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Faith and Fate: Limits of Transformers on Compositionality

Written for the Research library (claude-opus-5-5) from the paper text, in our own words: the license "arXiv — non-exclusive licence to distribute" does not allow redistributing the text itself. Original — arxiv.org/pdf/2305.18654

Summary

Large transformer LLMs can handle some demanding reasoning tasks yet fail on simple procedural ones. The authors ask whether these failures are accidental or reflect deeper structural limits. They examine three compositional tasks: long-form multiplication with operands of up to 5 digits, Einstein-style puzzles that require deducing a solution grid, and a well-known problem solved through dynamic programming. Each problem instance is encoded as a computation graph, with intermediate values as nodes and primitive operations as edges. This lets them quantify complexity with graph metrics (reasoning depth, reasoning width, average parallelism). It also lets them use relative information gain to predict which surface shortcuts a model may pick up. They test models zero-shot, with explicit step-by-step reasoning, and after task-specific fine-tuning. In all cases, models do well only on in-distribution, low-complexity cases, and accuracy collapses as problems grow. Error analysis suggests that models match subgraphs seen in training rather than learning the underlying algorithm. A theoretical argument shows that errors in autoregressive generation can compound exponentially with the number of steps. The work questions whether more data or better prompting alone can produce reliable systematic reasoning.

Key points

  • Off-the-shelf ChatGPT and GPT4 reach only about 55% and 59% accuracy on 3-digit × 3-digit multiplication.
  • Zero-shot accuracy falls to near zero as problem size grows, measured by digits, by houses × attributes in the puzzle, or by sequence length in the DP task. Average parallelism correlates negatively with accuracy.
  • Fine-tuning gives near-perfect in-domain results at low complexity but fails badly out-of-distribution. Success largely depends on training examples containing the same sub-computations as the test examples.
  • Models can memorize single-step operations but fail to chain them correctly. No grokking was observed for multiplication.
  • The paper was published at NeurIPS 2023 (Allen Institute for AI, University of Washington, and others). Code and data are at github.com/nouhadziri/faith-and-fate.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

Fields: Mathematics & statistics

Cited by

207 papers of our library cite it (of the 140673 whose bibliographies we read); 6 of them have a page here, 201 not yet.

Cite

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.48550/arxiv.2305.18654 · arXiv 2305.18654

@misc{dziri2023faith,
  title = {{Faith and Fate: Limits of Transformers on Compositionality}},
  author = {Dziri, Nouha and Lu, Ximing and Sclar, Melanie and Li, Xiang Lorraine and Jiang, Liwei and Lin, Bill Yuchen and West, Peter and Bhagavatula, Chandra and Bras, Ronan Le and Hwang, Jena D. and Sanyal, Soumya and Welleck, Sean and Ren, Xiang and Ettinger, Allyson and Harchaoui, Zaid and Choi, Yejin},
  year = {2023},
  doi = {10.48550/arxiv.2305.18654},
  eprint = {2305.18654},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2305.18654}
}

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