POEM: 1-Bit Point-Wise Operations Based on E-M for Point Cloud Processing

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TABLE 6.2

Ablation study on hyperparameters λ and τ. We vary λ

from 1×10⁻³ to 0 and τ from 1×10⁻² to 0, respectively.

We show the overall accuracy (OA) in this table.

1-bit PointNet

λ

1 × 10⁻³

1 × 10⁻⁴

1 × 10⁻⁵

0

τ

1 × 10⁻²

89.3

89.0

86.3

81.9

1 × 10⁻³

88.3

90.2

87.9

82.5

1 × 10⁻⁴

86.5

87.1

85.5

81.4

0

82.7

85.3

83.7

80.1

decrease τ. We get the optimal 1-bit PointNet with POEM with {λ, τ} set as {1×10⁻⁴, 1×

10⁻³}. Hence, we extend this hyperparameter set to the other experiments involved in this

paper.

We also set τ as 1×10⁻³ and plot the growth curve of POEM training accuracies with

different λ and XNOR-Net. Figure 6.7 shows that the 1-bit PointNet obtained by POEM

achieves optimal training accuracy when λ is set as 1×10⁻⁴. Also, with EM-optimized back

propagation, the weight convergence becomes better than XNOR-Net (in purple), as shown

in Fig. 6.7.

Evaluating the components of POEM: In this part, we evaluate every critical part

of POEM to show how we compose the novel and effective POEM. We first introduce our

baseline network by adding a single BN layer ahead of the 1-bit convolutions of XNOR-Net,

which brings about an improvement 2.8% in OA. As shown in Table 6.5, the introduction

of PReLU, EM, and the learnable scale factor improves accuracy by 1.9%, 3.1%, and 3.4%,

respectively, over the baseline network, as shown in the second section of Table 6.5. By

adding all the PReLU, EM and the learnable scale factor, our POEM achieves 7.1% higher

accuracy than the baseline, even surpassing the accuracy of the corresponding real-valued

network.

Compared to merely using the PReLU, the use of our main contributions, EM and

the learnable scale factor, increases the accuracy by 5.2%, which is very significant for the

point cloud classification task. The 1-bit PointNet achieves the performance, which even

approaches the real-valued PointNet++ baseline within 2.0% (90.2% vs. 91.9%).

FIGURE 6.7

Training accuracies of POEM (τ = 1 × 10⁻³) with different λ and XNOR-Net.