# Neuron Empirical Gradient: Discovering and Quantifying Neurons Global Linear Controllability

arXiv: https://arxiv.org/abs/2412.18053 · HTML: https://mlsanity.com/paper/2412.18053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 53 references that are in the map.
- First posted on arXiv 24 Dec 2024.

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

- [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)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [StereoSet: Measuring stereotypical bias in pretrained language models](https://mlsanity.com/paper/2004.09456/) (2020)
- [XNLI: Evaluating Cross-lingual Sentence Representations](https://mlsanity.com/paper/1809.05053/) (2018)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [PAWS: Paraphrase Adversaries from Word Scrambling](https://mlsanity.com/paper/1904.01130/) (2019)
- [SWAG: A Large-Scale Adversarial Dataset for Grounded Commonsense Inference](https://mlsanity.com/paper/1808.05326/) (2018)
- [Time-Aware Language Models as Temporal Knowledge Bases](https://mlsanity.com/paper/2106.15110/) (2021)
- [Bridging Language and Items for Retrieval and Recommendation: Benchmarking LLMs as Semantic Encoders](https://mlsanity.com/paper/2403.03952/) (2024)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [A Mechanistic Understanding of Alignment Algorithms: A Case Study on DPO and Toxicity](https://mlsanity.com/paper/2401.01967/) (2024)
- [The Multilingual Amazon Reviews Corpus](https://mlsanity.com/paper/2010.02573/) (2020)
- [Multilingual LAMA: Investigating Knowledge in Multilingual Pretrained Language Models](https://mlsanity.com/paper/2102.00894/) (2021)
- [A Simple Recipe for Multilingual Grammatical Error Correction](https://mlsanity.com/paper/2106.03830/) (2021)
- [A Rigorous Study of Integrated Gradients Method and Extensions to Internal Neuron Attributions](https://mlsanity.com/paper/2202.11912/) (2022)
- [Journey to the Center of the Knowledge Neurons: Discoveries of Language-Independent Knowledge Neurons and Degenerate Knowledge Neurons](https://mlsanity.com/paper/2308.13198/) (2023)
- [SEACrowd: A Multilingual Multimodal Data Hub and Benchmark Suite for Southeast Asian Languages](https://mlsanity.com/paper/2406.10118/) (2024)
- [Style-Specific Neurons for Steering LLMs in Text Style Transfer](https://mlsanity.com/paper/2410.00593/) (2024)
- [Neuron Specialization: Leveraging intrinsic task modularity for multilingual machine translation](https://mlsanity.com/paper/2404.11201/) (2024)
- [Unveiling Factual Recall Behaviors of Large Language Models through Knowledge Neurons](https://mlsanity.com/paper/2408.03247/) (2024)
- [What Matters in Memorizing and Recalling Facts? Multifaceted Benchmarks for Knowledge Probing in Language Models](https://mlsanity.com/paper/2406.12277/) (2024)

## Built on by (most cited first, 2 of 2)

- [Deconstructing Pre-training: Knowledge Attribution Analysis in MoE and Dense Models](https://mlsanity.com/paper/2601.08383/) (2026)
- [Tracing Multilingual Knowledge Acquisition Dynamics in Domain Adaptation: A Case Study of English-Japanese Biomedical Adaptation](https://mlsanity.com/paper/2510.12115/) (2025)

## Abstract (arXiv)

While feed-forward neurons in pre-trained language models (PLMs) can encode knowledge, past research targeted a small subset of neurons that heavily influence outputs. This leaves the broader role of neuron activations unclear, limiting progress in areas like knowledge editing. We uncover a global linear relationship between neuron activations and outputs using neuron interventions on a knowledge probing dataset. The gradient of this linear relationship, which we call the neuron empirical gradient (NEG), captures how changes in activations affect predictions. To compute NEG efficiently, we propose NeurGrad, enabling large-scale analysis of neuron behavior in PLMs. We also show that NEG effectively captures language skills across diverse prompts through skill neuron probing. Experiments on MCEval8k, a multi-genre multiple-choice knowledge benchmark, support NEG's ability to represent model knowledge. Further analysis highlights the key properties of NEG-based skill representation: efficiency, robustness, flexibility, and interdependency. The code and data are released.