Welcome!

I’m a researcher at the Computer Vision Laboratory, Linköping University, Sweden, where I earned my PhD in Computer Vision, with a focus on Geometric Deep Learning, supervised by Michael Felsberg and funded by WASP. You can find more details in my CV. My research interests include equivariant neural networks, AI for Science, and AI for Good. I am currently exploring postdoctoral opportunities and welcome any inquiries.

Interests
  • Geometric Deep Learning
  • Computer Vision
  • AI for Science
  • AI for Good
Education

  • PhD in Computer Vision (Geometric Deep Learning), 2024

    Linköping University (Sweden)

  • Master of Engineering in Computer Science and Technology, 2019

    Hunan University (China)

  • Bachelor in Information Security Systems, 2016

    Donetsk National Technical University (Pokrovsk, Ukraine)

News

My PhD Defense

On this day, I defended my PhD thesis on “Spherical Neur$\text{O}(n)$s for Geometric Deep Learning”.

Featured Publications
O$n$ Learning Deep O$(n)$ Equivariant Hyperspheres
Equivariance

O$n$ Learning Deep O$(n)$ Equivariant Hyperspheres

In this paper, we utilize hyperspheres and regular $n$-simplexes and propose an approach to learning deep features equivariant under the transformations of $n$D reflections and rotations, encompassed by the powerful group of $\text{O}(n)$. Namely, we propose $\text{O}(n)$-equivariant neurons with spherical decision surfaces that generalize to any dimension $n$, which we call Deep Equivariant Hyperspheres. We demonstrate how to combine them in a network that directly operates on the basis of the input points and propose an invariant operator based on the relation between two points and a sphere, which as we show, turns out to be a Gram matrix. Using synthetic and real-world data in $n$D, we experimentally verify our theoretical contributions and find that our approach is superior to the competing methods for $\text{O}(n)$-equivariant benchmark datasets (classification and regression), demonstrating a favorable speed/performance trade-off.

TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis
Point Clouds

TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis

In many practical applications 3D point cloud analysis requires rotation invariance. In this paper we present a learnable descriptor invariant under 3D rotations and reflections i.e. the O(3) actions utilizing the recently introduced steerable 3D spherical neurons and vector neurons. Specifically we propose an embedding of the 3D spherical neurons into 4D vector neurons which leverages end-to-end training of the model. In our approach we perform TetraTransform—an equivariant embedding of the 3D input into 4D constructed from the steerable neurons—and extract deeper O(3)-equivariant features using vector neurons. This integration of the TetraTransform into the VN-DGCNN framework termed TetraSphere negligibly increases the number of parameters by less than 0.0002%. TetraSphere sets a new state-of-the-art performance classifying randomly rotated real-world object scans of the challenging subsets of ScanObjectNN. Additionally TetraSphere outperforms all equivariant methods on randomly rotated synthetic data: classifying objects from ModelNet40 and segmenting parts of the ShapeNet shapes. Thus our results reveal the practical value of steerable 3D spherical neurons for learning in 3D Euclidean space.

Steerable 3D Spherical Neurons
Steerability

Steerable 3D Spherical Neurons

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings.

Embed Me If You Can: A Geometric Perceptron
Conformal Embedding

Embed Me If You Can: A Geometric Perceptron

Solving geometric tasks involving point clouds by using machine learning is a challenging problem. Standard feed-forward neural networks combine linear or, if the bias parameter is included, affine layers and activation functions. Their geometric modeling is limited, which motivated the prior work introducing the multilayer hypersphere perceptron (MLHP). Its constituent part, i.e., the hypersphere neuron, is obtained by applying a conformal embedding of Euclidean space. By virtue of Clifford algebra, it can be implemented as the Cartesian dot product of inputs and weights. If the embedding is applied in a manner consistent with the dimensionality of the input space geometry, the decision surfaces of the model units become combinations of hyperspheres and make the decision-making process geometrically interpretable for humans. Our extension of the MLHP model, the multilayer geometric perceptron (MLGP), and its respective layer units, i.e., geometric neurons, are consistent with the 3D geometry and provide a geometric handle of the learned coefficients. In particular, the geometric neuron activations are isometric in 3D, which is necessary for rotation and translation equivariance. When classifying the 3D Tetris shapes, we quantitatively show that our model requires no activation function in the hidden layers other than the embedding to outperform the vanilla multilayer perceptron. In the presence of noise in the data, our model is also superior to the MLHP.

Publications
Pavlo Melnyk, Michael Felsberg, Mårten Wadenbäck, Andreas Robinson, Cuong Le (2024). O$n$ Learning Deep O$(n)$ Equivariant Hyperspheres. ICML 2024.
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Pavlo Melnyk, Andreas Robinson, Michael Felsberg, Mårten Wadenbäck (2024). TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis. CVPR 2024.
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Pavlo Melnyk, Mårten Wadenbäck, Michael Felsberg (2022). Steerable 3D Spherical Neurons. ICML 2022.
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Pavlo Melnyk, Mårten Wadenbäck, Michael Felsberg (2021). Embed Me If You Can: A Geometric Perceptron. ICCV 2021.
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Pavlo Melnyk, Zhiqiang You, Keqin Lin (2020). A High-Performance CNN Method for Offline Handwritten Chinese Character Recognition and Visualization. Soft Computing.
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