Multimodal large language models (MLLMs) have achieved strong performance on perception-oriented tasks, yet their ability to perform mathematical spatial reasoning, defined as the capacity to parse and manipulate two- and three-dimensional relations, remains unclear. While humans easily master textbook-style spatial problems, current MLLMs exhibit substantially higher error rates, exposing a fundamental weakness in spatial comprehension. To investigate this gap, we present MathSpatial, the first large-scale and systematic dataset resource dedicated to mathematical spatial reasoning in MLLMs. MathSpatial provides two complementary subsets: MathSpatial-Bench (2,000 problems) for evaluating spatial reasoning isolated from perceptual noise, and MathSpatial-Corpus (8,000 problems) equipped with structured reasoning traces for training. Benchmarking 20+ MLLMs reveals a severe deficit: non-reasoning models largely languish below 60% accuracy, and even the strongest reasoning models fall ~16 percentage points behind human performance (96.3%). Crucially, we demonstrate that fine-tuning on MathSpatial-Corpus yields consistent performance gains across model families. MathSpatial provides a vital resource for diagnosing and advancing spatial reasoning in MLLMs. The dataset and related resources are available at https://github.com/shuolucs/MathSpatial.

Test-time reinforcement learning (TTRL) always adapts models at inference time via pseudo-labeling, leaving it vulnerable to spurious optimization signals from label noise.Through an empirical study, we observe that responses with medium consistency form an ambiguity region and constitute the primary source of reward noise.Crucially, we find that such spurious signals can be even amplified through group-relative advantage estimation.Motivated by these findings, we propose a unified framework, Debiased and Denoised test-time Reinforcement Learning (DDRL), to mitigate spurious signals.Concretely, DDRL first applies a frequency-based sampling strategy to exclude ambiguous samples while maintaining a balanced set of positive and negative examples.It then adopts a debiased advantage estimation with fixed advantages, removing the bias introduced by group-relative policy optimization.Finally, DDRL incorporates a consensus-based off-policy refinement stage, which leverages the rejection-sampled dataset to enable efficient and stable model updates.Experiments on three large language models across multiple mathematical reasoning benchmarks demonstrate that DDRL consistently outperforms existing TTRL baselines.The code is available at https://github.com/yuyongcan/DDRL.

Large reasoning models have recently demonstrated remarkable capabilities in solving complex tasks, where supervised fine-tuning (SFT) on long chain-of-thought data serves as a crucial foundation for eliciting and enhancing their reasoning abilities. Despite rapid progress in both improving and analyzing reasoning-oriented SFT, the field still lacks a systematic survey that consolidates its fast-growing literature. To fill this gap, we present a comprehensive review of recent advancements in reasoning SFT, examining the literature through the dual lenses of methodological design and analytical investigation. First, we review methodological improvements across the SFT pipeline and categorize them into data-centric approaches and algorithm-centric innovations. Second, we reorganize analytical studies along three dimensions: data characteristics, optimization dynamics, and mechanistic insights. Finally, by synthesizing current research focuses and remaining bottlenecks, we outline promising future directions for reasoning SFT. We hope this survey deepens the understanding of reasoning SFT and paves the way for advanced reasoning models.