SlowGuess/NeurIPS_2023_OCR huggingface dataset:
To further investigate our proposed model components, we conduct additional ablation experiments in Tab. 8. In  $②$ ,  $③$  and  $④$ , both Poincaré distance and  $L_{sd}$  are proposed to encourage sharper part concept activation. Each of these two modules can be used individually to obtain performance gains  $(+3.7\%)$  vs  $+8.5\%$ ,  $+5.1\%$  vs  $+7.4\%$  and they can be used together to achieve an even bigger improvement  $(+9.5\%)$  vs  $+15.2\%$  Without Poincaré distance and  $L_{sd}$ , using  $L_{sc}$  and  $L_{cd}$  alone can only achieve minor improvements as shown in  $⑤$  and  $⑥$ . This is because that part concepts are less diverse and tend to encode the global feature of known classes that are hard to be generalized to novel classes. Since novel shapes may contain new part concepts that are not present in known classes, we concatenate the local part features  $Z_{l}$  with the part composite features  $Z_{p}$ . As shown in  $⑧$ , this design can obtain better results on low-similarity novel classes  $(+0.7\%)$  vs  $+1.8\%$  We also evaluate the performance of only using the PRE module as shown in the  $⑩$ . The results show that using PRE alone can already achieve considerable performance gains (4.75% on average).
Ablation on different known classes number. Training on more known categories can certainly benefit novel class discovery. As shown in Tab.9, increasing the number of known classes leads to improved performance. Because with multiple categories we can learn more diverse part concepts that further will help us recognize novel objects better. In the table below, we evaluated the performance by training the method with an increasing number of known categories and the fixed number of novel categories. The results show that training the method with more categories does enhance the recognition of novel shapes.
C Different Backbones
We inspect how different network backbones impact the performance of 3D NCD. The comparisons are conducted on three popular 3D backbones including PointNet++ [25], DGCNN [37], and PointNeXt [26]. Among them, the PointNeXt achieves state-of-the-art performance for 3D classification and segmentation. We replace the backbone of compared methods with the above network architec
Table 8: Ablation experiments. PCB means part concept bank. LGA, Poincaré, Concat and PRE are local geometric aggregation, Poincaré distance, concatenate the local part features  $Z_{l}$  and position relation encoder as shown in Fig. 2.
LGA	PCB	Poincaré	Lsd	Lsc	Lcd	Concat	PRE	High	Low
①	✓	✓	✓	58.4	48.7
②	✓	✓	✓	✓	62.1	57.2
③	✓	✓	✓	✓	63.5	56.1
④	✓	✓	✓	✓	✓	67.9	63.9
⑤	✓	✓	✓	✓	60.1	51.5
⑥	✓	✓	✓	✓	59.8	49.3
⑦	✓	✓	✓	✓	✓	✓	70.6	63.3
⑧	✓	✓	✓	✓	✓	✓	✓	71.3	65.1
⑨	48.8	37.8
⑩	✓	52.4	43.7
⑩	✓	✓	✓	✓	✓	✓	✓	✓	73.2	66.4
Table 9: The results of different known class number.
ModelNet	5-10	10-10	20-10	30-10
Novel Acc	57.9	61.3	64.0	66.2
tures and evaluate their performance on the ModelNet high similarity task. The results are shown in Tab. 10. the known class accuracy of the same 3D NCD method on different backbones does not vary too much (within  $1\%$ ). On the other hand, the backbone has a significant influence on the novel-class performance for all the compared methods. For example, the weaker backbone DGCNN can achieve better novel class accuracy than the other two backbones. This is because DGCNN uses graphs to represent the local features of the point cloud, thus increasing the feature generalization on novel classes. Our method can surpass all the baselines by a very large margin (at least  $+8.9\%$  ) on the novel-class accuracy even using a weak backbone (PointNet), while attaining comparable good performance on the known-class recognition. This superiority is primarily attributed to the part concept-based features that are more generalizable to novel classes than other backbones.
