LMSYS Arena Score

An LMSYS Arena Score is an ELO score that quantifies the LLM performance within the LMSYS arena leaderboard (by evaluating it against other models through crowdsourced human pairwise comparisons).

• Context:
  • It can (typically) be calculated using the Elo rating system, which is adapted to handle the unique challenges of LLM comparison.
  • It can (often) include confidence intervals or other statistical measures to represent the reliability and uncertainty of the score.
  • It can (often) be adjusted or recalibrated as the underlying algorithms or comparison methodologies evolve, ensuring that the score remains a relevant and fair measure of performance.
  • ...
  • It can be used to compare LLMs across different languages, domains, and tasks, providing a comprehensive view of their capabilities.
  • It can reflect the relative performance of an LLM based on direct comparison with other models, ensuring that models are ranked according to their observed strengths and weaknesses.
  • It can be used by developers and researchers to assess the progress and effectiveness of their models within the competitive landscape of the LMSYS Arena.
  • It can serve as a key indicator of model performance in different categories, such as general conversation, coding, or specific knowledge domains.
  • It can be integrated with other performance metrics, such as perplexity or accuracy, to offer a multifaceted evaluation of an LLM's performance.
  • It can guide decisions on model deployment and further development by highlighting areas where a model excels or underperforms relative to its peers.
  • ...
• Example(s):
  • Past LMSYS Arena Scores, such as:
    • A score of 1600 for Model A in the LMSYS Chatbot Arena in June 2024, which indicated its relative performance before the latest update.
    • A score of 1450 for Model B in July 2024, reflecting its struggle against newer models during that period.
  • Present LMSYS Arena Scores, such as:
    • A current score of 1700 for Model C, highlighting its strong performance in the most recent evaluations.
    • A score of 1520 for Model D, showing steady improvement as it adapts to user feedback in August 2024.
  • Future Predicted LMSYS Arena Scores, such as:
    • An anticipated increase to 1750 for Model E after a planned update expected to enhance its conversational capabilities.
    • A predicted drop to 1400 for Model F as newer, more advanced models enter the competition in the upcoming months.
  • ...
• Counter-Example(s):
  • ...
• See: LMSYS Chatbot Arena Leaderboard, Elo Rating System, Large Language Model.

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References

2024

• LLM
  • The LMSYS Arena Score is indeed an Elo rating that quantifies the performance of large language models (LLMs) within the LMSYS Chatbot Arena leaderboard. Here are some key points about the LMSYS Arena Score:
  • Elo Rating System: The LMSYS Arena uses the Elo rating system, which was originally developed for chess rankings but has been adapted for comparing LLMs[1]. Some key aspects of this system include:
    • It calculates relative skill levels between LLMs
    • The difference in ratings between two models predicts the outcome of a match
    • Ratings are updated based on actual outcomes compared to expected outcomes
  • Data Collection: The LMSYS Arena collects data through the following process:
    • Users chat with two anonymous models side-by-side on the arena website
    • After interacting, users vote for which model they think performed better
    • Only votes cast when model names are hidden are used for rankings
    • The platform logs all user interactions[1]
  • Scoring and Ranking: The Elo scores on the leaderboard represent:
    • A model's relative performance against other models in the arena
    • Higher scores indicate better performance as judged by human evaluators
    • Scores are dynamically updated as more user votes come in
  • Interpretation: When interpreting LMSYS Arena Scores:
    • The absolute score values are less important than the differences between models
    • Small differences (e.g. 5-10 points) may not be statistically significant[2]
    • Larger gaps indicate more consistent preference by human evaluators
  • Limitations: It's important to note some limitations of this scoring system:
    • Scores can potentially be manipulated, though measures are in place to prevent this[5]
    • The types of prompts and tasks users choose may favor certain models
    • Factors like response speed can influence user preferences beyond just answer quality[2]
  • Current Leaderboard: As of the most recent data, top performers on the LMSYS Arena leaderboard include models like GPT-4, Claude, and Mixtral. However, the rankings can shift as new models are added and more evaluations are conducted[4].
  • The LMSYS Arena Score provides a useful benchmark for comparing LLM performance, but it should be considered alongside other evaluation metrics for a comprehensive assessment of model capabilities.
  • Citations:

[1] https://lmsys.org/blog/2023-05-03-arena/
[2] https://news.ycombinator.com/item?id=40088727
[3] https://www.reddit.com/r/LocalLLaMA/comments/18r56fq/chatbot_arena_elo_ratings_overtime/
[4] https://arena.lmsys.org
[5] https://www.reddit.com/r/LocalLLaMA/comments/1ac9k8f/why_do_you_trust_lmsys_arena_leaderboard_it_can/
[6] https://arxiv.org/html/2403.04132v1
[7] https://twitter.com/lmsysorg?lang=en

2024

• LLM
  • ... the method for calculating the LMSYS Arena Score, emphasizing the iterative nature of the Elo-based updates and the reliance on crowdsourced human pairwise comparisons.
  • Pseudo Code:

1. Initialize the score for each model with a base score (e.g., 1500).

for each model in LMSYS_Arena:

   model.score = 1500

1. For each comparison between two models (Model A and Model B):

for each comparison in pairwise_comparisons:

   Model_A = comparison.model_A
   Model_B = comparison.model_B
   Result = comparison.result  # Result is either 1 (A wins), 0 (B wins), or 0.5 (Draw)

   # Calculate the expected score for each model based on the current scores
   Expected_A = 1 / (1 + 10 ** ((Model_B.score - Model_A.score) / 400))
   Expected_B = 1 / (1 + 10 ** ((Model_A.score - Model_B.score) / 400))

   # Determine the K-factor (a constant that influences score updates)
   K = 32  # Typical value, but can be adjusted based on the number of comparisons

   # Update the scores based on the result of the comparison
   Model_A.score = Model_A.score + K * (Result - Expected_A)
   Model_B.score = Model_B.score + K * ((1 - Result) - Expected_B)

   # Optionally, apply confidence intervals or other statistical adjustments
   # Model_A.confidence_interval = calculate_confidence_interval(Model_A)
   # Model_B.confidence_interval = calculate_confidence_interval(Model_B)

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