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arXiv:2608. 08922v1 Announce Type: cross Abstract: Transformer layers generate state-dependent interaction networks: token representations determine the attention matrix, which in turn updates the representations.
arXiv:2607. 24502v1 Announce Type: cross Abstract: Rotary position embeddings (RoPE) modify attention scores through position-dependent rotations, but their effect on normalized token dynamics is not captured by the vanilla spherical self-attention model.
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.
The paper investigates the training dynamics of attention mechanisms in high-dimensional settings, focusing on attention-indexed models that encompass multi-layer and multi-head architectures. It shows that while the loss landscape can be described by a finite set of trace order parameters, the online stochastic gradient descent dynamics involve an infinite hierarchy of matrix moments that can be accurately approximated by a finite truncated system. The study further reveals that the choice of attention parameterization acts as an implicit bias: untied attention can get trapped in uninformative states, whereas tied attention induces symmetry breaking and enables weak recovery with θ(d² log d) samples, and untied attention exhibits a fast-slow dynamic leading to weak recovery when symmetry is broken.
arXiv:2609.24202v1 Announce Type: new Abstract: Sparse attention reduces the quadratic cost of global self-attention while retaining strong empirical performance, but how its restricted interactions...
arXiv:2606. 11585v1 Announce Type: new Abstract: We introduce Kuramoto attention, a self-attention layer in which each hidden coordinate is an angle.