OpenRaiser/Intern-Atlas huggingface dataset:
Cycles of Well-Linked Sets II: an Elementary Bound for the Directed Grid Theorem
Venue: arXiv cs.DM 2026
Year: 2026

In 2015, Kawarabayashi and Kreutzer proved the Directed Grid Theorem - the generalisation of the well-known Excluded Grid Theorem to directed graphs - confirming a conjecture by Reed, Johnson, Robertson, Seymour and Thomas from the mid-nineties. The theorem states that there is a function $f$ such that every digraph of directed treewidth $f(k)$ contains a cylindrical grid of order $k$ as a butterfly minor. However, the given function grows faster than any non-elementary function of the size of the grid minor. More precisely, it is larger than a power tower whose height depends on the size of the grid. In this paper, we present an alternative proof of the Directed Grid Theorem which is conceptually much simpler, more modular in composition and improves the upper bound for the function $f$ to a power tower of height $22$. A key concept of our proof is a new structure called cycles of well-linked sets (CWS). We show that any digraph of large directed treewidth contains a large CWS, which in turn contains a large cylindrical grid.
Uncertainty-aware Generative Recommendation
Venue: arXiv cs.IR 2026
Year: 2026

Generative Recommendation has emerged as a transformative paradigm, reformulating recommendation as an end-to-end autoregressive sequence generation task. Despite its promise, existing preference optimization methods typically rely on binary outcome correctness, suffering from a systemic limitation we term uncertainty blindness. This issue manifests in the neglect of the model's intrinsic generation confidence, the variation in sample learning difficulty, and the lack of explicit confidence expression, directly leading to unstable training dynamics and unquantifiable decision risks. In this paper, we propose Uncertainty-aware Generative Recommendation (UGR), a unified framework that leverages uncertainty as a critical signal for adaptive optimization. UGR synergizes three mechanisms: (1) an uncertainty-weighted reward to penalize confident errors; (2) difficulty-aware optimization dynamics to prevent premature convergence; and (3) explicit confidence alignment to empower the model with confidence expression capabilities. Extensive experiments demonstrate that UGR not only yields superior recommendation performance but also fundamentally stabilizes training, preventing the performance degradation often observed in standard methods. Furthermore, the learned confidence enables reliable downstream risk-aware applications.
Cross-Architecture Model Diffing with Crosscoders: Unsupervised Discovery of Differences Between LLMs
Venue: arXiv cs.AI 2026
Year: 2026

Model diffing, the process of comparing models' internal representations to identify their differences, is a promising approach for uncovering safety-critical behaviors in new models. However, its application has so far been primarily focused on comparing a base model with its finetune. Since new LLM releases are often novel architectures, cross-architecture methods are essential to make model diffing widely applicable. Crosscoders are one solution capable of cross-architecture model diffing but have only ever been applied to base vs finetune comparisons. We provide the first application of crosscoders to cross-architecture model diffing and introduce Dedicated Feature Crosscoders (DFCs), an architectural modification designed to better isolate features unique to one model. Using this technique, we find in an unsupervised fashion features including Chinese Communist Party alignment in Qwen3-8B and Deepseek-R1-0528-Qwen3-8B, American exceptionalism in Llama3.1-8B-Instruct, and a copyright refusal mechanism in GPT-OSS-20B. Together, our results work towards establishing cross-architecture crosscoder model diffing as an effective method for identifying meaningful behavioral differences between AI models.
U-Former ODE: Fast Probabilistic Forecasting of Irregular Time Series
Venue: arXiv cs.LG 2026
Year: 2026

