The emergence of similar representations between independently trained neural
models has sparked significant interest in the representation learning
community, leading to the development of various methods to obtain
communication between latent spaces. "Latent space communication" can be
achieved in two ways: i) by independently mapping the original spaces to a
shared or relative one; ii) by directly estimating a transformation from a
source latent space to a target one. In this work, we combine the two into a
novel method to obtain latent space translation through the relative space. By
formalizing the invertibility of angle-preserving relative representations and
assuming the scale invariance of decoder modules in neural models, we can
effectively use the relative space as an intermediary, independently projecting
onto and from other semantically similar spaces. Extensive experiments over
various architectures and datasets validate our scale invariance assumption and
demonstrate the high accuracy of our method in latent space translation. We
also apply our method to zero-shot stitching between arbitrary pre-trained text
and image encoders and their classifiers, even across modalities. Our method
has significant potential for facilitating the reuse of models in a practical
manner via compositionality.

通过对相对空间的角度保持相对表示的可逆性进行形式化，并假设神经模型中解码器模块的尺度不变性，我们将两种方法结合起来，通过相对空间获得潜在空间转换的新方法。通过在各种架构和数据集上进行大量实验证实了我们的尺度不变性假设，并证明了我们方法在潜在空间转换中的高准确性。我们还将我们的方法应用于任意预训练文本和图像编码器及其分类器之间的零射缝，甚至跨模态。通过组合性，我们的方法具有促进模型实际重用的显著潜力。