Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve (Novikov et al., 2025; Georgiev et al., 2025), have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. However, the high-level descriptions in published work leave many implementation details unspecified, hindering reproducibility and further research. In this report we present GigaEvo, an extensible open-source framework that enables researchers to study and experiment with hybrid LLM-evolution approaches inspired by AlphaEvolve. Our system provides modular implementations of key components: MAP-Elites quality-diversity algorithms, asynchronous DAG-based evaluation pipelines, LLM-driven mutation operators with insight generation and bidirectional lineage tracking, and flexible multi-island evolutionary strategies. In order to assess reproducibility and validate our implementation we evaluate GigaEvo on challenging problems from the AlphaEvolve paper: Heil-bronn triangle placement, circle packing in squares, and high-dimensional kissing numbers. The framework emphasizes modularity, concurrency, and ease of experimentation, enabling rapid prototyping through declarative configuration. We provide detailed descriptions of system architecture, implementation decisions, and experimental methodology to support further research in LLM-driven evolutionary methods. The recent paper (Novikov et al., 2025) introduced AlphaEvolve, a framework that combines large language model (LLM) code generation with evolutionary computation, achieving state-of-the-art results on challenging algorithmic and mathematical problems.

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations between triples of points and other points. More significantly, based on this curvature profile, we introduce a quantitative measure to evaluate the effectiveness of data representations, such as those produced by dimensionality reduction techniques. Furthermore, Our experiments demonstrate that this curvature-based analysis can be employed to estimate the intrinsic dimensionality of datasets. We use this to explore the large-scale geometry of empirical networks and to evaluate the effectiveness of dimensionality reduction techniques.

Recent advancements in large reasoning models (LRMs) have demonstrated the effectiveness of scaling test-time computation to enhance reasoning capabilities on various tasks. However, LRMs often suffer from an ``overthinking'' problem, where the model generates excessively redundant reasoning steps with limited performance gains. In this work, we empirically reveal an important characteristic of LRM behaviors that placing external CoTs generated by smaller models between the thinking token (\texttt{} and \texttt{}) can effectively manipulate the model to generate fewer thoughts. Building on this finding, we propose a simple yet efficient pipeline, \Method, to enable LRMs to bypass unnecessary intermediate steps, thereby significantly reducing computational costs. We conduct extensive experiments to evaluate the utility and efficiency of \Method. For instance, when applied to QwQ-32B on the LiveBench/Code dataset, \Method keeps the original performance while reducing output token counts by approximately 30\%, with minimal overhead introduced by the CoT generator. Furthermore, we identify two suboptimal modes, blindly following flawed external thoughts and unnecessary rethinking, and show that simple mitigations, such as difficulty-aware fallbacks, can further improve performance. Overall, \Method offers a practical, general, and efficient way to optimize LRM inference, making powerful reasoning models more accessible and scalable for real-world applications.

Localization of mobile robots is crucial for deploying robots in real-world applications such as search and rescue missions. This work aims to develop an accurate localization system applicable to swarm robots equipped only with low-cost monocular vision sensors and visual markers. The system is designed to operate in fully open spaces, without landmarks or support from positioning infrastructures. To achieve this, we propose a localization method based on equilateral triangular formations. By leveraging the geometric properties of equilateral triangles, the accurate two-dimensional position of each participating robot is estimated using one-dimensional lateral distance information between robots, which can be reliably and accurately obtained with a low-cost monocular vision sensor. Experimental and simulation results demonstrate that, as travel time increases, the positioning error of the proposed method becomes significantly smaller than that of a conventional dead-reckoning system, another low-cost localization approach applicable to open environments.

Recent advancements in large language models (LLMs) have demonstrated impressive chain-of-thought reasoning capabilities, with reinforcement learning (RL) playing a crucial role in this progress. While "aha moment" patterns--where models exhibit self-correction through reflection--are often attributed to emergent properties from RL, we first demonstrate that these patterns exist in multimodal LLMs (MLLMs) prior to RL training but may not necessarily correlate with improved reasoning performance. Building on these insights, we present a comprehensive study on enhancing multimodal reasoning through a two-stage approach: (1) supervised fine-tuning (SFT) as a cold start with structured chain-of-thought reasoning patterns, followed by (2) reinforcement learning via GRPO to further refine these capabilities. Our extensive experiments show that this combined approach consistently outperforms both SFT-only and RL-only methods across challenging multimodal reasoning benchmarks. The resulting models achieve state-of-the-art performance among open-source MLLMs at both 3B and 7B scales, with our 7B model showing substantial improvements over base models (e.g., 66.3 %$\rightarrow$73.4 % on MathVista, 62.9 %$\rightarrow$70.4 % on We-Math) and our 3B model achieving performance competitive with several 7B models. Overall, this work provides practical guidance for building advanced multimodal reasoning models. Our code is available at https://github.com/waltonfuture/RL-with-Cold-Start.

