The current study of human-machine alignment aims at understanding the
geometry of latent spaces and the correspondence to human representations.
G\"ardenfors' conceptual spaces is a prominent framework for understanding
human representations. Convexity of object regions in conceptual spaces is
argued to promote generalizability, few-shot learning, and intersubject
alignment. Based on these insights, we investigate the notion of convexity of
concept regions in machine-learned latent spaces. We develop a set of tools for
measuring convexity in sampled data and evaluate emergent convexity in layered
representations of state-of-the-art deep networks. We show that convexity is
robust to basic re-parametrization, hence, meaningful as a quality of
machine-learned latent spaces. We find that approximate convexity is pervasive
in neural representations in multiple application domains, including models of
images, audio, human activity, text, and brain data. We measure convexity
separately for labels (i.e., targets for fine-tuning) and other concepts.
Generally, we observe that fine-tuning increases the convexity of label
regions, while for more general concepts, it depends on the alignment of the
concept with the fine-tuning objective. We find evidence that pre-training
convexity of class label regions predicts subsequent fine-tuning performance.

本文探讨了测量人 - 机器对齐中机器学习的潜在空间中概念凸性的方法，并在多个应用领域的深度神经网络中评估了这种_convexity_。研究表明，类标签区域的预训练凸性预测了随后的微调表现。