Daily Papers

Test-time scaling has become an effective paradigm for improving the reasoning ability of large language models by allocating additional computation during inference. Recent structured approaches have further advanced this paradigm by organizing inference across multiple trajectories, refinement rounds, and verification-based feedback. However, existing structured test-time scaling methods either weakly coordinate parallel reasoning trajectories or rely on noisy historical information without explicitly deciding what should be retained and reused, limiting their ability to balance exploration and exploitation. In this work, we propose TMAS, a framework for scaling test-time compute via multi-agent synergy. TMAS organizes inference as a collaborative process among specialized agents, enabling structured information flow across agents, trajectories, and refinement iterations. To support effective cross-trajectory collaboration, TMAS introduces hierarchical memories: the experience bank reuses low-level reliable intermediate conclusions and local feedback, while the guideline bank records previously explored high-level strategies to steer subsequent rollouts away from redundant reasoning patterns. Furthermore, we design a hybrid reward reinforcement learning scheme tailored to TMAS, which jointly preserves basic reasoning capability, enhances experience utilization, and encourages exploration beyond previously attempted solution strategies. Extensive experiments on challenging reasoning benchmarks demonstrate that TMAS achieves stronger iterative scaling than existing test-time scaling baselines, while hybrid reward training further improves scaling effectiveness and stability across iterations. Code and data are available at https://github.com/george-QF/TMAS-code.

Prompt design plays a crucial role in text-to-video (T2V) generation, yet user-provided prompts are often short, unstructured, and misaligned with training data, limiting the generative potential of diffusion-based T2V models. We present RAPO++, a cross-stage prompt optimization framework that unifies training-data--aligned refinement, test-time iterative scaling, and large language model (LLM) fine-tuning to substantially improve T2V generation without modifying the underlying generative backbone. In Stage 1, Retrieval-Augmented Prompt Optimization (RAPO) enriches user prompts with semantically relevant modifiers retrieved from a relation graph and refactors them to match training distributions, enhancing compositionality and multi-object fidelity. Stage 2 introduces Sample-Specific Prompt Optimization (SSPO), a closed-loop mechanism that iteratively refines prompts using multi-source feedback -- including semantic alignment, spatial fidelity, temporal coherence, and task-specific signals such as optical flow -- yielding progressively improved video generation quality. Stage 3 leverages optimized prompt pairs from SSPO to fine-tune the rewriter LLM, internalizing task-specific optimization patterns and enabling efficient, high-quality prompt generation even before inference. Extensive experiments across five state-of-the-art T2V models and five benchmarks demonstrate that RAPO++ achieves significant gains in semantic alignment, compositional reasoning, temporal stability, and physical plausibility, outperforming existing methods by large margins. Our results highlight RAPO++ as a model-agnostic, cost-efficient, and scalable solution that sets a new standard for prompt optimization in T2V generation. The code is available at https://github.com/Vchitect/RAPO.

We introduce SIRI, Scaling Iterative Reinforcement Learning with Interleaved Compression, a simple yet effective RL approach for Large Reasoning Models (LRMs) that enables more efficient and accurate reasoning. Existing studies have observed repetitive thinking patterns in LRMs, and attempts to reduce them often come at the cost of performance. In this paper, we show that this trade-off can be overcome through a training regime that iteratively alternates between compressing and expanding the reasoning budget, by dynamically adjusting the maximum rollout length during training. The compression phase cuts the rollout length, forcing the model to make precise and valuable decisions within a limited context, which effectively reduces redundant tokens and increases reasoning density. The expansion phase then relaxes the length limit, providing space for the model to explore and plan in long-horizon settings. Remarkably, we find that after each compression-expansion cycle, the model's performance improves even as its output length decreases, steadily pushing it closer to the Pareto frontier in the performance-efficiency trade-off. Training on DeepSeek-R1-Distill-Qwen-1.5B, SIRI-low improves performance on AIME24 by 43.2% while reducing token usage by 46.9% after three iterations, and SIRI-high achieves the highest accuracy compared to all other methods (Figure 1). Our findings shed light on the potential of periodically oscillating the LRM's output truncation length during training to dynamically balance exploration and efficiency in reasoning, converging towards an optimal "sweet spot" between the two. Our models are publicly available.

This report presents CharacterFlywheel, an iterative flywheel process for improving large language models (LLMs) in production social chat applications across Instagram, WhatsApp, and Messenger. Starting from LLaMA 3.1, we refined models across 15 generations using data from both internal and external real-user traffic. Through continuous deployments from July 2024 to April 2025, we conducted controlled 7-day A/B tests showing consistent engagement improvements: 7 of 8 newly deployed models demonstrated positive lift over the baseline, with the strongest performers achieving up to 8.8% improvement in engagement breadth and 19.4% in engagement depth. We also observed substantial gains in steerability, with instruction following increasing from 59.2% to 84.8% and instruction violations decreasing from 26.6% to 5.8%. We detail the CharacterFlywheel process which integrates data curation, reward modeling to estimate and interpolate the landscape of engagement metrics, supervised fine-tuning (SFT), reinforcement learning (RL), and both offline and online evaluation to ensure reliable progress at each optimization step. We also discuss our methods for overfitting prevention and navigating production dynamics at scale. These contributions advance the scientific rigor and understanding of LLMs in social applications serving millions of users.

LLM agents are increasingly expected to function as general-purpose systems capable of resolving open-ended user requests. While existing benchmarks focus on domain-aware environments for developing specialized agents, evaluating general-purpose agents requires more realistic settings that challenge them to operate across multiple skills and tools within a unified environment. We introduce General AgentBench, a benchmark that provides such a unified framework for evaluating general LLM agents across search, coding, reasoning, and tool-use domains. Using General AgentBench, we systematically study test-time scaling behaviors under sequential scaling (iterative interaction) and parallel scaling (sampling multiple trajectories). Evaluation of ten leading LLM agents reveals a substantial performance degradation when moving from domain-specific evaluations to this general-agent setting. Moreover, we find that neither scaling methodology yields effective performance improvements in practice, due to two fundamental limitations: context ceiling in sequential scaling and verification gap in parallel scaling. Code is publicly available at https://github.com/cxcscmu/General-AgentBench.

Diffusion Multi-modal Large Language Models (dMLLMs) have recently emerged as a novel architecture unifying image generation and understanding. However, developing effective and efficient Test-Time Scaling (TTS) methods to unlock their full generative potential remains an underexplored challenge. To address this, we propose dMLLM-TTS, a novel framework operating on two complementary scaling axes: (1) trajectory exploration scaling to enhance the diversity of generated hypotheses, and (2) iterative refinement scaling for stable generation. Conventional TTS approaches typically perform linear search across these two dimensions, incurring substantial computational costs of O(NT) and requiring an external verifier for best-of-N selection. To overcome these limitations, we propose two innovations. First, we design an efficient hierarchical search algorithm with O(N+T) complexity that adaptively expands and prunes sampling trajectories. Second, we introduce a self-verified feedback mechanism that leverages the dMLLMs' intrinsic image understanding capabilities to assess text-image alignment, eliminating the need for external verifier. Extensive experiments on the GenEval benchmark across three representative dMLLMs (e.g., Lumina-DiMOO, MMaDA, Muddit) show that our framework substantially improves generation quality while achieving up to 6x greater efficiency than linear search. Project page: https://github.com/Alpha-VLLM/Lumina-DiMOO.

Looping, reusing a block of layers across depth, and depth growing, training shallow-to-deep models by duplicating middle layers, have both been linked to stronger reasoning, but their relationship remains unclear. We provide a mechanistic unification: looped and depth-grown models exhibit convergent depth-wise signatures, including increased reliance on late layers and recurring patterns aligned with the looped or grown block. These shared signatures support the view that their gains stem from a common form of iterative computation. Building on this connection, we show that the two techniques are adaptable and composable: applying inference-time looping to the middle blocks of a depth-grown model improves accuracy on some reasoning primitives by up to 2times, despite the model never being trained to loop. Both approaches also adapt better than the baseline when given more in-context examples or additional supervised fine-tuning data. Additionally, depth-grown models achieve the largest reasoning gains when using higher-quality, math-heavy cooldown mixtures, which can be further boosted by adapting a middle block to loop. Overall, our results position depth growth and looping as complementary, practical methods for inducing and scaling iterative computation to improve reasoning.

State-of-the-art (SOTA) Text-to-SQL methods still lag significantly behind human experts on challenging benchmarks like BIRD. Current approaches that explore test-time scaling lack an orchestrated strategy and neglect the model's internal reasoning process. To bridge this gap, we introduce Agentar-Scale-SQL, a novel framework leveraging scalable computation to improve performance. Agentar-Scale-SQL implements an Orchestrated Test-Time Scaling strategy that synergistically combines three distinct perspectives: i) Internal Scaling via RL-enhanced Intrinsic Reasoning, ii) Sequential Scaling through Iterative Refinement, and iii) Parallel Scaling using Diverse Synthesis and Tournament Selection. Agentar-Scale-SQL is a general-purpose framework designed for easy adaptation to new databases and more powerful language models. Extensive experiments show that Agentar-Scale-SQL achieves SOTA performance on the BIRD benchmark, reaching 81.67% execution accuracy on the test set and ranking first on the official leaderboard, demonstrating an effective path toward human-level performance.

Teaching large language models (LLMs) to critique and refine their outputs is crucial for building systems that can iteratively improve, yet it is fundamentally limited by the ability to provide accurate judgments and actionable suggestions. In this work, we study LLM critics for code generation and propose CTRL, a framework for Critic Training via Reinforcement Learning, which trains a critic model to generate feedback that maximizes correction performance for a fixed generator model without human supervision. Our results demonstrate that critics trained with CTRL significantly enhance pass rates and mitigate compounding errors across both base and stronger generator models. Furthermore, we show that these critic models act as accurate generative reward models and enable test-time scaling through iterative critique-revision, achieving up to 106.1% relative improvements across challenging code generation benchmarks.

Inducing reasoning in multimodal large language models (MLLMs) is critical for achieving human-level perception and understanding. Existing methods mainly leverage LLM reasoning to analyze parsed visuals, often limited by static perception stages. This paper introduces Visual Test-Time Scaling (VTTS), a novel approach to enhance MLLMs' reasoning via iterative perception during inference. VTTS mimics humans' hierarchical attention by progressively refining focus on high-confidence spatio-temporal regions, guided by updated textual predictions. Specifically, VTTS employs an Iterative Perception (ITP) mechanism, incorporating reinforcement learning with spatio-temporal supervision to optimize reasoning. To support this paradigm, we also present VTTS-80K, a dataset tailored for iterative perception. These designs allows a MLLM to enhance its performance by increasing its perceptual compute. Extensive experiments validate VTTS's effectiveness and generalization across diverse tasks and benchmarks. Our newly introduced Videochat-R1.5 model has achieved remarkable improvements, with an average increase of over 5\%, compared to robust baselines such as Qwen2.5VL-3B and -7B, across more than 15 benchmarks that encompass video conversation, video reasoning, and spatio-temporal perception.

Current Vision-Language-Action (VLA) models rely on fixed computational depth, expending the same amount of compute on simple adjustments and complex multi-step manipulation. While Chain-of-Thought (CoT) prompting enables variable computation, it scales memory linearly and is ill-suited for continuous action spaces. We introduce Recurrent-Depth VLA (RD-VLA), an architecture that achieves computational adaptivity via latent iterative refinement rather than explicit token generation. RD-VLA employs a recurrent, weight-tied action head that supports arbitrary inference depth with a constant memory footprint. The model is trained using truncated backpropagation through time (TBPTT) to efficiently supervise the refinement process. At inference, RD-VLA dynamically allocates compute using an adaptive stopping criterion based on latent convergence. Experiments on challenging manipulation tasks show that recurrent depth is critical: tasks that fail entirely (0 percent success) with single-iteration inference exceed 90 percent success with four iterations, while simpler tasks saturate rapidly. RD-VLA provides a scalable path to test-time compute in robotics, replacing token-based reasoning with latent reasoning to achieve constant memory usage and up to 80x inference speedup over prior reasoning-based VLA models. Project page: https://rd-vla.github.io/

Large language models (LLMs) exhibit hallucinations in long-form question-answering tasks across various domains and wide applications. Current hallucination detection and mitigation datasets are limited in domains and sizes, which struggle to scale due to prohibitive labor costs and insufficient reliability of existing hallucination annotators. To facilitate the scalable oversight of LLM hallucinations, this paper introduces an iterative self-training framework that simultaneously and progressively scales up the hallucination annotation dataset and improves the accuracy of the hallucination annotator. Based on the Expectation Maximization (EM) algorithm, in each iteration, the framework first applies a hallucination annotation pipeline to annotate a scaled dataset and then trains a more accurate hallucination annotator on the dataset. This new hallucination annotator is adopted in the hallucination annotation pipeline used for the next iteration. Extensive experimental results demonstrate that the finally obtained hallucination annotator with only 7B parameters surpasses the performance of GPT-4 and obtains new state-of-the-art hallucination detection results on HaluEval and HalluQA by zero-shot inference. Such an annotator can not only evaluate the hallucination levels of various LLMs on the large-scale dataset but also help to mitigate the hallucination of LLMs generations, with the Natural Language Inference (NLI) metric increasing from 25% to 37% on HaluEval.

Recent advances in visual reasoning have leveraged vision transformers to tackle the ARC-AGI benchmark. However, we argue that the feed-forward architecture, where computational depth is strictly bound to parameter size, falls short of capturing the iterative, algorithmic nature of human induction. In this work, we propose a recursive architecture called Loop-ViT, which decouples reasoning depth from model capacity through weight-tied recurrence. Loop-ViT iterates a weight-tied Hybrid Block, combining local convolutions and global attention, to form a latent chain of thought. Crucially, we introduce a parameter-free Dynamic Exit mechanism based on predictive entropy: the model halts inference when its internal state ``crystallizes" into a low-uncertainty attractor. Empirical results on the ARC-AGI-1 benchmark validate this perspective: our 18M model achieves 65.8% accuracy, outperforming massive 73M-parameter ensembles. These findings demonstrate that adaptive iterative computation offers a far more efficient scaling axis for visual reasoning than simply increasing network width. The code is available at https://github.com/WenjieShu/LoopViT.

