Test-Time Scaling

Test-time scaling with parallel branches is widely adopted to improve performance on challenging reasoning tasks. The predominant approach, repeated sampling, draws branches independently from a single policy, which can produce redundant attempts and thereby limit the gains from additional inference compute. To address this limitation, we propose Planned Test-Time Scaling (PTTS), which replaces independent sampling with a coordinated joint policy: a planner generates a solution outline for each branch, steering the branches toward distinct reasoning paths, and an executor produces a full solution conditioned on each outline. Formally, we show that PTTS strictly generalizes repeated sampling and, in a stylized setting, provably promotes coverage of complementary reasoning modes and yields better pass@k scaling. We instantiate PTTS on top of strong reasoning models, keeping them fixed as executors while replacing repeated sampling with PTTS inference to further enhance test-time scaling. Concretely, we develop two variants: PTTS-ZS prompts a model to jointly generate outlines for all branches in a single autoregressive pass, while PTTS-RL directly optimizes the planner against the pass@k reward using truncated execution rollouts for efficient training and a sharper reward signal. Across five mathematical reasoning benchmarks with Qwen3-1.7B and 4B, PTTS-ZS improves pass@64 over repeated sampling by up to 6.7 points, while PTTS-RL further increases the gain to up to 13.4 points. Further analysis indicates that broader coverage of distinct reasoning paths contributes to these gains. Overall, PTTS provides a general framework for improving test-time scaling by coordinating reasoning branches, with zero-shot and trainable instantiations that yield substantial performance gains.

Test-time scaling can improve large language model reasoning by generating and combining multiple candidate responses. In sampling-based methods, the inference budget is often described by the number of generated candidates, N. However, N tells us how many candidates are generated, not how they are executed. The same candidate budget can be produced in one batched generation call or split across several sequential calls with smaller batch sizes. We first study the effect of increasing N on reasoning accuracy using Phi-3-mini and Qwen2.5-1.5B on 500 GSM8K prompts. As expected, increasing N from 1 to 8 improves accuracy by 8.4 percentage points for Phi-3-mini and 18.4 points for Qwen2.5-1.5B. However, accuracy alone does not show the systems cost of using a larger candidate budget. We therefore fix N = 8 and compare four generation schedules: 1x8, 2x4, 4x2, and 8x1, where axb denotes a generation calls with b candidates per call. We measure latency, throughput, GPU-hours, and gross GPU-device energy while keeping the total candidate count fixed. On A100 GPUs, eight serial calls use 4.64-4.86x as much gross GPU-device energy and have 5.77-6.12x the P95 latency of one batched call with eight candidates. The same pattern appears across three independently scheduled A100 nodes per model and in short-output SciQ/V100 experiments. These results show that candidate count alone is not enough to describe the systems cost of multi-candidate test-time scaling. When candidates are independent and memory allows it, fewer generation calls with larger batch sizes are more efficient. Evaluations should therefore report not only candidate count and accuracy, but also generation schedule and GPU-level systems metrics.

Looped Transformers offer a parameter-efficient route to test-time scaling by reusing shared layers for iterative latent reasoning. However, additional iterations can reduce support for a reference answer, leaving unclear whether an update's direction is locally unhelpful or its full displacement moves too far. We study this distinction by analysing reference utility, which measures this support, along the model's own update direction, varying the fraction of the proposed displacement supplied to the readout. This reveals finite-step failures in which a locally improving direction produces a harmful full update. A pathwise curvature decomposition characterises how initial progress is lost, while a local quadratic model predicts full-step gains and useful step scales. Bounds based on accumulated curvature variation characterise the approximation error of these predictions. Experiments across two model families reveal this separation on mathematical and commonsense tasks. A fixed quarter step produces positive gains in reference utility for 72.2--83.2% of selected failures across four settings. These findings identify a mismatch between update direction and step scale as a mechanism of lost progress, explaining how some harmful updates retain useful computation.

As pretraining scaling laws approach saturation, Test-Time Scaling (TTS) has emerged as an important direction for improving reasoning by allocating inference-time compute to a fixed model prior. Viewed at a high level, TTS reframes inference as search over a space of partial reasoning states. While Chain-of-Thought (CoT) exposes intermediate steps, common instantiations rely on single-trajectory decoding, limiting recovery from early errors and exploration. This survey systematizes recent progress in tree-search-based reasoning, viewing inference as instance-specific optimization rather than decoding. We trace the evolution from uninformed search to Monte Carlo Tree Search (MCTS), highlighting how sampling-based control supports principled exploration-exploitation trade-offs. To unify a fragmented literature, we introduce a Unified Design Space spanning search topology, evaluation signals, and control dynamics, and advocate a standardized compute-reporting abstraction to make compute-accuracy trade-offs explicit and comparable.

Diffusion models have recently advanced text-to-video (T2V) generation, yet they still struggle with fine-grained compositional alignment, such as attribute binding, spatial relations, and object interactions. While reward-based fine-tuning improves alignment, it is susceptible to reward hacking and adapts poorly to new prompt distributions. In this work, we propose NoisEasier, a test-time scaling framework that improves T2V generation through differentiable reward-guided noise optimization without modifying the underlying model. By combining efficient short-step generators with a multi-objective reward formulation, NoisEasier enables stable and practical test-time optimization under realistic inference budgets. Our key insight is that jointly optimizing the entire stochastic trajectory accelerates reward convergence and improves compositional alignment over optimizing only the initial latent, with negligible additional computational and time cost. Experiments on VBench and T2V-CompBench demonstrate consistent improvements across multiple backbones, achieving over 10% average gains on challenging dimensions such as attribute binding, object interaction, and numeracy. Overall, NoisEasier serves as both a flexible alternative and a complementary enhancement to reward-based fine-tuning, establishing test-time scaling as an effective paradigm for controllable text-to-video generation.

Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precise multi-step symbolic deduction. Although test-time scaling (TTS) has demonstrated remarkable success in general mathematical reasoning, it fails to scale effectively under the symbolic-program paradigm for plane geometry. We identify two key obstacles: limited reasoning diversity induced by rigid symbolic programs and insufficient explicit visual grounding before symbolic deduction. To address these issues, we propose Multi-Trace Synthesis (MTS), which converts each symbolic program into heterogeneous reasoning traces, including executable Python scripts and CoT-augmented variants. We further propose Perception-Augmented (PA) training, which parses diagrams into structured semantic clauses before deduction, and Consensus-Guided Multi-Trace Ensemble (CG-MTE) for efficient self-adaptive inference. Experiments on three geometry benchmarks show that our method consistently improves PGP-solving across model scales and achieves strong performance against both general-purpose MLLMs and specialized geometry solvers. Under test-time scaling, CG-MTE achieves comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8x. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.

Two forms of test-time scaling for Large Language Models (LLMs) have emerged as effective and widely adopted paradigms: sequential, in which later answer attempts depend on earlier ones, and parallel, such as i.i.d. sampling with reranking. In this study, we investigate their properties in translation. First, our study shows that sequential sampling has a higher performance ceiling, providing a more diverse and effective pool of samples, particularly under smaller sampling budgets. Second, we interrogate the nature of test-time scaling through a multidimensional manual analysis. Human analysis of the Best-of-N translations demonstrates that sequential sampling substantially improves translation fluency and naturalness, but can degrade accuracy when inference budgets are large. Finally, we suggest an explanation of the mechanism through which sequential scaling improves machine translation. Our controlled analysis partially attributes the success of sequential self-improvement to the model's access to a larger target-side context. Ablation experiments on sequential sampling demonstrate its robustness across different sampling temperatures, while also revealing sensitivity to context construction, suggesting directions for future improvement.

We propose claim-level falsification as a principle for test-time scaling and instantiate it through Claim-Level Reliability Assessment (CLR), a training-free framework that reallocates test-time compute from additional solution sampling to targeted verification. Since whole-trace evaluation often obscures decisive errors due to signal dilution from routine tokens, CLR condenses each reasoning trace into a compact set of decision-critical claims, thereby isolating its logical anchors. Furthermore, recognizing the inherent difficulty of generating entirely correct solutions under fixed model capabilities, CLR shifts the focus to semantic falsification. This approach exploits a fundamental asymmetry between solution construction and claim refutation. Constructing a valid solution requires a flawless reasoning path, whereas refuting an incorrect claim requires identifying only a single decisive flaw. This targeted search for negative evidence systematically compresses the survival space of high-confidence incorrect traces, effectively suppressing erroneous consensus via nonlinear reliability scoring. Across four LLMs and four reasoning benchmarks under matched budgets, CLR generally improves upon pass@1 and self-consistency. On GPT-OSS-20B/CMIMC25, for instance, CLR exceeds pass@1 by 27.15 percentage-points and raises self-consistency accuracy from 77.50% to 82.19% with 37.0% fewer tokens.

