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Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.
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Deep Unfolded Variable Projection Networks.

Gergő Bognár1, Manuel Feindert2, Christian Huber2,3

  • 1Department of Numerical Analysis, ELTE Eotvos Lorand University, Pázmány Péter stny 1/C, Budapest 1117, Hungary.

International Journal of Neural Systems
|August 27, 2025
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Summary
This summary is machine-generated.

A new hybrid AI framework, VPNet, effectively classifies cardiac arrhythmias using deep unfolding and Variable Projections. This model-driven approach achieves 95% accuracy with a compact architecture, suitable for edge computing.

Keywords:
ECG signal processingHermite functionsVariable projectiondeep unfoldingembedded systemsmodel-driven neural network

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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Signal Processing

Background:

  • Model-driven AI integrates prior knowledge for enhanced performance.
  • Separable Nonlinear Least Squares (SNLLS) problems are common in signal processing.
  • Variable Projections (VPs) offer a structured approach to solving SNLLS problems.

Purpose of the Study:

  • To introduce a hybrid learning framework combining Deep Unfolding and Variable Projections (VPs).
  • To develop a neural network capable of learning optimal nonlinear VP parameters.
  • To adapt the framework for ECG arrhythmia classification.

Main Methods:

  • Unfolding VP solver iterations into trainable neural network layers.
  • Incorporating prior knowledge (basis functions, signal structure) into the network architecture.
  • Case study: VPNet for ECG representation learning and arrhythmia classification.

Main Results:

  • VPNet achieved 95% accuracy on the MIT-BIH Arrhythmia Database.
  • The network learned optimal nonlinear VP parameters, demonstrating model-based meta-learning.
  • The compact architecture and low computational complexity enable efficient training and inference.

Conclusions:

  • The proposed deep unfolded VPNet is a powerful tool for ECG arrhythmia classification.
  • The hybrid approach enhances interpretability, reduces model size, and lowers data requirements.
  • VPNet's efficiency makes it suitable for real-time, power-efficient edge computing applications, validated on microcontrollers.