Iterative data generation and model retraining are widely used to align large language models (LLMs). It typically involves a policy model to generate on-policy responses and a reward model to guide training data selection. Direct Preference Optimization (DPO) further enhances this process by constructing preference pairs of chosen and rejected responses. In this work, we aim to scale up the number of on-policy samples via repeated random sampling to improve alignment performance. Conventional practice selects the sample with the highest reward as chosen and the lowest as rejected for DPO. However, our experiments reveal that this strategy leads to a decline in performance as the sample size increases. To address this, we investigate preference data construction through the lens of underlying normal distribution of sample rewards. We categorize the reward space into seven representative points and systematically explore all 21 (C_7^2) pairwise combinations. Through evaluations on four models using AlpacaEval 2, we find that selecting the rejected response at reward position mu - 2sigma rather than the minimum reward, is crucial for optimal performance. We finally introduce a scalable preference data construction strategy that consistently enhances model performance as the sample scale increases.

LLM-based agents can autonomously accomplish complex tasks across various domains. However, to further cultivate capabilities such as adaptive behavior and long-term decision-making, training on static datasets built from human-level knowledge is insufficient. These datasets are costly to construct and lack both dynamism and realism. A growing consensus is that agents should instead interact directly with environments and learn from experience through reinforcement learning. We formalize this iterative process as the Generation-Execution-Feedback (GEF) loop, where environments generate tasks to challenge agents, return observations in response to agents' actions during task execution, and provide evaluative feedback on rollouts for subsequent learning. Under this paradigm, environments function as indispensable producers of experiential data, highlighting the need to scale them toward greater complexity, realism, and interactivity. In this survey, we systematically review representative methods for environment scaling from a pioneering environment-centric perspective and organize them along the stages of the GEF loop, namely task generation, task execution, and feedback. We further analyze benchmarks, implementation strategies, and applications, consolidating fragmented advances and outlining future research directions for agent intelligence.

Instruction tuning has become a foundation for unlocking the capabilities of large-scale pretrained models and improving their performance on complex tasks. Thus, the construction of high-quality instruction datasets is crucial for enhancing model performance and generalizability. Although current instruction datasets have reached tens of millions of samples, models finetuned on them may still struggle with complex instruction following and tasks in rare domains. This is primarily due to limited expansion in both ``coverage'' (coverage of task types and knowledge areas) and ``depth'' (instruction complexity) of the instruction set. To address this issue, we propose a systematic instruction data construction framework, which integrates a hierarchical labeling system, an informative seed selection algorithm, an evolutionary data synthesis process, and a model deficiency diagnosis with targeted data generation. These components form an iterative closed-loop to continuously enhance the coverage and depth of instruction data. Based on this framework, we construct InfinityInstruct-Subject, a high-quality dataset containing ~1.5 million instructions. Experiments on multiple foundation models and benchmark tasks demonstrate its effectiveness in improving instruction-following capabilities. Further analyses suggest that InfinityInstruct-Subject shows enlarged coverage and depth compared to comparable synthesized instruction datasets. Our work lays a theoretical and practical foundation for the efficient, continuous evolution of instruction datasets, moving from data quantity expansion to qualitative improvement.

Large Language Models (LLMs) achieve superior performance through training-time scaling, and test-time scaling further enhances their capabilities by conducting effective reasoning during inference. However, as the scale of reasoning increases, existing test-time scaling methods suffer from accumulated historical information, which not only wastes computational resources but also interferes with effective reasoning. To address this issue, we observe that complex reasoning progress is often achieved by solving a sequence of independent subquestions, each being self-contained and verifiable. These subquestions are essentially atomic questions, relying primarily on their current state rather than accumulated history, similar to the memoryless transitions in a Markov process. Based on this observation, we propose Atom of Thoughts (AoT), where each state transition in the reasoning process consists of decomposing the current question into a dependency-based directed acyclic graph and contracting its subquestions, forming a new atomic question state. This iterative decomposition-contraction process continues until reaching directly solvable atomic questions, naturally realizing Markov transitions between question states. Furthermore, these atomic questions can be seamlessly integrated into existing test-time scaling methods, enabling AoT to serve as a plug-in enhancement for improving reasoning capabilities. Experiments across six benchmarks demonstrate the effectiveness of AoT both as a standalone framework and a plug-in enhancement. Notably, on HotpotQA, when applied to gpt-4o-mini, AoT achieves an 80.6% F1 score, surpassing o3-mini by 3.4% and DeepSeek-R1 by 10.6%. The code will be available at https://github.com/qixucen/atom.

The scaling of inference computation has unlocked the potential of long-context large language models (LLMs) across diverse settings. For knowledge-intensive tasks, the increased compute is often allocated to incorporate more external knowledge. However, without effectively utilizing such knowledge, solely expanding context does not always enhance performance. In this work, we investigate inference scaling for retrieval augmented generation (RAG), exploring strategies beyond simply increasing the quantity of knowledge. We focus on two inference scaling strategies: in-context learning and iterative prompting. These strategies provide additional flexibility to scale test-time computation (e.g., by increasing retrieved documents or generation steps), thereby enhancing LLMs' ability to effectively acquire and utilize contextual information. We address two key questions: (1) How does RAG performance benefit from the scaling of inference computation when optimally configured? (2) Can we predict the optimal test-time compute allocation for a given budget by modeling the relationship between RAG performance and inference parameters? Our observations reveal that increasing inference computation leads to nearly linear gains in RAG performance when optimally allocated, a relationship we describe as the inference scaling laws for RAG. Building on this, we further develop the computation allocation model to estimate RAG performance across different inference configurations. The model predicts optimal inference parameters under various computation constraints, which align closely with the experimental results. By applying these optimal configurations, we demonstrate that scaling inference compute on long-context LLMs achieves up to 58.9% gains on benchmark datasets compared to standard RAG.

Recent advances in large multimodal models have leveraged image-based tools with reinforcement learning to tackle visual problems. However, existing open-source approaches often exhibit monotonous reasoning patterns and allow only a limited number of interaction turns, making them inadequate for difficult tasks that require trial-and-error exploration. In this work, we address this limitation by scaling up tool-based interactions and introduce Mini-o3, a system that executes deep, multi-turn reasoning -- spanning tens of steps -- and achieves state-of-the-art performance on challenging visual search tasks. Our recipe for reproducing OpenAI o3-style behaviors comprises three key components. First, we construct the Visual Probe Dataset, a collection of thousands of challenging visual search problems designed for exploratory reasoning. Second, we develop an iterative data collection pipeline to obtain cold-start trajectories that exhibit diverse reasoning patterns, including depth-first search, trial-and-error, and goal maintenance. Third, we propose an over-turn masking strategy that prevents penalization of over-turn responses (those that hit the maximum number of turns) during reinforcement learning, thereby balancing training-time efficiency with test-time scalability. Despite training with an upper bound of only six interaction turns, our model generates trajectories that naturally scale to tens of turns at inference time, with accuracy improving as the number of turns increases. Extensive experiments demonstrate that Mini-o3 produces rich reasoning patterns and deep thinking paths, effectively solving challenging visual search problems.

Recent advances in reinforcement learning (RL) with verifiable outcome rewards have significantly improved the reasoning capabilities of large language models (LLMs), especially when combined with multi-turn tool interactions. However, existing methods lack both meaningful verification signals from realistic environments and explicit optimization for verification, leading to unreliable self-verification. To address these limitations, we propose ReVeal, a multi-turn reinforcement learning framework that interleaves code generation with explicit self-verification and tool-based evaluation. ReVeal enables LLMs to autonomously generate test cases, invoke external tools for precise feedback, and improves performance via a customized RL algorithm with dense, per-turn rewards. As a result, ReVeal fosters the co-evolution of a model's generation and verification capabilities through RL training, expanding the reasoning boundaries of the base model, demonstrated by significant gains in Pass@k on LiveCodeBench. It also enables test-time scaling into deeper inference regimes, with code consistently evolving as the number of turns increases during inference, ultimately surpassing DeepSeek-R1-Zero-Qwen-32B. These findings highlight the promise of ReVeal as a scalable and effective paradigm for building more robust and autonomous AI agents.

Large language models have achieved strong performance on medical reasoning benchmarks, yet their deployment in clinical settings demands rigorous verification to ensure factual accuracy. While reward models offer a scalable approach for reasoning trace verification, existing methods face two limitations: they produce only scalar reward values without explicit justification, and they rely on single-pass retrieval that precludes adaptive knowledge access as verification unfolds. We introduce method, an agentic framework that addresses these limitations by training medical reasoning verifiers to iteratively query external medical corpora during evaluation. Our approach combines tool-augmented verification with an iterative reinforcement learning paradigm that requires only trace-level supervision, alongside an adaptive curriculum mechanism that dynamically adjusts training data distribution. Across four medical reasoning benchmarks, method achieves substantial gains over existing methods, improving MedQA accuracy by 23.5% and MedXpertQA by 32.0% relative to the base generator in particular. Crucially, method demonstrates an 8times reduction in sampling budget requirement compared to prior reward model baselines. These findings establish that grounding verification in dynamically retrieved evidence offers a principled path toward more reliable medical reasoning systems.

The recent release of OpenAI's o1 models and other similar frameworks showcasing test-time scaling laws has demonstrated their exceptional capability to tackle complex reasoning tasks. Inspired by this, subsequent research has revealed that such test-time scaling laws hinge on the model's ability to search both within a single response (intra-response) and across multiple responses (inter-response) during training. Crucially, beyond selecting a single optimal response, the model must also develop robust self-correction capabilities within its own outputs. However, training models to achieve effective self-evaluation and self-correction remains a significant challenge, heavily dependent on the quality of self-reflection data. In this paper, we address this challenge by focusing on enhancing the quality of self-reflection data generation for complex problem-solving, which can subsequently improve the training of next-generation large language models (LLMs). Specifically, we explore how manually triggering a model's self-correction mechanisms can improve performance on challenging reasoning tasks. To this end, we propose a novel iterative deepening sampling algorithm framework designed to enhance self-correction and generate higher-quality samples. Through extensive experiments on Math500 and AIME benchmarks, we demonstrate that our method achieves a higher success rate on difficult tasks and provide detailed ablation studies to analyze its effectiveness across diverse settings.

Large language models (LLMs) have demonstrated remarkable proficiency in mainstream academic disciplines such as mathematics, physics, and computer science. However, human knowledge encompasses over 200 specialized disciplines, far exceeding the scope of existing benchmarks. The capabilities of LLMs in many of these specialized fields-particularly in light industry, agriculture, and service-oriented disciplines-remain inadequately evaluated. To address this gap, we present SuperGPQA, a comprehensive benchmark that evaluates graduate-level knowledge and reasoning capabilities across 285 disciplines. Our benchmark employs a novel Human-LLM collaborative filtering mechanism to eliminate trivial or ambiguous questions through iterative refinement based on both LLM responses and expert feedback. Our experimental results reveal significant room for improvement in the performance of current state-of-the-art LLMs across diverse knowledge domains (e.g., the reasoning-focused model DeepSeek-R1 achieved the highest accuracy of 61.82% on SuperGPQA), highlighting the considerable gap between current model capabilities and artificial general intelligence. Additionally, we present comprehensive insights from our management of a large-scale annotation process, involving over 80 expert annotators and an interactive Human-LLM collaborative system, offering valuable methodological guidance for future research initiatives of comparable scope.

Recent advances in Deep Research Agents (DRAs) are transforming automated knowledge discovery and problem-solving. While the majority of existing efforts focus on enhancing policy capabilities via post-training, we propose an alternative paradigm: self-evolving the agent's ability by iteratively verifying the policy model's outputs, guided by meticulously crafted rubrics. This approach gives rise to the inference-time scaling of verification, wherein an agent self-improves by evaluating its generated answers to produce iterative feedback and refinements. We derive the rubrics based on an automatically constructed DRA Failure Taxonomy, which systematically classifies agent failures into five major categories and thirteen sub-categories. We present DeepVerifier, a rubrics-based outcome reward verifier that leverages the asymmetry of verification and outperforms vanilla agent-as-judge and LLM judge baselines by 12%-48% in meta-evaluation F1 score. To enable practical self-evolution, DeepVerifier integrates as a plug-and-play module during test-time inference. The verifier produces detailed rubric-based feedback, which is fed back to the agent for iterative bootstrapping, refining responses without additional training. This test-time scaling delivers 8%-11% accuracy gains on challenging subsets of GAIA and XBench-DeepResearch when powered by capable closed-source LLMs. Finally, to support open-source advancement, we release DeepVerifier-4K, a curated supervised fine-tuning dataset of 4,646 high-quality agent steps focused on DRA verification. These examples emphasize reflection and self-critique, enabling open models to develop robust verification capabilities.

Recent text-to-image diffusion models achieve impressive visual quality through extensive scaling of training data and model parameters, yet they often struggle with complex scenes and fine-grained details. Inspired by the self-reflection capabilities emergent in large language models, we propose ReflectionFlow, an inference-time framework enabling diffusion models to iteratively reflect upon and refine their outputs. ReflectionFlow introduces three complementary inference-time scaling axes: (1) noise-level scaling to optimize latent initialization; (2) prompt-level scaling for precise semantic guidance; and most notably, (3) reflection-level scaling, which explicitly provides actionable reflections to iteratively assess and correct previous generations. To facilitate reflection-level scaling, we construct GenRef, a large-scale dataset comprising 1 million triplets, each containing a reflection, a flawed image, and an enhanced image. Leveraging this dataset, we efficiently perform reflection tuning on state-of-the-art diffusion transformer, FLUX.1-dev, by jointly modeling multimodal inputs within a unified framework. Experimental results show that ReflectionFlow significantly outperforms naive noise-level scaling methods, offering a scalable and compute-efficient solution toward higher-quality image synthesis on challenging tasks.

In this paper, we argue that iterative computation with diffusion models offers a powerful paradigm for not only generation but also visual perception tasks. We unify tasks such as depth estimation, optical flow, and segmentation under image-to-image translation, and show how diffusion models benefit from scaling training and test-time compute for these perception tasks. Through a careful analysis of these scaling behaviors, we present various techniques to efficiently train diffusion models for visual perception tasks. Our models achieve improved or comparable performance to state-of-the-art methods using significantly less data and compute. To use our code and models, see https://scaling-diffusion-perception.github.io .

