A Linear Time and Space Local Point Cloud Geometry Encoder via Vectorized Kernel Mixture (VecKM)

We propose VecKM, a novel local point cloud geometry encoder that is descriptive, efficient and robust to noise. VecKM leverages a unique approach by vectorizing a kernel mixture to represent the local point clouds. Such representation is descriptive and robust to noise, which is supported by two theorems that confirm its ability to reconstruct and preserve the similarity of the local shape. Moreover, VecKM is the first successful attempt to reduce the computation and memory costs from $O(n^2+nKd)$ to $O(nd)$ by sacrificing a marginal constant factor, where $n$ is the size of the point cloud and $K$ is neighborhood size. The efficiency is primarily due to VecKM's unique factorizable property that eliminates the need of explicitly grouping points into neighborhoods. In the normal estimation task, VecKM demonstrates not only 100x faster inference speed but also strongest descriptiveness and robustness compared with existing popular encoders. In classification and segmentation tasks, integrating VecKM as a preprocessing module achieves consistently better performance than the PointNet, PointNet++, and point transformer baselines, and runs consistently faster by up to 10x.

Decodable and Sample Invariant Continuous Object Encoder

We propose Hyper-Dimensional Function Encoding (HDFE). Given samples of a continuous object (e.g. a function), HDFE produces an explicit vector representation of the given object, invariant to the sample distribution and density. Sample distribution and density invariance enables HDFE to consistently encode continuous objects regardless of their sampling, and therefore allows neural networks to receive continuous objects as inputs for machine learning tasks, such as classification and regression. Besides, HDFE does not require any training and is proved to map the object into an organized embedding space, which facilitates the training of the downstream tasks. In addition, the encoding is decodable, which enables neural networks to regress continuous objects by regressing their encodings. Therefore, HDFE serves as an interface for processing continuous objects. We apply HDFE to function-to-function mapping, where vanilla HDFE achieves competitive performance as the state-of-the-art algorithm. We apply HDFE to point cloud surface normal estimation, where a simple replacement from PointNet to HDFE leads to immediate 12% and 15% error reductions in two benchmarks. In addition, by integrating HDFE into the PointNet-based SOTA network, we improve the SOTA baseline by 2.5% and 1.7% in the same benchmarks.

Gluing Neural Networks Symbolically Through Hyperdimensional Computing

Hyperdimensional Computing affords simple, yet powerful operations to create long Hyperdimensional Vectors (hypervectors) that can efficiently encode information, be used for learning, and are dynamic enough to be modified on the fly. In this paper, we explore the notion of using binary hypervectors to directly encode the final, classifying output signals of neural networks in order to fuse differing networks together at the symbolic level. This allows multiple neural networks to work together to solve a problem, with little additional overhead. Output signals just before classification are encoded as hypervectors and bundled together through consensus summation to train a classification hypervector. This process can be performed iteratively and even on single neural networks by instead making a consensus of multiple classification hypervectors. We find that this outperforms the state of the art, or is on a par with it, while using very little overhead, as hypervector operations are extremely fast and efficient in comparison to the neural networks. This consensus process can learn online and even grow or lose models in real time. Hypervectors act as memories that can be stored, and even further bundled together over time, affording life long learning capabilities. Additionally, this consensus structure inherits the benefits of Hyperdimensional Computing, without sacrificing the performance of modern Machine Learning. This technique can be extrapolated to virtually any neural model, and requires little modification to employ - one simply requires recording the output signals of networks when presented with a testing example.