Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects

Covariance estimation yields a fundamental second-order statistic underlying representation learning, dimension reduction, and dependence modeling. While covariance has been well understood in Euclidean spaces, it is ill-defined for random objects residing on nonlinear Riemannian manifolds, which increasingly arise in modern machine learning applications involving shapes, symmetric positive definite (SPD) matrices, etc. This paper introduces an intrinsic Riemannian cross-covariance for manifold-valued random objects. Our approach defines covariance and correlation by transporting local variations to a common tangent space via parallel transport, yielding a second-order descriptor that is independent of arbitrary coordinate choices. We establish that the proposed covariance inherits desirable properties of its Euclidean counterparts and characterize its asymptotic behavior. Numerical studies on spheres and SPD manifolds, together with real-data experiments on heart valve shapes in Kendall's shape space, demonstrate the effectiveness of our estimators and verify the stated properties. Our results position the Riemannian covariance as a fundamental tool for second-order learning and analysis in non-Euclidean representation spaces.

Intrinsic Footpoint-invariant Riemannian Cross-covariance

Covariance estimation yields a fundamental second-order statistic underlying representation learning, dimension reduction, and dependence modeling. While covariance has been well understood in Euclidean spaces, it is ill-defined for random objects residing on nonlinear Riemannian manifolds, which increasingly arise in modern machine learning applications involving shapes, symmetric positive definite (SPD) matrices, etc. This paper introduces an intrinsic Riemannian cross-covariance for manifold-valued random objects. Our approach defines covariance and correlation by transporting local variations to a common tangent space via parallel transport, yielding a second-order descriptor that is independent of arbitrary coordinate choices. We establish that the proposed covariance inherits desirable properties of its Euclidean counterparts and characterize its asymptotic behavior. Numerical studies on spheres and SPD manifolds, together with real-data experiments on heart valve shapes in Kendall's shape space, demonstrate the effectiveness of our estimators and verify the stated properties. Our results position the Riemannian covariance as a fundamental tool for second-order learning and analysis in non-Euclidean representation spaces.

Synthetic Data from Cross-Domain Events for Large-Scale Recommendation Systems

Large-scale recommendation systems operate across diverse domains, yet they face the challenges of data sparsity and noisy implicit feedback. Traditional approaches mitigate this via model-specific knowledge distillation from source domains to a target domain. Inspired by the transformative success of synthetic data generation in large language models (LLMs), we introduce Synthetic Cross-domain Augmentation and Learning for Recommendation (SCALR), a framework that generates synthetic user-item interaction events for a target recommendation domain by leveraging observed events from a source domain. SCALR decomposes cross-domain learning into two modular stages. First, it translates observed user events in source domains by framing event generation as estimating the likelihood that a user would interact with a target-domain item, conditioned on their observed interactions in a source domain. Second, downstream models train on these synthetic events as cross-domain learning objectives, where the synthetic events augment the target domain's training data in a model-agnostic manner. Our approach yields statistically significant improvements in online A/B tests on an industrial recommendation platform. To the best of our knowledge, this is among the first works to explicitly frame cross-domain event transfer as synthetic data generation for recommendation systems.

BORA: Bridging Offline Reinforcement Learning and Online Residual Adaptation for Real-World Dexterous VLA Models

Vision-Language-Action (VLA) models have emerged as a promising paradigm for grounding visual-language understanding into real-world robotic manipulation. However, dexterous manipulation remains challenging for VLA policies due to high-dimensional hand control and compounding execution errors, which makes real-world RL post-training essential for bridging the gap between visually grounded action generation and physically reliable dexterous execution. However, high-dimensional dexterous exploration often triggers temporal inconsistency, sample inefficiency and hardware risks in the real world. To address these challenges, we propose BORA, an offline-to-online RL post-training framework designed for real-world dexterous VLA models. In the offline phase, BORA constructs a critic that takes both the VLM's cognition tokens and action chunks as inputs. This design enables action-conditioned value guidance, allowing the critic to evaluate dexterous hand motions beyond visual context alone. During the subsequent online phase, BORA freezes the VLA base and introduces a lightweight, Human-in-the-Loop (HiL) chunk-wise residual adaptation mechanism to mitigate real-world execution errors and further correct the offline-learned intents within the actual physical environment. By inheriting the offline critic and employing intervention-driven rewards, BORA effectively corrects execution discrepancies and adapts to real-world physical variances while preserving the pretrained policy as a stable prior. Extensive evaluations across five complex real-world dexterous tasks demonstrate that BORA significantly outperforms pure imitation learning and traditional decoupled RL baselines, achieving a 33% absolute increase in average success rate under standard settings and up to a 43% improvement in unseen object generalization.