On-policy distillation (OPD) has emerged as a promising post-training technique for enhancing LLM reasoning. It is commonly believed to enable the student model to distill knowledge from a stronger teacher model, thereby expanding capabilities beyond the pre-OPD base model. In this study, we examine this view through the lens of test-time scaling by varying the sampling budget K and evaluating performance with pass@K and avg@K. Specifically, across several OPD variants, we observe that OPD-trained models maintain superior avg@K performance across sampling budgets, while the advantage in pass@K gradually shifts to the pre-OPD base models as K increases. These results suggest that OPD primarily improves sampling efficiency rather than consistently expanding the student's reasoning capability boundary. The pass@K dynamics throughout OPD training further reveal a progressive shift toward stronger small-K performance at the expense of the large-K capability boundary. Furthermore, a problem-level solvability analysis using pass@1024 as the criterion reveals an asymmetry: OPD causes more previously solvable problems to become unsolvable than previously unsolvable problems to become solvable. Together, these findings suggest that, from the perspective of capability expansion, OPD behaves more like an "illusory distillation": its apparent gains arise primarily from improved sampling efficiency rather than from acquiring genuinely new reasoning capabilities from the teacher.

Large Reasoning Models (LRMs) improve performance by allocating additional inference-time compute to generate extended chain-of-thought reasoning. However, recent studies reveal that sequential test-time scaling often yields diminishing or even negative returns, as longer traces exhibit increased uncertainty, error compounding, and drift from the original problem. We propose ThinkRetrieve, a test-time scaling framework that augments the reasoning traces of LRMs with dynamically retrieved solved examples at each reasoning step. Given an external corpus of problems paired with step-by-step solutions, ThinkRetrieve retrieves relevant exemplars at each intermediate step and injects them directly into the thinking trace, providing the model with guidance on how to reason rather than merely what facts are relevant. Experiments across five reasoning models (1.5B--8B parameters) on GSM-8K, MATH-500, AIME 2025, and SciQ demonstrate that ThinkRetrieve consistently improves accuracy over standard test-time scaling, with relative gains of up to $60\%$ on AIME 2025.

Test-time scaling often uses an external verifier, such as compilers and test cases in coding or trained value functions in robotics applications, to obtain high-quality rollouts. Verifier-free test-time scaling (or VF-TTS) is gaining extensive attention as a mechanism to enhance Large Language Model (LLM) reasoning, primarily because we do not have access to such high-quality verifiers in many real-world applications. Among existing VF-TTS methods, confidence-based VF-TTS methods, which compute and rank rollouts solely by confidence, are particularly promising. Such methods introduce near-zero overhead for sample evaluation and require minimal access to internal model states, making the methods highly flexible across models and tasks. In this paper, we demonstrate a critical limitation of existing confidence-based VF-TTS methods by showing that such methods catastrophically break down on complex tasks. We observe a very interesting phenomenon: uniformly high confidence frequently indicates a failure to explore, favoring confidently wrong answers. To address this, our core insight is that robust cognitive search requires a specific confidence trajectory pattern: such methods perform exploratory branching at the beginning, as manifested by low initial confidence, and converge to a high final confidence solution. To implement this insight, we introduce consilience, a novel selection framework that explicitly evaluates the temporal asymmetry of confidence in reasoning. We operationalize this via a combinatorial metric that actively penalizes high initial confidence while strictly demanding final certainty. Extensive experiments covering both graduate-level mathematics problems and free-form code generation demonstrate that consilience effectively outperforms existing baselines, validating our novel perspective on completion confidence.

Long-term time series forecasting benefits from preserving global structure such as trends and seasonality. Recent LLM-based forecasters often improve accuracy through test-time scaling (e.g., iterative refinement), but these methods are computationally expensive and increasingly prone to global-shape mismatch as the prediction horizon extends. We propose SCALER, a coarse-to-fine forecasting framework that first employs a lightweight Transformer tailored to long-term shape modeling to predict a coarse representation of future dynamics. This predicted shape then serves as a compact guide for an LLM to perform test-time scaling via iterative coarse-to-fine residual token refinement, while processing substantially fewer tokens at each step. By guiding refinement with an explicit future-shape prediction, SCALER reduces reliance on long description prompts, and its fixed-step refinement avoids costly reward-model-based selection, further lowering computational overhead. Experimental results demonstrate that SCALER outperforms strong forecasting baselines in long-term, short-term and zero-shot forecasting while significantly reducing the inference cost associated with scaled LLM for time series forecasting. Code: https://github.com/xuanmay2701/SCALER.

Test-time compute scaling is a primary driver of performance in large reasoning models (LRMs), but extreme inefficiency bounds current approaches, shifting the critical question from \emph{how much} compute to spend, to \emph{where} to allocate it. We formalize test-time reasoning as a constrained compute allocation problem over partial trajectories. Under a fixed hardware budget, existing paradigms fail to actively allocate the compute to the most promising partial progress: traditional parallel sampling treats traces independently and induces severe memory bottlenecks, while subtractive pruning starves hardware and fails to actively and sufficiently shift the output distribution. To overcome this dichotomy, we introduce Gambit, an inference algorithm that executes \emph{thought-level beam search}. By periodically pruning unpromising trajectories and immediately branching from high-quality prefixes, Gambit dynamically concentrates compute onto the most promising reasoning traces via a light-weight scorer probing hidden states while maintaining continuous high hardware utilization. Extensive evaluations across multiple models and benchmarks demonstrate that Gambit strictly dominates existing baselines. Under identical hardware constraints, our method yields up to a +6.7% absolute accuracy gain on HMMT-24 and +3.3% on AIME-25 over pruning baselines, delivers $>2\times$ higher throughput on trace completion, and reduces total token consumption by up to 68.5% relative to standard parallel sampling.

Test-time scaling is often implemented by spending more compute along one axis: sampling more solutions, extending a chain of thought, or applying a stronger evaluator. Under a fixed inference budget, these choices compete. This paper formulates test-time reasoning as a compute-allocation problem in which a system must decide whether the next unit of compute should be spent on generation, verification, or stopping. We introduce CoBa, a compute-balanced routing policy that first obtains a small set of candidates, applies cheap verification broadly, and routes uncertain or high-value candidates to stronger verification. On 3,129 example-generator evaluations spanning MATH-500, AIME 2024/2025, AMC 2023, and procedural symbolic reasoning, CoBa-Routed-Strong reaches 85.13% macro accuracy, statistically matching a self-evaluation weighted-voting proxy at 85.20% while using 49.1% fewer parameter-weighted tokens. It also matches best-of-16 majority voting within 0.01 macro-accuracy points while using 58.9% fewer parameter-weighted tokens; paired tests retain a small best-of-16 edge at substantially higher cost. Paired bootstrap tests show significant gains over single-sample decoding, while the remaining gap to the pool oracle exposes headroom for sharper routing. For local reasoning systems, test-time scaling becomes a question of where the next computation is most valuable.

Test-time scaling can correct difficult text-to-SQL queries, but the extra computation is normally discarded after each answer. Systems increasingly retain verified repair episodes, yet evaluations still report one end-to-end score. It cannot distinguish replay on recurring questions from help on unseen questions, or identify the responsible memory choice. We call measuring this future value the crystallization problem. Our controlled evaluation holds the single-shot solver fixed and varies one memory choice at a time. We separately measure replay, cross-question retention, and held-out same-database transfer. On BIRD, storing verified corrected queries improves held-out first-attempt accuracy by 4.34 percentage points. This gain captures 44.4% of the accuracy headroom provided by on-demand repair on the same questions. Controlled interventions identify database-specific content as the main operating ingredient. Reliable verification and broader retrieval coverage yield supported gains; richer formats and elaborate retrievers do not. Open-source code, evaluation artifacts, and reproduction instructions are available at https://github.com/ai-jiaqian/text-to-sql-memory-crystallization.

