Field-Fusion: Vacancy-Gated Complex Recurrent Fields for Efficient Long-Context Language Modeling

Field-Fusion introduces a hybrid language-model architecture built around an original vacancy-gated complex recurrent operator called the Field. The operator maintains a diagonal complex state, transports it through a learned phase-and-radius carrier, writes bounded complex injections through an input-dependent vacancy, and exposes both the updated resident state and the content displaced during replacement. The physical Theory of the Board served only as a source of computational hypotheses; all claims reported here are mathematical, engineering, and empirical machine-learning claims. The frozen approximately 300M-parameter configuration contains 18 native Field blocks, two official Mamba-2 blocks, four refresh-attention blocks, an output-side Parallel Causal Associative Field (PCAF), and implementation-level boundary corrections. On WikiText-103, using 49.152 million training tokens per model and three paired seeds, Field-Fusion obtained mean test NLL 3.54578 ± 0.00143, compared with 3.56423 ± 0.01190 for a parameter-matched Flash-SDPA Transformer and 3.57711 ± 0.02947 for official Mamba-2. In a prespecified three-seed PG-19 arena, all five approximately parameter-matched systems were trained from initialization on the same document-boundary-safe 2K windows. Field-Fusion without PCAF remained essentially flat from 2K to 64K matched-suffix evaluation, changing from NLL 3.68877 to 3.68862. A 24-layer decoder-only Flash-SDPA Transformer configured with YaRN for 2K-to-64K extension increased from 3.75055 to 5.54830. At 64K, the PCAF-on and PCAF-off Field profiles outperformed the YaRN Transformer by 1.81557 and 1.85968 NLL, respectively. At the ordinary 2K test window, Fields with PCAF remained 0.03824 ± 0.00369 NLL behind official Mamba-2 while delivering 48.5% higher training throughput. The report describes the Field equations, exact chunk-parallel Triton implementation, frozen hybrid topology, experimental protocols, systems measurements from 2K to 64K, negative ablations, the open attention-free research line, limitations, and the provenance of incorporated external techniques. Code and documentation:https://github.com/Multisymboliccore/fields-lm Frozen software release v0.1.0:https://github.com/Multisymboliccore/fields-lm/releases/tag/v0.1.0 Published Fields 300M PG-19 checkpoint:https://huggingface.co/Multisymboliccore/fields-300m-pg19 Exact checkpoint commit:https://huggingface.co/Multisymboliccore/fields-300m-pg19/commit/476fb068b2efd752c983e098afb4a7df565c52dd