Differentially Private Two-Stage Empirical Risk Minimization and Applications to Individualized Treatment Rule

Differential Privacy (DP) provides a rigorous framework for deriving privacy-preserving estimators by injecting calibrated noise to mask individual contributions while preserving population-level insights. Its central challenge lies in the privacy-utility trade-off: calibrating noise levels to ensure robust protection without compromising statistical performance. Standard DP methods struggle with a particular class of two-stage problems prevalent in individualized treatment rules (ITRs) and causal inference. In these settings, data-dependent weights are first computed to satisfy distributional constraints, such as covariate balance, before the final parameter of interest is estimated. Current DP approaches often privatize stages independently, which either degrades weight efficacy-leading to biased and inconsistent estimates-or introduces excessive noise to account for worst-case scenarios. To address these challenges, we propose the Differentially Private Two-Stage Empirical Risk Minimization (DP-2ERM), a framework that injects a carefully calibrated noise only into the second stage while maintaining privacy for the entire pipeline and preserving the integrity of the first stage weights. Our theoretical contributions include deterministic bounds on weight perturbations across various widely used weighting methods, and probabilistic bounds on sensitivity for the final estimator. Simulations and real-world applications in ITR demonstrate that DP-2ERM significantly enhances utility over existing methods while providing rigorous privacy guarantees.

Towards Fair and Comprehensive Evaluation of Routers in Collaborative LLM Systems

Large language models (LLMs) have achieved success, but cost and privacy constraints necessitate deploying smaller models locally while offloading complex queries to cloud-based models. Existing router evaluations are unsystematic, overlooking scenario-specific requirements and out-of-distribution robustness. We propose RouterXBench, a principled evaluation framework with three dimensions: router ability, scenario alignment, and cross-domain robustness. Unlike prior work that relies on output probabilities or external embeddings, we utilize internal hidden states that capture model uncertainty before answer generation. We introduce ProbeDirichlet, a lightweight router that aggregates cross-layer hidden states via learnable Dirichlet distributions with probabilistic training. Trained on multi-domain data, it generalizes robustly across in-domain and out-of-distribution scenarios. Our results show ProbeDirichlet achieves 16.68% and 18.86% relative improvements over the best baselines in router ability and high-accuracy scenarios, with consistent performance across model families, model scales, heterogeneous tasks, and agentic workflows.

BiasScope: Towards Automated Detection of Bias in LLM-as-a-Judge Evaluation

LLM-as-a-Judge has been widely adopted across various research and practical applications, yet the robustness and reliability of its evaluation remain a critical issue. A core challenge it faces is bias, which has primarily been studied in terms of known biases and their impact on evaluation outcomes, while automated and systematic exploration of potential unknown biases is still lacking. Nevertheless, such exploration is crucial for enhancing the robustness and reliability of evaluations. To bridge this gap, we propose BiasScope, a LLM-driven framework for automatically and at scale discovering potential biases that may arise during model evaluation. BiasScope can uncover potential biases across different model families and scales, with its generality and effectiveness validated on the JudgeBench dataset. It overcomes the limitations of existing approaches, transforming bias discovery from a passive process relying on manual effort and predefined bias lists into an active and comprehensive automated exploration. Moreover, based on BiasScope, we propose JudgeBench-Pro, an extended version of JudgeBench and a more challenging benchmark for evaluating the robustness of LLM-as-a-judge. Strikingly, even powerful LLMs as evaluators show error rates above 50\% on JudgeBench-Pro, underscoring the urgent need to strengthen evaluation robustness and to mitigate potential biases further.