Large language models can solve harder reasoning problems with more inference-time compute. The term "test-time scaling," however, covers several inference algorithms: extending deliberation along one trajectory, sampling completed candidates and aggregating them by voting or verification, and searching over partial states. These algorithms differ in statistical structure, compute requirements, and failure modes. Treating them as interchangeable under a scalar "budget," or reporting accuracy without specifying the inference protocol, makes results difficult to compare across studies. We study test-time scaling along three axes. First, we formalize it as budgeted inference over the implicit prefix tree of an autoregressive model and distinguish single-trajectory sequential scaling, leaf-level scaling with terminal reduction, and prefix-level scaling. Second, we treat the full inference system as the evaluated object and separate end-to-end performance from candidate-bank diagnostics. We introduce an evaluation profile whose coordinates and simple functionals recover or bound common repeated-sampling metrics, and require compute accounting and uncertainty estimates that match the protocol. Third, we distinguish exact replay from distributional reproducibility and state the requirements for each. We also organize open-weight reasoning models by model-side and interface mechanisms. Our empirical study covers broad knowledge, symbolic reasoning, and competition mathematics, and we publicly release 1,403,520 sampled model attempts. The project website is available at https://mohsenhariri.github.io/scorio/tts. The released datasets are Trace (https://huggingface.co/datasets/harimo/scorio-trace), Lite (https://huggingface.co/datasets/harimo/scorio-lite), Math (https://huggingface.co/buckets/harimo/scorio-math), and SuperGPQA (https://huggingface.co/buckets/harimo/scorio-gpqa).

Test-time scaling improves LLM reasoning by generating and aggregating multiple candidate answers, yet many pipelines use fixed per-query budgets that spend the same compute on easy and difficult prompts. These fixed budgets are also difficult to inspect because they do not explain why a given prompt receives a particular number of samples. We propose adaptive} test-time scaling with a lightweight fuzzy controller that maps interpretable signals, including estimated prompt complexity and model confidence, to a per-query sampling budget. The controller assigns fewer samples to easier or more confident prompts and more samples to harder or less certain prompts, making inference-time compute inspectable rather than fixed or opaque. We evaluate under a fair-alignment protocol with matched decoding settings and controlled answer selection, and compare against best-of-$N$, compute-aware scaling, and self-certainty-based baselines on question-answering and mathematical reasoning tasks. Across models and datasets, adaptive fuzzy control improves over several standard baselines and remains close to a selector-matched full-budget control while reducing the average number of samples. These findings suggest that interpretable adaptive sampling is a practical direction for more efficient test-time reasoning in large language models.

Ensuring safety and policy compliance in text-to-image diffusion models remains a critical challenge, as benign or adversarial prompts can often elicit prohibited content, e.g. nudity and protected intellectual property. While training-based unlearning methods are effective, they are computationally expensive and prone to catastrophic interference with general capabilities. Conversely, existing test-time defenses are primarily prompt-centric, relying on modifying textual descriptions only, and overlook the visual signals for detection. In this paper, we propose to leverage the intermediate clean image estimated during the generation process and employ a sparse margin objective to detect prohibited concepts. When a violation is detected, we immediately intervene by optimizing a structured low-rank residual in the text-conditioning space via truncated backpropagation. This design allows weight-preserving detection, keeps non-violating inference latency nearly unchanged as the maximum budget increases, and offers flexibility in safety performance via test-time scaling. Extensive experiments on Stable Diffusion v1.4 and v3.5 across nudity removal, IP protection, and style erasure demonstrate superior performance across suppression, fidelity and preservation compared to prior weight-preserving baselines, providing a scalable and flexible solution for safe generative deployment.

Test-time search lets small video diffusion models rival larger ones, but costs 2-10x more. All candidates are fully denoised, although most are discarded. Training-free caching makes each rollout 2-3x faster at near-lossless quality. Composition is safe only if lossy caching preserves verifier rankings. We present the first study of whether caching corrupts candidate ranking in video test-time search. On Wan2.1-T2V-1.3B with an adaptive caching wrapper (~2x per-candidate speedup), ImageReward scores seed-matched cached and full rollouts. Median per-prompt Spearman rank correlation is 0.905, with 72% top-1 agreement on the VBench suite. VBench-2.0 replicates this result on a harder suite. Recomputing the cached winner at full compute retains 90-94% of the full-search gain. Errors cluster among near-tied candidates, making corruption self-limiting. This finding leads to CachedSearch. It explores every candidate with aggressive caching, then re-generates only the winner at full compute. At N=8, it captures 94.7% of best-of-N's gain at 63% of the cost. Capture rises with width. At matched budget, it searches twice as wide for 38% more gain. The result holds from 1.3B-14B across six models and four families: Wan, LTX, CogVideoX, and Hunyuan. Wan2.1-14B matches the 1.3B model's fidelity. Mid-trajectory pruning multiplies the exploration saving to 3.11x at 88.6% capture. Ports to other model families require recalibrating a single parameter, showing that fidelity tracks architecture rather than parameter count. CachedSearch is training-free, verifier-agnostic, and orthogonal to the search algorithm, making it a plug-in multiplier for test-time scaling.

Scaling inference-time computation has emerged as a reliable method to improve the performance of large language models on complex reasoning and programming tasks. However, standard approaches such as independent sampling and sequential multi-turn refinement operate without token-level credit assignment, resulting in computational inefficiency, since valid reasoning prefixes are frequently discarded. In this work, we introduce Test-Time Scaling via Error Localization (TTEL), an inference-time algorithm that utilizes fixed or environment feedback to perform token-level error localization. By comparing conditional probabilities under informed feedback against a null-context baseline, TTEL isolates the step at which an error occurred. The algorithm then truncates the trajectory and branches a new generation, maximally reusing the valid prefix. Extensive evaluations demonstrate that TTEL establishes strictly dominating Pareto frontiers across sequential reasoning domains, measured by pass-at-k vs. generated-token cost. With Qwen3-8B on LiveCodeBench, TTEL attains a pass@64 of 71.0% while generating approximately half as many tokens as independent sampling (360.4k vs. 735.0k). Generalizing to math benchmarks AIME-2025 and HMMT-2025, TTEL cleanly outperforms competing test-time baselines across both Qwen3-8B and Qwen3-4B-Thinking-2507.

Reinforcement learning with verifiable rewards has become the predominant recipe for eliciting test-time scaling in explicit Chain-of-Thought reasoners. Yet this scaling path remains computationally costly, since every intermediate step must be decoded as a language token. Latent reasoning instead carries intermediate computation as continuous vectors and already matches or surpasses explicit CoT at far shorter horizons. Despite this promise, latent reasoners remain largely imitation-bound, while explicit CoT has already moved past imitation via outcome-reward RL. Latent trajectories lack a tractable per-step likelihood and an adaptive stopping interface under fixed thinking budgets, so outcome rewards cannot elicit latent test-time scaling. We introduce Surrogate Latent Policy Optimization (SLPO) to bring outcome-reward RL to autoregressive latent reasoners: an empirical surrogate policy density over latent transitions for trajectory-level credit assignment, and a correctness-supervised stopping head that outcome-reward optimization refines into a variable-horizon policy. Across continuous and soft thinking settings, SLPO improves Pass@$k$ under parallel sampling and allocates longer latent computation to harder instances with higher deterministic accuracy.

Test-time scaling offers a promising method to improve the inference performance of Vision-Language Models (VLMs) without additional training. Existing approaches to vision-language navigation (VLN) for Unmanned Aerial Vehicle (UAV) typically relies on a single inference pass, which can falter in complex environments by producing suboptimal or unsafe trajectories. In this paper, we explore a simple and effective approach to apply test-time scaling to VLN for UAV. We enhance navigation reasoning through an iterative refinement process that requires no extra model training, guiding the model to re-evaluate its initial navigation plan for better accuracy and safety. Our method first prompts the model to generate multiple parallel candidates and then performs a self-correction step, achieving deeper and more robust planning without changing the underlying model. To further strengthen decision-making, we design a multi-criteria scoring function to evaluate the refined candidates based on safety, goal alignment, and forward-progress. This simple yet powerful combination enables a frozen UAV navigation VLMs to self-correct and generate more accurate and reliable flight plans, achieving SOTA performance in this task.

