cs.LGFeb 17, 2026

Operationalising the Superficial Alignment Hypothesis via Task Complexity

Authors: Tomás Vergara-Browne, Darshan Patil, Ivan Titov, Siva Reddy, Tiago Pimentel, Marius Mosbach

Organizations: Mila Quebec AI Institute · McGill University · Université de Montréal · University of Edinburgh · 

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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.

Figures & tables

Figure 1: Pareto curve of program length vs. performance for Olmo3-7B on GSM8K. We argue that prior works about the superficial alignment hypothesis can be seen as proposing different approaches to find short programs to solve a task, and we find that these different views inform different regions of this Pareto curve.
Figure 2: Pseudo-code of the programs {\color[rgb]{0.75,0,0.25}\mathsf{P}} constructed by strategies in Section 4 . Each program includes its compressed data or parameters, and its size is usually dominated by such terms ( Figure 10 ). We explain the details of how we measure program size in our experiments in Appendix B .
Figure 3: The program length vs. performance Pareto curves for SmolLM3 and Olmo3 in our three analysed tasks: mathematical reasoning, machine translation, and instruction following. We test each method described in Section 4 , but show only the optimal lengths and performances. To provide some intuition about these program lengths, we also mark the size in bits of more commonly known references.
Figure 4: Performance of the linear projection fine-tuning proposed by Chen et al. (2025) in comparison to our estimated Pareto curve. The performance of the method is far from the Pareto curve.
Figure 5: Estimated complexity curves conditioned on pre- and post- trained checkpoints of SmolLM3 and Olmo3 for math (GSM8K) and instruction (IFEval) tasks. Pre-training allows access of strong performance in these tasks. Post-training improves these performances, but more importantly, it greatly reduces the complexity to reach such performance.
Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 6: Length–performance Pareto curve of SmolLM3 3B, Olmo3 7B, and Olmo3 32B in Math (GSM8K), Translation (FLORES) and Instruction (IFEval). Different views of superficiality inform different regions of the Pareto curve, with some variance depending on the choice of model and task.
Figure 7: Performance of the linear (head-only) fine-tuning approach proposed by Chen et al. (2025) and our estimated Pareto curves in Math (GSM8K), Translation (FLORES) and Instruction (IFEval).
Figure 8: Estimated complexity curves conditioned on pre- and post- trained checkpoints of SmolLM3 and Olmo3 for FLORES and eSNLI.
Figure 9: The program lengths vs. performance Pareto curves for SmolLM3 and Olmo3 in GSM8K and FLORES. We test each method described in Section 4 , and show their message lengths and performances obtained. This is an extended version of Figure 3 with all the results from our hyperparameter sweep.
Figure 10: Distribution of percentage of the contribution to program length made by measuring the script size of each method described in Section 4 across all of our experiments. The script size mostly makes a substantial contribution in the Base Model, ICL and URIAL methods.
Figure 11: Pareto curves in Math (GSM8K), Translation (FLORES) and Instruction (IFEval) compared to our method proposed in Appendix G . We are not able to push the Pareto frontier with our method.
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