# Decodable But Not Detachable: Training Data Granularity Determines Parametric Modularity in Large Language Models

arXiv: https://arxiv.org/abs/2608.10214 · HTML: https://mlsanity.com/paper/2608.10214/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 20 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Do Llamas Work in English? On the Latent Language of Multilingual Transformers](https://mlsanity.com/paper/2402.10588/) (2024)
- [Language-Specific Neurons: The Key to Multilingual Capabilities in Large Language Models](https://mlsanity.com/paper/2402.16438/) (2024)
- [Identifying and Controlling Important Neurons in Neural Machine Translation](https://mlsanity.com/paper/1811.01157/) (2018)
- [Finding Skill Neurons in Pre-trained Transformer-based Language Models](https://mlsanity.com/paper/2211.07349/) (2022)

## Abstract (arXiv)

Do large language models contain domain-specific parametric shells: concentrated, causally necessary neuron populations whose removal selectively degrades a target domain while sparing others? We apply a uniform causal methodology across two domain granularities, three model families (1.5B to 7B parameters), and eight domains. At the academic subject level, zero neurons exceed 60% domain selectivity across 939,008 combined FFN neurons and causal damage matrices are flat, despite domain identity being linearly decodable above 85% accuracy. At the language and modality level, 0.65--1.14% of neurons exceed 60% selectivity, damage matrices are near-perfectly diagonal (ratios up to 595:1), and shell neuron sets are essentially disjoint (IoU < 0.003). Masking code-selective neurons reduces mathematical reasoning accuracy by 16--24 percentage points across all models; masking Spanish or Chinese neurons leaves it at or below random. Shell strength increases monotonically with scale and shells are spatially interleaved in a pattern that precludes group-level selective quantization. Parametric shells form where and only where training data was modular at the token level.