Test-time scaling improves foundation-model inference by spending additional computation, but robot control requires deciding whether extra compute is useful before executing an action. World Action Models (WAMs) make this decision natural: each rollout exposes both an action chunk and predicted future observations. We propose \methodgated, a training-free selective test-time scaling framework for WAMs. We first instantiate \method, a fixed-budget Best-of-$N$ selector that ranks sampled rollouts by cross-view depth reprojection consistency of their predicted futures, computed with a frozen geometry foundation model. \methodgated\ adds a lightweight action--future consistency gate that invokes \method\ only when the initial rollout appears internally inconsistent. Across five benchmark--backbone settings on RoboCasa, LIBERO Long, and RoboTwin~2.0, fixed-budget \method\ improves $N{=}8$ task success in every setting, e.g., raising the RoboCasa group average from $66.3\%$ to $68.4\%$ with Cosmos Policy and from $80.8\%$ to $82.5\%$ with X-WAM. With gating enabled, \methodgated\ recovers on average $74.8\%$ of the always-on success gain while triggering additional sampling on only $26.2\%$ of decision points. Offline diagnostics show that cross-view reprojection is a strong task-label-free selector, and we identify false low-score selections as a failure mode that helps explain why performance can saturate or degrade as $N$ increases.

Data science tasks span from closed-ended information extraction to open-ended analysis, presenting significant challenges for automation. Recent AI agents powered by language models show promise for handling such complex tasks. However, existing agents typically rely on a single initial state that conditions the entire agent's execution, making them vulnerable to cascading errors initiated by a suboptimal initial state. To mitigate this, we present CIPHER, an automated data science agent that leverages test-time scaling through the generation and selection of multiple initial states for concurrent execution. Unlike existing works on test-time scaling of AI agents, CIPHER explicitly decouples the generation of candidate initial states from their strategic selection for parallel execution. Through extensive evaluation on two benchmarks (closed-form and open-form tasks), we demonstrate that CIPHER exceeds state-of-the-art performance in matched-model comparisons, and remains competitive against larger-model baselines despite relying on a substantially smaller base LM. Our empirical study characterizes the design space of the Decoupled Exploration-Selection (DES) framework: we quantify how generation strategy, selection strategy, and aggregator model capacity contribute to overall performance, and derive actionable design recommendations for practitioners.

We revisit the evaluation of automatic harness evolution for LLM agents. Existing harness evolution methods use unit test cases to search for harness configurations and then report final performance on the same public benchmark. This protocol raises two fundamental concerns. First, harness evolution is itself an iterative search procedure that repeatedly evaluates and revises candidate harnesses using task feedback. As in agentic test-time scaling, it should therefore be compared with simple task-level search baselines under matched feedback and inference budgets to determine whether its gains arise from improved harness design or from additional search alone. Second, because the search and the final evaluation share the same benchmark, the reported gains risk overfitting to that specific task set. To address these concerns, we conduct an extensive evaluation comparing harness evolution with simple test-time scaling and discovery baselines under comparable feedback and inference budgets, and also evaluate evolved harnesses on held-out tasks to assess whether the discovered improvements generalize. Experiments on Terminal-Bench 2.1 with GPT-5.4 and Claude Opus 4.6 show that automatic harness evolution does not consistently outperform simple test-time scaling methods and exhibits limited generalization. Our results raise important questions about the effectiveness of automatic harness evolution and highlight the need for fairer evaluation protocols and benchmarks for automatic harness design. Our code is available at https://github.com/rethinking-harness-evolution.

Test-time scaling (TTS) reliably improves reasoning in large language models, but whether it transfers to small open vision-language models remains unclear. We examine this on EXAMS-V, a multilingual visual multiple-choice benchmark, comparing self-consistency, describe-then-reason with PRM-guided beam search, and two post-hoc selectors across Qwen2.5-VL-7B-Instruct and Qwen3.5-4B. What matters is the conditions under which TTS runs, not the search or verification machinery. The largest factor is parseability: an early prompt format left many chains reasoning correctly yet never committing to an answer letter, which a standard answer cue and a guided repair step largely remove. A larger decoding budget removes the rest: raising the per-chain token limit from 1k to 2k recovers 3.7 pp, whereas sampling more chains (8 to 16) adds only 0.15 pp. Once chains have room to finish, elaborate methods contribute little: PRM-guided beam search trails plain self-consistency by 0.39 pp at over eight times the cost, and neither a training-free generative critic nor a trained multimodal PRM beats majority vote across both policies. The largest gain comes instead from the policy model itself (+11.4 pp). Our best configuration reaches 84.1% on the held-out ImageCLEF 2026 test split, ranking first on the Visual MCQ leaderboard.

Process Reward Models (PRMs) have been proven to be highly effective in guiding test-time scaling (TTS) methods, which significantly boost the capabilities of LLM-based multi-agent systems. However, existing PRMs are text-based: they re-encode the entire trajectory text from scratch. In long multi-agent rollouts, the scoring cost, growing quadratically with respect to sequence length L, creates a severe computational bottleneck, severely limiting PRMs' application in long-context scenarios. To resolve this, we introduce KV-PRM, a highly efficient process reward model that eliminates the heavy text re-encoding by directly reading the KV cache produced naturally during the LLM's generation phase. By processing a single "verify token" against the pre-existing KV cache, KV-PRM reduces the scoring cost from O(L^2) to O(L). We formally prove that the KV cache contains strictly greater information capacity than text, and is more efficient for downstream reward modeling. Empirically, across the MATH, GSM8K, and AIME benchmarks, KV-PRM matches or strictly outperforms text-PRMs under various TTS methods such as Beam Search, MCTS, and Weighted Voting, with up to a 5,000x reduction in scoring FLOPs, a 37x reduction in latency, and a 34x reduction in per-sequence memory footprint compared to text-based PRMs.

Rotary Position Embeddings (RoPE) provide transformers with a fixed grid of positional frequencies, yet trained models use these frequencies highly non-uniformly. We study what determines this frequency usage and propose a data-centered explanation: RoPE frequencies are selected to match the relative-distance structure of the training data. Viewing each frequency as a positional lens, we formalize a field-resolution tradeoff and show that, for a data-induced dependency profile of width $W$, the optimal frequency scales as $1/W$. This frequency-matching principle explains controlled observations on synthetic and text-based data, and suggests that the mid-low frequency bands observed in language models arise from the multi-scale dependency structure of natural language. We further connect frequency selection to position-interpolation-based length generalization: scaling frequencies down expands the effective field while reducing resolution. This helps when longer-context dependencies are approximate dilations of those seen during training, but can fail when relevant dependencies do not scale with context length. Empirically, we show that natural language exhibits approximate self-similarity across positional scales, explaining why test-time frequency scaling can support long-context generalization. Overall, our results identify a data-driven mechanism behind emergent RoPE frequency usage and show that long-context generalization depends on two forms of scale matching: between learned frequencies and training-time dependencies, and between frequency scaling and how those dependencies extend to longer contexts.

End-to-end ASR models transcribe in a single pass, leaving no room for the decoder to revisit hard inputs. We propose LatentASR, a parameter-efficient method that adds continuous latent test-time scaling to a frozen ASR backbone. Two small trainable modules drive it: a Latent Adapter that iteratively refines a few latent prefix positions through bounded, stabilized updates, and a Value Head that predicts whether extra computation will help and halts the loop early. The Qwen3-ASR-0.6B backbone stays fully frozen, and we train only ~4M extra parameters. We activate this loop with a deliberately small, diverse 500-utterance training set. Under this minimal-data regime, standard adaptation methods all regress: full fine-tuning, LoRA, and prompt tuning each increase WER. LatentASR is the only tested method that reduces WER on both clean benchmarks (FLEURS -2.54% and VoxPopuli -0.47% relative). The reductions are concentrated on intrinsically hard inputs. On accented and code-switched speech (ASCEND), LatentASR achieves a 16.0% relative CER reduction. Across 30 FLEURS languages (23,049 utterances), the multilingual WER decreases uniformly across resource tiers, confirming that the adapter generalizes without overfitting. Dynamic halting preserves most of the clean-set reduction at a fraction of the compute, skipping roughly half of all utterances at the entry gate. Our results show that a small, carefully chosen activation set can switch on test-time scaling inside a frozen ASR model without corrupting the model itself, converting fixed per-utterance compute into input-dependent compute where it is most needed.

