Deciphering the Impact of Pretraining Data on Large Language Models through Machine Unlearning (2024)

Abstract: August 11-16, 2024 ©2024 Association for Computational Linguistics Deciphering the Impact of Pretraining Data on Large Language Models through Machine Unlearning Yang Zhao♠†, Li Du ♡†, Xiao Ding♠*, Kai Xiong♠, Zhouhao Sun♠, Jun Shi♣, Ting Liu ♠ and Bing Qin♠ ♠Research Center for Social Computing and Information Retrieval Harbin Institute of Technology, China ♡Beijing Academy of Artificial Intelligence, Beijing, China ♣Academy of Cyber, Beijing, China {yangzhao, xding, kxiong, hzsun, tliu, qinb}@ir.hit.edu.cn duli@baai.ac.cn junshi1770@gmail.com , Abstract

text: Findings of the Association for Computational Linguistics ACL 2024, pages 9386–9406 August 11-16, 2024 ©2024 Association for Computational Linguistics
Deciphering the Impact of Pretraining Data on Large Language Models through Machine Unlearning
Yang Zhao♠†, Li Du ♡†, Xiao Ding♠*, Kai Xiong♠, Zhouhao Sun♠, Jun Shi♣, Ting Liu ♠ and Bing Qin♠
♠Research Center for Social Computing and Information Retrieval Harbin Institute of Technology, China
♡Beijing Academy of Artificial Intelligence, Beijing, China ♣Academy of Cyber, Beijing, China
{yangzhao, xding, kxiong, hzsun, tliu, qinb}@ir.hit.edu.cn duli@baai.ac.cn junshi1770@gmail.com
,Abstract
Through pretraining on a corpus with various sources, Large Language Models (LLMs) have gained impressive performance. However, the impact of each component of the pretraining corpus remains opaque. As a result, the organization of the pretraining corpus is still empirical and may deviate from the optimal. To address this issue, we systematically analyze the impact of 48 datasets from 5 major categories of pretraining data of LLMs and measure their impacts on LLMs using benchmarks about nine major categories of model capabilities. Our analyses provide empirical results about the contribution of multiple corpora on the performances of LLMs, along with their joint impact patterns, including complementary, orthogonal, and correlational relationships. We also identify a set of “high-impact data” such as Books that is significantly related to a set of model capabilities. These findings provide insights into the organization of data to support more efficient pretraining of LLMs.

heading: 1 Introduction
text: Under the data-driven paradigm, Large Language Models (LLMs) have demonstrated promising performance and showcased immense potential in further promotion (OpenAI et al., 2023; Touvron et al., 2023b; Du et al., 2021; Bai et al., 2023a). Previous analyses have suggested that the composition of the pretraining corpus may exert a significant impact upon the performance of LLMs (Longpre et al., 2023; Shen et al., 2023a). However, how different sources and types of pertaining corpora influence the knowledge and reasoning ability of LLMs largely remains opaque, or stays at the qualitative level. As a result, it still heavily relies on the experiences of trainers to organize the pre-training
†These authors contributed equally to this work. *Corresponding Author. The official implementation of this paper is available at
https://github.com/zy125413/GRACE
corpus. Such experiences may deviate from the optimal, and hence limit the efficiency and effectiveness of model training.
In this paper, we propose to quantify how components with different sources and types in the pretraining corpus contribute to the performance of LLMs. Previous literature refers to such analyses as Data Influence Analysis (DIA) (Akyürek et al., 2022). However, due to the limitations of previous DIA methods, the DIA of LLMs remains challenging. Primary DIA methods can be mainly categorized into two lines: the retraining-based methods and gradient-based methods. Retraining-based methods work by removing specific data from the training corpus and retraining the model, then comparing changes in model performance. Considering the prohibitive training cost of LLMs, retrainingbased methods would be impractical (Nguyen et al., 2023). While the gradient-based methods may not be applicable in analyzing the source of the complex reasoning ability of LLMs, as they assume that the performance upon a test instance is determined by several independent training instances. However, such an assumption may not hold for LLMs, especially for the ability to complete reasoning tasks, as it may originate from groups of correlated instances that jointly contribute to the performance of LLMs. For example, solving math problems requires understanding a knowledge taxonomy, and the taxonomy is described by a set of interdependent instances holistically. Missing one component would lead to the collapse of the whole taxonomy. Hence, the gradient-based methods may fail to trace the influence of such a whole corpus, which is of vital importance (Grosse et al., 2023).
To address these issues, we resort to another strand of method, Machine Unlearning. Prior research (Eldan and Russinovich, 2023; Jang et al., 2022) suggests that Machine Unlearning can selectively erase specific knowledge from a model through gradient ascent on corresponding instances.
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-w/o Algorithm -w/o ArXiv -w/o Books -w/o C4
-w/o Github -w/o StackExchange -w/o Wikipedia Llama2-7B
Examinations
Safety
Code Generation
Long Context
Textual Understanding
Mathematical Reasoning Textual Inference
Knowledge
Language Modeling
Figure 1: The impact of Unlearning different types of corpus on different abilities of the llama2-7B model.
This enables us to investigate the influence of a certain pretraining corpus on an LLMs by “Unlearning” instances from it, and then compare the performance of the “forgotten” LLMs with the original LLMs. Meanwhile, different from previous Machine Unlearning methods, to avoid unintended impacts on non-targeted samples, we incorporate additional regularization by retraining samples from non-targeted domains during the Unlearning process. Experiments demonstrate that our method can effectively remove information contained in the target samples, without significantly affecting other unrelated samples.
Based on our customized Machine Unlearning method, we systematically investigated the quantitative contribution of multiple important resources and types of training corpora on the performance of LLMs. We covered widely adopted high-quality corpora GitHub, Wikipedia, ArXiv, Books, StackExchange and C4, and conducted an in-depth analysis of their contributions to the model performance by segmenting them into subsets based on the type of knowledge. From the content dimension, the abovementioned corpora covered text, commonsense knowledge, domain-specific knowledge, math, and coding. Additionally, to investigate the source of the reasoning abilities of LLMs, we analyzed the impact of over ten kinds of programming languages with different coding paradigms, and 17 kinds of common algorithms such as Dynamic Programming. Programming paradigms essentially represent different abstractions of real-world problems, and an algorithm corresponds to a common solution for a particular type of reasoning problems. To comprehensively assess the impact of these corpora, we evaluated the “forgotten” LLMs across
various downstream tasks as illustrated in Figure 1 and detailed illustrated in Figure 4.
With our proposed gradient ascent-based Machine Unlearning method, we identify a range of corpora that have a significant impact on the capabilities of LLMs, and reveal previously unreported influences of certain corpus (such as algorithms) on model capabilities. Furthermore, we discovered the interaction among corpora which jointly affects the capabilities of LLMs, and the existence of “high-energy” corpora, like Books in the data. Our research underscores the importance of further studying the impact of pre-training data, to provide foundations for future research on the optimization of pre-training datasets to support a more efficient pre-training process.
Based on our analysis results, we provide several hints about the organization of the pretraining corpus, such how should the proportion of each category of pretraining corpus be set, the arrangement of datasets during the pretraining process, and the evaluation of the pretraining process of the LLMs.

