Datasets:

MarkrAI

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AutoRAG-evaluation-2024-LLM-paper-v1

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | Anomaly Detection | Prompt-based | HDFS, BGL | Precision, | | F1-Score, Accuracy | | | | | | | [55] | BERT | Forecasting | Foundation Model | | | | METR-LA, PeMS- | | | | | | | L, PeMS-Bay | | | | | | | RMSE, | MAE,

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | | RMSE, | MAE, | | | | | | MASE, MAPE | | | | | | | [24] | BERT | Anomaly Detection | Fine-tuning | KPI, Yahoo | Precision, | | F1-Score | | | | |

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research , Yahoo | Precision, | | F1-Score | | | | | | | [56] | BERT | Anomaly Detection | Fine-tuning, | | | | Foundation Model, | | | | | | | Prompt-based | | | | | | | LFD, GSC, FC | | |

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | LFD, GSC, FC | | | | | | | Precision, | Recall, | | | | | | F1-Score | | | | | | | [57] | BERT | Anomaly Detection | Few-shot, | | | | Fine-tuning,

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | [57] | BERT | Anomaly Detection | Few-shot, | | | | Fine-tuning, | | | | | | | Zero-shot | | | | | | | MSE, MAE | | | | | | | [58] | BERT | Anomaly Detection | Foundation

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | | [58] | BERT | Anomaly Detection | Foundation Model | HDFS, BGL, | | | Thunderbird | | | | | | | Accuracy, | Recall, | | | | | | F1-Score | | | | | | | [59]

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | | | [59] | BERT | Anomaly Detection | Fine-tuning | | | | BGL, Thunderbird, | | | | | | | HDFS | | | | | | | Precision, | Recall, | | |

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | Precision, | Recall, | | | | | | F1-Score | | | | | | | [60] | BERT | Anomaly Detection | Foundation Model | ECML/PKDD, | | | CSIC, Apache | | | | | | | F1-Score, Precision, | |

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | | F1-Score, Precision, | | | | | | | Recall | | | | | | | [61] | Transformer | Forecasting | Foundation Model | ETT, Weather, Elec- | | | tricity, | | | | | | | Traffic

e82fb48a-099c-43c3-a24f-9cc237d17bd0

## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research tricity, | | | | | | | Traffic | | | | | | | [62] | BERT | Anomaly Detection | Foundation Model | HDFS, OpenStack | Precision, | | F1-Score | | | | | | | [63] | BERT | Anomaly Detection | Foundation Model | HDFS, BGL, | | | Thunderbird |

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | [63] | BERT | Anomaly Detection | Foundation Model | HDFS, BGL, | | | Thunderbird | | | | | | | Precision, | Recall, | | | | | | F1-Score | | | | | | | [64] | BERT | Anomaly Detection | Foundation Model | HDFS

cdc8cc8d-dc0e-481c-a6f3-b72dd1166400

## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | [64] | BERT | Anomaly Detection | Foundation Model | HDFS | Precision, | | F1-Score | | | | | | | [65] | BERT | Anomaly Detection | Foundation Model | HDFS, BGL, | | | Thunderbird, Spirit | | | | | | | Precision, | Recall, | |

39d2c607-a056-4583-b836-04a59aa2c900

## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | Precision, | Recall, | | | | | | F1-Score | | | | | | | [66] | BERT | Anomaly Detection | Foundation Model | HDFS, BGL, | | | OpenStack | | | | | | | Precision, | Recall,

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## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research | | | | | | Precision, | Recall, | | | | | | F1-Score | | | | | | The selection process involved filtering papers published within a defined recent time frame to guarantee that the review accurately represented the current landscape of technology and research. This approach was adopted as studies outside the specified time frame may not accurately reflect current technologies and methodologies. Our selection criteria prioritized peer-reviewed articles, conference proceedings, and academic journals to maintain research credibility and rigor. In cases of multiple publications reporting identical research or data (e.g., a paper has an updated extended version), the most recent publication was chosen to eliminate redundancy. Table 3 provides a comprehensive overview of recent research studies focusing on the application of LLMs for forecasting and anomaly detection tasks. It systematically categorizes each piece of research according to the type of LLMs employed, the specific tasks addressed (forecasting, anomaly detection, or both), the methodological approach (e.g., zero-shot, few-shot, fine-tuning, foundation model, prompt

61cbba8b-943d-48bd-9a8c-a8927aba5a30

## Table 3: Overview Of Llm-Based Forecastor And Anomaly Detector Research and academic journals to maintain research credibility and rigor. In cases of multiple publications reporting identical research or data (e.g., a paper has an updated extended version), the most recent publication was chosen to eliminate redundancy. Table 3 provides a comprehensive overview of recent research studies focusing on the application of LLMs for forecasting and anomaly detection tasks. It systematically categorizes each piece of research according to the type of LLMs employed, the specific tasks addressed (forecasting, anomaly detection, or both), the methodological approach (e.g., zero-shot, few-shot, fine-tuning, foundation model, prompt-based), the datasets utilized in the studies, and the performance metrics used to evaluate the models' effectiveness. The subsequent sections of this review delve into the detailed analysis of the methodologies, challenges, datasets, and performance metrics employed in LLM-based forecasting and anomaly detection. We also discuss the specific applications of LLMs in these domains, highlighting the current state of research, inherent challenges, and prospective future directions.

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## 3 Overview The expansive domain of LLMs has ushered in unprecedented advancements in natural language processing, significantly impacting various tasks including forecasting and anomaly detection. This section provides a comprehensive overview of the current state and evolution of LLMs, delineating their foundational structures, development trajectories, and the pivotal role they play in transforming data analysis and predictive modeling. Beginning with a background on LLMs, we trace the evolution of language models from their nascent stages to the sophisticated pre-trained foundation models that serve as the backbone for contemporary applications. We then categorize tasks where LLMs have shown remarkable efficacy, specifically focusing on forecasting and anomaly detection, to illustrate the breadth of their applicability. Further exploration is dedicated to the diverse approaches employed to harness the power of LLMs, including promptbased techniques, fine-tuning mechanisms, the utilization of zero-shot, one-shot, and few-shot learning, reprogramming strategies, and hybrid methods that combine multiple approaches for enhanced performance. This section aims to equip readers with a thorough understanding of the intricate landscape of LLMs, setting the stage for deeper exploration of their capabilities and applications in the subsequent sections.

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## 3.1 Background Of Large Language Models In the evolution of language models, several iterative training paradigms have been applied. During the era of deep learning in NLP, models heavily relied on Long Short-Term Memory (LSTM) [67], Convolutional Neural Network (CNN) [68, 69, 70, 71], and other deep models as feature extractors and *Seq2Seq* was used as a basis for the framework, along with various modifications to the attention structures [72]. A key aspect of the technology was the design of intricate encoders and decoders. There was a marked gap between the effectiveness of NLP tasks and those in other domains, such as computer vision [73, 74], and NLP research was in a lukewarm state, with a focus on intermediate task results such as tokenization [75], part-of-speech tagging [76], and named entity recognition [77, 78]. The introduction of the Bidirectional Encoder Representations from Transformers (BERT) [2] and Generative Pretrained Transformer (GPT) [79] has significantly propelled the advancement of the NLP field, leading to the widespread adoption of the Pre-training and Fine-tuning paradigm [80, 81, 82, 83, 84]. Large-scale corpora were utilized through task-oriented objectives, often referred to as unsupervised training (strictly speaking, it is supervised but lacks manually annotated labels) [85, 8]. Following this, fine-tuning on downstream tasks was implemented to enhance the final model's applicability. Notably, these models outperformed earlier deep learning methods [86, 87, 88, 89, 90], prompting a focus on the meticulous design of pre-training and fine-tuning processes. The research tasks also shifted towards the ultimate goals of machine learning, such as text generation [91, 92, 93, 84], dialogue system [94, 95, 96], machine translation [97], and others [98], with Pre-trained Languge Models autonomously learning the intermediate elements of the tasks. For an extended period of time, Pre-trained Languge models based on BERT continued to receive most of the attention despite BERT and GPT series evolving in different directions [99, 100, 101, 102]. There were two primary reasons for this. To begin with, GPT creates greater difficulty when it attempts to predict the next context based on the preceding one, compared to BERT, which can detect both

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## 3.1 Background Of Large Language Models 91, 92, 93, 84], dialogue system [94, 95, 96], machine translation [97], and others [98], with Pre-trained Languge Models autonomously learning the intermediate elements of the tasks. For an extended period of time, Pre-trained Languge models based on BERT continued to receive most of the attention despite BERT and GPT series evolving in different directions [99, 100, 101, 102]. There were two primary reasons for this. To begin with, GPT creates greater difficulty when it attempts to predict the next context based on the preceding one, compared to BERT, which can detect both directions of context [79]. As a result, GPT series models were not as effective as BERT series models during the same period [103]. Rather than aligning itself with a deliberate God's perspective, the GPT design pattern is more aligned with human learning strategies [104]. Secondly, GPT-3 represents the culmination of a process of gradual accumulation, and despite its impressive nature, its 175 billion parameters indicate a significant investment in training and usage [105]. The high amount of investment in technology and funding did not result in a significant breakthrough in comparison to its potential benefits. Consequently, it failed to capture the attention of AI researchers, let alone those in other industries. The popularity of ChatGPT resulted in a surge of curiosity concerning the potential power of AI, marking a pivotal point in the progression of history. The subsequent emergence of GPT-4, which demonstrated multimodal intelligence, prompted speculation as to whether the AGI era had arrived [3]. OpenAI has taken a unique approach in developing GPT, which principally concentrates on the 'zero-shot' phenomenon from the Pre-trained Languge models era and implements prompt learning training methodologies that are more closely aligned with the trajectory of GPT [106]. In order to achieve few-shot capabilities, the model size had to be increased, in-context learning had to be implemented and later, the future of artificial intelligence had to be considered. An integral aspect of this is the use of more human-friendly methods, which align with human ethics and common sense [107]. A major development within GPT was the introduction of supervised fine-tuning (SFT) [108] and the integration of human feedback (RLHF), aiming to align the model's knowledge with human knowledge [109]. This ultimately led to the development of ChatGPT. In this section, we retrace and review the development

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## 3.1 Background Of Large Language Models few-shot capabilities, the model size had to be increased, in-context learning had to be implemented and later, the future of artificial intelligence had to be considered. An integral aspect of this is the use of more human-friendly methods, which align with human ethics and common sense [107]. A major development within GPT was the introduction of supervised fine-tuning (SFT) [108] and the integration of human feedback (RLHF), aiming to align the model's knowledge with human knowledge [109]. This ultimately led to the development of ChatGPT. In this section, we retrace and review the development trajectory of mainstream Large Language Models, from the first generation GPT-1 to GPT-4, marveling at the fact that the emergence of such powerful technologies does not occur overnight.