Scaling inference compute, by generating many parallel attempts per problem, is a costly but reliable lever for improving language model capabilities. By default these attempts are generated independently, wasting inference compute on redundant solutions. This waste seems unavoidable. After all, independence is what makes parallel sampling trivial to scale. However, this tradeoff is not fundamental: there is a rich design space of samplers that generate correlated but exact samples entirely in parallel. We explore this design space as an avenue for improving sample efficiency in scaling inference compute and reinforcement learning (RL). Concretely, we introduce QuasiMoTTo, which uses correlated samples as a drop-in replacement for i.i.d. samples. To generate these samples, QuasiMoTTo uses a reparameterization of autoregressive sampling as inverse-CDF sampling and draws the underlying uniforms with quasi-Monte Carlo (QMC); because QMC spreads the uniforms out more evenly than i.i.d., the resulting samples cover the output space with far less redundancy. Even though the batch is correlated, each sample is marginally distributed according to the language model, so we can use the batch for policy-gradient training. Our empirical analysis focuses on understanding how efficiently QuasiMoTTo can turn compute into performance. To evaluate correlated samplers, whose dependence breaks standard pass@k estimators, we first develop an unbiased bootstrap estimator. Across four reasoning benchmarks, QuasiMoTTo matches i.i.d. pass@k accuracy with 25-47% fewer samples. Strikingly, QuasiMoTTo often saturates an upper bound on pass@k that holds for any marginal-preserving sampler. We also apply QuasiMoTTo to policy-gradient RL (GRPO) where it matches i.i.d. performance with 50% fewer training steps. These gains come from higher coverage, which yields a stronger learning signal per batch.

Generative control policies (GCPs), such as diffusion policies and flow-based vision-language-action models, enable test-time scaling in robot control. Test-time compute can be allocated along two axes: sequential scaling, which increases denoising steps to refine actions, and parallel scaling, which samples multiple candidate actions to search across modes of the policy distribution. However, the optimal allocation of sequential and parallel compute is hard to know a priori as it is state-, task-, and policy-dependent. For example, early stages of a grasp may benefit from broader parallel exploration, while near-contact phases may require more sequential refinement for precision. We present ELASTIC, an algorithm that learns state-dependent test-time compute schedules for GCPs. We formulate compute allocation as a meta-Markov Decision Process in which a meta-policy interacts with a frozen pretrained robot policy and selects sequential steps and parallel samples at each denoising iteration to maximize task success while minimizing compute. Using reinforcement learning, this meta-policy also learns adaptive compute schedules without access to the GCP's training data. Across simulated manipulation benchmarks with diffusion policies, ELASTIC Pareto-dominates fixed and single-axis scaling baselines at matched compute budgets. On real-world robot manipulation with the $π_{0.5}$ vision-language-action model, ELASTIC matches best-of-$10$ success while reducing wall-clock latency by 34%.

Aligning large language models (LLMs) with diverse user preferences is a critical yet challenging task. While post-training methods can adapt models to specific needs, they often require costly data curation and additional training. Test-time scaling (TTS) presents an efficient, training-free alternative, but its application has been largely limited to verifiable domains like mathematics and coding, where response correctness is easily judged. To extend TTS to preference alignment, we introduce a novel framework that models the task as a realignment problem, since the base model often fails to sufficiently align with the stated preference. Our key insight is to decompose the underlying reward function into two components: one related to the question and the other to preference information. This allows us to derive a REAlignment Reward (REAR) that selectively rescales the proportions of these two reward terms. We then show that REAR can be formulated as a linear combination of token-level policy log-probabilities, making it computationally efficient and easy to integrate with various TTS algorithms such as best-of-$N$ sampling and tree search. Experiments show that compared to other test-time baselines, REAR not only enables scalable test-time realignment for preference alignment tasks under diverse user requirements, but also generalizes to mathematical and visual tasks under appropriate preference settings.

Test-time scaling is a paradigm where large models use additional compute at inference to achieve better performance, without changing model weights. While it has been widely studied for Large Language Models (LLMs), its applicability to Large Vision-Language Models (LVLMs) remains less explored and analyzed, with limited analysis of whether, when, and to what extent these approaches transfer to LVLMs. In this work, we ask a simple but fundamental question: can conventional test-time scaling methods developed for LLMs be directly applied to LVLMs? We present the first comprehensive study of test-time scaling for LVLMs, spanning multiple models and model sizes, nine test-time scaling methods, and six diverse benchmarks. Our main findings is that 1) different from previous findings, small, well-performing models benefit the most from test-time scaling, enabling performance improvements of up to around 30%, reaching large models performance, and often outperforming them, 2) LVLMs lose focus when given more compute than necessary, and 3) Visual information is encoded early in the reasoning chain, after which the chain is dominated by text-only reasoning and the contribution of image tokens drops significantly. Finally, we also provide a global and fine-grained analysis on the quality and information sufficiency of the reasoning chains produced. Overall, our findings and analysis provide practical guidance and insights into LVLMs and their deployment in research and industry.

People overthink; language models over-sample, and the extra effort can talk both into a worse answer. Reasoning systems answer a hard question by sampling it many times (test-time scaling), and the more they draw, the more often a correct answer turns up somewhere, so coverage, the fraction of problems with at least one correct try, climbs and appears to be progress. But a deployed system must return one answer, and choosing it, not knowing which try is right, is selection; selection is capped, and past a point extra samples only make the model surer of a confident mistake, even as every draw adds cost. The gap between climbing coverage and stalled selection, the identifiability gap, is the answer a model can produce but not pick. So the real question is not whether to sample but how far, and the answer is: not far. For picking an answer, the vote has already settled within a few dozen draws, the modal ceiling; for scoring a benchmark, sooner still, the correlation ceiling. Beyond that, extra draws cost compute and add nothing, and can even make the answer worse. This paper turns the cutoff into a single number, the effective number of samples, that any sampling run already reveals. The bottleneck is recognizing a right answer, not generating one.

Recently, a few works have made early attempts to study test-time scaling for embodied tasks. However, two major challenges remain unsolved: (1) reasoning can effectively improve the performance of the policy, but its scaling mechanism has seldom been studied; (2) historical information is essential, as embodied tasks are inherently long-horizon and sequential, making sole reliance on current observations for action scaling inadequate due to the lack of historical context utilization. To address these challenges, we introduce E-TTS, a modular and plug-and-play Embodied Test-Time Scaling framework that unifies reasoning and action scaling for robotic manipulation via history-aware iterative refinement with vision-language verifiers. To support joint reasoning-action scaling, E-TTS performs reasoning-action joint sampling and scoring in a pairwise manner. To better utilize historical information, E-TTS uses a history buffer to store historical context, which is then used by reasoning and action verifiers to evaluate the sampled candidates. Unlike conventional open-loop TTS methods, E-TTS introduces feedback generation into the sampling process to form a closed-loop iterative refinement mechanism, enhancing both inference efficiency and environmental adaptability. Each component functions as an independent and composable module, allowing flexible and adaptive configuration depending on task requirements. To evaluate the advantages of our framework, we conduct experiments across 4 different benchmarks, 6 environments, 3 embodiments, and 4 base vision-language-action models. The experimental results demonstrate that, without requiring additional expert data collection or retraining, E-TTS consistently improves performance, achieving up to a 33.14% increase in simulation and 26.62% in real-world scenarios.

Test-time scaling improves language-model reasoning, but existing approaches often face a difficult trade-off: long chain-of-thought sampling remains single-threaded, while sentence- or solution-level search can be computationally expensive and hard to train end-to-end. We introduce Local Branch Routing (LBR), a token-level test-time scaling framework that expands a small local lookahead tree, forwards all sampled branches through the language model, and uses a lightweight router to select the depth-1 subtree to commit. By routing over the hidden states of candidate local futures, LBR allows each token decision to use evidence beyond the root next-token distribution while avoiding full solution-level search. The resulting prune-shift-grow decoding process preserves discrete branch identities and defines a tractable tree-trajectory likelihood: newly grown nodes are counted when first sampled, and router decisions are assigned explicit probabilities. This enables end-to-end reinforcement learning with verifiable rewards, jointly optimizing the base model and router under the same likelihood-ratio principle as discrete-token RLVR. On synthetic hierarchical-planning tasks, LBR shows that post-candidate hidden states provide useful routing evidence. On mathematical reasoning benchmarks, LBR improves both Pass@1 and Pass@32 over discrete chain-of-thought, vanilla discrete-token RLVR, and RL-compatible soft-token branching baselines. These results suggest that lightweight local branching offers an efficient, trainable, and discrete form of language-model test-time scaling.