heading: 2 Methodology and Validity Analysis

heading: 2.1 Machine Unlearning Based Data Influence Analysis
text: Following Eldan and Russinovich (2023) and Jang et al. (2022), we devise our approach based on the Machine Unlearning to eliminate certain kinds of information from LLMs. Formally, given an LLMs M and a sample set DT , we analyze the influence of DT upon M by making M “unlearn” the information of DT to derive a model MuT , and then compare the performance between M and MuT . For clarity, we call MuT as the forgotten model, DT as the targeted corpus, and the rest parts of the whole pretraining corpora as the non-targeted corpora.
The key of Machine Unlearning-based data influence analysis lies in that: (1) Effectiveness: How to unlearn DT to make that M has never been trained upon DT . (2) Precision: Do not incur unintentional impacts upon the non-targeted parts of the training corpus. To this end, we devise an GRadient AsCent-based Machine Unlearning with rE-training (GRACE). In the following sections, we describe the mechanism of GRACE and show the effectiveness and precision of GRACE.
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heading: 2.2 Gradient-based Machine Unlearning with Retraining
text: During the training process, LLMs learn knowledge by maximize the likelihood of training corpora through gradient descent. Hence, in line with Eldan and Russinovich (2023); Jang et al. (2022), the information within a targeted corpus DT could be unlearned by reverting the learning process through gradient ascent on DT . Formally, the objective function of the Unlearning algorithm is to minimize the log-likelihood upon DT .
However, there remains the risk that the performances on non-target domains are unintentionally impacted. To avoid this problem, GRACE introduces an additional retraining regularization. Specifically, the information within a non-targeted corpus DN could be revisited through gradient descent upon DN .
Hence, the whole algorithm runs in the following manner. Before starting, we first divide the nontarget corpus DN into a 9:1 split as a retraining set and a dev set. Then during the Unlearning process, if the model M ’s Perplexity (PPL) on the dev set is higher than that before Unlearning, a retraining is started until the PPL of M on the dev set restore to the original level on the dev set. At this time the Unlearning process would restart. In this way, the Unlearning and retraining alternate until the PPL on the target corpus DT , reaches the endpoint (which is described below), and the GRACE algorithm would be ended.
In practice, the retraining set is constructed by randomly sampling instances from the rest of RedPajama dataset (Computer, 2023) after excluding the target corpus. For instance, if we aim to unlearn the C language, the retraining set is set to be a random subset of the remainder of the RedPajama dataset after excluding the C language portion. Note that, to increase the diversity of the retraining dataset and prevent model performance degradation on unrelated domains, at each round of retraining, we would resample 30, 000 new instances.
Endpoint of the Unlearning Process A critical issue of the Machine Unlearning algorithm is when to stop the Unlearning process, so that the forgotten model MTu can approximate the state as if the original model M has never seen the target corpus DT . Prior methods achieve this by case study (Eldan and Russinovich, 2023) or manually selecting certain corpus DS that is highly similar to DT , whereas M has never been trained on it. So
that the performance of M on the unlearned dataset DS can be taken as the endpoint of Unlearning on DT . However, since the data filtering process of LLMs is opaque, it is hard to find a specific corpus that the model has not been trained on for each kind of target corpus.
To address this issue, we propose a randomized text-based method. Specifically, given an instance from DT , we tokenize it and randomly split the tokens into pieces with a length range from 1 to n, and then we shuffle their order and paste the shuffled pieces into a randomized text. The endpoint of the Unlearning process is defined to be the point that the MuT ’s PPL on DT equals M ’s PPL on the randomized text.
This is because: (1) Through randomizing, the knowledge, semantic, and logical relationship within DT are disrupted, hence, if the PPL of MuT on DT is close to the PPL of M on the corresponding randomized text, it suggests that MuT has completely forgotten DT ; (2) Compared to DT , the randomized text shares a similar lexical distribution, which would eliminate the influence of domainspecific vocabulary distribution.
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heading: 2.3 Validity Analysis of GRACE
text: Previous analyses demonstrate the effectiveness of gradient ascent-based Machine Unlearning methods in eliminating certain knowledge of LLMs (Eldan and Russinovich, 2023). We conduct further analyses to show the effectiveness of GRACE in Unlearning certain domains of knowledge and certain kinds of reasoning abilities, and the precision of not incurring unwanted impacts.
Experimental Settings To validate the precision and effectiveness of our methodology in selectively Unlearning certain domains of knowledge, we conduct Machine Unlearning using GRACE and take the mathematical subset of the Wikipedia corpus (Computer, 2023) as the target corpus Dmath. For the non-target dataset, we randomly select samples from the rest of Redpajama corpus (Computer, 2023) which explicitly excluded Dmath. To analyze the impact of GRACE, we not only evaluate the performance on the targeted domain math, but also include potentially related domains physics, chemistry, and biology and unrelated domains: economics history, psychology, law andlinguistics. Experiments are conducted with Llama-2-7B (Touvron et al., 2023b), more details are provided in Appendix A.
Analyses We demonstrate the loss curve on the target corpus and the non-target corpora in Figure 2, and the final PPL of the forgotten model Mu on each domain in Table 1. It can be observed that the loss of the model on Dmath continuously increases during the Unlearning process. In contrast, due to the additional retraining process of GRACE, there is no significant increase in the loss for the nontarget data. This suggests that GRACE would not incur unintentional model performance on the nontarget domains. Moreover, as shown in Table 1, after the Unlearning process, the performances on the physics, chemistry, biology and economics domains, demonstrate a degradation, while the model performance upon history, psychology, law and linguistics, remain unaffected. Interestingly, the extent of performance degradation in these domains is consistent with human cognition about the relevance of these domains with math: physics and mathematics are rather closely related; chemistry, biology, and economics share certain common grounds with mathematics. In contrast, the correlation between historical, psychological, legal, and linguistic knowledge with mathematical knowledge is quite limited. These
observations suggest that GRACE can eliminate certain domains of knowledge from LLMs without involving unwanted impacts, indicating the effectiveness and precision of our proposed method. In the Appendix C, we provide more evidences about the validity of our analysis method.

