Self-Consistent Generative Paths via Admissible Random Variational Transport

Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map. Diffusion models follow stochastic denoising paths, flow matching learns transport fields, consistency and distillation methods compress paths into one or a few steps, adversarial models match terminal distributions, and VAEs generate through latent kernels. Existing unifying views mainly describe how such paths are constructed. We study a complementary question: when is a generated probability path self-consistent? We define a self-consistent generative path as a random fixed point of admissible local variational transport corrections. In this framework, a local correction is specified by a random variational transport operator combining a divergence or geometry term, an energy term, and a structural constraint. The framework contains random regularized optimal-transport proximal steps as a structured instance, while also allowing non-OT divergences, latent kernels, adversarial constraints, causal discrete kernels, and terminal one-step maps. The theory yields a random fixed-point path residual (R-FPR), which measures the gap between the actual generated path and an admissible local correction. We prove well-posedness, random fixed-point existence and attraction, non-contractive existence, residual-to-generation error bounds, empirical residual concentration, proxy perturbation bounds, continuous-time limits, and operator-level generalization with model-specific corollaries. The resulting theory turns endpoint matching into path self-consistency testing and provides a residual-control principle for diagnosing failures, regularizing training, and guiding adaptive sampling across diffusion, flow, one-step, VAE, GAN/WGAN, and autoregressive generators.

Conditional Random Ordered Transport Spaces

A small Wasserstein distance does not certify that a transformation is admissible. In evidence-constrained, semantic, causal, physical, monotone, or risk-sensitive learning, one must ask not only how far two probability laws are, but whether mass has moved in a direction allowed by available information. We introduce conditional random ordered transport spaces (CROTS), a class of \(L^0\)-valued spaces of random probability measures equipped with a Wasserstein ambient metric, a closed stochastic order, hard and soft ordered transport discrepancies, and a conditional risk functional for evaluating order violation under an evidence sigma-field. The central object is an order-admissible transport geometry for random measure-valued dynamics, distinct from cone-valued metrics, ordered Kantorovich constructions, random Wasserstein spaces alone, and model-specific residuals for generative paths. We develop the foundations of CROTS as a space theory for reliable distributional learning. The results include well-posedness and duality for hard and soft ordered transport, soft-to-hard variational convergence, measurability and completeness of the random lifted space, reductions to classical Wasserstein and ordered geometries, ordered geodesics, constrained barycenters and projections, conditional risk-transport duality, and separation of order-violating distributions. The main stability theorem shows that random learning dynamics may converge in the ambient Wasserstein metric while its local admissibility leakage follows a separate conditional order-risk recursion. The resulting asymptotic order-risk floor provides a mathematical language for evidence overreach, ordered distribution shift, robustness failure, and admissible distributional dynamics.

MARDoc: A Memory-Aware Refinement Agent Framework for Multimodal Long Document QA

Iterative retrieval-reasoning agents have recently shown promise for multimodal long-document question answering. However, most existing systems maintain a single growing context that mixes retrieval traces, observations, and intermediate reasoning. As interactions accumulate, key evidence becomes scattered and diluted, making multi-hop reasoning noisy. We propose MARDoc, a Memory-Aware Refinement Agent framework that decouples long-document QA into three specialized agents: an Explorer for multi-granularity multimodal retrieval, a Refiner for distilling interaction traces into structured evidence and reasoning memories, and a Reflector for checking evidence sufficiency and providing targeted feedback. Across iterations, the agents rely on a dynamically updated structured memory rather than a full accumulated interaction history. This design reduces context noise while preserving answer-critical facts and their logical dependencies. Experiments on MMLongBench-Doc and DocBench show that MARDoc achieves strong results, outperforming same-backbone baselines and demonstrating the effectiveness of structured memory for agentic document QA.