Looped Transformers scale latent computation by repeatedly applying shared blocks, but sequential looping increases latency and KV-cache memory with the loop count. Parallel loop Transformers (PLT) alleviate this cost through cross-loop position offsets (CLP) and shared-KV gated sliding-window attention, making loop count a practical design choice. We therefore study PLT loop-count selection through a gain--cost view: an extra loop may refine representations, but CLP also introduces a positional mismatch at each loop boundary. We instantiate this study by training LoopCoder-v2, a family of 7B PLT coders with different loop counts, from scratch on 18T tokens, followed by matched instruction tuning and evaluation. Empirically, the two-loop variant delivers broad gains over the non-looped baseline across code generation, code reasoning, agentic software engineering, and tool-use benchmarks, improving SWE-bench Verified from 43.0 to 64.4 points and Multi-SWE from 14.0 to 31.0 points. In contrast, variants with three or more loops regress, revealing a strongly non-monotonic loop-count effect. Our diagnostics show that loop 2 provides the main productive refinement, while later loops yield diminishing, oscillatory updates and reduced representational diversity. Because the CLP-induced mismatch remains roughly fixed as refinement gains shrink, the offset cost increasingly dominates. This gain--cost trade-off explains PLT's saturation at two loops and provides diagnostics for loop-count selection.

By incorporating test-time compute scaling, large reasoning models (LRMs) can solve complex problems through explicit chain-of-thought (CoT) reasoning processes. However, they often suffer from overthinking, resulting in redundant token outputs and degraded accuracy. Current methods to mitigate this issue remain limited: training-based approaches require substantial computational resources, while training-free methods rely on well-crafted prompts or unreliable confidence signals. In this work, we investigate early stopping from the perspective of attention distributions and propose a simple method, ASAG, which infers the model's reasoning state and adaptively adjusts the generation strategy. The proposed framework is training-free and plug-and-play, enabling seamless integration into existing LRMs. Extensive experiments on nine benchmarks demonstrate consistent improvements across mainstream LRMs with varying parameter scales, including the DeepSeek-R1-Distill and Qwen3 series. Specifically, ASAG improves average accuracy by 3.2% while reducing the number of generated tokens by nearly 40% across all reasoning tasks on Qwen3-8B.

While test-time scaling has revolutionized reasoning in large language models, generative video reasoning remains bottlenecked by a single-shot paradigm. We demonstrate that searching over denoising steps cannot rescue logically flawed rollouts because spatial trajectories commit early in the diffusion process. Root-level Best-of-N (BoN) sampling is similarly inefficient: reasoning errors cluster early in the temporal axis, and resampling blindly discards verified upstream progress. To unlock effective test-time scaling for video models, we introduce Temporal Backtracking Search (TBS), which shifts the search space to the temporal axis. TBS transforms video generation into an iterative generate-verify-restart loop via three core mechanisms: (1) variable-K conditioning to resume generation from arbitrary clean prefixes; (2) temporal process verification to localize failures and extract valid restart anchors; and (3) prefix-based search to reallocate compute toward extending correct trajectories rather than root resampling. Across algorithmic, navigation, and robotics domains, TBS Pareto-dominates matched-budget BoN. In a strict out-of-distribution setting where one-shot generation collapses (0.7% for BoN), TBS achieves 22.7%, with every solved episode stemming from a restarted branch. Ultimately, TBS reveals that the local reasoning competence of video models far exceeds what single-shot rollouts indicate, providing a scalable test-time framework to unlock it.

We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.

Automated testbench generation has become a critical bottleneck in large language model (LLM)-driven Register Transfer Level (RTL) workflows, where large numbers of candidate designs must be verified rapidly and reliably. Existing prompt-based approaches treat testbench generation as unconstrained code synthesis, yielding stochastic outputs with high token cost, low reproducibility, and insufficient coverage. To address this gap, we present STG, a Structured Testbench Generation framework that exploits the inherent structure of hardware designs to generate deterministic testbenches. As a direct verification tool, STG runs 720x faster than an iterative LLM-based testbench generation flow and higher rate of successful compilation, achieves higher coverage, and reduces false-pass verdicts on incorrect DUTs. STG also helps identify errors in RTL generation benchmarks by exposing faulty benchmark testbenches. As a data curation engine, it is 11x faster than LLM-based filtering on a single CPU core with 127x less energy, and the resulting distilled models provide state-of-the-art performance in our multi-benchmark evaluation. As a test-time scaling oracle, it reduces node count by 14-47%. Our models are available at https://huggingface.co/collections/AS-SiliconMind/siliconmind-v12.

Despite strong performance in competitive programming, the role of Large Language Models (LLMs) in supporting human learning in the same setting remains largely unexplored. In this work, we introduce UOJ-Bench, a benchmark designed to evaluate not only the problem-solving ability of LLMs, but also their ability to identify errors in human-written code -- a crucial educational activity traditionally supported by running test cases over online judge systems. UOJ-Bench consists of three distinct tasks: code generation, code hacking, and code repair, all constructed from real-world code submissions on the Universal Online Judge (UOJ) and evaluated through UOJ's native judging infrastructure. Our results show that under one-shot evaluation, even the strongest models fail to identify errors in more than 50% of a set of submissions that have been found to be incorrect by UOJ users. While test-time scaling improves success rates to above 90%, the substantial computational costs incurred from model inference limit its practicality for large-scale deployment. Despite these limitations, we find that the best-performing models under test-time scaling can uncover errors in over 5% of full-score submissions across roughly 30 problems, suggesting that frontier LLMs can already provide complementary signals beyond standard judging systems.

Modern Vision-Language Models (VLMs) benefit from chain-of-thought prompting and test-time scaling, but these gains often come with prohibitive inference cost due to large visual contexts and long decoding chains. We view this cost through two coupled axes: Visual Context Scaling (VCS), which controls how much visual evidence is passed to the language model, and Visual Reasoning Scaling (VRS), which controls how much inference-time reasoning search is performed. Existing methods typically optimize one axis at a time, leaving the joint allocation of compute across these axes underexplored. We introduce Adaptive Visual Inference Scaling (AVIS), a lightweight policy that adapts both VCS and VRS per query. AVIS realizes VCS through Key Diversity Visual (KDV) pruning, a training-free $O(N)$ key-based rule for removing redundant visual tokens before prefilling, and realizes VRS through adaptive self-consistency, using a learned difficulty predictor to select the number of reasoning rollouts. AVIS is deployment-friendly and compatible with shared-prefill inference, where all rollouts reuse a single prefilling pass and KV cache. Across diverse image and video reasoning benchmarks, AVIS improves the accuracy--compute trade-off relative to VCS-only and VRS-only baselines, and remains effective on top of RL post-trained VLMs while keeping compute and latency low.

Multi-agent systems (MAS) can scale large language model reasoning at test time by decomposing complex problems into parallel subtasks. However, most existing MAS rely on centralized orchestration, where a main agent assigns work, collects outputs, and merges results. As the number of subtasks grows, this controller becomes a communication and integration bottleneck. We propose Decentralized Language Models (DeLM), a MAS framework that decentralizes coordination through parallel agents, a shared verified context, and a task queue. Agents asynchronously claim subtasks, read accumulated progress, perform local reasoning, and write back compact verified updates. The shared context acts as a common communication substrate, enabling agents to build on one another's verified progress without routing every update through a central controller. Empirically, DeLM improves both software-engineering test-time scaling and long-context reasoning. On SWE-bench Verified, DeLM achieves the best performance across Avg.@1, Pass@2, and Pass@4, with gains of up to 10.5 percentage points over the strongest baseline, while reducing cost per task by roughly 50%. On LongBench-v2 Multi-Doc QA, DeLM achieves the highest average accuracy across four frontier model families, improving over the strongest baseline by up to 5.7 percentage points. The code is available on our project website at https://yuzhenmao.github.io/DeLM/.

