DynImmune-BERT: Dynamic Immune Repertoire Modeling with Neural ODE Driven Continuous Transformers

Event-Based Models (EBMs) infer biomarker progression from cross-sectional data but typically only as ordinal sequences and rely on rigid model assumptions. We propose \textsc{Tempo}, a Transformer architecture that learns both ordinal and continuous event sequences through simulation-based supervised learning. \textsc{Tempo} uses two Transformer modules: one treats biomarkers as tokens to infer event sequencing; the other treats patients as tokens, representing each by their per-biomarker abnormality profile, to infer patients' disease stages. On synthetic benchmarks, \textsc{Tempo} reduces normalized Kendall's Tau distance by 52.89% and staging MAE by 25.33% compared to state-of-the-art SA-EBM, with larger reductions in high-dimensional settings (58.88% and 61.10%). Applied to ADNI, \textsc{Tempo} recovers a biologically plausible Alzheimer's progression: early medial temporal atrophy, followed by amyloid accumulation and cognitive decline, and late-stage tau pathology with terminal acceleration of global neurodegeneration -- broadly consistent with established disease models. \textsc{Tempo} also eliminates the need to derive custom inference algorithms and enables rapid empirical comparison of generative hypotheses.

Accurately predicting the temporal evolution of clinical biomarkers is crucial for the early diagnosis and management of neurodegenerative diseases such as Alzheimer's disease. However, this relies on longitudinal data to capture biomarker changes over time, which is often sparse and irregular due to the high cost, labor-intensive nature, and patient burden. To address these challenges, we propose ENC-ODE, an Event-level Neurodegenerative modeling in Continuous time with neural Ordinary Differential Equations. ENC-ODE predicts future biomarker evolution by modeling clinical events through diagnosis-conditioned continuous dynamics. A target-conditioned attention mechanism weights and aggregates event-level predictions for the target time and modality without history compression. Extensive experiments on Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate that ENC-ODE outperforms representative sequence models while offering a scalable and neuroscientifically grounded solution for clinical support. The code is available at https://github.com/JardinDelSol/enc-ode.

Existing sequence models, including RNNs, LSTMs, continuous-time networks, and Transformers, share a common structural principle: layer-wise dynamics, where all neurons in the same layer co-evolve through a shared parameterized operator, leaving individual neurons no freedom to evolve independently. Yet in many complex dynamical systems, rich global behavior emerges precisely from locally evolving units interacting through structured connectivity. Inspired by this principle, we introduce Topological Neural Dynamics (TND), a sequence modeling framework that shifts computation from layer-wise to neuron-wise dynamics. TND represents a neural system as a directed neuron graph, an interaction operator, and a local dynamics function, where each neuron evolves independently and collective computation emerges from interactions through the explicit graph topology. We instantiate TND as a discrete-time graph-coupled dynamical system and evaluate it as a case study on a behavior cloning task in single-player Pong. Compared with Vanilla RNN, Sparse RNN, LSTM, Closed-form continuous-time neural network (CfC), and Transformer baselines, TND achieves the best catch rate and a mean of 17.47 consecutive catches per round, more than three times that of the strongest baseline. These results suggest that shifting from layer-wise to neuron-wise dynamics provides an effective inductive bias for sequence modeling.