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.
Fuchs et al. introduce the SE(3)-Transformer, which combines self-attention with SE(3)-equivariance for 3D point clouds and graphs. Invariant attention weights modulate equivariant value messages from tensor field networks, resolving angular filter constraints while enabling data-adaptive, anisotropic processing.
Cohen et al. introduce Spherical CNNs that achieve SO(3)-equivariance by defining cross-correlation on the sphere and rotation group, computed efficiently via generalized FFT algorithms from non-commutative harmonic analysis.
Baldi and Vershynin systematically classify the fundamental building blocks of attention (activation attention, output gating, synaptic gating) by source, target, and mechanism, then prove capacity bounds showing that gating introduces quadratic terms sparsely, gaining expressiveness without the full cost of polynomial activations.
ChemDFM-R is a 14B-parameter chemical reasoning model that integrates a 101B-token dataset of atomized chemical knowledge. Using a mix-sourced distillation strategy and domain-specific reinforcement learning, it outperforms similarly sized models and DeepSeek-R1 on ChemEval.
A theoretical paper that introduces displacement interpolation (optimal transport) to establish a new convexity principle for energy functionals. It proves the uniqueness of ground states for interacting gases and generalizes the Brunn-Minkowski inequality, providing mathematical tools later used in flow matching and optimal transport-based generative models.
Proposes ‘InterFlow’, a method to learn continuous normalizing flows between arbitrary densities using stochastic interpolants. It avoids ODE backpropagation by minimizing a quadratic objective on the velocity field, enabling scalable ODE-based generation. On CIFAR-10, NLL matches ScoreSDE (2.99 bits per dim) with simulation-free training, though FID (10.27) trails dedicated image models (ScoreSDE: 2.92); the primary strength is tractable likelihood with efficient training cost.
Introduces Flow Matching, a scalable method for training CNFs by regressing vector fields of conditional probability paths. It generalizes diffusion and enables Optimal Transport paths for straighter, more efficient sampling.
This paper replaces discrete network layers with continuous ordinary differential equations (ODEs), allowing for adaptive computation depth and constant memory cost during training via the adjoint sensitivity method. It introduces Continuous Normalizing Flows and latent ODEs for time-series.
Introduces ‘Rectified Flow,’ a method to transport distributions via ODEs with straight paths. Uses a ‘reflow’ procedure to iteratively straighten trajectories, enabling high-quality 1-step generation with optional lightweight distillation.
This paper provides a rigorous probabilistic foundation for Denoising Autoencoders by proving they are mathematically equivalent to Score Matching on a kernel-smoothed data distribution. It derives a specific energy function for DAEs and justifies the use of tied weights.
This paper unifies previous score-based methods (SMLD and DDPM) under a continuous-time SDE framework. It introduces Predictor-Corrector samplers for improved generation and Probability Flow ODEs for near-exact likelihood computation, setting new records on CIFAR-10.