ONE-SHOT: Compositional Human-Environment Video Synthesis via Spatial-Decoupled Motion Injection and Hybrid Context Integration
Recent advances in Video Foundation Models (VFMs) have revolutionized human-centric video synthesis, yet fine-grained and independent editing of subjects and scenes remains a critical challenge. Recent attempts to incorporate richer environment control through rigid 3D geometric compositions often encounter a stark trade-off between precise control and generative flexibility. Furthermore, the heavy 3D pre-processing still limits practical scalability. In this paper, we propose ONE-SHOT, a parameter-efficient framework for compositional human-environment video generation. Our key insight is to factorize the generative process into disentangled signals. Specifically, we introduce a canonical-space injection mechanism that decouples human dynamics from environmental cues via cross-attention. We also propose Dynamic-Grounded-RoPE, a novel positional embedding strategy that establishes spatial correspondences between disparate spatial domains without any heuristic 3D alignments. To support
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프록시 탐색과 재사용 가능한 가이던스: 프록시 기반 업데이트 신호를 활용한 모듈형 LLM 포스트트레이닝 패러다임
Post-training is essential for refining the domain-specific capabilities of large language models (LLMs), yet existing reward optimization and distribution matching methods tightly couple policy exploration with distribution alignment. This coupling forces expensive exploration directly on the policy model and severely hinders the asynchronous generation, reuse, and cross-model transfer of optimization signals. In this paper, we propose Proxy-guided Update Signal Transfer (PUST), a novel post-training framework that fundamentally decouples update-signal exploration from distribution alignment. Instead of utilizing the primary model for costly exploration, PUST employs a lightweight proxy model as an efficient testbed to discover high-reward behaviors. We extract the relative improvement signal between the proxy's initial and optimized states, transferring this directional update to the primary model to guide its policy alignment. This decoupled pipeline, comprising proxy exploration, u
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Synthetic Sandbox for Training Machine Learning Engineering Agents
As large language model agents advance beyond software engineering (SWE) tasks toward machine learning engineering (MLE), verifying agent behavior becomes orders of magnitude more expensive: while SWE tasks can be verified via fast-executing unit tests, MLE verification requires running full ML pipelines -- data preprocessing, model training, and metric evaluation -- on large datasets at each rollout step, rendering trajectory-wise on-policy reinforcement learning (RL) prohibitively slow. Existing approaches retreat to supervised fine-tuning (SFT) or offline proxy rewards, sacrificing the exploration and generalization benefits of on-policy RL. We observe that sandbox data size is the primary source of this bottleneck. Based on this insight, we introduce SandMLE, a multi-agent framework that generates diverse, verifiable synthetic MLE environments from a small number of seed tasks, preserving the structural and technical complexity of real-world problems while constraining datasets to
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LLM의 메타인지: 기초와 진전, 그리고 기회
Metacognition is a foundational component of intelligence critical to effective learning, problem solving, decision-making, communication, and more. In recent years, it has become increasingly recognized as a cornerstone of capable, transparent AI systems. Yet while LLMs have made significant progress across diverse real-world tasks, it is not yet clear when, how, or to what extent they can exhibit or be endowed with effective metacognitive abilities, nor how such abilities can be adapted to advance the fundamental capabilities, reliability, and intelligence of AI systems. This paper bridges this gap by presenting the first comprehensive overview of the current state of knowledge on metacognition for LLMs. We analyze and taxonomize the landscape of this emerging field and summarize recent technical advancements, including methods and benchmarks to measure and evaluate LLMs' metacognitive abilities, techniques to elicit, improve, and apply metacognition in LLMs, and findings and implica
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낮은 중첩 캡처만으로 구현한 4D 인간-장면 복원
Existing volumetric capture of dynamic human performance achieves high fidelity with dense camera arrays. However, in real-world scenarios, only a handful of low-overlap cameras are available, which degrades the output quality and leaves large areas unobserved. Recent 4D reconstruction methods have focused on low-overlap settings, yet they still produce noticeable artifacts in under-observed regions. Video diffusion models have emerged as another option, but they show geometrically inconsistent results for humans. To address these limitations, we propose StudioRecon, a pipeline that reconstructs 4D human scenes from sparse, low-overlap cameras by decoupling background and humans. We densify background supervision by synthesizing hundreds of camera-controlled novel views with a video diffusion model. We also robustly initialize deformable Gaussian humans with cross-view identity association and triangulated multi-view keypoint fitting. Finally, our recursive enhancement module with moti
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Paper Espresso: From Paper Overload to Research Insight
The accelerating pace of scientific publishing makes it increasingly difficult for researchers to stay current. We present Paper Espresso, an open-source platform that automatically discovers, summarizes, and analyzes trending arXiv papers. The system uses large language models (LLMs) to generate structured summaries with topical labels and keywords, and provides multi-granularity trend analysis at daily, weekly, and monthly scales through LLM-driven topic consolidation. Over 35 months of continuous deployment, Paper Espresso has processed over 13,300 papers and publicly released all structured metadata, revealing rich dynamics in the AI research landscape: a mid-2025 surge in reinforcement learning for LLM reasoning, non-saturating topic emergence (6,673 unique topics), and a positive correlation between topic novelty and community engagement (2.0x median upvotes for the most novel papers). A live demo is available at https://huggingface.co/spaces/Elfsong/Paper_Espresso.