Probabilistic forecasting of irregularly sampled time series is crucial in domains such as healthcare and finance, yet it remains a formidable challenge. Existing Neural Controlled Differential Equation (Neural CDE) approaches, while effective at modelling continuous dynamics, suffer from slow, inherently sequential computation, which restricts scalability and limits access to global context. We introduce UFO (U-Former ODE), a novel architecture that seamlessly integrates the parallelizable, multiscale feature extraction of U-Nets, the powerful global modelling of Transformers, and the continuous-time dynamics of Neural CDEs. By constructing a fully causal, parallelizable model, UFO achieves a global receptive field while retaining strong sensitivity to local temporal dynamics. Extensive experiments on five standard benchmarks -- covering both regularly and irregularly sampled time series -- demonstrate that UFO consistently outperforms ten state-of-the-art neural baselines in predictive accuracy. Moreover, UFO delivers up to 15$\times$ faster inference compared to conventional Neural CDEs, with consistently strong performance on long and highly multivariate sequences.
Designing Scalable Rate Limiting Systems: Algorithms, Architecture, and Distributed Solutions
Venue: arXiv cs.DC 2026
Year: 2026

Designing a rate limiter that is simultaneously accurate, available, and scalable presents a fundamental challenge in distributed systems, primarily due to the trade-offs between algorithmic precision, availability, consistency, and partition tolerance. This article presents a concrete architecture for a distributed rate limiting system in a production-grade environment. Our design chooses the in-memory cache database, the Redis, along with its Sorted Set data structure, which provides $O(log (N))$ time complexity operation for the key-value pair dataset with efficiency and low latency, and maintains precision. The core contribution is quantifying the accuracy and memory cost trade-off of the chosen Rolling Window as the implemented rate limiting algorithm against the Token Bucket and Fixed Window algorithms. In addition, we explain how server-side Lua scripting is critical to bundling cleanup, counting, and insertion into a single atomic operation, thereby eliminating race conditions in concurrent environments. In the system architecture, we propose a three-layer architecture that manages the storage and updating of the limit rules. Through script load by hashing the rule parameters, rules can be changed without modifying the cached scripts. Furthermore, we analyze the deployment of this architecture on a Redis Cluster, which provides the availability and scalability by data sharding and replication. We explain the acceptance of AP (Availability and Partition Tolerance) from the CAP theorem as the pragmatic engineering trade-off for this use case.
Reliable and Private Anonymous Routing for Satellite Constellations
Venue: arXiv cs.CR 2026
Year: 2026

Shared, dynamic network infrastructures, such as dual-use LEO satellite constellations, pose critical threats to metadata privacy, particularly for state actors operating in mixed-trust environments. This work proposes an enhanced anonymity architecture, evolving the Loopix mix-network, to provide robust security and reliability in these volatile topologies. We introduce three primary contributions: (1) A multi-path transport protocol utilizing $(n, k)$ erasure codes, which is demonstrated to counteract the high link volatility and intermittent connectivity that renders standard mix-networks unreliable. (2) The integration of a computationally efficient Private Information Retrieval (PIR) protocol during route discovery. (3) The introduction of adaptive, centrality-based delay strategies that efficiently mitigate the inherent topological bias of LEO networks, providing a superior anonymity-to-latency trade-off. This mechanism provably prevents metadata leakage at the user-provider directory, mitigating profiling and correlation attacks. We validate this architecture via high-fidelity, packet-level simulations of a LEO constellation. Empirical results show our multi-path transport achieves near-zero message loss, establishing a quantifiable trade-off between reliability and bandwidth overhead. Furthermore, microbenchmarks of the PIR protocol quantify its computational and latency overheads, confirming its feasibility for practical deployment. This work provides a validated blueprint for deployable high-anonymity communication systems, demonstrating the viability of securely multiplexing sensitive operations within large-scale commercial network infrastructures.
Light4D: Training-Free Extreme Viewpoint 4D Video Relighting
Venue: arXiv cs.CV 2026
Year: 2026

Recent advances in diffusion-based generative models have established a new paradigm for image and video relighting. However, extending these capabilities to 4D relighting remains challenging, due primarily to the scarcity of paired 4D relighting training data and the difficulty of maintaining temporal consistency across extreme viewpoints. In this work, we propose Light4D, a novel training-free framework designed to synthesize consistent 4D videos under target illumination, even under extreme viewpoint changes. First, we introduce Disentangled Flow Guidance, a time-aware strategy that effectively injects lighting control into the latent space while preserving geometric integrity. Second, to reinforce temporal consistency, we develop Temporal Consistent Attention within the IC-Light architecture and further incorporate deterministic regularization to eliminate appearance flickering. Extensive experiments demonstrate that our method achieves competitive performance in temporal consistency and lighting fidelity, robustly handling camera rotations from -90 to 90. Code: https://github.com/AIGeeksGroup/Light4D. Website: https://aigeeksgroup.github.io/Light4D.
Evaluating LLM Safety Under Repeated Inference via Accelerated Prompt Stress Testing
Venue: arXiv cs.LG 2026
Year: 2026