Memento: Personalized RAG-Style Long-Retention Data Scaling for META Ads Recommendation

Modeling of long history data suffers from long-context window attention dilution, system efficiency and catastrophic forgetting problems, where naive linear scaling approach like LastN would fail. We introduce Memento, a personalized retrieval-augmented framework that treats historical user engagements as a document corpus and ad requests as queries, retrieving relevant interactions via Maximal Marginal Relevance (MMR) to balance similarity with diversity. We identify two complementary applications: Representation Memento, which retrieves historical embeddings for feature augmentation, and Data Memento, which retrieves past training examples for multipass training. Through infrastructure co-design -- temporal chunking, INT8 quantization, and asynchronous serving -- Memento achieves 5-10$\times$ resource efficiency over linear scaling. Memento processes daily requests with sub-10ms latency, yielding 0.25-0.3% Normalized Entropy gain on both click-through and conversion prediction. In production, Memento delivers a 1% CTR lift on Facebook Feed and Reels and a 1.2% CVR lift, scaling personalization to 365+ days of history.

VLA-GSE: Boosting Parameter-Efficient Fine-Tuning in VLA with Generalized and Specialized Experts

Vision-language-action (VLA) models inherit rich visual-semantic priors from pre-trained vision-language backbones, but adapting them to robotic control remains challenging. Full fine-tuning (FFT) is prone to overfitting on downstream robotic data and catastrophic forgetting of pretrained vision-language capabilities. Parameter-efficient fine-tuning (PEFT) better preserves pre-trained knowledge, yet existing PEFT methods still struggle to adapt effectively to robot control tasks. To address this gap, we propose VLA-GSE, a parameter-efficient VLA fine-tuning framework that improves control adaptation while retaining PEFT's knowledge preservation advantage. Specifically, VLA-GSE (Generalized and Specialized Experts) is initialized by spectrally decomposing the frozen backbone, assigning leading singular components to generalized experts (shared experts) and disjoint residual components to specialized experts (routed experts). This decomposition improves adaptation capacity under a fixed trainable-parameter budget. Under a comparable parameter budget, VLA-GSE updates only 2.51% of the full model parameters and consistently outperforms strong FFT and PEFT baselines. It achieves 81.2% average zero-shot success on LIBERO-Plus, preserves pre-trained VLM capability comparably to LoRA on multimodal understanding benchmarks, and improves real-world manipulation success under multiple distribution shifts. Code is available at: https://github.com/YuhuaJiang2002/VLA-GSE

EOS-Bench: A Comprehensive Benchmark for Earth Observation Satellite Scheduling

Earth observation satellite imaging scheduling is a challenging NP-hard combinatorial optimisation problem central to space mission operations. While next-generation agile Earth observation satellites (EOS) increase operational flexibility, they also significantly raise scheduling complexity. The lack of a unified, open-source benchmark makes it difficult to compare algorithms across studies. This paper introduces EOS-Bench, a comprehensive framework for systematic and reproducible evaluation of scheduling methods. By integrating high-fidelity orbital dynamics and platform constraints, EOS-Bench generates 1,390 scenarios and 13,900 benchmark instances, spanning from small-scale validation cases to large coordination problems with up to 1,000 satellites and 10,000 requests. We further propose a scenario characterisation scheme to quantify structural difficulty based on factors such as opportunity density, task flexibility, conflict intensity, and satellite congestion. A multidimensional evaluation protocol is introduced, assessing performance across five metrics: task profit, completion rate, workload balance, timeliness, and runtime. The framework is evaluated using mixed-integer programming, heuristics, meta-heuristics, and deep reinforcement learning across both agile and non-agile settings. Results show that EOS-Bench effectively distinguishes solver performance across scales and conditions, revealing trade-offs between solution quality and computational efficiency, and providing deeper insight into scenario complexity. EOS-Bench offers a unified and extensible open testbed for advancing research in Earth observation satellite scheduling. The code and data are available at https://github.com/Ethan19YQ/EOS-Bench.

