Cross-Capability Evaluation of Large Language Models: Uncovering the Law of the Weakest Link

Table of Contents

Overall Summary

Overview

This research paper introduces a novel approach to evaluating Large Language Models (LLMs) by focusing on "cross-capabilities," which are combinations of individual skills like reasoning, coding, and tool use required for complex, real-world tasks. Current LLM evaluations often assess these skills in isolation, overlooking the crucial interplay between them. The study introduces CrossEval, a benchmark designed to assess both individual and cross-capabilities using a diverse set of human-annotated prompts and an LLM-based evaluator. The key finding reveals a "Law of the Weakest Link" phenomenon, where an LLM's performance on cross-capability tasks is predominantly limited by its weakest individual skill, highlighting the need for balanced capability development. This has significant implications for LLM training and deployment, suggesting that focusing solely on maximizing individual strengths may not translate to effective real-world performance.

Key Findings

Strengths

Areas for Improvement

Significant Elements

Table 3

Description: Table 3 presents the performance scores of various LLMs across different individual and cross-capabilities in CrossEval. It uses color-coding to highlight where cross-capability performance is limited by weaker individual skills. This table provides the core empirical evidence for the "Law of the Weakest Link."

Relevance: This table is crucial as it provides direct evidence for the central finding of the paper, showing how weaker individual skills limit cross-capability performance.

Figure 3

Description: Figure 3 visually represents the "Law of the Weakest Link" using density distributions, illustrating how cross-capability performance tends to cluster around the level of the weakest individual skill rather than the average of all involved skills.

Relevance: This figure provides a clear and intuitive visualization of the central finding, making it easier to grasp the implications of the "Law of the Weakest Link."

Conclusion

This research makes a significant contribution to the field of LLM evaluation by introducing the concept of cross-capabilities and the CrossEval benchmark. The study reveals a "Law of the Weakest Link" phenomenon, demonstrating that an LLM's effectiveness in complex tasks is limited by its weakest individual skill, even when other skills are strong. This highlights the critical need for future research to focus on balanced capability development rather than solely maximizing individual strengths. Future work should investigate potential synergistic effects between capabilities and develop targeted strategies for improving weaker areas, especially in critical domains like tool use. CrossEval can serve as a valuable tool for researchers and developers to assess and improve LLM performance for real-world applications, paving the way for more robust and versatile LLMs capable of handling complex, multifaceted tasks.

Section Analysis

Abstract

Overview

Large Language Models (LLMs) are typically evaluated on their individual capabilities, such as reasoning or coding. However, real-world tasks often require a combination of skills, which this paper terms "cross capabilities." The research introduces CrossEval, a benchmark designed to assess both individual and cross capabilities in LLMs. The key finding is that LLM performance on cross-capability tasks is limited by the weakest individual capability, a phenomenon referred to as the "Law of the Weakest Link." This means that even if an LLM excels in one area, its performance on a complex task will be dragged down if it's weak in another required skill. The paper emphasizes the importance of identifying and improving these weaker capabilities for better real-world performance.

Key Aspects

Strengths

Suggestions for Improvement

Introduction

Overview

This introduction sets the stage for a research paper exploring how the combination of different skills, or "cross capabilities," in Large Language Models (LLMs) impacts their performance. It points out that current evaluations often focus on individual skills, like coding or reasoning, separately. However, real-world tasks often require multiple skills working together. The paper introduces a new benchmark, CrossEval, to test these combined skills and investigates how a weakness in one skill can affect performance on complex tasks.

Key Aspects

Strengths

Suggestions for Improvement

Defining Individual & Cross Capabilities in LLMs

Overview

This section explains how the research paper categorizes the skills of Large Language Models (LLMs), both individually and in combination. It defines seven core individual capabilities, like English language proficiency and coding skills. Then, it explains how these individual skills are paired to represent common combined skills needed for real-world tasks, called "cross capabilities." The paper creates a structured system (a taxonomy) to organize these skills and the specific tasks they enable, much like organizing animals into different species and families.

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

figure 1

Figure 1 presents three taxonomy visualizations using circular diagrams. Diagram (a) visualizes the taxonomy for 'Image Recognition,' showing categories like 'Object Recognition,' 'Scene Understanding,' and 'Image Captioning.' Diagram (b) illustrates the 'Reasoning' taxonomy, with categories such as 'Mathematical Calculation,' 'Commonsense Reasoning,' and 'Logic / Problem Solving.' Diagram (c) depicts the 'Image Recognition & Reasoning' cross-capability taxonomy, combining elements from both individual taxonomies to represent tasks requiring both skills, like 'Diagram Understanding' and 'Visual Math and Science.'

