We introduce a new construction of embeddings of arbitrary recursive data structures into high dimensional vectors. These embeddings provide an interpretable model for the latent state vectors of transformers. We demonstrate that these embeddings can be decoded to the original data structure when the embedding dimension is sufficiently large. This decoding algorithm has a natural implementation as a transformer. We also show that these embedding vectors can be manipulated directly to perform computations on the underlying data without decoding. As an example we present an algorithm that constructs the embedded parse tree of an embedded token sequence using only vector operations in embedding space.

翻译：我们提出一种将任意递归数据结构嵌入到高维向量的新构造方法。这些嵌入为Transformer的潜在状态向量提供了可解释的模型。我们证明当嵌入维度足够大时，这些嵌入可被解码为原始数据结构。该解码算法具有作为Transformer的自然实现。我们还展示了这些嵌入向量可直接进行操控，无需解码即可对底层数据执行计算。作为示例，我们提出一种算法，该算法仅使用嵌入空间中的向量运算即可构建嵌入令牌序列的解析树。