Test-time Scaling (TTS) has emerged as a pivotal research direction for enhancing model performance by dynamically allocating computational resources during inference. Recent advancements have adapted this paradigm to Multimodal Foundation Models (MFMs), unlocking their potential in multimodal reasoning and generation. Despite rapid progress, the field lacks a systematic survey and unified theoretical framework to delineate the developmental landscape of multimodal TTS. To bridge this gap, we present the first comprehensive review of TTS research for MFMs, proposing a unified taxonomic framework that categorizes existing methodologies into three distinct strategies: sampling-based, feedback-based, and search-based approaches. We further summarize representative applications and benchmarks commonly utilized to evaluate multimodal TTS capabilities in generation and reasoning tasks. Finally, this survey discusses open challenges and outlines future research directions, providing a systematic roadmap for subsequent studies in this rapidly evolving field.

Test-time compute (TTC) scaling has emerged as a powerful paradigm for improving large language model (LLM) reasoning by allocating additional compute during inference, e.g., via multi-sample generation and verifier-based reranking. Existing TTC scaling strategies and reasoning scorers remain fragmented, evaluated under inconsistent protocols, and are rarely analyzed through the lens of quality-cost trade-offs. We introduce ThinkBooster, a unified framework for seamless test-time compute scaling of LLM reasoning, which consists of (i) a modular Python library implementing state-of-the-art TTC scaling strategy and scorer families, (ii) a benchmark that jointly evaluates performance and computational efficiency, and (iii) a deployable OpenAI-compatible proxy service that enables drop-in integration of adaptive reasoning into real-world applications. We further provide a demo visual debugger for inspecting the reasoning trajectories, intermediate selection decisions, and alternative reasoning paths. Empirical results on mathematical and coding tasks reveal the performance-compute trade-offs of TTC scaling strategies and scoring methods and demonstrate that ThinkBooster provides practical gains in real-world tasks. The code is available online under an MIT license.

When post-trained language models fail on reasoning problems, the common test-time-scaling response is to spend more compute on additional attempts, and the failed traces play no further role. We argue this discards a crucial signal; some failures come from unlucky sampling, where more rollouts help, while others are structural and resist resampling regardless of budget. We propose that failed traces encode recoverability structure: the inference-time signature of which test-time interventions can rescue a given failure. Three problem-level trajectory features, derived from the structure of available interventions, recover this structure from the distributional signature of failed rollouts, not their text. They cluster failures into stable regimes, characterize the failure topography of different post-training methods ($84.3{\pm}4.3\%$ accuracy, $+20\%$ over a majority-class baseline), and support a training-free routing rule that lifts rescue by $+12.2\%$ on the deployment-relevant Steerable-Hard subset (failures where retry is insufficient and a bounded intervention is reachable). The features and the routing rule transfer across two cross-family probes. The same three features thus convert failed traces from discarded data into a diagnostic object, supporting test-time routing and post-training analysis without training-time or weight-space access.

End-to-end ASR systems typically use fixed-depth acoustic encoders at inference, making it difficult to trade additional test-time computation for improved recognition without training a larger model. A natural approach is to reuse a shared Transformer block recurrently, but we find that naive looping does not fully exploit additional recurrent compute. We introduce LARM, a depth-conditioned looped Transformer that turns recurrent encoder depth into a controllable test-time compute axis. LARM combines sparse CTC checkpoints, supervision-clock embeddings, FiLM depth conditioning, and delayed soft-posterior feedback. These components structure the loop into recognition checkpoints separated by latent refinement phases and allow shared weights to specialize across recurrent steps. On LibriSpeech, LARM improves WER as the number of inference loops increases and achieves performance competitive with deeper unshared-parameter baselines. Our results show that test-time compute scaling can extend beyond autoregressive language-model reasoning to continuous non-autoregressive speech recognition.

Test-time scaling improves the reasoning performance of large language models but incurs substantial cost in both total computation and latency. Existing adaptive sampling methods partially mitigate this issue by dynamically deciding when to stop sampling, yet they typically rely on heuristic rules or rely on distribution assumptions. In this work, we formulate adaptive sampling as a Markov decision process (MDP). We train a lightweight sampling controller with reinforcement learning (RL) to jointly balance answer correctness, latency, and computation cost. At each round, the controller decides to stop sampling or to acquire additional samples. Our method is lightweight which only relies on statistics of final answers, and can be trained and deployed on CPU. We further show that the resulting framework admits an interpretation as the Lagrangian relaxation of a constrained optimization problem with explicit budget constraints. Experiments against strong baselines such as ASC and ESC show that our method achieves improved trade-offs among answer correctness, sampling rounds, and total samples required.

Test-time scaling has become a major way to improve large language model reasoning, but its orchestration has remained designer-engineered: a fixed sample budget, a fixed refinement loop, a fixed scoring rule, or a fixed search policy decides how compute is spent, leaving the model in charge of solving but not of orchestration. We introduce ATLAS, an agentic test-time scaling framework in which an LLM orchestrator owns the control loop end-to-end. Through a single action, explore, which dispatches a fresh independent solver on the original problem, the orchestrator decides whether to gather more evidence, when to stop, and how to synthesize the final answer; the action space is extensible, with each explore call optionally specifying solver, reasoning effort, or prompting strategy. We evaluate ATLAS on four benchmarks covering scientific question answering, code generation, and multimodal reasoning under a Claude Sonnet 4.6 backbone, where it reaches 56.00% on HLE-Verified, 82.29% on LiveCodeBench, 85.75% on GPQA-Diamond, and 23.71% on BabyVision while using far fewer API calls than fixed-workflow baselines. A multi-model extension, ATLAS-MM, that exposes solver choice as an additional action dimension further improves HLE-Verified to 60.00% and LiveCodeBench to 85.63%, with consistent gains on GPQA-Diamond and BabyVision. Ablations replacing the orchestrator's direct synthesis with a separate integrator degrade or fail to improve accuracy on three of four benchmarks, consistent with the role of stateful evidence management in producing the gains.

In real-world deployments of large language models (LLMs), balancing inference quality and computational cost has become a central challenge. Existing approaches tackle this trade-off along two largely independent dimensions: model routing, which switches among models of different scales to match request complexity, and test-time scaling (TTS), which adjusts inference-time compute within a fixed model for fine-grained control. However, this decoupled design introduces inherent limitations. Model routing yields coarse-grained, discrete performance changes due to the sparse set of model scales, while single-model TTS often encounters capacity ceilings and exhibits diminishing returns as compute increases. Moreover, treating the two mechanisms separately restricts adaptability in dynamic inference environments. To overcome these limitations, we introduce Unified Inference Scaling (UIS), which unifies model routing and TTS in a single optimization space. Building on this formulation, we propose UniScale, an online framework that models adaptive UIS as a contextual multi-armed bandit problem and learns inference policies via LinUCB. The framework incorporates efficiency-aware learning and cost modeling to ensure stable and scalable optimization over high-dimensional action spaces. Evaluation shows that UniScale effectively exploits the synergy in the UIS space to deliver a fine-grained and consistently better quality-cost trade-off across diverse, dynamic inference scenarios.

Benchmarking is mature where answers are verifiable -- math, code, reasoning -- but the fastest-growing uses of LLMs are subjective and human-facing: companionship, emotional support, counseling. There the default validity test, correlating a metric to human judgment, has no stable anchor: inter-rater agreement is low, structured by annotator identity, barely reproducible, and length-biased. So we cannot answer the question that matters: does capability that scales on objective benchmarks transfer to subjective behavior, and would our instruments even tell us if it did not? We build an instrument for this regime and report what it reveals at the frontier. We contribute, first, a self-evolving instrument that selects and then authors its own behavioral dimensions under a multiplicative anti-gaming fitness, self-halting when it stops improving; second, a trust-by-construction paradigm that earns belief through three certificates established without a human gold standard, where human raters saturate (rho ~ 0.45); and third, the finding it makes visible -- capability transfer is dissociable. Across 49 models, 8 families, and 24 months, subjective behaviors are where objective-benchmark scaling fails to carry over: the sharpest case, advice-restraint (knowing when not to give advice), is the frontier's universal-lowest dimension, and at gpt-4.1->gpt-5 it ran backwards while the aggregate score hid it -- a regression one instruction recovers. Warm restraint is moved by model generation, not by raw scale, MoE width, inference budget, or reasoning mode; the open-weight Pareto frontier matches closed flagships at ~10-80x lower per-call cost; and four judge families replicate the rubric on held-out human ESConv conversations. Data, code, the locked rubric, and judge prompts will be released upon publication.