First Mention

Text: "As illustrated in Figure 1, these taxonomies follow a hierarchical design"

Context: The section discusses the hierarchical design of taxonomies for individual and cross capabilities, explaining how they categorize tasks from general to specific. Figure 1 is introduced to visually represent these taxonomies.

Relevance: This figure is crucial for understanding how the research defines and categorizes individual and cross capabilities. It visually represents the breakdown of broad capabilities into specific tasks, providing a clear framework for the benchmark development and subsequent analysis.

Critique
Visual Aspects
  • The circular layout, while visually appealing, might make it difficult to compare the number of subcategories within each capability directly. A tree-like structure could offer a clearer comparison.
  • The figure could benefit from a brief explanation of how the cross-capability taxonomy (c) is derived from the individual taxonomies (a) and (b). Visual cues connecting related categories across the diagrams could enhance understanding.
  • Using different colors or patterns for the segments in the cross-capability diagram could highlight which sub-tasks originate from which individual capability.
Analytical Aspects
  • The figure effectively visualizes the hierarchical structure of the taxonomies. However, it doesn't explicitly show the number of level-2 categories within each level-1 category, which is mentioned in the text. Including this information in the figure would make it more self-contained.
  • The figure focuses on the structure of the taxonomies but doesn't provide examples of specific tasks within each category. Including a few illustrative examples within each segment could make the taxonomy more concrete and relatable.
  • While the figure shows the breakdown of capabilities into subcategories, it doesn't explain why these specific categories were chosen. A brief justification in the caption or a reference to a more detailed explanation elsewhere in the paper would strengthen the figure's analytical value.
Numeric Data

CrossEval Benchmark Construction

Overview

This section details the creation of CrossEval, a benchmark to assess the performance of Large Language Models (LLMs) on tasks requiring both individual and combined skills (cross capabilities). It explains how the prompts were designed, how multiple model responses were collected and rated by humans, and how an LLM was trained to act as an evaluator, mimicking human judgment.

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

table 1

Table 1 presents statistics about the prompt sets used in the CrossEval benchmark. It's organized into two main sections: 'Individual' and 'Cross' capabilities. For each capability, the table lists the number of prompts, Level-1 (L1) categories, and Level-2 (L2) categories. All capabilities have 100 prompts. For example, 'English' has 8 L1 categories and 45 L2 categories, while 'Coding & Reasoning' has 4 L1 categories and 19 L2 categories.

First Mention

Text: "Table 1 details the number of task categories for each capability in CrossEval."

Context: This table is introduced during the discussion of the CrossEval benchmark construction, specifically after describing the prompt set annotation process and the difficulty distribution of the prompts.

Relevance: Table 1 is important because it provides a clear overview of the scope and structure of the CrossEval benchmark. It shows how many different categories of tasks are included for each capability, indicating the breadth and depth of the evaluation.

Critique
Visual Aspects
  • The table is well-organized and easy to read. The division into 'Individual' and 'Cross' capabilities helps clarify the structure of the benchmark.
  • The consistent number of prompts (100) for each capability simplifies comparison across different skills and skill combinations.
  • Visually separating the individual and cross capabilities further, perhaps with a thicker line or some spacing, could improve readability.
Analytical Aspects
  • The table effectively summarizes the number of categories at each level. This information is important for understanding the granularity of the benchmark and the coverage of different sub-tasks.
  • The table could benefit from a brief explanation of what the L1 and L2 categories represent. While the text describes this, including a short explanation in the table caption would make it more self-contained.
  • While the table shows the number of categories, it doesn't provide information about the distribution of prompts across different difficulty levels. Including this information could provide a more complete picture of the benchmark's composition.
Numeric Data
  • Number of Prompts (English): 100
  • L1 Categories (English): 8
  • L2 Categories (English): 45
  • Number of Prompts (Coding & Reasoning): 100
  • L1 Categories (Coding & Reasoning): 4
  • L2 Categories (Coding & Reasoning): 19
table 2

Table 2 shows the correlations between human ratings of LLM responses and the ratings given by different LLMs acting as evaluators. It includes several LLMs (like GPT-4o mini, Llama 3.1 405B, Claude 3.5 Sonnet) and calculates Pearson, Spearman, and Kendall correlations for each LLM across various individual and cross capabilities. The higher the correlation, the better the LLM agrees with human judgments.

