A Dynamical Systems Equivalence Model of Brain and Transformer-Based Language Models

In this study, a dynamical systems framework for biological neural systems and transformer-based large language models (LLMs) is presented along with a systematic empirical test of brain-transformer representational equivalence across five distinct model architectures. Both the brain and LLMs are formalised as high-dimensional nonlinear state-space dynamical systems, with structural mappings between neural population activity, EEG observables, transformer residual-stream activations, and output logits. Using the ZuCo naturalistic reading (Task-NR) EEG dataset, a layer-wise Representational Similarity Analysis (RSA) and linear encoding modelling are conducted on GPT-2, BERT-Large, Mistral-7B, DeepSeek-7B, and Qwen3.5-9B equipped with a Sparse Autoencoder (SAE). Dense model architectures produced peak RSA alignment of ρ ≈ 0.054-0.055 with EEG theta and alpha bands, and negative cross-validated encoding model R2, indicating a fundamental geometric mismatch between polysemantic dense representations and neural codes. In contrast, sparse, monosemantic SAE features extracted from Qwen3.5-9B yielded a peak RSA alignment of ρ = 0.221 at layer 0 of a 32-layer sweep, representing a 4.3x improvement in biological alignment and saturating the lower noise ceiling (ρ_half = 0.221, ρ_upper = 0.362). The SAE encoding model achieves positive cross-validated R2 (0.15-0.27 across EEG channels), confirming linearly decodable neural predictions. Partial RSA controlling for sentence length and word length yields ρ = 0.044 (p = 1.8 x 10^-26) with a suppressor effect, ruling out surface-level confounds. It is argued that this improvement reflects a deep convergence. Biological brains and SAE-disentangled transformers both implement sparse distributed codes over a high-dimensional state space, and this shared representational geometry underpins the observed equivalence. The results of this study could have implications for AI interpretability, the mechanistic basis of machine psychology, and the neuroscience of semantic processing.