SlowGuess/NeurIPS_2023_OCR huggingface dataset:
We investigate the effect of the adaptation process in  $\mathrm{CQD}^{\mathcal{A}}$  by comparing the score of the neural link predictor before and after applying the adaptation layer. As we see from Figure 5, the scores before adaptation have a variation of 5.04 with the boundaries at  $[-8,12]$ . This makes them problematic for complex query answering as discussed in Section 4. The Adapted scores have a smaller variation at 0.03 while the maximum and minimum lie in the  $[0,1]$  range.
B On data efficiency and generalisation of  $\mathbf{CQD}^A$
We conduct a series of experiments comparing the performance of  $\mathrm{CQD}^A$  trained while only using  $1\%$  of the training data to the complete training set in FB15K-237. We see from Figure 6 (top) that the model maintains a strong performance on the complex reasoning task with a 2.4 averaged MRR degradation compared to using the complete data. This phenomenon is even more pronounced when we use only  $1\%$  of the queries while using  $2i$  as our training query types Figure 6 (bottom). In this data and query type constrained mode  $\mathrm{CQD}^A$  maintains competitive performance with a degradation of 2.7 averaged MRR for complex queries compared to training with complete data. This highlights the data-efficient nature of  $\mathrm{CQD}^A$  and shows that training a score adaptation layer does not require significant data for training. This is also accompanied by the observation that  $\mathrm{CQD}^A$  is able to generalise to unseen query types while training only on 2i. This behaviour is not inherent, as seen from Table 4.