# Conditional Memory via Scalable Lookup: A New Axis of Sparsity for Large Language Models

arXiv: https://arxiv.org/abs/2601.07372 · HTML: https://mlsanity.com/paper/2601.07372/

## Key facts

- Cited by 86 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 106 of its 140 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Placed in

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

## Builds on (most cited first, 30 of 106)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [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)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [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)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)

## Built on by (most cited first, 30 of 86)

- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [Externalization in LLM Agents: A Unified Review of Memory, Skills, Protocols and Harness Engineering](https://mlsanity.com/paper/2604.08224/) (2026)
- [On the Design of Qwen3.8-Next Architecture: Evaluation, Efficiency, and Training Stability](https://mlsanity.com/paper/2608.30320/) (2026)
- [Mousse: Rectifying the Geometry of Muon with Curvature-Aware Preconditioning](https://mlsanity.com/paper/2603.09697/) (2026)
- [Scaling Embeddings Outperforms Scaling Experts in Language Models](https://mlsanity.com/paper/2601.21204/) (2026)
- [HRM-Text: Efficient Pretraining Beyond Scaling](https://mlsanity.com/paper/2605.20613/) (2026)
- [UMEM: Unified Memory Extraction and Management Framework for Generalizable Memory](https://mlsanity.com/paper/2602.10652/) (2026)
- [ThinkRouter: Efficient Reasoning via Routing Thinking between Latent and Discrete Spaces](https://mlsanity.com/paper/2602.11683/) (2026)
- [Towards Multimodal Lifelong Understanding: A Dataset and Agentic Baseline](https://mlsanity.com/paper/2603.05484/) (2026)
- [MeKi: Memory-based Expert Knowledge Injection for Efficient LLM Scaling](https://mlsanity.com/paper/2602.03359/) (2026)
- [PM-Bench: Evaluating Prospective Memory in LLM Agents](https://mlsanity.com/paper/2607.12385/) (2026)
- [MSA: Memory Sparse Attention for Efficient End-to-End Memory Model Scaling to 100M Tokens](https://mlsanity.com/paper/2603.23516/) (2026)
- [Kernel-Smith: A Unified Recipe for Evolutionary Kernel Optimization](https://mlsanity.com/paper/2603.28342/) (2026)
- [MoE-SpAc: Efficient MoE Inference Based on Speculative Activation Utility in Heterogeneous Edge Scenarios](https://mlsanity.com/paper/2603.09983/) (2026)
- [Memory Grafting: Scaling Language Model Pre-training via Offline Conditional Memory](https://mlsanity.com/paper/2605.20948/) (2026)
- [go-mHC: Direct Parameterization of Manifold-Constrained Hyper-Connections via Generalized Orthostochastic Matrices](https://mlsanity.com/paper/2604.02309/) (2026)
- [Persistent Visual Memory: Sustaining Perception for Deep Generation in LVLMs](https://mlsanity.com/paper/2605.00814/) (2026)
- [Memory for Large Language Models](https://mlsanity.com/paper/2607.25380/) (2026)
- [LiteToken: Removing Intermediate Merge Residues From BPE Tokenizers](https://mlsanity.com/paper/2602.04706/) (2026)
- [Cram Less to Fit More: Training Data Pruning Improves Memorization of Facts](https://mlsanity.com/paper/2604.08519/) (2026)
- [Mem-π: Adaptive Memory through Learning When and What to Generate](https://mlsanity.com/paper/2605.21463/) (2026)
- [Lngram: N-gram Conditional Memory in Latent Space](https://mlsanity.com/paper/2605.24869/) (2026)
- [Tensorizing Engram: Sharing Latents Across N-Gram Embeddings is Beneficial in LLMs](https://mlsanity.com/paper/2606.08347/) (2026)
- [User as Engram: Internalizing Per-User Memory as Local Parametric Edits](https://mlsanity.com/paper/2606.19172/) (2026)
- [MemSFT: Mitigating Alignment Tax with an External Parametric Memory](https://mlsanity.com/paper/2607.25614/) (2026)
- [Frozen Memory Is Not Enough: Rethinking External Memory as Extraction](https://mlsanity.com/paper/2608.17050/) (2026)
- [A Collision-Free Hot-Tier Extension for Engram-Style Conditional Memory: A Controlled Study of Training Dynamics](https://mlsanity.com/paper/2601.16531/) (2026)
- [L3: Large Lookup Layers](https://mlsanity.com/paper/2601.21461/) (2026)
- [AllMem: A Memory-centric Recipe for Efficient Long-context Modeling](https://mlsanity.com/paper/2602.13680/) (2026)
- [Simple is Better: Multiplication May Be All You Need for LLM Request Scheduling](https://mlsanity.com/paper/2603.15202/) (2026)

## Abstract (arXiv)

While Mixture-of-Experts (MoE) scales capacity via conditional computation, Transformers lack a native primitive for knowledge lookup, forcing them to inefficiently simulate retrieval through computation. To address this, we introduce conditional memory as a complementary sparsity axis, instantiated via Engram, a module that modernizes classic N-gram embedding for O(1) lookup. By formulating the Sparsity Allocation problem, we uncover a U-shaped scaling law that optimizes the trade-off between neural computation (MoE) and static memory (Engram). Guided by this law, we scale Engram to 27B parameters, achieving superior performance over a strictly iso-parameter and iso-FLOPs MoE baseline. Most notably, while the memory module is expected to aid knowledge retrieval (e.g., MMLU +3.4; CMMLU +4.0), we observe even larger gains in general reasoning (e.g., BBH +5.0; ARC-Challenge +3.7) and code/math domains~(HumanEval +3.0; MATH +2.4). Mechanistic analyses reveal that Engram relieves the backbone's early layers from static reconstruction, effectively deepening the network for complex reasoning. Furthermore, by delegating local dependencies to lookups, it frees up attention capacity for global context, substantially boosting long-context retrieval (e.g., Multi-Query NIAH: 84.2 to 97.0). Finally, Engram establishes infrastructure-aware efficiency: its deterministic addressing enables runtime prefetching from host memory, incurring negligible overhead. We envision conditional memory as an indispensable modeling primitive for next-generation sparse models.