Traditional benchmarks for large language models (LLMs) primarily assess safety risk through breadth-oriented evaluation across diverse tasks. However, real-world deployment exposes a different class of risk: operational failures arising from repeated inference on identical or near-identical prompts rather than broad task generalization. In high-stakes settings, response consistency and safety under sustained use are critical. We introduce Accelerated Prompt Stress Testing (APST), a depth-oriented evaluation framework inspired by reliability engineering. APST repeatedly samples identical prompts under controlled operational conditions (e.g., decoding temperature) to surface latent failure modes including hallucinations, refusal inconsistency, and unsafe completions. Rather than treating failures as isolated events, APST models them as stochastic outcomes of independent inference events. We formalize safety failures using Bernoulli and binomial models to estimate per-inference failure probabilities, enabling quantitative comparison of reliability across models and decoding configurations. Applying APST to multiple instruction-tuned LLMs evaluated on AIR-BENCH-derived safety prompts, we find that models with similar benchmark-aligned scores can exhibit substantially different empirical failure rates under repeated sampling, particularly as temperature increases. These results demonstrate that shallow, single-sample evaluation can obscure meaningful reliability differences under sustained use. APST complements existing benchmarks by providing a practical framework for evaluating LLM safety and reliability under repeated inference, bridging benchmark alignment and deployment-oriented risk assessment.
The Arithmetic Singleton Bound on the Hamming Distances of Simple-rooted Constacyclic Codes over Finite Fields
Venue: arXiv cs.IT 2026
Year: 2026

This paper establishes a novel upper bound-termed the arithmetic Singleton bound-on the Hamming distance of any simple-root constacyclic code over a finite field. The key technical ingredient is the notion of multiple equal-difference (MED) representations of the defining set of a simple-root polynomial, which generalizes the MED representation of a cyclotomic coset. We prove that every MED representation induces an upper bound on the minimum distance; the classical Singleton bound corresponds to the coarsest representation, while the strongest among these bounds is defined as the arithmetic Singleton bound. It is shown that the arithmetic Singleton bound is always at least as tight as the Singleton bound, and a precise criterion for it to be strictly tighter is obtained. For irreducible constacyclic codes, the bound is given explicitly by $ω+1$, where $ω$ is a constant closely related to the order of $q$ modulo the radical of the polynomial order. This work provides the first systematic translation of arithmetic structure-via MED representations-into restrictive constraints on the minimum distance, revealing that the Singleton bound may be unattainable not because of linear limitations, but due to underlying algebraic obstructions.
Latent-Variable Learning of SPDEs via Wiener Chaos
Venue: arXiv cs.LG 2026
Year: 2026

We study the problem of learning the law of linear stochastic partial differential equations (SPDEs) with additive Gaussian forcing from spatiotemporal observations. Most existing deep learning approaches either assume access to the driving noise or initial condition, or rely on deterministic surrogate models that fail to capture intrinsic stochasticity. We propose a structured latent-variable formulation that requires only observations of solution realizations and learns the underlying randomly forced dynamics. Our approach combines a spectral Galerkin projection with a truncated Wiener chaos expansion, yielding a principled separation between deterministic evolution and stochastic forcing. This reduces the infinite-dimensional SPDE to a finite system of parametrized ordinary differential equations governing latent temporal dynamics. The latent dynamics and stochastic forcing are jointly inferred through variational learning, allowing recovery of stochastic structure without explicit observation or simulation of noise during training. Empirical evaluation on synthetic data demonstrates state-of-the-art performance under comparable modeling assumptions across bounded and unbounded one-dimensional spatial domains.
PuYun-LDM: A Latent Diffusion Model for High-Resolution Ensemble Weather Forecasts
Venue: arXiv cs.AI 2026
Year: 2026