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## 3.1.1 Evolution Of Language Models The journey of language models from simple rule-based systems to today's sophisticated LLMs represents a significant evolution in the field of NLP. This section delves into the chronological development of language models, highlighting key milestones and technological breakthroughs that have shaped their growth. Beginning with early statistical models that relied on N-gram probabilities, we trace the path towards the emergence of neural network-based models, which introduced a deeper understanding of context and semantics. The advent of transformer architectures marked a turning point, enabling models to process sequences of text with unprecedented efficiency and accuracy. We examine the transition from early transformers to the development of pre-trained foundation models, such as GPT-1 and BERT, which have set new standards for performance across a wide range of NLP tasks. This section not only charts the technological advancements that have propelled the evolution of language models but also sets the stage for understanding the current capabilities and limitations of LLMs in the broader context of forecasting and anomaly detection.

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## - Statistical Language Models Statistical Language Models (SLMs), developed in the 1990s, are based on statistical theories such as Markov Chains [110]. These models use probabilistic methods to predict the next word in a sentence. The basic assumption behind SLMs is that the probability of each word depends only on the previous few words. This dependency length is fixed, forming the n in N-gram models. SLMs include Unigram, Bigram, and Trigram models, each with its unique operating principle [111]: Unigram Model: Each word in the text is independent of other words. Therefore, the likelihood of a sentence is calculated as the product of the probabilities of each word. Bigram Model: The Bigram Model extends the concept of Unigram, assuming dependence on the previous word. Therefore, the likelihood of a sentence here is calculated as the product of the probabilities of each pair of consecutive words in the sentence. Trigram Model: The Trigram Model takes this one step further, considering the probability of a word given its previous two words, thus creating a three-word context. However, despite their simplicity and effectiveness, these models have limitations due to their design. Firstly, they encounter difficulties when dealing with contexts longer than the fixed length n [112]. Secondly, they face challenges when dealing with high-dimensional data. As n increases, the number of transition probabilities grows exponentially, greatly reducing the accuracy of the model [113]. To alleviate this problem, smoothing algorithms like Backoff Estimation and Good-Turing Estimation are used [114]. When higher-order probabilities are unavailable, Backoff Estimation regresses to lower-order N-grams, effectively reducing the dimensionality. Conversely, Good-Turing Estimation adjusts the probability distribution for unseen events to deal with the problem of zero probability for unfamiliar word combinations - a problem known as data sparsity [115]. While SLMs are computationally inexpensive, easy to implement, and interpretable, their inability to capture long-term dependencies and semantic relationships between words limits their use in complex language tasks [116].

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## - Neural Network Language Model With the development of neural networks, Neural Network Language Models (NNLM) have demonstrated stronger learning capabilities than Statistical Language Models, overcoming the dimensionality disaster of N-gram language models and greatly improving the performance of traditional language models. The advanced structure of neural networks enables them to effectively model long-distance context dependencies. The idea of training language models with neural networks was first proposed by Wei Xu and Alexander Rudnicky (2000) [117]. In their paper, they proposed a method of constructing a Bigram language model with neural networks. After that, the most classic work in training language models is proposed by Bengio *et al.* (2000) [118] published at NIPS. However, due to the difficulty of training neural network models, it wasn't until Bengio *et al.* (2003) [119] proposed the Feed-forward Neural Network language model (FNNLM) that neural network language models aroused the interest of academia and industry. Subsequently, Mikolov *et al.* (2010) [120] introduced recurrent neural networks (RNNs) into language modeling, greatly improving the performance of language models. Following this, improved versions of recurrent neural networks, such as Long Short Term Memory (LSTM) recurrent neural networks [121] and Gated Recurrent Unit (GRU) neural networks [122], were successively used to further improve the performance of language modeling. In addition, convolutional neural networks [123, 124] have unexpectedly achieved success in language modeling, and their performance can be compared with recurrent neural networks. FFNNLM: Feed Forward Neural Network Language Models consist of three layers: the embedding layer, the fully connected layer, and the output layer [119]. The embedding layer maps the current word to a vector. It first obtains the n-1 words before the current word position, then obtains the word vectors of these *n-1* words according to the word embedding matrix, and finally combines them together as the representation of the current word. It can be understood that the word embedding here is to get the representation of the *n-1* words before the current word. The fully connected layer and the output layer receive the word vectors of the *n-1* context words of the current word as input, and then predict the probability of the current word. By mapping words to a low-dimensional space for representation, the problem of sparsity can be solved, and

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## - Neural Network Language Model the current word position, then obtains the word vectors of these *n-1* words according to the word embedding matrix, and finally combines them together as the representation of the current word. It can be understood that the word embedding here is to get the representation of the *n-1* words before the current word. The fully connected layer and the output layer receive the word vectors of the *n-1* context words of the current word as input, and then predict the probability of the current word. By mapping words to a low-dimensional space for representation, the problem of sparsity can be solved, and the model has a certain generalization ability. However, this method still has certain defects. The first is the limitation of the context window, that is, the limitation of the *n-1* context words related to the current word. In real scenarios, people's understanding of sentences does not have the restriction of only being able to see the previous *n-1* words. Secondly, it does not take into account temporal information. The words in the sequence have a front-to-back relationship, but this method will ignore the temporal information and treat words at different positions uniformly [125]. RNNLM: Recurrent Neural Network Language Models were proposed as a solution to the window limitation issue [120]. Using Recurrent Neural Networks, historical context information can be stored without being limited by the window length. The probability of the current word is calculated at each time step based on the current word and all previous contexts recorded by the RNN [126, 127]. Even though RNN language models are capable of using unlimited context for prediction, the inherent challenges of RNNs make training the model quite challenging. It is common to encounter issues such as gradient vanishing or gradient explosion during the training process [128]. Consequently, a proposal was made to replace RNNs with Long Short-Term Memory networks. LSTM-RNN: LSTM is a variant of RNN, and a more advanced RNN [121]. The essence of the algorithm remains the same, and it is capable of effectively processing sequence data [129]. In RNN, the value of the hidden layer is stored at every moment and is used at the next moment to ensure that every moment contains information from the previous moment. We refer to the place where information about each moment is stored as a Memory Cell. The RNN stores all information as it does not have the capability of selecting

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## - Neural Network Language Model replace RNNs with Long Short-Term Memory networks. LSTM-RNN: LSTM is a variant of RNN, and a more advanced RNN [121]. The essence of the algorithm remains the same, and it is capable of effectively processing sequence data [129]. In RNN, the value of the hidden layer is stored at every moment and is used at the next moment to ensure that every moment contains information from the previous moment. We refer to the place where information about each moment is stored as a Memory Cell. The RNN stores all information as it does not have the capability of selecting information. The LSTM, however, is distinct because it is powerful and incorporates a gate mechanism. The LSTM consists of three additional gates that allow information to be selectively stored. As part of the information transmission process, the information is transmitted in the following order: the information is initially input through the input gate, then the forget gate determines whether the information has been forgotten in the Memory Cell, and finally it determines whether the information should be output at this time through the output gate. Compared with the above three classic LMs, the performance of RNNLM (including LSTM-RNNLM) is superior to FFNNLM, and LSTM-RNNLM has always been the most advanced LM. The current NNLM is mainly based on RNN or LSTM. However, the representations of words learned by the previous models are unique and context-independent, which is evidently not the case in real-world situations. Language models should also allow words to learn related information from their contexts, as the same word can have different semantics in different contexts. Prior methods are unidirectional, that is, when calculating probability for the current word, only the information from the previous context is considered. In spite of this, people's understanding habits can be influenced by the context of the current semantics. ELMo: Embeddings from Language Model refers to a deep contextualized word representation that simulates both the complexity of word forms and the variability of word form across linguistic contexts [130]. Multidirectional LSTMs are used in ELMo. This representation is comprised of the word vector of the word itself as well as the current state of the LSTM at the current word position. Bidirectional LSTM is used to capture context features, and the stacking of multiple layers of LSTM is used to enhance feature extraction capabilities. Because of

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## - Neural Network Language Model habits can be influenced by the context of the current semantics. ELMo: Embeddings from Language Model refers to a deep contextualized word representation that simulates both the complexity of word forms and the variability of word form across linguistic contexts [130]. Multidirectional LSTMs are used in ELMo. This representation is comprised of the word vector of the word itself as well as the current state of the LSTM at the current word position. Bidirectional LSTM is used to capture context features, and the stacking of multiple layers of LSTM is used to enhance feature extraction capabilities. Because of the bidirectional nature, ELMo will divide the calculation of conditional probability into two parts, including using the previous context to calculate the probability of the current word and using the next context to calculate the probability of the current word. In the specific training process, the state of the last layer of LSTM is used to predict the probability of the word at the next position (whether forward or backward). In specific downstream tasks, the relevant word vectors obtained from the text through ELMo and the LSTM state values can be used as additional features of the current word to enhance the effect of downstream tasks through weighted averaging [131]. This is also a typical feature-based pre-training model method.

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## - Attention Mechanism The attention mechanism was first proposed by Bahdanau *et al.* (2014) [132].The purpose of this mechanism is to address the bottleneck found in RNNs that only support fixed length inputs (as sentences grow longer, the amount of information that needs to be carried forward will also grow, so embeddings of fixed size may be insufficient). This paper proposes a structure for translation tasks in which the encoder in *Seq2Seq* is replaced by a bidirectional recurrent network (BiRNN) and the decoding part is based on an attention model. Since Attention Mechanism gives the model the ability to distinguish and identify, it is widely used in a variety of applications, including machine translation [133], speech recognition [134], recommender system [135, 136, 137] and image captioning [138]. For example, in machine translation and speech recognition applications, different weights are assigned to each word in the sentence, making the learning of the neural network model more soft. At the same time, Attention Mechanism itself can serve as a kind of alignment relationship, explaining the alignment relationship between the input/output sentences in translation, and explaining what knowledge the model has learned. The Attention Mechanism mimics the human visual and cognitive system [139], allowing neural networks to focus on relevant parts when processing input data. By introducing the attention mechanism, neural networks can automatically learn and selectively focus on important information in the input, improving the performance and generalization ability of the model. The attention mechanism is essentially similar to the human selective attention mechanism, and the core goal is also to select more critical information from a large amount of information. The most typical attention mechanisms include self-attention mechanism, spatial attention mechanism, and temporal attention mechanism. These attention mechanisms allow the model to allocate different weights to different positions in the input sequence, so as to focus on the most relevant part when processing each sequence element. Self-attention Mechanism: Self-attention consists of the idea that when processing sequence data, each element is associated with other elements in the sequence, rather than solely dependent on its adjacent position [140]. It adaptively captures the long-term dependencies between elements by calculating the relative importance between elements. Specifically, for each element in the sequence, the self-attention mechanism calculates its similarity with other elements and normalizes these similarities into attention weights. As a result of summing each element with its respective attention weight, the output of the self-attention mechanism can be determined

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## - Attention Mechanism part when processing each sequence element. Self-attention Mechanism: Self-attention consists of the idea that when processing sequence data, each element is associated with other elements in the sequence, rather than solely dependent on its adjacent position [140]. It adaptively captures the long-term dependencies between elements by calculating the relative importance between elements. Specifically, for each element in the sequence, the self-attention mechanism calculates its similarity with other elements and normalizes these similarities into attention weights. As a result of summing each element with its respective attention weight, the output of the self-attention mechanism can be determined. Multi-head Attention Mechanism: Multi-head attention mechanism is developed based on the self-attention mechanism, which is a variant of the self-attention mechanism, aimed at enhancing the expressive power and generalization ability of the model [140]. It uses multiple independent attention heads to calculate attention weights separately, and concatenates or sums their results to obtain richer representations. Channel Attention Mechanism: This mechanism is based on calculating the importance degree of each channel; therefore, it is used frequently in convolutional neural networks [141]. At present, the SENet model is considered the classic channel attention mechanism. SENet increases the network's ability to represent features by learning the relationship between channels (the importance of each channel), thus enhancing its performance. Due to its spatial modeling capacity, this CBAM has been widely used in vision tasks [142]. Spatial Attention Mechanism: Spatial attention and channel attention both strive to accomplish the same goal in different ways [143]. The channel attention algorithm is intended to capture the degree of importance of the channel whereas the spatial attention algorithm is intended to introduce an attention module that allows the model to learn the weights of the attention for different regions according to their importance. As a result, the model can pay more attention to important areas of the image and ignore areas of less importance. Among them, Convolutional Block Attention Module (CBAM), is the most typical. CBAM is a model designed to enhance the convolutional neural network's attention to images by combining channel and spatial attention [144].

