A Unifying View of Attention Sinks: Two Algorithms, Two Solutions

When attention concentrates on a single token, a sink, what is the model actually computing? Attention sinks are ubiquitous in softmax transformers, yet this shared visual signature can hide fundamentally different algorithms. We show that visually similar sink patterns can reflect two distinct mechanisms: {i} adaptive nop, where a head suppresses its update by routing to a null token, and {ii} broadcast, where a sink aggregates and redistributes global information. In that case, sinks serve an analogous role: a safe destination when there is nothing useful to compute. Proposed interventions like gating or registers work because they implicitly target one or the other, revealing a duality between method and assumed mechanism: gating implicitly assumes nop; registers implicitly assume broadcast. Each mechanism leaves distinct traces (nop sinks exhibit negligible value norms; broadcast sinks induce low-rank outputs) which we formalize on synthetic tasks and use to derive practical diagnostics. Applied to pretrained vision transformers, these diagnostics reveal that both mechanisms exist at scale: sinks transition from CLS in early layers to patches in deeper layers, and concentrate in specialized heads. Strikingly, register tokens, designed for broadcast, are repurposed to also serve nop, confirming that neither intervention alone suffices. Combining gating with registers yields complementary gains in stability and performance. Overall, we find that the same attention pattern can reflect two very different computations and effective intervention requires first asking what the model is actually computing.

Latent Traversals in Generative Models as Potential Flows

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data.