The Causal Uncertainty Principle: Manifold Tearing and the Topological Limits of Counterfactual Interventions

Judea Pearl's do-calculus provides a foundation for causal inference, but its translation to continuous generative models remains fraught with geometric challenges. We establish the fundamental limits of such interventions. We define the Counterfactual Event Horizon and prove the Manifold Tearing Theorem: deterministic flows inevitably develop finite-time singularities under extreme interventions. We establish the Causal Uncertainty Principle for the trade-off between intervention extremity and identity preservation. Finally, we introduce Geometry-Aware Causal Flow (GACF), a scalable algorithm that utilizes a topological radar to bypass manifold tearing, validated on high-dimensional scRNA-seq data.

Cohomological Obstructions to Global Counterfactuals: A Sheaf-Theoretic Foundation for Generative Causal Models

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails fundamentally when the causal graph exhibits non-trivial homology (e.g., structural conflicts or hidden confounders). We formalize structural causal models as cellular sheaves over Wasserstein spaces, providing a strict algebraic topological definition of cohomological obstructions in measure spaces. To ensure computational tractability and avoid deterministic singularities (which we define as manifold tearing), we introduce entropic regularization and derive the Entropic Wasserstein Causal Sheaf Laplacian, a novel system of coupled non-linear Fokker-Planck equations. Crucially, we prove an entropic pullback lemma for the first variation of pushforward measures. By integrating this with the Implicit Function Theorem (IFT) on Sinkhorn optimality conditions, we establish a direct algorithmic bridge to automatic differentiation (VJP), achieving O(1)-memory reverse-mode gradients strictly independent of the iteration horizon. Empirically, our framework successfully leverages thermodynamic noise to navigate topological barriers ("entropic tunneling") in high-dimensional scRNA-seq counterfactuals. Finally, we invert this theoretical framework to introduce the Topological Causal Score, demonstrating that our Sheaf Laplacian acts as a highly sensitive algebraic detector for topology-aware causal discovery.

Dr.Occ: Depth- and Region-Guided 3D Occupancy from Surround-View Cameras for Autonomous Driving

3D semantic occupancy prediction is crucial for autonomous driving perception, offering comprehensive geometric scene understanding and semantic recognition. However, existing methods struggle with geometric misalignment in view transformation due to the lack of pixel-level accurate depth estimation, and severe spatial class imbalance where semantic categories exhibit strong spatial anisotropy. To address these challenges, we propose Dr. Occ, a depth- and region-guided occupancy prediction framework. Specifically, we introduce a depth-guided 2D-to-3D View Transformer (D$^2$-VFormer) that effectively leverages high-quality dense depth cues from MoGe-2 to construct reliable geometric priors, thereby enabling precise geometric alignment of voxel features. Moreover, inspired by the Mixture-of-Experts (MoE) framework, we propose a region-guided Expert Transformer (R/R$^2$-EFormer) that adaptively allocates region-specific experts to focus on different spatial regions, effectively addressing spatial semantic variations. Thus, the two components make complementary contributions: depth guidance ensures geometric alignment, while region experts enhance semantic learning. Experiments on the Occ3D--nuScenes benchmark demonstrate that Dr. Occ improves the strong baseline BEVDet4D by 7.43% mIoU and 3.09% IoU under the full vision-only setting.

Bumper Drone: Elastic Morphology Design for Aerial Physical Interaction

Aerial robots are evolving from avoiding obstacles to exploiting the environmental contact interactions for navigation, exploration and manipulation. A key challenge in such aerial physical interactions lies in handling uncertain contact forces on unknown targets, which typically demand accurate sensing and active control. We present a drone platform with elastic horns that enables touch-and-go manoeuvres - a self-regulated, consecutive bumping motion that allows the drone to maintain proximity to a wall without relying on active obstacle avoidance. It leverages environmental interaction as a form of embodied control, where low-level stabilisation and near-obstacle navigation emerge from the passive dynamic responses of the drone-obstacle system that resembles a mass-spring-damper system. Experiments show that the elastic horn can absorb impact energy while maintaining vehicle stability, reducing pitch oscillations by 38% compared to the rigid horn configuration. The lower horn arrangement was found to reduce pitch oscillations by approximately 54%. In addition to intermittent contact, the platform equipped with elastic horns also demonstrates stable, sustained contact with static objects, relying on a standard attitude PID controller.

Causal Schrödinger Bridges: Constrained Optimal Transport on Structural Manifolds

Generative modeling typically seeks the path of least action via deterministic flows (ODE). While effective for in-distribution tasks, we argue that these deterministic paths become brittle under causal interventions, which often require transporting probability mass across low-density regions ("off-manifold") where the vector field is ill-defined. This leads to numerical instability and spurious correlations. In this work, we introduce the Causal Schrödinger Bridge (CSB), a framework that reformulates counterfactual inference as Entropic Optimal Transport. Unlike deterministic approaches that require strict invertibility, CSB leverages diffusion processes (SDEs) to robustly "tunnel" through support mismatches while strictly enforcing structural admissibility constraints. We prove the Structural Decomposition Theorem, showing that the global high-dimensional bridge factorizes into local, robust transitions. Empirical validation on high-dimensional interventions (Morpho-MNIST) demonstrates that CSB significantly outperforms deterministic baselines in structural consistency, particularly in regimes of strong, out-of-distribution treatments.

