Operationalising the Superficial Alignment Hypothesis via Task Complexity

TL;DR

This paper introduces a task complexity metric to operationalize the Superficial Alignment Hypothesis, showing pre-training drastically reduces the complexity needed for high performance on various tasks, often requiring only a few kilobytes of information.

Contribution

It defines task complexity as the shortest program achieving high performance, unifying prior arguments and empirically demonstrating pre-training reduces this complexity significantly.

Findings

Pre-trained models drastically lower task complexity.

High performance can be achieved with programs of gigabytes in size.

Post-training reduces complexity by several orders of magnitude.

Abstract

The superficial alignment hypothesis (SAH) posits that large language models learn most of their knowledge during pre-training, and that post-training merely surfaces this knowledge. The SAH, however, lacks a precise definition, which has led to (i) different and seemingly orthogonal arguments supporting it, and (ii) important critiques to it. We propose a new metric called task complexity: the length of the shortest program that achieves a target performance on a task. In this framework, the SAH simply claims that pre-trained models drastically reduce the complexity of achieving high performance on many tasks. Our definition unifies prior arguments supporting the SAH, interpreting them as different strategies to find such short programs. Experimentally, we estimate the task complexity of mathematical reasoning, machine translation, and instruction following; we then show that these complexities can be remarkably low when conditioned on a pre-trained model. Further, we find that pre-training enables access to strong performances on our tasks, but it can require programs of gigabytes of length to access them. Post-training, on the other hand, collapses the complexity of reaching this same performance by several orders of magnitude. Overall, our results highlight that task adaptation often requires surprisingly little information -- often just a few kilobytes.