Latent diffusion models (LDMs) suffer from limited diffusability in high-resolution (<=0.25°) ensemble weather forecasting, where diffusability characterizes how easily a latent data distribution can be modeled by a diffusion process. Unlike natural image fields, meteorological fields lack task-agnostic foundation models and explicit semantic structures, making VFM-based regularization inapplicable. Moreover, existing frequency-based approaches impose identical spectral regularization across channels under a homogeneity assumption, which leads to uneven regularization strength under the inter-variable spectral heterogeneity in multivariate meteorological data. To address these challenges, we propose a 3D Masked AutoEncoder (3D-MAE) that encodes weather-state evolution features as an additional conditioning for the diffusion model, together with a Variable-Aware Masked Frequency Modeling (VA-MFM) strategy that adaptively selects thresholds based on the spectral energy distribution of each variable. Together, we propose PuYun-LDM, which enhances latent diffusability and achieves superior performance to ENS at short lead times while remaining comparable to ENS at longer horizons. PuYun-LDM generates a 15-day global forecast with a 6-hour temporal resolution in five minutes on a single NVIDIA H200 GPU, while ensemble forecasts can be efficiently produced in parallel.
Deep Kernel Fusion for Transformers
Venue: arXiv cs.LG 2026
Year: 2026

Agentic LLM inference with long contexts is increasingly limited by memory bandwidth rather than compute. In this setting, SwiGLU MLP blocks, whose large weights exceed cache capacity, become a major yet under-optimized bottleneck. We propose DeepFusionKernel, a deeply fused kernel that cuts HBM traffic and boosts cache reuse, delivering up to 13.2% speedup on H100 and 9.7% on A100 over SGLang. Integrated with SGLang and paired with a kernel scheduler, DeepFusionKernel ensures consistent accelerations over generation lengths, while remaining adaptable to diverse models, inference configurations, and hardware platforms.
Combinatorial Perpetual Scheduling
Venue: arXiv cs.DS 2026
Year: 2026

This paper introduces a framework for combinatorial variants of perpetual-scheduling problems. Given a set system $(E,\mathcal{I})$, a schedule consists of an independent set $I_t \in \mathcal{I}$ for every time step $t \in \mathbb{N}$, with the objective of fulfilling frequency requirements on the occurrence of elements in $E$. We focus specifically on combinatorial bamboo garden trimming, where elements accumulate height at growth rates $g(e)$ for $e \in E$ given as a convex combination of incidence vectors of $\mathcal{I}$ and are reset to zero when scheduled, with the goal of minimizing the maximum height attained by any element. Using the integrality of the matroid-intersection polytope, we prove that, when $(E,\mathcal{I})$ is a matroid, it is possible to guarantee a maximum height of at most 2, which is optimal. We complement this existential result with efficient algorithms for specific matroid classes, achieving a maximum height of 2 for uniform and partition matroids, and 4 for graphic and laminar matroids. In contrast, we show that for general set systems, the optimal guaranteed height is $Θ(\log |E|)$ and can be achieved by an efficient algorithm. For combinatorial pinwheel scheduling, where each element $e\in E$ needs to occur in the schedule at least every $a_e \in \mathbb{N}$ time steps, our results imply bounds on the density sufficient for schedulability.
Towards Sustainable Investment Policies Informed by Opponent Shaping
Venue: arXiv cs.LG 2026
Year: 2026

Addressing climate change requires global coordination, yet rational economic actors often prioritize immediate gains over collective welfare, resulting in social dilemmas. InvestESG is a recently proposed multi-agent simulation that captures the dynamic interplay between investors and companies under climate risk. We provide a formal characterization of the conditions under which InvestESG exhibits an intertemporal social dilemma, deriving theoretical thresholds at which individual incentives diverge from collective welfare. Building on this, we apply Advantage Alignment, a scalable opponent shaping algorithm shown to be effective in general-sum games, to influence agent learning in InvestESG. We offer theoretical insights into why Advantage Alignment systematically favors socially beneficial equilibria by biasing learning dynamics toward cooperative outcomes. Our results demonstrate that strategically shaping the learning processes of economic agents can result in better outcomes that could inform policy mechanisms to better align market incentives with long-term sustainability goals.
LAMP: Implicit Language Map for Robot Navigation
Venue: arXiv cs.RO 2026
Year: 2026