Recently, Multimodal Large Language Models (MLLMs) have been widely integrated into diffusion frameworks primarily as text encoders to tackle complex tasks such as spatial reasoning. However, this paradigm suffers from two critical limitations: (i) MLLMs text encoder exhibits insufficient reasoning depth. Single-step encoding fails to activate the Chain-of-Thought process, which is essential for MLLMs to provide accurate guidance for complex tasks. (ii) The guidance remains invariant during the decoding process. Invariant guidance during decoding prevents DiT from progressively decomposing complex instructions into actionable denoising steps, even with correct MLLM encodings. To this end, we propose Endogenous Chain-of-Thought (EndoCoT), a novel framework that first activates MLLMs' reasoning potential by iteratively refining latent thought states through an iterative thought guidance module, and then bridges these states to the DiT's denoising process. Second, a terminal thought grounding module is applied to ensure the reasoning trajectory remains grounded in textual supervision by aligning the final state with ground-truth answers. With these two components, the MLLM text encoder delivers meticulously reasoned guidance, enabling the DiT to execute it progressively and ultimately solve complex tasks in a step-by-step manner. Extensive evaluations across diverse benchmarks (e.g., Maze, TSP, VSP, and Sudoku) achieve an average accuracy of 92.1%, outperforming the strongest baseline by 8.3 percentage points.

Transcribing and understanding multi-speaker conversations requires speech recognition, speaker attribution, and timestamp localization. While speech LLMs excel at single-speaker tasks, multi-speaker scenarios remain challenging due to overlapping speech, backchannels, rapid turn-taking, and context window constraints. We propose Speaker-Reasoner, an end-to-end Speech LLM with agentic multi-turn temporal reasoning. Instead of single-pass inference, the model iteratively analyzes global audio structure, autonomously predicts temporal boundaries, and performs fine-grained segment analysis, jointly modeling speaker identity, gender, timestamps, and transcription. A speaker-aware cache further extends processing to audio exceeding the training context window. Trained with a three-stage progressive strategy, Speaker-Reasoner achieves consistent improvements over strong baselines on AliMeeting and AISHELL-4 datasets, particularly in handling overlapping speech and complex turn-taking.

We introduce GenAgent, unifying visual understanding and generation through an agentic multimodal model. Unlike unified models that face expensive training costs and understanding-generation trade-offs, GenAgent decouples these capabilities through an agentic framework: understanding is handled by the multimodal model itself, while generation is achieved by treating image generation models as invokable tools. Crucially, unlike existing modular systems constrained by static pipelines, this design enables autonomous multi-turn interactions where the agent generates multimodal chains-of-thought encompassing reasoning, tool invocation, judgment, and reflection to iteratively refine outputs. We employ a two-stage training strategy: first, cold-start with supervised fine-tuning on high-quality tool invocation and reflection data to bootstrap agent behaviors; second, end-to-end agentic reinforcement learning combining pointwise rewards (final image quality) and pairwise rewards (reflection accuracy), with trajectory resampling for enhanced multi-turn exploration. GenAgent significantly boosts base generator(FLUX.1-dev) performance on GenEval++ (+23.6\%) and WISE (+14\%). Beyond performance gains, our framework demonstrates three key properties: 1) cross-tool generalization to generators with varying capabilities, 2) test-time scaling with consistent improvements across interaction rounds, and 3) task-adaptive reasoning that automatically adjusts to different tasks. Our code will be available at https://github.com/deep-kaixun/GenAgent{this url}.

We introduce the Autoregressive Block-Based Iterative Encoder (AbbIE), a novel recursive generalization of the encoder-only Transformer architecture, which achieves better perplexity than a standard Transformer and allows for the dynamic scaling of compute resources at test time. This simple, recursive approach is a complement to scaling large language model (LLM) performance through parameter and token counts. AbbIE performs its iterations in latent space, but unlike latent reasoning models, does not require a specialized dataset or training protocol. We show that AbbIE upward generalizes (ability to generalize to arbitrary iteration lengths) at test time by only using 2 iterations during train time, far outperforming alternative iterative methods. AbbIE's ability to scale its computational expenditure based on the complexity of the task gives it an up to 12\% improvement in zero-shot in-context learning tasks versus other iterative and standard methods and up to 5\% improvement in language perplexity. The results from this study open a new avenue to Transformer performance scaling. We perform all of our evaluations on model sizes up to 350M parameters.

Unified models can handle both multimodal understanding and generation within a single architecture, yet they typically operate in a single pass without iteratively refining their outputs. Many multimodal tasks, especially those involving complex spatial compositions, multiple interacting objects, or evolving instructions, require decomposing instructions, verifying intermediate results, and making iterative corrections. While test-time scaling (TTS) has demonstrated that allocating additional inference compute for iterative reasoning substantially improves language model performance, extending this paradigm to unified multimodal models remains an open challenge. We introduce UniT, a framework for multimodal chain-of-thought test-time scaling that enables a single unified model to reason, verify, and refine across multiple rounds. UniT combines agentic data synthesis, unified model training, and flexible test-time inference to elicit cognitive behaviors including verification, subgoal decomposition, and content memory. Our key findings are: (1) unified models trained on short reasoning trajectories generalize to longer inference chains at test time; (2) sequential chain-of-thought reasoning provides a more scalable and compute-efficient TTS strategy than parallel sampling; (3) training on generation and editing trajectories improves out-of-distribution visual reasoning. These results establish multimodal test-time scaling as an effective paradigm for advancing both generation and understanding in unified models.

Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an error. Here, we address this limitation by introducing the remasking diffusion model (ReMDM) sampler, a method that can be applied to pretrained masked diffusion models in a principled way and that is derived from a discrete diffusion model with a custom remasking backward process. Most interestingly, ReMDM endows discrete diffusion with a form of inference-time compute scaling. By increasing the number of sampling steps, ReMDM generates natural language outputs that approach the quality of autoregressive models, whereas when the computation budget is limited, ReMDM better maintains quality. ReMDM also improves sample quality of masked diffusion models for discretized images, and in scientific domains such as molecule design, ReMDM facilitates diffusion guidance and pushes the Pareto frontier of controllability relative to classical masking and uniform noise diffusion. We provide the code along with a blog post on the project page: https://remdm.github.io.

We address a persistent challenge in text-to-image models: accurately generating a specified number of objects. Current models, which learn from image-text pairs, inherently struggle with counting, as training data cannot depict every possible number of objects for any given object. To solve this, we propose optimizing the generated image based on a counting loss derived from a counting model that aggregates an object\'s potential. Employing an out-of-the-box counting model is challenging for two reasons: first, the model requires a scaling hyperparameter for the potential aggregation that varies depending on the viewpoint of the objects, and second, classifier guidance techniques require modified models that operate on noisy intermediate diffusion steps. To address these challenges, we propose an iterated online training mode that improves the accuracy of inferred images while altering the text conditioning embedding and dynamically adjusting hyperparameters. Our method offers three key advantages: (i) it can consider non-derivable counting techniques based on detection models, (ii) it is a zero-shot plug-and-play solution facilitating rapid changes to the counting techniques and image generation methods, and (iii) the optimized counting token can be reused to generate accurate images without additional optimization. We evaluate the generation of various objects and show significant improvements in accuracy. The project page is available at https://ozzafar.github.io/count_token.

The emergent abilities of large language models (LLMs) have demonstrated great potential in solving medical questions. They can possess considerable medical knowledge, but may still hallucinate and are inflexible in the knowledge updates. While Retrieval-Augmented Generation (RAG) has been proposed to enhance the medical question-answering capabilities of LLMs with external knowledge bases, it may still fail in complex cases where multiple rounds of information-seeking are required. To address such an issue, we propose iterative RAG for medicine (i-MedRAG), where LLMs can iteratively ask follow-up queries based on previous information-seeking attempts. In each iteration of i-MedRAG, the follow-up queries will be answered by a vanilla RAG system and they will be further used to guide the query generation in the next iteration. Our experiments show the improved performance of various LLMs brought by i-MedRAG compared with vanilla RAG on complex questions from clinical vignettes in the United States Medical Licensing Examination (USMLE), as well as various knowledge tests in the Massive Multitask Language Understanding (MMLU) dataset. Notably, our zero-shot i-MedRAG outperforms all existing prompt engineering and fine-tuning methods on GPT-3.5, achieving an accuracy of 69.68\% on the MedQA dataset. In addition, we characterize the scaling properties of i-MedRAG with different iterations of follow-up queries and different numbers of queries per iteration. Our case studies show that i-MedRAG can flexibly ask follow-up queries to form reasoning chains, providing an in-depth analysis of medical questions. To the best of our knowledge, this is the first-of-its-kind study on incorporating follow-up queries into medical RAG.

Retrieval-Augmented Generation (RAG) grounds large language model outputs in external evidence, but remains challenged on multi-hop question answering that requires long reasoning. Recent works scale RAG at inference time along two complementary dimensions: sequential depth for iterative refinement and parallel width for coverage expansion. However, naive scaling causes context contamination and scaling inefficiency, leading to diminishing or negative returns despite increased computation. To address these limitations, we propose SPARC-RAG, a multi-agent framework that coordinates sequential and parallel inference-time scaling under a unified context management mechanism. SPARC-RAG employs specialized agents that maintain a shared global context and provide explicit control over the scaling process. It generates targeted, complementary sub-queries for each branch to enable diverse parallel exploration, and explicitly regulates exiting decisions based on answer correctness and evidence grounding. To optimize scaling behavior, we further introduce a lightweight fine-tuning method with process-level verifiable preferences, which improves the efficiency of sequential scaling and effectiveness of parallel scaling. Across single- and multi-hop QA benchmarks, SPARC-RAG consistently outperforms previous RAG baselines, yielding an average +6.2 F1 improvement under lower inference cost.

The rapid advancements in large Language models (LLMs) have significantly enhanced their reasoning capabilities, driven by various strategies such as multi-agent collaboration. However, unlike the well-established performance improvements achieved through scaling data and model size, the scaling of reasoning in LLMs is more complex and can even negatively impact reasoning performance, introducing new challenges in model alignment and robustness. In this survey, we provide a comprehensive examination of scaling in LLM reasoning, categorizing it into multiple dimensions and analyzing how and to what extent different scaling strategies contribute to improving reasoning capabilities. We begin by exploring scaling in input size, which enables LLMs to process and utilize more extensive context for improved reasoning. Next, we analyze scaling in reasoning steps that improves multi-step inference and logical consistency. We then examine scaling in reasoning rounds, where iterative interactions refine reasoning outcomes. Furthermore, we discuss scaling in training-enabled reasoning, focusing on optimization through iterative model improvement. Finally, we review applications of scaling across domains and outline future directions for further advancing LLM reasoning. By synthesizing these diverse perspectives, this survey aims to provide insights into how scaling strategies fundamentally enhance the reasoning capabilities of LLMs and further guide the development of next-generation AI systems.

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

Agentic systems operating over large tool ecosystems must plan and execute long-horizon workflows under weak or non-verifiable supervision. While frontier models mitigate these challenges through scale and large context budgets, small language models (SLMs) remain brittle: eager tool loading saturates context, execution errors compound over time, and sparse rewards limit learning. We introduce ATLAS, a reinforcement finetuning framework that enables SLMs to operate effectively in large-scale toolspace environments by learning how to acquire context and how to execute actions. Our approach makes two key contributions. First, we treat context control and execution structure as learnable decisions, combining iterative tool loading with programmatic tool orchestration to bound context growth and stabilize long-horizon trajectories. Second, we propose rubric-based reinforcement finetuning, which decomposes task success into structured, task-aligned criteria and enables scalable training using small judge models. Across MCP benchmarks, these design choices yield large and consistent gains over generic RL baselines, allowing a 4B SLM to approach frontier-agent performance under far tighter parameter and context budgets.

Test-time scaling has emerged as a powerful technique for enhancing the reasoning capabilities of large language models. However, its effectiveness in medical reasoning remains uncertain, as the medical domain fundamentally differs from mathematical tasks in terms of knowledge representation and decision-making processes. In this paper, we provide the first comprehensive investigation of test-time scaling for medical reasoning and present m1, a simple yet effective approach that increases a model's medical reasoning capability at inference. Our evaluation across diverse medical tasks demonstrates that test-time scaling consistently enhances medical reasoning, enabling lightweight fine-tuned models under 10B parameters to establish new state-of-the-art performance, while our 32B model rivals previous 70B-scale medical LLMs. However, we identify an optimal reasoning token budget of approximately 4K, beyond which performance may degrade due to overthinking. Budget forcing, which extends test-time computation through iterative prompts, helps models double-check answers but does not necessarily improve the overall medical QA performance and, in some cases, even introduces errors into previously correct responses. Our case-by-case analysis identifies insufficient medical knowledge as a key bottleneck that prevents further performance gains through test-time scaling. We find that increasing data scale, improving data quality, and expanding model capacity consistently enhance medical knowledge grounding, enabling continued performance improvements, particularly on challenging medical benchmarks where smaller models reach saturation. These findings underscore fundamental differences between medical and mathematical reasoning in LLMs, highlighting that enriched medical knowledge, other than increased reasoning depth alone, is essential for realizing the benefits of test-time scaling.

We build upon vec2vec, a procedure designed to align text embedding spaces without parallel data. vec2vec finds a near-perfect alignment, but it is expensive and unstable. We present mini-vec2vec, a simple and efficient alternative that requires substantially lower computational cost and is highly robust. Moreover, the learned mapping is a linear transformation. Our method consists of three main stages: a tentative matching of pseudo-parallel embedding vectors, transformation fitting, and iterative refinement. Our linear alternative exceeds the original instantiation of vec2vec by orders of magnitude in efficiency, while matching or exceeding their results. The method's stability and interpretable algorithmic steps facilitate scaling and unlock new opportunities for adoption in new domains and fields.

