XLGoBench: Detecting cross-lingual skill gaps with algorithmic tasks

We introduce a set of synthetic algorithmic tasks to detect cross-lingual gaps in the abilities of large language models. Our benchmark is commensurate across languages, since it requires models to perform the same underlying task in different languages; scalable, since each task can be generated at varying levels of complexity allowing it to be adapted to models with different capabilities; quantifiable, since every task admits an objective notion of correctness; and transparent, since tasks are generated from simple templates that can be readily audited for translation errors. Because our benchmark focuses on algorithmic tasks, differential performance is a sufficient -- but not necessary -- indicator of cross-lingual gaps. Nevertheless, we show through extensive experiments that our benchmark exposes persistent cross-lingual gaps in multiple state-of-the-art models.

A model of errors in transformers

We study the error rate of LLMs on tasks like arithmetic that require a deterministic output, and repetitive processing of tokens drawn from a small set of alternatives. We argue that incorrect predictions arise when small errors in the attention mechanism accumulate to cross a threshold, and use this insight to derive a quantitative two-parameter relationship between the accuracy and the complexity of the task. The two parameters vary with the prompt and the model; they can be interpreted in terms of an elementary noise rate, and the number of plausible erroneous tokens that can be predicted. Our analysis is inspired by an ``effective field theory'' perspective: the LLM's many raw parameters can be reorganized into just two parameters that govern the error rate. We perform extensive empirical tests, using Gemini 2.5 Flash, Gemini 2.5 Pro and DeepSeek R1, and find excellent agreement between the predicted and observed accuracy for a variety of tasks, although we also identify deviations in some cases. Our model provides an alternative to suggestions that errors made by LLMs on long repetitive tasks indicate the ``collapse of reasoning'', or an inability to express ``compositional'' functions. Finally, we show how to construct prompts to reduce the error rate.