# Hitting "Probe"rty with Non-Linearity, and More

arXiv: https://arxiv.org/abs/2402.16168 · HTML: https://mlsanity.com/paper/2402.16168/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge and representations inside LLMs, one of 13 directions in Mechanistic interpretability.
- Builds on 8 of its 13 references that are in the map.
- First posted on arXiv 25 Feb 2024.

## Placed in

- Mechanistic interpretability / [Knowledge and representations inside LLMs](https://mlsanity.com/mechinterp/knowledge-and-representations-inside-llms/)

## Builds on (most cited first, 8 of 8)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Visualizing and Measuring the Geometry of BERT](https://mlsanity.com/paper/1906.02715/) (2019)
- [Colorless green recurrent networks dream hierarchically](https://mlsanity.com/paper/1803.11138/) (2018)
- [Neural Language Models as Psycholinguistic Subjects: Representations of Syntactic State](https://mlsanity.com/paper/1903.03260/) (2019)
- [A Non-Linear Structural Probe](https://mlsanity.com/paper/2105.10185/) (2021)
- [Distinct patterns of syntactic agreement errors in recurrent networks and humans](https://mlsanity.com/paper/1807.06882/) (2018)

## Abstract (arXiv)

Structural probes learn a linear transformation to find how dependency trees are embedded in the hidden states of language models. This simple design may not allow for full exploitation of the structure of the encoded information. Hence, to investigate the structure of the encoded information to its full extent, we incorporate non-linear structural probes. We reformulate the design of non-linear structural probes introduced by White et al. making its design simpler yet effective. We also design a visualization framework that lets us qualitatively assess how strongly two words in a sentence are connected in the predicted dependency tree. We use this technique to understand which non-linear probe variant is good at encoding syntactical information. Additionally, we also use it to qualitatively investigate the structure of dependency trees that BERT encodes in each of its layers. We find that the radial basis function (RBF) is an effective non-linear probe for the BERT model than the linear probe.