Recent advancements in reasoning-focused language models such as OpenAI's O1 and DeepSeek-R1 have shown that scaling test-time computation-through chain-of-thought reasoning and iterative exploration-can yield substantial improvements on complex tasks like mathematics and code generation. These breakthroughs have been driven by large-scale reinforcement learning (RL), particularly when combined with verifiable reward signals that provide objective and grounded supervision. In this report, we investigate the effects of prolonged reinforcement learning on a small language model across a diverse set of reasoning domains. Our work identifies several key ingredients for effective training, including the use of verifiable reward tasks, enhancements to Group Relative Policy Optimization (GRPO), and practical techniques to improve training stability and generalization. We introduce controlled KL regularization, clipping ratio, and periodic reference policy resets as critical components for unlocking long-term performance gains. Our model achieves significant improvements over strong baselines, including +14.7% on math, +13.9% on coding, and +54.8% on logic puzzle tasks. To facilitate continued research, we release our model publicly.

Recent work in probability-domain knowledge distillation has established axiomatic frameworks for temperature scaling, multi-teacher aggregation, and bias-variance trade-offs in single-stage settings. However, the mathematical behavior of recursive or multi-generation distillation remains poorly understood, with prior approaches relying primarily on empirical heuristics. In this work, we introduce an axiomatic and operator-theoretic framework for recursive meta-distillation, formalizing iterative knowledge distillation as a sequence of probability-distribution operators with explicit anchoring to base teachers. We define structural axioms for valid meta-teacher construction and prove the existence of non-trivial operator families satisfying these axioms without specifying particular algorithms or loss functions. Under mild realizability and convexity assumptions, we show that anchored recursive distillation induces contraction in KL divergence, yielding geometric convergence to base teacher distributions and a unique, globally attractive fixed point. The contribution is foundational rather than algorithmic: the framework characterizes when recursive distillation is mathematically well-posed and convergent rather than error-accumulating, independent of model architecture, optimization details, or specific operator instantiations. These results provide a theoretical basis for understanding stability, bias-variance behavior, and failure modes in iterative and multi-teacher distillation under capacity constraints.

The rapid evolution of e-commerce has exposed the limitations of traditional product retrieval systems in managing complex, multi-turn user interactions. Recent advances in multimodal generative retrieval -- particularly those leveraging multimodal large language models (MLLMs) as retrievers -- have shown promise. However, most existing methods are tailored to single-turn scenarios and struggle to model the evolving intent and iterative nature of multi-turn dialogues when applied naively. Concurrently, test-time scaling has emerged as a powerful paradigm for improving large language model (LLM) performance through iterative inference-time refinement. Yet, its effectiveness typically relies on two conditions: (1) a well-defined problem space (e.g., mathematical reasoning), and (2) the model's ability to self-correct -- conditions that are rarely met in conversational product search. In this setting, user queries are often ambiguous and evolving, and MLLMs alone have difficulty grounding responses in a fixed product corpus. Motivated by these challenges, we propose a novel framework that introduces test-time scaling into conversational multimodal product retrieval. Our approach builds on a generative retriever, further augmented with a test-time reranking (TTR) mechanism that improves retrieval accuracy and better aligns results with evolving user intent throughout the dialogue. Experiments across multiple benchmarks show consistent improvements, with average gains of 14.5 points in MRR and 10.6 points in nDCG@1.

Natural data is redundant yet predominant architectures tile computation uniformly across their input and output space. We propose the Recurrent Interface Networks (RINs), an attention-based architecture that decouples its core computation from the dimensionality of the data, enabling adaptive computation for more scalable generation of high-dimensional data. RINs focus the bulk of computation (i.e. global self-attention) on a set of latent tokens, using cross-attention to read and write (i.e. route) information between latent and data tokens. Stacking RIN blocks allows bottom-up (data to latent) and top-down (latent to data) feedback, leading to deeper and more expressive routing. While this routing introduces challenges, this is less problematic in recurrent computation settings where the task (and routing problem) changes gradually, such as iterative generation with diffusion models. We show how to leverage recurrence by conditioning the latent tokens at each forward pass of the reverse diffusion process with those from prior computation, i.e. latent self-conditioning. RINs yield state-of-the-art pixel diffusion models for image and video generation, scaling to 1024X1024 images without cascades or guidance, while being domain-agnostic and up to 10X more efficient than 2D and 3D U-Nets.

We present Uni-MoE 2.0 from the Lychee family. As a fully open-source omnimodal large model (OLM), it substantially advances Lychee's Uni-MoE series in language-centric multimodal understanding, reasoning, and generating. Based on the Qwen2.5-7B dense architecture, we build Uni-MoE-2.0-Omni from scratch through three core contributions: dynamic-capacity Mixture-of-Experts (MoE) design, a progressive training strategy enhanced with an iterative reinforcement strategy, and a carefully curated multimodal data matching technique. It is capable of omnimodal understanding, as well as generating images, text, and speech. Architecturally, our new MoE framework balances computational efficiency and capability for 10 cross-modal inputs using shared, routed, and null experts, while our Omni-Modality 3D RoPE ensures spatio-temporal cross-modality alignment in the self-attention layer. For training, following cross-modal pretraining, we use a progressive supervised fine-tuning strategy that activates modality-specific experts and is enhanced by balanced data composition and an iterative GSPO-DPO method to stabilise RL training and improve reasoning. Data-wise, the base model, trained on approximately 75B tokens of open-source multimodal data, is equipped with special speech and image generation tokens, allowing it to learn these generative tasks by conditioning its outputs on linguistic cues. Extensive evaluation across 85 benchmarks demonstrates that our model achieves SOTA or highly competitive performance against leading OLMs, surpassing Qwen2.5-Omni (trained with 1.2T tokens) on over 50 of 76 benchmarks. Key strengths include video understanding (+7% avg. of 8), omnimodallity understanding (+7% avg. of 4), and audiovisual reasoning (+4%). It also advances long-form speech processing (reducing WER by 4.2%) and leads in low-level image processing and controllable generation across 5 metrics.

Software engineering (SWE) has recently emerged as a crucial testbed for next-generation LLM agents, demanding inherent capabilities in two critical dimensions: sustained iterative problem-solving (e.g., >50 interaction rounds) and long-context dependency resolution (e.g., >32k tokens). However, the data curation process in SWE remains notoriously time-consuming, as it heavily relies on manual annotation for code file filtering and the setup of dedicated runtime environments to execute and validate unit tests. Consequently, most existing datasets are limited to only a few thousand GitHub-sourced instances. To this end, we propose an incremental, automated data-curation pipeline that systematically scales both the volume and diversity of SWE datasets. Our dataset comprises 10,169 real-world Python task instances from 2,531 distinct GitHub repositories, each accompanied by a task specified in natural language and a dedicated runtime-environment image for automated unit-test validation. We have carefully curated over 8,000 successfully runtime-validated training trajectories from our proposed SWE dataset. When fine-tuning the Skywork-SWE model on these trajectories, we uncover a striking data scaling phenomenon: the trained model's performance for software engineering capabilities in LLMs continues to improve as the data size increases, showing no signs of saturation. Notably, our Skywork-SWE model achieves 38.0% pass@1 accuracy on the SWE-bench Verified benchmark without using verifiers or multiple rollouts, establishing a new state-of-the-art (SOTA) among the Qwen2.5-Coder-32B-based LLMs built on the OpenHands agent framework. Furthermore, with the incorporation of test-time scaling techniques, the performance further improves to 47.0% accuracy, surpassing the previous SOTA results for sub-32B parameter models. We release the Skywork-SWE-32B model checkpoint to accelerate future research.

Deep research is emerging as a representative long-horizon task for large language model (LLM) agents. However, long trajectories in deep research often exceed model context limits, compressing token budgets for both evidence collection and report writing, and preventing effective test-time scaling. We introduce FS-Researcher, a file-system-based, dual-agent framework that scales deep research beyond the context window via a persistent workspace. Specifically, a Context Builder agent acts as a librarian which browses the internet, writes structured notes, and archives raw sources into a hierarchical knowledge base that can grow far beyond context length. A Report Writer agent then composes the final report section by section, treating the knowledge base as the source of facts. In this framework, the file system serves as a durable external memory and a shared coordination medium across agents and sessions, enabling iterative refinement beyond the context window. Experiments on two open-ended benchmarks (DeepResearch Bench and DeepConsult) show that FS-Researcher achieves state-of-the-art report quality across different backbone models. Further analyses demonstrate a positive correlation between final report quality and the computation allocated to the Context Builder, validating effective test-time scaling under the file-system paradigm. The code and data are anonymously open-sourced at https://github.com/Ignoramus0817/FS-Researcher.

The rise of test-time scaling has remarkably boosted the reasoning and agentic proficiency of Large Language Models (LLMs). Yet, standard Transformers struggle to scale inference-time compute efficiently, as conventional looping strategies suffer from high computational overhead and a KV cache that inflates alongside model depth. We present Universal YOCO (YOCO-U), which combines the YOCO decoder-decoder architecture with recursive computation to achieve a synergistic effect greater than either alone. Built on the YOCO framework, YOCO-U implements a Universal Self-Decoder that performs multiple iterations via parameter sharing, while confining the iterative process to shallow, efficient-attention layers. This combination yields a favorable capability-efficiency tradeoff that neither YOCO nor recursion achieves independently. The YOCO architecture provides a constant global KV cache and linear pre-filling, while partial recursion enhances representational depth with limited overhead. Together, YOCO-U improves token utility and scaling behavior while maintaining efficient inference. Empirical results confirm that YOCO-U remains highly competitive in general and long-context benchmarks, demonstrating that the integration of efficient-attention architectures and recursive computation is a promising direction for scalable LLMs.

Finetuning specialized generative evaluators has emerged as a popular paradigm to meet the increasing demand for scalable evaluation during both training and test-time. However, recent work has largely focused on applying new methodology, such as reinforcement learning (RL), to training evaluators, shying away from large-scale, data-driven development. In this work, we focus on data scaling, curating a set of 2.5M samples spanning five unique evaluation tasks (pairwise, step-level, reference-free and reference-based verification, and single rating) and multiple domains focused on reasoning evaluation. With our data, we train Foundational Automatic Reasoning Evaluators (FARE), a family of 8B and 20B (with 3.6B active) parameter evaluators, with a simple iterative rejection-sampling supervised finetuning (SFT) approach. FARE-8B challenges larger specialized RL-trained evaluators and FARE-20B sets the new standard for open-source evaluators, surpassing specialized 70B+ evaluators. Beyond static benchmarks, we evaluate FARE in real-world tasks: As inference-time rerankers, FARE-20B achieves near-oracle performance on MATH. As verifiers in RL training, FARE improves the downstream RL-trained model performance by up to 14.1% vs. string-matching verifiers. When initialized from FARE, a continually-finetuned FARE-Code outperforms gpt-oss-20B by 65% on evaluating test-case quality.

Test-time scaling has shown considerable success in improving the performance of language models on complex reasoning tasks without requiring fine-tuning. However, current strategies such as self-reflection primarily focus on logical or structural refinement. They do not leverage the guiding potential of affective feedback. Inspired by psychological research showing that emotions can modulate cognitive performance, we introduce HEART--a novel framework that uses emotionally-driven prompts for iterative self-correction. HEART provides feedback on a model's incorrect response using a curated set of concise, emotionally charged phrases based on the six universal emotions categorized by Dr. Paul Ekman. By systematically varying the emotional tone of the feedback across iterations, our method guides the model to escape flawed reasoning paths and explore more promising alternatives. We evaluate our framework on challenging reasoning benchmarks including OlympiadBench, Humanity's Last Exam, and SimpleQA. Our results reveal a significant new phenomenon: when guided by an oracle verifier, this affective iteration protocol unlocks significantly deeper reasoning, leading to consistent and substantial increases in accuracy over state-of-the-art baselines with the same verifier. However, we also identify a critical bottleneck for practical deployment. In a verifier-free setting, it struggles to harness these gains consistently, highlighting as a key challenge for future work. Our findings suggest that the next frontier in machine reasoning may lie not just in refining logic, but also in understanding and leveraging the `HEART' of the models.

Multi-modal large language models (MLLMs) have achieved remarkable capabilities by integrating visual perception with language understanding, enabling applications such as image-grounded dialogue, visual question answering, and scientific analysis. However, most MLLMs adopt a static inference paradigm, encoding the entire image into fixed visual tokens upfront, which limits their ability to iteratively refine understanding or adapt to context during inference. This contrasts sharply with human perception, which is dynamic, selective, and feedback-driven. In this work, we introduce a novel framework for inference-time visual token scaling that enables MLLMs to perform iterative, verifier-guided reasoning over visual content. We formulate the problem as a Markov Decision Process, involving a reasoner that proposes visual actions and a verifier, which is trained via multi-step Direct Preference Optimization (DPO), that evaluates these actions and determines when reasoning should terminate. To support this, we present a new dataset, VTS, comprising supervised reasoning trajectories (VTS-SFT) and preference-labeled reasoning comparisons (VTS-DPO). Our method significantly outperforms existing approaches across diverse visual reasoning benchmarks, offering not only improved accuracy but also more interpretable and grounded reasoning processes. These results demonstrate the promise of dynamic inference mechanisms for enabling fine-grained, context-aware visual reasoning in next-generation MLLMs.

Existing large language model (LLM)-based embeddings typically adopt an encoder-only paradigm, treating LLMs as static feature extractors and overlooking their core generative strengths. We introduce GIRCSE (Generative Iterative Refinement for Contrastive Sentence Embeddings), a novel framework that leverages autoregressive generation to iteratively refine semantic representations. By producing sequences of soft tokens optimized under contrastive objective, GIRCSE captures latent concepts and implicit semantics that encoder-only methods often miss. To guide this process, we propose an Iterative Contrastive Refinement (ICR) objective that encourages each refinement step to yield better representations. Extensive experiments show that GIRCSE outperforms strong LLM-based embedding baselines on the MTEB benchmark and instruction-following tasks. Moreover, GIRCSE exhibits an emergent test-time scaling property: generating more tokens at inference steadily improves embedding quality. Our results establish generative iterative refinement as a new paradigm for representation learning.

