The paper investigates causal self‑attention dynamics in decoder Transformers, modeling them as a non‑exchangeable interacting particle system. Using cumulant expansions and Glauber calculus, the authors prove a quantitative mean‑field limit and a next‑order correlation characterization. For i.i.d. uniformly distributed tokens, they solve the limiting correlation equation in closed form and rigorously explain the empirically observed lost‑in‑the‑middle phenomenon, showing a U‑shaped token retrieval profile with primacy, recency, and a unique interior minimum under a smallness condition.
arXiv:2605. 10931v2 Announce Type: replace-cross Abstract: Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models.
arXiv:2607. 15449v1 Announce Type: new Abstract: Using the language of Wilsonian renormalization group theory (RG), we treat the Transformer's attention mechanism as a perturbation of the trained MLP residual-stack fixed point and ask whether it constitutes a relevant, marginal, or irrelevant operator.
arXiv:2610.17347v1 Announce Type: cross Abstract: We revisit the statistical mechanics of Transformer attention via modern Hopfield models. We present a free-energy formalism to characterize paramete...
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.
The paper introduces a Mixture‑Gated Theory of Anisotropic Representation Dynamics that decomposes Transformer self‑attention into value transport, query gating, and key gating. It shows that the geometry of attended representations can cause a representation difference to contract or expand, a phenomenon termed gating‑induced regime switching. The authors derive a spectral criterion to predict switching, quantify its strength, and identify subspaces where switching occurs, validating these predictions experimentally across four Transformer architectures.
arXiv:2610.23242v2 Announce Type: replace Abstract: Small differences between internal representations can shrink or grow as they pass through a Transformer layer, affecting how information is preser...
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.
arXiv:2609.36230v1 Announce Type: new Abstract: We study the dynamical behavior of tokens in transformers from a control-theoretic perspective. Our model includes the feed-forward layer present after...
arXiv:2604. 09560v2 Announce Type: replace Abstract: Softmax attention is the row-normalized operator of a diffusion map: both normalize a learned score into a Markov operator, and differ only in what the score is allowed to contain.
arXiv:2608. 03629v1 Announce Type: new Abstract: A companion paper studies when activation patching and weight-space ablation agree, inside an idealized model where a conditional computation is carried additively through a residual stream.
The paper investigates attention sinks—tokens or positions that attract disproportionate attention—in text-to-image transformers, comparing bidirectional diffusion models and causal autoregressive models. It finds that both model types exhibit attention sinks, but with distinct patterns: autoregressive models focus on the first and global tokens, while diffusion models develop sinks near modality boundaries, within text regions, and at spatial corners. Perturbation experiments show that sink-related heads influence generation more than non-sink heads, and introducing register tokens can redistribute attention without harming performance.
arXiv:2606. 29139v1 Announce Type: new Abstract: We study how the next-token prediction of an autoregressive Transformer language model changes under small perturbations of earlier input token embeddings.