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HDP: A Lightweight Cryptographic Protocol for Human Delegation Provenance in Agentic AI Systems
Agentic AI systems increasingly execute consequential actions on behalf of human principals, delegating tasks through multi-step chains of autonomous agents. No existing standard addresses a fundamental accountability gap: verifying that terminal actions in a delegation chain were genuinely authorized by a human principal, through what chain of delegation, and under what scope. This paper presents the Human Delegation Provenance (HDP) protocol, a lightweight token-based scheme that cryptographically captures and verifies human authorization context in multi-agent systems. An HDP token binds a human authorization event to a session, records each agent's delegation action as a signed hop in an append-only chain, and enables any participant to verify the full provenance record using only the issuer's Ed25519 public key and the current session identifier. Verification is fully offline, requiring no registry lookups or third-party trust anchors. We situate HDP within the existing landscape
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SciLT: Long-Tailed Classification in Scientific Image Domains
Long-tailed recognition has benefited from foundation models and fine-tuning paradigms, yet existing studies and benchmarks are mainly confined to natural image domains, where pre-training and fine-tuning data share similar distributions. In contrast, scientific images exhibit distinct visual characteristics and supervision signals, raising questions about the effectiveness of fine-tuning foundation models in such settings. In this work, we investigate scientific long-tailed recognition under a purely visual and parameter-efficient fine-tuning (PEFT) paradigm. Experiments on three scientific benchmarks show that fine-tuning foundation models yields limited gains, and reveal that penultimate-layer features play an important role, particularly for tail classes. Motivated by these findings, we propose SciLT, a framework that exploits multi-level representations through adaptive feature fusion and dual-supervision learning. By jointly leveraging penultimate- and final-layer features, SciLT
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BidirLM: From Text to Omnimodal Bidirectional Encoders by Adapting and Composing Causal LLMs
Transforming causal generative language models into bidirectional encoders offers a powerful alternative to BERT-style architectures. However, current approaches remain limited: they lack consensus on optimal training objectives, suffer from catastrophic forgetting at scale, and fail to flexibly integrate the vast ecosystem of specialized generative models. In this work, through systematic ablations on the Gemma3 and Qwen3 families, we identify the key factors driving successful adaptation, highlighting the critical role of an often-omitted prior masking phase. To scale this process without original pre-training data, we introduce a dual strategy combining linear weight merging with a lightweight multi-domain data mixture that mitigates catastrophic forgetting. Finally, we augment our encoders by merging them with specialized causal models, seamlessly transferring modality- and domain-specific capabilities. This open-source recipe, designed for any causal decoder LLM, yields BidirLM, a
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Nexus : An Agentic Framework for Time Series Forecasting
Time series forecasting is not just numerical extrapolation, but often requires reasoning with unstructured contextual data such as news or events. While specialized Time Series Foundation Models (TSFMs) excel at forecasting based on numerical patterns, they remain unaware to real-world textual signals. Conversely, while LLMs are emerging as zero-shot forecasters, their performance remains uneven across domains and contextual grounding. To bridge this gap, we introduce Nexus, a multi-agent forecasting framework that decomposes prediction into specialized stages: isolating macro-level and micro-level temporal fluctuations, and integrating contextual information when available before synthesizing a final forecast. This decomposition enables Nexus to adapt from seasonal signals to volatile, event-driven information without relying on external statistical anchors or monolithic prompting. We show that current-generation LLMs possess substantially stronger intrinsic forecasting ability than
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직접 온폴리시 증류로 구현한 Weak-to-Strong 일반화
Reinforcement learning with verifiable rewards (RLVR) is a powerful recipe for improving language-model reasoning, but it is expensive to repeat on every new strong model because the target model must generate many rollouts during training. As models scale, post-training itself becomes a bottleneck. We study a weak-to-strong alternative: run RL on a smaller model where rollouts are cheaper, then reuse what that RL run learned to improve a stronger target model. Directly distilling the post-RL weak teacher is not enough, because the teacher's final policy mixes useful RL gains with the limitations of the smaller model. We propose Direct On-Policy Distillation (Direct-OPD), which transfers the teacher's RL-induced policy shift instead. Direct-OPD compares the post-RL teacher with its own pre-RL reference and treats their log-ratio as a dense implicit reward for the student. In plain terms, the checkpoint pair tells us which actions RL made the weak model more or less likely to take, and