First Mention

Text: "Table 2 shows that different LLMs excel at different capabilities."

Context: This table appears in the section discussing building LLM-based evaluators. It's presented after explaining the prompting strategies and the need for a reliable evaluation method.

Relevance: Table 2 is crucial for demonstrating the effectiveness of using LLMs as evaluators. It shows how well different LLMs can mimic human judgment, which is important for automating the evaluation process and scaling up benchmark analysis.

Critique
Visual Aspects
  • The table is well-structured, but the large number of values can make it visually overwhelming. Highlighting the highest correlations in each row could improve readability and focus attention on the best-performing LLMs.
  • Using a color scale to represent the correlation values could make it easier to quickly identify trends and compare performance across different LLMs and capabilities.
  • Separating the overall correlation rows from the individual capability rows with a thicker line or more spacing would improve visual clarity.
Analytical Aspects
  • The table effectively presents the correlation values for different LLMs and capabilities. However, it doesn't provide any statistical significance tests for these correlations. Including p-values or confidence intervals would strengthen the analysis.
  • The table caption mentions that GPT-4o achieves the highest overall correlations. Quantifying this by stating the actual correlation values in the caption would make the point more impactful.
  • The table focuses on correlations but doesn't provide insights into the types of errors made by the LLMs or the reasons for disagreements with human judgments. A brief discussion of these aspects would enhance the analytical value of the table.
Numeric Data
  • Pearson Correlation (GPT-4o mini, Reasoning): 0.681
  • Pearson Correlation (Llama 3.1 405B, Reasoning): 0.699
  • Pearson Correlation (Claude 3.5 Sonnet, Reasoning): 0.704
  • Pearson Correlation (GPT-4o-05-13, Reasoning): 0.731
figure 2

This figure shows how the quality of an LLM's evaluation improves when it has more examples to learn from. It's like a student studying for a test; the more practice tests they take with answers, the better they understand what a good answer looks like. The graph uses three different ways of measuring this improvement (Pearson, Spearman, and Kendall correlations), and all of them go up as the number of examples increases. This means that giving the LLM more examples makes its evaluations more accurate and closer to what a human expert would say.

First Mention

Text: "Figure 2 illustrates the results."

Context: The section discusses the importance of reference examples for LLM evaluation and introduces Figure 2 to show the results of an ablation study on the number of reference examples.

Relevance: This figure is highly relevant because it demonstrates the importance of reference examples for effective LLM evaluation. It directly supports the argument that more reference examples lead to better evaluation quality, justifying the use of multiple references in the CrossEval benchmark.

Critique
Visual Aspects
  • The y-axis label could be more descriptive, such as 'Correlation with Human Judgment' instead of just 'Correlation'. This would clarify what is being measured.
  • Adding the actual correlation values above each bar would make it easier to compare the precise improvements. Currently, readers have to estimate the values from the y-axis.
  • While the color coding distinguishes the three correlation types, it might be helpful to use a different visual encoding (like patterns or bar widths) to further differentiate them, especially for readers with color blindness.
Analytical Aspects
  • The figure clearly shows the positive trend of increasing correlation with more reference examples. However, it doesn't discuss the potential limitations or diminishing returns of adding even more examples. Is there a point where adding more examples doesn't provide much further improvement?
  • The figure focuses on the overall correlation but doesn't break down the analysis by different capabilities. Does the impact of reference examples vary across different skills like reasoning or coding?
  • The figure mentions using GPT-4o for the ablation study, but it doesn't discuss whether the findings generalize to other LLMs. Would similar trends be observed with other evaluators?
Numeric Data
  • Pearson Correlation (w/o Ref): 0.578
  • Pearson Correlation (w/ 1 Ref): 0.655
  • Pearson Correlation (w/ 2 Refs): 0.697
  • Spearman Correlation (w/o Ref): 0.55
  • Spearman Correlation (w/ 1 Ref): 0.63
  • Spearman Correlation (w/ 2 Refs): 0.679
  • Kendall Correlation (w/o Ref): 0.44
  • Kendall Correlation (w/ 1 Ref): 0.52
  • Kendall Correlation (w/ 2 Refs): 0.56

Exploring Relationship between Individual and Cross Capabilities

Overview

This section investigates how individual LLM capabilities influence their performance on tasks requiring multiple skills (cross capabilities). Using the CrossEval benchmark, the research reveals that LLMs often follow the "Law of the Weakest Link," meaning their performance on combined tasks is limited by their weakest individual skill. For example, an LLM might be great at reasoning but struggle with tool use. When faced with a task requiring both, its overall performance will be closer to its tool use skill level than its reasoning skill level. The section also highlights that tool use is currently a major challenge for LLMs and that they generally underperform on cross-capability tasks compared to individual ones.

