A differentiable point-set alignment library implementing N-dimensional Kabsch, Horn quaternion, and Umeyama scaling algorithms with per-point weights, batch dimensions, and custom autograd across NumPy, PyTorch, JAX, TensorFlow, and MLX.
Presents a concise SVD-based algorithm for finding the optimal rotation and translation between two 3D point sets, with analysis of the degenerate reflection case that Umeyama later corrected.
The matrix-based companion to Horn’s 1987 quaternion method, deriving the optimal rotation as the orthonormal factor in the polar decomposition of the cross-covariance matrix via eigendecomposition of a 3x3 symmetric matrix.
Corrects a flaw in prior SVD-based alignment methods (Arun et al., Horn et al.) that could produce reflections instead of rotations under noisy data, and provides a complete closed-form solution for similarity transformations in arbitrary dimensions.
This paper introduces consistency models, a new family of generative models that map any point on a Probability Flow ODE trajectory to its origin. They support fast one-step generation by design, while allowing multi-step sampling for improved quality and zero-shot editing tasks like inpainting and colorization.
This paper introduces Discrete Denoising Diffusion Probabilistic Models (D3PMs), which generalize diffusion to discrete state-spaces using structured Markov transition matrices. D3PMs include uniform, absorbing-state, and discretized Gaussian corruption processes, drawing a connection between diffusion and masked language models.
GraphReco presents a rule-based OCSR system with two key innovations: a Fragment Merging line detection algorithm for precise bond identification and a Markov network for probabilistic resolution of atom/bond ambiguity during graph assembly. Achieves 94.2% accuracy on USPTO-10K, outperforming both traditional rule-based and some ML-based methods.
Derives the optimal rotation between two 3D point sets as the eigenvector of a 4x4 symmetric matrix built from cross-covariance sums, using unit quaternions to enforce the orthogonality constraint.
A foundational 1976 short communication presenting a direct, non-iterative method for finding the best rotation matrix between two point sets via eigendecomposition of a cross-covariance matrix.
This paper introduces Latent Diffusion Models (LDMs), which apply denoising diffusion in the latent space of pretrained autoencoders. By separating perceptual compression from generative learning and adding cross-attention conditioning, LDMs achieve FID 1.50 on Places inpainting and FID 3.60 on ImageNet class-conditional synthesis, with competitive text-to-image generation, at a fraction of the compute cost of pixel-space diffusion.
Tallec and Ollivier show that requiring invariance to time transformations in recurrent models leads to gating mechanisms, recovering key LSTM components from first principles. They propose the chrono initialization for gate biases that improves learning of long-term dependencies.
Battaglia et al. argue that combinatorial generalization requires structured representations, systematically analyze the relational inductive biases in standard deep learning architectures (MLPs, CNNs, RNNs), and present the graph network as a unifying framework that generalizes and extends prior graph neural network approaches.