LiAuto-GeoX: Efficient Grounded Driving Transformer

Dense 3D reconstruction has demonstrated immense potential for spatial understanding, yet its viability as a real-time, onboard representation for autonomous driving remains an open challenge. Existing large-scale visual geometry models typically require substantial computational resources and lack the long-range geometric fidelity, surround-view consistency, and real-time efficiency demanded by dynamic driving environments. To bridge this gap, we present \textbf{LiAuto-GeoX}, an efficient grounded driving transformer designed for deployable, ego-centric 3D scene understanding. Our approach begins by learning a high-capacity driving geometry model from large-scale surround-view data, utilizing sparse LiDAR priors to provide robust geometric grounding in distant, ambiguous, or structure-sparse regions. We then instantiate this capability into a highly compact 155M-parameter onboard model through a novel geometry-preserving distillation framework. This framework employs mask-guided depth-aware distillation to retain fine-grained metric structures by emphasizing geometrically informative regions, and relative-pose relational distillation to enforce cross-view spatial consistency through pose-induced geometric relations. Extensive evaluations reveal that \textbf{LiAuto-GeoX} runs at 220 FPS on KITTI while maintaining high-fidelity dense reconstruction, enabling real-time deployment. The learned geometry transfers seamlessly to downstream autonomy tasks, achieving 90.6 PDMS in trajectory prediction, 24.63 mIoU in occupancy prediction, and 47.67 IoU in future-frame prediction. These all demonstrate that efficient dense 3D reconstruction can transcend its traditional role as a perception target to serve as a scalable, foundational geometric representation for next-generation autonomous driving.

Cone-Compatible Monge Geometry for High-Dimensional Ordered Optimal Transport

High-dimensional optimal transport is seldom available in closed form. The one-dimensional case is exceptional because the order of the real line is compatible with convex transport costs, making monotone rearrangement optimal. This paper studies when an analogous Monge structure can be recovered in higher dimensions from a partial order. We introduce a cone-compatible Monge geometry: a closed convex cone (K) induces the order (x\preceq_K y) whenever (y-x\in K), and is compatible with a cost if ordered pairs satisfy a Monge exchange inequality. For squared Mahalanobis costs (c_M(x,y)=(x-y)^\top M(x-y)), we prove a sharp characterization: compatibility holds exactly when (K) is acute under the (M)-inner product, namely (u^\top Mv\ge0) for all (u,v\in K), equivalently (K\subseteq K_M^*). Under this condition, measures supported on cone chains admit a quantile-type closed-form optimal coupling, yielding exact transport under the original ground cost rather than after projection or metric replacement. We distinguish the resulting cone-chain Wasserstein metric on canonically ordered chain distributions from an extended directed cone transport cost on general measures, and develop feasibility, duality, stability, approximation, Gaussian recovery, statistical, and computational results. The theory is complementary to sliced and tree Wasserstein distances: it is not a universal fast surrogate, but a way to obtain interpretable, direction-valid, original-space monotone transport for ordered high-dimensional data.

Preserving Data Privacy in Learning Causal Structure with Fully Homomorphic Encryption

Preserving data privacy is an important topic in structural data management and data mining. However, the issue of privacy leakage in distributed causal structure learning is a persistent challenge, especially in cases where data transmission and computation are required. In this paper, we propose a method based on fully homomorphic encryption (FHE) that performs calculations on ciphertexts, keeping data encrypted in transition and computation. Nevertheless, adopting FHE to causal structure learning is challenging due to the high computation cost and limited support on division as well as logarithm operations in FHE. To tackle this challenge, we propose a series of novel techniques including (i) circuit simplification for better efficiency, (ii) approximation of division and logarithm through Newton-Raphson Reciprocal and Taylor expansion, and (iii) a batching technique with SIMD-acceleration to enhance the whole learning process. Additionally, our method can be easily extended beyond FHE by demonstration of its portability to support differential privacy. Empirical results show that our method achieves high consistency and comparable causal structure with the plaintext version in the datasets tested. Last, our method is efficient and practical to complete learning causal structures in tens of minutes even under the privacy protection of FHE.

Shape-Prior-Based Point Cloud Completion for Single-Stage Fully Sparse 3D Object Detection

Single-stage fully sparse 3D object detectors rely on point clouds data to detect objects in autonomous driving scenarios. However, the sparsity and incompleteness of point clouds significantly limit the performance of 3D object detection. To address this issue, this paper proposes a point clouds completion method specifically designed for single-stage fully sparse detectors. The entire shape-prior-based completion process consists of two consecutive steps. In the first step, we design a novel Instance Selection module, which is capable of identifying point clouds corresponding to foreground objects even when the baseline model does not generate proposals, while effectively ignoring the point clouds of background regions. In the second step, we introduce a novel Alignment-Based Point Completion module, which aligns the point clouds of foreground objects with prototypes in terms of both their centers and orientations. Subsequently, points are selected from the prototype to fill in the missing parts of the foreground object. We evaluated our method on two single-stage fully sparse detectors using the KITTI dataset. The experimental results demonstrate that the proposed method significantly improves the detection performance, confirming its effectiveness and generalizability.

