Attention-based Iterative Decomposition for Tensor Product Representation

TL;DR

This work addresses the challenge of incomplete decomposition in Tensor Product Representations (TPR) that hinders systematic generalization. It introduces Attention-based Iterative Decomposition (AID), a slot-based competitive-attention module that iteratively binds input features to TPR roles and fillers, with a context-dependent routing mechanism to map components to symbols. By integrating AID into TPR-RNN, Fast Weight Memory, and Linear Transformer architectures, the paper demonstrates consistent improvements across synthetic SAR, systematic bAbI, Sort-of-CLEVR, and WikiText-103 tasks, supported by disentanglement and orthogonality analyses. The findings indicate that better decomposition yields more compositional, well-bound representations and enhances generalization to unseen compositions, with practical implications for scalable, real-world applications of TPR-based models.

Abstract

In recent research, Tensor Product Representation (TPR) is applied for the systematic generalization task of deep neural networks by learning the compositional structure of data. However, such prior works show limited performance in discovering and representing the symbolic structure from unseen test data because their decomposition to the structural representations was incomplete. In this work, we propose an Attention-based Iterative Decomposition (AID) module designed to enhance the decomposition operations for the structured representations encoded from the sequential input data with TPR. Our AID can be easily adapted to any TPR-based model and provides enhanced systematic decomposition through a competitive attention mechanism between input features and structured representations. In our experiments, AID shows effectiveness by significantly improving the performance of TPR-based prior works on the series of systematic generalization tasks. Moreover, in the quantitative and qualitative evaluations, AID produces more compositional and well-bound structural representations than other works.

Figures (13)

• Figure 1: Overview of AID assisted TPR decomposition. We illustrate the overall operations of the AID-assisted part of the TPR-based model (with $N_{\text{inputs}}=5$ and $N_{\text{com}}=3$). In the natural language task, each input feature is a word vector for the sentence-level TPR models, while input features are $N_{\text{inputs}}$ sub-vectors partitioned from the word vector for the word-level TPR models. From those input features, the initial TPR components are obtained with a linear projection, and routed to structural representation slots of AID which iteratively decomposes TPR components with a competitive attention mechanism.
• Figure 2: Test accuracy curve [%] on the SAR task for 10 seeds with varying values of $p$. As $p$ increases, the models can learn more combinatorial information of data during training.
• Figure 3: The heatmap for the cosine similarity between roles on the SAR task.
• Figure 4: The heatmap for the cosine similarity between roles (x-axis) and unbinding operators (y-axis) on the SAR task.
• Figure 5: Test accuracy over different settings on the SAR task for 10 seeds. (a) Varying $N_{\text{inputs}}$ with $N_{\text{iters}}=2$. (b) Varying training iterations with $N_{\text{inputs}}=3$. (c) Varying test iterations for the models trained with $N_{\text{inputs}}=3$ and $N_{\text{iters}}=5$.