The transition rule is usually defined to update the state of each cell as a function of its current state and the state of its neighbours.

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph cellular automata (GCA), in which the lattice structure is replaced by an arbitrary graph. In particular, we extend previous work that used convolutional neural networks to learn the transition rule of conventional CA and we use graph neural networks to learn a variety of transition rules for GCA. First, we present a general-purpose architecture for learning GCA, and we show that it can represent any arbitrary GCA with finite and discrete state space. Then, we test our approach on three different tasks: 1) learning the transition rule of a GCA on a Voronoi tessellation; 2) imitating the behaviour of a group of flocking agents; 3) learning a rule that converges to a desired target state.

Vision Language Models (VLMs) exhibit a fundamental semantic-to-geometric gap in spatial reasoning: they excel at qualitative semantic inference but their reasoning operates within a lossy semantic space, misaligned with high-fidelity geometry. Current paradigms fail to bridge this gap. Training-based methods suffer from an ``oracle paradox,'' learning flawed spatial logic from imperfect oracles. Tool-integrated methods constrain the final computation but critically leave the VLM's planning process unconstrained, resulting in geometrically flawed plans. In this work, we propose Geometrically-Constrained Agent (GCA), a training-free agentic paradigm that resolves this gap by introducing a formal task constraint. Specifically, we strategically decouples the VLM's role into two stages. First, acting as a semantic analyst, the VLM translates the user's ambiguous query into the formal, verifiable task constraint, which defines the reference frame and objective. Second, acting as a task solver, the VLM generates and executes tool calls strictly within the deterministic bounds defined by the constraint. This geometrically-constrained reasoning strategy successfully resolve the semantic-to-geometric gap, yielding a robust and verifiable reasoning pathway for spatial reasoning. Comprehensive experiments demonstrate that GCA achieves SOTA performance on multiple spatial reasoning benchmarks, surpassing existing training-based and tool-integrated methods by ~27%. Please see our homepage at https://gca-spatial-reasoning.github.io.

Measuring similarity in urban spatial networks is key to understanding cities as complex systems. Yet most existing methods are not tailored for spatial networks and struggle to differentiate them effectively. We propose GCA-Sim, a similarity-evaluation framework based on graph cellular automata. Each submodel measures similarity by the divergence between value distributions recorded at multiple stages of an information evolution process. We find that some propagation rules magnify differences among network signals; we call this "network resonance." With an improved differentiable logic-gate network, we learn several submodels that induce network resonance. We evaluate similarity through clustering performance on fifty city-level and fifty district-level road networks. The submodels in this framework outperform existing methods, with Silhouette scores above 0.9. Using the best submodel, we further observe that planning-led street networks are less internally homogeneous than organically grown ones; morphological categories from different domains contribute with comparable importance; and degree, as a basic topological signal, becomes increasingly aligned with land value and related variables over iterations.

Online shopping giant Temu has agreed to work with the greeting card industry to remove copied designs from its site more quickly. Designers told the BBC the process for getting the plagiarised listings removed has been like the fairground game'whack-a-mole' with copied products re-appearing within days. Temu said protecting intellectual property was a top priority and that it was encouraging sellers to join the trial of a new takedown process specifically for the greetings card industry. Amanda Mountain, the co-founder of York-based Lola Design, discovered the catalogue of designs she had built up over a decade had nearly all been copied. She found the images she had created had been lifted and were being advertised by other sellers on cards and other products like t-shirts.

Cross-domain sequential recommendation (CDSR) aims to align heterogeneous user behavior sequences collected from different domains. While cross-attention is widely used to enhance alignment and improve recommendation performance, its underlying mechanism is not fully understood. Most researchers interpret cross-attention as residual alignment, where the output is generated by removing redundant and preserving non-redundant information from the query input by referencing another domain data which is input key and value. Beyond the prevailing view, we introduce Orthogonal Alignment, a phenomenon in which cross-attention discovers novel information that is not present in the query input, and further argue that those two contrasting alignment mechanisms can co-exist in recommendation models We find that when the query input and output of cross-attention are orthogonal, model performance improves over 300 experiments. Notably, Orthogonal Alignment emerges naturally, without any explicit orthogonality constraints. Our key insight is that Orthogonal Alignment emerges naturally because it improves scaling law. We show that baselines additionally incorporating cross-attention module outperform parameter-matched baselines, achieving a superior accuracy-per-model parameter. We hope these findings offer new directions for parameter-efficient scaling in multi-modal research.

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph cellular automata (GCA), in which the lattice structure is replaced by an arbitrary graph. In particular, we extend previous work that used convolutional neural networks to learn the transition rule of conventional CA and we use graph neural networks to learn a variety of transition rules for GCA. First, we present a general-purpose architecture for learning GCA, and we show that it can represent any arbitrary GCA with finite and discrete state space. Then, we test our approach on three different tasks: 1) learning the transition rule of a GCA on a Voronoi tessellation; 2) imitating the behaviour of a group of flocking agents; 3) learning a rule that converges to a desired target state.

This study addresses the issue of graph generation with generative models. In particular, we are concerned with graph community augmentation problem, which refers to the problem of generating unseen or unfamiliar graphs with a new community out of the probability distribution estimated with a given graph dataset. The graph community augmentation means that the generated graphs have a new community. There is a chance of discovering an unseen but important structure of graphs with a new community, for example, in a social network such as a purchaser network. Graph community augmentation may also be helpful for generalization of data mining models in a case where it is difficult to collect real graph data enough. In fact, there are many ways to generate a new community in an existing graph. It is desirable to discover a new graph with a new community beyond the given graph while we keep the structure of the original graphs to some extent for the generated graphs to be realistic. To this end, we propose an algorithm called the graph community augmentation (GCA). The key ideas of GCA are (i) to fit Gaussian mixture model (GMM) to data points in the latent space into which the nodes in the original graph are embedded, and (ii) to add data points in the new cluster in the latent space for generating a new community based on the minimum description length (MDL) principle. We empirically demonstrate the effectiveness of GCA for generating graphs with a new community structure on synthetic and real datasets.

Deploying deep reinforcement learning (DRL) in real-world inventory management presents challenges, including dynamic environments and uncertain problem parameters, e.g. demand and lead time distributions. These challenges highlight a research gap, suggesting a need for a unifying framework to model and solve sequential decision-making under parameter uncertainty. We address this by exploring an underexplored area of DRL for inventory management: training generally capable agents (GCAs) under zero-shot generalization (ZSG). Here, GCAs are advanced DRL policies designed to handle a broad range of sampled problem instances with diverse inventory challenges. ZSG refers to the ability to successfully apply learned policies to unseen instances with unknown parameters without retraining. We propose a unifying Super-Markov Decision Process formulation and the Train, then Estimate and Decide (TED) framework to train and deploy a GCA tailored to inventory management applications. The TED framework consists of three phases: training a GCA on varied problem instances, continuously estimating problem parameters during deployment, and making decisions based on these estimates. Applied to periodic review inventory problems with lost sales, cyclic demand patterns, and stochastic lead times, our trained agent, the Generally Capable Lost Sales Network (GC-LSN) consistently outperforms well-known traditional policies when problem parameters are known. Moreover, under conditions where demand and/or lead time distributions are initially unknown and must be estimated, we benchmark against online learning methods that provide worst-case performance guarantees. Our GC-LSN policy, paired with the Kaplan-Meier estimator, is demonstrated to complement these methods by providing superior empirical performance.