Smooth, Sparse, and Stable: Finite-Time Exact Skeleton Recovery via Smoothed Proximal Gradients

Continuous optimization has significantly advanced causal discovery, yet existing methods (e.g., NOTEARS) generally guarantee only asymptotic convergence to a stationary point. This often yields dense weighted matrices that require arbitrary post-hoc thresholding to recover a DAG. This gap between continuous optimization and discrete graph structures remains a fundamental challenge. In this paper, we bridge this gap by proposing the Hybrid-Order Acyclicity Constraint (AHOC) and optimizing it via the Smoothed Proximal Gradient (SPG-AHOC). Leveraging the Manifold Identification Property of proximal algorithms, we provide a rigorous theoretical guarantee: the Finite-Time Oracle Property. We prove that under standard identifiability assumptions, SPG-AHOC recovers the exact DAG support (structure) in finite iterations, even when optimizing a smoothed approximation. This result eliminates structural ambiguity, as our algorithm returns graphs with exact zero entries without heuristic truncation. Empirically, SPG-AHOC achieves state-of-the-art accuracy and strongly corroborates the finite-time identification theory.

Chinese Labor Law Large Language Model Benchmark

Recent advances in large language models (LLMs) have led to substantial progress in domain-specific applications, particularly within the legal domain. However, general-purpose models such as GPT-4 often struggle with specialized subdomains that require precise legal knowledge, complex reasoning, and contextual sensitivity. To address these limitations, we present LabourLawLLM, a legal large language model tailored to Chinese labor law. We also introduce LabourLawBench, a comprehensive benchmark covering diverse labor-law tasks, including legal provision citation, knowledge-based question answering, case classification, compensation computation, named entity recognition, and legal case analysis. Our evaluation framework combines objective metrics (e.g., ROUGE-L, accuracy, F1, and soft-F1) with subjective assessment based on GPT-4 scoring. Experiments show that LabourLawLLM consistently outperforms general-purpose and existing legal-specific LLMs across task categories. Beyond labor law, our methodology provides a scalable approach for building specialized LLMs in other legal subfields, improving accuracy, reliability, and societal value of legal AI applications.

Reasoning over Precedents Alongside Statutes: Case-Augmented Deliberative Alignment for LLM Safety

Ensuring that Large Language Models (LLMs) adhere to safety principles without refusing benign requests remains a significant challenge. While OpenAI introduces deliberative alignment (DA) to enhance the safety of its o-series models through reasoning over detailed ``code-like'' safety rules, the effectiveness of this approach in open-source LLMs, which typically lack advanced reasoning capabilities, is understudied. In this work, we systematically evaluate the impact of explicitly specifying extensive safety codes versus demonstrating them through illustrative cases. We find that referencing explicit codes inconsistently improves harmlessness and systematically degrades helpfulness, whereas training on case-augmented simple codes yields more robust and generalized safety behaviors. By guiding LLMs with case-augmented reasoning instead of extensive code-like safety rules, we avoid rigid adherence to narrowly enumerated rules and enable broader adaptability. Building on these insights, we propose CADA, a case-augmented deliberative alignment method for LLMs utilizing reinforcement learning on self-generated safety reasoning chains. CADA effectively enhances harmlessness, improves robustness against attacks, and reduces over-refusal while preserving utility across diverse benchmarks, offering a practical alternative to rule-only DA for improving safety while maintaining helpfulness.

AlignDrive: Aligned Lateral-Longitudinal Planning for End-to-End Autonomous Driving

End-to-end autonomous driving has rapidly progressed, enabling joint perception and planning in complex environments. In the planning stage, state-of-the-art (SOTA) end-to-end autonomous driving models decouple planning into parallel lateral and longitudinal predictions. While effective, this parallel design can lead to i) coordination failures between the planned path and speed, and ii) underutilization of the drive path as a prior for longitudinal planning, thus redundantly encoding static information. To address this, we propose a novel cascaded framework that explicitly conditions longitudinal planning on the drive path, enabling coordinated and collision-aware lateral and longitudinal planning. Specifically, we introduce a path-conditioned formulation that explicitly incorporates the drive path into longitudinal planning. Building on this, the model predicts longitudinal displacements along the drive path rather than full 2D trajectory waypoints. This design simplifies longitudinal reasoning and more tightly couples it with lateral planning. Additionally, we introduce a planning-oriented data augmentation strategy that simulates rare safety-critical events, such as vehicle cut-ins, by adding agents and relabeling longitudinal targets to avoid collision. Evaluated on the challenging Bench2Drive benchmark, our method sets a new SOTA, achieving a driving score of 89.07 and a success rate of 73.18%, demonstrating significantly improved coordination and safety

The Causal Round Trip: Generating Authentic Counterfactuals by Eliminating Information Loss

Judea Pearl's vision of Structural Causal Models (SCMs) as engines for counterfactual reasoning hinges on faithful abduction: the precise inference of latent exogenous noise. For decades, operationalizing this step for complex, non-linear mechanisms has remained a significant computational challenge. The advent of diffusion models, powerful universal function approximators, offers a promising solution. However, we argue that their standard design, optimized for perceptual generation over logical inference, introduces a fundamental flaw for this classical problem: an inherent information loss we term the Structural Reconstruction Error (SRE). To address this challenge, we formalize the principle of Causal Information Conservation (CIC) as the necessary condition for faithful abduction. We then introduce BELM-MDCM, the first diffusion-based framework engineered to be causally sound by eliminating SRE by construction through an analytically invertible mechanism. To operationalize this framework, a Targeted Modeling strategy provides structural regularization, while a Hybrid Training Objective instills a strong causal inductive bias. Rigorous experiments demonstrate that our Zero-SRE framework not only achieves state-of-the-art accuracy but, more importantly, enables the high-fidelity, individual-level counterfactuals required for deep causal inquiries. Our work provides a foundational blueprint that reconciles the power of modern generative models with the rigor of classical causal theory, establishing a new and more rigorous standard for this emerging field.