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## - Transformer Transformer was introduced in 2017, and its proposal attracted widespread attention to the Self-attention Mechanism, which further advanced the development of attention mechanisms [140]. In the past, the NLP field mainly relied on models such as recurrent neural networks (RNN) and convolutional neural networks (CNN) to process sequence data. However, these models often face problems such as gradient vanishing and low computational efficiency when dealing with long sequences [128]. The emergence of the Transformer broke this limitation. Transformer abandoned the traditional recursive structure and adopted a new self-attention mechanism to process sequence data in a more efficient and accurate way, enabling independent and parallel calculations at each position [140]. The capabilities of this feature are aligned perfectly with those of modern AI accelerators, thus enhancing the efficiency of model computation. This innovation not only accelerates model training and inference but also opens up possibilities for distributed applications. The self-attention mechanism is one of the core principles of the Transformer. It captures long-term dependencies by calculating the relationship between each element and other elements in the sequence. This mechanism allows the Transformer to compute in parallel when processing sequence data, greatly improving computational efficiency. At the same time, the self-attention mechanism can dynamically adjust weights according to different parts of the input sequence, making the model more flexible. Through the self-attention mechanism, the Transformer can perform parallel computations on each element in the input sequence and capture their relationships. This mechanism allows the model to better handle long sequence data and retain more context information during processing. In addition, the Transformer also uses techniques such as residual connections and normalization to effectively alleviate the problem of gradient vanishing and improve the training effect of the model. As a revolutionary natural language processing model, the Transformer plays an important role in the field of artificial intelligence. It has pushed natural language processing to a new height and brought us great opportunities and challenges. The introduction of the Transformer model has changed the way traditional sequence models are processed and adopted the self-attention mechanism. Through the self-attention mechanism, the Transformer can capture longterm dependencies in the input sequence and better understand and generate natural language text. This revolution has enabled the Transformer to achieve outstanding performance in NLP tasks, with machine translation being the most outstanding representative. Translation models based on the Transformer, such as OpenAI's GPT [79] and Google's BERT [2], have achieved unprecedented breakthroughs in translation quality

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## - Transformer natural language processing to a new height and brought us great opportunities and challenges. The introduction of the Transformer model has changed the way traditional sequence models are processed and adopted the self-attention mechanism. Through the self-attention mechanism, the Transformer can capture longterm dependencies in the input sequence and better understand and generate natural language text. This revolution has enabled the Transformer to achieve outstanding performance in NLP tasks, with machine translation being the most outstanding representative. Translation models based on the Transformer, such as OpenAI's GPT [79] and Google's BERT [2], have achieved unprecedented breakthroughs in translation quality, greatly improving the accuracy and fluency of translation. In addition, the Transformer has also shown strong capabilities in summarization and generation tasks [145], bringing us a more intelligent and natural interactive experience.

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## 3.1.2 Pre-Trained Foundation Models Pre-trained foundation models have become the cornerstone of modern NLP, heralding a new era of language understanding and generation. This section explores the inception, development, and impact of these models, which are characterized by their vast knowledge bases, acquired through extensive pre-training on diverse and large-scale datasets. We delve into the mechanics behind their architecture, primarily focusing on transformer models such as GPT, BERT, and their successors, which have demonstrated remarkable versatility and performance across a multitude of NLP tasks. The discussion extends to the strategies employed in pre-training these models, including the objectives, datasets, and computational resources involved, as well as the challenges and ethical considerations arising from their deployment. Additionally, we explore how these foundation models serve as a platform for further fine-tuning and adaptation, enabling customization for specific tasks or domains, including forecasting and anomaly detection. By examining the pivotal role of pre-trained foundation models, this section aims to provide insights into their transformative potential in advancing the capabilities of large language models and their applications in real-world scenarios.

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## - Bert By introducing the bidirectional concept, Bidirectional Encoder Representations from Transformers (BERT) innovatively predicts both preceding and succeeding contexts [146]. As a pre-trained model, BERT significantly improves learning efficiency by requiring only a small number of parameters for fine-tuning in practical applications. In terms of structure, BERT is relatively simple, with Bert-Base and Bert-Large models composed of 12 and 24 repeated basic transformer blocks. The transformer block consists of three modules: Multi-Head Attention, Add&Norm, and FFN. While the original transformer used triangular positional encoding [140], BERT adopts learnable positional encoding with a preset position count of 512, limiting the maximum sequence length to 512. BERT utilizes two unsupervised pre-training tasks: Masked LM, where some words are masked, and the network predicts their meaning based on context; and Next Sentence Prediction, a task determining whether two sentences are consecutive. It's worth noting that BERT encounters challenges in handling consecutive Mask Tokens and is not directly applicable to variable-length text generation tasks.

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## - Gpt-1 There has been a long history behind GPT-1 dating back to the groundbreaking paper *"Attention is all you need"* [140]. According to it, Transformer is divided into two parts: encoder and decoder, both of which perform Multi-Head Self Attention, though the encoder is able to observe information from the entire source sequence while the decoder does not. The Bert model adapts the encoder, and when designing pre-training tasks, it predicts the missing intermediate words based on context, similar to filling in the blanks. Alternatively, GPT-1 utilises a decoder, which predicts the next context based on the previous context, thus allowing it to effectively perform masked multi-head self attention. There are two stages in the PLM paradigm: *pre-training* and *fine-tuning*. The pre-training stage involves generating context predictions from a large-scale corpus of data. The fine-tuning stage involves training the model using downstream data and feeding the embedding of the last token into the prediction layer, which fits the label distribution of the downstream data. With an increase in layers, the accuracy and generalization capabilities of the model continue to improve, and further improvement is possible. Moreover, GPT-1 possesses an inherent capability for zero-shot learning, and this capability augments in tandem with the model's size. It is these two points that directly contribute to the emergence of subsequent GPT models.

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## - Gpt-2 GPT-2 is an enhanced version of GPT-1, based on the Transformer architecture for language modeling. GPT-2 can train models from massive unlabeled data, and the fine-tuning process enhances model performance, optimizing it for downstream tasks [34]. In GPT-2, the language model is given greater emphasis in a zero-shot scenario, in which the model has not been trained or fine-tuned for downstream tasks prior to its application. A difference between GPT-2 and GPT-1 is that GPT-2 does not undergo fine-tuning for different tasks. Rather, it transforms the input sequences of downstream tasks. GPT-1 introduced special tokens, like start and separator symbols, but zero-shot scenarios prevent them from being used to fine-tune downstream tasks, as the model can't recognize these symbols without additional training. Therefore, in a zero-shot setting, input sequences for different tasks would be similar to the text seen during training, taking the form of natural language without task-specific identifiers. The GPT-1 model is composed of 12 layers, whereas the BERT model is composed of 24 layers. However, the GPT-2 model consists of 48 layers with 1.5 billion parameters. The training data is derived from the WebText dataset, which undergoes some basic data cleaning. In accordance with the paper [34], larger language models such as GPT-2 require more data to reach convergence, and experimental results indicate that current models are still underfitted. GPT-2 uses unidirectional transformers as opposed to BERT, which uses bidirectional transformers, and adopts a multitasking approach during the pre-training stage. Rather than learning on a single task, it learns across multiple tasks, which ensures that the losses of each task converge. The main transformer parameters are shared across different tasks. MT-DNN [147] was the inspiration for this approach, which further enhanced the generalization ability of the GPT-2 model. As a result, GPT-2 exhibits impressive performance even without fine-tuning. GPT-2 performs better than unsupervised algorithms in many tasks, showcasing its zero-shot capabilities. However, it still exhibits some deficiencies compared to fine-tuning algorithms with supervised feedback.

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## - Gpt-3 GPT-3 maintains the concept of excluding fine-tuning and focusing solely on a universal language model, as does the previous model. However, there are some technical replacements: GPT-3 introduces the sparse attention module from Sparse Transformer, aimed at reducing computational load [148]. It is necessary to make this adaptation since GPT-3 has increased the parameter size even further compared to GPT-2, reaching a staggering number of 175 billion parameters. When it comes to downstream tasks, GPT-3 utilizes a few-shot approach without fine-tuning, highlighting substantial differences in accuracy between varying parameter magnitudes and showing the extraordinary capabilities of large models.The training data for GPT-3 includes the Common Crawl dataset for lower quality, as well as the WebText2 dataset for higher quality, as well as the Books1, Books2, and Wikipedia datasets for higher quality [148]. GPT-3 assigns different weights to datasets according to their quality, with higher-weighted datasets being more likely to be sampled during training. Additionally, according to the paper [148], the one-shot effectiveness shows a significant and noticeable improvement when applied to large language models. As prompts are added, this improvement is further amplified, while marginal returns for few-shot decline gradually as prompts are added. Prompts are evident up to a point around eight-shot, but once eight-Shot is reached, their influence diminishes. Prompts are effectively ineffective beyond ten-shots. GPT-3 differs from previous models in that it is capable of achieving few-shot capabilities through constructing prompts. This capability is referred to as In Context Learning. Even though both fine-tuning and In Context Learning may appear to provide examples of large language models, they are fundamentally different. During fine-tuning, downstream tasks are performed, examples are provided, and parameter gradients are updated. As opposed to this, In Context Learning focuses on downstream tasks using examples without updating the parameters. GPT-3 has the advantage of a high degree of generalization. The model can perform various subtasks without having to be fine-tuned because natural language instructions can be included in the input sequence without requiring any adjustments. GPT-3 achieves or exceeds state-of-the-art in some tasks, thus confirming that larger model sizes are associated with higher task performance. The few-shot capability of GPT-3 is more powerful than both one-shot and zero-shot capabilities in most situations.

