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A Survey on Large Language Models with some Insights on their Capabilities and Limitations

Andrea Matarazzo, Riccardo Torlone

arXiv:2501.04040v2cs.CLcs.AIcs.LGcs.NE

TL;DR

LLMs have achieved broad language-task performance and developed emergent capabilities, while raising questions about how those capabilities arise and where they fail. This survey examines architectures, scaling, applications, reasoning and planning, and external-system frameworks, concluding that LLM progress coexists with important reliability and reasoning limitations.

  • Problem

    LLMs exhibit powerful and sometimes value-inconsistent behavior, creating questions about their applicability, ethical use, generalization, emergent abilities, and inherent limitations.

  • Method

    The paper surveys LLM foundations, scaling, applications, prompting, CoT and planning, pre-training influences, and LLM-modulo frameworks integrating external systems.

  • Results

    LLM performance scales with parameters under sufficient data, alongside emergent in-context learning and CoT reasoning abilities across language tasks.

  • Takeaways & Limitations

    LLMs show transformative potential across diverse fields, but their development and application require continued attention to ethical, technical, and practical challenges.

  • Takeaways & Limitations

    LLMs can produce plausible but incorrect information and may mimic reasoning without truly handling complex multistep problem-solving, planning, or logical inference.

Abstract

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The rapid advancement of artificial intelligence, particularly with the development of Large Language Models (LLMs) built on the transformer architecture, has redefined the capabilities of natural language processing. These models now exhibit remarkable performance across various language-related tasks, such as text generation, question answering, translation, and summarization, often rivaling human-like comprehension. More intriguingly, LLMs have demonstrated emergent abilities extending beyond their core functions, showing proficiency in tasks like commonsense reasoning, code generation, and arithmetic. This survey paper explores the foundational components, scaling mechanisms, and architectural strategies that drive these capabilities. Emphasizing models like GPT and LLaMA, we analyze the impact of exponential data and computational growth on LLM performance, while also addressing the trade-offs associated with scaling. We also examine LLM applications across sectors, such as healthcare, finance, education, and law, highlighting their adaptability and potential to solve domain-specific challenges. Central to this work are the questions of how LLMs generalize across diverse tasks, exhibit planning, and reasoning abilities, and whether these emergent abilities can be systematically elicited or enhanced. In particular, we provide some insights into the CoT (Chain of Thought) and PoT (Plan of Thought) abilities within LLMs, focusing on how pre-training data influences their emergence. Additionally, we investigate LLM-modulo frameworks that integrate external systems, allowing LLMs to handle complex, dynamic tasks. By analyzing these factors, this paper aims to foster the ongoing discussion on the capabilities and limits of LLMs, promoting their responsible development and application in novel and increasingly complex environments.

1 Introduction

This introduction presents LLMs as transformer-based systems with broad language capabilities and emerging abilities beyond text generation. It frames the paper as a survey of their foundations, applications, mechanisms, and boundaries, including responsible development challenges.

  • Motivations: Transformer-based LLMs have advanced text generation, question answering, translation, and summarization while exhibiting abilities beyond text generation.The introduction identifies commonsense reasoning among these broader abilities.
  • Motivations: The field’s progress has been driven by expanding data and computational resources that support training models with billions or trillions of parameters.The cited passage attributes this growth to diverse information sources and powerful GPUs, TPUs, and distributed frameworks.
  • Goals of the paper: The survey examines LLM development, pre-training, architectures, scaling laws, applications across domains, and trade-offs of building larger models.Applications discussed include healthcare, finance, education, law, and scientific research.
  • Goals of the paper: It investigates how LLMs learn and generalize, how emergent abilities can be elicited, which factors shape them, and what limitations remain.The paper focuses particularly on model size, data, architecture, and the abilities to generalize, plan, and execute tasks autonomously.
  • Paper organization: The paper’s structure covers LLM history and scaling, training and adaptation, prompting and planning, CoT origins, and ethical and practical challenges.Its CoT analysis considers whether code in pre-training data contributes to reasoning abilities and reports experiments on Llama-family models.

