They can only forecast in a specific domain and fail when applied to systems with different parameters, external forces, or boundary conditions. We propose a model-based meta-learning method called DyAd which can generalize across heterogeneous domains by partitioning them into different tasks. DyAd has two parts: an encoder that infers the time-invariant hidden features of the task with weak supervision, and a forecaster which learns the shared dynamics of the entire domain. The encoder adapts and controls the forecaster during inference using adaptive instance normalization and adaptive padding. Theoretically, we prove that the generalization error of such a procedure is related to the task relatedness in the source domain, as well as the domain differences between source and target. Experimentally, we demonstrate that our model outperforms state-of-the-art approaches on forecasting complex physical dynamics including turbulent flow, real-world sea surface temperature, and ocean currents.

We report in experiment and simulation the spontaneous formation of dynamically bound pairs of shape changing robots undergoing locally repulsive collisions. These physical `gliders' robustly emerge from an ensemble of individually undulating three-link two-motor robots and can remain bound for hundreds of undulations and travel for multiple robot dimensions. Gliders occur in two distinct binding symmetries and form over a wide range of angular oscillation extent. This parameter sets the maximal concavity which influences formation probability and translation characteristics. Analysis of dynamics in simulation reveals the mechanism of effective dynamical attraction -- a result of the emergent interplay of appropriately oriented and timed repulsive interactions. Tactile sensing stabilizes the short-lived conformation via concavity modulation.

A key feature of human collaboration is the ability to iteratively refine the concepts we have communicated. In contrast, while generative AI excels at the \textit{generation} of content, it often struggles to make specific language-guided \textit{modifications} of its prior outputs. To bridge the gap between how humans and machines perform edits, we present mrCAD, a dataset of multimodal instructions in a communication game. In each game, players created computer aided designs (CADs) and refined them over several rounds to match specific target designs. Only one player, the Designer, could see the target, and they must instruct the other player, the Maker, using text, drawing, or a combination of modalities. mrCAD consists of 6,082 communication games, 15,163 instruction-execution rounds, played between 1,092 pairs of human players. We analyze the dataset and find that generation and refinement instructions differ in their composition of drawing and text. Using the mrCAD task as a benchmark, we find that state-of-the-art VLMs are better at following generation instructions than refinement instructions. These results lay a foundation for analyzing and modeling a multimodal language of refinement that is not represented in previous datasets.

Real-world networks grow over time; statistical models based on node exchangeability are not appropriate. Instead of constraining the structure of the \textit{distribution} of edges, we propose that the relevant symmetries refer to the \textit{causal structure} between them. We first enumerate the 96 causal directed acyclic graph (DAG) models over pairs of nodes (dyad variables) in a growing network with finite ancestral sets that are invariant to node deletion. We then partition them into 21 classes with ancestral sets that are closed under node marginalization. Several of these classes are remarkably amenable to distributed and asynchronous evaluation. As an example, we highlight a simple model that exhibits flexible power-law degree distributions and emergent phase transitions in sparsity, which we characterize analytically. With few parameters and much conditional independence, our proposed framework provides natural baseline models for causal inference in relational data.