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## - Gpt-3 gradients are updated. As opposed to this, In Context Learning focuses on downstream tasks using examples without updating the parameters. GPT-3 has the advantage of a high degree of generalization. The model can perform various subtasks without having to be fine-tuned because natural language instructions can be included in the input sequence without requiring any adjustments. GPT-3 achieves or exceeds state-of-the-art in some tasks, thus confirming that larger model sizes are associated with higher task performance. The few-shot capability of GPT-3 is more powerful than both one-shot and zero-shot capabilities in most situations. Moreover, the authors anticipate that GPT-3 could potentially have societal implications [148]. For instance, it has the potential to facilitate the generation of fake news, spam, and academic papers. Given the likely influence of the biases present in GPT-3's training data, namely racial, religious, and gender biases, the generated text might mirror these issues.

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## - Instructgpt (Gpt-3.5) According to the paper [149], the InstructGPT model is proposed to enhance the alignment between the outputs of the model and the user's intentions. Despite GPT-3's remarkable capabilities in diverse NLP tasks and text generation, it can still generate inaccurate, misleading, and harmful information that can negatively impact society. Moreover, GPT-3 often does not communicate in a form that is accepted by the human audience. Consequently, OpenAI introduces the concept of "Alignment", which strives to align model outputs with human preferences and intentions. InstructGPT defines three key objectives for an idealized model of language: helpful, honest, and harmless [149]. InstructGPT requires two rounds of fine-tuning for its model: from GPT-3 to SFT (supervised fine-tuning), and then to RL (reinforcement learning). As a result of the SFT model, it can be addressed the problem of GPT-3's inability to guarantee answers based on human instructions, to be helpful, and to generate safe responses without the need for manual annotation data to refine the answers. Using the reward model, a ranking-based discriminative annotation is introduced, which is much less costly than generative annotation. Furthermore, through the use of reinforcement learning capabilities, the model is able to gain a deeper understanding of human intentions. When comparing InstructGPT to GPT-3, several advancements can be observed. It has the capacity to comprehend user instructions, explicit or implicit, encompassing goals, constraints, and preferences, subsequently generating outputs that align more closely with user expectations and needs. InstructGPT is capable of more effectively utilizing information or structures provided in prompts, and can make reasonable inferences or creations based on that information. By consistently maintaining output quality, errors or failures can be reduced. Furthermore, InstructGPT, with 13 billion parameters, significantly outperforms GPT-3, which consists of 175 billion parameters.

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## - Gpt-4 According to the paper and experiments [3], GPT-4 significantly improves the GPT model scale and training methods, while having over a trillion parameters compared to GPT-3. By utilizing a novel training technique, known as Reinforcement Learning from Human Feedback (RLHF), the GPT-4 model is able to generate text in a more natural and accurate manner. RLHF utilizes a combination of pre-training and fine-tuning strategies, engaging in interactive conversations with human operators in order to train through reinforcement learning. This enhances GPT-4's understanding of context and questions and improves its performance on specific tasks [150, 151, 152]. In general, GPT-4 follows the same training strategy as ChatGPT, based on the principles of pre-training, prompting, and prediction. GPT-4 introduces three significant enhancements: 1. The implementation of a rule-based reward model (RBRM); 2. Integration of multi-modal prompt Learning to support various prompts; 3. Incorporation of a chain of thought mechanism to enhance overall coherence in thinking. According to the paper [3], GPT-4 is a robust multimodal model able to process both image and text inputs, generating text outputs that are ranked in the top 10% of test takers. Compared to GPT-3.5, which falls within the bottom 10%, this is a significant improvement. The GPT-4 language model outperforms many state-of-the-art NLP systems on traditional benchmarks [153, 154, 155]. Specifically, the report addresses a key project challenge involving the development of deep learning infrastructure and optimization methods that exhibit predictable behavior across a wide range of scales. Additionally, it discusses interventions implemented to address potential risks associated with GPT-4 deployment, such as adversarial testing with domain experts and the implementation of a model-assisted safety pipeline. Since ChatGPT-3 and GPT-4 are trained on large amounts of text from the internet, they may be subject to biases and inaccurate information. The OpenAI team has implemented additional filters in GPT-4 to address this issue, reducing the likelihood of inappropriate content being generated and improving control over the generated text [3]. The GPT-4 has a number of challenges and issues, however, it demonstrates considerable potential in several different application scenarios, opening up a wide range of possibilities for the development of artificial intelligence.

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## - Ai21 Jurassic-2 According to the document in the website [156], Jurassic-2, a customizable language model designed to power natural language use cases, is considered one of the largest and most complex models in the world. Jurassic-2, developed based on Jurassic-1, includes three base models in different size: Large, Grande, and Jumbo. In addition to comprehensive enhancements in text generation, API latency, and language support, Jurassic-2 also opens up command fine-tuning and data fine-tuning to help businesses and individual developers create customized ChatGPT assistants. Certain types of specific fine-tuning are realized in Jurassic-2. To perform semantic search, Jurassic-2 understands the intent and context of queries and retrieves relevant text snippets from documents. As part of its context-based Q&A service, Jurassic-2 provides answers based solely on specific contexts, with automatic retrieval from document libraries. When it comes to summarizing content, it can be used to obtain documents (original texts or URLs) and provide key points within them. According to the input requirements of the user, the obtained text can be output in a specific style, etc., resulting in nine fine-tuning options.

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## - Claude According to the website introduction [157], Claude is an artificial intelligence assistant developed by Anthropic with a cheerful personality and a rich individuality, designed to provide users with accurate information and answers. Anthropic was established in 2021, co-founded by several former OpenAI members, including Dario Amodei, Daniela Amodei, Tom Brown, Chris Olah, Sam McCandlish, Jack Clarke, and Jared Kaplan. They have rich experience in the field of language models and have participated in the development of models such as GPT-3. Google is the main investor of the company, having invested 300 million dollars in it. There is not much information available as of yet, but Anthropic's research paper mentions AnthropicLM v4-s3 as a 52-billion-parameter model that has already been trained [158]. The model is an autoregressive one trained on a large text corpus unsupervised, similar to the GPT-3 model. To generate fine-tuned outputs, Anthropic uses a unique process known as *"Constitutional AI"*, which uses a model rather than humans. Anthropic names it "Constitutional AI" because they began with a list of ten principles that constituted a "constitution". Despite not being publicly disclosed, Anthropic says its principles are based on beneficence (maximizing positive impact), nonmaleficence (avoiding giving harmful advice) and autonomy (respecting freedom of choice).

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## - Bloom BLOOM, an acronym for BigScience Large Open-science Open-access Multilingual Language Model, is a language model possessing 176 billion parameters that has been trained on 59 natural languages and 13 programming languages. The model was trained on *Jean Zay*, a supercomputer funded by the French government and managed by GENCI (donation number *2021-A0101012475*), installed at the National Computing Center IDRIS of the French National Center for Scientific Research (CNRS) [159]. Each component of BLOOM was carefully designed, including the training data, the model architecture and the training objectives, as well as the engineering strategies for distributed learning. BLOOM was trained based on modifications to Megatron-LM GPT2, using Megatron-DeepSpeed for training. This model is divided into two parts: Megatron-LM provides Transformer implementation, tensor parallelism, and data loading primitives, while DeepSpeed provides ZeRO optimizer, model pipeline, and general distributed training components [159]. As a rule of thumb, it mainly utilizes the decoder-only structure, normalization of the word embedding layer, linear bias attention position encoding with GeLU activation function, etc. Currently, it is the largest open-source language model in the world, and it is transparent in many ways, disclosing the materials used for training, the difficulties encountered during development, and the methods for evaluating its performance. In addition, it is also important to note that the BLOOM model is subject to the same disadvantages as other large language models, in the sense that inaccurate or biased language may be hidden. On the one hand, the project adopts the new *"Responsible AI License"* in order to avoid being applied to high-risk areas such as law enforcement or healthcare, and it is also prohibited from use in harm, deception, exploit, or impersonation. On the other hand, Hugging Face believes that open source will enable the AI community to contribute to the improvement of this model.

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## - Hugging Face Hugging Face is a platform that focuses on natural language processing (NLP) and artificial intelligence (AI). The platform currently hosts over 320,000 models and 50,000 datasets, allowing machine learning practitioners around the world to collaborate on developing models, datasets, and applications [160]. Its abundant repository of pre-trained models and codes is widely used in academic research. It helps people keep track of popular new models and provides a unified coding style to use various different models such as Bert, XLNet, and GPT. Its Transformers library has also been open-sourced on GitHub [161], which provides pre-trained models and fine-tuned models for different tasks. The Hugging Face website allows users to compare models easily, and they can find a pre-trained model and train it using their own data. Whatever the task is, Hugging Face provides the appropriate models and tools. This includes text classification, question answering systems, machine translation, text generation, or sentiment analysis. Developers are thus able to quickly and effectively build and deploy NLP solutions across a variety of applications. Hugging Face not only provides a wide range of pre-trained models, but it also supports customization and extension. Developers can adjust the model according to their specific needs, or further train on the basis of existing models.

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## 3.2 Task Categorization The versatility of LLMs is showcased through their application across a diverse range of tasks, each presenting unique challenges and opportunities for innovation. This section categorizes and examines the specific roles LLMs play in two critical areas: forecasting and anomaly detection. In forecasting, we explore how LLMs contribute to predicting future events, trends, and behaviors, leveraging historical data and linguistic patterns to generate insights with significant accuracy. Anomaly detection, on the other hand, highlights the models' ability to identify outliers or unusual patterns within data, which is pivotal for security, quality control, and operational efficiency. Through a detailed exploration of these tasks, we aim to elucidate the methodologies and approaches employed by LLMs, ranging from direct application in a zero-shot or few-shot context to more complex fine-tuning and hybrid strategies. This section not only underscores the broad applicability of LLMs but also sets the stage for a deeper dive into the specific techniques and challenges associated with each task, providing a structured framework for understanding the multifaceted impact of language models in contemporary computational linguistics and data analysis domains.

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## 3.2.1 Forecasting The work of large language models in time series forecasting can basically be divided into two types. One method involves applying large language models directly to time series predictions, focusing on converting time series data into input data suitable for the models, such as GPT, Llama, and others. Another type is to train a large language model in the domain of time series, by using a large amount of data from several time series datasets to jointly train a large language model in the domain of time series, which can then be used for downstream time series tasks. Specifically, the paper focuses on the second type, examining the ways in which researchers train large language models across a variety of domains.

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## 3.2.2 Anomaly Detection Anomaly detection can be divided into two categories. In the first category of anomaly detection, training data with labels are provided, and a classifier is first trained using these data, and there is no "unknown" in the data and labels. However, it is expected that the classifier will be able to determine that the newly acquired training data differ from the original training data and label the new training data as "unknown". This is also known as Open-set Recognition. A second category consists of all training data that are unlabeled and anomalies are determined based on similarity between the data. The second category includes two situations: clean data, which means that all data is normal data, and polluted data, which means that some abnormal data has been mixed in with the training data. Specifically, the paper focuses on the second subcategory of the second type of anomaly detection, examining the ways in which researchers train large language models across a variety of domains.

