BOTS-LM: Training Large Language Models for Setswana (2024)

Nathan Brown
School of Computing
Clemson University
nbrown9@clemson.edu
Vukosi Marivate
Department of Computer Science
University of Pretoria
vukosi.marivate@cs.up.ac.za

Abstract

In this work we present BOTS-LM, a series of bilingual language models proficient in both Setswana and English. Leveraging recent advancements in data availability and efficient fine-tuning, BOTS-LM achieves performance similar to models significantly larger than itself while maintaining computational efficiency. Our initial release features an 8 billion parameter generative large language model, with upcoming 0.5 billion and 1 billion parameter large language models and a 278 million parameter encoder-only model soon to be released. We find the 8 billion parameter model significantly outperforms Llama-3-70B and Aya 23 on English-Setswana translation tasks, approaching the performance of dedicated machine translation models, while approaching 70B parameter performance on Setswana reasoning as measured by a machine translated subset of the MMLU benchmark. To accompany the BOTS-LM series of language models, we release the largest Setswana web dataset, SetsText, totalling over 267 million tokens. In addition, we release the largest machine translated Setswana dataset, the first and largest synthetic Setswana dataset, training and evaluation code, training logs, and MMLU-tsn, a machine translated subset of MMLU.

1 Introduction

Setswana, also known as Tswana, is a Bantu language spoken by an estimated five to ten million people worldwide [Bennett etal., 2016]. Closely related to Northern Sotho and Southern Sotho, Setswana holds official status in Botswana [Government of Botswana, 2024], South Africa [The Republic of South Africa, 1996], and Zimbabwe [The Parliament of Zimbabwe, 2013], and is also used in countries like Namibia, often interchangeably with English. Despite its significance in millions of lives, Setswana has been largely overlooked in traditional natural language processing research. This work aims to bridge the gap between Setswana and other high-resource languages by making generative large language models capable of high-quality Setswana available to the open research community for the first time, significantly increasing data availability, and laying the groundwork for future Setswana-centric research.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various domains after training on web and synthetic data [OpenAI etal., 2023, Dubey etal., 2024, Anthropic, 2024, Gunasekar etal., 2023], excelling in areas such as mathematics [Mistral AI, 2024], programming [Guo etal., 2024], creative writing [Wang etal., 2024], and translation tasks [Vaswani etal., 2017]. However, many developments surrounding this technology remain English-centric, with most non-English languages targeted for training and evaluation being "high-resource languages" with abundant available data. While this approach yields impressive capabilities, it results in models that may lack knowledge of certain cultures, limits production use-cases outside majority demographics, and prevents a significant portion of the global population from utilizing language models effectively. African languages like Setswana, with comparatively little webtext data available, subsequently suffer in performance and are underutilized in research.

Recent progress has been made to address the lack of language diversity in language models. Releases such as mBART [Liu etal., 2020], XLM-RoBERTa [Conneau etal., 2019], and BLOOM [BigScience Workshop etal., 2022] were among the earliest and most influential advancements in multilingual NLP. Building upon these technologies, newer models like GPT-4 [OpenAI etal., 2023], Claude [Anthropic, 2024], Gemini [Gemini Team etal., 2023], Llama [Dubey etal., 2024], and Gemma [Gemma Team etal., 2024] have also found success in multilingual domains, often demonstrating reasoning and translation capabilities in languages not officially supported. Releases such as Aya 101 [Üstün etal., 2024] and Aya 23 [Aryabumi etal., 2024] have continued to improve language coverage while maintaining high performance in generative models, and open corpora like ROOTS [Laurençon etal., 2023], OSCAR [Suárez etal., 2019], and mc4 [Caswell etal., 2021] have made multilingual data readily available. However, Setswana comprises only a small fraction of these datasets, with just 0.0002% of the ROOTS corpus being written in Setswana. Moreover, much of the available Setswana text in open multilingual corpora is of lower quality, resulting in existing generative models displaying significantly worse conversational, translation, and reasoning capabilities compared to other languages.

