Paper:
RNNS IMPLICITLY IMPLEMENT TENSOR-PRODUCT REPRESENTATIONS
Recurrent neural networks (RNNs) can learn continuous vector representations of symbolic structures such as sequences and sentences; these representations often exhibit linear regularities (analogies). Such regularities motivate our hypothesis that RNNs that show such regularities implicitly compile symbolic structures into tensor product representations (TPRs; Smolensky, 1990), which additively combine tensor products of vectors representing roles (e.g., sequence positions) and vectors representing fillers (e.g., particular words). To test this hypothesis, we introduce Tensor Product Decomposition Networks (TPDNs), which use TPRs to approximate existing vector representations. We demonstrate using synthetic data that TPDNs can successfully approximate linear and tree-based RNN autoencoder representations, suggesting that these representations exhibit interpretable compositional structure; we explore the settings that lead RNNs to induce such structuresensitive representations. By contrast, further TPDN experiments show that the representations of four models trained to encode naturally-occurring sentences can be largely approximated with a bag of words, with only marginal improvements from more sophisticated structures. We conclude that TPDNs provide a powerful method for interpreting vector representations, and that standard RNNs can induce compositional sequence representations that are remarkably well approximated by TPRs; at the same time, existing training tasks for sentence representation learning may not be sufficient for inducing robust structural representations.

Review:
This paper presents an analysis of popularly-use RNN model for structure modeling abilities by designing Tensor Product Decomposition Networks to approximate the encoder. The results show that the representations exhibit interpretable compositional structure. To provide better understanding, the paper evaluates the performance on synthesized digit sequence data as well as several sentence-encoding tasks.
Pros:
1. The paper is well-written and easy to follow. The design of the TPDN and corresponding settings (including what an filler is and what roles are included) for experiments are understandable. It makes good point at the end of the paper (section 4) on how these analysis contribute to further design of RNN models, which seems useful.
2. The experiments are extensive to support their claims. Not only synthetic data but also several popularly-used data and models are being conducted and compared. An addition of analogy dataset further demonstrate the effect of TPDN on modeling structural regularities.
Cons:
1. More detailed and extensive discussion on the contribution of the paper should be included in the introduction part to help readers understand what's the point of investigating TPDN on RNN models.
2. Some details are missing to better understand the construction. For example, on page 4, Evaluation, it is unclear of how TPDN encoder is trained, specifically, which parameters are updated? What's the objective for training? It is also unclear of whether the models in Figure 3(c) use bidirectional or unidirectional or tree decoder? In Section 3, it could be better to roughly introduce each of the existing 4 models. How do TPDN trained for these 4 sentence encoding models need to be further illustrated. More reasons should be discussed for the results in Table 2 (why bag-of-words role seem to be ok, why skip-thought cannot be approximated well).
3. It could be better to provide the actual performance (accuracy) given by TPDN on the 4 existing tasks.
4. Further thoughts: have you considered applying these analysis on other models besides RNN?