Vision-language models achieve strong performance across a wide range of multimodal understanding and reasoning tasks, yet their multi-step reasoning remains unstable. Repeated sampling over the same input often produces divergent reasoning trajectories and inconsistent final predictions. To address this, we introduce two complementary approaches inspired by test-time scaling: (1) CASHEW, an inference-time framework that stabilizes reasoning by iteratively aggregating multiple candidate trajectories into higher-quality reasoning traces, with explicit visual verification filtering hallucinated steps and grounding reasoning in visual evidence, and (2) CASHEW-RL, a learned variant that internalizes this aggregation behavior within a single model. CASHEW-RL is trained using Group Sequence Policy Optimization (GSPO) with a composite reward that encourages correct answers grounded in minimal yet sufficient visual evidence, while adaptively allocating reasoning effort based on task difficulty. This training objective enables robust self-aggregation at inference. Extensive experiments on 13 image understanding, video understanding, and video reasoning benchmarks show significant performance improvements, including gains of up to +23.6 percentage points on ScienceQA and +8.1 percentage points on EgoSchema.

Reasoning reinforcement learning (RL) has recently revealed a new scaling effect: test-time scaling. Thinking models such as R1 and o1 improve their reasoning accuracy at test time as the length of the reasoning context increases. However, compared with training-time scaling, test-time scaling is fundamentally limited by the limited context length of base models, which remains orders of magnitude smaller than the amount of tokens consumed during training. We revisit test-time enhancement techniques through the lens of scaling effect and introduce a unified framework of multi-dimensional test-time scaling to extend the capacity of test-time reasoning. Beyond conventional context-length scaling, we consider two additional dimensions: batch scaling, where accuracy improves with parallel sampling, and turn scaling, where iterative self-refinement enhances reasoning quality. Building on this perspective, we propose 3D test-time scaling, which integrates context, batch, and turn scaling. We show that: (1) each dimension demonstrates a test-time scaling effect, but with a bounded capacity; (2) combining all three dimensions substantially improves the reasoning performance of challenging testbeds, including IOI, IMO, and CPHO, and further benefits from human preference feedback; and (3) the human-in-the-loop framework naturally extends to a more open-ended domain, i.e., embodied learning, which enables the design of humanoid control behaviors.

Flow matching and diffusion models have shown impressive results in text-to-image generation, producing photorealistic images through an iterative denoising process. A common strategy to speed up synthesis is to perform early denoising at lower resolutions. However, traditional methods that downscale and upscale in pixel space often introduce artifacts and distortions. These issues arise when the upscaled images are re-encoded into the latent space, leading to degraded final image quality. To address this, we propose {\bf Latent Space Scaling Generation (LSSGen)}, a framework that performs resolution scaling directly in the latent space using a lightweight latent upsampler. Without altering the Transformer or U-Net architecture, LSSGen improves both efficiency and visual quality while supporting flexible multi-resolution generation. Our comprehensive evaluation covering text-image alignment and perceptual quality shows that LSSGen significantly outperforms conventional scaling approaches. When generating 1024^2 images at similar speeds, it achieves up to 246\% TOPIQ score improvement.

Non-cooperative game theory provides a robust framework for analyzing distributed resource allocation in multi-user wireless networks, with Iterative Water-Filling (IWF) emerging as a canonical solution for power control problems. Although classical fixed-point theorems guarantee the existence of a Nash Equilibrium (NE) under mild concavity and compactness conditions, the convergence of practical iterative algorithms to that equilibrium remains a challenging endeavor. This challenge intensifies under varying update schedules, interference regimes, and imperfections such as channel estimation errors or feedback delay. In this paper, we present an in-depth examination of IWF in multi-user systems under three different update schemes: (1) synchronous sequential updates, (2) synchronous simultaneous updates, and (3) totally asynchronous updates. We first formulate the water-filling operator in a multi-carrier environment, then recast the iterative process as a fixed-point problem. Using contraction mapping principles, we demonstrate sufficient conditions under which IWF converges to a unique NE and highlight how spectral radius constraints, diagonal dominance, and careful step-size selection are pivotal for guaranteeing convergence. We further discuss robustness to measurement noise, partial updates, and network scaling to emphasize the practical viability of these schemes. This comprehensive analysis unifies diverse threads in the literature while offering novel insights into asynchronous implementations. Our findings enable network designers to ascertain system parameters that foster both stable convergence and efficient spectrum usage.

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and capturing both global and local graph structures simultaneously. To overcome these issues, we introduce a method that generates a graph by progressively expanding a single node to a target graph. In each step, nodes and edges are added in a localized manner through denoising diffusion, building first the global structure, and then refining the local details. The local generation avoids modeling the entire joint distribution over all node pairs, achieving substantial computational savings with subquadratic runtime relative to node count while maintaining high expressivity through multiscale generation. Our experiments show that our model achieves state-of-the-art performance on well-established benchmark datasets while successfully scaling to graphs with at least 5000 nodes. Our method is also the first to successfully extrapolate to graphs outside of the training distribution, showcasing a much better generalization capability over existing methods.

The Multi-Prize Lottery Ticket Hypothesis posits that randomly initialized neural networks contain several subnetworks that achieve comparable accuracy to fully trained models of the same architecture. However, current methods require that the network is sufficiently overparameterized. In this work, we propose a modification to two state-of-the-art algorithms (Edge-Popup and Biprop) that finds high-accuracy subnetworks with no additional storage cost or scaling. The algorithm, Iterative Weight Recycling, identifies subsets of important weights within a randomly initialized network for intra-layer reuse. Empirically we show improvements on smaller network architectures and higher prune rates, finding that model sparsity can be increased through the "recycling" of existing weights. In addition to Iterative Weight Recycling, we complement the Multi-Prize Lottery Ticket Hypothesis with a reciprocal finding: high-accuracy, randomly initialized subnetwork's produce diverse masks, despite being generated with the same hyperparameter's and pruning strategy. We explore the landscapes of these masks, which show high variability.

General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in specialized languages like Lean 4 remains a significant challenge for these models, limiting their application in complex theorem proving and automated verification. Current approaches typically require specializing models through fine-tuning on dedicated formal corpora, incurring high costs for data collection and training. In this work, we introduce Delta Prover, an agent-based framework that orchestrates the interaction between a general-purpose LLM and the Lean 4 proof environment. Delta Prover leverages the reflection and reasoning capabilities of general-purpose LLMs to interactively construct formal proofs in Lean 4, circumventing the need for model specialization. At its core, the agent integrates two novel, interdependent components: an algorithmic framework for reflective decomposition and iterative proof repair, and a custom Domain-Specific Language (DSL) built upon Lean 4 for streamlined subproblem management. Delta Prover achieves a state-of-the-art 95.9\% success rate on the miniF2F-test benchmark, surpassing all existing approaches, including those requiring model specialization. Furthermore, Delta Prover exhibits a significantly stronger test-time scaling law compared to standard Best-of-N proof strategies. Crucially, our findings demonstrate that general-purpose LLMs, when guided by an effective agentic structure, possess substantial untapped theorem-proving capabilities. This presents a computationally efficient alternative to specialized models for robust automated reasoning in formal environments.

While AI agents have shown remarkable performance at various tasks, they still struggle with complex multi-modal applications, structured generation and strategic planning. Improvements via standard fine-tuning is often impractical, as solving agentic tasks usually relies on black box API access without control over model parameters. Inference-time methods such as Best-of-N (BON) sampling offer a simple yet effective alternative to improve performance. However, BON lacks iterative feedback integration mechanism. Hence, we propose Iterative Agent Decoding (IAD) which combines iterative refinement with dynamic candidate evaluation and selection guided by a verifier. IAD differs in how feedback is designed and integrated, specifically optimized to extract maximal signal from reward scores. We conduct a detailed comparison of baselines across key metrics on Sketch2Code, Text2SQL, and Webshop where IAD consistently outperforms baselines, achieving 3--6% absolute gains on Sketch2Code and Text2SQL (with and without LLM judges) and 8--10% gains on Webshop across multiple metrics. To better understand the source of IAD's gains, we perform controlled experiments to disentangle the effect of adaptive feedback from stochastic sampling, and find that IAD's improvements are primarily driven by verifier-guided refinement, not merely sampling diversity. We also show that both IAD and BON exhibit inference-time scaling with increased compute when guided by an optimal verifier. Our analysis highlights the critical role of verifier quality in effective inference-time optimization and examines the impact of noisy and sparse rewards on scaling behavior. Together, these findings offer key insights into the trade-offs and principles of effective inference-time optimization.

Understanding information from visually rich documents remains a significant challenge for traditional Retrieval-Augmented Generation (RAG) methods. Existing benchmarks predominantly focus on image-based question answering (QA), overlooking the fundamental challenges of efficient retrieval, comprehension, and reasoning within dense visual documents. To bridge this gap, we introduce ViDoSeek, a novel dataset designed to evaluate RAG performance on visually rich documents requiring complex reasoning. Based on it, we identify key limitations in current RAG approaches: (i) purely visual retrieval methods struggle to effectively integrate both textual and visual features, and (ii) previous approaches often allocate insufficient reasoning tokens, limiting their effectiveness. To address these challenges, we propose ViDoRAG, a novel multi-agent RAG framework tailored for complex reasoning across visual documents. ViDoRAG employs a Gaussian Mixture Model (GMM)-based hybrid strategy to effectively handle multi-modal retrieval. To further elicit the model's reasoning capabilities, we introduce an iterative agent workflow incorporating exploration, summarization, and reflection, providing a framework for investigating test-time scaling in RAG domains. Extensive experiments on ViDoSeek validate the effectiveness and generalization of our approach. Notably, ViDoRAG outperforms existing methods by over 10% on the competitive ViDoSeek benchmark.

Test-time scaling (TTS) enhances the performance of large language models (LLMs) by allocating additional compute resources during inference. However, existing research primarily investigates TTS in single-stage tasks; while many real-world problems are multi-stage complex tasks, composed of a sequence of heterogeneous subtasks with each subtask requires LLM of specific capability. Therefore, we study a novel problem: the test-time compute-optimal scaling in multi-stage complex tasks, aiming to select suitable models and allocate budgets per subtask to maximize overall performance. TTS in multi-stage tasks introduces two fundamental challenges: (i) The combinatorial search space of model and budget allocations, combined with the high cost of inference, makes brute-force search impractical. (ii) The optimal model and budget allocations across subtasks are interdependent, increasing the complexity of the compute-optimal search. To address this gap, we conduct extensive pilot experiments on four tasks across six datasets, deriving three empirical insights characterizing the behavior of LLMs in multi-stage complex tasks. Informed by these insights, we propose AgentTTS, an LLM-agent-based framework that autonomously searches for compute-optimal allocations through iterative feedback-driven interactions with the execution environment. Experimental results demonstrate that AgentTTS significantly outperforms traditional and other LLM-based baselines in search efficiency, and shows improved robustness to varying training set sizes and enhanced interpretability.

We develop a unified theoretical framework for sparse knowledge distillation based on probability-domain softening operators. While the equivalence p^{1/T} propto softmax(z/T) is well known, our contribution is an operator-level analytical framework built on this foundation rather than the equivalence itself. The framework comprises four core components: (i) operator-agnostic bias--variance decompositions that characterize when sparse students outperform dense teachers, (ii) a homotopy path formalization of multi-stage pruning in function space explaining why iterative compression succeeds where one-shot pruning fails, (iii) convergence guarantees establishing O(1/n) rates for n-stage distillation with explicit parameter dependence, and (iv) equivalence class characterizations identifying distinct probability-domain operators that yield identical student models under capacity constraints. We introduce an axiomatic definition of probability-domain softening operators based on ranking preservation, continuity, entropy monotonicity, identity, and boundary behavior, and show that multiple non-equivalent operator families satisfy these axioms. All learning-theoretic guarantees are shown to hold uniformly across this operator class, independent of implementation details. These results provide theoretical grounding for black-box teacher distillation, partial-access settings such as top-k truncation and text-only outputs, and privacy-preserving model compression.

Recent advances in long-context large language models (LLMs) have led to the emerging paradigm of many-shot in-context learning (ICL), where it is observed that scaling many more demonstrating examples beyond the conventional few-shot setup in the context can lead to performance benefits. However, despite its promise, it is unclear what aspects dominate the benefits and whether simply scaling to more examples is the most effective way of improving many-shot ICL. In this work, we first provide an analysis of the factors driving many-shot ICL, and we find that 1) many-shot performance can still be attributed to often a few disproportionately influential examples and 2) identifying such influential examples ("optimize") and using them as demonstrations to regenerate new examples ("generate") can lead to further improvements. Inspired by the findings, we propose BRIDGE, an algorithm that alternates between the optimize step with Bayesian optimization to discover the influential sets of examples and the generate step to reuse this set to expand the reasoning paths of the examples back to the many-shot regime automatically. On Gemini, Claude, and Mistral LLMs of different sizes, we show that BRIDGE to significant improvements across a diverse set of tasks, including symbolic reasoning, numerical reasoning, and code generation.

Effectively retrieving, reasoning and understanding visually rich information remains a challenge for RAG methods. Traditional text-based methods cannot handle visual-related information. On the other hand, current vision-based RAG approaches are often limited by fixed pipelines and frequently struggle to reason effectively due to the insufficient activation of the fundamental capabilities of models. As RL has been proven to be beneficial for model reasoning, we introduce VRAG-RL, a novel RL framework tailored for complex reasoning across visually rich information. With this framework, VLMs interact with search engines, autonomously sampling single-turn or multi-turn reasoning trajectories with the help of visual perception tokens and undergoing continual optimization based on these samples. Our approach highlights key limitations of RL in RAG domains: (i) Prior Multi-modal RAG approaches tend to merely incorporate images into the context, leading to insufficient reasoning token allocation and neglecting visual-specific perception; and (ii) When models interact with search engines, their queries often fail to retrieve relevant information due to the inability to articulate requirements, thereby leading to suboptimal performance. To address these challenges, we define an action space tailored for visually rich inputs, with actions including cropping and scaling, allowing the model to gather information from a coarse-to-fine perspective. Furthermore, to bridge the gap between users' original inquiries and the retriever, we employ a simple yet effective reward that integrates query rewriting and retrieval performance with a model-based reward. Our VRAG-RL optimizes VLMs for RAG tasks using specially designed RL strategies, aligning the model with real-world applications. The code is available at https://github.com/Alibaba-NLP/VRAG.