To help address this issue, we introduce the Bilingual Open Tswana Suite of Language Models (BOTS-LM). This suite consists of Quantized LoRA (QLoRA) fine-tuned versions of Qwen2 0.5B Yang etal. [2024], DCLM 1B Li etal. [2024], Llama 3 8B Dubey etal. [2024], and AfroXLMR-base (279M) [Alabi etal., 2022]. By training a range of models across different parameter counts, we aim to provide the research community and millions of Setswana speakers with models that are not only highly performant, but also capable of running on various hardware configurations ranging from data centers to consumer laptops and mobile phones. Following the approach of projects like OMLo [Groeneveld etal., 2024] and Dolma [Soldaini etal., 2024], we release all training and evaluation data, associated code, and training logs. We release a preliminary training checkpoint of our 8B model, with additional models being released soon. The 8B model and all future BOTS-LM models can be accessed here, training data can be accessed here, and the training Weights & Biases logs can be accessed here. Additionally, we utilize GPT-4o to generate over 1.5 million tokens of synthetic Setswana text, which we release here. Last, we release the code used for dataset curation, model training, and model evaluation here.

2 Related Work

Despite the focus on other languages in research, there have been recent significant advancements in Setswana-centric NLP. TswanaBERT [Motsoehli, 2020] represents one of the earliest examples, trained on over ten thousand Setswana sentences from the Leipzig Corpora Collection [Goldhahn etal., 2012], SABC news headlines [Marivate etal., 2020], and various blogs and websites. More recently, the NCHLT Setswana RoBERTa model [Eiselen etal., 2023] was released, having been trained on over fourteen million tokens of Setswana text from the NCHLT [Eiselen and Puttkammer, 2014], Autshumato [McKellar etal., 2016], Leipzig [Goldhahn etal., 2012], and Common Crawl corpora, and an internal CTexT corpus. PuoBERTa [Marivate etal., 2023] marked a significant step forward in masked language modeling, achieving state of the art performance while being the first model targeted at Setswana trained from scratch with a custom tokenizer developed for Setswana. PuoBERTa was released alongside PuoData, the largest collection of primarily Setswana hand-curated text at the time, totaling four and a half million PuoBERTa tokens excluding the JW300 Setswana dataset [Agić and Vulić, 2019].

Much of the recent work on African languages has targeted multilingual developments with a focus on machine translation and transfer learning. Corpora such as OPUS [Tiedemann, 2012] and MADLAD-400 [Kudugunta etal., 2023] provide access to large volumes of parallel web text data, while datasets like MAFAND-MT [Adelani etal., 2022] have enabled improved translation performance across many languages through additional human-generated data. Meta’s No Language Left Behind (NLLB) [NLLB Team etal., 2022] has facilitated high-quality machine translation between over 200 languages, including Setswana, although it is noted as being one of the 21 languages with the lowest accuracy on FLORES-200 [Goyal etal., 2022]. MADLAD-400 [Kudugunta etal., 2023] has allowed for increased multilinguality but suffers from worse performance on Setswana-English translations, as seen in Table 3. Furthermore, models such as AfriBERTa [Ogueji etal., 2021] and AfroXLMR [Alabi etal., 2022] have found success in training across multiple African and low-resource languages in the masked language modeling regime, and LlamaX [Lu etal., 2024] has demonstrated high degrees of translation performance across over 100 languages as a generative LLM while retaining generalization capabilities.

Thanks to the cumulative improvements made by the research community in Setswana-centric NLP and increased levels of multilinguality, we believe there are significant opportunities to enhance existing Setswana NLP systems. Several smaller datasets of Setswana text are often underutilized in the literature, potentially due to their differing formats and distribution methods. For example, the South African Center for Digital Language Resources (SADiLaR)111https://sadilar.org[SADiLaR, 2024] has made publicly available several datasets of Setswana text and audio. However, as the format for this distributed text is non-standardized and data is typically not available on commonly used external platforms such as Hugging Face, much of this data is left out of massive public datasets. We also find many websites and corresponding PDF contents written in Setswana are excluded from existing datasets, meaning a significant portion of the available high-quality Setswana text is not being utilized. Additionally, we find the advent of improved machine translation and large language models capable of generating text in Setswana allows for the creation of synthetic datasets and translated benchmarks to further improve and better gauge downstream performance on various tasks.