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## 3.3 Approaches The application of LLMs across various tasks, including forecasting and anomaly detection, involves a spectrum of innovative approaches, each tailored to optimize performance and accuracy. This section delves into the core methodologies employed to leverage LLMs, presenting a comprehensive overview of the strategies that have emerged as most effective in harnessing their potential. We begin with prompt-based methods, which involve crafting input prompts that guide the model toward generating desired outputs, demonstrating the flexibility and creativity inherent in interacting with LLMs. The discussion then moves to fine-tuning, a process of adjusting a pre-trained model's parameters to better suit specific tasks or datasets, enhancing its applicability and precision. The exploration of zero-shot, one-shot, and few-shot learning highlights how LLMs can perform tasks with minimal to no task-specific data, showcasing their remarkable adaptability. Reprogramming introduces the concept of modifying input data in ways that exploit the model's latent knowledge without altering its parameters, offering an innovative angle on model utilization. Lastly, hybrid approaches that combine multiple techniques are examined, illustrating the dynamic and evolving landscape of LLM application methods. This section aims to provide a thorough understanding of the diverse approaches to deploying LLMs, paving the way for their effective use in addressing complex challenges in NLP and beyond.

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## 3.3.1 Prompt-Based Prompt-based refers to the transformation of input text information according to a specific template, restructuring the task into a form that can make full use of pre-trained language models [162]. Different from traditional supervised learning, Prompt-based learning directly utilizes language models pre-trained on a large amount of raw text, and by defining a new prompt function, allows the model to perform few-shot or even zero-shot learning, adapting to new scenarios with only a small amount of annotated data or no annotated data.Unlike traditional fine-tuning methods, prompt learning adapts to various downstream tasks based on language model methods, usually without the need for parameter updates.

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## 3.3.2 Fine-Tuning Fine-tuning fundamentally involves the transformation of general-purpose models into specialized ones. It entails taking pre-trained models and further training them on smaller, specific datasets to refine their capabilities and enhance their performance in a particular task or domain. This process serves as a bridge between generic pre-trained models and the unique requirements of specific applications, ensuring that the language model aligns closely with human expectations. The procedure of fine-tuning is more resource-efficient and cost-effective in comparison to training a model from scratch. The latter necessitates extensive text datasets, significant computational resources, and substantial financial investment. In contrast, fine-tuning involves the adaptation of a pre-trained model to a smaller, task-specific dataset, which necessitates fewer resources, less time, and less financial investment.

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## 3.3.3 Zero-Shot, One-Shot, And Few-Shot Zero-shot is a machine learning paradigm where the model is capable of making predictions about unseen classes without explicit training on these classes, this approach is widely used in industry research [163]. This is achieved by leveraging the model's understanding of other, analogous classes to infer characteristics of the new classes. For instance, consider a model trained on a dataset of various types of birds. This model could be utilized to predict new bird species, such as sparrows and eagles, without explicit training on these species. This is possible because the model understands that all birds share certain common characteristics, such as feathers, beaks, and wings, which allows it to make educated guesses about the new bird species. The one-shot is a machine learning paradigm where the model is capable of making predictions about new classes after being trained on a single instance of that class [163]. This task is more challenging than zero-shot learning, as the model has limited data to work with. For example, a model trained on a dataset of various types of flowers could be used to predict a new flower, such as a daisy, after being trained on a single image of a daisy. The model can use this image to learn about the daisy's features, such as its petals, stem, and leaves. Few-shot is a machine learning paradigm that lies between zero-shot and one-shot. In few-shot, the model is trained on a handful of examples from each new class. This task is more challenging than one-shot but less so than zero-shot [164]. For instance, a model trained on a dataset of various types of trees could be used to predict a new type of tree, such as a Japanese maple tree, after being trained on a few images of Sugar maple trees, Norway maple trees, and Field maple trees. The model can use these images to learn about the maple tree's features and make inferences about how the maple tree is similar to and different from other types of trees.

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## 3.3.4 Reprogramming Model Reprogramming, alternatively referred to as Adversarial Reprogramming [165], represents a burgeoning field within Machine Learning. This approach involves repurposing an existing model for a novel task, circumventing the necessity for retraining, or fine-tuning the original model. Instead, the methodology modifies the inputs of the model to facilitate its application to a new adversarial task. Given that Model Reprogramming incurs a lower computational cost and necessitates less access to the model parameters in comparison to retraining or fine-tuning, it has been successfully extended for applications such as domain adaptation [166], knowledge transfer, and bias elimination in models [167].

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## 3.3.5 Hybrid Hybrid methodologies amalgamate the strengths of diverse approaches to augment the performance and versatility of LLM models. Typically, these methodologies incorporate both rule-based and machine learning methods, capitalizing on the benefits of each. The rule-based approaches are reliant on pre-established linguistic rules and knowledge graphs, offering an explicit representation of knowledge with rich, expressive, and actionable descriptions of concepts. The machine learning approaches employ statistical techniques to learn from data. They are particularly adept at managing large-scale, complex tasks where manually crafting rules would be impractical. Hybrid approaches have also been extended for a variety of applications. They present a promising direction for enhancing the capabilities of LLMs, empowering them to handle more complex tasks and adapt to new domains effectively.

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## 4 Challenges In the realm of forecasting and anomaly detection, the deployment of LLMs represents a paradigm shift towards leveraging vast amounts of data for predictive insights. However, this approach is fraught with significant challenges that stem from the inherent properties of time series data, the lack of labeled instances, the prevalence of missing values, and the complexity of processing noisy and unstructured text data. These obstacles necessitate a sophisticated understanding and innovative methodologies to harness the full potential of LLMs in these applications. The intricate nature of time series data, characterized by complex seasonality and patterns, demands models capable of capturing and forecasting dynamic temporal behaviors. This complexity is compounded by the multifaceted influences affecting time series, including but not limited to economic indicators, weather conditions, and social events, which introduce additional layers of difficulty in modeling efforts. Moreover, the scarcity of labeled data, especially in the context of anomaly detection, poses a significant hurdle. The effectiveness of LLMs in such scenarios is contingent upon developing and applying advanced strategies that can leverage limited annotations to discern patterns indicative of anomalies. Another pervasive issue in time series analysis is the occurrence of missing data, a consequence of various disruptions in data collection and transmission processes. Different from the computer vision models that can be trained from a small amount of data [168, 169], LLMs require huge natural language corpora for training. Addressing this challenge requires robust imputation methods that can seamlessly integrate with LLMs to ensure the integrity and continuity of the data being analyzed. In order to get reproducible and reusable datasets for analytics, the cORe [170] platform can be exploited. Furthermore, the analysis of unstructured text data introduces additional complexity, as such data often contain high noise and irrelevant information. Effective preprocessing and feature extraction methods are imperative to distill valuable insights from unstructured text, necessitating a nuanced approach to understanding and extracting pertinent information. These challenges underscore the necessity for innovative solutions that adapt to the complexities of time series data and unstructured text, ensuring that LLMs can be effectively applied to forecasting and anomaly detection tasks. The development of such solutions remains an active area of research, with the potential to significantly advance predictive analytics capabilities.

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## 4.1 Complex Seasonality And Patterns The challenge of modeling complex seasonality and patterns in time series data is a formidable obstacle in the application of LLMs to forecasting and anomaly detection tasks. Time series data can exhibit a wide range of seasonal behaviors, from simple annual cycles to intricate patterns that span multiple temporal resolutions, such as daily, weekly, and monthly fluctuations. These patterns may also interact with each other, creating complex seasonal dynamics that are difficult to predict. One of the primary challenges in addressing complex seasonality is the requirement for LLMs to not only recognize these patterns but also to understand their underlying causes and interactions. Traditional models might struggle to capture such complexities without significant customization or the inclusion of domain-specific knowledge. With their vast parameter spaces and deep learning capabilities, LLMs offer a potential solution to this problem by learning from large datasets encompassing the full range of seasonal variations and their associated factors. However, this requires a substantial volume of high-quality, granular data spanning multiple seasonal cycles to train these models effectively. Moreover, the presence of external factors such as holidays, economic fluctuations, and weather conditions further complicates the modeling of seasonality. These factors can introduce additional variance into the time series, making it challenging to isolate and predict the impact of seasonality on the data. For LLMs to accurately forecast under these conditions, they must be capable of integrating external data sources and contextual information into their predictions. This requires advanced data processing capabilities and the ability to infer causal relationships and adapt to changing conditions over time. Another aspect of complexity arises from the non-linear interactions between different seasonal patterns. For instance, the effect of a holiday on consumer behavior might vary significantly depending on the day of the week it occurs or its proximity to other events. Capturing such non-linearity and interactions is crucial for accurate forecasting and anomaly detection, demanding sophisticated modeling techniques that can account for a wide range of dependencies and conditional effects. Addressing complex seasonality in time series data with LLMs requires not only extensive training data but also advanced optimization techniques. Stochastic optimization methods [171, 172, 173], including multi-stage stochastic programming and stochastic integer programming, play a pivotal role in enhancing LLMs' ability to capture intricate patterns and variations inherent in temporal dynamics. These approaches introduce flexibility and adaptability, allowing the model to make sequential decisions over different time horizons and incorporate discrete variables, thereby improving its performance in forecasting and anomaly detection tasks amidst complex seasonal behaviors. The synergy between deep learning capabilities and stochastic optimization equ

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## 4.1 Complex Seasonality And Patterns . Addressing complex seasonality in time series data with LLMs requires not only extensive training data but also advanced optimization techniques. Stochastic optimization methods [171, 172, 173], including multi-stage stochastic programming and stochastic integer programming, play a pivotal role in enhancing LLMs' ability to capture intricate patterns and variations inherent in temporal dynamics. These approaches introduce flexibility and adaptability, allowing the model to make sequential decisions over different time horizons and incorporate discrete variables, thereby improving its performance in forecasting and anomaly detection tasks amidst complex seasonal behaviors. The synergy between deep learning capabilities and stochastic optimization equips LLMs to recognize, understand, and adapt to diverse temporal patterns, emphasizing the importance of careful parameter tuning for optimal performance across various time series scenarios. In summary, addressing the challenge of complex seasonality and patterns in time series data with LLMs involves a multifaceted approach that includes the development of models capable of learning from large and diverse datasets, the integration of external factors and contextual information, and the ability to model non-linear interactions and dependencies. Success in these endeavors can significantly enhance the accuracy and reliability of forecasting and anomaly detection, unlocking new possibilities for predictive analytics in various domains.