heading: 3 Main Analysis
text: After the validity analysis, we employ GRACE to investigate the impact of various corpora on the performance of LLMs. Specifically, Section 3.1 introduces the experimental settings. Section 3.2 explains how different types of data affect model performance individually. Section 3.3 discusses the joint impact of various types of data on the abilities of LLMs.

heading: 3.1 Experimental Settings

heading: 3.1.1 Target Corpora
text: Since the ultimate goal of data influence analysis is to provide empirical guidance for optimizing the organization of the pretraining corpus of LLMs, among various open-sourced datasets, we focus our study on various subsets of the Redpajama dataset (Computer, 2023), a replication version of the pretraining corpus of Llama (Touvron et al., 2023a; Chen et al., 2023; Fu et al., 2024). Moreover, considering the importance of complex reasoning ability, to further investigate the source of such ability, we include a set of programming algorithmics, as they can be viewed as an abstraction of thought patterns. As shown in Table 3, these datasets have been further divided into subsets, a total of 48 distinct datasets are chosen as target corpora. Specifically: • All subsets of RedPajama (Computer, 2023), including: C4, Github, Books, ArXiv, Wikipedia, StackExchange. These corpora play pivotal roles in the pretraining corpus of various LLMs (Ren et al., 2023; Zhang et al., 2024). • The ArXivs contains eight subsets of the Arxiv dataset, as listed in Figure 3 • The StackExchanges dataset is obtained by dividing the StackExchange portion of the Redpajama.This subsets into two subsets based on the number of “likes” each Q&A pair has received. Intuitively, the more likes an answer receives, the more likely it is to be a high-quality answer. • CodeAlgorithm contains 17 kinds of important leetcode algorithm problems (Hartford, 2023). • The CodeLanguage dataset is derived from the
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GitHub corpus, encompassing 15 types of programming language, spanning a variety of programming paradigms including Object-Oriented and Procedure-oriented languages, Declarative languages, Scripting languages, Front-end languages, as well as unctional language.
We provide more details about the target corpora in the Appendix E.

heading: 3.1.2 Evaluation Benchmarks
text: To comprehensively evaluate the influence of target corpora on LLMs’ performance, following Contributors (2023); Gao et al. (2023), as shown in Figure 3, we select a totally of 31 benchmarks covering 9 major ability of tasks and 21 sub-categories of capabilities. Details about these datasets and the experimental settings are provided in Appendix D.

heading: 3.1.3 Model for Analysis
text: We conducted all experiments using the widely adopted open-source decoder-based generative LLMs Llama-2-7B. The reasons lie in that: (1) llama2-7B is large and powerful enough to represent LLMs; (2) The training process of the llama27B is typical; and (3) The existence of the Scaling Law (Kaplan et al., 2020) allows us to infer the impact of various types of data on larger models by examining their effects on the Llama2 model.

