arXiv:2607. 18584v1 Announce Type: new Abstract: We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems.
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We study the inference-time behavior of deep linear encoder-only transformers through the lens of interacting particle systems. In this perspective, tokens are modeled as particles that interact dynamically through successive linear self-attention layers.
arXiv:2501. 18322v2 Announce Type: replace Abstract: Transformers, which are state-of-the-art in most machine learning tasks, represent the data as sequences of vectors called tokens.
arXiv:2609.37921v1 Announce Type: new Abstract: What are the inductive biases of a Transformer architecture? Existing theory on how the forward pass shapes representations either considers whether Tr...
Selective state space models (SSMs) use a recurrence to mix token information, a process analogous to attention in transformers. By modeling token evolution as an ordinary differential equation and applying input‑to‑state stability, the study proves that SSMs exhibit local exponential stability of consensus equilibria and delineates their domain of attraction for time‑varying weight matrices. Experiments on a pretrained Mamba‑2 model reveal that the output gate controls the degree of consensus, preventing tokens from fully converging.
Autoregressive transformers trained on limited trajectories of nonlinear dynamical systems can extrapolate to unseen parameter regimes, reproducing period-doubling cascades, chaotic dynamics, and attractor structures with high fidelity. In the logistic map, the model captures successive period doublings up to period 128, achieving a scaling ratio within $5 imes10^{-4}$ of the Feigenbaum constant. The study also shows how control‑parameter information is processed via attention, shaping the closed‑loop dynamics during training.
arXiv:2601.19567v3 Announce Type: replace-cross Abstract: We address the intrinsic dimensionality (ID) of high-dimensional trajectories, comprising $n_s = 4\,000\,000$ data points, of the Fermi-Pasta...