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## 4.2 Label Deficiency The issue of label deficiency represents a significant challenge in the deployment of LLMs for forecasting and anomaly detection tasks, particularly in domains where labeled data are scarce or expensive to obtain. This scarcity is acutely felt in anomaly detection, where anomalous events are inherently rare and thus less likely to be represented in training datasets. The lack of labeled examples hampers the ability of models to learn the nuanced patterns that differentiate normal from anomalous behavior, leading to decreased accuracy and increased false positives or negatives. In the context of forecasting, the challenge of label deficiency arises from the need to train models on historical data that may not contain explicit labels for future events or outcomes. While some forecasting tasks may have access to labeled data for past time periods, the absence of labels for future time points makes it difficult to evaluate the accuracy of predictions and to train models on the specific patterns associated with future events. Several strategies have been proposed and adopted within the machine learning community to combat label deficiency. One such strategy involves using semi-supervised learning techniques, which allow models to learn from labeled and unlabeled data. This approach leverages the abundant unlabeled data to improve model generalization, thereby mitigating the effects of limited labeled data. With their capacity to understand and generate human-like text, LLMs can be particularly adept at exploiting the context provided by unlabeled data to infer underlying patterns and relationships. Data augmentation is another critical strategy for addressing label deficiency. By artificially augmenting the dataset with synthetic examples through techniques like oversampling, undersampling, or generating new instances via transformations, models can be exposed to a broader range of scenarios than those represented in the original labeled dataset. This exposure helps improve the robustness and generalizability of the model. However, generating realistic and relevant synthetic data that accurately captures the complexity of real-world scenarios is challenging and requires sophisticated approaches. Transfer learning has also emerged as a potent solution to the challenge of label deficiency. By pre-training models on large, diverse datasets and then fine-tuning them on the target task with limited labeled data, LLMs can leverage learned representations and knowledge to enhance their performance on tasks with scarce labels. This approach is particularly effective in domains where pre-trained models have been exposed to relevant contexts or languages during their initial training phase. Despite these strategies, the challenge of label deficiency remains a significant barrier to the effective application of LLMs in forecasting and anomaly detection tasks. The development of more advanced techniques for semi-supervised learning, data augmentation, and transfer learning

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## 4.2 Label Deficiency as a potent solution to the challenge of label deficiency. By pre-training models on large, diverse datasets and then fine-tuning them on the target task with limited labeled data, LLMs can leverage learned representations and knowledge to enhance their performance on tasks with scarce labels. This approach is particularly effective in domains where pre-trained models have been exposed to relevant contexts or languages during their initial training phase. Despite these strategies, the challenge of label deficiency remains a significant barrier to the effective application of LLMs in forecasting and anomaly detection tasks. The development of more advanced techniques for semi-supervised learning, data augmentation, and transfer learning continues to be a crucial area of research. Additionally, exploring innovative ways to leverage unlabeled data, such as unsupervised anomaly detection methods that do not rely on labeled examples, may offer new pathways to overcoming the limitations imposed by label scarcity.

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## 4.3 Missing Data In Time Series Addressing missing data in time series is a critical challenge when applying LLMs for forecasting and anomaly detection. Missing data can arise from many sources, including equipment malfunctions, data transmission errors, or simply gaps in data collection. These missing values pose a significant problem, as they can lead to inaccuracies in predictions and analyses if not properly handled. The issue is further complicated by the sequential nature of time series data, where the temporal dependencies and patterns play a crucial role in forecasting and anomaly detection tasks. One common approach to managing missing data is through imputation, where missing values are filled in based on available data. The complexity of imputation varies with the amount and type of data missing, as well as the patterns and dependencies present in the time series. Simple imputation methods, such as mean or median imputation, are often inadequate for time series data due to their inability to capture temporal dynamics. More sophisticated techniques, such as linear interpolation or time series-specific methods like ARIMA-based imputation, can provide better results by leveraging the temporal structure of the data. However, these methods may still fall short when dealing with non-linear patterns or long gaps of missing data. LLMs offer promising avenues for addressing the challenges of missing data through their ability to model complex patterns and relationships in data. By training on large datasets, LLMs can learn the underlying structures and dependencies in time series, potentially enabling them to predict missing values with higher accuracy than traditional methods. Moreover, LLMs can incorporate contextual information and external variables, providing a more nuanced approach to imputation that considers both temporal dynamics and external influences. Despite the potential of LLMs to handle missing data, several challenges remain. Ensuring the quality and reliability of imputed values is paramount, as inaccuracies can propagate through subsequent analyses and lead to misleading conclusions. Furthermore, the computational complexity of using LLMs for imputation can be significant, particularly for large datasets with extensive missingness. There is also the need for careful model tuning and validation to avoid overfitting and ensure that the imputation method generalizes well across different time series. In summary, while LLMs present a promising solution to the challenge of missing data in time series, their effective application requires careful consideration of the methods used for imputation, the potential for model overfitting, and the computational demands of the task. Ongoing research into more advanced imputation techniques and the development of LLMs designed explicitly for time series data will be crucial in overcoming these challenges and unlocking the full potential of LLMs in forecasting

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## 4.3 Missing Data In Time Series significant, particularly for large datasets with extensive missingness. There is also the need for careful model tuning and validation to avoid overfitting and ensure that the imputation method generalizes well across different time series. In summary, while LLMs present a promising solution to the challenge of missing data in time series, their effective application requires careful consideration of the methods used for imputation, the potential for model overfitting, and the computational demands of the task. Ongoing research into more advanced imputation techniques and the development of LLMs designed explicitly for time series data will be crucial in overcoming these challenges and unlocking the full potential of LLMs in forecasting and anomaly detection.

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## 4.4 Noisy And Unstructured Text Data The challenge of noisy and unstructured text data is particularly pronounced in applications involving LLMs for forecasting and anomaly detection. Unstructured text, which includes various formats such as social media posts, news articles, and log files, often contains a significant amount of noise—irrelevant information, typos, slang, and ambiguous expressions that can obfuscate meaningful insights. This noise complicates the task of extracting valuable features and patterns that are critical for accurate predictions and anomaly identification. To effectively harness the power of LLMs in processing noisy and unstructured text data, a comprehensive approach to data preprocessing is essential. This involves cleaning the data by removing or correcting typos, standardizing terminology, and filtering out irrelevant information. Such preprocessing steps are crucial for reducing the noise in the data and making it more amenable to analysis by LLMs. However, the challenge lies in executing these steps without losing important contextual or nuanced information that may be crucial for the task at hand. Beyond preprocessing, feature extraction from unstructured text represents another significant challenge. Traditional methods may not fully capture the complexity and richness of the data, limiting the model's ability to understand and predict based on the text. LLMs, with their advanced natural language processing capabilities, offer a promising solution by automatically identifying and extracting relevant features directly from text. They can discern patterns, sentiments, and relationships that are not immediately apparent, providing a deeper understanding of the data. However, leveraging LLMs for feature extraction from noisy and unstructured text also requires careful model tuning and validation. The models must be trained on sufficiently diverse datasets to ensure they can generalize well across different types of text and noise levels. Moreover, there is a need for mechanisms to assess the relevance and importance of the extracted features, as not all information gleaned from the text may be useful for forecasting or anomaly detection purposes. Incorporating external knowledge bases and ontologies is another strategy that can enhance the performance of LLMs in dealing with unstructured text. By providing additional context and background information, these resources can help the model disambiguate and interpret complex or ambiguous text more effectively. However, integrating such external sources into the modeling process introduces additional complexity and raises questions about the scalability and adaptability of the solution. In conclusion, while noisy and unstructured text data presents a significant challenge for forecasting and anomaly detection, LLMs hold considerable promise in addressing this issue. Through advanced preprocessing, intelligent feature extraction, and the integration of external knowledge, LLMs can unlock valuable

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## 4.4 Noisy And Unstructured Text Data and ontologies is another strategy that can enhance the performance of LLMs in dealing with unstructured text. By providing additional context and background information, these resources can help the model disambiguate and interpret complex or ambiguous text more effectively. However, integrating such external sources into the modeling process introduces additional complexity and raises questions about the scalability and adaptability of the solution. In conclusion, while noisy and unstructured text data presents a significant challenge for forecasting and anomaly detection, LLMs hold considerable promise in addressing this issue. Through advanced preprocessing, intelligent feature extraction, and the integration of external knowledge, LLMs can unlock valuable insights hidden within unstructured text. Continued advancements in model development and training methodologies will be vital in overcoming the obstacles posed by noise and unstructured data, enabling more accurate and insightful predictive analyses.

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## 5 Datasets In the realm of forecasting and anomaly detection research, the availability of high-quality datasets is a critical factor for advancement. These datasets facilitate rapid development and fine-tuning of effective detection algorithms while also setting benchmarks for evaluating methodological performance. However, the acquisition of such datasets often entails significant financial, material, and workforce investments. The field is currently experiencing early development stages, characterized by challenges such as limited data quantity, complex sample characteristics, and missing labels, both essential for developing effective approaches. This section highlights prominent datasets utilized in LLM for forecasting and anomaly detection, which have been contributed by recent studies. An assessment of these datasets is conducted, pinpointing prevailing limitations and challenges in dataset generation, with the objective of guiding the creation of future datasets in this domain.

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## 5.1 Forecasting In the field of forecasting, the attributes of datasets hold paramount importance in determining the success and accuracy of predictive models. Essential characteristics include temporal resolution and range, where the granularity of time intervals and the overall time span covered by the dataset are critical for capturing the necessary details and trends. Completeness and continuity are equally important; datasets should be devoid of gaps and missing values to avoid inaccuracies and the need for complex imputation techniques. Variability and diversity within the data ensure the model is exposed to various scenarios, thus enhancing its ability to generalize and perform under varying conditions. The presence of non-stationary elements, which cause statistical properties to change over time, poses significant challenges and must be carefully considered and addressed. Seasonality and cyclic patterns are also crucial, as datasets must capture these recurring behaviors for models to forecast periodic fluctuations accurately. We have found the following datasets utilized in recent research of LLM for forecasting:

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## - Amazon Review The Amazon Review dataset [174] is a collection of reviews from Amazon.com. The dataset contains user reviews on Amazon shopping website from 2014-01-04 to 2016-10-02, with each review consisting of a product ID, reviewer ID, rating, and text. This dataset is used for time series rating forecasting and can be found in paper [47].

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## - Darts Darts [175] is a Python library designed for easy manipulation, forecasting, and anomaly detection on time series data. Darts contains popular time series datasets for quick and reproducible experiments with A collection of 8 real univariate time series datasets. This dataset found application in the evaluation setup of works [45].

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## - Electricity Consumption Load (Ecl) The ECL dataset [176] from UCI collected in 2011 includes the electricity consumption values (in Kwh) of 321 users and 370 points per client. The dataset ensured that it contained no missing values. The analysis conducted in paper [9, 48, 52, 61] was significantly based on this dataset.

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## - Integrated Crisis Early Warning System (Icews) The ICEWS dataset [177] is a collection of events extracted from news articles and other sources. The dataset contains 4.5 million events from 1995 to 2014, with each event consisting of a source, target, and type. These data consist of coded interactions between socio-political actors (i.e., cooperative or hostile actions between individuals, groups, sectors and nation states). Events are automatically identified and extracted from news articles. The research outlined in [47] employed this dataset for its analysis.

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## - Informer / Ett / Etdataset The ETT or ETDataset proposed in the Informer paper [178], includes data from 69 transformer stations at 39 locations, covering aspects such as load, oil temperature, location, climate, and demand. This dataset is designed to support investigations into long sequence forecasting problems and includes subsets like ETTh1, ETTh2 for 1-hour-level data, and ETTm1 for 15-minute-level data. Each data point in the ETT dataset consists of the target oil temperature value and six power load features, with the data split into training, validation, and test sets. This dataset is commonly used for long-term forecasting and can be found in paper [45, 46, 9, 52, 61].

