A Simple Model of Inference Scaling Laws (2410.16377v2)

Abstract: Neural scaling laws have garnered significant interest due to their ability to predict model performance as a function of increasing parameters, data, and compute. In this work, we propose a simple statistical ansatz based on memorization to study scaling laws in the context of inference, specifically how performance improves with multiple inference attempts. We explore the coverage, or pass@k metric, which measures the chance of success over repeated attempts and provide a motivation for the observed functional form of the inference scaling behavior of the coverage in LLMs on reasoning tasks. We then define an "inference loss", which exhibits a power law decay as the number of trials increases, and connect this result with prompting costs. We further test our construction by conducting experiments on a simple generative model, and find that our predictions are in agreement with the empirical coverage curves in a controlled setting. Our simple framework sets the ground for incorporating inference scaling with other known scaling laws.

A Simple Model of Inference Scaling Laws: An Expert Overview

This paper introduces a statistical model designed to understand inference scaling laws in neural networks, with a particular emphasis on LLMs. The authors focus on how model performance can improve through repeated inference attempts, exploring the implications of this phenomenon for practical and theoretical applications in machine learning.

Key Contributions

The core contribution of this work is a statistical framework based on a memorization premise to analyze inference scaling behaviors. The focus is on the pass@k metric, which evaluates the probability of success over multiple inference attempts. This approach stands apart by predicting model performance improvements without additional training, achieved simply by increasing inference trials.

The paper also introduces the concept of "inference loss", defined as a power-law decay function of the number of trials, and establishes a connection between this loss and total inference costs. This insight offers a predictive tool for evaluating the trade-offs between model performance and computational expenses.

Methodology

1. Memorization and Inference Model: The authors present a joint model of memory and inference. The memory component perfectly memorizes training data, whereas the inference model may generate errors due to probabilistic sampling. This structure allows a focus on inference performance as separate from training.
2. Failure Probability Distribution: To capture variations in sample complexity, the authors employ a Beta distribution to model sample-specific inference error probabilities. This distribution helps in predicting the pass@k metric analytically.
3. Correlation Between Trials: The paper addresses the possible correlations between inference trials by introducing an effective number of independent trials, $k_{\text{eff}}$, which accounts for correlation decay. This approximation is used to predict coverage improvements.

Experimental Validation

The authors conduct empirical validation using a simple generative model, such as a Variational Autoencoder (VAE), trained on the Fashion-MNIST dataset. The results illustrate the practical applicability of their theoretical approach and confirm the analytical predictions of pass@k behavior.

Implications and Future Directions

The proposed model provides a theoretical foundation for understanding inference scaling behavior, fostering a deeper comprehension of how LLMs operate when subjected to repeated prompting. The reduction of inference loss to cost metrics offers valuable insights for optimizing inference efficiency.

Future research could explore integrating these findings with other known scaling laws to improve overall model efficiency. It would also be interesting to investigate the implications of these scaling properties in real-world model applications, such as interactive AI systems requiring repeated user interactions.

In essence, this work lays the groundwork for a systematic examination of the trade-offs between training and inference strategies, aiming to minimize both computational overhead and performance loss, thereby achieving balanced and efficient AI systems.