Graph Machine: Towards Better Pretraining via Edges
cs.LG
Submitted: 2026-09-02
Updated: 2026-09-02
License: http://creativecommons.org/licenses/by/4.0/
The gist: We introduce the Graph Machine (GM), an architecture that maintains an O(n) -sized state and accesses it through sparse, dynamic routing.
Terminology
Abstract
We introduce the Graph Machine (GM), an architecture that maintains an O(n) -sized state and accesses it through sparse, dynamic routing. Unlike methods with fixed-size states or sparse but static routing, GM preserves O(n) complexity in its sparse layers without restricting the potentially accessible state size to O(1). Instead, GM uses edges - pointer-like objects updated differentiably by a referral mechanism resembling pointer chasing. We replace 75% of the dense Transformer layers in Qwen3-0.6B with GM sparse layers and pretrain from scratch on 15.7B tokens. With only 2 of 4,096 tokens retrieved per KV head in each sparse layer, loss degrades only slightly; with 4, the best model marginally improves loss.
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