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## - M3 The M3-Competition dataset [179] is a collection of time series data used in the M3-Competition, which is the third iteration of the M-Competitions. The M3-Competition dataset contains 3003 time series, selected to include various types of data (micro, industry, macro, etc.) and different time intervals. The time series in the dataset are either annual, quarterly, or monthly, and the number of observations for each series ranges between 14 and 126 observations. All values in the dataset are positive. This dataset constituted the core empirical basis for the investigation in paper [52].

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## - M4 The M4 dataset [180] is a collection of 100,000 time series used for the M4 competition. The dataset consists of a time series of yearly, quarterly, monthly, and other frequencies (weekly, daily, and hourly) data, which are divided into training and test sets. The minimum number of observations in the training test is 13 for yearly, 16 for quarterly, 42 for monthly, 80 for weekly, 93 for daily, and 700 for hourly series. The participants were asked to produce the following numbers of forecasts beyond the available data: six for yearly, eight for quarterly, 18 for monthly series, 13 for weekly series, and 14 and 48 forecasts, respectively, for the daily and hourly ones. This dataset played a crucial role in the research outcomes presented in paper [52].

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## - Monash The Monash [181] forecasting archive contains 20 publicly available time series datasets from varied domains. The utilization of this dataset is documented in paper [45].

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## - Text For Time Series (Tets) The TETS benchmark dataset was proposed and used in [9] for short-term forecasting experiments. It is built upon the S&P 500 dataset, combining contextual information and time series.

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## 5.2 Anomaly Detection In the realm of anomaly detection, the attributes of datasets are critical in shaping the efficacy and reliability of detection models. Anomaly detection tasks hinge on the ability to identify deviations from normal patterns, thus necessitating meticulously curated datasets to capture these nuances. One of the primary attributes of such datasets is the representation of ordinary versus anomalous data. The datasets must include a sufficient representation of normal data to establish a typical behavior baseline. Equally important is the inclusion of a diverse range of anomalies. These anomalies should vary in terms of their nature, intensity, and duration to ensure that the detection models can identify a broad spectrum of deviations. The balance between normal and anomalous data is also a critical factor. Typically, anomalies are rare occurrences in real-world scenarios, and this rarity needs to be reflected in the datasets. However, having too few anomalies can hinder the model's ability to learn to detect them effectively. Thus, a delicate balance must be struck to create a realistic and useful dataset. Another crucial aspect is the contextual richness of the datasets. Anomalies often make sense only within a specific context, and datasets need to provide sufficient contextual information. This includes temporal context, which can be crucial for identifying time-based anomalies, and other domain-specific information that helps understand the significance of the data points. The quality and cleanliness of the data are also paramount. Anomaly detection models can be sensitive to noise and errors in the data. High-quality datasets with minimal noise and errors are essential for developing robust models. Additionally, the presence of labeled anomalies, which have been accurately identified and categorized, can significantly aid in the training and evaluating detection models. In recent studies on LLM for anomaly detection, the following datasets have been identified as commonly employed:

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## - Blue Gene/L (Bgl) BGL [182] is an open dataset containing 4,747,963 logs collected from a BlueGene/L supercomputer system consisting of 131,072 processors and 32,768GB of memory and was deployed at Lawrence Livermore National Labs in Livermore, California. The log contains alert and non-alert messages identified by alert category tags. Each log in the BGL dataset was manually labeled as either normal or anomalous. Out of the total, 348,460 log messages, which represent 7.34% of the dataset, were identified as anomalous. The analysis conducted in paper [10, 49, 54, 56, 58, 59, 63, 65, 66] was significantly based on this dataset.

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## - Hadoop Distributed File System (Hdfs) The HDFS dataset [183] is collected from more than 200 Amazon EC2 nodes. It consists of 11,175,629 log events, each associated with a block ID. These log messages form different log windows according to their block ID, reflecting a program execution in the HDFS system. For each execution, labels are provided to indicate whether anomalies exist. This dataset has 16,838 blocks of logs (2.93%) indicating system anomalies. The analysis conducted in paper [10, 49, 54, 56, 58, 59, 62, 63, 64, 65, 66] was significantly based on this dataset.

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## - Openstack The OpenStack log datasets from CloudLab [184] contain 1,335,318 log entries. Both normal logs and abnormal cases with failure injection are provided in this dataset. This dataset was crucial to the research outcomes presented in paper [51, 62].

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## - Spirit Spirit dataset [182] aggregates system log data from the Spirit supercomputing system at Sandia National Labs. There are more than 272 million log messages in total, of which more than 172 million log messages are labeled as anomalous on the Spirit dataset. The empirical evidence in [65] was derived using this particular dataset.

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## - Server Machine Dataset (Smd) SMD [185] is a 5-week-long dataset collected from 28 server machines at a large Internet company. It includes data from 38 different sensors or metrics per machine, which monitor various aspects of the server's operation, such as CPU load, network usage, and memory usage. The data was recorded at 1-minute intervals, and domain experts have labeled anomalies and their anomalous dimensions in the SMD testing set. The research outlined in [53] employed this dataset for its analysis.

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## - Thunderbird The Thunderbird dataset [182] is an open dataset of logs collected from a Thunderbird supercomputer at Sandia National Labs. There are around 211 million log messages, and the log data contains normal and abnormal messages that are manually identified. This dataset played a crucial role in the research outcomes presented in paper [49, 58, 59, 63, 65].

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## - Yahoo S5 The Yahoo S5 dataset is a labeled open dataset for anomaly detection released by Yahoo Lab. Part of the time series is synthetic (i.e., simulated). In contrast, the other part comes from the real traffic of Yahoo services. The anomaly points in the simulated curves are algorithmically generated, and those in the real-traffic curves are labeled by editors manually. The dataset was prominently featured in the experimental findings of paper [24].

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## 5.3 Summary In forecasting, the emphasis on temporal resolution and range, completeness, continuity, variability, diversity, nonstationarity, and the presence of cyclic patterns and seasonality are fundamental for the success of predictive models. These attributes ensure that the datasets are reflective of real-world complexities and variations, enabling the models to capture and predict trends and fluctuations accurately. The datasets identified in recent research have been tailored to address these needs, although challenges in data acquisition, quality, and representation persist. For anomaly detection, the focus is on the representation of normal versus anomalous data, the diversity of anomalies, the balance between normal and anomalous instances, contextual richness, and data quality. These factors are crucial in crafting datasets that accurately reflect real-world scenarios and enable LLMs to identify and distinguish between normal and anomalous behaviors effectively. The challenge lies in assembling datasets that are both realistic in their rarity of anomalies and rich in contextual detail to facilitate effective learning and detection. Both fields face common challenges in dataset generation, including the need for large-scale, high-quality data that accurately captures the complexities of real-world scenarios. The issues of missing labels, noise in data, and the balance between various data characteristics are ongoing concerns. Future dataset creation in these domains should focus on addressing these challenges, ensuring greater accuracy and efficacy in forecasting and anomaly detection tasks. This will not only enhance the performance of current models but also pave the way for new advancements in the field.

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## 6 Evaluation Metrics Evaluation metrics are indispensable tools for evaluating and comparing models in machine learning and statistical analysis, especially in domains such as forecasting and anomaly detection. In these areas, the ability of a model to predict future values based on historical data or identify irregular patterns that deviate from the norm is critical. Metrics in these contexts serve as quantitative indicators of a model's performance, offering insights into its predictive accuracy, reliability, and robustness under various conditions.

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## 6.1 Definition For forecasting, metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) are commonly employed to measure the deviation of predicted values from actual values, providing a clear picture of prediction accuracy. Additionally, the Mean Absolute Percentage Error (MAPE) and Symmetric Mean Absolute Percentage Error (sMAPE) offer insights into the relative prediction errors, making them particularly useful for comparing models across different scales or datasets. In this context, we have the following definitions: - N: the number of forecasting data points - n: n ∈ {1, . . . , N} - Yn: the n-th ground truth - ˆYn: the n-th forecasting value In the realm of anomaly detection, the focus shifts towards identifying outliers effectively. Precision, Recall, and the F1 Score became crucial, quantifying the model's ability to correctly identify anomalies (true positives) while minimizing false alarms (false positives) and missed detections (false negatives). The Area Under the Receiver Operating Characteristic (AUROC) further provide comprehensive measures of a model's discriminative ability, balancing the trade-off between true positive rates and false positive rates across different threshold settings. In this given scope, the definitions are as follows: - **True Positive (TP)**: the total number of data samples that are correctly identified to be positive. This refers to the number of anomalies (or outliers) that the system correctly identifies as anomalies. Essentially, these are the instances where the system correctly detects an abnormal behavior or pattern that deviates from what's expected or normal. - **True Negative (TN)**: the total number of data samples that are correctly identified to be negative. This refers to the number of normal instances that the system correctly identifies as normal. In other words, these are the cases where the system accurately recognizes that there is no anomaly present, and the behavior or pattern is as expected. - **False Positive (FP)**: the total number of data samples that are incorrectly identified to be positive. This occurs when the system incorrectly identifies a normal instance as an anomaly. False positives are essentially false alarms, where the system flags normal behavior or data as being abnormal or suspicious when it is not. This can lead to unnecessary investigations or actions. - **False Negative (FN)**: the total number of data samples that are incorrectly

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## 6.1 Definition correctly identifies as normal. In other words, these are the cases where the system accurately recognizes that there is no anomaly present, and the behavior or pattern is as expected. - **False Positive (FP)**: the total number of data samples that are incorrectly identified to be positive. This occurs when the system incorrectly identifies a normal instance as an anomaly. False positives are essentially false alarms, where the system flags normal behavior or data as being abnormal or suspicious when it is not. This can lead to unnecessary investigations or actions. - **False Negative (FN)**: the total number of data samples that are incorrectly identified to be negative. This occurs when the system fails to identify an actual anomaly as an anomaly. In these cases, the system incorrectly considers abnormal behavior or patterns to be normal, potentially missing important or critical incidents. These terms are crucial for evaluating the accuracy and effectiveness of applying LLM for anomaly detection. A high number of false positives might lead to wasted resources and desensitization to alerts, whereas a high number of false negatives could mean missing critical issues or breaches. Balancing sensitivity (minimizing FNs) and specificity (minimizing FPs) is critical to designing an effective anomaly detection system.

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## 6.2 Metrics In the pursuit of advancing the effectiveness and precision of LLMs in forecasting and anomaly detection, it is imperative to employ robust metrics that accurately capture the models' performance. This subsection delves into the diverse array of metrics that are instrumental in evaluating the outcomes of LLMs within these domains. Forecasting metrics offer unique insights into the model's predictive accuracy and reliability, while anomaly detection metrics provide a multi-dimensional view of model efficacy, balancing the detection accuracy with the rate of false alarms. This systematic exploration underscores the importance of choosing appropriate evaluation metrics and highlights how these metrics can guide the development and refinement of LLMs for enhanced performance in forecasting and anomaly detection tasks.

