# Conditional probing: measuring usable information beyond a baseline

arXiv: https://arxiv.org/abs/2109.09234 · HTML: https://mlsanity.com/paper/2109.09234/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 52 references that are in the map.
- First posted on arXiv 19 Sep 2021.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Stanza: A Python Natural Language Processing Toolkit for Many Human Languages](https://mlsanity.com/paper/2003.07082/) (2020)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [What do you learn from context? Probing for sentence structure in contextualized word representations](https://mlsanity.com/paper/1905.06316/) (2019)
- [AllenNLP: A Deep Semantic Natural Language Processing Platform](https://mlsanity.com/paper/1803.07640/) (2018)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [Universal Dependencies v2: An Evergrowing Multilingual Treebank Collection](https://mlsanity.com/paper/2004.10643/) (2020)
- [Information-Theoretic Probing with Minimum Description Length](https://mlsanity.com/paper/2003.12298/) (2020)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Information-Theoretic Probing for Linguistic Structure](https://mlsanity.com/paper/2004.03061/) (2020)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [Dissecting Contextual Word Embeddings: Architecture and Representation](https://mlsanity.com/paper/1808.08949/) (2018)
- [Perturbed Masking: Parameter-free Probing for Analyzing and Interpreting BERT](https://mlsanity.com/paper/2004.14786/) (2020)
- [Low-Complexity Probing via Finding Subnetworks](https://mlsanity.com/paper/2104.03514/) (2021)
- [Pareto Probing: Trading Off Accuracy for Complexity](https://mlsanity.com/paper/2010.02180/) (2020)
- [Probing BERT in Hyperbolic Spaces](https://mlsanity.com/paper/2104.03869/) (2021)
- [Fast and Accurate Entity Recognition with Iterated Dilated Convolutions](https://mlsanity.com/paper/1702.02098/) (2017)
- [A Non-Linear Structural Probe](https://mlsanity.com/paper/2105.10185/) (2021)
- [Introducing Orthogonal Constraint in Structural Probes](https://mlsanity.com/paper/2012.15228/) (2020)
- [Language Modeling Teaches You More Syntax than Translation Does: Lessons Learned Through Auxiliary Task Analysis](https://mlsanity.com/paper/1809.10040/) (2018)
- [Probing artificial neural networks: insights from neuroscience](https://mlsanity.com/paper/2104.08197/) (2021)
- [Bird's Eye: Probing for Linguistic Graph Structures with a Simple Information-Theoretic Approach](https://mlsanity.com/paper/2105.02629/) (2021)
- [A multilabel approach to morphosyntactic probing](https://mlsanity.com/paper/2104.08464/) (2021)

## Built on by (most cited first, 30 of 62)

- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [ReCEval: Evaluating Reasoning Chains via Correctness and Informativeness](https://mlsanity.com/paper/2304.10703/) (2023)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [Probing for the Usage of Grammatical Number](https://mlsanity.com/paper/2204.08831/) (2022)
- [Towards Reliable Evaluation of Behavior Steering Interventions in LLMs](https://mlsanity.com/paper/2410.17245/) (2024)
- [Diff-eRank: A Novel Rank-Based Metric for Evaluating Large Language Models](https://mlsanity.com/paper/2401.17139/) (2024)
- [When classifying grammatical role, BERT doesn't care about word order... except when it matters](https://mlsanity.com/paper/2203.06204/) (2022)
- [The Quest for the Right Mediator: Surveying Mechanistic Interpretability Through the Lens of Causal Mediation Analysis](https://mlsanity.com/paper/2408.01416/) (2024)
- [REV: Information-Theoretic Evaluation of Free-Text Rationales](https://mlsanity.com/paper/2210.04982/) (2022)
- [Naturalistic Causal Probing for Morpho-Syntax](https://mlsanity.com/paper/2205.07043/) (2022)
- [A layer-wise analysis of Mandarin and English suprasegmentals in SSL speech models](https://mlsanity.com/paper/2408.13678/) (2024)
- [Understanding Multimodal LLMs Under Distribution Shifts: An Information-Theoretic Approach](https://mlsanity.com/paper/2502.00577/) (2025)
- [Dual Process Learning: Controlling Use of In-Context vs. In-Weights Strategies with Weight Forgetting](https://mlsanity.com/paper/2406.00053/) (2024)
- [Probing for Constituency Structure in Neural Language Models](https://mlsanity.com/paper/2204.06201/) (2022)
- [Operationalising Representation in Natural Language Processing](https://mlsanity.com/paper/2306.08193/) (2023)
- [Tokenization and Morphology in Multilingual Language Models: A Comparative Analysis of mT5 and ByT5](https://mlsanity.com/paper/2410.11627/) (2024)
- [Accurate and Nuanced Open-QA Evaluation Through Textual Entailment](https://mlsanity.com/paper/2405.16702/) (2024)
- [Gaussian Process Probes (GPP) for Uncertainty-Aware Probing](https://mlsanity.com/paper/2305.18213/) (2023)
- [Probing Graph Representations](https://mlsanity.com/paper/2303.03951/) (2023)
- [Cross-Refine: Improving Natural Language Explanation Generation by Learning in Tandem](https://mlsanity.com/paper/2409.07123/) (2024)
- [Morphosyntactic probing of multilingual BERT models](https://mlsanity.com/paper/2306.06205/) (2023)
- [Finding Structural Knowledge in Multimodal-BERT](https://mlsanity.com/paper/2203.09306/) (2022)
- [Latent Topology Induction for Understanding Contextualized Representations](https://mlsanity.com/paper/2206.01512/) (2022)
- [Trustworthy Social Bias Measurement](https://mlsanity.com/paper/2212.11672/) (2022)
- [Linguistic Interpretability of Transformer-based Language Models: a systematic review](https://mlsanity.com/paper/2504.08001/) (2025)
- [Schr"odinger's Tree -- On Syntax and Neural Language Models](https://mlsanity.com/paper/2110.08887/) (2021)
- [It Takes Two Flints to Make a Fire: Multitask Learning of Neural Relation and Explanation Classifiers](https://mlsanity.com/paper/2204.11424/) (2022)
- [OOD-Probe: A Neural Interpretation of Out-of-Domain Generalization](https://mlsanity.com/paper/2208.12352/) (2022)

## Abstract (arXiv)

Probing experiments investigate the extent to which neural representations make properties -- like part-of-speech -- predictable. One suggests that a representation encodes a property if probing that representation produces higher accuracy than probing a baseline representation like non-contextual word embeddings. Instead of using baselines as a point of comparison, we're interested in measuring information that is contained in the representation but not in the baseline. For example, current methods can detect when a representation is more useful than the word identity (a baseline) for predicting part-of-speech; however, they cannot detect when the representation is predictive of just the aspects of part-of-speech not explainable by the word identity. In this work, we extend a theory of usable information called V-information and propose conditional probing, which explicitly conditions on the information in the baseline. In a case study, we find that after conditioning on non-contextual word embeddings, properties like part-of-speech are accessible at deeper layers of a network than previously thought.