heading: 3.2 Impact of Individual Corpus on Model Capabilities
text: Analysis Method As the difficulty of benchmarks is different, to make the performance changes on these benchmarks comparable, we first normalize them to the performance degradation ratio, which is defined as γi,u =
Aui,j−Aoj Aoj , where Aui,j is the model’s performance on task j after unlearning the target-datai, and A o j represents the performance of the original model on task j. In the below, we measure the impact brought by Machine Unlearning using the performance degradation ratio.
Analysis Results Figure 4 lists the Top and Bottom 5 datasets that have the most and the least impact on each type of model capability. From which we can observe that: • Language Modeling As a fundamental of LLMs, the language modeling ability is seldom significantly impacted by a specific type of corpus alone. As an (approximate) multi-lingual parallel corpus, the Wikipedia corpus may play a critical role in aligning different languages for an LLM, and influence the multilingual ability of LLMs. • Textual Understanding One prominent phenomenon is that programming language corpora have a high impact on the textual understanding ability of LLMs. Heuristically, codes are abstractions of relationships between real-world objections and could be helpful for understanding the semantic and logical relationships among text. Moreover, knowledge-rich corpora such as books and
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Arxiv, and corpora with high diversity such as books and C4 profoundly influence the textual understanding ability of LLMs. Hence, corpora with diversity, rich commonsense knowledge and code corpus may constitute three foundations for the textual understanding ability of LLMs. • Textual Inference Text inference tasks depend on a wide range of corpora. Notably, besides commonsense-related corpora, text reasoning tasks also extensively rely on various types of code corpora, algorithm corpora, and mathematical corpora. For example, tasks like Big Bench Hard (Suzgun et al., 2022) significantly depend on high-quality StackExchange content and algorithms such as breadth-first search. This demonstrates the importance of symbolic reasoning capabilities represented by mathematics and code in understanding the deep logical relationships within texts. • Knowledge Reasoning Datasets such as Books, and are invaluable for solving real-world knowledge problems. Programming languages, as an integral part of the global knowledge system, significantly influence the model’s knowledge capabilities. The ArXivs dataset, due to its complexity and deviation from common world knowledge, has a lesser impact. • Mathematical Reasoning The source of LLMs’ math reasoning capabilities has drawn great attention from researchers, as it could be an indicator
of the complex reasoning ability of LLMs (Ernest, 2023). From the results in Figure 4, high-quality mathematical texts and code corpora (especially algorithms) have a significant impact on LLMs’ math reasoning abilities. This demonstrates: (1) There is a close relationship between mathematical and coding abilities (Soldaini et al., 2024; Shen et al., 2023b). To some extent, both math and code problems are abstractions of real-world problems, and involve complex symbolic reasoning processes to solve them. Hence, model performances demonstrate high sensitivity upon the algorithmic. (2) High-quality mathematical texts are key to the model learning of mathematical abilities. • Code Generation Compared to text-based tasks, the range of knowledge for code generation tasks is relatively narrow, only limited to mathematics and code-related corpora Shen et al. (2023a). This again demonstrates the close relationship between mathematics and coding. Overall, forgetting algorithmic knowledge has a greater impact on the model’s coding ability than specific programming languages. This suggests that the model’s understanding of algorithms does not depend on specific program languages. In other words, LLMs could understand the logic of algorithms, instead of memory algorithmic knowledge depending on certain programming languages. • Long Text GitHub, Wikipedia, Books, and
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“High-liked” StackExchanges significantly impact the model’s long text capabilities, as these corpora are composed of long texts, entailing complex logical relationships and abundant common sense knowledge. • Examination Completing exam questions requires extensive knowledge and strong reasoning abilities. Hence, code, commonsense, mathematics, and books corpora all form the foundation of an LLMs’s examination capabilities. • Safety Interestingly, the model’s security is enhanced after forgetting the code corpora. This might be due to the absence of emotional factors in the code corpora and its straightforward logic, thus making the generated results more crude and aggressive. More detailed experimental data and results can be found in Appendix F.

heading: 3.2.1 Corpus with Broad Influences
text: We calculate corpora that can influence multiple capabilities. Since they may lead to a broad influence on model capabilities, these datasets may serve as the foundation of the training corpus.
Analysis Method In the target-data, certain datasets significantly influence numerous capabilities of the model. We adopted the same method for data processing as described in Section 3.2. Furthermore, we define a dataset as “High-impact data” if its removal leads to a performance decline in over 70% of capabilities, which exceeds the average decline observed across all datasets.
Analysis Results Among the selected target-data, four categories—Books, Shell, and Github meet the criteria for High-impact data. Unlearning Books datasets result in a decline in 16 capabilities beyond the average, whereas Unlearning Shell and GitHub leads to a decline in 14 capabilities beyond the average. These datasets significantly impact multiple model capabilities and play a crucial role in model training.