3 Data

A key focus in the design of our selected training data is the languages to be targeted. While several parallel corpora are available for Setswana, with some containing Setswana text alongside multiple other languages, there is significantly more English-Setswana parallel text available. For example, OPUS contains over four times more parallel Setswana-English sentences than it does Setswana-French sentences222https://opus.nlpl.eu/results/tn&en/corpus-result-table. In addition, the majority of publicly available, high-quality, educational, and instruction-tuning datasets are written in English. Consequently, many state-of-the-art large language models excel in English tasks, including the models we select for continued pre-training. Additionally, South Africa and Botswana, the two countries with the largest Setswana-speaking populations, often utilize English in legal, official, and government documents, with English sometimes being spoken interchangeably with Setswana. We observe this trend in web text documents, where many data sources are written in both English and Setswana, either incorporating code-switching or providing direct translations. As such, and to reduce computational demands, we focus our efforts primarily on curating a high-quality dataset consisting of Setswana and English texts, though other languages may be present. We refer to this training dataset as SetsText.

SetsText builds upon several previous works in the African NLP research community. For consistency, when measuring token counts, we utilize the Llama 3 tokenizer throughout this paper. The most significant source of high-quality Setswana data in SetsText is PuoData [Marivate etal., 2023], which consists of over eight million tokens sourced from various government documents, books, educational materials, and other online content, including the NCHLT [Eiselen and Puttkammer, 2014], Leipzig [Goldhahn etal., 2012], and SABC [Marivate etal., 2020] corpora. However, PuoData was originally curated for training PuoData on masked language modeling, resulting in training sequences of individual sentences instead of entire documents. To ensure our data is in a format most useful for LLM training, we reconstruct the Wikipedia333https://huggingface.co/datasets/wikimedia/wikipedia, Nalibali444https://nalibali.org/, and Setswana Bible555https://www.bible.com/versions/185-tsw70-setswana-1970 subsets of PuoData to retain the original documents in their entirety. The second largest source of Setswana text we utilize is the OPUS corpus [Tiedemann, 2012], which includes over six million parallel English-Setswana sentences. This subset of OPUS comprises the NLLB [Schwenk etal., 2021, Fan etal., 2021], CCAligned [El-Kishky etal., 2020], XLEnt [El-Kishky etal., 2021], Wikimedia666https://opus.nlpl.eu/wikimedia/tn&en/v20230407/wikimedia, and Tatoeba777https://tatoeba.org/en/[Tatoeba, 2024] corpora. However, we find that training on the entire English-Setswana subset of OPUS often yields models which suffer from catastrophic forgetting, likely due to the sheer number of sequences present in the dataset as well as lower overall quality. To mitigate this issue, we include only one-third of this data in SetsText, totaling 210M tokens.

To further improve BOTS-LM’s generalization capabilities and to make large swaths of Setswana data more easily available to researchers, we expand some existing data sources through additional data collection and hand-curate data from new publicly available sources. We begin by obtaining PDF data from the Parliament of Botswana’s Hansard888https://www.parliament.gov.bw/index.php?option=com_documents&view=files&catid=87&Itemid=438[Parliament of Botswana, 2022], a collection of documents written in English and Setswana containing the "printed verbatim record of all Parliamentary debates and proceedings which take place in the Chamber of the National Assembly." Additionally, we source all texts from the Rare Tswana Books collection999https://wiredspace-extra.wits.ac.za/collections/286d8e41-cb6e-4679-9ed7-97a4e3d0d3de[Rahlao etal., 2021], which consists of rare African books written in Setswana dating back to the 1800s. We also obtain additional PDF data from Nalibali that was not present in PuoData, nearly doubling the number of available tokens in that subset. Furthermore, we scrape the contents of certain websites containing predominantly Setswana text, such as iAfrika101010https://iafrika.org/[iAfrika, 2024], Setswana Mo Botswana111111https://setswanabwa.com/[TRK, 2021], Tlhalefang Communications121212https://tlhalefang.com/setswana/[Tlhalefang, 2009], and Unisa131313https://www.unisa.ac.za/sites/corporate/default/Unisa-Open/OER-@-Unisa/Learn-to-speak-an-African-Language[Unisa, 2023]. We also include a small corpus of parallel text consisting of monolingual English mathematical text translated into code-mixed English and Setswana [Mokoka, 2024]. Finally, we include miscellaneous individual documents such as the United States Peace Corps’ Intro to Spoken Setswana141414https://files.eric.ed.gov/fulltext/ED283381.pdf[Mistry and Gare, 1987], Peace Corps Setswana language lessons on Live Lingua151515https://www.livelingua.com/courses/setswana[Lingua, 2024], and the Setswana Universal Declaration of Human Rights161616https://www.ohchr.org/en/human-rights/universal-declaration/translations/western-sothotswanasetswana[Nations, 1998]. For the majority of PDFs we extract text using the pypdfium2 Python library. However, while the Peace Corps’ Intro to Spoken Setswana is one of the most comprehensive public teaching materials on the Setswana language, the respective text is not embedded into the published PDF, nor is the text available in any other form to our knowledge. Due to the lower quality scan and the occasionallly complex formatting, we also found existing OCR systems performed rather poorly at properly extracting the text. To better improve the quality of this text prior to its inclusion in SetsText, we convert each page to an image, perform image processing to remove noise, then utilize Florence-2 [Xiao etal., 2023] Large to extract the text from each image. This text is then sent to Llama-3-70B-Instruct, which adjusts the text in an attempt to restore the original formatting.