Anchored Policy Optimization: Mitigating Exploration Collapse Via Support-Constrained Rectification

Reinforcement Learning with Verifiable Rewards (RLVR) is increasingly viewed as a tree pruning mechanism. However, we identify a systemic pathology termed Recursive Space Contraction (RSC), an irreversible collapse driven by the combined dynamics of positive sharpening and negative squeezing, where the sampling probability of valid alternatives vanishes. While Kullback-Leibler (KL) regularization aims to mitigate this, it imposes a rigid Shape Matching constraint that forces the policy to mimic the reference model's full density, creating a gradient conflict with the sharpening required for correctness. We propose Anchored Policy Optimization (APO), shifting the paradigm from global Shape Matching to Support Coverage. By defining a Safe Manifold based on the reference model's high-confidence support, APO permits aggressive sharpening for efficiency while selectively invoking a restorative force during error correction to prevent collapse. We theoretically derive that APO serves as a gradient-aligned mechanism to maximize support coverage, enabling an Elastic Recovery that re-inflates valid branches. Empirical evaluations on mathematical benchmarks demonstrate that APO breaks the accuracy-diversity trade-off, significantly improving Pass@1 while restoring the Pass@K diversity typically lost by standard policy gradient methods.

Rethinking the Role of Entropy in Optimizing Tool-Use Behaviors for Large Language Model Agents

Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing latency and degrading inference performance, making managing tool-use behavior challenging. In this work, we conduct entropy-based pilot experiments and observe a strong positive correlation between entropy reduction and high-quality tool calls. Building on this finding, we propose using entropy reduction as a supervisory signal and design two reward strategies to address the differing needs of optimizing tool-use behavior. Sparse outcome rewards provide coarse, trajectory-level guidance to improve efficiency, while dense process rewards offer fine-grained supervision to enhance performance. Experiments across diverse domains show that both reward designs improve tool-use behavior: the former reduces tool calls by 72.07% compared to the average of baselines, while the latter improves performance by 22.27%. These results position entropy reduction as a key mechanism for enhancing tool-use behavior, enabling agents to be more adaptive in real-world applications.

From Abstract to Contextual: What LLMs Still Cannot Do in Mathematics

Large language models now solve many benchmark math problems at near-expert levels, yet this progress has not fully translated into reliable performance in real-world applications. We study this gap through contextual mathematical reasoning, where the mathematical core must be formulated from descriptive scenarios. We introduce ContextMATH, a benchmark that repurposes AIME and MATH-500 problems into two contextual settings: Scenario Grounding (SG), which embeds abstract problems into realistic narratives without increasing reasoning complexity, and Complexity Scaling (CS), which transforms explicit conditions into sub-problems to capture how constraints often appear in practice. Evaluating 61 proprietary and open-source models, we observe sharp drops: on average, open-source models decline by 13 and 34 points on SG and CS, while proprietary models drop by 13 and 20. Error analysis shows that errors are dominated by incorrect problem formulation, with formulation accuracy declining as original problem difficulty increases. Correct formulation emerges as a prerequisite for success, and its sufficiency improves with model scale, indicating that larger models advance in both understanding and reasoning. Nevertheless, formulation and reasoning remain two complementary bottlenecks that limit contextual mathematical problem solving. Finally, we find that fine-tuning with scenario data improves performance, whereas formulation-only training is ineffective. However, performance gaps are only partially alleviated, highlighting contextual mathematical reasoning as a central unsolved challenge for LLMs.

ARGOS: Automated Functional Safety Requirement Synthesis for Embodied AI via Attribute-Guided Combinatorial Reasoning

Ensuring functional safety is essential for the deployment of Embodied AI in complex open-world environments. However, traditional Hazard Analysis and Risk Assessment (HARA) methods struggle to scale in this domain. While HARA relies on enumerating risks for finite and pre-defined function lists, Embodied AI operates on open-ended natural language instructions, creating a challenge of combinatorial interaction risks. Whereas Large Language Models (LLMs) have emerged as a promising solution to this scalability challenge, they often lack physical grounding, yielding semantically superficial and incoherent hazard descriptions. To overcome these limitations, we propose a new framework ARGOS (AttRibute-Guided cOmbinatorial reaSoning), which bridges the gap between open-ended user instructions and concrete physical attributes. By dynamically decomposing entities from instructions into these fine-grained properties, ARGOS grounds LLM reasoning in causal risk factors to generate physically plausible hazard scenarios. It then instantiates abstract safety standards, such as ISO 13482, into context-specific Functional Safety Requirements (FSRs) by integrating these scenarios with robot capabilities. Extensive experiments validate that ARGOS produces high-quality FSRs and outperforms baselines in identifying long-tail risks. Overall, this work paves the way for systematic and grounded functional safety requirement generation, a critical step toward the safe industrial deployment of Embodied AI.