heading: 3.3 Joint Impact of Multiple Corpora on Model Capabilities
text: Previous research indicates that LLMs can combine information from multiple kinds of corpora, and generalize it to new tasks. Hence, during the pretraining stage, multiple corpora may perform joint impact upon LLMs. In this section, we explore measuring the joint contribution of multiple datasets upon the LLMs.
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0.87 0.90 0.97 0.93 1.00 0.98 0.96 0.95 0.94 0.95 0.67 0.79 0.76 0.77 0.81 0.60 0.48 0.56 0.65 0.60 0.02 0.07 -0.19 -0.23 0.64 0.58 0.55 0.51 0.38 0.62 0.47 0.71 0.87 0.94 0.96 0.93 0.98 1.00 0.96 0.95 0.97 0.96 0.63 0.73 0.76 0.74 0.76 0.56 0.47 0.50 0.61 0.57 -0.03 0.19 -0.07 -0.17 0.70 0.59 0.59 0.54 0.43 0.61 0.50 0.57 0.85 0.94 0.97 0.91 0.96 0.96 1.00 0.98 0.94 0.95 0.72 0.79 0.67 0.76 0.80 0.65 0.43 0.59 0.56 0.54 -0.10 0.27 -0.03 -0.10 0.67 0.63 0.60 0.57 0.49 0.67 0.49 0.56 0.86 0.93 0.95 0.88 0.95 0.95 0.98 1.00 0.94 0.95 0.70 0.79 0.69 0.78 0.81 0.66 0.48 0.57 0.55 0.53 -0.10 0.24 -0.01 -0.10 0.68 0.62 0.62 0.61 0.47 0.57 0.42 0.61 0.84 0.93 0.94 0.94 0.94 0.97 0.94 0.94 1.00 0.97 0.61 0.68 0.70 0.73 0.74 0.61 0.47 0.44 0.59 0.51 -0.07 0.28 0.06 -0.17 0.62 0.57 0.53 0.54 0.40 0.68 0.55 0.65 0.82 0.95 0.92 0.90 0.95 0.96 0.95 0.95 0.97 1.00 0.60 0.73 0.70 0.77 0.80 0.61 0.44 0.39 0.55 0.44 -0.16 0.25 0.02 -0.25 0.63 0.29 0.46 0.26 0.31 0.30 0.30 0.13 0.69 0.54 0.75 0.70 0.67 0.63 0.72 0.70 0.61 0.60 1.00 0.86 0.57 0.56 0.65 0.68 0.49 0.78 0.72 0.75 0.38 0.03 -0.26 -0.10 0.46 0.22 0.27 0.19 0.16 0.53 0.62 0.43 0.67 0.65 0.79 0.70 0.79 0.73 0.79 0.79 0.68 0.73 0.86 1.00 0.62 0.73 0.84 0.62 0.44 0.61 0.67 0.68 0.23 -0.15 -0.46 -0.36 0.43 0.35 0.35 0.22 0.18 0.53 0.34 0.71 0.84 0.60 0.69 0.72 0.76 0.76 0.67 0.69 0.70 0.70 0.57 0.62 1.00 0.70 0.70 0.65 0.74 0.52 0.78 0.59 0.20 -0.13 -0.23 -0.16 0.26 0.41 0.36 0.51 0.37 0.57 0.62 0.58 0.72 0.62 0.70 0.63 0.77 0.74 0.76 0.78 0.73 0.77 0.56 0.73 0.70 1.00 0.97 0.74 0.45 0.48 0.40 0.29 -0.18 -0.08 -0.10 -0.16 0.29 0.30 0.27 0.37 0.25 0.61 0.73 0.59 0.70 0.66 0.74 0.67 0.81 0.76 0.80 0.81 0.74 0.80 0.65 0.84 0.70 0.97 1.00 0.72 0.42 0.51 0.48 0.36 -0.12 -0.10 -0.24 -0.31 0.57 0.55 0.59 0.53 0.59 0.32 0.12 0.12 0.78 0.48 0.62 0.59 0.60 0.56 0.65 0.66 0.61 0.61 0.68 0.62 0.65 0.74 0.72 1.00 0.78 0.52 0.60 0.41 0.08 0.09 0.10 0.04 0.54 0.55 0.52 0.36 0.48 0.32 -0.13 0.20 0.78 0.35 0.48 0.48 0.48 0.47 0.43 0.48 0.47 0.44 0.49 0.44 0.74 0.45 0.42 0.78 1.00 0.35 0.72 0.56 0.41 -0.09 -0.07 0.07 0.40 0.25 0.37 0.22 0.24 0.13 0.14 0.17 0.60 0.34 0.63 0.56 0.56 0.50 0.59 0.57 0.44 0.39 0.78 0.61 0.52 0.48 0.51 0.52 0.35 1.00 0.53 0.63 0.30 -0.00 -0.21 0.24 0.55 0.17 0.28 0.01 0.05 0.16 0.11 0.35 0.68 0.46 0.67 0.74 0.65 0.61 0.56 0.55 0.59 0.55 0.72 0.67 0.78 0.40 0.48 0.60 0.72 0.53 1.00 0.83 0.59 -0.20 -0.41 -0.34 0.51 0.20 0.32 0.05 0.09 0.05 0.01 0.23 0.60 0.39 0.69 0.69 0.60 0.57 0.54 0.53 0.51 0.44 0.75 0.68 0.59 0.29 0.36 0.41 0.56 0.63 0.83 1.00 0.74 -0.21 -0.47 -0.19 0.08 -0.20 -0.08 -0.30 -0.17 -0.37 -0.34 -0.16 0.12 -0.22 0.10 0.14 0.02 -0.03 -0.10 -0.10 -0.07 -0.16 0.38 0.23 0.20 -0.18 -0.12 0.08 0.41 0.30 0.59 0.74 1.00 -0.50 -0.58 -0.19 0.58 0.55 0.60 0.48 0.52 0.19 -0.19 -0.12 0.15 0.40 0.17 0.20 0.07 0.19 0.27 0.24 0.28 0.25 0.03 -0.15 -0.13 -0.08 -0.10 0.09 -0.09 -0.00 -0.20 -0.21 -0.50 1.00 0.82 0.44 0.32 0.56 0.58 0.60 0.62 0.00 -0.41 -0.30 -0.00 0.10 -0.11 -0.06 -0.19 -0.07 -0.03 -0.01 0.06 0.02 -0.26 -0.46 -0.23 -0.10 -0.24 0.10 -0.07 -0.21 -0.41 -0.47 -0.58 0.82 1.00 0.60 0.24 0.54 0.54 0.47 0.58 -0.11 -0.55 -0.32 0.10 -0.12 -0.14 -0.21 -0.23 -0.17 -0.10 -0.10 -0.17 -0.25 -0.10 -0.36 -0.16 -0.16 -0.31 0.04 0.07 0.24 -0.34 -0.19 -0.19 0.44 0.60 1.00 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75
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Figure 5: A correlation matrix based on the model’s performance across 19 capabilities after experiencing data Unlearning. Among them, “Algorithm” is the average value of all Algorithm.

