CAT: Curvature-Adaptive Transformers for Geometry-Aware Learning

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic and spherical spaces show promise for hierarchical and cyclical patterns, respectively, they require committing to a single geometry a priori, reducing flexibility when data exhibits mixed geometric properties. We introduce the Curvature-Adaptive Transformer (CAT), a novel architecture that dynamically learns per-token routing across three geometric attention branches through a lightweight, differentiable gating mechanism. Unlike fixed-geometry approaches, CAT enables adaptive geometric specialization, routing tokens to the appropriate curvature based on their local relational structure. The routing network provides interpretable curvature preferences while each branch employs geometry-specific operations optimized for its respective manifold. On knowledge graph completion benchmarks (FB15k-237, WN18RR), CAT achieves approximately 10% improvements in MRR and Hits@10 over fixed-geometry baselines with minimal overhead (5% parameter increase, comparable inference time). These results demonstrate that learned geometric adaptation outperforms any single fixed geometry for complex relational reasoning, establishing CAT as a scalable and interpretable foundation for mixture-of-geometry architectures across language, vision, and multimodal domains.

Describe-and-Dissect: Interpreting Neurons in Vision Networks with Language Models

In this paper, we propose Describe-and-Dissect (DnD), a novel method to describe the roles of hidden neurons in vision networks. DnD utilizes recent advancements in multimodal deep learning to produce complex natural language descriptions, without the need for labeled training data or a predefined set of concepts to choose from. Additionally, DnD is training-free, meaning we don't train any new models and can easily leverage more capable general purpose models in the future. We have conducted extensive qualitative and quantitative analysis to show that DnD outperforms prior work by providing higher quality neuron descriptions. Specifically, our method on average provides the highest quality labels and is more than 2 times as likely to be selected as the best explanation for a neuron than the best baseline.