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

table 3

Table 3 presents the performance scores of 17 different Large Language Models (LLMs) on individual and cross-capability tasks using the CrossEval benchmark. Individual capabilities include skills like English, Reasoning, Coding, Image recognition, Tool Use, Long Context understanding, and Spanish. Cross-capabilities combine two individual skills, such as Coding & Reasoning or Tool Use & Reasoning. Scores are presented on a 1-100 scale. Color-coding highlights cases where cross-capability performance is lower than both individual capabilities (red) or falls between the two but closer to the weaker capability (blue). GPT models' results are presented as a reference and not considered in the best performance comparisons (bolded).

First Mention

Text: "The full results are provided in Table 3."

Context: After explaining the experimental setup, including model selection and evaluation parameters, the paper refers to Table 3 to present the complete results of the benchmark evaluations.

Relevance: Table 3 is the core of the experimental results, showing how different LLMs perform on various individual and cross-capability tasks. It provides the evidence for the paper's main finding about the 'Law of the Weakest Link.'

Critique
Visual Aspects
  • The table is very dense and could benefit from visual simplification. Grouping related capabilities (e.g., all reasoning-related tasks) could improve readability.
  • Highlighting the 'strong' and 'weak' individual capabilities within each cross-capability column would make it easier to see the relationship between them and the cross-capability score.
  • Instead of color-coding entire cells, consider using color bars or symbols within the cells to indicate whether the cross-capability score is below both, between, or above the individual capability scores. This would make the table less visually overwhelming.
Analytical Aspects
  • While the table shows the scores, it doesn't provide any measure of statistical significance or variance. Including standard deviations or confidence intervals would strengthen the analysis.
  • The table caption explains the color-coding but doesn't clearly define how 'strong' and 'weak' capabilities are determined. Explicitly stating the threshold (delta = 3) in the caption would be helpful.
  • The table focuses on the overall performance scores but doesn't provide insights into the types of errors made by the LLMs or the reasons for performance differences. A more detailed analysis of error patterns would enhance the paper's findings.
Numeric Data
  • English (GPT-4o mini): 73.64
  • Reasoning (GPT-4o mini): 69.31
  • Coding (GPT-4o mini): 71.17
  • Coding & Rea. (GPT-4o mini): 72.03
figure 3

Figure 3 visually represents the 'Law of the Weakest Link' using density distributions. Imagine two hills representing how good an LLM is at two different skills. The figure shows that when the LLM needs to use both skills together, its performance looks more like a hill centered around its weaker skill, not the average of both. This is shown for two different 'judges' (GPT and Claude) that scored the LLMs, and the pattern is similar for both, meaning the 'weakest link' effect is consistent.

First Mention

Text: "As shown in Figure 3, the 'Law of the Weakest Link' effect holds true regardless of the evaluator used."

Context: After explaining the 'Law of the Weakest Link' and how it's observed in the CrossEval results, the paper introduces Figure 3 to provide a visual representation of this phenomenon.

Relevance: Figure 3 is essential for visually demonstrating the central finding of the paper. It provides a clear and intuitive way to understand the 'Law of the Weakest Link' and its consistency across different evaluators.

Critique
Visual Aspects
  • The x-axis label 'Cross Performance' could be more explicit, such as 'Normalized Cross-Capability Performance'. This would clarify what values are being plotted.
  • The colored dots below the x-axis are not clearly explained. Adding a legend or explanation in the caption would clarify their meaning.
  • The vertical dashed lines representing single, weak, and strong capabilities could be labeled directly on the graph for better readability.
Analytical Aspects
  • The figure effectively shows the density distributions, but it doesn't explain the normalization process used. Describing how the scores were normalized to the -1 to 1 range would make the figure more self-contained.
  • The figure could benefit from a brief explanation of why the density peaks slightly below the weaker capability for GPT and slightly above for Claude. Discussing potential reasons for this difference would enhance the analysis.
  • While the figure shows the 'Law of the Weakest Link' for two evaluators, it doesn't discuss whether this pattern holds for other LLMs or evaluation metrics. Mentioning the consistency across different delta values in the caption would strengthen the conclusion.
Numeric Data

How Individual-Capability Alterations Impact Cross-Capability Performance?