To further increase the size of our collective dataset, we employ machine translation to translate existing high-quality English datasets into Setswana. Specifically, we use Meta’s 3.3B parameter No Language Left Behind translation model (NLLB-200-3.3B) [NLLB Team etal., 2022] to translate portions of two English datasets to Setswana. We translate 20,000 sequences from the TinyStories dataset [Eldan and Li, 2023], which has shown success in training small language models and which we found via round-trip translation evaluations [Moon etal., 2020] to often yield high-quality translations. To ensure our models can effectively follow instructions and interact as assistants, we translate 15,201 conversations from OpenHermes-2.5 [Teknium, 2023], a corpus consisting of several open instruction-tuning datasets. However, as most of these conversations are single-turn, we also translate 5,201 conversations from Wildchat-1M [Zhao etal., 2024], a collection of one million conversations between human users and ChatGPT. We filter for conversations longer than three utterances and exclude conversations labeled as toxic or in any language other than English. To further augment our instruction tuning dataset, we utilize the translations in the training split of the MAFAND-MT dataset [Adelani etal., 2022], which consists of several human-translated parallel English-Setswana sentences from news publications. We format each translation into a user-assistant interaction, randomizing source language, target language, query language, and formatting of the corresponding question and response to increase prompt diversity.

While we find specialized machine translation models such as NLLB-200 [NLLB Team etal., 2022] and MADLAD-400 Kudugunta etal. [2023] useful for translating simpler texts, we note two problems with this methodology. First, while these models can achieve state-of-the-art translations, they typically do not preserve the formatting of the original text. Additionally, when provided with text that may be outside the training distribution, which we find to be the case with especially noisy text or text with increased technical jargon, these models may repeat the input text verbatim rather than generating a proper translation. To obtain additional high-quality, well-formatted diverse Setswana text while avoiding the problem of verbatim repetition, we utilize gpt-4o-2024-05-13 [OpenAI, 2024] to generate synthetic Setswana text. To achieve data diversity between samples, we use existing web data as a seed. First, a random subset of FineWeb and FineWeb-edu [Penedo etal., 2024] is selected. Then, given a sequence from one of these datasets, Llama-3-70B is prompted to determine five new pieces of writing that cover similar topics. For example, given a web document discussing the mathematics behind gravity, Llama 3 may suggest "A children’s book explaining the story of an apple landing on Isaac Newton’s head." Additionally, Llama 3 is prompted to select the 5 most unique words present in the provided sequence. We then cross-reference the Setswana-English split of Google Research’s GATITOS171717https://github.com/google-research/url-nlp/tree/main/gatitosGoogle Research [2024], a human-translated lexicon, and filter to only include instances where Llama 3 selected at least one English word which is present in GATITOS. Finally, prompts are constructed to be provided to GPT-4 consisting of: 1) A system prompt to instruct the model to write in Setswana, 2) One of the five pieces of writing, randomly selected, and 3) Each English word selected by Llama 3 which is present in GATITOS as well as its Setswana translation. We find that utilizing this methodology allows GPT-4o to generate high-quality Setswana texts while maintaining a high degree of diversity between texts.

We release a preliminary version of SetsText in its entirety on Hugging Face181818https://huggingface.co/datasets/OxxoCodes/SetsText. To assist researchers in future potential analysis and deduplication work, we provide alongside each sequence information regarding its source, including the original corpus or other category and an exact source URL where available. A full breakdown of the SetsText dataset, including data sources and token counts, is made available in Table 1.