Large language models (LLMs) have demonstrated strong capabilities in programming and mathematical reasoning tasks, but are constrained by limited high-quality training data. Synthetic data can be leveraged to enhance fine-tuning outcomes, but several factors influence this process, including model size, synthetic data volume, pruning strategy, and number of fine-tuning rounds. We explore these axes and investigate which conditions enable model self-improvement. We introduce the Think, Prune, Train process, a scalable framework that iteratively fine-tunes models on their own reasoning traces, using ground-truth pruning to ensure high-quality training data. This approach yields improved performance: on GSM8K, Gemma2-2B achieves a Pass@1 of 57.6% (from 41.9%), Gemma2-9B reaches 82%, matching LLaMA-3.1-70B, and LLaMA-3.1-70B attains 91%, even surpassing GPT-4o, demonstrating the effectiveness of self-generated reasoning and systematic data selection for improving LLM capabilities.

Recent years have witnessed the success of foundation models pre-trained with self-supervised learning (SSL) in various music informatics understanding tasks, including music tagging, instrument classification, key detection, and more. In this paper, we propose a self-supervised music representation learning model for music understanding. Distinguished from previous studies adopting random projection or existing neural codec, the proposed model, named MuQ, is trained to predict tokens generated by Mel Residual Vector Quantization (Mel-RVQ). Our Mel-RVQ utilizes residual linear projection structure for Mel spectrum quantization to enhance the stability and efficiency of target extraction and lead to better performance. Experiments in a large variety of downstream tasks demonstrate that MuQ outperforms previous self-supervised music representation models with only 0.9K hours of open-source pre-training data. Scaling up the data to over 160K hours and adopting iterative training consistently improve the model performance. To further validate the strength of our model, we present MuQ-MuLan, a joint music-text embedding model based on contrastive learning, which achieves state-of-the-art performance in the zero-shot music tagging task on the MagnaTagATune dataset. Code and checkpoints are open source in https://github.com/tencent-ailab/MuQ.

Iterative improvement of model architectures is fundamental to deep learning: Transformers first enabled scaling, and recent advances in model hybridization have pushed the quality-efficiency frontier. However, optimizing architectures remains challenging and expensive. Current automated or manual approaches fall short, largely due to limited progress in the design of search spaces and due to the simplicity of resulting patterns and heuristics. In this work, we propose a new approach for the synthesis of tailored architectures (STAR). Our approach combines a novel search space based on the theory of linear input-varying systems, supporting a hierarchical numerical encoding into architecture genomes. STAR genomes are automatically refined and recombined with gradient-free, evolutionary algorithms to optimize for multiple model quality and efficiency metrics. Using STAR, we optimize large populations of new architectures, leveraging diverse computational units and interconnection patterns, improving over highly-optimized Transformers and striped hybrid models on the frontier of quality, parameter size, and inference cache for autoregressive language modeling.

Large Language Models (LLMs) have demonstrated exceptional capabilities across diverse natural language processing (NLP) tasks. The release of open-source LLMs like LLaMA and Qwen has triggered the development of numerous fine-tuned models tailored for various tasks and languages. In this paper, we explore an important question: is it possible to combine these specialized models to create a unified model with multi-task capabilities. We introduces Hierarchical Iterative Merging (Hi-Merging), a training-free method for unifying different specialized LLMs into a single model. Specifically, Hi-Merging employs model-wise and layer-wise pruning and scaling, guided by contribution analysis, to mitigate parameter conflicts. Extensive experiments on multiple-choice and question-answering tasks in both Chinese and English validate Hi-Merging's ability for multi-task learning. The results demonstrate that Hi-Merging consistently outperforms existing merging techniques and surpasses the performance of models fine-tuned on combined datasets in most scenarios. Code is available at: https://github.com/Applied-Machine-Learning-Lab/Hi-Merging.

Recursive or looped language models have recently emerged as a new scaling axis by iteratively refining the same model computation over latent states to deepen reasoning. We extend such scaling principle from a single model to multi-agent systems, and ask: Can agent collaboration itself be scaled through recursion? To this end, we introduce RecursiveMAS, a recursive multi-agent framework that casts the entire system as a unified latent-space recursive computation. RecursiveMAS connects heterogeneous agents as a collaboration loop through the lightweight RecursiveLink module, enabling in-distribution latent thoughts generation and cross-agent latent state transfer. To optimize our framework, we develop an inner-outer loop learning algorithm for iterative whole-system co-optimization through shared gradient-based credit assignment across recursion rounds. Theoretical analyses of runtime complexity and learning dynamics establish that RecursiveMAS is more efficient than standard text-based MAS and maintains stable gradients during recursive training. Empirically, we instantiate RecursiveMAS under 4 representative agent collaboration patterns and evaluate across 9 benchmarks spanning mathematics, science, medicine, search, and code generation. In comparison with advanced single/multi-agent and recursive computation baselines, RecursiveMAS consistently delivers an average accuracy improvement of 8.3%, together with 1.2times-2.4times end-to-end inference speedup, and 34.6%-75.6% token usage reduction. Code and Data are provided in https://recursivemas.github.io.

Deep research agents rely on iterative retrieval and reasoning to answer complex queries, but scaling test-time computation raises significant efficiency concerns. We study how to allocate reasoning budget in deep search pipelines, focusing on the role of listwise reranking. Using the BrowseComp-Plus benchmark, we analyze tradeoffs between model scale, reasoning effort, reranking depth, and total token cost via a novel effective token cost (ETC) metric. Our results show that reranking consistently improves retrieval and end-to-end accuracy, and that moderate reranking often yields larger gains than increasing search-time reasoning, achieving comparable accuracy at substantially lower cost. All our code is available at https://github.com/texttron/BrowseComp-Plus.git

The space of task-agnostic feature upsampling has emerged as a promising area of research to efficiently create denser features from pre-trained visual backbones. These methods act as a shortcut to achieve dense features for a fraction of the cost by learning to map low-resolution features to high-resolution versions. While early works in this space used iterative upsampling approaches, more recent works have switched to cross-attention-based methods, which risk falling into the same efficiency scaling problems of the backbones they are upsampling. In this work, we demonstrate that iterative upsampling methods can still compete with cross-attention-based methods; moreover, they can achieve state-of-the-art performance with lower inference costs. We propose UPLiFT, an architecture for Universal Pixel-dense Lightweight Feature Transforms. We also propose an efficient Local Attender operator to overcome the limitations of prior iterative feature upsampling methods. This operator uses an alternative attentional pooling formulation defined fully locally. We show that our Local Attender allows UPLiFT to maintain stable features throughout upsampling, enabling state-of-the-art performance with lower inference costs than existing pixel-dense feature upsamplers. In addition, we apply UPLiFT to generative downstream tasks and show that it achieves competitive performance with state-of-the-art Coupled Flow Matching models for VAE feature upsampling. Altogether, UPLiFT offers a versatile and efficient approach to creating denser features.

Recent advances in deep-research agents have shown promise for autonomous knowledge construction through dynamic reasoning over external sources. However, existing approaches rely on a mono-contextual paradigm that accumulates all information in a single, expanding context window, leading to context suffocation and noise contamination that limit their effectiveness on long-horizon tasks. We introduce IterResearch, a novel iterative deep-research paradigm that reformulates long-horizon research as a Markov Decision Process with strategic workspace reconstruction. By maintaining an evolving report as memory and periodically synthesizing insights, our approach preserves consistent reasoning capacity across arbitrary exploration depths. We further develop Efficiency-Aware Policy Optimization (EAPO), a reinforcement learning framework that incentivizes efficient exploration through geometric reward discounting and enables stable distributed training via adaptive downsampling. Extensive experiments demonstrate that IterResearch achieves substantial improvements over existing open-source agents with average +14.5pp across six benchmarks and narrows the gap with frontier proprietary systems. Remarkably, our paradigm exhibits unprecedented interaction scaling, extending to 2048 interactions with dramatic performance gains (from 3.5\% to 42.5\%), and serves as an effective prompting strategy, improving frontier models by up to 19.2pp over ReAct on long-horizon tasks. These findings position IterResearch as a versatile solution for long-horizon reasoning, effective both as a trained agent and as a prompting paradigm for frontier models.

We introduce Pencil Puzzle Bench, a framework for evaluating large language model reasoning through pencil puzzles, a family of constraint-satisfaction problems closely related to NP-complete problems, with deterministic, step-level verification. From a database of 62,231 puzzles across 94 varieties with verified unique solutions, we select a benchmark of 300 puzzles spanning 20 varieties and evaluate 51 models from 11 providers in two modes: direct ask (single-shot) and agentic (multi-turn with iterative verification). A key differentiator of our benchmark is that every intermediate board state can be checked against variety-specific constraints, localizing errors to the exact rule violated, providing the infrastructure for dense, per-move reward signals for process supervision and reinforcement learning. Our evaluation reveals two distinct axes of capability: (1) reasoning effort scaling, where GPT-5.2 improves 81x from no reasoning to maximum effort; and (2) agentic iteration, where Claude Opus 4.6 rises from 0.3% to 30.0% through iterative checking, while GPT-5.2@xhigh improves from 20.2% to 56.0%. Agentic attempts span a median of 29 turns over 17 minutes, with the longest exceeding 1,221 turns and 14.3 hours - a demanding test of long-context utilization, not just reasoning.

Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines a population of candidate reasoning chains through aggregation of subsets to yield a population of improved solutions, which are then used as the candidate pool for the next iteration. Empirically, RSA delivers substantial performance gains with increasing compute budgets across diverse tasks, model families and sizes. Notably, RSA with Gemini 3 Flash attains performance near the top of the ARC-AGI-2 public leaderboard. RSA also enables Qwen3-4B-Instruct-2507 to achieve competitive performance with larger reasoning models, including DeepSeek-R1 and o3-mini (high), outperforming purely parallel and sequential scaling strategies across AIME-25, HMMT-25, Reasoning Gym, LiveCodeBench-v6, and SuperGPQA. We further propose a novel aggregation-aware reinforcement learning approach that yields significant performance gains by training the model to combine solutions.

We introduce Generative Universal Verifier, a novel concept and plugin designed for next-generation multimodal reasoning in vision-language models and unified multimodal models, providing the fundamental capability of reflection and refinement on visual outcomes during the reasoning and generation process. This work makes three main contributions: (1) We build ViVerBench, a comprehensive benchmark spanning 16 categories of critical tasks for evaluating visual outcomes in multimodal reasoning. Results show that existing VLMs consistently underperform across these tasks, underscoring a substantial gap from human-level capability in reliable visual verification. (2) We design two automated pipelines to construct large-scale visual verification data and train OmniVerifier-7B, the first omni-capable generative verifier trained for universal visual verification and achieves notable gains on ViVerBench(+8.3). Through training, we identify three atomic capabilities in visual verification and demonstrate how they generalize and interact synergistically. (3) We propose OmniVerifier-TTS, a sequential test-time scaling paradigm that leverages the universal verifier to bridge image generation and editing within unified models, enhancing the upper bound of generative ability through iterative fine-grained optimization. Beyond generation, we extend universal verifier to broader world-modeling interleaved reasoning scenarios. Empirically, OmniVerifier-TTS achieves improvements on T2I-ReasonBench(+3.7), and GenEval++(+4.3), outperforming existing parallel test-time scaling methods, such as Best-of-N. By endowing multimodal reasoning with reliable visual verification, OmniVerifier advances both reliable reflection during generation and scalable test-time refinement, marking a step toward more trustworthy and controllable next-generation reasoning systems.

Multimodal Large Language Model (MLLM)-based Graphical User Interface (GUI) agents develop rapidly, with visual grounding that maps natural language instructions to target UI elements serving as the core capability. Existing GUI agents typically fine-tune MLLM on massive datasets to handle challenges in understanding instructions and UI interfaces, which not only incurs high data annotation costs but also makes performance dependent on data quality and distribution. To avoid such cumbersome yet ineffective training, we notice that complex UI interfaces can be decomposed into basic visual elements directly understandable by common MLLMs. Consequently, we propose ZoomUI that leverages inference scaling to guide common MLLMs in progressively anchor instruction elements to increasingly detailed interface elements. Specifically, ZoomUI first optimizes the latent thinking to transform original instruction into element visual features description, and subsequently leverages internal attention to iteratively zoom in target element interface region. Evaluations on extensive benchmarks demonstrate that ZoomUI reaches or even surpasses SOTA baselines.

Vision-Language-Action (VLA) models enable robots to understand and perform complex tasks from multimodal input. Although recent work explores using reinforcement learning (RL) to automate the laborious data collection process in scaling supervised fine-tuning (SFT), applying large-scale RL to flow-based VLAs (e.g., pi_0, pi_{0.5}) remains challenging due to intractable action log-likelihoods from iterative denoising. We address this challenge with pi_{RL}, an open-source framework for training flow-based VLAs in parallel simulation. pi_{RL} implements two RL algorithms: (1) {Flow-Noise} models the denoising process as a discrete-time MDP with a learnable noise network for exact log-likelihood computation. (2) {Flow-SDE} integrates denoising with agent-environment interaction, formulating a two-layer MDP that employs ODE-to-SDE conversion for efficient RL exploration. We evaluate pi_{RL} on LIBERO and ManiSkill benchmarks. On LIBERO, pi_{RL} boosts few-shot SFT models pi_0 and pi_{0.5} from 57.6% to 97.6% and from 77.1% to 98.3%, respectively. In ManiSkill, we train pi_{RL} in 320 parallel environments, improving pi_0 from 41.6% to 85.7% and pi_{0.5} from 40.0% to 84.8% across 4352 pick-and-place tasks, demonstrating scalable multitask RL under heterogeneous simulation. Overall, pi_{RL} achieves significant performance gains and stronger generalization over SFT-models, validating the effectiveness of online RL for flow-based VLAs.

