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Kelly Cui

Publications and source records attributed to Kelly Cui.

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The Dual Mechanisms of Spatial Variable Binding in Vision-Language Models

Many multimodal tasks, such as image captioning and visual question answering, require vision-language models (VLMs) to bind objects with their properties and spatial relations. Yet it remains unclear where and how such associations are computed within VLMs. In this work, we show that VLMs rely on two concurrent mechanisms to represent spatial variable binding. In the language model backbone, intermediate layers represent content-independent spatial relations on top of visual tokens corresponding to objects. However, this mechanism plays only a secondary role in shaping model predictions. Instead, the dominant source of spatial information originates in the vision encoder, whose representations encode the layout of objects and are directly exploited by the language model backbone. Notably, this spatial signal is distributed globally across visual tokens, extending beyond object regions into surrounding background areas. We show that enhancing these vision-derived spatial representations globally across all image tokens improves spatial variable binding performance across models of various sizes on complex natural images from the COCO datasets. Together, our results clarify how spatial variable binding is computed within VLMs and highlight the central role of vision encoders in enabling it.

cs.CV

Ulam Sets in New Settings

The classical Ulam sequence is defined recursively as follows: $a_1=1$, $a_2=2$, and $a_n$, for $n > 2$, is the smallest integer not already in the sequence that can be written uniquely as the sum of two distinct earlier terms. This sequence is known for its mysterious quasi-periodic behavior and its surprising rigidity when we let $a_2$ vary. This definition can be generalized to other sets of generators in different settings with a binary operation and a valid notion of size. Since there is not always a natural linear ordering of the elements, the resulting collections are called Ulam sets. In this paper, we study Ulam sets in new settings. First, we investigate the structure of canonical Ulam sets in free groups; this is the first investigation of Ulam sets in noncommutative groups. We prove several symmetry results and prove a periodicity result for eventually periodic words with fixed prefixes. Then, we study Ulam sets in $\mathbb{Z}\times (\mathbb{Z}/n\mathbb{Z})$ and prove regularity for an infinite class of initial sets. We also examine an intriguing phenomenon about decompositions of later elements into sums of the generators. Finally, we consider $\mathcal{V}$-sets, a variant where the summands are not required to be distinct; we focus on $\mathcal{V}$-sets in $\mathbb{Z}^2$.

math.CO