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Revealing the structure of language model capabilities

Ryan Burnell, Han Hao, Andrew R. A. Conway, Jose Hernandez Orallo

arXiv:2306.10062v1cs.CLcs.AIcs.LG

TL;DR

Existing benchmarks test LLMs on varied tasks but offer limited explanation or prediction of their performance, while the abilities underlying that performance remain poorly understood. The paper uses factor analysis on benchmark data from a varied set of LLMs to identify latent abilities. It finds three factors corresponding to comprehension, language modeling, and reasoning, with different relationships to model properties.

  • Problem

    Benchmarks cover varied LLM tasks but offer limited explanation of poor performance or prediction on untested tasks, and the abilities underlying performance remain poorly understood.

    Source: §1 · p. 1

  • Method

    The authors apply factor analysis to HELM performance data from 29 LLMs to extract latent abilities and examine their relationships with model properties.

    Source: §1 · p. 2, §2.1 · p. 3

  • Results

    LLM capabilities were multidimensional, with three factors corresponding to comprehension, language modeling, and reasoning; all correlated positively with model size, but comprehension more strongly.

    Source: §4 · pp. 8–9

  • Takeaways & Limitations

    A small set of tasks estimating reasoning, comprehension, and language modeling could support more cost-efficient, empirically driven benchmark selection.

    Source: §4 · p. 9

    The HELM task set may omit abilities such as creative writing, and the factor structure may change when other tasks are added.

    Source: §4 · p. 9

Abstract

from arXiv · show

Building a theoretical understanding of the capabilities of large language models (LLMs) is vital for our ability to predict and explain the behavior of these systems. Here, we investigate the structure of LLM capabilities by extracting latent capabilities from patterns of individual differences across a varied population of LLMs. Using a combination of Bayesian and frequentist factor analysis, we analyzed data from 29 different LLMs across 27 cognitive tasks. We found evidence that LLM capabilities are not monolithic. Instead, they are better explained by three well-delineated factors that represent reasoning, comprehension and core language modeling. Moreover, we found that these three factors can explain a high proportion of the variance in model performance. These results reveal a consistent structure in the capabilities of different LLMs and demonstrate the multifaceted nature of these capabilities. We also found that the three abilities show different relationships to model properties such as model size and instruction tuning. These patterns help refine our understanding of scaling laws and indicate that changes to a model that improve one ability might simultaneously impair others. Based on these findings, we suggest that benchmarks could be streamlined by focusing on tasks that tap into each broad model ability.

1 Introduction

Broad benchmarks test LLMs across varied tasks, but they do not explain poor performance or reliably predict behavior on untested tasks. This paper motivates identifying the latent abilities behind task performance to better understand model capabilities and their relationships with model properties.

  • Big-BENCH and HELM test varied tasks, but they offer limited explanation or prediction, while the abilities underlying LLM performance remain poorly characterized.The introduction frames these gaps as obstacles to understanding and anticipating performance across deployment scenarios.Source: §1 · pp. 1–2
  • Human psychometric theories describe separable but interrelated broad abilities; whether LLM tasks rely on distinct abilities or a single underlying reasoning ability remains unclear.The introduction also asks whether language comprehension reflects one broad ability or multiple abilities in LLMs.Source: §1 · pp. 2–3
  • A better account of LLM capabilities could inform more robust evaluation benchmarks and help target efforts to address specific model deficiencies.The introduction also identifies improved understanding of model processing as a potential benefit.Source: §1 · p. 2
  • Factor analysis can extract latent factors explaining variance across tasks, offering a data-driven starting point for investigating LLM capability structure.The approach draws on a method long used in cognitive science to study intelligence.Source: §1 · p. 2
  • Identifying abilities may clarify why model size relates to performance on some tasks but not others, and help predict how model-property changes affect specific domains.The paper points to differences in task-level scale relationships as a possible reflection of different abilities.Source: §1 · p. 3

2 Methods

The methods use HELM benchmark data from a varied population of LLMs to extract latent abilities and examine their relationships with model properties.

2 Methods

  • The analysis used HELM performance data to extract latent abilities and examine their relationships with properties such as model size and instruction tuning.The dataset and analysis code are described as publicly available.Source: §2 · p. 3

2.1 HELM data

  • The HELM data covered 29 LLMs varying in size, release date, training data, and architecture; models missing data on three or more included tasks were excluded.Instruction tuning and reinforcement learning from human feedback are defined as fine-tuning processes in the methods.Source: §2.1 · p. 3

2.2 Task selection

  • From HELM's 34 tasks, the analysis excluded tasks with missing data, unclear cognitive basis, or redundant NaturalQuestions variants, while retaining two synthetic reasoning versions.The retained synthetic reasoning tasks used abstract symbols and natural language.Source: §2.2 · p. 3

2.3 Task demand coding

  • A cognitive science expert annotated each task by its primary cognitive demand, with MMLU marked mixed because its subtasks draw on domain knowledge and fluid reasoning.Source: §2.3 · p. 3

3 Results

Across the analyzed tasks, three broad factors capture distinct LLM abilities, and the factors show different relationships with model properties. Bayesian and frequentist analyses produce closely aligned three-factor solutions.

