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 language model (LLM)-based agents have demonstrated remarkable capabilities in tool use, but their ability to follow user preferences when calling tools remains underexplored. To address this gap, we introduce APOLLO, a benchmark designed to evaluate agents’ ability to identify personalized user preferences from interaction histories and to adhere to these preferences when calling tools to solve user queries. In APOLLO, user preferences expressed in the interaction history take two forms: explicit preferences stated directly, and implicit preferences conveyed through behaviors such as option selection and comparison. In addition, the benchmark includes two types of queries, reactive and proactive, which pose challenges for LLMs to ground user queries in the corresponding preferences. Using APOLLO, we evaluate and analyze both language models and reasoning models, and investigate the impact of different agent frameworks, such as Reflexion, on model performance. Experimental results show that current models still struggle to follow user preferences when calling tools. For instance, GPT-4o achieves only 51.16% accuracy on the benchmark. Furthermore, we develop a reinforcement learning-based approach to improve LLMs, achieving substantial performance gains on APOLLO. Our dataset and code are publicly available at https://github.com/zhiyuanc2001/APOLLO.