Test-Time Scaling (TTS) enhances the reasoning capabilities of large language models by allocating additional inference compute to explore the solution space. However, existing parallel TTS methods typically keep branches isolated during search: intermediate discoveries remain branch-private and cannot guide other branches in time. This information isolation causes substantial redundant exploration, as branches repeatedly rediscover information already found elsewhere and require more search steps to collect complete decision information needed to reach correct answers. To bridge this gap, we propose \textbf{Collaborative Parallel Thinking (CPT)}, a training-free inference framework that enables search-time information sharing across parallel branches. CPT extracts compact intermediate information from ongoing branches, maintains a deduplicated query-level information pool, and broadcasts pool entries through the input context, allowing each branch in subsequent search steps to reuse discoveries made by other branches rather than rediscover the same information. Empirically, experiments on HMMT and AIME benchmarks show that CPT establishes a stronger accuracy--latency Pareto frontier than strong baselines across rollout budgets and model scales, highlighting search-time collaboration as an effective direction for efficient parallel TTS.

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence. Through latent dynamics analysis, we find an inherent trade-off between stability and effectiveness in existing architectures and strategies. By conceptualizing reasoning as uncertainty reduction, we propose that convergence toward stable fixed points while preserving effectiveness represents a promising way. To this end, we propose STARS (STAbility-driven Recurrent Scaling), a training framework that constrains latent states to approach asymptotically stable fixed points. This is realized via efficient Jacobian Spectral Radius Regularization with random loop sampling, enabling STARS to maximize effectiveness while ensuring rigorous stability. Experiments on arithmetic tasks show that STARS achieves reliable test-time scaling, and on complex mathematical reasoning it substantially mitigates performance degradation as recurrence depth increases while also improving peak performance.

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce stochastic backtracking over a persistent pool of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. Subpool Selection strengthens greedy PRM-guided search by applying Top-N selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. Power Backtrack Sequential Monte Carlo extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy-token trade-off in test-time scaling.

Recently, Reinforcement Learning with Verifiable Rewards (RLVR) and Test-Time Scaling (TTS) have advanced LLM code generation through executable verification. Yet Ground-Truth Unit Tests (GT UTs) remain a bottleneck: SOTA RLVR methods require them for costly training, while existing TTS methods lose competitiveness without them. This motivates GT-free TTS, where existing methods directly use self-generated UTs to refine and select code candidates. Yet such UTs are often noisy or spuriously coupled with wrong code, and UT quality in turn cannot be validated without reliable code. The key challenge is therefore to jointly improve both. To this end, we present CoSPlay, a GT-free, training-free framework that jointly improves codes and UTs through cooperative self-play. It first explores diverse solution ideas and identifies their potential failure modes to produce discriminative UT ideas. It then uses bidirectional pass-count signals from the Code-UT execution matrix to iteratively prune or fix weak codes and refresh or replace unreliable UTs, letting the two pools co-evolve. Finally, when multiple codes remain tied at the highest pass count, it picks the final code from the largest output-consensus cluster, since correct codes agree on the same inputs while wrong codes diverge. Experiments on four challenging benchmarks show that CoSPlay on Qwen2.5-7B-Instruct improves average BoN from 22.1% to 33.2% and UT accuracy from 14.6% to 78.3%, matching or surpassing the RLVR model CURE-7B. When applied to CURE-7B, it further improves BoN by 5.7%. CoSPlay also generalizes across diverse backbones and outperforms GT-free TTS baselines under comparable token budgets, with continued gains as the budget scales up. These results suggest a scalable inference strategy for competitive code generation without any GT data.

A common failure mode in long-horizon agentic test-time scaling is error propagation, where factual errors or invalid deductions introduced at intermediate steps persist in the agent's belief state and contaminate later reasoning. Existing test-time scaling methods provide limited control over this process, as they often rely on agents to detect their own mistakes, select among flawed trajectories, or refine solutions only after errors have already shaped the reasoning path. We propose ExComm, a communication protocol for exploration-stage agentic test-time scaling. ExComm is motivated by the empirical observation that the majority of intermediate errors in parallel agentic reasoning produce detectable cross-agent factual conflicts. Leveraging the iterative structure of agentic workflows, ExComm periodically audits agent belief states to detect such conflicts, resolves them through a dedicated tool-based verification loop, and returns concise, targeted feedback to the involved agents. Corrections are incorporated through soft belief updates, which append verified feedback rather than overwriting existing beliefs. Furthermore, to prevent collapsing trajectory diversity due to communication, ExComm further introduces a trajectory diversification module that redirects redundant trajectories toward orthogonal strategies. Experiments on AIME 2024, AIME 2025, and GAIA with Gemini-2.5-Flash-Lite and Qwen3.5-4B show that ExComm consistently outperforms strong test-time scaling baselines, achieving average performance gains of 5.7% and 5.0% over the best-performing baselines, respectively. Further analyses demonstrate improved error recovery, favorable scaling behavior, stronger diversity than adapted communication baselines, and the best performance-cost trade-off among the evaluated methods.

The efficient Test-Time Scaling (TTS) paradigm offers a promising perspective for enhancing the generation performance of diffusion models. However, current solutions are limited to a static, pre-defined noise pool and suffer from inflexible noise exploration across the denoising trajectory. To bridge this gap, we propose RTS, a novel Reward-guided Trajectory Scaling method to fully unlock the generative potential of diffusion models. Unlike existing methods, RTS facilitates the synthesis of refined, high-fidelity images via two core innovations: 1) a reward-guided noise optimization strategy to actively direct the search towards promising regions; and 2) a sparse test-time scaling framework together with a PCA-driven curvature analysis scheme to prioritize key intermediate steps in the entire denoising space, effectively compressing the search space. Experiments show our approach outperforms baselines by 15.6% across GenEval Score, and a 60.4% enhancement in ImageReward score, setting a new SOTA while providing a practical guideline for more effective test-time scaling across diffusion-specific architectures.

Complex Verilog Design Problems (CVDP) challenge hardware LLM agents because solving them requires localizing verifier-relevant RTL, testbenches, include paths, and build dependencies inside large repository snapshots, making precise edits, and recovering from sparse hidden-verifier failures. We present Trace2Skill, a test-time scaling framework that improves a hardware agent without RTL-specialized model fine-tuning. Rather than training a new model or only sampling more candidate solutions, Trace2Skill treats the agent's natural-language skill as an evolvable policy. It mines repeated rollout traces for success and failure modes, converts them into dense diagnostics and oracle lessons, and uses an oracle, mutator, and selector loop to produce task-specific skills that guide later search, editing, validation, and recovery. Because final pass/fail labels are often too coarse for hard failures, Trace2Skill also supports bounded runtime dense verifier feedback that returns sanitized functional observations while keeping hidden harnesses and reference solutions inaccessible to the agent. This feedback helps guide skill evolution and agent execution by connecting skill text, verifier evidence, and downstream behavior. Across hard CVDP tasks that defeat the seed CVDP agent, including tasks that also defeat frontier coding agents, Trace2Skill with dense verifier feedback substantially improves task pass rates and produces breakthrough passes on previously unsolved tasks, without requiring high-quality fine-tuning data, specialized RTL model training, or model weight updates. The same framework provides a general test-time scaling strategy that can extend beyond digital design to other verifiable EDA tasks.

Scaling test-time compute by iteratively updating a latent state has emerged as a powerful paradigm for reasoning. Yet the internal mechanisms that enable these iterative models to generalize beyond memorized patterns remain unclear. We hypothesize that generalizable reasoning arises from learning task-conditioned attractors: latent dynamical systems whose stable fixed points correspond to valid solutions. We formalize this process through Equilibrium Reasoners (EqR), which enable test-time scaling without external verifiers or task-specific priors. EqR scales internal dynamics along two axes: depth, by running more iterations, and breadth, by aggregating stochastic trajectories from multiple initializations. Empirically, gains from test-time scaling are tightly coupled with stronger convergence toward solution-aligned attractors. This attractor perspective allows neural networks to adaptively allocate test-time compute based on task difficulty. While simple cases converge within 1 to 5 iteration steps, harder cases benefit from massive test-time scaling. By unrolling up to the equivalent of 40,000 layers, scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme. These results suggest that learned attractor landscapes provide a useful mechanistic lens for understanding scalable reasoning in iterative latent models.