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H^2SD: 하이브리드 하인드사이트 자기 증류
Reinforcement learning with verifiable rewards (RLVR) has substantially improved the reasoning capabilities of large language models on tasks such as mathematical reasoning and code generation. However, most RLVR methods assign a scalar outcome reward to an entire trajectory, resulting in sparse supervision and limited token-level credit assignment. On-policy distillation (OPD) provides denser supervision by distilling token-level distributions from a stronger teacher model, but requires an additional teacher and typically assumes a shared vocabulary. On-policy self-distillation (OPSD) removes this dependency by conditioning the same model on privileged information to construct a teacher policy. However, directly matching the teacher distribution may cause information leakage and unstable optimization. RLSD avoids direct matching by using the teacher signal only to modulate update magnitudes, but it cannot provide an explicit correction direction when the sampled reasoning fails. To ad
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Delineate Anything v2: 필드 경계 추출을 위한 글로벌 파운데이션 모델
Accurate agricultural field boundary delineation at large scale is a foundational task for food security, supply chain transparency, and carbon accounting. While vision foundation models like SAM show remarkable zero-shot capabilities, they frequently fail in geospatial domains due to topological complexity, cropland texturing patterns, and a lack of physical scale awareness. In this work, we introduce Delineate Anything v2, a globally scalable foundation model designed specifically for wide-area field boundary mapping. We construct FBIS-73M, a 73-million-instance multi-resolution dataset spanning 61 countries. To address the pervasive issue of multi-field administrative parcel merging, we introduce a resolution-specific data curation pipeline that leverages topological image-space adaptation to homogenize merged parcels and strengthen weak physical boundaries. Furthermore, we establish a novel, manually curated evaluation benchmark covering 100 countries to assess independent zero-sho
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Struct-Searcher: 에이전트형 구조적 사고로 멀티모달 심층 정보 탐색 고도화
Deep research agents have attracted increasing attention for their ability to collect large-scale online information to acquire target knowledge, with recent efforts shifting from purely text-based information seeking to multimodal settings. However, existing agentic workflows are largely aligned with evidence accumulation models, which linearly aggregate evidence and lack principled mechanisms for handling contradictory information across heterogeneous modalities. Towards this end, we propose Struct-Searcher, a structural agentic workflow grounded in belief revision theory that explicitly maintains an evolving multimodal structural graph throughout the reasoning process, enabling effective conflict-aware multimodal deep information seeking. Extensive experiments across multiple benchmark datasets and backbone models demonstrate that Struct-Searcher is (1) plug-and-play and model-agnostic, yielding an average relative accuracy improvement of 17.2% on BrowseComp-VL across five different
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Workflow-GYM: 실제 전문 업무 환경에서 컴퓨터 사용 에이전트 작업의 장기 과제 평가
Recent years have witnessed the rapid evolution of AI agents toward handling increasingly complex, real-world tasks. However, existing benchmarks rarely evaluate whether agents can operate graphical user interfaces to complete long-horizon, high-value professional workflows across diverse domains. Current GUI benchmarks still predominantly focus on general-purpose software, relatively simple applications, and short-horizon tasks, leaving it largely unknown whether modern agents can follow user instructions to autonomously operate domain-specific professional software and accomplish economically valuable work in an end-to-end manner. To bridge this gap, we introduce Workflow-GYM, a benchmark for long-horizon GUI tasks centered on professional domains and specialized software environments. Through extensive experiments on state-of-the-art models, we find that even the strongest models achieve only slightly above 30% success rates, highlighting that professional long-horizon GUI workflows
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AgentKernel: 신뢰 중심의 에이전트 운영체제
Modern AI agents routinely cross trust boundaries: they ingest untrusted content, combine it with privileged instructions, persist intermediate beliefs in long-term memory, and invoke privileged tools. This creates an attack surface in which malicious payloads can enter through model inputs and cause harmful tool actions. Yet current governance stacks remain application-level middleware that share a process trust boundary with the agents they monitor. We argue that agents need an operating-system substrate providing mandatory, non-bypassable services for identity, input mediation, memory governance, and execution control.
