A classical problem in continuous sparse Fourier transforms, which dates back to Prony's work in 1795, is to learn a $k$-Fourier-sparse signal $x(t):=\sum_{j=1}^k α_j e^{2 π\mathbf{i} f_j t}$ with arbitrary $k$ frequencies $f_1,\ldots,f_k \in \mathbb{R}$. We consider this learning problem within a fixed time window $t \in [-1,1]$ in the presence of bounded $L_2$ adversarial noise. Because the frequencies $f_1,\ldots,f_k$ can be arbitrarily close, accurately recovering individual frequencies is information-theoretically impossible even under exponentially small noise from Moitra (STOC 2015). This work therefore examines two fundamental questions: If an algorithm uses $\tilde{O}(k)$ frequencies to approximate $f_1,\ldots,f_k$ of $x$, what is the optimal covering error? And how can we efficiently learn the continuous signal $x(t)$ as a whole over the time window? Our main result is an algorithm running in time $\tilde{O}(k)$ that outputs a list $L$ of $\tilde{O}(k)$ frequencies with covering error $O(k)$ --- meaning that for most frequencies $f_j$ of $x$, $L$ guarantees $\min_{\tilde{f} \in L} |f_j-\tilde{f}| = O(k)$ --- and an reconstruction $\tilde{x}(t) \approx x(t)$ over $[-1,1]$. When constrained to outputting $\tilde{O}(k)$ frequencies, this $O(k)$ covering error is nearly optimal: Chen and Price (ICALP 2019) demonstrated two indistinguishable $k$-Fourier-sparse signals separated by distance $\tildeΩ(k^2)$ in the frequency domain, which implies an amortized lower bound of $\tildeΩ(k)$ per frequency. Furthermore, our sample and time complexities are nearly optimal, dramatically improving upon the previous best algorithm by Song, Sun, Weinstein, and Zhang (FOCS 2023), which required $\tilde{O}(k^4)$ samples and $\tilde{O}(k^{4ω})$ running time.
Machine-learning weather models now rival or surpass operational numerical weather prediction (NWP), yet no single model dominates across variables, pressure levels, lead times, or regions, and the returns from ever-larger individual models are diminishing. We present TaiJi (after the yin-yang concept of complementary opposites), a spatiotemporal adaptive ensemble framework that recasts optimal model-weight combination as a learned prediction problem: a lightweight convolutional neural network, conditioned on the recent atmospheric state, predicts at every grid point and lead time affine combination weights and an additive residual for the constituent forecasts. The combiner is trained end-to-end over Pangu-Weather, GraphCast, FuXi, IFS-HRES, and the IFS-ENS ensemble mean, a hybrid set of ML and NWP constituents, at less than a tenth of the cost of training any of its ML constituents. Under the WeatherBench 2 protocol (2020 test year), TaiJi outperforms the strongest baseline in nearly every combination of the eight core variables, lead times up to 10 days and two skill metrics (RMSE and ACC), and this advantage extends to heavy-precipitation extremes. The same state-conditional principle transfers to tropical-cyclone track forecasting: by fusing constituent tracks rather than gridded fields, TaiJi-TC reduces track error relative to the equally weighted multi-model consensus at lead times up to 96 h, by about 10% at 36 h, halves the slow along-track bias shared by all constituents up to 60 h, and lowers landfall position error by 13-15% at 60-84 h. The learned weights vary coherently with latitude, season and lead time rather than following a fixed rule. TaiJi thus offers an inexpensive route to better global forecasts that builds on, rather than replaces, existing forecast models.
Xiao Yang, Aishan Liu, Siyuan Liang, Zonghao Ying, Le Wang, Jiakai Wang, Xianglong Liu, Dacheng Tao
Large language model (LLM) agents increasingly operate in open-world environments where safety risks cannot be fully predefined. However, most existing guardrail mechanisms remain static, relying on fixed rules, prompts, or classifiers that generalize poorly to emerging risks. Here we present EVOLVE, a tool-level self-evolving defense framework that formulates agent security as a process of cumulative security evolution. Inspired by how human societies transform experiences into transferable protective knowledge, EVOLVE externalizes security knowledge into executable guardrail tools that are continuously inherited, independently audited, and iteratively refined through lifelong interaction. Across multiple benchmarks, backbone models, and embodied environments, EVOLVE consistently outperforms existing defenses across diverse risk scenarios with +22\% average F1 score. We further validate the framework in real-world robotic and autonomous agent systems. Our results suggest that scalable agent safety may require continuously evolving defense systems rather than static guardrails.