heading: 3.3.1 Interrelationships Among Data
text: Analysis Method To explore the relationships between datasets from different domains, we calculated the Pearson correlation coefficient between any two target corpus TA and TB , based on the model’s performance degradation ratio upon 19 capabilities after Unlearning TA and TB . Within each category of abilities, each subtype was given an equal weight. When a subtype included multiple datasets, we averaged the performance changes across these datasets to calculate the coefficients. These coefficients form a correlation matrix. If the correlation coefficient between two datasets is positive, it indicates that the impact of these two datasets on downstream tasks is similar, and vice versa. Subsequently, we conducted hierarchical clustering on the correlation matrix to categorize datasets. Figure 5 displays the correlation matrix rearranged according to the categories defined by the hierarchical clustering.
Analysis Results As shown in Figure 5, according to their relationships, the corpora could be categorized into three types, which we name as “Correlated Corpora”, “Complementary Corpora”, and “Orthogonal Corpora”, respectively. Specifically: • Correlated Corpora refers to corpora that the model has similar performance changes after Unlearning them. In other words, they have a similar influence on LLMs. For instance, the correlation coefficients among Economics, Quantitative Finance, and Statistics are all greater than 0.95. Hence, to some extent, the correlated corpora can
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substitute for each other in the training corpus, leading to redundancy in the training corpus and a waste of computation resources. Hence, it would be necessary to reorganize these corpora to enhance pre-training efficiency. • Complementary Corpora refers to corpora that the model performance alternations are different after Unlearning them. Interestingly, our analyses suggest that there may exist certain corpora that have a complementary influence on the model’s performance. For example, the Wikipedia corpus and SE-qs-lower corpus have a negative correlation coefficient of -0.58. As detailed illustrated in Appendix F, this negative correlation is because both Wikipedia and SE qs lower have impacts on multiple capabilities, while the capabilities influenced by these two datasets seldom overlap. Thus, these two corpora could act simultaneously as a critical composition of the pretraining corpus. In general, the math corpora (e.g., StackExchange) have a complementary relationship with commonsense-related corpora such as Books or Wikipedia. Note that our results also suggest the existence of an extreme case that the involvement of one dataset can cause a decline in the performance of another dataset. This situation requires further verification. If it indeed exists, then in organizing the pre-training data, a trade-off must be made between the two datasets. • Orthogonal Corpora refers to two corpora having a correlation coefficient near zero. For example, the correlation coefficient between Wikipedia and ArXiv is -0.07. This suggests that these corpora independently contribute to the model’s different capabilities with low redundancy. Hence, when optimizing the organization of the pretraining corpus, each of the orthogonal corpora should not be recklessly excluded to avoid impairing the comprehensiveness of the pre-training dataset.
Discussions About groups of the pretraining data: Moreover, according to the correlation matrix, there seem to be several groups of data: (1) Math-related group composed of StackExchangerelated corpora; (2) Knowledge-related group including the subsets of Arxivs (e.g., Statistics / Economic). Note that, group (1) and (2) seems to be complementary; (3) The intermediate group between (1) and (2) composed of C, python, prolog, etc., bridges (1) and (2). More groups could be identified by further dividing the pretraining corpus.

heading: 3.3.2 Interrelationships Among Model Capbilities
text: Additionally, for an arbitrary kind of capability benchmark, we can obtain a model performance after forgetting each category of pretraining data. Hence, using a similar methodology, we can calculate a correlation matrix between the capabilities of an LLM and analyze the relationship patterns between model abilities. Owing to space constraints, the results are presented in Figure 6. From which we can (clearly) observe three groups of abilities: (1) Textual modeling-related abilities, such as Coreference Resolution, Content summary, and Reading Comprehension; (2) (Symbolic) Reasoning-related abilities, such as Base Mathematical Reasoning, Code Generation, and Long Context Modeling. (Interestingly, long context modeling shows a strong correlation with code generation and math reasoning. This indicates that the essential difficulty in long context modeling may be under the complex relationship among the context); (3) Composition of the above two kinds of abilities, such as Advanced Mathematical Reasoning, Complex Textual Reasoning, and Examinations. These results suggest that there are categories of fundamental abilities of LLM and the complex or advanced abilities are essentially built upon these categories of fundamental abilities.
Moreover, it could be observed that these abilities can be both positively correlated (synergistic)
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and negatively related (antagonistic). For example, the Advanced Mathematical Reasoning ability is positively related to code generation and Long Text Modeling, indicating that enhancing these two kinds of abilities will also enhance the Advanced Mathematical Reasoning ability of an LLM, and vice versa, demonstrating a synergistic relationship between these three kinds of abilities. However, multi-hop knowledge inference shows a negative correlation relationship between several reasoningrelated tasks, such as code generation, and mathematical reasoning. This indicates that there are inherent conflicts between certain capabilities. For example, increasing the commonsense-related ability would be at the cost of reasoning ability.
The relationship patterns of the contribution of different datasets and the relationship patterns model abilities highlight the necessity of optimizing the pretraining corpus’s organization to enhance the pretraining process’s efficiency and effectiveness.

heading: 4 Related Work
text: The Data Influence Analysis (DIA) task aims at finding how each training data contributes to a model’s performance. DIA methods can be mainly classified into two categories (Hammoudeh and Lowd, 2022). The first category, the RetrainingBased approach (Jia et al., 2021; Kandpal et al., 2022; Ghorbani and Zou, 2019), assesses the influence of certain instances by comparing the model performance with and without these instances. However, due to the prohibitive training costs, these methods have only been extensively applied in the ‘small” models (Jia et al., 2021; Ghorbani and Zou, 2019; Kandpal et al., 2022; Nguyen et al., 2023).
The second category Gradient-Based methods (Koh and Liang, 2017; Koh et al., 2019; Pruthi et al., 2020; Hara et al., 2019) discover training samples with greater influence by comparing gradient similarities between training and test instances. These methods demonstrate efficacy in finding instances contributing to knowledge memorization of models. However, they may fail to find instances related to the reasoning abilities of models, which is especially important for LLMs, as it may originate from groups of correlated instances that jointly contribute to the performance of LLMs. Considering the limitations of these methods, we propose a Machine Unlearning-based DIA approach to investigate the impact of corpora upon LLMs.
Machine Unlearning is devised to erase certain knowledge from a model. Prior research (Jang et al., 2022; Graves et al., 2021; Gupta et al., 2021; Sekhari et al., 2021) suggests that machine unlearning can selectively erase specific knowledge from a model through gradient ascent on corresponding instances. Eldan and Russinovich (2023) has shown that gradient ascent methods would still be effective in LLMs, and can accurately unlearn targeted samples. In this paper, we further extend the gradient ascent-based machine unlearning methods by involving an additional retraining process and a random text-based stop criterion.

