# CORTEX: Learning to Share and Specialize in Dense Language Models

arXiv: https://arxiv.org/abs/2609.34449 · HTML: https://mlsanity.com/paper/2609.34449/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 55 of its 62 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 55)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
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- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
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- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
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- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Documenting Large Webtext Corpora: A Case Study on the Colossal Clean Crawled Corpus](https://mlsanity.com/paper/2104.08758/) (2021)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)

## Abstract (arXiv)

Large language models are trained on heterogeneous data mixtures, where different knowledge domains require both shared knowledge and specialization. Existing modular approaches typically impose explicit components or discover modules through interpretability analysis after training. In this work, we propose CORTEX, a learning dynamics-inspired framework that learns internal modularization within dense language models. CORTEX partitions trainable matrices into parameter groups and learns module assignments from domain-conditioned gradient and cross-domain gradient similarity. We introduce the selective lesion score and module-domain mutual information to characterize the target-domain lesion effects and alignment, and analyze how module assignment affects the trade-off between assignment bias and update magnitude. Experiments with 160M, Qwen3-8B, and Qwen3-32B backbone models show that CORTEX achieves the highest synthetic-domain exact match and largest average perplexity reduction, while remaining competitive on real-domain evaluations and forming identifiable modules.