TableVision: A Large-Scale Benchmark for Spatially Grounded Reasoning over Complex Hierarchical Tables

Structured tables are essential for conveying high-density information in professional domains such as finance, healthcare, and scientific research. Despite the progress in Multimodal Large Language Models (MLLMs), reasoning performance remains limited for complex tables with hierarchical layouts. In this paper, we identify a critical Perception Bottleneck through quantitative analysis. We find that as task complexity scales, the number of involved discrete visual regions increases disproportionately. This processing density leads to an internal "Perceptual Overload," where MLLMs struggle to maintain accurate spatial attention during implicit generation. To address this bottleneck, we introduce TableVision, a large-scale, trajectory-aware benchmark designed for spatially grounded reasoning. TableVision stratifies tabular tasks into three cognitive levels (Perception, Reasoning, and Analysis) across 13 sub-categories. By utilizing a rendering-based deterministic grounding pipeline, the dataset explicitly couples multi-step logical deductions with pixel-perfect spatial ground truths, comprising 6,799 high-fidelity reasoning trajectories. Our empirical results, supported by diagnostic probing, demonstrate that explicit spatial constraints significantly recover the reasoning potential of MLLMs. Furthermore, our two-stage decoupled framework achieves a robust 12.3% overall accuracy improvement on the test set. TableVision provides a rigorous testbed and a fresh perspective on the synergy between perception and logic in document understanding.

Learning Additively Compositional Latent Actions for Embodied AI

Latent action learning infers pseudo-action labels from visual transitions, providing an approach to leverage internet-scale video for embodied AI. However, most methods learn latent actions without structural priors that encode the additive, compositional structure of physical motion. As a result, latents often entangle irrelevant scene details or information about future observations with true state changes and miscalibrate motion magnitude. We introduce Additively Compositional Latent Action Model (AC-LAM), which enforces scene-wise additive composition structure over short horizons on the latent action space. These AC constraints encourage simple algebraic structure in the latent action space~(identity, inverse, cycle consistency) and suppress information that does not compose additively. Empirically, AC-LAM learns more structured, motion-specific, and displacement-calibrated latent actions and provides stronger supervision for downstream policy learning, outperforming state-of-the-art LAMs across simulated and real-world tabletop tasks.

UniG2U-Bench: Do Unified Models Advance Multimodal Understanding?

Unified multimodal models have recently demonstrated strong generative capabilities, yet whether and when generation improves understanding remains unclear. Existing benchmarks lack a systematic exploration of the specific tasks where generation facilitates understanding. To this end, we introduce UniG2U-Bench, a comprehensive benchmark categorizing generation-to-understanding (G2U) evaluation into 7 regimes and 30 subtasks, requiring varying degrees of implicit or explicit visual transformations. Extensive evaluation of over 30 models reveals three core findings: 1) Unified models generally underperform their base Vision-Language Models (VLMs), and Generate-then-Answer (GtA) inference typically degrades performance relative to direct inference. 2) Consistent enhancements emerge in spatial intelligence, visual illusions, or multi-round reasoning subtasks, where enhanced spatial and shape perception, as well as multi-step intermediate image states, prove beneficial. 3) Tasks with similar reasoning structures and models sharing architectures exhibit correlated behaviors, suggesting that generation-understanding coupling induces class-consistent inductive biases over tasks, pretraining data, and model architectures. These findings highlight the necessity for more diverse training data and novel paradigms to fully unlock the potential of unified multimodal modeling.