Title: Improving Out-of-distribution Generalization with Indirection Representations. Abstract: We propose a generic module named Indirection Layer (InLay), which leverages indirection and data internal relationships to effectively construct symbolic indirect representations to improve out-of-distribution generalization capabilities of various neural architectures. InLay receives data input in the form of a sequence of objects, treats it as a complete weighted graph whose vertices are the objects and edge weights are scalars representing relationships between vertices. The input is first mapped via indirection to a symbolic graph with data-independent and trainable vertices. This symbolic graph is then propagated, resulting in new vertex features whose indirection will be used for prediction steps afterward. Theoretically, we show that the distances between indirection representations are bounded by the distances between corresponding graphs, implying that unseen samples with very different surface statistics can still be close in the representation space to the seen samples if they share similar internal relationships. We demonstrate that InLay is consistently effective in improving out-of-distribution generalization throughout a comprehensive suite of experiments, including IQ problems, distorted image classification, and few-shot domain adaptation NLP classification. We also conduct ablation studies to verify different design choices of InLay.