Proposing and solving olympiad geometry with guided tree search

Mathematics olympiads are prestigious competitions, with problem proposing and solving highly honored. Building artificial intelligence that proposes and solves olympiads presents an unresolved challenge in automated theorem discovery and proving, especially in geometry for its combination of numerical and spatial elements. We introduce TongGeometry, a Euclidean geometry system supporting tree-search-based guided problem proposing and solving. The efficient geometry system establishes the most extensive repository of geometry theorems to date: within the same computational budget as the existing state-of-the-art, TongGeometry discovers 6.7 billion geometry theorems requiring auxiliary constructions, including 4.1 billion exhibiting geometric symmetry. Among them, 10 theorems were proposed to regional mathematical olympiads with 3 of TongGeometry's proposals selected in real competitions, earning spots in a national team qualifying exam or a top civil olympiad in China and the US. Guided by fine-tuned large language models, TongGeometry solved all International Mathematical Olympiad geometry in IMO-AG-30, outperforming gold medalists for the first time. It also surpasses the existing state-of-the-art across a broader spectrum of olympiad-level problems. The full capabilities of the system can be utilized on a consumer-grade machine, making the model more accessible and fostering widespread democratization of its use. By analogy, unlike existing systems that merely solve problems like students, TongGeometry acts like a geometry coach, discovering, presenting, and proving theorems.

Evaluating and Modeling Social Intelligence: A Comparative Study of Human and AI Capabilities

Facing the current debate on whether Large Language Models (LLMs) attain near-human intelligence levels (Mitchell & Krakauer, 2023; Bubeck et al., 2023; Kosinski, 2023; Shiffrin & Mitchell, 2023; Ullman, 2023), the current study introduces a benchmark for evaluating social intelligence, one of the most distinctive aspects of human cognition. We developed a comprehensive theoretical framework for social dynamics and introduced two evaluation tasks: Inverse Reasoning (IR) and Inverse Inverse Planning (IIP). Our approach also encompassed a computational model based on recursive Bayesian inference, adept at elucidating diverse human behavioral patterns. Extensive experiments and detailed analyses revealed that humans surpassed the latest GPT models in overall performance, zero-shot learning, one-shot generalization, and adaptability to multi-modalities. Notably, GPT models demonstrated social intelligence only at the most basic order (order = 0), in stark contrast to human social intelligence (order >= 2). Further examination indicated a propensity of LLMs to rely on pattern recognition for shortcuts, casting doubt on their possession of authentic human-level social intelligence. Our codes, dataset, appendix and human data are released at https://github.com/bigai-ai/Evaluate-n-Model-Social-Intelligence.

Brain in a Vat: On Missing Pieces Towards Artificial General Intelligence in Large Language Models

In this perspective paper, we first comprehensively review existing evaluations of Large Language Models (LLMs) using both standardized tests and ability-oriented benchmarks. We pinpoint several problems with current evaluation methods that tend to overstate the capabilities of LLMs. We then articulate what artificial general intelligence should encompass beyond the capabilities of LLMs. We propose four characteristics of generally intelligent agents: 1) they can perform unlimited tasks; 2) they can generate new tasks within a context; 3) they operate based on a value system that underpins task generation; and 4) they have a world model reflecting reality, which shapes their interaction with the world. Building on this viewpoint, we highlight the missing pieces in artificial general intelligence, that is, the unity of knowing and acting. We argue that active engagement with objects in the real world delivers more robust signals for forming conceptual representations. Additionally, knowledge acquisition isn't solely reliant on passive input but requires repeated trials and errors. We conclude by outlining promising future research directions in the field of artificial general intelligence.

XBound-Former: Toward Cross-scale Boundary Modeling in Transformers

Skin lesion segmentation from dermoscopy images is of great significance in the quantitative analysis of skin cancers, which is yet challenging even for dermatologists due to the inherent issues, i.e., considerable size, shape and color variation, and ambiguous boundaries. Recent vision transformers have shown promising performance in handling the variation through global context modeling. Still, they have not thoroughly solved the problem of ambiguous boundaries as they ignore the complementary usage of the boundary knowledge and global contexts. In this paper, we propose a novel cross-scale boundary-aware transformer, \textbf{XBound-Former}, to simultaneously address the variation and boundary problems of skin lesion segmentation. XBound-Former is a purely attention-based network and catches boundary knowledge via three specially designed learners. We evaluate the model on two skin lesion datasets, ISIC-2016\&PH$^2$ and ISIC-2018, where our model consistently outperforms other convolution- and transformer-based models, especially on the boundary-wise metrics. We extensively verify the generalization ability of polyp lesion segmentation that has similar characteristics, and our model can also yield significant improvement compared to the latest models.