The Sword, Shield, and Achilles' Heel: Characterizing the Linguistic Inductive Bias of Large Language Models for Spatial Reasoning in Navigation Planning

Large Language Model (LLM)-based navigation systems commonly construct explicit spatial representations (e.g., topological graphs, semantic raster maps) and translate them into textual descriptions as LLMs' inputs. However, the linguistic structures of such text-based spatial representations and the choices of contextual features (e.g., topology, geometry) they contain are often treated as neutral engineering decisions rather than key factors that shape LLMs' behavior. To fill the gap, we propose a dual-interventional framework that disentangles linguistic structures from different contextual cues to evaluate the linguistic inductive bias of LLMs for navigation planning. In the framework, representation intervention varies the linguistic format and the degree of linguistic compression, clarifying when linguistic representations support or inhibit navigation planning. Context intervention, combined with contextual feature combination and conflict probing, explicitly clarifies the preferences and weaknesses of LLMs when processing different contextual cues. Experiments across diverse spatial reasoning tasks and multiple model scales reveal a consistent pattern: topological information is a sturdy shield and the backbone of robust planning; linguistic format is a double-edged sword whose effect depends on model size, task demands, and the compression level; and semantic information is a fatal Achilles' heel -- incorrect semantic cues can systematically derail the planning process. Overall, our study shows that effective text-based spatial representations in LLM-based navigation should preserve topological integrity, calibrate representational compression to model capacity, and ensure semantic correctness, rather than simply adopting a single representation. Our code is publicly available at https://github.com/jonesdong150/LLM-Navigation-Inductive-Bias.

F-RNG: Feed-Forward Relightable Neural Gaussians

Capturing relightable 3D assets from real-world objects is a widely researched problem. Several per-scene optimization-based methods, based on 3D Gaussian splatting (3DGS), support relighting; however, they usually require dense input views, and their overfitting nature makes it difficult to generalize across scenes. Unlike per-scene optimization methods, generalized feed-forward models can directly reconstruct Gaussians from sparse input views. However, the resulting assets have baked-in illumination and cannot be easily used for relighting. In this paper, we present F-RNG, a feed-forward framework that directly generates relightable 3DGS assets from sparse-view inputs. Training such a model from scratch can require massive data and computing resources, and it is especially challenging to generate relightable assets in a feed-forward manner with acceptable cost. We develop F-RNG upon an existing large reconstruction model (LRM) to extract relightable representations, while also utilizing priors from an intrinsic decomposition model (IDM). Specifically, we first introduce a latent-interpolated fine-grained geometry synthesis to enhance the LRM's geometry representation. Second, we propose a prior-guided relightable appearance distillation to extract relightable neural representations by incorporating IDM priors. Finally, a universal neural renderer enables flexible and high-fidelity relighting. F-RNG requires neither re-training nor fine-tuning of the underlying LRMs, thus can automatically benefit from better LRMs and IDMs in the future. With only small networks that can be trained with affordable data and computational resources, F-RNG avoids the repetitive inference of large models under different light conditions. By comparison to the state-of-the-art LRM-based relighting method, F-RNG achieves ~25x faster relighting, as well as superior quality (~+2.0 dB).

MIRA: Mid-training Rubric Anchoring for Source-Aware Data Selection

Mid-training has become an important stage in modern LLM development, using large-scale curated mixtures to strengthen capabilities before final post-training. Its data selection problem is distinct: the data are optimized under a pretraining-style objective at near-pretraining scale, but are curated toward downstream capabilities and drawn from heterogeneous sources with different formats and training roles. As a result, effective selection requires both scalability and source-adaptive semantic criteria. Existing model-based methods scale well, but provide only implicit quality signals. Semantic selection methods offer stronger judgments, but usually assume fixed rubrics or standardized data formats. To address this mismatch, we propose MIRA, a source-aware filtering framework based on self-anchored rubric discovery. The key idea is to make rubric construction part of data selection: MIRA first discovers what should be evaluated for each source group, then distills those judgments into scalable student scorers for full-corpus filtering. On code-oriented mid-training with 21 sources and 5 source groups, MIRA outperforms selection baselines across nine code benchmarks and matches the full-corpus run while using only half the tokens.