Tabular data remain the predominant format for real-world applications. Yet, developing effective neural models for tabular data remains challenging due to heterogeneous feature types and complex interactions occurring at multiple scales. Recent advances in tabular in-context learning (ICL), such as TabPFN and TabICL, have achieved state-of-the-art performance comparable to gradient-boosted trees (GBTs) without task-specific fine-tuning. However, current architectures exhibit key limitations: (1) single-scale feature processing that overlooks hierarchical dependencies, (2) dense attention with quadratic scaling in table width, and (3) strictly sequential component processing that prevents iterative representation refinement and cross-component communication. To address these challenges, we introduce Orion-MSP, a tabular ICL architecture featuring three key innovations: (1) multi-scale processing to capture hierarchical feature interactions; (2) block-sparse attention combining windowed, global, and random patterns for scalable efficiency and long-range connectivity; and (3) a Perceiver-style memory enabling safe bidirectional information flow across components. Across diverse benchmarks, Orion-MSP matches or surpasses state-of-the-art performance while scaling effectively to high-dimensional tables, establishing a new standard for efficient tabular in-context learning. The model is publicly available at https://github.com/Lexsi-Labs/Orion-MSP .

Powerful large language models (LLMs) from different providers have been expensively trained and finetuned to specialize across varying domains. In this work, we introduce a new kind of Conductor model trained with reinforcement learning to automatically discover powerful coordination strategies among LLMs. Our Conductor learns not only to design targeted communication topologies for effective agent-to-agent collaboration, but also to prompt engineer focused instructions to the LLMs to maximally leverage their individual capabilities. We show that, by learning optimal coordination strategies over pools of powerful worker LLMs, a 7B Conductor achieves significant performance gains beyond any individual worker, attaining state-of-the-art results in challenging reasoning benchmarks, such as LiveCodeBench and GPQA. By training with randomized agent pools, our conductor effectively adapts to arbitrary sets of open- and closed-source agents, meeting any user requirements. Furthermore, allowing the Conductor to select itself as a worker gives rise to recursive topologies, elevating performance with a new form of dynamic test-time scaling through online iterative adaptation. More broadly, ours is among the early work demonstrating language model coordination can be unlocked through RL, where powerful coordination strategies emerge naturally in LLMs through pure end-to-end reward maximization.

This paper introduces the N-Way Self-Evaluating Deliberation (NSED) protocol, a Runtime Mixture-of-Models (MoM) architecture that constructs emergent composite models from a plurality of distinct expert agents. Unlike traditional Mixture-of-Experts (MoE) which rely on static gating networks, NSED employs a Dynamic Expertise Broker - a runtime optimization engine that treats model selection as a variation of the Knapsack Problem, binding heterogeneous checkpoints to functional roles based on live telemetry and cost constraints. At the execution layer, we formalize deliberation as a Macro-Scale Recurrent Neural Network (RNN), where the consensus state loops back through a semantic forget gate to enable iterative refinement without proportional VRAM scaling. Key components include an orchestration fabric for trustless N-to-N peer review, a Quadratic Voting activation function for non-linear consensus, and a feedback-driven state update. Empirical validation on challenging benchmarks (AIME 2025, LiveCodeBench) demonstrates that this topology allows ensembles of small (less than 20B) consumer-grade models to match or exceed the performance of state-of-the-art 100B+ parameter models, establishing a new hardware arbitrage efficiency frontier. Furthermore, testing on the DarkBench safety suite reveals intrinsic alignment properties, with peer-mediated correction reducing sycophancy scores below that of any individual agent.

The rapid evolution of generative AI necessitates robust safety evaluations. However, current safety datasets are predominantly English-centric, failing to capture specific risks in non-English, socio-cultural contexts such as Korean, and are often limited to the text modality. To address this gap, we introduce AssurAI, a new quality-controlled Korean multimodal dataset for evaluating the safety of generative AI. First, we define a taxonomy of 35 distinct AI risk factors, adapted from established frameworks by a multidisciplinary expert group to cover both universal harms and relevance to the Korean socio-cultural context. Second, leveraging this taxonomy, we construct and release AssurAI, a large-scale Korean multimodal dataset comprising 11,480 instances across text, image, video, and audio. Third, we apply the rigorous quality control process used to ensure data integrity, featuring a two-phase construction (i.e., expert-led seeding and crowdsourced scaling), triple independent annotation, and an iterative expert red-teaming loop. Our pilot study validates AssurAI's effectiveness in assessing the safety of recent LLMs. We release AssurAI to the public to facilitate the development of safer and more reliable generative AI systems for the Korean community.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We show that this departure may lead to arbitrary deterioration of model performance. Based on our analysis, we introduce a novel training method for learning-based acceleration of iterative methods. Furthermore, we theoretically prove that the proposed method improves upon the existing methods, and demonstrate its significant advantage and versatility through various numerical applications.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Scaling up language models has been empirically shown to improve performance on a wide range of downstream tasks. However, if we were to observe worse performance as a function of scale ("inverse scaling") on certain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al. 2022) identified eleven such inverse scaling tasks, evaluated on models of up to 280B parameters and up to 500 zettaFLOPs of training compute. This paper takes a closer look at these inverse scaling tasks. We evaluate models of up to 540B parameters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and training compute, only four out of the eleven tasks remain inverse scaling. Six out of the eleven tasks exhibit "U-shaped scaling", where performance decreases up to a certain size, and then increases again up to the largest model evaluated (the one remaining task displays positive scaling). In addition, we find that 1-shot examples and chain-of-thought can help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed in McKenzie et al. (2022) may not continue to hold for larger models, which we attribute to the presence of distractor tasks that only sufficiently large models can avoid.

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law assumes every training token is unique. This limits its ability to guide pretraining decisions in data-constrained regimes. We model the excess loss under repetition with a simple additive overfitting penalty and find that it accurately describes model behavior. Our scaling law yields qualitatively new compute-optimal allocation advice. Beyond a point, further repetition is counterproductive and compute is better spent on model capacity. We show that following our law's recommended configuration improves performance in data-constrained regimes. Finally, because our one-parameter form isolates overfitting in a single coefficient, it enables direct comparison across training configurations. As a case study, we show that strong weight decay (λ=1.0) reduces this coefficient by approximately 70%, providing a scaling-law explanation for recent findings that optimal weight decay in data-constrained regimes is an order of magnitude larger than standard practice.

The push to train ever larger neural networks has motivated the study of initialization and training at large network width. A key challenge is to scale training so that a network's internal representations evolve nontrivially at all widths, a process known as feature learning. Here, we show that feature learning is achieved by scaling the spectral norm of weight matrices and their updates like texttt{fan-out/fan-in}, in contrast to widely used but heuristic scalings based on Frobenius norm and entry size. Our spectral scaling analysis also leads to an elementary derivation of maximal update parametrization. All in all, we aim to provide the reader with a solid conceptual understanding of feature learning in neural networks.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.

Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by demonstrating or judging performance, but this approach fails if the task is too complicated for a human to directly evaluate. We propose Iterated Amplification, an alternative training strategy which progressively builds up a training signal for difficult problems by combining solutions to easier subproblems. Iterated Amplification is closely related to Expert Iteration (Anthony et al., 2017; Silver et al., 2017), except that it uses no external reward function. We present results in algorithmic environments, showing that Iterated Amplification can efficiently learn complex behaviors.

The scaling hypothesis motivates the expansion of models past trillions of parameters as a path towards better performance. Recent significant developments, such as GPT-3, have been driven by this conjecture. However, as models scale-up, training them efficiently with backpropagation becomes difficult. Because model, pipeline, and data parallelism distribute parameters and gradients over compute nodes, communication is challenging to orchestrate: this is a bottleneck to further scaling. In this work, we argue that alternative training methods can mitigate these issues, and can inform the design of extreme-scale training hardware. Indeed, using a synaptically asymmetric method with a parallelizable backward pass, such as Direct Feedback Alignement, communication needs are drastically reduced. We present a photonic accelerator for Direct Feedback Alignment, able to compute random projections with trillions of parameters. We demonstrate our system on benchmark tasks, using both fully-connected and graph convolutional networks. Our hardware is the first architecture-agnostic photonic co-processor for training neural networks. This is a significant step towards building scalable hardware, able to go beyond backpropagation, and opening new avenues for deep learning.

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We then propose an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, our method consistently outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.

Scaling imitation learning is fundamentally constrained by the efficiency of data collection. While handheld interfaces have emerged as a scalable solution for in-the-wild data acquisition, they predominantly operate in an open-loop manner: operators blindly collect demonstrations without knowing the underlying policy's weaknesses, leading to inefficient coverage of critical state distributions. Conversely, interactive methods like DAgger effectively address covariate shift but rely on physical robot execution, which is costly and difficult to scale. To reconcile this trade-off, we introduce RoboPocket, a portable system that enables Robot-Free Instant Policy Iteration using single consumer smartphones. Its core innovation is a Remote Inference framework that visualizes the policy's predicted trajectory via Augmented Reality (AR) Visual Foresight. This immersive feedback allows collectors to proactively identify potential failures and focus data collection on the policy's weak regions without requiring a physical robot. Furthermore, we implement an asynchronous Online Finetuning pipeline that continuously updates the policy with incoming data, effectively closing the learning loop in minutes. Extensive experiments demonstrate that RoboPocket adheres to data scaling laws and doubles the data efficiency compared to offline scaling strategies, overcoming their long-standing efficiency bottleneck. Moreover, our instant iteration loop also boosts sample efficiency by up to 2times in distributed environments a small number of interactive corrections per person. Project page and videos: https://robo-pocket.github.io.

Scaling visual generation models is essential for real-world content creation, yet requires substantial training and computational expenses. Alternatively, test-time scaling has garnered growing attention due to resource efficiency and promising performance. In this work, we present TTS-VAR, the first general test-time scaling framework for visual auto-regressive (VAR) models, modeling the generation process as a path searching problem. To dynamically balance computational efficiency with exploration capacity, we first introduce an adaptive descending batch size schedule throughout the causal generation process. Besides, inspired by VAR's hierarchical coarse-to-fine multi-scale generation, our framework integrates two key components: (i) At coarse scales, we observe that generated tokens are hard for evaluation, possibly leading to erroneous acceptance of inferior samples or rejection of superior samples. Noticing that the coarse scales contain sufficient structural information, we propose clustering-based diversity search. It preserves structural variety through semantic feature clustering, enabling later selection on samples with higher potential. (ii) In fine scales, resampling-based potential selection prioritizes promising candidates using potential scores, which are defined as reward functions incorporating multi-scale generation history. Experiments on the powerful VAR model Infinity show a notable 8.7% GenEval score improvement (from 0.69 to 0.75). Key insights reveal that early-stage structural features effectively influence final quality, and resampling efficacy varies across generation scales. Code is available at https://github.com/ali-vilab/TTS-VAR.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at https://inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

Writing GPU kernels is a challenging task and critical for AI systems' efficiency. It is also highly iterative: domain experts write code and improve performance through execution feedback. Moreover, it presents verifiable rewards like correctness and speedup, making it a natural environment to apply Reinforcement Learning (RL). To explicitly incorporate the iterative nature of this process into training, we develop a flexible multi-turn RL recipe that addresses unique challenges encountered in real-world settings, such as learning from long trajectories and effective reward attribution across turns. We present Kevin - K(ernel D)evin, the first model trained with multi-turn RL for CUDA kernel generation and optimization. In our evaluation setup, Kevin shows significant gains over its base model (QwQ-32B), improving correctness of generated kernels (in pure CUDA) from 56% to 82% and mean speedup from 0.53x to 1.10x of baseline (PyTorch Eager), and surpassing frontier models like o4-mini (0.78x). Finally, we study its behavior across test-time scaling axes: we found scaling serial refinement more beneficial than parallel sampling. In particular, when given more refinement turns, Kevin shows a higher rate of improvement.

Modern LLMs scale at test-time, e.g. via repeated sampling, where inference cost grows with model size and the number of samples. This creates a trade-off that pretraining scaling laws, such as Chinchilla, do not address. We present Train-to-Test (T^2) scaling laws that jointly optimize model size, training tokens, and number of inference samples under fixed end-to-end budgets. T^2 modernizes pretraining scaling laws with pass@k modeling used for test-time scaling, then jointly optimizes pretraining and test-time decisions. Forecasts from T^2 are robust over distinct modeling approaches: measuring joint scaling effect on the task loss and modeling impact on task accuracy. Across eight downstream tasks, we find that when accounting for inference cost, optimal pretraining decisions shift radically into the overtraining regime, well-outside of the range of standard pretraining scaling suites. We validate our results by pretraining heavily overtrained models in the optimal region that T^2 scaling forecasts, confirming their substantially stronger performance compared to pretraining scaling alone. Finally, as frontier LLMs are post-trained, we show that our findings survive the post-training stage, making T^2 scaling meaningful in modern deployments.

Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform resource distribution across all reasoning sub-problems, creating fundamental bottlenecks where challenging sub-problems receive insufficient attention while routine operations consume disproportionate resources. This uniform allocation creates performance bottlenecks where additional computational resources yield diminishing returns. Inspired by dual-process theory, we propose SCALE (Selective Resource Allocation), a framework that selectively allocates computational resources based on sub-problem difficulty. SCALE operates through four stages: (1) problem decomposition into sequential reasoning sub-problems, (2) difficulty assessment of each sub-problem to distinguish between routine operations and computationally challenging sub-problems, (3) selective processing mode assignment between System 1 for simple sub-problems and System 2 for complex ones, and (4) sequential execution with context propagation. By concentrating resources on challenging sub-problems while processing routine operations efficiently, SCALE achieves substantial performance improvements with superior resource utilization. Extensive experiments demonstrate that SCALE significantly outperforms uniform scaling baselines, achieving accuracy improvements of up to 13.75 percentage points (57.50% to 71.25% on AIME25) while reducing computational costs by 33%-53%, representing a major advance in test-time scaling that addresses fundamental limitations of current approaches.

