Understanding both the question and image, as well as modelling their interactions requires us to combine Computer Vision and NLP techniques. The problem is generally framed in terms of classification, such that the network learns to produce answers from a finite set of classes which facilitates training and evaluation.

Large Reasoning Models (LRMs) achieve superior performance by extending the thought length. However, a lengthy thinking trajectory leads to reduced efficiency. Most of the existing methods are stuck in the assumption of overthinking and attempt to reason efficiently by compressing the Chain-of-Thought, but this often leads to performance degradation. To address this problem, we introduce A*-Thought, an efficient tree search-based unified framework designed to identify and isolate the most essential thoughts from the extensive reasoning chains produced by these models. It formulates the reasoning process of LRMs as a search tree, where each node represents a reasoning span in the giant reasoning space. By combining the A* search algorithm with a cost function specific to the reasoning path, it can efficiently compress the chain of thought and determine a reasoning path with high information density and low cost. In addition, we also propose a bidirectional importance estimation mechanism, which further refines this search process and enhances its efficiency beyond uniform sampling. Extensive experiments on several advanced math tasks show that A*-Thought effectively balances performance and efficiency over a huge search space. Specifically, A*-Thought can improve the performance of QwQ-32B by 2.39$\times$ with low-budget and reduce the length of the output token by nearly 50% with high-budget. The proposed method is also compatible with several other LRMs, demonstrating its generalization capability. The code can be accessed at: https://github.com/AI9Stars/AStar-Thought.

Although LLMs have achieved remarkable performance, the inherent stochasticity of their reasoning process and varying conclusions present significant challenges. Majority voting or Best-of-N with external verification models has been explored to find the most promising solution among multiple LLM outputs. However, these approaches have certain limitations, such as limited applicability or the cost of an additional training step. To address this problem, we propose a novel and effective framework that Recycles Few-shot examples to verify LLM outputs (ReFeri). Our key idea is to additionally utilize the given few-shot examples to evaluate the candidate outputs of the target query, not only using them to generate outputs as the conventional few-shot prompting setup. Specifically, ReFeri evaluates the generated outputs by combining two different scores, designed motivated from Bayes' rule, and subsequently selects the candidate that is both confidently determined and contextually coherent through a few additional LLM inferences. Experiments with three different LLMs and across seven diverse tasks demonstrate that our framework significantly improves the accuracy of LLMs-achieving an average gain of 4.8%-through effective response selection, without additional training.

Abstract-- Since the mid-1990s, it has been known that, unlike in Cartesian form where Brockett's condition rules out static feedback stabilization, the unicycle is globally asymptotically stabilizable by smooth feedback in polar coordinates. In this note, we introduce a modular framework for designing smooth feedback laws that achieve global asymptotic stabilization in polar coordinates. These laws are bidirectional, enabling efficient parking maneuvers, and are paired with families of strict control Lyapunov functions (CLFs) constructed in a modular fashion. The resulting CLFs guarantee global asymptotic stability with explicit convergence rates and include barrier variants that yield "almost global" stabilization, excluding only zero-measure subsets of the rotation manifolds. The strictness of the CLFs is further leveraged in our companion paper, where we develop inverse-optimal redesigns with meaningful cost functions and infinite gain margins.

Abstract-- In a companion paper, we present a modular framework for unicycle stabilization in polar coordinates that provides smooth steering laws through backstepping. Surprisingly, the same problem also allows application of integrator forwarding. In this work, we leverage this feature and construct new smooth steering laws together with control Lyapunov functions (CLFs), expanding the set of CLFs available for inverse optimal control design. In the case of constant forward velocity (Dubins car), backstepping produces finite-time (deadbeat) parking, and we show that integrator forwarding yields the very same class of solutions. This reveals a fundamental connection between backstepping and forwarding in addressing both the unicycle and, the Dubins car parking problems.

Trajectory prediction and planning in autonomous driving are highly challenging due to the complexity of predicting surrounding agents' movements and planning the ego agent's actions in dynamic environments. Existing methods encode map and agent positions and decode future trajectories in Cartesian coordinates. However, modeling the relationships between the ego vehicle and surrounding traffic elements in Cartesian space can be suboptimal, as it does not naturally capture the varying influence of different elements based on their relative distances and directions. To address this limitation, we adopt the Polar coordinate system, where positions are represented by radius and angle. This representation provides a more intuitive and effective way to model spatial changes and relative relationships, especially in terms of distance and directional influence. Based on this insight, we propose Polaris, a novel method that operates entirely in Polar coordinates, distinguishing itself from conventional Cartesian-based approaches. By leveraging the Polar representation, this method explicitly models distance and direction variations and captures relative relationships through dedicated encoding and refinement modules, enabling more structured and spatially aware trajectory prediction and planning. Extensive experiments on the challenging prediction (Argoverse 2) and planning benchmarks (nuPlan) demonstrate that Polaris achieves state-of-the-art performance.