2 Large Language Models

Large language models scale capabilities across tasks, with emergent abilities such as in-context learning, instruction following, and step-by-step reasoning. This survey examines their architectures, scaling behavior, applications, reasoning capacities, and limitations, including how data and computation shape performance.

  • Reasoning and Planning: The survey investigates whether code in pre-training data contributes to chain-of-thought and Program of Thought reasoning abilities using Llama-family experiments on GSM8k and gsm-hard.Chain-of-thought prompting uses intermediate reasoning steps to derive final solutions for complex tasks.
  • Capabilities: Large language models outperform smaller models and exhibit emergent abilities, including in-context learning, instruction following, and step-by-step reasoning.The survey focuses mainly on models larger than 10B parameters and compares how model parameters affect performance.
  • Scaling Law: Scaling improves performance across language generation, sentiment analysis, question answering, and summarization, while improving long-range dependency handling and contextual understanding.The survey describes a phase change associated with some emergent abilities as model size increases exponentially.
  • Capabilities: GPT models generate coherent, contextually relevant text and perform diverse NLP tasks in few-shot, one-shot, and zero-shot settings without task-specific training.Larger models also capture subtler patterns in data and tend to perform better.
  • Limitations: LLM limitations include high data and computation demands, environmental concerns, hallucinations, and difficulty interpreting or correcting model decisions and biases.These limitations motivate continued work on responsible development and application.
  • Reasoning and Planning: Reasoning models show strong domain performance but remain uneven: o1 is proficient in mathematics, coding, and science, yet struggles with optimal solutions and cross-scenario generalization.Human evaluations preferred o1-preview for data analysis, coding, and math, but not for some natural-language tasks.

3 Foundations of Large Language Models

LLM foundations combine pre-training, tokenization, instruction and alignment tuning, efficient adaptation, and computational strategies that support performance, generalization, and scalable deployment.

  • Pre-training: Supervised pre-training reduces labelled data requirements for downstream fine-tuning and can improve generalization to unseen data or tasks.This benefit follows from learning robust representations before task-specific adaptation.
  • Tokenization: Unigram tokenization probabilistically segments text using iterative vocabulary pruning, expectation-maximization, and dynamic programming.The Viterbi algorithm identifies likely word decompositions under the evolving unigram model.
  • Instruction Tuning: Synthetic instruction generation reduces reliance on extensive human annotation by iteratively expanding task datasets from a small initial pool.Self-Instruct starts with about 100 examples and applies quality and diversity checks before adding generated instances.
  • Instruction Tuning: Instruction tuning improves performance, task generalization, multilingual transfer, and domain specialization across model scales and architectures.Reported applications include zero-shot learning, unseen-task execution, and adaptation of general-purpose models to medical tasks.
  • Alignment Tuning: RLHF is presented as a complex training approach for improving alignment between LLM outputs and human values.The approach uses sophisticated training regimes and multiple feedback mechanisms to support ethical and practical outputs.
  • Parameter-efficient model adaptation: Parameter-efficient adaptation methods approach full fine-tuning performance while training substantially fewer parameters.Adapter tuning uses about 3.6% of parameters per GLUE task, while prefix-tuning learns about 0.1% and P-Tuning v2 tunes 0.1%-3%.

4 Utilization Strategies and Techniques

LLMs can be utilized through in-context learning, chain-of-thought prompting, automated reasoning strategies, and planning frameworks, but their performance depends strongly on demonstrations, reasoning complexity, and task characteristics. External execution, feedback, and modular critics can improve results, while generalization and autonomous reasoning remain limited.

