# Probing as Quantifying Inductive Bias

arXiv: https://arxiv.org/abs/2110.08388 · HTML: https://mlsanity.com/paper/2110.08388/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 58 references that are in the map.
- First posted on arXiv 15 Oct 2021.

## Builds on (most cited first, 30 of 37)

- [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)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Enriching Word Vectors with Subword Information](https://mlsanity.com/paper/1607.04606/) (2016)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Linguistic Knowledge and Transferability of Contextual Representations](https://mlsanity.com/paper/1903.08855/) (2019)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Learning Word Vectors for 157 Languages](https://mlsanity.com/paper/1802.06893/) (2018)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [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)
- [What do Neural Machine Translation Models Learn about Morphology?](https://mlsanity.com/paper/1704.03471/) (2017)
- [What Is One Grain of Sand in the Desert? Analyzing Individual Neurons in Deep NLP Models](https://mlsanity.com/paper/1812.09355/) (2018)
- [Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning](https://mlsanity.com/paper/2104.04975/) (2021)
- [Repulsive Deep Ensembles are Bayesian](https://mlsanity.com/paper/2106.11642/) (2021)
- [Analyzing Individual Neurons in Pre-trained Language Models](https://mlsanity.com/paper/2010.02695/) (2020)
- [Word Representations via Gaussian Embedding](https://mlsanity.com/paper/1412.6623/) (2014)
- [On the Pitfalls of Analyzing Individual Neurons in Language Models](https://mlsanity.com/paper/2110.07483/) (2021)
- [Pareto Probing: Trading Off Accuracy for Complexity](https://mlsanity.com/paper/2010.02180/) (2020)

## Built on by (most cited first, 12 of 12)

- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximations](https://mlsanity.com/paper/2202.10638/) (2022)
- [Geographic and Geopolitical Biases of Language Models](https://mlsanity.com/paper/2212.10408/) (2022)
- [Gaussian Stochastic Weight Averaging for Bayesian Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2405.03425/) (2024)
- [Improving Neural Additive Models with Bayesian Principles](https://mlsanity.com/paper/2305.16905/) (2023)
- [Promises and Pitfalls of the Linearized Laplace in Bayesian Optimization](https://mlsanity.com/paper/2304.08309/) (2023)
- [Stochastic Marginal Likelihood Gradients using Neural Tangent Kernels](https://mlsanity.com/paper/2306.03968/) (2023)
- [Unraveling the Key Components of OOD Generalization via Diversification](https://mlsanity.com/paper/2312.16313/) (2023)
- [Latent Causal Probing: A Formal Perspective on Probing with Causal Models of Data](https://mlsanity.com/paper/2407.13765/) (2024)
- [Estimating Implicit Regularization in Deep Learning](https://mlsanity.com/paper/2605.05436/) (2026)
- [Multilingual Text Representation](https://mlsanity.com/paper/2309.00949/) (2023)
- [Loss-Invariant Projections as Passive Probes of Learned Representations](https://mlsanity.com/paper/2610.06195/) (2026)

## Abstract (arXiv)

Pre-trained contextual representations have led to dramatic performance improvements on a range of downstream tasks. Such performance improvements have motivated researchers to quantify and understand the linguistic information encoded in these representations. In general, researchers quantify the amount of linguistic information through probing, an endeavor which consists of training a supervised model to predict a linguistic property directly from the contextual representations. Unfortunately, this definition of probing has been subject to extensive criticism in the literature, and has been observed to lead to paradoxical and counter-intuitive results. In the theoretical portion of this paper, we take the position that the goal of probing ought to be measuring the amount of inductive bias that the representations encode on a specific task. We further describe a Bayesian framework that operationalizes this goal and allows us to quantify the representations' inductive bias. In the empirical portion of the paper, we apply our framework to a variety of NLP tasks. Our results suggest that our proposed framework alleviates many previous problems found in probing. Moreover, we are able to offer concrete evidence that -- for some tasks -- fastText can offer a better inductive bias than BERT.