SourceTokensSourceTokens
OPUS (NLLB)208,344,324BW 2018 Leipzig434,011
TinyStories-tsn13,328,020OPUS (Wikimedia)429,552
MADLAD-40010,952,546SABC Dikgang358,844
WildChat-tsn10,533,874MAFAND-MT328,281
Rare Tswana Books4,971,441Tlhalefang268,115
BW Hansard4,223,058Vukuzenzele232,012
NCHLT 20191,990,720Nalibali205,657
Bible1,742,663Miscellaneous193,597
OPUS (CCAligned)1,664,478Setswanabwa180,042
Department Basic Education1,628,799ZA Constitution140,479
Wikipedia1,519,214iAfrika136,673
ZA Gov Cabinet Speeches1,311,903OPUS (XLEnt)109,625
GlotCC-v1941,585SABC Motsweding66,459
ZA 2020 Leipzig471,773Math Code-Switch4,710
Leipzig Wiki454,660OPUS (Tatoeba)930

4 Training

Training is performed utilizing the Hugging Face transformers, trl, and peft libraries. Our approach involves performing continued pre-training for each model to ensure robust learning without encountering catastrophic forgetting. As opposed to performing continued fine-tuning on a base model, then performing instruction fine-tuning, we train models which have already been finetuned on instruction-following data. By utilizing a mixture of raw web text and instruction data in our training dataset, we yield models which are capable of instruction-following without the additional compute required for a separate instruction fine-tuning stage. In addition, to retain English generalization capabilities, we include a 15% misture of English FineWeb Penedo etal. [2024], OpenHermes-2.5 Teknium [2023], and Glaive Code191919https://huggingface.co/datasets/glaiveai/glaive-code-assistant[Glaive AI, 2023].

Furthermore, we train using Quantized Low Rank Adaptation (QLoRA) across the Query, Key, Value, Output, Gate, Up, and Down projection matrices. This technique not only allows for effective learning without significant computational and memory requirements, but also mitigates the risk of overfitting and catastrophic forgetting. To ensure the models can effectively adapt to the Setswana langauge, we train the embedding layers and the language modeling head in full precision.

All models are trained using DeepSpeed [Rasley etal., 2020] and ZeRO Stage 3 Rajbhandari etal. [2020] on two NVIDIA A100 80GB GPUs. We provide the hyperparameters utilized during training in Table 2.

ParameterValue
Max Seq Length2048 tokens
LoRA Alpha32
LoRA Dropout0.05
LoRA Rank64
BiasNone
Precisionbf16
OptimizerAdamW 8bit
Weight Decay0.0
Learning Rate6e-05
LR SchedulerCosine
Epochs3
Packing
Per-Device Batch Size2
Gradient Accumulation Steps8
Effective Batch Size32 (64k tokens)

5 Evaluation

In this section we discuss the steps taken to evaluate the BOTS-LM suite of models. We place a large emphasis on translation performance in this initial release, as this is a common area of focus in the literature. In future releases we will integrate additional evaluations such as news and document classification.

To evaluate translation performance, we evaluate on the MAFAND-MT [Adelani etal., 2022], Lego-MT [Yuan etal., 2023], and Flores-200 [NLLB Team etal., 2022] benchmarks. These benchmarks cover a variety of translation domains, ranging from news articles to miscellaneous crawled web documents. To measure translation performance numerically, we utilize the BLEU [Papineni etal., 2002] and CHRF Popović [2015] measurements. We indicate translating from English to Setswana with en-tn, and translating from Setswana to English with tn-en. Our results are presented in Table 3.

To further evaluate the general performance of BOTS-LM, as well as other language models, on general reasoning in Setswana, we develop MMLU-tsn. This is a machine translated NLLB Team etal. [2022] subset of approximately 1,000 questions and answers from the Massive Multitask Language Understanding (MMLU) [Hendrycks etal., 2021b, a] benchmark validation split. A translation of the test split is in development. This benchmark measures multiple-choice answering capabilities of language models on various topics such as humanities, social science, and STEM. We acknowledge this method of relying on machine translation systems to translate this text, especially given its technical nature, is likely to suffer from "translationese" and other translation errors which can impact a model’s performance on the benchmark [Plaza etal., 2024]. As such, many sequences may be incorrectly translated, biased, or subsequently impossible to solve. However, we find this translated benchmark to still be a useful proxy for a model’s performance in downstream reasoning performance in Setswana. As open models become more capable of Setswana and minute differences in scores become more important in evaluating performance, it will be necessary for benchmarks to be either human-translated or designed from the ground-up for Setswana.