  • In-context learning: ICL performance depends on diverse, simple, structurally similar demonstrations and their ordering, while scaling demonstrations does not fully close the gap with fine-tuning.Pre-training domain source may matter more than corpus size, and lower perplexity or downstream-related data does not always improve ICL.
  • Chain-of-thought prompting: CoT enables sufficiently large models to perform complex reasoning without explicit task-specific training, but its origins in code training remain an unverified hypothesis.Models larger than 100 billion parameters have been reported to benefit from CoT prompting, while instruction tuning does not significantly improve CoT performance.
  • Reasoning strategies: Complexity-based prompting and Auto-CoT improve reasoning by encouraging complex or diverse reasoning chains, including on arithmetic and symbolic tasks.Complexity-based consistency selects outputs with more complex reasoning chains, while Auto-CoT generates representative demonstrations from clustered questions.
  • Program-of-thought reasoning: PoT significantly improves mathematical performance over CoT, but its effectiveness is weaker for diverse algebraic questions and semantic reasoning, where CoT covers broader tasks.PoT can struggle on AQuA because demonstrations cannot cover the diversity of complex questions, and it is not the best option for commonsense reasoning.
  • Planning limitations: LLMs can imitate planning through retrieved patterns but struggle with instance-specific reasoning, optimal decisions, unseen scenarios, and symbolic action semantics.Reported limitations include insufficient self-verification, suboptimal solutions, and weak generalization despite techniques such as CoT, ReAct, and fine-tuning.
  • Planning and execution: Planning and execution frameworks improve task performance by decomposing problems, using interpreters, or generating explicit plans for external execution.DECOMP routes sub-queries to auxiliary functions, while PaL uses Python execution to avoid arithmetic errors and incorrect reasoning; PaL can outperform much larger CoT-based models and performs strongly on GSM-HARD.

5 Testing the CoT Capabilities of LLMs

This section examines the origins of Chain-of-Thought capabilities through evidence from prior experiments and tests on publicly available models.

  • The analysis investigates how certain abilities demonstrated by LLMs, particularly CoT, originate.It focuses on whether proposed hypotheses are supported by experiments using publicly available models.
  • The reviewed evidence concerns Chain-of-Thought, a form of multi-step reasoning demonstrated by LLMs.
  • The section examines hypotheses using tests conducted through LMStudio on HuggingFace models.

5.1 What is eliciting the Chain-of-Thought?

The section asks what elicits LLM Chain-of-Thought abilities and reviews evidence involving pre-training data, model scale, code training, and instruction tuning. The evidence suggests code-trained models can perform better on CoT tasks, but the source of the ability remains unresolved.

  • The central question is what elicits the CoT and other emergent abilities demonstrated by LLMs.
  • The source of CoT remains unclear, and model scale alone does not consistently determine whether models can use CoT.OPT175B and BLOOM176B reportedly cannot use CoT, whereas smaller UL220B and Codex12B models can improve performance with it.
  • Code training is proposed as a source of CoT ability, but the evidence is described as speculative and requiring further verification.
  • code-davinci-002 is consistently better on CoT than text-davinci-002 on language tasks.
  • HELM findings report strong language reasoning abilities for models trained on or for code.The paper relates procedure-oriented programming to step-by-step solving and object-oriented programming to task decomposition.
  • Instruction tuning may help elicit existing abilities, while evidence also shows improved CoT performance in instruction-tuned models.GPT-3 text-davinci-002 leveraged CoT more effectively than text-davinci-001, and PaLM instruction tuning was associated with CoT elicitation.

5.2 Empirical evidences

The empirical evaluation examines whether pre-training code content relates to Chain-of-Thought and Program-of-Thought reasoning in Llama models. Results indicate that code-rich pre-training improves reasoning performance, while experiments remain constrained by available resources and model access.