Table 10: The accuracy results of different backbones on the similarity split 3D NCD task. High, Low denote the novel classes have High, Low semantic similarity with known classes.
PointNeXt	PointNet++	DGCNN
High	Low	Known	High	Low	Known	High	Low	Known
DTC [9]	43.8	32.6	93.9	50.9	44.4	94.3	51.3	38.0	94.6
AutoNovel [10]	51.6	46.5	96.0	59.0	43.4	96.7	49.0	40.9	96.7
NCL [48]	59.9	46.5	95.9	51.3	37.6	97.0	64.3	44.9	95.1
UNO [7]	61.6	32.9	95.8	53.0	43.2	93.0	62.9	45.6	96.7
IIC [19]	62.3	49.7	95.3	57.6	46.0	94.6	64.0	51.8	96.8
Kmeans+	61.2	50.9	96.4	55.2	40.7	96.2	64.0	45.5	92.3
Ours (PointNet)	73.2	66.4	95.2	73.2	66.4	95.2	73.2	66.4	95.2
Improvement	+10.9	+15.5	-1.2	+14.2	+20.4	-1.8	+8.9	+14.6	-1.6
Ours (PointNet++)	73.2	66.4	95.2	73.2	66.4	95.2	73.2	66.4	95.2
Improvement	+10.9	+15.5	-1.2	+14.2	+20.4	-1.8	+8.9	+14.6	-1. 6
Ours (DGCNN)	73.2	66.4	95.2	73.2	66.4	95.2	73.2	66.4	95.2
Improvement	+10.9	+15.5	-1.2	+14.2	+20.4	-1.8	+8.9	+14.6	-1 . 6
D Results on Large-Scale Datasets
The large-scale 3D datasets (MVimgNet [43]) are available and we conduct an MVimgNet50-100 task as shown in the Tab.11. In this task, we selected 50 classes as known classes and another 100 classes as novel classes from the large-scale MVimgNet dataset. Despite the challenges when increasing the number of unknown classes, our method can still outperform baselines by a large margin.
Table 11: The results on large-scale datasets.
Novel	Known
AutoNovel [10]	12.8	47.8
NCL [48]	11.3	53.9
UNO [7]	10.7	44.3
IIC [19]	12.5	58.2
Ours	43.9	64.0
Improvement	+31.1	+5.8
E Estimate Cluster Numbers
We fixed the number of unseen classes following the baseline methods [10]. However, the number of novel classes can be estimated by following the strategy in AutoNovel [10] and GCD [35], where semi-supervised k-means and a validation set can be used to select the optimal number of unseen classes. We estimate the number of clusters using the above method on the ModelNet similarity task as shown in Tab. 12. The results show the estimation method may slightly underestimate the novel class number when similarities between novel classes and known classes are high. This is because some highly related classes are clustered together. Meanwhile, it slightly overestimates the number of novel classes when similarities decrease.
Table 12: Estimate cluster numbers on modelnet dataset.
High	Medium	Low
Ground Truth	26	27	27
Ours	24	30	31
In all experiments, we adopt PointNet [24] as the backbone for point-wise feature learning and sample 1024 points from the original point clouds as inputs. We use scaling, rotation, jittering, and translation as data augmentation to generate two augmented point clouds for both labeled and unlabeled inputs respectively during training. The network is optimized with the Adam optimizer with an initial learning rate of 0.001. In our experiments, we first train the network for 30 epochs with labeled dataset  $D^{l}$  to learn the part concept bank, then we train all networks for another 220 epochs with both labeled and unlabeled datasets. We specify both the feature vector size  $D$  and the dimension of the part concepts to 256. The overall method is implemented in PyTorch, and we conduct all experiments on a computer with an NVIDIA Tesla V100 GPU. Our method takes 1.26M parameters, 14.7G memory cost and 0.43s train time per batch measured on ModelNet. Readers are encouraged to refer to the released code for detailed implementation.