# Information-Theoretic Probing with Minimum Description Length

arXiv: https://arxiv.org/abs/2003.12298 · HTML: https://mlsanity.com/paper/2003.12298/

## Key facts

- Cited by 232 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

## Built on by (most cited first, 30 of 232)

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- [Finding Neurons in a Haystack: Case Studies with Sparse Probing](https://mlsanity.com/paper/2305.01610/) (2023)
- [Factual Probing Is [MASK]: Learning vs. Learning to Recall](https://mlsanity.com/paper/2104.05240/) (2021)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
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- [Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks](https://mlsanity.com/paper/2311.12786/) (2023)
- [Are Emergent Abilities in Large Language Models just In-Context Learning?](https://mlsanity.com/paper/2309.01809/) (2023)
- [What Artificial Neural Networks Can Tell Us About Human Language Acquisition](https://mlsanity.com/paper/2208.07998/) (2022)
- [An Information-theoretic Approach to Prompt Engineering Without Ground Truth Labels](https://mlsanity.com/paper/2203.11364/) (2022)
- [A Theory of Emergent In-Context Learning as Implicit Structure Induction](https://mlsanity.com/paper/2303.07971/) (2023)
- [Neuron-level Interpretation of Deep NLP Models: A Survey](https://mlsanity.com/paper/2108.13138/) (2021)
- [Do Language Models Have Beliefs? Methods for Detecting, Updating, and Visualizing Model Beliefs](https://mlsanity.com/paper/2111.13654/) (2021)
- [Decoupling the Role of Data, Attention, and Losses in Multimodal Transformers](https://mlsanity.com/paper/2102.00529/) (2021)
- [Low-Complexity Probing via Finding Subnetworks](https://mlsanity.com/paper/2104.03514/) (2021)
- [Conditional probing: measuring usable information beyond a baseline](https://mlsanity.com/paper/2109.09234/) (2021)
- [Cognitive Dissonance: Why Do Language Model Outputs Disagree with Internal Representations of Truthfulness?](https://mlsanity.com/paper/2312.03729/) (2023)
- [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)
- [Measuring Inductive Biases of In-Context Learning with Underspecified Demonstrations](https://mlsanity.com/paper/2305.13299/) (2023)
- [Usable XAI: 10 Strategies Towards Exploiting Explainability in the LLM Era](https://mlsanity.com/paper/2403.08946/) (2024)
- [Structural Persistence in Language Models: Priming as a Window into Abstract Language Representations](https://mlsanity.com/paper/2109.14989/) (2021)
- [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)
- [Transformer Grammars: Augmenting Transformer Language Models with Syntactic Inductive Biases at Scale](https://mlsanity.com/paper/2203.00633/) (2022)

## Abstract (arXiv)

To measure how well pretrained representations encode some linguistic property, it is common to use accuracy of a probe, i.e. a classifier trained to predict the property from the representations. Despite widespread adoption of probes, differences in their accuracy fail to adequately reflect differences in representations. For example, they do not substantially favour pretrained representations over randomly initialized ones. Analogously, their accuracy can be similar when probing for genuine linguistic labels and probing for random synthetic tasks. To see reasonable differences in accuracy with respect to these random baselines, previous work had to constrain either the amount of probe training data or its model size. Instead, we propose an alternative to the standard probes, information-theoretic probing with minimum description length (MDL). With MDL probing, training a probe to predict labels is recast as teaching it to effectively transmit the data. Therefore, the measure of interest changes from probe accuracy to the description length of labels given representations. In addition to probe quality, the description length evaluates "the amount of effort" needed to achieve the quality. This amount of effort characterizes either (i) size of a probing model, or (ii) the amount of data needed to achieve the high quality. We consider two methods for estimating MDL which can be easily implemented on top of the standard probing pipelines: variational coding and online coding. We show that these methods agree in results and are more informative and stable than the standard probes.