Beyond N-gram: Data-Aware X-GRAM Extraction for Efficient Embedding Parameter Scaling

Transformers lack a native lookup mechanism, requiring repeated dense computation to recognize and reuse local static patterns. Lngram v1 introduces tokenizer-independent conditional memory through discrete latent n-gram addressing, but its memory capacity is coupled with the backbone width, limiting scalability due to high parameter and activation costs. We propose Lngram v2, which decouples the number of routes, memory dimension, and backbone width, and introduces a context-aware grouped-query attention readout to scale memory capacity independently. A zero-value Sink and counterfactual surrogate gradients further improve readout selectivity and routing trainability while preserving hard discrete addressing. Experiments across vision--language models (VLMs) of different scales show consistent improvements, including successful scaling to a 30B-parameter model. Compared with Lngram v1, Lngram v2 substantially reduces both total and activated memory parameters while maintaining or improving language modeling performance. Further analysis shows that its discrete IDs preserve substantial semantic structure of continuous hidden states, enabling semantic recovery from IDs alone and stable ID--semantic associations across datasets. These results establish Lngram v2 as an efficient and scalable latent conditional memory mechanism whose discrete addresses also provide a structured interface for analyzing internal model representations.

Modern language models represent text using discrete token-level embeddings, which forces recurring multi-token patterns to be learned implicitly across Transformer layers. Both Over-tokenized Transformers and Engram attempt to address this limitation by explicitly incorporating multi-token (n-gram) memories. However, they rely on separate hash tables for each n-gram order, which introduces hash collisions and prevents nested n-grams from sharing the underlying latent structures. To address these issues, we propose Tensorized Engram (TN-gram), a compact memory module that represents tensorized n-gram embeddings through shared factors in the Canonical Polyadic (CP) form. TN-gram learns shared token-position factors together with order-absorption vectors to encode the embeddings of different n-gram order. Comprehensive experiments demonstrate that TN-gram matches or even outperforms Engram-style n-gram modules while requiring much fewer parameters.

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.