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.

Trans4D: Realistic Geometry-Aware Transition for Compositional Text-to-4D Synthesis

Recent advances in diffusion models have demonstrated exceptional capabilities in image and video generation, further improving the effectiveness of 4D synthesis. Existing 4D generation methods can generate high-quality 4D objects or scenes based on user-friendly conditions, benefiting the gaming and video industries. However, these methods struggle to synthesize significant object deformation of complex 4D transitions and interactions within scenes. To address this challenge, we propose Trans4D, a novel text-to-4D synthesis framework that enables realistic complex scene transitions. Specifically, we first use multi-modal large language models (MLLMs) to produce a physic-aware scene description for 4D scene initialization and effective transition timing planning. Then we propose a geometry-aware 4D transition network to realize a complex scene-level 4D transition based on the plan, which involves expressive geometrical object deformation. Extensive experiments demonstrate that Trans4D consistently outperforms existing state-of-the-art methods in generating 4D scenes with accurate and high-quality transitions, validating its effectiveness. Code: https://github.com/YangLing0818/Trans4D

MIO: A Foundation Model on Multimodal Tokens

In this paper, we introduce MIO, a novel foundation model built on multimodal tokens, capable of understanding and generating speech, text, images, and videos in an end-to-end, autoregressive manner. While the emergence of large language models (LLMs) and multimodal large language models (MM-LLMs) propels advancements in artificial general intelligence through their versatile capabilities, they still lack true any-to-any understanding and generation. Recently, the release of GPT-4o has showcased the remarkable potential of any-to-any LLMs for complex real-world tasks, enabling omnidirectional input and output across images, speech, and text. However, it is closed-source and does not support the generation of multimodal interleaved sequences. To address this gap, we present MIO, which is trained on a mixture of discrete tokens across four modalities using causal multimodal modeling. MIO undergoes a four-stage training process: (1) alignment pre-training, (2) interleaved pre-training, (3) speech-enhanced pre-training, and (4) comprehensive supervised fine-tuning on diverse textual, visual, and speech tasks. Our experimental results indicate that MIO exhibits competitive, and in some cases superior, performance compared to previous dual-modal baselines, any-to-any model baselines, and even modality-specific baselines. Moreover, MIO demonstrates advanced capabilities inherent to its any-to-any feature, such as interleaved video-text generation, chain-of-visual-thought reasoning, visual guideline generation, instructional image editing, etc.

GenMapping: Unleashing the Potential of Inverse Perspective Mapping for Robust Online HD Map Construction

Online High-Definition (HD) maps have emerged as the preferred option for autonomous driving, overshadowing the counterpart offline HD maps due to flexible update capability and lower maintenance costs. However, contemporary online HD map models embed parameters of visual sensors into training, resulting in a significant decrease in generalization performance when applied to visual sensors with different parameters. Inspired by the inherent potential of Inverse Perspective Mapping (IPM), where camera parameters are decoupled from the training process, we have designed a universal map generation framework, GenMapping. The framework is established with a triadic synergy architecture, including principal and dual auxiliary branches. When faced with a coarse road image with local distortion translated via IPM, the principal branch learns robust global features under the state space models. The two auxiliary branches are a dense perspective branch and a sparse prior branch. The former exploits the correlation information between static and moving objects, whereas the latter introduces the prior knowledge of OpenStreetMap (OSM). The triple-enhanced merging module is crafted to synergistically integrate the unique spatial features from all three branches. To further improve generalization capabilities, a Cross-View Map Learning (CVML) scheme is leveraged to realize joint learning within the common space. Additionally, a Bidirectional Data Augmentation (BiDA) module is introduced to mitigate reliance on datasets concurrently. A thorough array of experimental results shows that the proposed model surpasses current state-of-the-art methods in both semantic mapping and vectorized mapping, while also maintaining a rapid inference speed. The source code will be publicly available at https://github.com/lynn-yu/GenMapping.

Geo-Llama: Leveraging LLMs for Human Mobility Trajectory Generation with Spatiotemporal Constraints

Simulating human mobility data is essential for various application domains, including transportation, urban planning, and epidemic control, since real data are often inaccessible to researchers due to expensive costs and privacy issues. Several existing deep generative solutions propose learning from real trajectories to generate synthetic ones. Despite the progress, most of them suffer from training stability issues and scale poorly with growing data size. More importantly, they generally lack control mechanisms to steer the generated trajectories based on spatiotemporal constraints such as fixing specific visits. To address such limitations, we formally define the controlled trajectory generation problem with spatiotemporal constraints and propose Geo-Llama. This novel LLM-inspired framework enforces explicit visit constraints in a contextually coherent way. It fine-tunes pre-trained LLMs on trajectories with a visit-wise permutation strategy where each visit corresponds to a time and location. This enables the model to capture the spatiotemporal patterns regardless of visit orders and allows flexible and in-context constraint integration through prompts during generation. Extensive experiments on real-world and synthetic datasets validate the effectiveness of Geo-Llama, demonstrating its versatility and robustness in handling a broad range of constraints to generate more realistic trajectories compared to existing methods.

Group-Control Motion Planning Framework for Microrobot Swarms in a Global Field

This paper investigates how group-control can be effectively used for motion planning for microrobot swarms in a global field. We prove that Small-Time Local Controllability (STLC) in robot positions is achievable through group-control, with the minimum number of groups required for STLC being $\log_2(n + 2) + 1$ for $n$ robots. We then discuss the complexity trade-offs between control and motion planning. We show how motion planning can be simplified if appropriate primitives can be achieved through more complex control actions. We identify motion planning problems that balance the number of robot groups and motion primitives with planning complexity. Various instantiations of these motion planning problems are explored, with simulations to demonstrate the effectiveness of group-control.