  • Limitations: The experiments are limited by machine resources, time constraints, publicly available models, and a focus on similarly architected Llama models.The study uses public HuggingFace models because many larger or closed-source models were unavailable for local testing.
  • Experimental setup: The experiments compare Llama models on GSM8k and gsm-hard using Chain-of-Thought and, for code-expressed reasoning, Program-of-Thought.PoT evaluates extracted reasoning code by executing it with Python.
  • CoT results: Llama 3 outperforms Llama 2, and its CoT performance improves from 0-shot to 5-shot prompting.The models have similar sizes and architectures, while their pre-training code shares differ.
  • CoT results: CoT reasoning ability increases with the percentage of code in pre-training data across the evaluated models.The reported Llama code shares range from about 5% in Llama to 17% in Llama 3 and 3.1.
  • PoT results: PoT performance also increases with pre-training code content, improves gsm-hard results, and exceeds the improvement from using the model’s own solution.The authors report low overall gsm-hard success rates and interpret the results as evidence that models learn pre-training distributions when they cannot infer the underlying algorithm.

5.3 Prompting

The prompting setup uses configurable sampling and generation parameters together with role-based messages following the OpenAI API request format. These choices are treated as important determinants of model performance and reproducibility.

  • Prompt configuration: Prompt and request parameters significantly affect model performance, so the experiments use a specified prompt format and parameter configuration.The authors report selecting these settings after experimentation.
  • Prompt configuration: The configuration uses top-p sampling of 0.912 and a maximum generation length of 1024 tokens.These settings are listed as request parameters for the experiments.
  • Role-based messages: Each prompt contains role-labeled messages, and the system message specifies the task and instructions for producing a solution.The format follows the OpenAI API request structure.

5.4 Examples of generated text

The generated-text examples show that models can produce correct answers with absent, incoherent, noisy, or incorrect reasoning. Code execution sometimes recovers correct answers, but gsm-hard examples expose substantial failures on larger-number variants.

  • Prompting examples: In 0-shot CoT prompting, the system instruction asks the model to solve mathematical questions step by step and place the numerical answer last.The prompt uses the phrase “Let’s think step by step.”
  • Prompting examples: The 5-shot setup adds five user–assistant example pairs before the final question, allowing assistant responses to guide the reasoning.The assistant examples do not trigger inference.
  • GSM8k examples: A Llama 27B GSM8k answer is correct but contains no reasoning, while another response is incorrect despite producing an answer.The examples illustrate variation in both answer correctness and reasoning presence.
  • Code-generation examples: Executing Code Llama’s generated code can return the correct answer, but other code outputs are wrong because they omit or mishandle final calculations.One example gives 70 dollars correctly after execution, whereas another misses the final multiplication to obtain 24.
  • gsm-hard examples: On gsm-hard, one generated response contains the correct answer amid noisy reasoning, whereas another produces an incorrect result.The examples include large-number variants designed to test reasoning beyond familiar numerical distributions.

Llama2 13B GSM8k 0-shot

The Llama 13B examples on GSM8k and gsm-hard show mixed 0-shot behavior: some answers are correct with partially coherent reasoning, while others are incorrect or incoherent. The examples therefore illustrate uneven reasoning quality across ordinary and large-number problems.

  • GSM8k 0-shot: A GSM8k example receives the correct answer of 20 cups, and its reasoning is described as partially coherent.The problem asks for the final meal after morning and afternoon feedings.
  • GSM8k 0-shot: A separate GSM8k example is also reported as incorrect, with the correct answer given as 62.This result is presented as an additional 0-shot example outcome.
  • gsm-hard 0-shot: A gsm-hard candle problem receives the correct answer, but the reasoning is described as incoherent.The response tracks cumulative candle shortening before giving the interval result.
  • gsm-hard 0-shot: Another gsm-hard response is incorrect, with the reported answer differing from the correct value of 1806106.8000000003.The task concerns the number of girls not in the girl scout.

Llama 3 7B GSM8k 0-shot

Llama 3 7B produces step-by-step solutions for GSM8k 0-shot problems, with mixed correctness across arithmetic and word-problem examples. Some responses are correct and coherent, while others produce incorrect answers despite structured reasoning.

  • Algebraic reasoning: The model solves the coin problem by defining gold and silver variables, forming G + S = 110 and G - S = 30, then deriving G = 70.The response adds the equations to eliminate one unknown before dividing by two.
  • Arithmetic word problems: The rice example applies a step-by-step multiplication procedure using the number of sacks and kilograms per sack, but the reported answer is incorrect.The evaluation identifies the correct answer as 175.
  • Rate reasoning: The car-time example computes 8 hours for the fast lane and approximately 16 hours for the slow lane.The slow lane is modeled at half the fast-lane speed, making its travel time twice as long for the same distance.

