On the Number of Conditional Independence Tests in Constraint-based Causal Discovery

Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests. However, existing algorithms such as the prominent PC algorithm need to perform a large number of independence tests, which in the worst case is exponential in the maximum degree of the causal graph. Despite extensive research, it remains unclear if there exist algorithms with better complexity without additional assumptions. Here, we establish an algorithm that achieves a better complexity of $p^{\mathcal{O}(s)}$ tests, where $p$ is the number of nodes in the graph and $s$ denotes the maximum undirected clique size of the underlying essential graph. Complementing this result, we prove that any constraint-based algorithm must perform at least $2^{Ω(s)}$ conditional independence tests, establishing that our proposed algorithm achieves exponent-optimality up to a logarithmic factor in terms of the number of conditional independence tests needed. Finally, we validate our theoretical findings through simulations, on semi-synthetic gene-expression data, and real-world data, demonstrating the efficiency of our algorithm compared to existing methods in terms of number of conditional independence tests needed.

SEA-Nav: Efficient Policy Learning for Safe and Agile Quadruped Navigation in Cluttered Environments

Efficiently training quadruped robot navigation in densely cluttered environments remains a significant challenge. Existing methods are either limited by a lack of safety and agility in simple obstacle distributions or suffer from slow locomotion in complex environments, often requiring excessively long training phases. To this end, we propose SEA-Nav (Safe, Efficient, and Agile Navigation), a reinforcement learning framework for quadruped navigation. Within diverse and dense obstacle environments, a differentiable control barrier function (CBF)-based shield constraints the navigation policy to output safe velocity commands. An adaptive collision replay mechanism and hazardous exploration rewards are introduced to increase the probability of learning from critical experiences, guiding efficient exploration and exploitation. Finally, kinematic action constraints are incorporated to ensure safe velocity commands, facilitating successful physical deployment. To the best of our knowledge, this is the first approach that achieves highly challenging quadruped navigation in the real world with minute-level training time.

Parallax to Align Them All: An OmniParallax Attention Mechanism for Distributed Multi-View Image Compression

Multi-view image compression (MIC) aims to achieve high compression efficiency by exploiting inter-image correlations, playing a crucial role in 3D applications. As a subfield of MIC, distributed multi-view image compression (DMIC) offers performance comparable to MIC while eliminating the need for inter-view information at the encoder side. However, existing methods in DMIC typically treat all images equally, overlooking the varying degrees of correlation between different views during decoding, which leads to suboptimal coding performance. To address this limitation, we propose a novel $\textbf{OmniParallax Attention Mechanism}$ (OPAM), which is a general mechanism for explicitly modeling correlations and aligned features between arbitrary pairs of information sources. Building upon OPAM, we propose a Parallax Multi Information Fusion Module (PMIFM) to adaptively integrate information from different sources. PMIFM is incorporated into both the joint decoder and the entropy model to construct our end-to-end DMIC framework, $\textbf{ParaHydra}$. Extensive experiments demonstrate that $\textbf{ParaHydra}$ is $\textbf{the first DMIC method}$ to significantly surpass state-of-the-art MIC codecs, while maintaining low computational overhead. Performance gains become more pronounced as the number of input views increases. Compared with LDMIC, $\textbf{ParaHydra}$ achieves bitrate savings of $\textbf{19.72%}$ on WildTrack(3) and up to $\textbf{24.18%}$ on WildTrack(6), while significantly improving coding efficiency (as much as $\textbf{65}\times$ in decoding and $\textbf{34}\times$ in encoding).