Protection levels (PLs) bound position errors under specified fault hypotheses and risk budgets, but advanced receiver autonomous integrity monitoring (ARAIM) is formulated for snapshot GNSS estimation rather than the correlated posterior of tightly coupled GNSS/IMU factor graph optimization (FGO). This paper formulates ARAIM solution separation and PL computation on the FGO posterior. Because current-epoch pseudorange factors enter only the current-state block of the fixed-lag information matrix, the fault-excluded position covariance, solution separation, and nominal-bias propagation follow exactly from the linearized current-state marginal, which re-tains correlations with velocity, IMU-bias, and clock states and with historical information. Woodbury updates with selected-output evaluation compute these quantities for fault-free, single-satellite, constellation-wide, and second-order hypotheses with-out repeated full-state inversion or graph reoptimization. Surrounding monitoring layers screen measurements, handle post-fit outliers, and determine PL validity and availability. In two road experiments, both nominal sequences achieve 100% horizontal and vertical empirical bounding over PL-valid epochs, with a maximum error-to-PL ratio of 0.96. Normalized errors show that the posterior covariance alone does not capture slowly varying ranging biases: a covariance-only bound computed from the same posteriors retains no resolvable margin, and strong temporal correlation limits the empirical evidence to consistency checks rather than validation of the integrity budget. On identical Experiment A posteriors, the proposed method reduces fault-hypothesis evaluation and PL solving time by 65.2% relative to direct full-state inversion with matching integrity decisions, and controlled fault injections demonstrate fail-safe PL invalidation while navigation continues.
Feed-forward Gaussian Splatting enables efficient novel view synthesis, but pixel-aligned prediction makes the primitive count grow with image resolution and view count, leading to substantial redundancy and increased computational cost. Non-pixel-aligned methods address this limitation by predicting a fixed number of Gaussians. Without explicit ray and depth constraints, these methods yield misplaced Gaussian centers, causing rendering artifacts under large viewpoint changes. To address this issue, we introduce GeoGSplat, a geometry-grounded feed-forward model that explicitly incorporates geometric priors into the non-pixel-aligned framework. A dual-branch encoder constructs Anchors and Triplane to capture coarse 3D structure and fine-grained scene features, respectively. Subsequently, a hierarchical decoder progressively decodes dense 3D points and Gaussian primitives, enabling 3D reconstruction and novel view synthesis. GeoGSplat surpasses both state-of-the-art pixel-aligned and non-pixel-aligned Gaussian Splatting methods on DTU and NRGBD in terms of novel view synthesis and reconstruction. The advantage of our geometry-grounded paradigm further increases as target viewpoints move farther from the input cameras, demonstrating stronger generalization to large viewpoint changes. Project Page: https://comedy0913.github.io/projects/geogsplat
Zike Wu, Ahmed Hatem, Chintan Trivedi, Wallace Michel Pinto Lira, Xuebin Qin, Lele Wang, Renjie Liao
We tackle the challenge of building real-time interactive video worlds with user-defined behaviors. Such worlds must track object states, apply interaction rules, and render the resulting consequences as users act. Yet existing end-to-end video world models typically learn interaction dynamics within the generator, making it difficult to specify object-level rules and reason about their consequences. In this work, we introduce BoxWorld, which separates interaction reasoning from generative rendering. Given user-specified rules, a coding agent creates a Box World Engine that determines interaction outcomes and exposes the resulting object states through a lightweight interface of layout boxes, persistent object attributes, and dynamic status variables, leaving appearance and physical effects to generative rendering. A Box-State Generative Renderer then renders this evolving state stream into video autoregressively, enabling online control over object motion, state switches, and conditional events. Rendering this state stream is non-trivial: the renderer must respond to object-level state updates in real time while remaining coherent with the generated history. To this end, we introduce a three-stage training strategy that learns object grounding from open-domain videos and state transitions from gameplay videos, both annotated automatically, and finally performs rollout distillation on self-generated histories. We further propose PairedStateBench, a paired benchmark for fine-grained interaction control. BoxWorld substantially outperforms end-to-end world models and remains competitive across multiple public benchmarks. Project page: https://boxworld-web.github.io.
Weiqin Wang, Yile Wang Shenzhen University, Kehao Chen Fuzhou University, Hui Huang Shenzhen University
Test-time reinforcement learning mitigates the reliance on annotated data by using majority voting results as pseudo-labels, emerging as a complementary direction to reinforcement learning with verifiable rewards (RLVR) for improving reasoning ability of large language models (LLMs). However, this voting strategy often induces confirmation bias and suffers from sparse rewards, limiting the overall performance. In this work, we propose subgroup-specific step-wise confidence-weighted pseudo-label estimation (SCOPE), a framework integrating model confidence and dynamic subgroup partitioning to address these issues. Specifically, SCOPE integrates the proposed step-wise confidence into pseudo-label estimation, prioritizing high-quality reasoning paths over simple frequency count. Furthermore, it dynamically partitions the candidate outputs pool into independent subgroups by balancing reasoning quality against exploration diversity. By deriving local consensus via repeat sampling for each subgroup, SCOPE provides diverse supervision targets to encourage broader exploration. We conduct experiments across various models and benchmarks, experimental results show that SCOPE consistently outperforms recent baselines. Notably, SCOPE achieves relative improvements of 13.1% on challenging AIME 2025 and 8.1% on AMC.
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Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表