Language models have been shown to exhibit positive scaling, where performance improves as models are scaled up in terms of size, compute, or data. In this work, we introduce NeQA, a dataset consisting of questions with negation in which language models do not exhibit straightforward positive scaling. We show that this task can exhibit inverse scaling, U-shaped scaling, or positive scaling, and the three scaling trends shift in this order as we use more powerful prompting methods or model families. We hypothesize that solving NeQA depends on two subtasks: question answering (task 1) and negation understanding (task 2). We find that task 1 has linear scaling, while task 2 has sigmoid-shaped scaling with an emergent transition point, and composing these two scaling trends yields the final scaling trend of NeQA. Our work reveals and provides a way to analyze the complex scaling trends of language models.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

Scaling has been critical in improving model performance and generalization in machine learning. It involves how a model's performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in other areas, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations. The dominant paradigm here is to incorporate many physical domain constraints into the model, such as rotational equivariance. We contend that these complex constraints inhibit the scaling ability of NNIPs, and are likely to lead to performance plateaus in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling strategies. Our findings indicate that scaling the model through attention mechanisms is efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency--at least 10x faster inference, 5x less memory usage--compared to existing NNIPs. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). We emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept for developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

We revisit test-time scaling for language model reasoning and ask a fundamental question: at equal token budget and compute, is it better to run multiple independent chains in parallel, or to run fewer chains that iteratively refine through sequential steps? Through comprehensive evaluation across 5 state-of-the-art open source models and 3 challenging reasoning benchmarks, we find that sequential scaling where chains explicitly build upon previous attempts consistently outperforms the dominant parallel self-consistency paradigm in 95.6% of configurations with gains in accuracy upto 46.7%. Further, we introduce inverse-entropy weighted voting, a novel training-free method to further boost the accuracy of sequential scaling. By weighing answers in proportion to the inverse entropy of their reasoning chains, we increase our success rate over parallel majority and establish it as the optimal test-time scaling strategy. Our findings fundamentally challenge the parallel reasoning orthodoxy that has dominated test-time scaling since Wang et al.'s self-consistency decoding (Wang et al., 2022), positioning sequential refinement as the robust default for modern LLM reasoning and necessitating a paradigm shift in how we approach inference-time optimization.

The scientific scale-up of large language models (LLMs) necessitates a comprehensive understanding of their scaling properties. However, the existing literature on the scaling properties only yields an incomplete answer: optimization loss decreases predictably as the model size increases, in line with established scaling law; yet no scaling law for task has been established and the task performances are far from predictable during scaling. Task performances typically show minor gains on small models until they improve dramatically once models exceed a size threshold, exemplifying the ``emergent abilities''. In this study, we discover that small models, although they exhibit minor performance, demonstrate critical and consistent task performance improvements that are not captured by conventional evaluation strategies due to insufficient measurement resolution. To measure such improvements, we introduce PassUntil, an evaluation strategy through massive sampling in the decoding phase. We conduct quantitative investigations into the scaling law of task performance. Firstly, a strict task scaling law is identified, enhancing the predictability of task performances. Remarkably, we are able to predict the performance of the 2.4B model on code generation with merely 0.05\% deviation before training starts. Secondly, underpinned by PassUntil, we observe concrete evidence of emergent abilities and ascertain that they are not in conflict with the continuity of performance improvement. Their semblance to break-through is that their scaling curve cannot be fitted by standard scaling law function. We then introduce a mathematical definition for the emergent abilities. Through the definition, we refute a prevalent ``multi-step reasoning hypothesis'' regarding the genesis of emergent abilities and propose a new hypothesis with a satisfying fit to the observed scaling curve.

The performance of time series forecasting has recently been greatly improved by the introduction of transformers. In this paper, we propose a general multi-scale framework that can be applied to the state-of-the-art transformer-based time series forecasting models (FEDformer, Autoformer, etc.). By iteratively refining a forecasted time series at multiple scales with shared weights, introducing architecture adaptations, and a specially-designed normalization scheme, we are able to achieve significant performance improvements, from 5.5% to 38.5% across datasets and transformer architectures, with minimal additional computational overhead. Via detailed ablation studies, we demonstrate the effectiveness of each of our contributions across the architecture and methodology. Furthermore, our experiments on various public datasets demonstrate that the proposed improvements outperform their corresponding baseline counterparts. Our code is publicly available in https://github.com/BorealisAI/scaleformer.

It is commonly believed that scaling language models should commit a significant space or time cost, by increasing the parameters (parameter scaling) or output tokens (inference-time scaling). We introduce the third and more inference-efficient scaling paradigm: increasing the model's parallel computation during both training and inference time. We apply P diverse and learnable transformations to the input, execute forward passes of the model in parallel, and dynamically aggregate the P outputs. This method, namely parallel scaling (ParScale), scales parallel computation by reusing existing parameters and can be applied to any model structure, optimization procedure, data, or task. We theoretically propose a new scaling law and validate it through large-scale pre-training, which shows that a model with P parallel streams is similar to scaling the parameters by O(log P) while showing superior inference efficiency. For example, ParScale can use up to 22times less memory increase and 6times less latency increase compared to parameter scaling that achieves the same performance improvement. It can also recycle an off-the-shelf pre-trained model into a parallelly scaled one by post-training on a small amount of tokens, further reducing the training budget. The new scaling law we discovered potentially facilitates the deployment of more powerful models in low-resource scenarios, and provides an alternative perspective for the role of computation in machine learning.

Large language models (LLMs) benefit from test-time scaling but are often hampered by high inference latency. Speculative decoding is a natural way to accelerate the scaling process; however, scaling along both the parallel and sequential dimensions poses significant challenges, including substantial memory-bound execution and synchronization overhead. We introduce ATTS (Asynchronous Test-Time Scaling), a statistically guaranteed adaptive scaling framework that follows the hypothesis testing process to address these challenges. By revisiting arithmetic intensity, ATTS identifies synchronization as the primary bottleneck. It enables asynchronous inference through online calibration and proposes an ordinal classification algorithm that supports a three-stage rejection sampling pipeline, scaling along both the sequential and parallel axes. Across experiments on the MATH, AMC23, AIME24, and AIME25 datasets and across multiple draft-target model families, we show that ATTS delivers up to 56.7x speedup in test-time scaling and a 4.14x throughput improvement, while maintaining accurate control of the rejection rate, reducing latency and memory overhead, and incurring no accuracy loss. By scaling both in parallel and sequential dimensions, we enable the 1.5B/70B draft/target model combination to achieve the performance of the state-of-the-art reasoning model o3-mini (high) on the AIME dataset. We have released the code at https://github.com/menik1126/asynchronous-test-time-scaling.

Recent years have witnessed success of sequential modeling, generative recommender, and large language model for recommendation. Though the scaling law has been validated for sequential models, it showed inefficiency in computational capacity when considering real-world applications like recommendation, due to the non-linear(quadratic) increasing nature of the transformer model. To improve the efficiency of the sequential model, we introduced a novel approach to sequential recommendation that leverages personalization techniques to enhance efficiency and performance. Our method compresses long user interaction histories into learnable tokens, which are then combined with recent interactions to generate recommendations. This approach significantly reduces computational costs while maintaining high recommendation accuracy. Our method could be applied to existing transformer based recommendation models, e.g., HSTU and HLLM. Extensive experiments on multiple sequential models demonstrate its versatility and effectiveness. Source code is available at https://github.com/facebookresearch/PerSRec{https://github.com/facebookresearch/PerSRec}.

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

The current paradigm of test-time scaling relies on generating long reasoning traces ("thinking" more) before producing a response. In agent problems that require interaction, this can be done by generating thinking traces before acting in the world. However, this process does not allow agents to acquire new information from the environment or adapt their behavior over time. In this work, we propose to scale test-time interaction, an untapped dimension of test-time scaling that increases the agent's interaction horizon to enable running rich behaviors such as exploration, backtracking, and dynamic re-planning within a single rollout. To demonstrate the promise of this scaling dimension, we study the domain of web agents. We first show that even prompting-based interaction scaling without any training can improve task success on web benchmarks non-trivially. Building on this, we introduce TTI (Test-Time Interaction), a curriculum-based online reinforcement learning (RL) approach that trains agents by adaptively adjusting their rollout lengths. Using a Gemma 3 12B model, TTI produces state-of-the-art open-source, open-data web agents on WebVoyager and WebArena benchmarks. We further show that TTI enables agents to balance exploration and exploitation adaptively. Our results establish interaction scaling as a powerful, complementary axis to scaling per-step compute, offering new avenues for training adaptive agents.

Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can be used to accelerate model development. In this work, we perform such an empirical investigation across a wide range of language understanding tasks, starting from models with as few as 10K parameters, and evaluate downstream performance across 9 language understanding tasks. We find that scaling laws emerge at finetuning time in some NLP tasks, and that they can also be exploited for debugging convergence when training large models. Moreover, for tasks where scaling laws exist, they can be used to predict the performance of larger models, which enables effective model selection. However, revealing scaling laws requires careful hyperparameter tuning and multiple runs for the purpose of uncertainty estimation, which incurs additional overhead, partially offsetting the computational benefits.

Traditionally, data selection has been studied in settings where all samples from prospective sources are fully revealed to a machine learning developer. However, in practical data exchange scenarios, data providers often reveal only a limited subset of samples before an acquisition decision is made. Recently, there have been efforts to fit scaling laws that predict model performance at any size and data source composition using the limited available samples. However, these scaling functions are black-box, computationally expensive to fit, highly susceptible to overfitting, or/and difficult to optimize for data selection. This paper proposes a framework called <projektor>, which predicts model performance and supports data selection decisions based on partial samples of prospective data sources. Our approach distinguishes itself from existing work by introducing a novel *two-stage* performance inference process. In the first stage, we leverage the Optimal Transport distance to predict the model's performance for any data mixture ratio within the range of disclosed data sizes. In the second stage, we extrapolate the performance to larger undisclosed data sizes based on a novel parameter-free mapping technique inspired by neural scaling laws. We further derive an efficient gradient-based method to select data sources based on the projected model performance. Evaluation over a diverse range of applications demonstrates that <projektor> significantly improves existing performance scaling approaches in terms of both the accuracy of performance inference and the computation costs associated with constructing the performance predictor. Also, <projektor> outperforms by a wide margin in data selection effectiveness compared to a range of other off-the-shelf solutions.

We propose ScaledGD(\lambda), a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor representations, ScaledGD(\lambda) starts from a small random initialization, and proceeds by gradient descent with a specific form of damped preconditioning to combat bad curvatures induced by overparameterization and ill-conditioning. At the expense of light computational overhead incurred by preconditioners, ScaledGD(\lambda) is remarkably robust to ill-conditioning compared to vanilla gradient descent (GD) even with overprameterization. Specifically, we show that, under the Gaussian design, ScaledGD(\lambda) converges to the true low-rank matrix at a constant linear rate after a small number of iterations that scales only logarithmically with respect to the condition number and the problem dimension. This significantly improves over the convergence rate of vanilla GD which suffers from a polynomial dependency on the condition number. Our work provides evidence on the power of preconditioning in accelerating the convergence without hurting generalization in overparameterized learning.

We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced by Zermelo almost a century ago. Here we describe an alternative and similarly simple iteration that provably returns identical results but does so much faster -- over a hundred times faster in some cases. We demonstrate this algorithm with applications to a range of example data sets and derive a number of results regarding its convergence.

On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is the compute-optimal scaling law, which reports the performance as a function of units of compute when choosing model sizes optimally. We analyze a random feature model trained with gradient descent as a solvable model of network training and generalization. This reproduces many observations about neural scaling laws. First, our model makes a prediction about why the scaling of performance with training time and with model size have different power law exponents. Consequently, the theory predicts an asymmetric compute-optimal scaling rule where the number of training steps are increased faster than model parameters, consistent with recent empirical observations. Second, it has been observed that early in training, networks converge to their infinite-width dynamics at a rate 1/width but at late time exhibit a rate width^{-c}, where c depends on the structure of the architecture and task. We show that our model exhibits this behavior. Lastly, our theory shows how the gap between training and test loss can gradually build up over time due to repeated reuse of data.

Given the variety of the visual world there is not one true scale for recognition: objects may appear at drastically different sizes across the visual field. Rather than enumerate variations across filter channels or pyramid levels, dynamic models locally predict scale and adapt receptive fields accordingly. The degree of variation and diversity of inputs makes this a difficult task. Existing methods either learn a feedforward predictor, which is not itself totally immune to the scale variation it is meant to counter, or select scales by a fixed algorithm, which cannot learn from the given task and data. We extend dynamic scale inference from feedforward prediction to iterative optimization for further adaptivity. We propose a novel entropy minimization objective for inference and optimize over task and structure parameters to tune the model to each input. Optimization during inference improves semantic segmentation accuracy and generalizes better to extreme scale variations that cause feedforward dynamic inference to falter.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

Recent advances in large language models (LLMs) have accelerated progress toward artificial general intelligence, with inference-time scaling emerging as a key technique. Contemporary approaches leverage either sequential reasoning (iteratively extending chains of thought) or parallel reasoning (generating multiple solutions simultaneously) to scale inference. However, both paradigms face fundamental limitations: sequential scaling typically relies on arbitrary token budgets for termination, leading to inefficiency or premature cutoff; while parallel scaling often lacks coordination among parallel branches and requires intrusive fine-tuning to perform effectively. In light of these challenges, we aim to design a flexible test-time collaborative inference framework that exploits the complementary strengths of both sequential and parallel reasoning paradigms. Towards this goal, the core challenge lies in developing an efficient and accurate intrinsic quality metric to assess model responses during collaborative inference, enabling dynamic control and early termination of the reasoning trace. To address this challenge, we introduce semantic entropy (SE), which quantifies the semantic diversity of parallel model responses and serves as a robust indicator of reasoning quality due to its strong negative correlation with accuracy...

Inspired by the principle of deliberate practice in human learning, we propose Deliberate Practice for Synthetic Data Generation (DP), a novel framework that improves sample efficiency through dynamic synthetic data generation. Prior work has shown that scaling synthetic data is inherently challenging, as naively adding new data leads to diminishing returns. To address this, pruning has been identified as a key mechanism for improving scaling, enabling models to focus on the most informative synthetic samples. Rather than generating a large dataset and pruning it afterward, DP efficiently approximates the direct generation of informative samples. We theoretically show how training on challenging, informative examples improves scaling laws and empirically validate that DP achieves better scaling performance with significantly fewer training samples and iterations. On ImageNet-100, DP generates 3.4x fewer samples and requires six times fewer iterations, while on ImageNet-1k, it generates 8x fewer samples with a 30 percent reduction in iterations, all while achieving superior performance compared to prior work.