Proving Theorems Recursively

Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or value function scores) that potentially lead to suboptimal or even distracting subgoals, preventing us from finding longer proofs. To address this challenge, we propose POETRY (PrOvE Theorems RecursivelY), which proves theorems in a recursive, level-by-level manner in the Isabelle theorem prover. Unlike previous step-by-step methods, POETRY searches for a verifiable sketch of the proof at each level and focuses on solving the current level's theorem or conjecture. Detailed proofs of intermediate conjectures within the sketch are temporarily replaced by a placeholder tactic called sorry, deferring their proofs to subsequent levels. This approach allows the theorem to be tackled incrementally by outlining the overall theorem at the first level and then solving the intermediate conjectures at deeper levels. Experiments are conducted on the miniF2F and PISA datasets and significant performance gains are observed in our POETRY approach over state-of-the-art methods. POETRY on miniF2F achieves an average proving success rate improvement of 5.1%. Moreover, we observe a substantial increase in the maximum proof length found by POETRY, from 10 to 26.

MagicDrive3D: Controllable 3D Generation for Any-View Rendering in Street Scenes

While controllable generative models for images and videos have achieved remarkable success, high-quality models for 3D scenes, particularly in unbounded scenarios like autonomous driving, remain underdeveloped due to high data acquisition costs. In this paper, we introduce MagicDrive3D, a novel pipeline for controllable 3D street scene generation that supports multi-condition control, including BEV maps, 3D objects, and text descriptions. Unlike previous methods that reconstruct before training the generative models, MagicDrive3D first trains a video generation model and then reconstructs from the generated data. This innovative approach enables easily controllable generation and static scene acquisition, resulting in high-quality scene reconstruction. To address the minor errors in generated content, we propose deformable Gaussian splatting with monocular depth initialization and appearance modeling to manage exposure discrepancies across viewpoints. Validated on the nuScenes dataset, MagicDrive3D generates diverse, high-quality 3D driving scenes that support any-view rendering and enhance downstream tasks like BEV segmentation. Our results demonstrate the framework's superior performance, showcasing its transformative potential for autonomous driving simulation and beyond.

DiM: Diffusion Mamba for Efficient High-Resolution Image Synthesis

Diffusion models have achieved great success in image generation, with the backbone evolving from U-Net to Vision Transformers. However, the computational cost of Transformers is quadratic to the number of tokens, leading to significant challenges when dealing with high-resolution images. In this work, we propose Diffusion Mamba (DiM), which combines the efficiency of Mamba, a sequence model based on State Space Models (SSM), with the expressive power of diffusion models for efficient high-resolution image synthesis. To address the challenge that Mamba cannot generalize to 2D signals, we make several architecture designs including multi-directional scans, learnable padding tokens at the end of each row and column, and lightweight local feature enhancement. Our DiM architecture achieves inference-time efficiency for high-resolution images. In addition, to further improve training efficiency for high-resolution image generation with DiM, we investigate ``weak-to-strong'' training strategy that pretrains DiM on low-resolution images ($256\times 256$) and then finetune it on high-resolution images ($512 \times 512$). We further explore training-free upsampling strategies to enable the model to generate higher-resolution images (e.g., $1024\times 1024$ and $1536\times 1536$) without further fine-tuning. Experiments demonstrate the effectiveness and efficiency of our DiM.

CAPE: Context-Adaptive Positional Encoding for Length Extrapolation

Positional encoding plays a crucial role in transformers, significantly impacting model performance and length generalization. Prior research has introduced absolute positional encoding (APE) and relative positional encoding (RPE) to distinguish token positions in given sequences. However, both APE and RPE remain fixed after model training regardless of input data, limiting their adaptability and flexibility. Hence, we expect that the desired positional encoding should be context-adaptive and can be dynamically adjusted with the given attention. In this paper, we propose a Context-Adaptive Positional Encoding (CAPE) method, which dynamically and semantically adjusts based on input context and learned fixed priors. Experimental validation on real-world datasets (Arxiv, Books3, and CHE) demonstrates that CAPE enhances model performances in terms of trained length and length generalization, where the improvements are statistically significant. The model visualization suggests that our model can keep both local and anti-local information. Finally, we successfully train the model on sequence length 128 and achieve better performance at evaluation sequence length 8192, compared with other static positional encoding methods, revealing the benefit of the adaptive positional encoding method.

ATG: Benchmarking Automated Theorem Generation for Generative Language Models

Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new or reusable theorems is still under-explored. Without the new theorems, current LMs struggle to prove harder theorems that are distant from the given hypotheses with the exponentially growing search space. Therefore, this paper proposes an Automated Theorem Generation (ATG) benchmark that evaluates whether an agent can automatically generate valuable (and possibly brand new) theorems that are applicable for downstream theorem proving as reusable knowledge. Specifically, we construct the ATG benchmark by splitting the Metamath library into three sets: axioms, library, and problem based on their proving depth. We conduct extensive experiments to investigate whether current LMs can generate theorems in the library and benefit the problem theorems proving. The results demonstrate that high-quality ATG data facilitates models' performances on downstream ATP. However, there is still room for current LMs to develop better ATG and generate more advanced and human-like theorems. We hope the new ATG challenge can shed some light on advanced complex theorem proving.