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## 6.2.1 Forecasting In the context of forecasting, a diverse array of metrics is employed to evaluate the accuracy and efficacy of predictive models meticulously. These metrics, each with its unique focus and application, serve as critical tools for quantitatively assessing how well a model's predictions align with actual outcomes. From the MAE, which provides a straightforward measure of average error magnitude, to the MAPE and its symmetric counterpart sMAPE, which offers insights into relative prediction errors, these metrics cater to various aspects of forecasting accuracy. The MSE and its derivative, the RMSE, emphasize the penalization of larger errors, making them especially pertinent in contexts where such errors are less tolerable. Additionally, the Root Mean Squared Percentage Error (RMSPE) and Mean Absolute Scaled Error (MASE) introduce normalized error measurements that facilitate model comparison across different scales or series. The Mean Absolute Ranged Relative Error (MARRE) and Overall Percentage Error (OPE) extend the toolkit by providing further nuances in error evaluation. Moreover, the Root Mean Squared Log Error (RMSLE) addresses handling asymmetric error distribution, which is particularly useful in skewed datasets. Lastly, the Overall Weighted Average (OWA) integrates multiple accuracy metrics into a single composite score, offering a holistic view of model performance. Collectively, these metrics equip forecasters with a comprehensive framework to scrutinize, compare, and enhance the predictive capabilities of their models, ensuring more informed decision-making and strategy development in various domains.

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## - Mean Absolute Error (Mae) MAE quantifies the average magnitude of errors in a collection of predictions, disregarding the errors' direction. It represents the mean of the absolute discrepancies between predicted values and actual observations across a dataset, treating all deviations with uniform importance. $$\text{MAE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\frac{1}{N}\sum_{n=1}^{N}\left|\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}\right|.$$ Recent works [45, 46, 9, 48, 50, 52, 55, 61] employed this particular metric for its evaluative procedures.

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## - Mean Absolute Percentage Error (Mape) MAPE quantifies the precision of forecasts by representing the error as a percentage of the total. It's calculated as the average of the absolute percentage errors of the predictions. This characteristic makes MAPE very easy to interpret but can also be misleading if dealing with values close to zero. $$\text{MAPE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\frac{100\%}{\mathcal{N}}\sum_{n=1}^{\mathcal{N}}\left|\frac{\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}}{\mathcal{Y}_{n}}\right|.$$ The research detailed in [46, 52, 55] incorporated this metric in its assessment.

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## - Symmetric Mean Absolute Percentage Error (Smape) sMAPE is a variation of MAPE that is symmetric, meaning it treats over-forecast and under-forecast equally. It's considered more accurate than MAPE by some because it normalizes errors by the sum of the forecast and actual values, thus avoiding the issue of division by a small number. $$\text{sMAPE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\frac{100\%}{\mathcal{N}}\sum_{n=1}^{\mathcal{N}}\frac{2\left|\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}\right|}{\left|\hat{\mathcal{Y}}_{n}\right|+\left|\mathcal{Y}_{n}\right|}.$$ The metric discussed was applied in the analysis presented in [46, 9, 52].

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## - Mean Squared Error (Mse) MSE calculates the mean of the squared discrepancies between predicted and true values, offering a measure of the average error magnitude. MSE gives more weight to more significant errors due to the squaring of each term, which can be particularly useful in some contexts where larger errors are more undesirable than smaller ones. $$\operatorname{MSE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})={\frac{1}{\mathcal{N}}}\sum_{n=1}^{\mathcal{N}}\left(\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}\right)^{2}.$$ The application of this metric is elaborated in the evaluation section of [46, 9, 52, 53, 186, 61].

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## - Root Mean Squared Error (Rmse) RMSE is the square root of the mean squared error. It's a measure of the magnitude of the difference between the predictions of a model and the observed values. By taking the square root of MSE, RMSE converts the units back to the original output units, making interpretation easier. $$\text{RMSE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\sqrt{\frac{1}{N}\sum_{n=1}^{N}\left(\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}\right)^{2}}.$$ Paper [47, 48, 50, 55, 186] features the use of this metric in its experimental validation phase.

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## - Root Mean Squared Percentage Error (Rmspe) RMSPE is a normalized metric that expresses the average of the squares of the percentage errors between actual and forecasted values. It is beneficial for comparing forecasting errors across different data sets because it is scaleindependent. The RMSPE is especially insightful when inspecting the error in terms of the percentage of the actual values, providing a clear picture of the relative size of the errors. $$\operatorname{RMSPE}(\mathcal{Y}_{n},{\hat{\mathcal{Y}}}_{n})={\sqrt{{\frac{1}{\mathcal{N}}}\,\sum_{n=1}^{\mathcal{N}}{\overline{{\left({\frac{{{\hat{\mathcal{Y}}}_{n}-{\mathcal{Y}}_{n}}{{\mathcal{Y}}_{n}}}\right)^{2}}}}}}}.$$

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## - Mean Absolute Scaled Error (Mase) MASE measures the accuracy of forecasts relative to a naive benchmark prediction, typically the naive forecast from the previous period. This scaling makes MASE an excellent tool for comparing the performance of forecasting models across different data sets with varying scales. MASE is particularly advantageous since it is easy to interpret and does not require the forecast errors to be normally distributed. $$\text{MASE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\frac{\frac{1}{N}\sum_{n=1}^{N}|\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}|}{\frac{1}{N-1}\sum_{n=2}^{N}|\mathcal{Y}_{n}-\mathcal{Y}_{n-1}|}.$$ As delineated in [52, 55], the metric was critical to their evaluative strategy.

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## - Mean Absolute Ranged Relative Error (Marre) MARRE is a metric that assesses the absolute errors in relation to a specific range of the dataset, making it particularly useful for datasets where the range of data points is significant. MARRE helps in understanding the magnitude of errors in the context of the overall variation in the dataset. $$\mathrm{MARRE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\frac{1}{\mathcal{N}}\sum_{n=1}^{\mathcal{N}}\left(\frac{|\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}|}{\operatorname*{max}(\mathcal{Y})-\operatorname*{min}(\mathcal{Y})}\right).$$

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## - Overall Percentage Error (Ope) OPE aggregates the total errors as a percentage of the total actual values. It provides a single, comprehensive figure that reflects the overall accuracy of the forecasts in relation to the actual observations, offering a macroscopic view of forecasting performance. $$\mathrm{OPE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})={\frac{\sum_{n=1}^{\mathcal{N}}|\hat{\mathcal{Y}}_{n}-\mathcal{Y}_{n}|}{\sum_{n=1}^{\mathcal{N}}\mathcal{Y}_{n}}}\times100\%.$$ r (RMSLE)

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## - Root Mean Squared Log Error (Rmsle) RMSLE is used to measure the ratio between actual and predicted values. By taking the log of the predictions and actual values before calculating the mean square error, RMSLE reduces the impact of significant errors and is less sensitive to outliers than RMSE. It's particularly useful when you don't want to penalize enormous differences when both the actual and predicted values are big numbers. $$\operatorname{RMSLE}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\sqrt{\frac{1}{\mathcal{N}}}\,\sum_{n=1}^{\mathcal{N}}\left(\log(\hat{\mathcal{Y}}_{n}+1)-\log(\mathcal{Y}_{n}+1)\right)^{2}.$$

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## - Overall Weighted Average (Owa) OWA is a specific metric that was introduced as part of the M4 forecasting competition [180], which aimed to advance the field of forecasting by comparing and evaluating the performance of various forecasting models across multiple time series datasets. OWA is particularly notable because it combines aspects of both accuracy and scalability into a single metric, making it a comprehensive measure for evaluating forecasting models. OWA is calculated by averaging two key components: the MASE and the sMAPE. These two metrics are chosen because they provide complementary perspectives on forecasting performance: MASE offers a scale-independent measure of error relative to a simple naive benchmark, and sMAPE provides a percentage-based measure of error that is symmetric, treating over-forecasts and under-forecasts equally. $$\mathrm{OWA}(\mathcal{Y}_{n},\hat{\mathcal{Y}}_{n})=\frac{1}{2}\left(\frac{\mathrm{MASE}}{\mathrm{MASE}_{\mathrm{Naive2}}}+\frac{\mathrm{sMAPE}}{\mathrm{sMAPE}_{\mathrm{Naive2}}}\right).$$ In this context, MASENaive2 and sMAPENaive2 refer to the MASE and sMAPE scores obtained by a naive forecasting method (Naive2), typically a seasonal naive method that uses the last observed value of the same season as the forecast. This normalization against a naive benchmark allows OWA to reflect both the absolute and relative improvement of a forecasting method over a simple but commonly applicable baseline. Paper [52] features the use of this metric in its experimental validation phase.

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## 6.2.2 Anomaly Detection In the field of anomaly detection, the effectiveness of a model is significantly determined by its ability to identify outliers and minimize missed detections and false alarms accurately. The key metrics used to evaluate such models include Accuracy, Precision, Recall, True Negative Rate (TNR), False Positive Rate (FPR), False Negative Rate (FNR), the F1 Score, and the AUROC. These metrics, derived from the fundamental concepts of TP, TN, FP, and FN, provide a comprehensive framework for assessing the performance of anomaly detection systems.

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## - Accuracy Accuracy quantifies the fraction of correct predictions, encompassing both true positives and true negatives, relative to the overall sample size evaluated. Accuracy is the most straightforward and intuitive performance measure, giving a general idea of how often the model is correct. While accuracy is straightforward, it may not always be the best metric for anomaly detection, especially in datasets where anomalies are rare (imbalanced datasets). In such cases, a model might achieve high accuracy by predicting the majority class (normal) most of the time while failing to detect many anomalies. $${\mathrm{Accuracy}}={\frac{T P+T N}{T P+T N+F P+F N}}.$$ The research detailed in [53, 54, 58] incorporated this metric in its assessment.

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## - Precision Precision, also known as Positive Predictive Value, quantifies the number of correct positive identifications made out of all positive identifications (correct and incorrect). Precision is crucial in scenarios where the cost of false positives is high. For instance, in transaction anomaly detection, a false positive (flagging a legitimate transaction as fraudulent) could inconvenience customers and erode trust. High precision indicates that when the model predicts an anomaly, it is likely to be a true anomaly. $$\mathrm{Precision}={\frac{T P}{T P+F P}}.$$ The application of this metric is elaborated in the evaluation section of [51, 53, 187, 54, 24, 56, 57, 60, 62, 63, 64, 65, 66].

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## - Recall / True Positive Rate (Tpr) Recall, also known as Sensitivity or True Positive Rate (TPR), measures the proportion of actual positives correctly identified, emphasizing the model's ability to capture all relevant positive outcomes. In the context of anomaly detection, a high recall means that the model is effective at catching anomalies, which is critical in situations where missing an anomaly can have severe consequences, such as in predictive maintenance or health monitoring. $$\mathrm{Recall}\,(\mathrm{TPR})={\frac{T P}{T P+F N}}.$$ The research detailed in [51, 53, 54, 24, 56, 57, 58, 188, 59, 60, 62, 63, 64, 65, 66] incorporated this metric in its assessment.

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## - True Negative Rate (Tnr) TNR, also known as Specificity, quantifies the proportion of actual negatives that are correctly identified, reflecting the model's ability to identify negative outcomes. High TNR means few normal instances are incorrectly flagged as anomalies, which helps reduce false alarms and maintain trust in the system's predictions. $$\mathrm{TNR}={\frac{T N}{T N+F P}}.$$