heading: 5 Conclusion
text: In this study, we employed a Machine-Unlearningbased data influence analysis method GRACE to investigate the complex effects of diverse types of pretraining data on the performance of Large LLMs. We gained empirical analysis results about how specific components of the pretraining corpus influence LLMs capabilities, and how they jointly contribute to multiple capabilities of LLMs. Our findings suggest the nuanced impact of data selection and organization in LLMs development. The identification of high-impact data and the delineation of complementary, antagonistic, and orthogonal data relationships offer guidance for optimizing pre-training data organization. In future work, we consider adapting our analysis methodology to other parts of LLMs training such as supervised fine-tuning.

heading: 6 Acknowledgements
text: This work extends its heartfelt gratitude to the National Natural Science Foundation of China (U22B2059, 62176079) and the Natural Science Foundation of Heilongjiang Province (YQ2022F005) for their generous support.

heading: 7 Limitations
text: This study systematically investigated the impact of various pre-training datasets on the capabilities of LLMs using the GRACE method. While our findings offer valuable insights into the subtle relationship between pre-training data and model capabilities, it is crucial to acknowledge the inherent limitations of our approach.
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heading: 7.1 Data Limitations
text: There remains a still remains space for exploration in the domain of data. In terms of breadth, our study primarily focused on the Redpajama dataset and its subsets. However, there are other datasets for LLMs, and Redpajama may not include all the corpora encountered during the training process of LLMs. In terms of depth, some important data domains may still possess ample subdivision space. For example, Books datasets can be segmented by books type, which could limit the comprehensiveness of our analysis.

heading: 7.2 Limitations of Evaluation Metrics
text: The existing evaluation systems might not adequately unearth the deeper capabilities of models, potentially overlooking subtle variations and thereby missing valuable insights.

heading: 7.3 Future Research Directions
text: Addressing these limitations provides opportunities for future research. Using a broader variety of data and applying our analytical framework to other models are key steps toward a more comprehensive understanding of the relationship between pre-training data and LLMs capabilities. These efforts will contribute to the ongoing discussions about optimizing pre-training strategies to enhance model performance and efficiency.

heading: A Experiment details
text: All experiments were conducted on an A100-SXM4-80GB cluster, with all models utilizing the bf16 precision format. Consistent hyperparameters were used across all target sets: the learning rate was set to 3e-6, the forgetting set contained 2,000 instances, the retraining set contained 20,000 instances, the batch size was 16, and the gradient accumulation steps were set to 10.

heading: B Hints about Optimization of the Pretraining Corpus and the Training Process
text: The above results imply several suggestions for optimizing the organization of the pretraining corpus and training process:
B.1 About the Proportion of Each Category of Pretraining Corpus To some extent, if the change in an LLM’s capability is more sensitive to a certain category of data, it indicates that this category of data is more important for enhancing this kind of capability, and therefore, its proportion should be increased accordingly. In Figure 4 ,Table 4,Table 5 and Table 6 of this paper, we demonstrate the sensitivity of model capability on the ablation of each category of the pretraining corpus in detail. For example, as Figure 4 shows, to increase the Advanced Mathematical Reasoning ability of an LLM, the GitHub corpus, Stack Exchange Corpus, and certain algorithms such as Graph Algorithm may be of vital importance and should be involved more, while Wikipedia, SQL, R, OWL, and Prolog have minimal influence upon the Advanced Mathematical Reasoning ability of an LLM, and should not be overinclusive. Moreover, in this sense, the “high-energy” data, such as books, GitHub, etc., should be included in the training corpus as much as possible.
This also highlights the necessity of subdividing the pretraining datasets, as they may indeed bring different capabilities for the LLM and should have different weights rather than be treated as a whole mixture. For example, further subdividing the GitHub corpus according to the type of programming language. This is because different programming languages may correspond to different programming paradigms and different modes of thinking, have different application scenarios, and would naturally bring different types of capabilities to the model.
B.2 About the Interrelationship between Corpora As Figure 5 shows, there are relationship patterns between different corpora, such as the correlated relationship. Such relationship patterns should also be considered when deciding the proportion of each kind of category of corpus. For example, for highly positively correlated corpora such as the Mathematics part of Arxiv and Computer Science and Arxiv, their weights in the pretraining corpus should be decreased because they can largely substitute each other. Incorporating the correlation patterns into the consideration would increase the information density of the pretraining corpus, and thus increase the efficiency and effectiveness of the pretraining process.
Moreover, the correlation matrix of pretraining corpora can be decomposed into several orthogonal “principle components”, with these components explaining most of the variation of the correlation matrix, and hence these principal components can be explained as a sort of “pivotal data” composed by the weighted mixture of several different components. Construct the pretraining corpora according to the principal components would

heading: C Example Appendix
text: Analysis Method As illustrated in Figure 7, we evaluate the performance of the model on an unaltered Python statement after selectively Unlearning programming languages, including Python, C, Shell, C++, HTML, and SQL. The darker the color, the greater the increase in token loss compared to the original model.
Analysis Results Notably, the most significant loss increase is observed after the model unlearns Python, indicating a profound impact on its ability to interpret Python statements. Furthermore, when Unlearning other languages, the changes in model loss predominantly occur in comments and certain keywords, which are syntactically or semantically shared across these languages. Languages like C++, C, and
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Shell, which structurally resemble Python to some extent, exhibit substantial loss variations. Conversely, HTML and SQL, being more distinct from Python, result in minimal changes in the model’s performance on Python statements after being forgotten. Additionally, we observe that due to the object-oriented features of Shell and C++, Unlearning these languages leads to a notable increase in the loss associated with the “class” token. In contrast, given C’s procedural nature, the loss related to “class” does not show significant variation. This analysis underscores the intertwined nature of programming language knowledge within the model and highlights the differential impact of Unlearning specific languages on the model’s comprehension of Python code.
Analysis Method As illustrated in Figure 8, we evaluate the model’s performance on Breadth-First search statements written in C++ after selectively applying Unlearning algorithms, including depth-first and graph algorithms. The darker the color, the greater the increase in token loss compared to the original model Analysis Results As illustrated in Figure 8, the performance of the model post-omission of the Depth-First Search (DFS) algorithm on Breath First Search (BFS) data is depicted at the right, while the performance post-omission of the Graph algorithm on BFS data is shown at the left. It is observable that there is a significant increase in loss for both cases in terms of variable definitions and certain key terms. However, during the execution phase of the BFS algorithm, the loss in the model after omitting the Graph algorithm is substantially greater than that after omitting the DFS algorithm.