We introduce AgentKernel, a trust-native agent operating system built around the premise that security must be a first-class design constraint. AgentKernel wraps the agent lifecycle in a mandatory enforcement boundary organized into four pillars: Identity, Perception, Cognition, and Execution. Each pillar adapts classical OS security principles to failures at the se
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World Action Agent: 월드 액션 리허설로 VLM 기반 로봇 조작 고도화
General-purpose vision-language models (VLMs) bring broad knowledge and spatial reasoning to robot manipulation, yet existing systems either use them indirectly, to predict constraints or write programs, or give them a view of the scene rather than a world in which to act. We present World Action Agent (WAA), a multi-agent harness through which VLMs pilot robots with basic tools, making every decision within a visual action workspace. The workspace has three properties. Contact views, selected automatically from the scene geometry, present the scene around the current interaction. Action rehearsal turns each action into an editable proposal that the agent, alone or through an Imagination Agent, previews and revises against planning feedback before execution. In-view correction closes the loop between observation, rehearsal, and low-level execution, letting the agent remove residual offsets in the view where it observes them. Through the same workspace, WAA acquires embodied procedural
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Combee: Scaling Prompt Learning for Self-Improving Language Model Agents
Recent advances in prompt learning allow large language model agents to acquire task-relevant knowledge from inference-time context without parameter changes. For example, existing methods (like ACE or GEPA) can learn system prompts to improve accuracy based on previous agent runs. However, these methods primarily focus on single-agent or low-parallelism settings. This fundamentally limits their ability to efficiently learn from a large set of collected agentic traces. It would be efficient and beneficial to run prompt learning in parallel to accommodate the growing trend of learning from many agentic traces or parallel agent executions. Yet without a principled strategy for scaling, current methods suffer from quality degradation with high parallelism. To improve both the efficiency and quality of prompt learning, we propose Combee, a novel framework to scale parallel prompt learning for self-improving agents. Combee speeds up learning and enables running many agents in parallel while
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Gemini Embedding 2: Gemini 기반 네이티브 멀티모달 임베딩 모델
We introduce Gemini Embedding 2, a native multimodal embedding model that allows embedding video, audio, image, and text modalities in a unified representation space. We leverage the multimodal capabilities of Gemini to produce embeddings for arbitrary combinations of interleaved inputs across all these modalities that generalize well across a wide variety of tasks. Applying large-scale contrastive learning in a multi-task multi-stage training setup, we achieve state-of-the-art performance on key embedding benchmarks including unimodal, cross-modal, and multimodal retrieval spanning a diverse set of tasks. We show that our embedding model demonstrates strong performance (with a score of 62.9 R@1 on MSCOCO, 68.8 NDCG@10 on Vatex, 69.9 on MTEB multilingual and 84.0 on MTEB Code) across a variety of tasks surpassing the performance of specialized models. These unified capabilities make Gemini Embedding 2 a promising candidate for downstream use cases such as RAG, recommendation and search
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Pantheon360: 3D 인식 360° 비디오 확산으로 디지털 트윈 생성 다루기
Generating complete digital twins from videos requires precise camera control, global scene coverage, and strict spatial-temporal consistency constraints that remain challenging for perspective video generators due to their limited field of view (FoV). Their narrow FoV forces long or multi-view trajectories, amplifying cross-view inconsistency and temporal drift. We argue that 360° video generation offers a natural solution: panoramic coverage simplifies trajectory design and provides a strong global context for maintaining coherence. We introduce Pantheon360: Taming Digital Twin Generation via 3D-Aware 360° Video Diffusion, a controllable 360° video generation framework that synthesizes high-fidelity videos from sparse 360° inputs. The key idea is an explicit 3D Cache, reconstructed from the input, which serves as a geometric scaffold for any user-defined camera path. This allows the diffusion model to focus on photorealistic texture refinement while the 3D Cache enforces global geome
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스칼라 보상을 넘어: 추론을 점수 분포에 내재화하기
