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Rethinking 3D Convolution in $\ell_p$-norm Space

NeurIPS 2024 · Point clouds › Point cloud classification · approach: Local feature aggregation networks · 3 citations (OpenAlex)

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Proposes replacing inner-product 3D convolution with l_p-norm based convolution, mainly l1-norm, with mixed gradient and dynamic learning-rate optimizers, and reports competitive results on ShapeNet, S3DIS and GarmentNets with lower energy.

Problem

Inner-product convolution in 3D backbones can lose features when inputs are symmetric or noisy, and multiplication-heavy operations are costly in energy and latency for point cloud tasks.

Approach

Replace the dot-product similarity in convolution with an l_p-norm distance (especially l1, Manhattan), prove universal approximation for l_p-norm nets, and stabilize l1 training with a mixed gradient strategy (blending sign and linear gradients) plus a dynamic learning-rate controller.

Key results

• On S3DIS, l1-PointNet++ reaches 53.9% mIoU vs 53.5% for PointNet++, with estimated energy 1.328 uJ vs 3.395 uJ.
• On ShapeNet part segmentation, l1-PointNet++ achieves 86.5% mIoU vs 86.2% for PointNet++.
• Ablation on S3DIS shows removing both MGS and DLC drops l1-PointNet++ mIoU from 53.9% to 48.4%... vanilla l1 reaches 38.9% mIoU.

Measured effects reported in the paper

Surprising findings

• Vanilla l1-norm training without the proposed optimizers degrades mIoU substantially (e.g., 38.9% vs 53.9% for l1-PointNet++ with both strategies).
• The authors note the l1-norm Net's inference is marginally slower than the traditional one due to lack of optimized kernels.

Limitations

• Other convolution types (sparse, group, dilated) and additional vision tasks are unexplored.
• Inference speed is marginally slower than traditional convolution due to lack of CUDA/cuDNN optimized Manhattan-distance ops.
• No error bars or multiple seeds reported for statistical significance.

Experimental setup

Datasets: ShapeNet part S3DIS GarmentNets Simulation

Benchmarks: ShapeNet part S3DIS GarmentNets Simulation

Metrics: mIoU overall accuracy energy (uJ) Chamfer distance

Baselines: PointNet PointNet++ 3DCNN GarmentNets

Builds on: PointNet++ PointNet signSGD AdamW GarmentNets

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