N-Gram Memories at Two Bits: Quantizing Lookup Tables in Large Language Models

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.

Recent studies introduce conditional memory modules that decouple knowledge storage from neural computation, enabling more direct knowledge access. Compared to MoE, which relies on dynamic computation paths, explicit lookup provides a more efficient knowledge retrieval mechanism. However, these approaches still depend on learned memory embeddings, requiring additional training and limiting flexibility. To address this, we propose N-gram Memory (NGM), a training-free, plug-and-play module composed of a Causal N-Gram Encoder and a Cosine-Gated Memory Injector. The Causal N-Gram Encoder directly averages the pretrained token embeddings of the backbone model to construct N-gram representations, thereby eliminating the need to train separate N-gram embeddings from scratch. This design requires neither an additional memory table nor a retrieval pipeline. The Cosine-Gated Memory Injector then uses a non-parametric cosine gate with ReLU to modulate the retrieved embeddings into the contextual representations. We evaluate NGM on the Qwen3 series from 0.6B to 14B across eight benchmarks. NGM improves average performance by 0.5 to 1.2 points, with particularly clear gains on code generation and knowledge-intensive tasks (e.g., +3.0 on LiveCodeBench and +3.03 on GPQA for Qwen3-14B). Moreover, NGM also improves performance in multimodal benchmarks (e.g., MMStar +1.53 on Qwen3-VL-2B).

Scaling conditional memory offers a promising way to increase language-model capacity, but existing methods such as Engram learn large memory tables from scratch during pre-training, making memory scaling expensive and sometimes ineffective. We propose Memory Grafting, a conditional memory scaling method that utilizes frozen hidden states from a grafting model as conditional n-gram memory. Given frequent local n-grams, we run the grafting model offline, store final-token hidden representations as memory values, and let the recipient model retrieve them through exact longest-match suffix lookup. Retrieved memories are adapted by lightweight projections and gates, while a hash-based Engram fallback preserves coverage for unmatched contexts. Since the grafting model is only run offline and exact lookup has expected O(1) complexity with respect to memory-bank size, Memory Grafting expands external latent capacity with limited training and inference overhead. Experiments under matched recipient architectures and pre-training budgets show that Memory Grafting improves over both MoE and vanilla Engram baselines. In the 2.8B-scale setting, it improves the average benchmark score from 51.95 for MoE and 52.43 for vanilla Engram to 53.86. In the 0.92B-scale setting, all grafting-model variants improve over the baselines, with Qwen3.5-35B-A3B giving the strongest gains. These results suggest that pretrained models can serve as reusable constructors of external latent memory, providing a practical step toward scaling future language models beyond trainable parameters alone.