. Semantic distance calculated by the cosine distance between embeddings of samples:
15

---

< emb((iz, ky)), emb( (y):
sim(i,
(5)
|lemb( (f2: 11
where emb(g) an embedding model with input data q. Similar to DELIFT, DELIFT (SE) also uses the Facility Location function to select small, information-rich subset of samples.
LESS [Xia et al., 2024] is model-dependent, gradient-based metric. Here, gradients between samples in D and D are matched by cosine similarity, and those that match the highest are chosen to represent Dy (where (1; 0) is the gradient of data point y from model with parameters 0):
Viiaa, by): 0), (a., sim(i, = ((L,, :):
During the data selection stage, the top-k matching gradients are chosen to be part of the subset. One thing notice is that the above equation implies quadratic computation while Table in the main text denotes 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 it uses model's 's uncertainty rank data samples. Still, as mentioned in Table from the main text, the linear time operations are forward propagations through LLMs.
SelectlT ranks data points based on their token-level, sentence-level, and model-level uncertainty ex- pressed 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 sentence, for each prompt in pool of prompts. Finally, the model-level uncertainty is calculated by taking a weighted average of the sentence-level uncer- tainty scores for multiple model sizes (the weights determined by model size). This three-stage process provides a ranking process thus, during data selection, the points with the top-k scores are chosen.
D License
All the code of this project is under the Apache 2.0 License. The datasets MixInstruct and Alpaca 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.
16