Llama3.1 7B GSM8k 0-shot

Llama3.1 7B GSM8k 0-shot responses use explicit multi-step calculations, but correctness varies substantially. The examples include coherent correct solutions as well as arithmetic and interpretation errors.

  • Percentage reasoning: The house-flipping response calculates $120,000 as the increased value and concludes a $10,000 loss, but the evaluation gives the correct answer as $70,000.The reported error is failing to add the original $80,000 after applying the 150% increase.
  • Overall evaluation: The examples show that the model can produce coherent reasoning while still making substantial numerical errors.The house-flipping example is explicitly described as incorrect despite coherent reasoning, while the bridge example is correct and coherent.
  • Constraint arithmetic: The bridge problem produces a final answer of 83 boxes, which the evaluation marks correct and coherent.The response first calculates 1,245 pounds of allowable additional weight and then divides by the 15-pound box weight.

Llama2 7B GSM8k 5-shot

Llama2 7B GSM8k 5-shot responses include both correct and incorrect answers, and correctness does not guarantee coherent reasoning. The examples illustrate variable reliability under five-shot prompting.

  • Answer correctness: One response gives the solution as 128, but the evaluation marks it incorrect against the correct answer of 310.The example is associated with a Llama27B GSM8k 5-shot task.
  • Reasoning coherence: Another response is marked correct, but its reasoning is judged incoherent.The reasoning includes an unrelated count of practice sessions and mishandles the juggling scenario.

Llama2 7B gsm-hard 5-shot

Llama2 7B gsm-hard 5-shot examples show mixed performance across arithmetic, probability, code, and word problems. Responses may be correct and coherent, incorrect despite coherent reasoning, or numerically wrong even when generated code is correct.

  • Task outcomes: The table-leg example is marked incorrect, with the correct answer given as 13.The supplied passages provide the task context and evaluation outcome but not the model’s intermediate calculation.
  • Task outcomes: The candy-weight response correctly totals 2,600 grams, and its reasoning is marked coherent.It combines 1,000 grams from chocolate bars with 1,600 grams from candied apples.
  • Code reasoning: The code-generation example produces correct executable code for 31,879,055 but gives the wrong textual answer, 43,581,690.0.The evaluation distinguishes the generated program’s result from the model’s stated answer.
  • Task outcomes: The probability response is marked correct and coherent, whereas the toy-value response is marked incorrect against 50.The probability example reports a solution of 0.25, while the toy example contains malformed arithmetic and markup.
  • Reasoning coherence: The ping-pong response is correct but its reasoning is not coherent, showing that answer accuracy and explanation quality can diverge.The evaluation explicitly separates correctness from coherence for this example.

Llama2 13B gsm-hard 5-shot

The Llama2 13B GSM-hard 5-shot examples show mixed mathematical performance: some answers are correct, while others are incorrect or contain flawed reasoning.

  • Llama2 13B gsm-hard 5-shot: The model gives an incorrect answer for the school-trip problem.The reported correct answer is -7494668.0.
  • Llama2 13B gsm-hard 5-shot: The model reaches the correct answer for the two-recipes problem, but its reasoning contains errors.The reported final answer is 60.
  • Llama2 13B gsm-hard 5-shot: The grocery-cost response reports a final answer of $40 after presenting inconsistent intermediate calculations.The generated calculation includes contradictory totals and formatting.
  • Llama2 13B gsm-hard 5-shot: Another tree-height response is judged correct and coherent despite being noisy and redundant.The response computes the shortest and second-tree heights before deriving the tallest tree.
  • Llama2 13B gsm-hard 5-shot: The tree-height example is described as incomplete and incorrect, although another output reports a solution of 34.0.The accompanying evaluation states that the answer is incorrect, with the correct answer given as 322886700.

