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This extended abstract describes a framework for analyzing the expressiveness, learning, and (structural) generalization of hypergraph neural networks (HyperGNNs). Specifically, we focus on how HyperGNNs can learn from finite datasets and generalize structurally to graph reasoning problems of arbitrary input sizes. Our first contribution is a fine-grained analysis of the expressiveness of HyperGNNs, that is, the set of functions that they can realize. Our result is a hierarchy of problems they can solve, defined in terms of various hyperparameters such as depths and edge arities. Next, we analyze the learning properties of these neural networks, especially focusing on how they can be trained on a finite set of small graphs and generalize to larger graphs, which we term structural generalization. Our theoretical results are further supported by the empirical results., Comment: Learning on Graphs Conference (LoG) 2022

We present a framework for learning useful subgoals that support efficient long-term planning to achieve novel goals. At the core of our framework is a collection of rational subgoals (RSGs), which are essentially binary classifiers over the environmental states. RSGs can be learned from weakly-annotated data, in the form of unsegmented demonstration trajectories, paired with abstract task descriptions, which are composed of terms initially unknown to the agent (e.g., collect-wood then craft-boat then go-across-river). Our framework also discovers dependencies between RSGs, e.g., the task collect-wood is a helpful subgoal for the task craft-boat. Given a goal description, the learned subgoals and the derived dependencies facilitate off-the-shelf planning algorithms, such as A* and RRT, by setting helpful subgoals as waypoints to the planner, which significantly improves performance-time efficiency., Comment: AAAI 2023. First two authors contributed equally. Project page: https://rsg.csail.mit.edu

We present Temporal and Object Quantification Networks (TOQ-Nets), a new class of neuro-symbolic networks with a structural bias that enables them to learn to recognize complex relational-temporal events. This is done by including reasoning layers that implement finite-domain quantification over objects and time. The structure allows them to generalize directly to input instances with varying numbers of objects in temporal sequences of varying lengths. We evaluate TOQ-Nets on input domains that require recognizing event-types in terms of complex temporal relational patterns. We demonstrate that TOQ-Nets can generalize from small amounts of data to scenarios containing more objects than were present during training and to temporal warpings of input sequences., Comment: IJCAI 2021. First two authors contributed equally. Project page: http://toqnet.csail.mit.edu/

We analyze the computational complexity of several new variants of edge-matching puzzles. First we analyze inequality (instead of equality) constraints between adjacent tiles, proving the problem NP-complete for strict inequalities but polynomial for nonstrict inequalities. Second we analyze three types of triangular edge matching, of which one is polynomial and the other two are NP-complete; all three are #P-complete. Third we analyze the case where no target shape is specified, and we merely want to place the (square) tiles so that edges match (exactly); this problem is NP-complete. Fourth we consider four 2-player games based on $1 \times n$ edge matching, all four of which are PSPACE-complete. Most of our NP-hardness reductions are parsimonious, newly proving #P and ASP-completeness for, e.g., $1 \times n$ edge matching., Comment: 29 pages, 18 figures. Thorough revisions of Sections 4, 5, and 6/7 (merged)