Reward models are central to text-to-image post-training, but visual preference is subjective and better represented as a distribution over rubric scores than as a deterministic scalar. Existing scalar, score-token, and pairwise reward models over-compress uncertainty and fine-grained score differences, while reasoning-based generative rewards provide stronger judgments but are costly to deploy and difficult to use as direct optimization signals. We propose Z-Reward, a teacher-student reward modeling framework that decouples reasoning-heavy judgment from efficient reward deployment. The teacher is a large VLM that uses reasoning to infer rubric-aligned score distributions, and is trained with Group-wise Direct Score Optimization (GDSO), which combines policy-gradient rewards from distribution expectations with direct pointwise and pairwise supervision on score distributions and score gaps. The student is trained with Reasoning-Internalized Score Distillation (RISD), which transfers the
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FP4 Explore, BF16 Train: Diffusion Reinforcement Learning via Efficient Rollout Scaling
Reinforcement-Learning-based post-training has recently emerged as a promising paradigm for aligning text-to-image diffusion models with human preferences. In recent studies, increasing the rollout group size yields pronounced performance improvements, indicating substantial room for further alignment gains. However, scaling rollouts on large-scale foundational diffusion models (e.g., FLUX.1-12B) imposes a heavy computational burden. To alleviate this bottleneck, we explore the integration of FP4 quantization into Diffusion RL rollouts. Yet, we identify that naive quantized pipelines inherently introduce risks of performance degradation. To overcome this dilemma between efficiency and training integrity, we propose Sol-RL (Speed-of-light RL), a novel FP4-empowered Two-stage Reinforcement Learning framework. First, we utilize high-throughput NVFP4 rollouts to generate a massive candidate pool and extract a highly contrastive subset. Second, we regenerate these selected samples in BF16 p
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Graph-Based Chain-of-Thought Pruning for Reducing Redundant Reflections in Reasoning LLMs
Extending CoT through RL has been widely used to enhance the reasoning capabilities of LLMs. However, due to the sparsity of reward signals, it can also induce undesirable thinking patterns such as overthinking, i.e., generating redundant intermediate reasoning content. In this work, we argue that a major source of such redundancy is inefficient reflection, which often manifests in two problematic patterns: Indiscriminate Reflection, where the model performs broad, low-impact checks throughout reasoning, and Repetitive Reflection, where it repeatedly re-verifies an already established conclusion. To address this, we introduce a graph-based CoT optimization framework. Specifically, we convert each linear CoT into a directed acyclic graph (DAG) with explicit dependency edges, and design a dual pruning strategy: branch-level pruning removes weakly contributing reflection branches, while depth-level pruning eliminates late-stage re-verification. We distill this behavior via a three-stage p
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EvoTrainer: 자율 에이전트형 강화학습을 위한 LLM 정책·학습 하니스 공동 진화
Autonomous LLM training is often framed as recipe search, which leaves the training harness largely static. This limitation sharpens in agentic RL, where shifting bottlenecks and scalar rewards mask diverse failure modes. We introduce EvoTrainer, an autonomous training framework that co-evolves LLM policies and training-side harnesses through empirical feedback: it diagnoses rollout-level evidence, revises diagnostics, backtests interventions, and accumulates reusable skills. Evaluated on mathematical reasoning, competitive-programming code generation, and repository-level software engineering, EvoTrainer matches or exceeds the human-engineered RL references under the same data, codebase, and evaluation protocol, with the largest gain on long-horizon agentic SWE. Trajectory analyses show that retained strategies diverge across domains, evolving diagnostics prevent invalid high-scoring branches from being promoted, and reusable skills shape later search. Autonomous LLM RL should move be
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엔트로피 한계 돌파: 거절 샘플링 기반 MTP로 RL 학습 가속
Reinforcement learning (RL) has become a key component in modern large language models, yet the rollout stage remains the key bottleneck in RL training pipelines. Although Multi-Token Prediction (MTP) offers a natural solution to accelerate rollouts through speculative decoding, many studies have observed that MTP acceptance rates degrade significantly during RL training, leading to limited speedup performance. To address this bottleneck, we present Bebop, a systematic study of MTP in LLM post-training, and offer practical recipes to integrate MTP into large-scale RL pipelines. First, we reveal that the MTP acceptance rate is fundamentally bounded by the fluctuation of model entropy, which demonstrates a clear negative linear relationship with the rise of entropy in the RL stage. Second, we show that probabilistic rejection sampling largely alleviates the disturbance introduced by entropy in RL compared to greedy draft sampling. We further identify that the conventional MTP training ob
