# Information-Theoretic Probing for Linguistic Structure

arXiv: https://arxiv.org/abs/2004.03061 · HTML: https://mlsanity.com/paper/2004.03061/

## Key facts

- Cited by 207 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2020.

## Built on by (most cited first, 30 of 207)

- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [Factual Probing Is [MASK]: Learning vs. Learning to Recall](https://mlsanity.com/paper/2104.05240/) (2021)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Masked Language Modeling and the Distributional Hypothesis: Order Word Matters Pre-training for Little](https://mlsanity.com/paper/2104.06644/) (2021)
- [What Artificial Neural Networks Can Tell Us About Human Language Acquisition](https://mlsanity.com/paper/2208.07998/) (2022)
- [Neuron-level Interpretation of Deep NLP Models: A Survey](https://mlsanity.com/paper/2108.13138/) (2021)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Probing Across Time: What Does RoBERTa Know and When?](https://mlsanity.com/paper/2104.07885/) (2021)
- [Chess as a Testbed for Language Model State Tracking](https://mlsanity.com/paper/2102.13249/) (2021)
- [Low-Complexity Probing via Finding Subnetworks](https://mlsanity.com/paper/2104.03514/) (2021)
- [How Large Language Models Encode Context Knowledge? A Layer-Wise Probing Study](https://mlsanity.com/paper/2402.16061/) (2024)
- [Conditional probing: measuring usable information beyond a baseline](https://mlsanity.com/paper/2109.09234/) (2021)
- [Probing for the Usage of Grammatical Number](https://mlsanity.com/paper/2204.08831/) (2022)
- [Spectral Filters, Dark Signals, and Attention Sinks](https://mlsanity.com/paper/2402.09221/) (2024)
- [What Context Features Can Transformer Language Models Use?](https://mlsanity.com/paper/2106.08367/) (2021)
- [Do language models plan ahead for future tokens?](https://mlsanity.com/paper/2404.00859/) (2024)
- [Usable XAI: 10 Strategies Towards Exploiting Explainability in the LLM Era](https://mlsanity.com/paper/2403.08946/) (2024)
- [Quantifying Context Mixing in Transformers](https://mlsanity.com/paper/2301.12971/) (2023)
- [Deep Subjecthood: Higher-Order Grammatical Features in Multilingual BERT](https://mlsanity.com/paper/2101.11043/) (2021)
- [Things not Written in Text: Exploring Spatial Commonsense from Visual Signals](https://mlsanity.com/paper/2203.08075/) (2022)
- [The Low-Dimensional Linear Geometry of Contextualized Word Representations](https://mlsanity.com/paper/2105.07109/) (2021)
- [What if This Modified That? Syntactic Interventions via Counterfactual Embeddings](https://mlsanity.com/paper/2105.14002/) (2021)
- [The Non-Linear Representation Dilemma: Is Causal Abstraction Enough for Mechanistic Interpretability?](https://mlsanity.com/paper/2507.08802/) (2025)
- [What do tokens know about their characters and how do they know it?](https://mlsanity.com/paper/2206.02608/) (2022)
- [Diff-eRank: A Novel Rank-Based Metric for Evaluating Large Language Models](https://mlsanity.com/paper/2401.17139/) (2024)
- [PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runs](https://mlsanity.com/paper/2503.09543/) (2025)
- [Low-Dimensional Structure in the Space of Language Representations is Reflected in Brain Responses](https://mlsanity.com/paper/2106.05426/) (2021)
- [Local Interpretations for Explainable Natural Language Processing: A Survey](https://mlsanity.com/paper/2103.11072/) (2021)

## Abstract (arXiv)

The success of neural networks on a diverse set of NLP tasks has led researchers to question how much these networks actually ``know'' about natural language. Probes are a natural way of assessing this. When probing, a researcher chooses a linguistic task and trains a supervised model to predict annotations in that linguistic task from the network's learned representations. If the probe does well, the researcher may conclude that the representations encode knowledge related to the task. A commonly held belief is that using simpler models as probes is better; the logic is that simpler models will identify linguistic structure, but not learn the task itself. We propose an information-theoretic operationalization of probing as estimating mutual information that contradicts this received wisdom: one should always select the highest performing probe one can, even if it is more complex, since it will result in a tighter estimate, and thus reveal more of the linguistic information inherent in the representation. The experimental portion of our paper focuses on empirically estimating the mutual information between a linguistic property and BERT, comparing these estimates to several baselines. We evaluate on a set of ten typologically diverse languages often underrepresented in NLP research---plus English---totalling eleven languages.