Recent advances in vision-language models have made zero-shot navigation feasible, enabling robots to follow natural language instructions without requiring labeling. However, existing methods that explicitly store language vectors in grid or node-based maps struggle to scale to large environments due to excessive memory requirements and limited resolution for fine-grained planning. We introduce LAMP (Language Map), a novel neural language field-based navigation framework that learns a continuous, language-driven map and directly leverages it for fine-grained path generation. Unlike prior approaches, our method encodes language features as an implicit neural field rather than storing them explicitly at every location. By combining this implicit representation with a sparse graph, LAMP supports efficient coarse path planning and then performs gradient-based optimization in the learned field to refine poses near the goal. This coarse-to-fine pipeline, language-driven, gradient-guided optimization is the first application of an implicit language map for precise path generation. This refinement is particularly effective at selecting goal regions not directly observed by leveraging semantic similarities in the learned feature space. To further enhance robustness, we adopt a Bayesian framework that models embedding uncertainty via the von Mises-Fisher distribution, thereby improving generalization to unobserved regions. To scale to large environments, LAMP employs a graph sampling strategy that prioritizes spatial coverage and embedding confidence, retaining only the most informative nodes and substantially reducing computational overhead. Our experimental results, both in NVIDIA Isaac Sim and on a real multi-floor building, demonstrate that LAMP outperforms existing explicit methods in both memory efficiency and fine-grained goal-reaching accuracy.
Where Bits Matter in World Model Planning: A Paired Mixed-Bit Study for Efficient Spatial Reasoning
Venue: arXiv cs.LG 2026
Year: 2026

Efficient spatial reasoning requires world models that remain reliable under tight precision budgets. We study whether low-bit planning behavior is determined mostly by total bitwidth or by where bits are allocated across modules. Using DINO-WM on the Wall planning task, we run a paired-goal mixed-bit evaluation across uniform, mixed, asymmetric, and layerwise variants under two planner budgets. We observe a consistent three-regime pattern: 8-bit and 6-bit settings remain close to FP16, 3-bit settings collapse, and 4-bit settings are allocation-sensitive. In that transition region, preserving encoder precision improves planning relative to uniform quantization, and near-size asymmetric variants show the same encoder-side direction. In a later strict 22-cell replication with smaller per-cell episode count, the mixed-versus-uniform INT4 sign becomes budget-conditioned, which further highlights the sensitivity of this transition regime. These findings motivate module-aware, budget-aware quantization policies as a broader research direction for efficient spatial reasoning. Code and run artifacts are available at https://github.com/suraj-ranganath/DINO-MBQuant.
Learning to Manipulate Anything: Revealing Data Scaling Laws in Bounding-Box Guided Policies
Venue: arXiv cs.RO 2026
Year: 2026

Diffusion-based policies show limited generalization in semantic manipulation, posing a key obstacle to the deployment of real-world robots. This limitation arises because relying solely on text instructions is inadequate to direct the policy's attention toward the target object in complex and dynamic environments. To solve this problem, we propose leveraging bounding-box instruction to directly specify target object, and further investigate whether data scaling laws exist in semantic manipulation tasks. Specifically, we design a handheld segmentation device with an automated annotation pipeline, Label-UMI, which enables the efficient collection of demonstration data with semantic labels. We further propose a semantic-motion-decoupled framework that integrates object detection and bounding-box guided diffusion policy to improve generalization and adaptability in semantic manipulation. Throughout extensive real-world experiments on large-scale datasets, we validate the effectiveness of the approach, and reveal a power-law relationship between generalization performance and the number of bounding-box objects. Finally, we summarize an effective data collection strategy for semantic manipulation, which can achieve 85\% success rates across four tasks on both seen and unseen objects. All datasets and code will be released to the community.