heading: D Test DaseSet
text: In Table 2, we integrate the frameworks (Contributors, 2023; Gao et al., 2023) to construct a comprehensive evaluation system for large models.
Language Modeling. The average performance on WiC (Pilehvar and Camacho-Collados, 2019), WSC (Levesque et al., 2012), and TyDiQa (Clark et al., 2020) is reported. These test sets are all evaluated with 0-shot results.
Knowledge. The average performance is reported using BooIQ (Clark et al., 2019), CommonSenseQA
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(Talmor et al., 2018), and NaturalQuestions (Kwiatkowski et al., 2019). We report 8-shot results for CommonSenseQA and 0-shot results for all other benchmarks.
Textual Inference. The average performance is reported using AXb (Wang et al., 2020), AXg (Wang et al., 2020), RTE (Wang et al., 2020), COPA (Roemmele et al., 2011), ReCoRD (Zhang et al., 2018), HellaSwag (Zellers et al., 2019), PIQA (Bisk et al., 2019), SIQA (Sap et al., 2019), BBH (Suzgun et al., 2022), LogiQA (Liu et al., 2020), DROP (Dua et al., 2019), and Qasc (Khot et al., 2020). We report 3-shot results for BBH, 2-shot results for DROP, and 0-shot results for all other benchmarks. Notably, AXb, AXg, and RTE are used for Textual Entailment tasks; COPA, ReCoRD, HellaSwag, PIQA, and SIQA for Commonsense Reasoning tasks; BBH for Complex Textual Reasoning; LogiQA for Logical Reasoning; DROP for Discrete Reasoning; and Qasc for Multi-hop Inference.
Mathematical Reasoning. The average performance is reported using GSM8K (Cobbe et al., 2021) and MATH (Hendrycks et al., 2021c). GSM8K represents Base Mathematical Reasoning, while MATH represents Advanced Mathematical Reasoning. These test sets are all evaluated with 4-shot results.
Textual Understanding. The average performance is reported using RACE (Middle and High) (Lai et al., 2017), OpenbookQA (Mihaylov et al., 2018), Xsum (Narayan et al., 2018), and LAMBADA (Paperno et al., 2016). RACE (Middle and high) and OpenbookQA are used for Reading Comprehension tasks, Xsum for Content Summary tasks, and LAMBADA for Content Analysis tasks. These test sets are all evaluated with 0-shot results.
Long Context. The model’s ability in long text understanding and reasoning is represented using English datasets within Longbench (Bai et al., 2023b).
Code Generation. We report the average pass@1 scores of models on HumanEval (Chen et al., 2021) and MBPP (Austin et al., 2021). MBPP is evaluated with 1-shot results, while HumanEval is evaluated with 0-shot results.
Examination. The average performance is reported using ARC (easy and challenge) (Clark et al., 2018), MMLU (Hendrycks et al., 2021b,a), and AGIEval (Zhong et al., 2023). We report 5-shot results for MMLU and 0-shot results for all other benchmarks. It is worth noting that for AGIEval, we only selected English datasets.
Safety. Performance is represented using TruthfulQA, evaluated with 0-shot results.

heading: E Target DaseSet
text: The CodeAlgorithm corpus contains building on the leetcode dataset created by Hartford (2023), selected 17 of the most important algorithms. Following the methodology of Wang et al. (2022), for algorithm types with not enough size, we utilized GPT-4 OpenAI et al. (2023) for data augmentation to ensure a minimum of 2, 000 samples per algorithm. Furthermore, to ensure the model’s Unlearning pertains to the algorithms themselves and not to a specific programming language, each algorithm problem was
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represented in five language formats: C++, Python, Java, JavaScript, and pseudocode. The CodeLanguage dataset is derived from the GitHub portion of the Redpajama dataset Computer (2023). In terms of language selection, based on the characteristics of programming languages, this study chose 15 types, including Object-Oriented, Procedure-oriented, Declarative programming, Scripting, frontend and other common languages. It is specifically filtered to include data where a single language proportion for more than 99.99% of the content and the total length is in excess of 2000 bytes, aiming to isolate target data for a specific language. From this filtered data, 2000 samples are randomly selected for each language to constitute the CodeLanguage dataset.
The Arxivs dataset is constructed based on the Arxiv part of the Redpajama dataset Computer (2023), which is further divided into eight main categories. Randomly select 2000 samples from each category to form the Arxiv dataset.
The StackExchanges dataset is constructed from the StackExchanges segment of the Redpajama dataset Computer (2023), comprising Q&A pairs that have garnered more than 5 “likes”. Subsequently, it is segregated into two tiers based on the count of “likes”. The underlying rationale is that the number of “likes” is indicative of an answer’s quality and popularity. Consequently, these five subsets encompass samples ranging in quality and popularity from the lowest to the highest.

heading: F Experimental Result and Joint Impact of Multiple Ability on Model Capabilities
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heading: Future Work
text: Addressing these limitations provides opportunities for future research. Using a broader variety of data and applying our analytical framework to other models are key steps toward a more comprehensive understanding of the relationship between pre-training data and LLMs capabilities