InstructDiff: Domain-Adaptive Data Selection via Differential Entropy for Efficient LLM Fine-Tuning

Supervised fine-tuning (SFT) is fundamental to adapting large language models, yet training on complete datasets incurs prohibitive costs with diminishing returns. Existing data selection methods suffer from severe domain specificity: techniques optimized for general instruction-following fail on reasoning tasks, and vice versa. We observe that measuring entropy differences between base models and minimally instruction-tuned calibrated models reveals a pattern -- samples with the lowest differential entropy consistently yield optimal performance across domains, yet this principle manifests domain-adaptively: reasoning tasks favor entropy increase (cognitive expansion), while general tasks favor entropy decrease (cognitive compression). We introduce InstructDiff, a unified framework that operationalizes differential entropy as a domain-adaptive selection criterion through warmup calibration, bi-directional NLL filtering, and entropy-based ranking. Extensive experiments show that InstructDiff achieves 17\% relative improvement over full data training on mathematical reasoning and 52\% for general instruction-following, outperforming prior baselines while using only 10\% of the data.

Generation Enhances Understanding in Unified Multimodal Models via Multi-Representation Generation

Unified Multimodal Models (UMMs) integrate both visual understanding and generation within a single framework. Their ultimate aspiration is to create a cycle where understanding and generation mutually reinforce each other. While recent post-training methods have successfully leveraged understanding to enhance generation, the reverse direction of utilizing generation to improve understanding remains largely unexplored. In this work, we propose UniMRG (Unified Multi-Representation Generation), a simple yet effective architecture-agnostic post-training method. UniMRG enhances the understanding capabilities of UMMs by incorporating auxiliary generation tasks. Specifically, we train UMMs to generate multiple intrinsic representations of input images, namely pixel (reconstruction), depth (geometry), and segmentation (structure), alongside standard visual understanding objectives. By synthesizing these diverse representations, UMMs capture complementary information regarding appearance, spatial relations, and structural layout. Consequently, UMMs develop a deeper and more comprehensive understanding of visual inputs. Extensive experiments across diverse UMM architectures demonstrate that our method notably enhances fine-grained perception, reduces hallucinations, and improves spatial understanding, while simultaneously boosting generation capabilities.

Spurious Rewards Paradox: Mechanistically Understanding How RLVR Activates Memorization Shortcuts in LLMs

Reinforcement Learning with Verifiable Rewards (RLVR) is highly effective for enhancing LLM reasoning, yet recent evidence shows models like Qwen 2.5 achieve significant gains even with spurious or incorrect rewards. We investigate this phenomenon and identify a "Perplexity Paradox": spurious RLVR triggers a divergence where answer-token perplexity drops while prompt-side coherence degrades, suggesting the model is bypassing reasoning in favor of memorization. Using Path Patching, Logit Lens, JSD analysis, and Neural Differential Equations, we uncover a hidden Anchor-Adapter circuit that facilitates this shortcut. We localize a Functional Anchor in the middle layers (L18-20) that triggers the retrieval of memorized solutions, followed by Structural Adapters in later layers (L21+) that transform representations to accommodate the shortcut signal. Finally, we demonstrate that scaling specific MLP keys within this circuit allows for bidirectional causal steering-artificially amplifying or suppressing contamination-driven performance. Our results provide a mechanistic roadmap for identifying and mitigating data contamination in RLVR-tuned models. Code is available at https://github.com/idwts/How-RLVR-Activates-Memorization-Shortcuts.