Mixture of insighTful Experts : The Synergy of Thought Chains and Expert Mixtures in Self-Alignment

As the capabilities of large language models (LLMs) have expanded dramatically, aligning these models with human values presents a significant challenge, posing potential risks during deployment. Traditional alignment strategies rely heavily on human intervention, such as Supervised Fine-Tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF), or on the self-alignment capacities of LLMs, which usually require a strong LLM's emergent ability to improve its original bad answer. To address these challenges, we propose a novel self-alignment method that utilizes a Chain of Thought (CoT) approach, termed AlignCoT. This method encompasses stages of Question Analysis, Answer Guidance, and Safe Answer production. It is designed to enable LLMs to generate high-quality, safe responses throughout various stages of their development. Furthermore, we introduce the Mixture of insighTful Experts (MoTE) architecture, which applies the mixture of experts to enhance each component of the AlignCoT process, markedly increasing alignment efficiency. The MoTE approach not only outperforms existing methods in aligning LLMs with human values but also highlights the benefits of using self-generated data, revealing the dual benefits of improved alignment and training efficiency.

Automated Evaluation of Large Vision-Language Models on Self-driving Corner Cases

Large Vision-Language Models (LVLMs), due to the remarkable visual reasoning ability to understand images and videos, have received widespread attention in the autonomous driving domain, which significantly advances the development of interpretable end-to-end autonomous driving. However, current evaluations of LVLMs primarily focus on the multi-faceted capabilities in common scenarios, lacking quantifiable and automated assessment in autonomous driving contexts, let alone severe road corner cases that even the state-of-the-art autonomous driving perception systems struggle to handle. In this paper, we propose CODA-LM, a novel vision-language benchmark for self-driving, which provides the first automatic and quantitative evaluation of LVLMs for interpretable autonomous driving including general perception, regional perception, and driving suggestions. CODA-LM utilizes the texts to describe the road images, exploiting powerful text-only large language models (LLMs) without image inputs to assess the capabilities of LVLMs in autonomous driving scenarios, which reveals stronger alignment with human preferences than LVLM judges. Experiments demonstrate that even the closed-sourced commercial LVLMs like GPT-4V cannot deal with road corner cases well, suggesting that we are still far from a strong LVLM-powered intelligent driving agent, and we hope our CODA-LM can become the catalyst to promote future development.

DetCLIPv3: Towards Versatile Generative Open-vocabulary Object Detection

Existing open-vocabulary object detectors typically require a predefined set of categories from users, significantly confining their application scenarios. In this paper, we introduce DetCLIPv3, a high-performing detector that excels not only at both open-vocabulary object detection, but also generating hierarchical labels for detected objects. DetCLIPv3 is characterized by three core designs: 1. Versatile model architecture: we derive a robust open-set detection framework which is further empowered with generation ability via the integration of a caption head. 2. High information density data: we develop an auto-annotation pipeline leveraging visual large language model to refine captions for large-scale image-text pairs, providing rich, multi-granular object labels to enhance the training. 3. Efficient training strategy: we employ a pre-training stage with low-resolution inputs that enables the object captioner to efficiently learn a broad spectrum of visual concepts from extensive image-text paired data. This is followed by a fine-tuning stage that leverages a small number of high-resolution samples to further enhance detection performance. With these effective designs, DetCLIPv3 demonstrates superior open-vocabulary detection performance, \eg, our Swin-T backbone model achieves a notable 47.0 zero-shot fixed AP on the LVIS minival benchmark, outperforming GLIPv2, GroundingDINO, and DetCLIPv2 by 18.0/19.6/6.6 AP, respectively. DetCLIPv3 also achieves a state-of-the-art 19.7 AP in dense captioning task on VG dataset, showcasing its strong generative capability.

CVT-xRF: Contrastive In-Voxel Transformer for 3D Consistent Radiance Fields from Sparse Inputs

Neural Radiance Fields (NeRF) have shown impressive capabilities for photorealistic novel view synthesis when trained on dense inputs. However, when trained on sparse inputs, NeRF typically encounters issues of incorrect density or color predictions, mainly due to insufficient coverage of the scene causing partial and sparse supervision, thus leading to significant performance degradation. While existing works mainly consider ray-level consistency to construct 2D learning regularization based on rendered color, depth, or semantics on image planes, in this paper we propose a novel approach that models 3D spatial field consistency to improve NeRF's performance with sparse inputs. Specifically, we first adopt a voxel-based ray sampling strategy to ensure that the sampled rays intersect with a certain voxel in 3D space. We then randomly sample additional points within the voxel and apply a Transformer to infer the properties of other points on each ray, which are then incorporated into the volume rendering. By backpropagating through the rendering loss, we enhance the consistency among neighboring points. Additionally, we propose to use a contrastive loss on the encoder output of the Transformer to further improve consistency within each voxel. Experiments demonstrate that our method yields significant improvement over different radiance fields in the sparse inputs setting, and achieves comparable performance with current works.

DriveCoT: Integrating Chain-of-Thought Reasoning with End-to-End Driving

End-to-end driving has made significant progress in recent years, demonstrating benefits such as system simplicity and competitive driving performance under both open-loop and closed-loop settings. Nevertheless, the lack of interpretability and controllability in its driving decisions hinders real-world deployment for end-to-end driving systems. In this paper, we collect a comprehensive end-to-end driving dataset named DriveCoT, leveraging the CARLA simulator. It contains sensor data, control decisions, and chain-of-thought labels to indicate the reasoning process. We utilize the challenging driving scenarios from the CARLA leaderboard 2.0, which involve high-speed driving and lane-changing, and propose a rule-based expert policy to control the vehicle and generate ground truth labels for its reasoning process across different driving aspects and the final decisions. This dataset can serve as an open-loop end-to-end driving benchmark, enabling the evaluation of accuracy in various chain-of-thought aspects and the final decision. In addition, we propose a baseline model called DriveCoT-Agent, trained on our dataset, to generate chain-of-thought predictions and final decisions. The trained model exhibits strong performance in both open-loop and closed-loop evaluations, demonstrating the effectiveness of our proposed dataset.