Training deep neural networks typically requires large datasets, which may not be available in privacy-sensitive or resource-constrained domains. Data-free knowledge distillation (DFKD) [1] has emerged as a promising approach where a student model learns from synthetic data generated via a pretrained teacher network. However, existing DFKD methods often fail to ensure structural alignment between synthetic and real data. We propose C2G-KD, a method leveraging PCA-derived constraints to guide a conditional generator in producing class-specific synthetic samples without direct access to real data. Central to this approach is the use of PCA [2] to impose topological constraints from minimal real samples, ensuring that generated images structurally align with class manifolds.

Large Language Models (LLMs) face significant challenges in edge deployment due to their massive parameter scale. Vector Quantization (VQ), a clustering-based quantization method, serves as a prevalent solution to this issue for its extremely low-bit (even at 2-bit) and considerable accuracy. Since a vector is a quantity in mathematics and physics that has both direction and magnitude, existing VQ works typically quantize them in a coupled manner. However, we find that direction exhibits significantly greater sensitivity to quantization compared to the magnitude. For instance, when separately clustering the directions and magnitudes of weight vectors in LLaMA-2-7B, the accuracy drop of zero-shot tasks are 46.5\% and 2.3\%, respectively. This gap even increases with the reduction of clustering centers. Further, Euclidean distance, a common metric to access vector similarities in current VQ works, places greater emphasis on reducing the magnitude error. This property is contrary to the above finding, unavoidably leading to larger quantization errors. To these ends, this paper proposes Polar Coordinate Decoupled Vector Quantization (PCDVQ), an effective and efficient VQ framework consisting of two key modules: 1) Polar Coordinate Decoupling (PCD), which transforms vectors into their polar coordinate representations and perform independent quantization of the direction and magnitude parameters.2) Distribution Aligned Codebook Construction (DACC), which optimizes the direction and magnitude codebooks in accordance with the source distribution. Experimental results show that PCDVQ outperforms baseline methods at 2-bit level by at least 1.5\% zero-shot accuracy, establishing a novel paradigm for accurate and highly compressed LLMs.

Human reasoning is flexible, adaptive, and grounded in prior experience-qualities that large language models (LLMs) still struggle to emulate. Existing methods either explore diverse reasoning paths at inference time or search for optimal workflows through expensive operations, but both fall short in leveraging multiple reusable strategies in a structured, efficient manner. We propose Guideline Forest, a framework that enhances LLMs reasoning by inducing structured reasoning strategies-called guidelines-from verified examples and executing them via step-wise aggregation. Unlike test-time search or single-path distillation, our method draws on verified reasoning experiences by inducing reusable guidelines and expanding each into diverse variants. Much like human reasoning, these variants reflect alternative thought patterns, are executed in parallel, refined via self-correction, and aggregated step by step-enabling the model to adaptively resolve uncertainty and synthesize robust solutions.We evaluate Guideline Forest on four benchmarks-GSM8K, MATH-500, MBPP, and HumanEval-spanning mathematical and programmatic reasoning. Guideline Forest consistently outperforms strong baselines, including CoT, ReAct, ToT, FoT, and AFlow. Ablation studies further highlight the effectiveness of multi-path reasoning and stepwise aggregation, underscoring the Guideline Forest's adaptability and generalization potential.

Recently, long-thought reasoning models achieve strong performance on complex reasoning tasks, but often incur substantial inference overhead, making efficiency a critical concern. Our empirical analysis reveals that the benefit of using Long-CoT varies across problems: while some problems require elaborate reasoning, others show no improvement, or even degraded accuracy. This motivates adaptive reasoning strategies that tailor reasoning depth to the input. However, prior work primarily reduces redundancy within long reasoning paths, limiting exploration of more efficient strategies beyond the Long-CoT paradigm. To address this, we propose a novel two-stage framework for adaptive and efficient reasoning. First, we construct a hybrid reasoning model by merging long and short CoT models to enable diverse reasoning styles. Second, we apply bi-level preference training to guide the model to select suitable reasoning styles (group-level), and prefer concise and correct reasoning within each style group (instance-level). Experiments demonstrate that our method (Ada-R1) significantly reduces inference costs compared to other baseline approaches, while maintaining performance. Notably, on five mathematical datasets, the average length of reasoning is reduced by more than 50%, highlighting the potential of adaptive strategies to optimize reasoning efficiency in large language models. Our code is coming soon at https://github.com/StarDewXXX/AdaR1