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Reviews:
[{"review_id": "SOGJR3OXqK", "reviewer": "Reviewer_R2g1", "summary": "This 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.", "questions": "Q1: 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?", "limitations": "Yes, 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 ??”", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Strengths:\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).", "was_revised": true, "final_justification": "The authors have adequately addressed my concerns. I have increased my score from 5 to 6 as a result.", "rebuttal": "We appreciate the reviewer for pointing out that **NN-CIFT \"generalizes across conditions\" and is evaluated with \"rigorous benchmarking with multiple metrics\"**. Below, we address the concerns and questions.\n\n> Table 3-6 don't address [the question of how to get equal quality with fewer data samples]. Rather, they just show that NN-CIFT is slightly better than alternative approaches/methods, and that it can achieve similar performance to [baselines] 77-99\\% of the time.\n\nThere is a slight misunderstanding here. The baselines SelectIT, LESS, DELIFT and DELIFT (SE) are influence functions that use large language models for influence estimation. Our method, NN-CIFT, replaces the language model with a small neural network. Tables 3-6 show that **the small neural network in NN-CIFT is able to perform similarly to the language model-based baselines**. Moreover, the 77-99\\% metric refers to the costs that were saved. In other words, **NN-CIFT uses 77-99\\% less time while achieving similar performance**. Finally, in Section 5, we show that selecting just 30% of data is able to achieve very similar performance to the full dataset -- showcasing how to achieve equal quality with fewer data samples.\n\n\n> Q1. DELIFT (SE) compares the similarity of sentence embeddings between pairs of data, and that this is computationally expensive.\n\nThis is a minor comment on the computational expensiveness of a baseline method.\n\n> Q2. in the example of \"DELIFT+NN-CIFT\", [was] DELIFT 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\nYes, that is correct! We show that **using 5\\% of the training data is effective** to learn to estimate influence values using a neural network.\n\n> Q3. Were [DELIFT and DELIFT (SE)] values recalculated in your paper?\n\nYes. Because their code base was available online, we reproduced their experiments and recalculated the values in our paper. The models and datasets are slightly different between the DELIFT paper and our paper, hence the values are slightly different as well. We choose more recent models, and we choose a more diverse set of tasks for datasets (MixInstruct is general instruction tuning, Alpaca is alignment, and MMLU is a knowledge-based task).\n\n> Q4.a 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.\n\nTable 1 is more for demonstration purposes. **Table 6 contains the end-to-end time costs** for training the network. We will add this note in Table 1 in the final version.\n\n> Q4.b how small are these subsets? Have you explored the effects of dataset size in this first step?\n\nThe subsets are 5\\% of the entire dataset. We do indeed explore the effects of the dataset size in Figure 2. We see that with larger subsets of data, the accuracy of the InfluenceNetwork does not change, hence **5\\% is sufficient and optimal**.\n\n> Q5. Why doesn't MSE decrease appreciably as the model size increases?\n\nA larger model would be able to choose better points and can better estimate the information present in a data point, but this doesn't change the fact that **influence values are in a small range and do not vary drastically, as analyzed in Section 4.4**. Hence, it is easy to use a neural network to learn a function to estimate influence values with high accuracy, regardless of the size of the language model.\n\nFinally, thank you to the reviewer for the grammatical suggestions and stylistic changes. We will incorporate them into the final version of the paper.\n\n----\nOverall, we thank Reviewer R2g1 for their time and thoughtful consideration. If we have addressed the concerns, we would greatly appreciate to see this reflected in an increase in the scores."}, {"review_id": "uEpzPdzLby", "reviewer": "Reviewer_AAYF", "summary": "This paper proposes using small neural networks—referred to as the InfluenceNetwork—to estimate influence values, thereby reducing the computational cost of calculating influence functions.", "questions": "This 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.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": true, "final_justification": "I'm convinced by the author's response.", "rebuttal": "We thank the reviewer for mentioning **NN-CIFT \"presents a promising direction with potentially impactful contributions\"** and that our paper is \"easy to follow\". Below we address the concerns and questions.\n\n> several existing approaches have been specifically designed to relax the computational burden of influence function estimation.\n\nGreat point -- these works, as the one mentioned, find optimal ways to estimate gradients, to which influence estimation is a downstream application. With such a process, we run the risk of overly lossy influence estimation, as more and more information is lost at each step. **NN-CIFT, on the other hand, compress information one-shot**. Hence, we do not compare our method against these baselines. Furthermore, for the particular baseline that the reviewer has mentioned ([1]), there is no public code available.\n\n> the paper does not clearly report the training time of the model or provide sufficient details to estimate it reliably.\n\nTable 6 contains the computational costs for influence estimation: this includes the time taken for language-model based influence estimation, as well as the InfluenceNetwork training time. We do not report downstream model fine-tuning time (after the subset of data is selected) because that is not directly related to our main contribution. **Our work focuses on reducing the time for influence estimation**. Also, in Table 6, the caption breaks down how each baseline's cost was measured. We'd be more than happy to clarify any questions here!\n\n---\n\nOverall, we thank Reviewer AAYF for their time and thoughtful consideration. If we have addressed the concerns, we would greatly appreciate to see this reflected in an increase in the scores."}, {"review_id": "37XdOxSIi0", "reviewer": "Reviewer_35kX", "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%.", "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\n- can the method be viewed as denoising noisy influence estimates?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths\n- 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.\n- the method can reduce computational cost, potentially adding only minimal complexity\n\nWeaknesses\n- 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?\n- 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?", "was_revised": true, "final_justification": "The authors performed experiments to show that the proposed method is not sensitive to the choice of embedding model, so that it can be used as-is on a variety of influence function methods without modification.", "rebuttal": "We appreciate the reviewer for pointing out that **NN-CIFT \"fills a missing gap in literature\"**. Below, we address the concerns and questions.\n\n> Justify the choice of the particular BAAI embedding ... does it generally work regardless of the underlying influence function being approximated?