Large Language Models (LLMs) have demonstrated impressive capabilities in complex reasoning tasks, yet they still struggle to reliably verify the correctness of their own outputs. Existing solutions to this verification challenge often depend on separate verifier models or require multi-stage self-correction training pipelines, which limit scalability. In this paper, we propose Policy as Generative Verifier (PAG), a simple and effective framework that empowers LLMs to self-correct by alternating between policy and verifier roles within a unified multi-turn reinforcement learning (RL) paradigm. Distinct from prior approaches that always generate a second attempt regardless of model confidence, PAG introduces a selective revision mechanism: the model revises its answer only when its own generative verification step detects an error. This verify-then-revise workflow not only alleviates model collapse but also jointly enhances both reasoning and verification abilities. Extensive experiments across diverse reasoning benchmarks highlight PAG's dual advancements: as a policy, it enhances direct generation and self-correction accuracy; as a verifier, its self-verification outperforms self-consistency.

Large Language Models (LLMs) have advanced rapidly in recent years, demonstrating strong capabilities in problem comprehension and reasoning. Inspired by these developments, researchers have begun exploring the use of LLMs as decentralized decision-makers for multi-robot formation control. However, prior studies reveal that directly applying LLMs to such tasks often leads to unstable and inconsistent behaviors, where robots may collapse to the centroid of their positions or diverge entirely due to hallucinated reasoning, logical inconsistencies, and limited coordination awareness. To overcome these limitations, we propose a novel framework that integrates LLMs with an influence-based plan consensus protocol. In this framework, each robot independently generates a local plan toward the desired formation using its own LLM. The robots then iteratively refine their plans through a decentralized consensus protocol that accounts for their influence on neighboring robots. This process drives the system toward a coherent and stable flocking formation in a fully decentralized manner. We evaluate our approach through comprehensive simulations involving both state-of-the-art closed-source LLMs (e.g., o3-mini, Claude 3.5) and open-source models (e.g., Llama3.1-405b, Qwen-Max, DeepSeek-R1). The results show notable improvements in stability, convergence, and adaptability over previous LLM-based methods. We further validate our framework on a physical team of Crazyflie drones, demonstrating its practical viability and effectiveness in real-world multi-robot systems.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higherquality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce highfidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closedsource model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT. Large Language Models (LLMs) exhibit excellent reasoning capabilities and draw extensive attention from the artificial intelligence research community (Lu et al., 2023b) to mathematical problemsolving in textual form (Chen et al., 2024b; Liao et al., 2024; Zhou et al., 2024; Zhao et al., 2024b; Zhou & Zhao, 2024; Kim et al., 2024). However, LLMs still struggle to solve mathematical problems involving images that require visual comprehension. Geometry problems, as typical mathematical problems with images, play an important role in evaluating mathematical reasoning skills (Zhang et al., 2023c), requiring a high level of visual comprehension. Besides, even though some problems are not related to geometry on the surface, they require the same skills for models (e.g., fine-grained image comprehension skills and multi-step reasoning skills). With the appearance of o1 (OpenAI, 2024), GPT-4o (Islam & Moushi, 2024), Gemini (Team et al., 2023), and numerous Large Multimodal Models (LMMs) (Li et al., 2024a; Liu et al., 2024; Chen et al., 2024d; Bai et al., 2023), recent researches progressively investigate using LMMs to solve mathematical geometry problems. Although LMMs show impressive results in general visual question-answering (VQA) tasks (Fan et al., 2024; Liu et al., 2024), they still face challenges in solving mathematical geometry problems. Adjust values in the question and generate answers.

Human cognition exhibits systematic compositionality, the algebraic ability to generate infinite novel combinations from finite learned components, which is the key to understanding and reasoning about complex logic. In this work, we investigate the compositionality of large language models (LLMs) in mathematical reasoning. Specifically, we construct a new dataset \textsc{MathTrap}\footnotemark[3] by introducing carefully designed logical traps into the problem descriptions of MATH and GSM8k. Since problems with logical flaws are quite rare in the real world, these represent ``unseen'' cases to LLMs. Solving these requires the models to systematically compose (1) the mathematical knowledge involved in the original problems with (2) knowledge related to the introduced traps. Our experiments show that while LLMs possess both components of requisite knowledge, they do not \textbf{spontaneously} combine them to handle these novel cases. We explore several methods to mitigate this deficiency, such as natural language prompts, few-shot demonstrations, and fine-tuning. We find that LLMs' performance can be \textbf{passively} improved through the above external intervention. Overall, systematic compositionality remains an open challenge for large language models.

An autonomous mobile robot system consisting of many mobile computational entities (called robots) attracts much attention of researchers, and to clarify the relation between the capabilities of robots and solvability of the problems is an emerging issue for a recent couple of decades. Generally, each robot can observe all other robots as long as there are no restrictions for visibility range or obstructions, regardless of the number of robots. In this paper, we provide a new perspective on the observation by robots; a robot cannot necessarily observe all other robots regardless of distances to them. We call this new computational model defected view model. Under this model, in this paper, we consider the gathering problem that requires all the robots to gather at the same point and propose two algorithms to solve the gathering problem in the adversarial ($N$,$N-2$)-defected model for $N \geq 5$ (where each robot observes at most $N-2$ robots chosen adversarially) and the distance-based (4,2)-defected model (where each robot observes at most 2 closest robots to itself) respectively, where $N$ is the number of robots. Moreover, we present an impossibility result showing that there is no (deterministic) gathering algorithm in the adversarial or distance-based (3,1)-defected model. Moreover, we show an impossibility result for the gathering in a relaxed ($N$, $N-2$)-defected model.