Generative Modeling
MNIST digit samples generated from a Variational Autoencoder latent space

Importance Weighted Autoencoders: Beyond the Standard VAE

The key difference between multi-sample VAEs and IWAEs: how log-of-averages creates a tighter bound on log-likelihood.

Computational Chemistry
Müller-Brown Potential Energy Surface showing the three minima and two saddle points

Implementing the Müller-Brown Potential in PyTorch

Guide to implementing the Müller-Brown potential in PyTorch, comparing analytical vs automatic differentiation with …

Computational Chemistry

Müller-Brown Basin MA: Langevin Dynamics Simulation

Langevin dynamics simulation showing particle motion in the deep reactant minimum (Basin MA) of the Müller-Brown …

Computational Chemistry

Müller-Brown Basin MB: Langevin Dynamics Simulation

Langevin dynamics simulation showing particle motion in the product minimum (Basin MB) of the Müller-Brown potential …

Computational Chemistry
Müller-Brown Potential Energy Surface showing the three minima and two saddle points

Müller-Brown Potential: A PyTorch ML Testbed

GPU-accelerated PyTorch framework for the Müller-Brown potential with JIT compilation and Langevin dynamics....

Computational Chemistry

Müller-Brown Transition: Langevin Dynamics Simulation

Extended Langevin dynamics simulation showing particle transitions between different basins of the Müller-Brown …

Natural Language Processing
Huffman Tree visualization for the input 'beep boop beer!' showing internal nodes with frequency counts and leaf nodes with characters

Vectorizing the Tree: High-Performance Word2Vec in Pure PyTorch

Production-grade Word2Vec in PyTorch with vectorized Hierarchical Softmax, Negative Sampling, and torch.compile support....

Generative Modeling
Variational Autoencoder architecture diagram showing encoder, latent space, and decoder

Modern PyTorch Techniques for VAEs: A Hands-On Tutorial

Learn to implement VAEs in PyTorch: ELBO objective, reparameterization trick, loss scaling, and MNIST experiments on …

Scientific Computing
Molecular structure alignment showing protein conformations and RMSD calculation

Kabsch Algorithm: NumPy, PyTorch, TensorFlow, and JAX

Learn about the Kabsch algorithm for optimal point alignment with implementations in NumPy, PyTorch, TensorFlow, and JAX …

Scientific Computing
Comparison of IQCRNN (Our Method) vs standard Policy Gradient showing training curves, phase portraits, and state trajectories for control tasks

IQCRNN: Certified Stability for Neural Networks

PyTorch IQCRNN enforcing stability guarantees on RNNs via Integral Quadratic Constraints and semidefinite programming....