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TRACE: 효율적인 에이전트형 강화학습을 위한 통합 롤아웃 예산 할당 프레임워크
Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Alloca
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PUBG Ally: AI 팀원으로 나선 대화형 embodied agent
We introduce PUBG Ally, an embodied agent for PUBG: BATTLEGROUNDS that can reason, act autonomously, and play alongside players as a voice-enabled teammate. Building such a teammate requires combining two difficult capabilities: it must perceive and respond to a constantly changing game world under strict latency constraints while interacting naturally with players, keeping its speech synchronized with its actions. Ally therefore combines agentic tool use with real-time game control. A language-model agent uses a controlled interface to inspect game information, interpret player speech, maintain context, decide what to say, and issue high-level action choices that steer a faster control layer for movement, combat, and recovery. Because the player's and Ally's speech and actions continually shape each other and the course of the match, training requires data from actual gameplay. We therefore collect data across nearly 39k sessions in which real players play alongside Ally, recording ga
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ACES: Who Tests the Tests? Leave-One-Out AUC Consistency for Code Generation
Selecting LLM-generated code candidates using LLM-generated tests is challenging because the tests themselves may be incorrect. Existing methods either treat all tests equally or rely on ad-hoc heuristics to filter unreliable tests. Yet determining test correctness requires knowing which codes are correct, creating a circular dependency. Our key insight is that we need not determine test correctness at all: test votes should rank, not merely count. What matters is not how many codes pass a test, but whether the test can distinguish correct from incorrect code. We break the circular dependency via leave-one-out evaluation: hold out one test, rank codes by their aggregate scores on all remaining tests, and measure whether the held-out test's pass/fail pattern agrees with this ranking. We formalize this agreement as the leave-one-out AUC~(LOO-AUC) and prove that the expected LOO-AUC is proportional to each test's ability to separate correct code from incorrect code. Building on this, we p
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Qwen-Planner-Agent: 현실 모바일 플래너 에이전트를 위한 폐쇄 루프 AI-for-AI 프레임워크
The rapid progression of large language models is extending AI from passive content generation into the active workflows of engineering and scientific discovery. This shift raises a compelling question: can AI be both the object of development and an active participant in building next-generation AI systems? We explore this question by building Qwen-Planner-Agent within a closed-loop AI-for-AI framework for scalable development and iterative improvement. Mobile planning offers a demanding test of this approach: complex, long-horizon tasks challenge agent reliability, while costly real-device interaction limits development scalability. The framework connects data production, model training, and deployment through a shared action-feedback-verification contract. (i) AI for Data builds a human-gated agentic data flywheel in which specialized agents construct tasks, collect interaction trajectories, curate and balance training data, and use training feedback to guide subsequent data generat
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흥미로운 수학을 발견하도록 학습시키기
Recently, Large Language Models (LLMs) have been increasingly able to solve advanced mathematical problems, including many that have been open for decades. This opens the door to expansion of mathematical knowledge at unprecedented scale. Yet, while LLMs may be able to conjecture and prove more and more theorems, it remains open whether this new mathematical knowledge is interesting or useful. We define intrinsic interestingness of a theorem as the ratio between the length of its proof and the length of its statement. We show that this correlates strongly with an extrinsic measure of the downstream utility of a theorem. We identify the difficulty of a proof conditioned on a set of premises as a useful primitive for computing these metrics, and train a 27B model that predicts proof difficulty more accurately than frontier general-purpose models. Optimizing for our metric creates a model capable of producing more interesting theorems, while also reducing substantial or full overlap with
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