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Spatial reasoning is a key capability in the field of artificial intelligence, especially crucial in areas such as robotics, computer vision, and natural language understanding. However, evaluating the ability of multimodal large language models (MLLMs) in complex spatial reasoning still faces challenges, particularly in scenarios requiring multi-step reasoning and precise mathematical constraints.

In pioneering work from 2019, Barceló and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this article, we give exact logical characterizations of recurrent GNNs in two scenarios: (1) in the setting with floating-point numbers and (2) with reals. For floats, the formalism matching recurrent GNNs is a rule-based modal logic with counting, while for reals we use a suitable infinitary modal logic, also with counting. These results give exact matches between logics and GNNs in the recurrent setting without rel-ativising to a background logic in either case, but using some natural assumptions about floating-point arithmetic. Applying our characterizations, we also prove that, relative to graph properties definable in monadic second-order logic (MSO), our infinitary and rule-based logics are equally expressive. This implies that recurrent GNNs with reals and floats have the same expressive power over MSO-definable properties and shows that, for such properties, also recurrent GNNs with reals are characterized by a (finitary!)

Inside the Colosseum's Passage of Commodus, where emperors once walked One theory suggests the infamous Roman emperor survived an assassination attempt in the tunnel now open to the public. From October 2024 to September 2025, a team of experts restored part of the tunnel that's open to visitors for the first time. Breakthroughs, discoveries, and DIY tips sent six days a week. They say all roads lead to Rome . But in the Eternal City, all of the major roads were thought to lead somewhere very specific--a single column called the Milliarium Auereum, or the golden milestone.

Spatial reasoning is a key capability in the field of artificial intelligence, especially crucial in areas such as robotics, computer vision, and natural language understanding. However, evaluating the ability of multimodal large language models(MLLMs) in complex spatial reasoning still faces challenges, particularly in scenarios requiring multi-step reasoning and precise mathematical constraints. This paper introduces ORIGAMISPACE, a new dataset and benchmark designed to evaluate the multi-step spatial reasoning ability and the capacity to handle mathematical constraints of MLLMs through origami tasks. The dataset contains 350 data instances,each comprising a strictly formatted crease pattern (CP diagram), the Compiled Flat Pattern, the complete Folding Process, and the final Folded Shape Image. We propose four evaluation tasks: Pattern Prediction, Multi-step Spatial Reasoning, Spatial Relationship Prediction, and End-to-End CP Code Generation. For the CP code generation task, we design an interactive environment and explore the possibility of using reinforcement learning methods to train MLLMs. Through experiments on existing MLLMs, we initially reveal the strengths and weaknesses of these models in handling complex spatial reasoning tasks.

In pioneering work from 2019, Barceló and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this article, we give exact logical characterizations of recurrent GNNs in two scenarios: (1) in the setting with floating-point numbers and (2) with reals. For floats, the formalism matching recurrent GNNs is a rule-based modal logic with counting, while for reals we use a suitable infinitary modal logic, also with counting. These results give exact matches between logics and GNNs in the recurrent setting without rel-ativising to a background logic in either case, but using some natural assumptions about floating-point arithmetic. Applying our characterizations, we also prove that, relative to graph properties definable in monadic second-order logic (MSO), our infinitary and rule-based logics are equally expressive. This implies that recurrent GNNs with reals and floats have the same expressive power over MSO-definable properties and shows that, for such properties, also recurrent GNNs with reals are characterized by a (finitary!)

Keep fake spider webs close to your house, and ditch the real pumpkins if you live near wildlife. Breakthroughs, discoveries, and DIY tips sent every weekday. With spooky season just on the horizon, Halloween decorations are beginning to pop up everywhere--tombstones, pumpkins, and of course, tons and tons of fake spiderwebs . Amidst all the autumnal celebrations, it's easy to forget those who not only can't join in on the celebration, but might even be threatened by the decorations: wildlife. While Jennifer Bloodgood, a Cornell University wildlife veterinarian, hasn't personally witnessed it before, she tells that she agrees with the dangers of some Halloween decorations. "Birds would definitely be the major concern," she says, referring specifically to fake spider webs.

Furniture decoration is an important task in various industrial applications. However, achieving a high-quality decorative result is often time-consuming and requires specialized artistic expertise. To tackle these challenges, we explore how multi-agent systems can assist in automating the decoration process. We propose FurniMAS, a multi-agent system for automatic furniture decoration. Specifically, given a human prompt and a household furniture item such as a working desk or a TV stand, our system suggests relevant assets with appropriate styles and materials, and arranges them on the item, ensuring the decorative result meets functionality, aesthetic, and ambiance preferences. FurniMAS assembles a hybrid team of LLM-based and non-LLM agents, each fulfilling distinct roles in a typical decoration project. These agents collaborate through communication, logical reasoning, and validation to transform the requirements into the final outcome. Extensive experiments demonstrate that our FurniMAS significantly outperforms other baselines in generating high-quality 3D decor.

President Trump's tariff standoff with China has caused chaos, confusion, and major delays for companies of all shapes and sizes. As everyone waits to see what happens next, some businesses that depend on international trade are already feeling major impacts, saying that they might not meet their production deadlines. And one of those deadlines is pretty important: Christmas. Today on the show, we're joined by WIRED's senior business editor Louise Matsakis to talk through the latest on tariffs. Mentioned in this episode: Donald Trump Is Already Ruining Christmas by Zeyi Yang OpenAI Adds Shopping to ChatGPT in a Challenge to Google by Reece Rogers The Agonizing Task of Turning Europe's Power Back On by Natasha Bernal Write to us at uncannyvalley@wired.com.

We introduce the dataset of Everyday Hard Optimization Problems (EHOP), a collection of NP-hard optimization problems expressed in natural language. EHOP includes problem formulations that could be found in computer science textbooks, versions that are dressed up as problems that could arise in real life, and variants of well-known problems with inverted rules. We find that state-of-the-art LLMs, across multiple prompting strategies, systematically solve textbook problems more accurately than their real-life and inverted counterparts. We argue that this constitutes evidence that LLMs adapt solutions seen during training, rather than leveraging reasoning abilities that would enable them to generalize to novel problems.