Fast Catch-Up, Late Switching: Optimal Batch Size Scheduling via Functional Scaling Laws

Batch size scheduling (BSS) plays a critical role in large-scale deep learning training, influencing both optimization dynamics and computational efficiency. Yet, its theoretical foundations remain poorly understood. In this work, we show that the functional scaling law (FSL) framework introduced in Li et al. (2025a) provides a principled lens for analyzing BSS. Specifically, we characterize the optimal BSS under a fixed data budget and show that its structure depends sharply on task difficulty. For easy tasks, optimal schedules keep increasing batch size throughout. In contrast, for hard tasks, the optimal schedule maintains small batch sizes for most of training and switches to large batches only in a late stage. To explain the emergence of late switching, we uncover a dynamical mechanism -- the fast catch-up effect -- which also manifests in large language model (LLM) pretraining. After switching from small to large batches, the loss rapidly aligns with the constant large-batch trajectory. Using FSL, we show that this effect stems from rapid forgetting of accumulated gradient noise, with the catch-up speed determined by task difficulty. Crucially, this effect implies that large batches can be safely deferred to late training without sacrificing performance, while substantially reducing data consumption. Finally, extensive LLM pretraining experiments -- covering both Dense and MoE architectures with up to 1.1B parameters and 1T tokens -- validate our theoretical predictions. Across all settings, late-switch schedules consistently outperform constant-batch and early-switch baselines.

QARM V2: Quantitative Alignment Multi-Modal Recommendation for Reasoning User Sequence Modeling

With the evolution of large language models (LLMs), there is growing interest in leveraging their rich semantic understanding to enhance industrial recommendation systems (RecSys). Traditional RecSys relies on ID-based embeddings for user sequence modeling in the General Search Unit (GSU) and Exact Search Unit (ESU) paradigm, which suffers from low information density, knowledge isolation, and weak generalization ability. While LLMs offer complementary strengths with dense semantic representations and strong generalization, directly applying LLM embeddings to RecSys faces critical challenges: representation unmatch with business objectives and representation unlearning end-to-end with downstream tasks. In this paper, we present QARM V2, a unified framework that bridges LLM semantic understanding with RecSys business requirements for user sequence modeling.

OneMall: One Architecture, More Scenarios -- End-to-End Generative Recommender Family at Kuaishou E-Commerce

In the wave of generative recommendation, we present OneMall, an end-to-end generative recommendation framework tailored for e-commerce services at Kuaishou. Our OneMall systematically unifies the e-commerce's multiple item distribution scenarios, such as Product-card, short-video and live-streaming. Specifically, it comprises three key components, aligning the entire model training pipeline to the LLM's pre-training/post-training: (1) E-commerce Semantic Tokenizer: we provide a tokenizer solution that captures both real-world semantics and business-specific item relations across different scenarios; (2) Transformer-based Architecture: we largely utilize Transformer as our model backbone, e.g., employing Query-Former for long sequence compression, Cross-Attention for multi-behavior sequence fusion, and Sparse MoE for scalable auto-regressive generation; (3) Reinforcement Learning Pipeline: we further connect retrieval and ranking models via RL, enabling the ranking model to serve as a reward signal for end-to-end policy retrieval model optimization. Extensive experiments demonstrate that OneMall achieves consistent improvements across all e-commerce scenarios: +13.01\% GMV in product-card, +15.32\% Orders in Short-Video, and +2.78\% Orders in Live-Streaming. OneMall has been deployed, serving over 400 million daily active users at Kuaishou.

Coordinate-conditioned Deconvolution for Scalable Spatially Varying High-Throughput Imaging

Wide-field fluorescence microscopy with compact optics often suffers from spatially varying blur due to field-dependent aberrations, vignetting, and sensor truncation, while finite sensor sampling imposes an inherent trade-off between field of view (FOV) and resolution. Computational Miniaturized Mesoscope (CM2) alleviate the sampling limit by multiplexing multiple sub-views onto a single sensor, but introduce view crosstalk and a highly ill-conditioned inverse problem compounded by spatially variant point spread functions (PSFs). Prior learning-based spatially varying (SV) reconstruction methods typically rely on global SV operators with fixed input sizes, resulting in memory and training costs that scale poorly with image dimensions. We propose SV-CoDe (Spatially Varying Coordinate-conditioned Deconvolution), a scalable deep learning framework that achieves uniform, high-resolution reconstruction across a 6.5 mm FOV. Unlike conventional methods, SV-CoDe employs coordinate-conditioned convolutions to locally adapt reconstruction kernels; this enables patch-based training that decouples parameter count from FOV size. SV-CoDe achieves the best image quality in both simulated and experimental measurements while requiring 10x less model size and 10x less training data than prior baselines. Trained purely on physics-based simulations, the network robustly generalizes to bead phantoms, weakly scattering brain slices, and freely moving C. elegans. SV-CoDe offers a scalable, physics-aware solution for correcting SV blur in compact optical systems and is readily extendable to a broad range of biomedical imaging applications.

