# L3: Large Lookup Layers

arXiv: https://arxiv.org/abs/2601.21461 · HTML: https://mlsanity.com/paper/2601.21461/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 27 of 27)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [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)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [Ring Attention with Blockwise Transformers for Near-Infinite Context](https://mlsanity.com/paper/2310.01889/) (2023)
- [QuIP: 2-Bit Quantization of Large Language Models With Guarantees](https://mlsanity.com/paper/2307.13304/) (2023)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks](https://mlsanity.com/paper/2402.04396/) (2024)
- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [Flex Attention: A Programming Model for Generating Optimized Attention Kernels](https://mlsanity.com/paper/2412.05496/) (2024)
- [Scaling Laws for Fine-Grained Mixture of Experts](https://mlsanity.com/paper/2402.07871/) (2024)
- [Large Memory Layers with Product Keys](https://mlsanity.com/paper/1907.05242/) (2019)
- [Cartridges: Lightweight and general-purpose long context representations via self-study](https://mlsanity.com/paper/2506.06266/) (2025)
- [Conditional Memory via Scalable Lookup: A New Axis of Sparsity for Large Language Models](https://mlsanity.com/paper/2601.07372/) (2026)
- [SuperBPE: Space Travel for Language Models](https://mlsanity.com/paper/2503.13423/) (2025)
- [Training LLMs with MXFP4](https://mlsanity.com/paper/2502.20586/) (2025)
- [STEP: Learning N:M Structured Sparsity Masks from Scratch with Precondition](https://mlsanity.com/paper/2302.01172/) (2023)
- [SonicMoE: Accelerating MoE with IO and Tile-aware Optimizations](https://mlsanity.com/paper/2512.14080/) (2025)
- [Scaling Embedding Layers in Language Models](https://mlsanity.com/paper/2502.01637/) (2025)
- [Ultra-Sparse Memory Network](https://mlsanity.com/paper/2411.12364/) (2024)
- [FlashMoE: Fast Distributed MoE in a Single Kernel](https://mlsanity.com/paper/2506.04667/) (2025)

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

- [On the Design of Qwen3.8-Next Architecture: Evaluation, Efficiency, and Training Stability](https://mlsanity.com/paper/2608.30320/) (2026)
- [NGM: A Plug-and-Play Training-Free Memory Module for LLMs](https://mlsanity.com/paper/2605.16893/) (2026)

## Abstract (arXiv)

Modern sparse language models typically achieve sparsity through Mixture-of-Experts (MoE) layers, which dynamically route tokens to dense MLP "experts." However, dynamic hard routing has a number of drawbacks, such as potentially poor hardware efficiency and needing auxiliary losses for stable training. In contrast, the tokenizer embedding table, which is natively sparse, largely avoids these issues by selecting a single embedding per token at the cost of not having contextual information. In this work, we introduce the Large Lookup Layer (L3), which generalizes embedding tables to model decoder layers as a means of further scaling sparsity. L3 layers use static token-based routing to aggregate a set of learned embeddings per token in a context-dependent way, allowing the model to efficiently balance memory and compute by caching information in embeddings. L3 has two main components: (1) a systems-friendly architecture that allows for fast training and CPU-offloaded inference with no overhead, and (2) an information-theoretic embedding allocation algorithm that effectively balances speed and quality. We empirically test L3 by training transformers with up to 2.6B active parameters and find that L3 strongly outperforms both dense models and iso-sparse MoEs in both language modeling and downstream tasks.