ModelMMLUMAFAND-MTLego-MTFLORES-200en-tntn-enen-tntn-enen-tntn-enCHRFBLEUCHRFBLEUCHRFBLEUCHRFBLEUCHRFBLEUCHRFBLEULlama 3 Instruct (8B)35.0422.902.6029.525.7311.021.6911.611.7020.782.3727.044.15Llama-3 Instruct (70B)47.5434.977.2637.336.4211.370.5811.930.7531.475.5033.105.07Aya 23 (8B)28.4114.850.7417.171.828.490.949.521.2514.190.8616.561.33Aya 23 (35B)36.7414.950.885.9628.888.370.8910.161.1913.050.6327.095.13LlamaX3 (8B)34.0923.392.0027.555.6211.571.2913.211.9821.511.6425.124.14NLLB-200 (3.3B)57.6428.1546.9920.6623.7613.5317.104.3650.1521.7341.3016.16MADLAD-400 MT (10B)22.066.0734.8614.0616.859.6622.3314.6019.393.5131.4011.14BOTS-LM (8B)42.4254.1026.1022.943.4314.962.3011.131.5145.8018.4221.302.73

We find our 8B BOTS-LM model excels in particular at English-Setswana translations. It exceeds the translation performance of the larger Aya 23 35B and the massively multilingual LlamaX3, even exceeding Llama models nearly nine times its size. When translating from English to Setswana, it reaches performance levels competitive with dedicated machine translation systems, on the MAFAND-MT benchmark exceeding MADLAD-400 MT and approaching the performance of NLLB-200. However, we do note worsened performance when translating from Setswna back to English, likely due to imbalances in the training dataset. When evaluated on multiple-choice Setswana questions in the MMLU-tsn benchmark, BOTS-LM significantly outperforms the original Llama-3-8B-Instruct model, only being beaten by the Llama-3-70B-Instruct model. This indicates that, while the 70B model may be suffer from worse Setswana translation and writing skills, it still retains a degree of understanding and reasoning capabilities.

Our 8B BOTS-LM model demonstrates exceptional performance in English-Setswana translations, surpassing larger multilingual models such as Aya 23 35B and the massively multilingual LlamaX3, even outperforming Llama models nearly nine times its size. In English to Setswana translation, BOTS-LM achieves results competitive with specialized machine translation systems, surpassing MADLAD-400 MT on the MAFAND-MT benchmark. However, we observe performance degredation in Setswana to English ttranslations, likely due to training dataset imabalances. On the MMLU-tsn benchmark of multiple choice Setswana questions, BOTS-LM significantly outperforms the original Llama-3-8B-Instruct model, only falling short of its 70B variant. This suggests that, while the 70B model may have infereior Setswana translation and writing skills, it retains superior understanding and reasoning capabilities thanks to its size. These results highlight the effectiveness of our fine-tuning approach on the Settswana corpus, particularly in enhancing translation and language understanding tasks, and demonstrates the potential for additional training to yield significant improvements.

6 Conclusion

In this work we introduce the first release in the BOTS-LM series of bilingual language models tailored for Setswana and English. Our models demonstrate significantly improved performance in English-Setswana translation tasks, rivaling models with significantly larger parameter counts. We introduce SetsText, the largest curated dataset of primarily Setswana text to date. By leveraging efficient fine-tuning techniques, we help to bridge the gap between Setswana and other high-resource languages, laying the groundwork for future enhanced Setswana-centric NLP. Our results indicate that BOTS-LM not only excels in translation but also demonstrates promising capabilities in reasoning and understanding tasks in Setswana. Future work will focus on expanding the suite with additional models and evaluations, ultimately aiming to bring small, truly open, and high-performance language models to the research community and the millions of Setswana speakers globally.

7 Acknowledgements

We would like to extend our gratitude to the OpenAI team for their invaluable support and for granting us the opportunity to utilize their models. Our appreciation also goes to Trelis Research for their generous financial backing. Additionally, we are deeply thankful to Dr. Jacob Sorber and Professor Carrie Russell of Clemson University, and Dr. Srinath Doss of Botho University. This work would not be possible without your guidance and support.

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