SpanNorm: Reconciling Training Stability and Performance in Deep Transformers

The success of Large Language Models (LLMs) hinges on the stable training of deep Transformer architectures. A critical design choice is the placement of normalization layers, leading to a fundamental trade-off: the ``PreNorm'' architecture ensures training stability at the cost of potential performance degradation in deep models, while the ``PostNorm'' architecture offers strong performance but suffers from severe training instability. In this work, we propose SpanNorm, a novel technique designed to resolve this dilemma by integrating the strengths of both paradigms. Structurally, SpanNorm establishes a clean residual connection that spans the entire transformer block to stabilize signal propagation, while employing a PostNorm-style computation that normalizes the aggregated output to enhance model performance. We provide a theoretical analysis demonstrating that SpanNorm, combined with a principled scaling strategy, maintains bounded signal variance throughout the network, preventing the gradient issues that plague PostNorm models, and also alleviating the representation collapse of PreNorm. Empirically, SpanNorm consistently outperforms standard normalization schemes in both dense and Mixture-of-Experts (MoE) scenarios, paving the way for more powerful and stable Transformer architectures.

OneMall: One Model, More Scenarios -- End-to-End Generative Recommender Family at Kuaishou E-Commerce

In the wave of generative recommendation, we present OneMall, an end-to-end generative recommendation framework tailored for e-commerce services at Kuaishou. Our OneMall systematically unifies the e-commerce's multiple item distribution scenarios, such as Product-card, short-video and live-streaming. Specifically, it comprises three key components, aligning the entire model training pipeline to the LLM's pre-training/post-training: (1) E-commerce Semantic Tokenizer: we provide a tokenizer solution that captures both real-world semantics and business-specific item relations across different scenarios; (2) Transformer-based Architecture: we largely utilize Transformer as our model backbone, e.g., employing Query-Former for long sequence compression, Cross-Attention for multi-behavior sequence fusion, and Sparse MoE for scalable auto-regressive generation; (3) Reinforcement Learning Pipeline: we further connect retrieval and ranking models via RL, enabling the ranking model to serve as a reward signal for end-to-end policy retrieval model optimization. Extensive experiments demonstrate that OneMall achieves consistent improvements across all e-commerce scenarios: +13.01\% GMV in product-card, +15.32\% Orders in Short-Video, and +2.78\% Orders in Live-Streaming. OneMall has been deployed, serving over 400 million daily active users at Kuaishou.

Scaling Embeddings Outperforms Scaling Experts in Language Models

While Mixture-of-Experts (MoE) architectures have become the standard for sparsity scaling in large language models, they increasingly face diminishing returns and system-level bottlenecks. In this work, we explore embedding scaling as a potent, orthogonal dimension for scaling sparsity. Through a comprehensive analysis and experiments, we identify specific regimes where embedding scaling achieves a superior Pareto frontier compared to expert scaling. We systematically characterize the critical architectural factors governing this efficacy -- ranging from parameter budgeting to the interplay with model width and depth. Moreover, by integrating tailored system optimizations and speculative decoding, we effectively convert this sparsity into tangible inference speedups. Guided by these insights, we introduce LongCat-Flash-Lite, a 68.5B parameter model with ~3B activated trained from scratch. Despite allocating over 30B parameters to embeddings, LongCat-Flash-Lite not only surpasses parameter-equivalent MoE baselines but also exhibits exceptional competitiveness against existing models of comparable scale, particularly in agentic and coding domains.