Vector Quantized Variational AutoEncoders (VQ-VAEs) are designed to compress a continuous input to a discrete latent space and reconstruct it with minimal distortion. They operate by maintaining a set of vectors---often referred to as the codebook---and quantizing each encoder output to the nearest vector in the codebook. However, as vector quantization is non-differentiable, the gradient to the encoder flows _around_ the vector quantization layer rather than _through_ it in a straight-through approximation. This approximation may be undesirable as all information from the vector quantization operation is lost. In this work, we propose a way to propagate gradients through the vector quantization layer of VQ-VAEs. We smoothly transform each encoder output into its corresponding codebook vector via a rotation and rescaling linear transformation that is treated as a constant during backpropagation. As a result, the relative magnitude and angle between encoder output and codebook vector becomes encoded into the gradient as it propagates through the vector quantization layer and back to the encoder. Across 11 different VQ-VAE training paradigms, we find this restructuring improves reconstruction metrics, codebook utilization, and quantization error.

Biomolecular structure determination is essential to a mechanistic understanding of diseases and the development of novel therapeutics. Machine-learning-based structure prediction methods have made significant advancements by computationally predicting protein and bioassembly structures from sequences and molecular topology alone. Despite substantial progress in the field, challenges remain to deliver structure prediction models to real-world drug discovery. Here, we present NeuralPLexer3 -- a physics-inspired flow-based generative model that achieves state-of-the-art prediction accuracy on key biomolecular interaction types and improves training and sampling efficiency compared to its predecessors and alternative methodologies. Examined through existing and new benchmarks, NeuralPLexer3 excels in areas crucial to structure-based drug design, including blind docking, physical validity, and ligand-induced protein conformational changes.