Overview

This section investigates how changing an LLM's individual skills affects its performance on tasks requiring multiple skills (cross-capabilities). Using a method called principle-based system prompting, the researchers boosted specific skills and observed the impact. They found that improving a weaker skill leads to more significant gains in cross-capability performance than improving an already strong skill. This reinforces the "Law of the Weakest Link," showing that even after targeted improvements, an LLM's performance on complex tasks is still largely determined by its weakest area.

Key Aspects

Strengths

Suggestions for Improvement

Non-Text Elements

table 4

Table 4 presents a case study investigating how changes in individual LLM capabilities affect their performance on cross-capability tasks. It focuses on two LLMs, Claude 3 Haiku and Gemini 1.5 Flash, and three cross-capability areas: Image & Rea., Spanish & Rea., and Spanish & Image. The table shows the baseline scores for each model on the individual capabilities (Reasoning, Image Recognition, Spanish) and the cross-capabilities. Then, it shows how the scores change when each individual capability is improved using 'principle-based system prompting,' indicated by '+ Reasoning,' '+ Image,' or '+ Spanish.'

First Mention

Text: "Table 4 presents the complete experimental results"

Context: The table is introduced in the context of a case study designed to investigate how changes in individual capabilities impact cross-capability performance. It follows the description of the principle-based system prompting method used to enhance specific capabilities.

Relevance: This table is highly relevant as it directly addresses the research question of how individual capability alterations influence cross-capability performance. It provides the empirical evidence for the conclusion that improving weaker capabilities leads to more significant gains in cross-capability performance.

Critique
Visual Aspects
  • The table is relatively clear, but highlighting the changes in scores (e.g., with bolding for increases and italics for decreases) would make it easier to quickly see the impact of the interventions.
  • Adding a visual separator between the individual and cross-capability sections would improve readability.
  • Consider using a color scale to represent the magnitude of the score changes. This would provide a more visual representation of the impact of each intervention.
Analytical Aspects
  • The table shows the scores after applying principle-based prompting, but it doesn't quantify the improvement or decrease in each capability. Including the actual change values (e.g., +2.85 or -0.99) would make the results more concrete.
  • The table caption mentions that improving weaker capabilities leads to more significant gains. Quantifying this by stating the average improvement for weaker vs. stronger capabilities would strengthen the conclusion.
  • The table focuses on two specific LLMs. While this provides a detailed case study, it doesn't address the generalizability of the findings. Discussing whether similar trends are observed in other LLMs would enhance the analysis.
Numeric Data
  • Reasoning (Claude 3 Haiku): 56.81
  • Image Recognition (Claude 3 Haiku): 59.66
  • Spanish (Claude 3 Haiku): 55.45
  • Image & Rea. (Claude 3 Haiku): 49.88
  • Reasoning (Claude 3 Haiku + Reasoning): 62.5
  • Image Recognition (Claude 3 Haiku + Image): 63.0

Related Work

Overview

This section discusses existing research related to LLM evaluation, focusing on two main areas: 1) Evaluating different LLM capabilities and 2) Evaluation metrics for open-ended tasks. It explains how LLM evaluation has evolved from assessing specific NLP tasks to broader capabilities like reasoning, coding, and tool use. The section also highlights the shift in evaluation metrics from traditional methods to using LLMs as judges, emphasizing the contribution of CrossEval as a meta-evaluation benchmark.

Key Aspects

Strengths

Suggestions for Improvement

Conclusion

Overview

This conclusion summarizes the paper's key contributions and findings regarding the evaluation of cross capabilities in Large Language Models (LLMs). It reiterates the importance of cross capabilities for real-world tasks and highlights the development of CrossEval, a benchmark designed to assess these combined skills. The central finding, the "Law of the Weakest Link," is emphasized, stating that an LLM's performance on complex tasks is limited by its weakest individual capability. The conclusion stresses the need for future research to focus on improving these weaker areas to enhance LLM effectiveness in real-world scenarios.

Key Aspects

Strengths

Suggestions for Improvement

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