\n\n| Embedding Model                         | Q1    | Q2    | Q3    | Q4    |\n|-----------------------------------------|-------|-------|-------|-------|\n| BAAI/bge-large-en-v1.5                  | 0.051 | 0.084 | 0.074 | 0.084 |\n| Qwen/Qwen3-Embedding-0.6B               | 0.076 | 0.087 | 0.087 | 0.089 |\n| intfloat/e5-mistral-7b-instruct         | 0.026 | 0.083 | 0.084 | 0.083 |\n| Snowflake/snowflake-arctic-embed-l-v2.0 | 0.077 | 0.087 | 0.087 | 0.088 |\n\nTable 12: Varying embedding models and their corresponding MSE values (averaged across 5 runs) between estimated influence values and ground truth influence values, with 5\\% selected data. These results are for learning DELIFT influence values. As shown, NN-CIFT is invariant to the embedding model selected and is able to effectively estimate the influence values.\n\nWe chose the BAAI embedding model because previous works (like DELIFT (SE)) had relied on the same embedding model. Please refer to Table 12 above-- it shows that **NN-CIFT is invariant to the embedding model**. We will add these results in the final version of the paper.\n\n> guidance on when the proposed method should or should not be used\n\n**NN-CIFT can be used to replace any language-model based influence function** that is later used to select a subset of data on which to fine-tune a language model. NN-CIFT's Step 1 assumes that the small subset of samples is representative of the rest of the dataset, hence it is difficult to say how well NN-CIFT will perform with distribution shifts. However, because NN-CIFT is lightweight, it can be retrained quickly to adapt to distribution shifts as well. We will add this analysis to the limitations section in the final version of our paper.\n\n> does it work better for some influence functions?\n\nNot necessarily -- we choose to evaluate with SelectIT, DELIFT, DELIFT (SE) and LESS to showcase the **wide applicability of NN-CIFT**. SelectIT uses model confidence, DELIFT uses model performance, DELIFT (SE) uses embedding model similarity, and LESS uses model gradients to inform data valuation. **NN-CIFT adapts to each case without modifications to the methodology**.\n\n> Q1. how sensitive is the training of the surrogate model to hyperparameters?\n\nWe show these results in Figure 2 and Appendix A. Figure 2 shows that small subsets of data are sufficient for learning the InfluenceNetwork, and Appendix A shows that small networks are sufficient for learning to estimate influence values with high accuracy. Hence, **the InfluenceNetwork does not require significant experimentation to achieve good performance**.\n\n> Q2. can the method be viewed as denoising noisy influence estimates?\n\nVery interesting point -- it depends on what we consider \"noisy influence estimates\". As mentioned in Section 4.4, the **InfluenceNetwork essentially learns to model the outliers** (where the influence values are very high and very low). The InfluenceNetwork can definitely smooth over influence values from non-interesting data, if we consider them noisy. We will add this note to the conclusion/future works section of our final paper.\n\n---\n\nOverall, we thank Reviewer 35kX for their time and thoughtful consideration. If we have addressed the concerns, we would greatly appreciate to see this reflected in an increase in the scores."}, {"review_id": "N9jSZu5xLF", "reviewer": "Reviewer_LcV6", "summary": "This 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.", "questions": "1. 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?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\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.", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate the reviewer for pointing out that **NN-CIFT achieves \"a significant reduction in time\" while \"maintaining a good estimation capability\"**. Below we address the concerns and questions.\n\n> the cost of the embedding model is not included, it is indispensable in training/inference\n\nWe agree that the cost of the embedding model is indispensable to the training of the InfluenceNetwork, but it is considered an **offline cost**, as mentioned in lines 158-161 of the manuscript.\n\n> [this work] explains from the perspective of the sparsity of the empirical distribution ... this method has practical value, it is more inclined towards accelerating optimization ... rather than fundamentally advancing the theory of influence functions.\n\nWhile we do not theoretically motivate the reason why influence values are generally sparse, our work is one of the first works to show that **influence values are sparse** (Section 4.4, specifically Figure 3 and lines 202-204), and we present a methodology that exploits this fact. We will clarify this in our conclusion/future works section in the final version of the paper.\n\n> Q1. How strongly bound is Influence Network to embedded models?\n\n| Embedding Model                         | Q1    | Q2    | Q3    | Q4    |\n|-----------------------------------------|-------|-------|-------|-------|\n| BAAI/bge-large-en-v1.5                  | 0.051 | 0.084 | 0.074 | 0.084 |\n| Qwen/Qwen3-Embedding-0.6B               | 0.076 | 0.087 | 0.087 | 0.089 |\n| intfloat/e5-mistral-7b-instruct         | 0.026 | 0.083 | 0.084 | 0.083 |\n| Snowflake/snowflake-arctic-embed-l-v2.0 | 0.077 | 0.087 | 0.087 | 0.088 |\n\nTable 12: Varying embedding models and their corresponding MSE values (averaged across 5 runs) between estimated influence values and ground truth influence values, with 5\\% selected data. These results are for learning DELIFT influence values. As shown, NN-CIFT is invariant to the embedding model selected, and is able to effectively estimate the influence values.\n\nPlease refer to Table 12 above -- we show that **NN-CIFT 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.\n\n> Q2. Why choose a single-layered MLP?\n\nWe address this in Appendix A.1 where we evaluate the InfluenceNetwork with varying sizes. For easy viewing, we plot the number of parameters versus the MSE and show that the **MSE remains very low for larger and smaller networks, alike**.\n\n> Q3. Can Influence Network be trained on one task and directly used under another task/distribution?\n\nThis is a great question -- we believe that the limitation of the InfluenceNetwork is that it is not robust to distribution shifts in the data. However, **because NN-CIFT is lightweight, it can be retrained quickly to adapt to distribution shifts as well**. We will add this discussion to the limitations section in the final version of our paper.\n\n---\n\nOverall, we thank Reviewer LcV6 for their time and thoughtful consideration. If we have addressed the concerns, we would greatly appreciate to see this reflected in an increase in the scores."}]

Author rebuttal:

Meta-review: This paper presents a method that uses a small surrogate neural network to approximate computationally expensive influence functions for data selection in LLM finetuning. The primary contribution is an empirical demonstration that this approach can reduce the time cost of data valuation while preserving the downstream performance of models finetuned on the selected data.

All reviewers are in agreement on the paper's acceptance based on extensive empirical validation across different models and tasks, and general applicability. The initial reviews raised several points for clarification, questioning the method's dependence on a specific embedding model and seeking more clarity on the end-to-end cost analysis and the choice of baselines. The reviewers were satisfied with the author's response, which included new experiments that addressed the main concerns.

For the camera-ready version, I recommend the authors integrate the clarifications and new results from their rebuttal into the main body of the paper. This includes: (1) the new experimental results demonstrating the method's robustness to different embedding models, (2) the clarification of the end-to-end cost analysis and the justification for the chosen baselines, and (3) the expanded discussion on the method's limitations, particularly concerning distribution shifts.

The key reason for my recommendation is the paper's practical utility: it offers a simple, general, and validated solution to the expensive problem of data selection for LLM finetuning, making it highly relevant to a broad audience of practitioners.
Decision: Accept (poster)