Llama3.1 7B GSM8k 5-shot

The Llama3.1 7B GSM8k 5-shot examples include both coherent correct solutions and substantial numerical or reasoning errors.

  • Llama3.1 7B GSM8k 5-shot: The robe-fiber problem is solved correctly with a coherent explanation and a total of 3 bolts.The response computes 1 bolt of white fiber from half of 2 blue bolts.
  • Llama3.1 7B GSM8k 5-shot: The walking-and-running problem receives a correct, coherent answer of 18.0.The response derives running and walking speeds from the skipping speed and combines the distances.
  • Llama3.1 7B GSM8k 5-shot: The ties example produces a solution of 4829138.0 after applying the stated price and quantity relationships.The passage reports the solution without an accompanying correctness judgment.
  • Llama3.1 7B GSM8k 5-shot: The geometric-progression solution for 16 discounted glasses is judged incorrect.The response identifies a common ratio of 3/5 but does not produce the correct total of 800.
  • Llama3.1 7B GSM8k 5-shot: The water-distribution example is correct and explicitly calculated by executing Python code.The code subtracts two one-sixth shares and 6 liters from the total.

Llama2 7B gsm-hard 5-shot PoT

The PoT examples show that code-based solutions can produce correct answers, but they also contain formula, variable, and interpretation errors across arithmetic tasks.

  • Llama2 7B gsm-hard 5-shot PoT: The download-total program returns the correct answer 3244047.0999999996 when its code is executed.The code models the second month as three times the first and the third as 70% of the second.
  • Llama2 7B gsm-hard 5-shot PoT: The ice-cream calculation is wrong because it multiplies days by servings per carton instead of dividing by servings per carton.The reported correct answer is 18286416.
  • Llama2 7B gsm-hard 5-shot PoT: The truck-and-bridge code returns the correct maximum of 83 boxes.It subtracts the empty-truck weight from the limit and divides by the box weight.
  • Llama2 7B gsm-hard 5-shot PoT: The gem-counting code returns the wrong answer because it misuses the total-gems variable instead of summing diamonds, rubies, and emeralds.The reported correct answer is 4029727.
  • Llama2 7B gsm-hard 5-shot PoT: The serum example returns the wrong answer of 8 after representing one leg every five days as 0.2 legs per day.The generated code computes arms and legs separately before adding them.
  • Llama2 7B gsm-hard 5-shot PoT: The history-test calculation returns the correct answer 6282701.800000001.The code weights long-answer questions at five points and applies the stated accuracy rates.

6 Conclusions

The paper concludes that LLMs have broad capabilities and domain applications, while scaling-related costs, hallucinations, reasoning limits, and ethical risks remain substantial constraints.

  • 6 Conclusions: Transformer-based LLMs have advanced NLP performance and demonstrated emergent abilities beyond earlier language models.The conclusion highlights models including BERT, T5, GPT-3, and their successors.
  • 6 Conclusions: Scaling laws associate larger models and sufficient data with super-linear performance and emergent in-context learning and chain-of-thought reasoning.The paper also notes computational and environmental costs from continued scaling.
  • 6 Conclusions: Specialized LLMs show potential in healthcare, finance, education, law, and scientific research, with examples including Med-PaLM and FinGPT.The paper also references LLM-Modulo planning frameworks and retrieval-augmented generation.
  • 6 Conclusions: Hallucinations can produce plausible but factually incorrect or misleading information, raising reliability concerns in high-accuracy settings.The paper specifically names medical diagnosis and legal interpretation as sensitive applications.
  • 6 Conclusions: LLMs remain limited in genuine multistep reasoning, planning, and logical inference despite exhibiting human-like reasoning patterns.The conclusion attributes many responses to learned training patterns rather than human-like reasoning.
  • 6 Conclusions: Responsible deployment must address bias, harmful or misleading content, and the environmental impact of training massive models.The paper recommends more efficient training and integration with external knowledge sources and tools.
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