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.

Generative Modeling
Flowchart comparing VAE and IWAE computation showing the key difference in where averaging occurs relative to the log operation

IWAE: Importance Weighted Autoencoders

Summary of Burda, Grosse & Salakhutdinov's ICLR 2016 paper introducing Importance Weighted Autoencoders for tighter …

Computational Biology
Protein folding energy landscape funnel showing high-energy unfolded states converging to the native state

How to Fold Graciously: The Levinthal Paradox

A perspective paper defining the Grand Challenge of protein folding: distinguishing kinetic pathways from thermodynamic …

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

Müller-Brown Potential

The Müller-Brown potential is a classic 2D benchmark for testing optimization algorithms and molecular dynamics methods.

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 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, Langevin dynamics, and …

Computational Chemistry
Spherical harmonics visualization

Efficient DFT Hamiltonian Prediction via Adaptive Sparsity

Luo et al. introduce SPHNet, using adaptive sparsity to dramatically improve SE(3)-equivariant Hamiltonian prediction …

Generative Modeling
Visualization of the VAE prior hole problem showing a ring-shaped aggregate posterior with an empty center where the Gaussian prior has highest density

Contrastive Learning for Variational Autoencoder Priors

Aneja et al.'s NeurIPS 2021 paper introducing Noise Contrastive Priors (NCPs) to address VAE's 'prior hole' problem with …

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

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 VAEs: A Detailed Implementation Guide

Complete PyTorch VAE tutorial: Copy-paste code, ELBO derivation, KL annealing, and stable softplus parameterization.

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.

Natural Language Processing
Heatmap visualization of the EigenNoise analytical co-occurrence prior matrix showing word rank relationships

EigenNoise: Data-Free Word Vector Initialization

Investigation into EigenNoise, a data-free initialization scheme for word vectors that approaches pre-trained model …