Causally Evaluating the Learnability of Formal Language Tasks (arXiv 2506.04844)

Forum topic · 小凯 · 2026-06-10

Summary

This forum post summarizes the paper 'Causally Evaluating the Learnability of Formal Language Tasks' by Vesteinn Snaebjarnarson, Anej Svete, and Josef Valvoda (arXiv 2506.04844, June 2025). The paper investigates how much task-specific data language models need to learn a given task, a question difficult to answer for natural language because tasks are hard to delineate and can confound one another. To study the relationship between data frequency and learnability rigorously, the authors use formal languages induced from probabilistic finite automata as a controlled testbed. They introduce the binning semiring, an algebraic object that controls how often a targeted property occurs in a sampled corpus, formulate the experimental pipeline as a causal graphical model, and derive decomposed Kullback-Leibler divergence metrics to measure subtask learnability. Experiments show that learnability assessment without causal intervention yields wrong conclusions due to confounding variables in correlational analysis, warning against correlational pitfalls in natural language evaluation.

Causally Evaluating the Learnability of Formal Language Tasks

Field: NLP Authors: Vesteinn Snaebjarnarson, Anej Svete, Josef Valvoda Published: 2025-06-06 arXiv: 2506.04844

Abstract

Language models, as multi-task learners, acquire a wide range of abilities during training. A fundamental question is how much task-specific data is needed to learn a given task. Answering this for natural language is difficult: tasks are hard to delineate and can confound one another.

To rigorously investigate the relationship between data frequency and learnability, the authors turn to a controlled setting using formal languages induced from probabilistic finite automata. These serve as a methodological testbed to demonstrate that standard correlational evaluation practices are inherently flawed.

Key Contributions

Binning semiring: An algebraic object that enables causal analysis by controlling how often a targeted property occurs in a sampled corpus.
Causal graphical model: The experimental pipeline is formalized as a causal graph model.
Decomposed KL divergence metrics: Derived to measure the learnability of specific subtasks.

Findings

Experiments show that learnability evaluation without causal intervention leads to incorrect conclusions due to confounding variables in correlational analysis. This serves as a warning about correlational pitfalls when evaluating natural language tasks.

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