What Are the Odds? Language Models Are Capable of Probabilistic Reasoning (2406.12830v3)

Abstract: LLMs (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we have released publicly.

• The paper demonstrates that language models can engage in probabilistic reasoning by estimating percentiles, drawing samples, and calculating probabilities across diverse distributions.
• The paper details a systematic methodology using zero-shot and few-shot prompting to assess performance variability on both idealized and real-world datasets.
• The paper shows that context-specific examples and normal approximations significantly enhance language models’ performance, paving the way for future research.

An Expert Analysis of "What Are the Odds? LLMs Are Capable of Probabilistic Reasoning"

The paper "What Are the Odds? LLMs Are Capable of Probabilistic Reasoning" provides an extensive analysis of LLMs' (LMs) capacities for probabilistic reasoning. Historically, LMs excel in complex linguistic tasks but falter at numerical reasoning. This work demonstrates a systematic approach to evaluating LMs' abilities to engage in probabilistic tasks using both idealized and real-world distributions.

Key Research Objectives and Tasks

The researchers designed their evaluation to address three primary tasks:

1. Estimating Percentiles: Determining the percentile rank of a value within a specified distribution.
2. Drawing Samples: Generating value samples from the given distribution.
3. Calculating Probabilities: Identifying the probability of a value falling within a specified range.

To facilitate this evaluation, the authors curated two comprehensive datasets: one comprising standard idealized distributions (e.g., Normal, Log-Normal, Power-Law) and another consisting of real-world distributions from domains such as health, finance, and climate.

Experimental Setup and Methodology

Zero-shot Performance

The evaluation of four state-of-the-art LMs (Gemini 1.0 Ultra, GPT4-Turbo, GPT3.5-Turbo, and Llama3-70B) in a zero-shot setting highlighted substantial variability in performance across different distributions and tasks. The zero-shot performance was primarily measured in terms of mean absolute error (MAE) for percentile estimation and probability calculation, and the Kolmogorov-Smirnov (K-S) statistic for sampling accuracy.

Influence of Context and Few-Shot Prompting

To further explore performance enhancements, the authors investigated the impact of providing additional context and few-shot examples. They categorized the context into:

1. Within Distribution Family Shots: Examples from a different distribution within the same family.
2. Within Distribution Shots: Examples from the exact distribution in question.

Notably, providing within distribution shots demonstrated a significant performance boost over within family shots, indicating that LMs benefit substantially from specific, distribution-aligned examples rather than more generalized distribution family examples.

Real-World Distribution Analysis

The researchers extended their analysis to real-world datasets to determine how well LMs could generalize probabilistic reasoning in practical scenarios. They explored three types of contextual enhancements:

1. Real-World Context: Providing detailed real-world distribution-specific context in the prompt.
2. Normal Distribution Approximation: Assuming a simplified Normal distribution for complex real-world data.
3. Real-World Context with Few-Shot Examples: Providing the specific context along with three examples.

The paper found that while real-world context improved performance significantly, the use of a Normal approximation surprisingly yielded consistent enhancements across many distributions. However, the most substantial gains were observed when using real-world context coupled with few-shot examples, underscoring the effectiveness of tailored example-based prompting.

Insights and Implications

The findings from this research hold several theoretical and practical implications:

1. Interpreting LM Performance: The performance variability across different distributions reveals inherent limitations in LMs' numerical reasoning capabilities, particularly in non-Normal distributions like Power Law or Skew-Normal.
2. Promising Improvement Strategies: Providing contextual examples and leveraging simplified assumptions such as the Normal approximation are effective in enhancing LMs' probabilistic reasoning performance.
3. Future Directions: The paper suggests future work on training LMs with diverse numerical reasoning tasks and fine-tuning with probabilistic reasoning-specific datasets. Moreover, improvements in representing and reasoning about extreme values and outliers are necessary to enhance reliability in practical applications.

Conclusion and Limitations

The paper concludes that LMs possess intrinsic capabilities for probabilistic reasoning, which can be significantly amplified through strategic context provision and example-based prompting. However, challenges remain, particularly in handling non-uniform and highly skewed distributions. Further research is essential to improve LMs' robustness in probabilistic reasoning, contributing to their applicability in critical fields such as health, finance, and climate science.

The release of the curated datasets and benchmarks will undoubtedly foster future research, enhancing the reliability and safety of LMs in performing complex numerical reasoning tasks.

References

The references provided in the original paper span a wide array of works, lending support to the claims and methodologies employed in this research. For further reading, references [Kojima et al., 2022], [Imani et al., 2023], and [Lewkowycz et al., 2022] offer additional context on numerical reasoning and prompting techniques in LMs.