ContextBLIP: Doubly Contextual Alignment for Contrastive Image Retrieval from Linguistically Complex Descriptions

Image retrieval from contextual descriptions (IRCD) aims to identify an image within a set of minimally contrastive candidates based on linguistically complex text. Despite the success of VLMs, they still significantly lag behind human performance in IRCD. The main challenges lie in aligning key contextual cues in two modalities, where these subtle cues are concealed in tiny areas of multiple contrastive images and within the complex linguistics of textual descriptions. This motivates us to propose ContextBLIP, a simple yet effective method that relies on a doubly contextual alignment scheme for challenging IRCD. Specifically, 1) our model comprises a multi-scale adapter, a matching loss, and a text-guided masking loss. The adapter learns to capture fine-grained visual cues. The two losses enable iterative supervision for the adapter, gradually highlighting the focal patches of a single image to the key textual cues. We term such a way as intra-contextual alignment. 2) Then, ContextBLIP further employs an inter-context encoder to learn dependencies among candidates, facilitating alignment between the text to multiple images. We term this step as inter-contextual alignment. Consequently, the nuanced cues concealed in each modality can be effectively aligned. Experiments on two benchmarks show the superiority of our method. We observe that ContextBLIP can yield comparable results with GPT-4V, despite involving about 7,500 times fewer parameters.

DTCLMapper: Dual Temporal Consistent Learning for Vectorized HD Map Construction

Temporal information plays a pivotal role in Bird's-Eye-View (BEV) driving scene understanding, which can alleviate the visual information sparsity. However, the indiscriminate temporal fusion method will cause the barrier of feature redundancy when constructing vectorized High-Definition (HD) maps. In this paper, we revisit the temporal fusion of vectorized HD maps, focusing on temporal instance consistency and temporal map consistency learning. To improve the representation of instances in single-frame maps, we introduce a novel method, DTCLMapper. This approach uses a dual-stream temporal consistency learning module that combines instance embedding with geometry maps. In the instance embedding component, our approach integrates temporal Instance Consistency Learning (ICL), ensuring consistency from vector points and instance features aggregated from points. A vectorized points pre-selection module is employed to enhance the regression efficiency of vector points from each instance. Then aggregated instance features obtained from the vectorized points preselection module are grounded in contrastive learning to realize temporal consistency, where positive and negative samples are selected based on position and semantic information. The geometry mapping component introduces Map Consistency Learning (MCL) designed with self-supervised learning. The MCL enhances the generalization capability of our consistent learning approach by concentrating on the global location and distribution constraints of the instances. Extensive experiments on well-recognized benchmarks indicate that the proposed DTCLMapper achieves state-of-the-art performance in vectorized mapping tasks, reaching 61.9% and 65.1% mAP scores on the nuScenes and Argoverse datasets, respectively. The source code will be made publicly available at https://github.com/lynn-yu/DTCLMapper.

MambaMOS: LiDAR-based 3D Moving Object Segmentation with Motion-aware State Space Model

LiDAR-based Moving Object Segmentation (MOS) aims to locate and segment moving objects in point clouds of the current scan using motion information from previous scans. Despite the promising results achieved by previous MOS methods, several key issues, such as the weak coupling of temporal and spatial information, still need further study. In this paper, we propose a novel LiDAR-based 3D Moving Object Segmentation with Motion-aware State Space Model, termed MambaMOS. Firstly, we develop a novel embedding module, the Time Clue Bootstrapping Embedding (TCBE), to enhance the coupling of temporal and spatial information in point clouds and alleviate the issue of overlooked temporal clues. Secondly, we introduce the Motion-aware State Space Model (MSSM) to endow the model with the capacity to understand the temporal correlations of the same object across different time steps. Specifically, MSSM emphasizes the motion states of the same object at different time steps through two distinct temporal modeling and correlation steps. We utilize an improved state space model to represent these motion differences, significantly modeling the motion states. Finally, extensive experiments on the SemanticKITTI-MOS and KITTI-Road benchmarks demonstrate that the proposed MambaMOS achieves state-of-the-art performance. The source code of this work will be made publicly available at https://github.com/Terminal-K/MambaMOS.

Text Classification Based on Knowledge Graphs and Improved Attention Mechanism

To resolve the semantic ambiguity in texts, we propose a model, which innovatively combines a knowledge graph with an improved attention mechanism. An existing knowledge base is utilized to enrich the text with relevant contextual concepts. The model operates at both character and word levels to deepen its understanding by integrating the concepts. We first adopt information gain to select import words. Then an encoder-decoder framework is used to encode the text along with the related concepts. The local attention mechanism adjusts the weight of each concept, reducing the influence of irrelevant or noisy concepts during classification. We improve the calculation formula for attention scores in the local self-attention mechanism, ensuring that words with different frequencies of occurrence in the text receive higher attention scores. Finally, the model employs a Bi-directional Gated Recurrent Unit (Bi-GRU), which is effective in feature extraction from texts for improved classification accuracy. Its performance is demonstrated on datasets such as AGNews, Ohsumed, and TagMyNews, achieving accuracy of 75.1%, 58.7%, and 68.5% respectively, showing its effectiveness in classifying tasks.