Dataset distillation, a training-aware data compression technique, has recently attracted increasing attention as an effective tool for mitigating costs of optimization and data storage. However, progress remains largely empirical. Mechanisms underlying the extraction of task-relevant information from the training process and the efficient encoding of such information into synthetic data points remain elusive. In this paper, we theoretically analyze practical algorithms of dataset distillation applied to the gradient-based training of two-layer neural networks with width $L$. By focusing on a non-linear task structure called multi-index model, we prove that the low-dimensional structure of the problem is efficiently encoded into the resulting distilled data. This dataset reproduces a model with high generalization ability for a required memory complexity of $\tildeΘ$$(r^2d+L)$, where $d$ and $r$ are the input and intrinsic dimensions of the task. To the best of our knowledge, this is one of the first theoretical works that include a specific task structure, leverage its intrinsic dimensionality to quantify the compression rate and study dataset distillation implemented solely via gradient-based algorithms.

Generative modeling of three-dimensional (3D) molecules is a fundamental yet challenging problem in drug discovery and materials science. Existing approaches typically represent molecules as 3D graphs and co-generate discrete atom types with continuous atomic coordinates, leading to intrinsic learning difficulties such as heterogeneous modality entanglement and geometry-chemistry coherence constraints. We propose VecMol, a paradigm-shifting framework that reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, where vectors point toward nearby atoms and implicitly encode molecular structure. The vector field is parameterized by a neural field and generated using a latent diffusion model, avoiding explicit graph generation and decoupling structure learning from discrete atom instantiation. Experiments on the QM9 and GEOM-Drugs benchmarks validate the feasibility of this novel approach, suggesting vector-field-based representations as a promising new direction for 3D molecular generation.

This work tackles the problem of robust planning in non-stationary stochastic environments.

Neural Information Processing Systems http://nips.cc/

Given a query text, the similarity is determined bythemost similar prototype tofind correspondence inthevideo, which is termed text-adaptive matching.

Though promising results have been reported on some RL application domains, policies learned with such representations usually fail to generalize well in a complex environment because minimizing a reconstruction loss may potentially introduce local (visual) features with task-irrelevant information.

A more detailed explanation is as follows. First, we agree that Equation 3is not aconcrete optimization procedure.9

Graph According graphs, T =[ Tij indicates Figure Graph Besides Recall 12]: for connecting sub-graph 21,47,34 graph K isolated, bycalculating dgw(G, Gdc), whereGdc = G(Vdc,diag whose Figure indicates 2.2 Gr Multi-graph Distinct focus byintroducing Based frame propose acceleration 3.1 Inspired 48,49...

We argue that this assumption is rarely verified in practice, as the recommendation process itself may impact the user's preferences.

In this paper we consider linearly constrained stochastic approximation problems with federated learning asaspecial case.