Inference-Time Scaling (ITS) has largely succeeded in verifiable domains like math and coding, where cheap verification enables scalable output selection. However, extending ITS to tasks prone to systematic failure - driven by faulty initial assumptions or unmet multidimensional constraints - typically relies on costly external solvers or brittle, model-based verifiers. Our key insight is that the intrinsic statistics of parallel sample sets, specifically length-adjusted tail entropy, provide a robust discriminative signal for solution quality without access to ground truth. Crucially, these statistics serve as a difficulty gate for adaptive compute allocation, dynamically routing problems across scaling regimes. First, Intrinsic Selection (iS) ranks candidates post-hoc, matching consensus-based algorithms across three domains and improving engineering design selection by 20% over pass@1 baselines. Second, Intrinsic Particle Filtering (iPF) generalizes this to step-level resampling, guiding generation toward high-confidence reasoning trajectories to improve pass@1 by 6.1 points on average on hard math problems. Finally, Particle Distillation (dPF) injects privileged guidance via early logit blending and KL-guided resampling, steering generation past systematic reasoning errors to satisfy expert rubrics, yielding up to 26.5% gains on complex clinical responses. Our pipeline applies seamlessly across broad-purpose, domain-specialized, and multimodal architectures, successfully extending ITS to open-ended domains without requiring trained reward models or exact ground-truth verification.

翻译：推断时间扩展（ITS）在数学和编码等可验证领域已取得显著成功，这类场景中低成本验证使输出可扩展选择成为可能。然而，将其推广至易受系统性失效影响的任务（由错误初始假设或未满足的多维约束导致）时，通常依赖昂贵的外部求解器或脆弱的基于模型的验证器。我们的核心洞察在于：平行样本集的固有统计特性——特别是长度调整后的尾熵——能在无真实标签情况下提供稳健的解质量判别信号。关键的是，这些统计特性可作为自适应计算分配的难度门控，动态地将问题路由至不同的扩展机制。首先，内在选择（iS）对候选解进行事后排序，在三个领域达到与基于共识的算法相当的性能，并在工程设计选择任务中比pass@1基线提升20%。其次，内在粒子滤波（iPF）将此方法推广至步骤级重采样，引导生成向高置信推理轨迹收敛，使困难数学问题的pass@1平均提升6.1个百分点。最后，粒子蒸馏（dPF）通过早期logit融合与KL引导重采样注入特权指导，引导生成避开系统性推理错误以符合专家评分标准，在复杂临床应答任务中取得高达26.5%的性能增益。本方法无缝适用于通用型、领域专精型及多模态架构，成功将ITS扩展至开放域任务，无需训练奖励模型或精确的真实标签验证。