3.1 Task correlations

  • Task performances were positively correlated overall (mean r = 0.56, median = 0.6), with stronger correlations generally among tasks annotated as relying on the same abilities.The authors note that raw correlations alone may not capture the full structure because tasks can require multiple abilities.Source: §3.1 · p. 4

3.2 Factor analysis

  • Three factors broadly represent comprehension, language modeling, and reasoning, with comprehension, next-token prediction, and reasoning tasks loading most strongly on their corresponding factors.Comprehension tasks include NaturalQuestions, XSUM, and NarrativeQA; language-modeling tasks include ICE, TwitterAAE, and The Pile; reasoning tasks include GSM8K, synthetic reasoning tasks, and BBQ.Source: §3.2 · pp. 5–6
  • Loading patterns complicate simple task labels: cognitive-bias tasks loaded strongly on reasoning, while deductive tasks loaded weakly and HellaSwag loaded on comprehension.The authors suggest the reasoning factor may primarily reflect complex inductive reasoning, a possibility requiring further investigation.Source: §3.2 · p. 6

3.3 Bayesian factor analysis

  • Bayesian factor analysis produced a closely aligned three-factor solution, supporting the reliability of the frequentist findings, although it left LSAT unassigned.LSAT loaded moderately on reasoning in the frequentist analysis.Source: §3.3 · p. 6

3.4 Model factor scores

  • InstructGPT davinci models scored highest on reasoning and near the top on comprehension, while BLOOM and GPT-NeoX led language modeling despite middling scores on the other abilities.InstructGPT ada and babbage had the lowest language-modeling scores among the models.Source: §3.4 · pp. 6–7

3.5 Relationships with model characteristics

  • Model size was positively correlated with all three factors, most strongly with comprehension; instruction tuning correlated positively with reasoning and negatively with language modeling.Its relationship with comprehension was not significantly different from zero.Source: §3.5 · pp. 7–8
  • The analysis found no clear relationship between training-token totals and any factor, but the dataset had little variation in training length.The authors note that testing these relationships properly would require models with substantially more varied training lengths.Source: §3.5 · p. 8

4 Discussion

The discussion argues that LLM capabilities are multidimensional, with three broad factors explaining much of the performance variation across tasks. It relates those abilities to model properties, proposes more focused benchmarks, and notes that the findings are bounded by the tasks and models studied.

4 Discussion

  • Three factors—reasoning, comprehension, and language modeling—explain a large proportion of performance variance across varied tasks, suggesting a shared underlying structure.The tasks span question answering, summarization, sentiment analysis, and different kinds of reasoning.Source: §4 · p. 8
  • Comprehension tasks such as question answering, summarization, and sentiment analysis appeared to share an underlying ability, as did mathematical and other inductive reasoning tasks.These are patterns suggested by the data, not claims that the task formats are identical.Source: §4 · p. 8
  • A small set of tasks estimating reasoning, comprehension, and language modeling may provide an efficient, empirically grounded alternative to benchmarks requiring many tasks.The authors contrast this approach with streamlined benchmarks that select tasks somewhat arbitrarily.Source: §4 · pp. 8–9
  • Because the factors describe high-level abilities rather than specific tasks, they may help predict performance on untested tasks when their required abilities are known.The authors present this as a possibility, not a demonstrated prediction result.Source: §4 · p. 9
  • The analysis is not a complete account of LLM abilities: HELM may omit abilities such as creative writing, and factor structure depends on which tasks are included.The discussion suggests that new task paradigms may be needed to investigate abilities beyond the three identified.Source: §4 · p. 9
  • Model size was positively related to all three factors, more strongly to comprehension, while instruction tuning related negatively to language modeling and positively to reasoning.The authors caution that changes improving one ability might impair another.Source: §4 · p. 9
  • The conclusions also need replication with more models, clearer validation of factor interpretations, and tasks designed around cognitive demands rather than format.Some tasks did not fit neatly into the factors, and many HELM tasks were designed around formats such as question answering.Source: §4 · p. 9
  • The authors describe the study as a first step and encourage public release of evaluation data to support deeper study of AI systems.They hope future work will use varied empirical methods to identify the building blocks of language model cognition.Source: §4 · pp. 9–10

A Correlations between tasks

The authors calculated Pearson correlations between tasks as an initial examination of how the HELM tasks relate. Figure 4 displays these correlations and groups tasks by their assigned Bayesian factors.

A Correlations between tasks

  • Pearson correlations were calculated between each task as an initial examination of task relationships.The resulting correlations are displayed in Figure 4.Source: A Correlations between tasks · p. 14
  • Column names are abbreviated, and their order corresponds to the row order.This note helps match the task labels across the displayed correlation matrix.Source: A Correlations between tasks · p. 14
  • Figure 4 encodes stronger positive correlations with darker greens and stronger negative correlations with darker reds, with lines separating tasks by assigned Bayesian factor.The caption identifies the values as Pearson correlations (r).Source: A Correlations between tasks · p. 14, Figure 4 · p. 15

B Determining Factor Structure

The authors compared scree-plot, Hull-method, and Bayesian evidence to determine the factor structure. These approaches converged on three factors for the final frequentist exploratory factor analysis.

B Determining Factor Structure

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