Abstract:The Context-Compliance Regime in Retrieval-Augmented Generation (RAG) occurs when retrieved context dominates the final answer even when it conflicts with the model's parametric knowledge. Accuracy alone does not reveal how retrieved context causally shapes answers under such conflict. We introduce Context-Driven Decomposition (CDD), a belief-decomposition probe that operates at inference time and serves as an intervention mechanism for controlled retrieval conflict. Across Epi-Scale stress tests, TruthfulQA misconception injection, and cross- model reruns, CDD exposes three patterns. P1: context compliance is measurable in an upper-bound adversarial setting, where Standard RAG reaches 15.0% accuracy on TruthfulQA misconception injection (N=500). P2: adversarial accuracy gains transfer across model families: CDD improves accuracy on Gemini-2.5-Flash and on Claude Haiku/Sonnet/Opus, but rationale-answer causal coupling does not transfer. CDD reaches 64.1% mistake- injection causal sensitivity on Gemini-2.5-Flash, while sensitivities for all three Claude variants fall in the [-3%, +7%] range, suggesting that the Claude-side accuracy gains operate through a mechanism distinct from the explicit conflict-resolution trace. P3: explicit conflict decomposition improves robustness under temporal drift and noisy distractors, with CDD reaching 71.3% on temporal shifts and 69.9% on distractor evidence on the full Epi-Scale adversarial benchmark. These three patterns identify context-compliance as a structural axis along which standard RAG can be probed and intervened on, distinct from retrieval-quality or single-method robustness questions, and motivate releasing Epi-Scale for systematic study across model families and retrieval pipelines.
Abstract:Reinforcement learning (RL) has been applied to improve large language model (LLM) reasoning, yet the systematic study of how training scales with task difficulty has been hampered by the lack of controlled, scalable environments. We introduce ScaleLogic, a synthetic logical reasoning framework that offers independent control over two axes of difficulty: the depth of the required proof planning (i.e., the horizon) and the expressiveness of the underlying logic. Our proposed framework supports a wide range of logics: from simple implication-only logic ("if-then") towards more expressive first-order reasoning with conjunction ("and"), disjunction ("or"), negation ("not"), and universal quantification ("for all"). Using this framework, we show that the RL training compute $T$ follows a power law with respect to reasoning depth $D$ ($T \propto D^γ$, $R^{2} > 0.99$), and that the scaling exponent $γ$ increases monotonically with logical expressiveness, from $1.04$ to $2.60$. On downstream mathematics and general reasoning benchmarks, more expressive training settings yield both larger performance gains (up to $+10.66$ points) and more compute-efficient transfer compared to less expressive settings, demonstrating that what a model is trained on, not just how much it is trained, shapes downstream transfer. We further show that the power-law relationship holds across multiple RL methods, and curriculum-based training substantially improves scaling efficiency.




Abstract:Bundle adjustment (BA) is a critical technique in various robotic applications, such as simultaneous localization and mapping (SLAM), augmented reality (AR), and photogrammetry. BA optimizes parameters such as camera poses and 3D landmarks to align them with observations. With the growing importance of deep learning in perception systems, there is an increasing need to integrate BA with deep learning frameworks for enhanced reliability and performance. However, widely-used C++-based BA frameworks, such as GTSAM, g$^2$o, and Ceres, lack native integration with modern deep learning libraries like PyTorch. This limitation affects their flexibility, adaptability, ease of debugging, and overall implementation efficiency. To address this gap, we introduce an eager-mode BA framework seamlessly integrated with PyPose, providing PyTorch-compatible interfaces with high efficiency. Our approach includes GPU-accelerated, differentiable, and sparse operations designed for 2nd-order optimization, Lie group and Lie algebra operations, and linear solvers. Our eager-mode BA on GPU demonstrates substantial runtime efficiency, achieving an average speedup of 18.5$\times$, 22$\times$, and 23$\times$ compared to GTSAM, g$^2$o, and Ceres, respectively.