# MIDUS: Memory-Infused Depth Up-Scaling

arXiv: https://arxiv.org/abs/2512.13751 · HTML: https://mlsanity.com/paper/2512.13751/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 55 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 30 of 49)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [LongBench: A Bilingual, Multitask Benchmark for Long Context Understanding](https://mlsanity.com/paper/2308.14508/) (2023)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [The FineWeb Datasets: Decanting the Web for the Finest Text Data at Scale](https://mlsanity.com/paper/2406.17557/) (2024)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Mixture-of-Depths: Dynamically allocating compute in transformer-based language models](https://mlsanity.com/paper/2404.02258/) (2024)
- [Sparse Upcycling: Training Mixture-of-Experts from Dense Checkpoints](https://mlsanity.com/paper/2212.05055/) (2022)
- [SOLAR 10.7B: Scaling Large Language Models with Simple yet Effective Depth Up-Scaling](https://mlsanity.com/paper/2312.15166/) (2023)
- [MoEfication: Transformer Feed-forward Layers are Mixtures of Experts](https://mlsanity.com/paper/2110.01786/) (2021)
- [Large Memory Layers with Product Keys](https://mlsanity.com/paper/1907.05242/) (2019)

## Abstract (arXiv)

Expanding pre-trained language models offers a practical way to increase capacity without training larger models from scratch. Depth Up-Scaling (DUS) does so by duplicating Transformer blocks and inserting them into a pre-trained backbone. This process also duplicates FFN-heavy blocks, increasing parameter and compute cost while adding capacity through a block-level dense residual branch. Yet prior work suggests that added capacity need not remain tied to dense FFN branches, while attention heads often play heterogeneous roles, motivating more efficient head-level residual corrections. We propose Memory-Infused Depth Up-Scaling (MIDUS), which replaces the duplicated FFN branches with memory layers and turns added depth into lightweight retrieval-based residual capacity. We introduce a Head-wise Memory Layer (HML), which combines multi-head product-key memory with Head-wise Implicit Value Expansion (HIVE). HML assigns each head a distinct key space, while HIVE realizes head-specific values from a shared latent bank through compact projections. Alongside empirical improvements in performance and efficiency, our head-importance and fixed-retrieval structural analyses characterize HML with HIVE as a structurally distinct, head-conditioned alternative to FFN-based residual expansion.