For a time-homogeneous Markov process, the fixed-lag solution operator \( (T_τf)(x)=\mathbb E[f(X_{t+τ})\mid X_t=x] \) of the Kolmogorov backward equation evolves observables linearly and deterministically, even when the dynamics are stochastic. We approximate this operator using a two-stage method where we first approximate this operator directly from data, without knowledge of the governing equation (e.g., Fourier Neural Operator), and then compress the Galerkin projection onto a finite-dimensional observable space that is fixed in advance or selected variationally. The error analysis traces the learning error of the estimator, the sampling error of the Galerkin inner products, and the invariance and reconstruction properties of the observable space to the computed spectra and forecasts. The sampling error enters only through a multiplicative factor. Near an isolated spectral cluster, the invariance defect of a subspace controls its distance from the target invariant subspace. The forecast error is controlled by the one-step error of the reduced model and the projection error of the observable; when the measure is invariant and the reduced model preserves constants and is stable on mean-zero observables, the bound is uniform in the horizon. For deterministic dynamics, a learning rate for Fourier neural operators (FNOs) gives one explicit bound for the learning error. Numerical experiments illustrate spectral approximation and forecasting, including long-rollout stability and a comparison with extended dynamic mode decomposition (EDMD) when fewer transition pairs than basis functions are observed.
Haocheng Mei, Yuchuan Tian, Ye Yuan, Chao Xu, Allen Chen, Kai Han, Yunhe Wang
Commercial language model APIs return only text, allowing a provider to cut costs by quietly routing a fraction of user requests to a cheaper substitute model while billing for the advertised one. Detecting such partial substitution is challenging because honest providers also alter the output distribution through undocumented decoding and serving choices, such as temperature scaling, sampling truncation, repetition and presence penalties, and default system prompts, forcing an audit to test against a composite null of legitimate configurations rather than a single reference. Our key insight is that these legitimate variations primarily shift response typicality across the entire batch, whereas partial substitution injects individual responses that remain anomalous under the claimed model. Building on this, we introduce API-TAIL, a typicality audit that first absorbs batch-level shifts by aligning a single effective temperature to center standardized surprisal scores across the audited batch, and then flags the endpoint if the number of remaining tail responses exceeds a threshold calibrated across legitimate configurations. Evaluated on real-world API responses and constructed substitution mixtures, API-TAIL controls false alarms across diverse honest providers and detects low-rate partial substitution with a small query budget. Under a common composite calibration, it outperforms the adapted rank- and MMD-based audit baselines.
Linear attention and state space models (SSMs) offer efficient alternatives to softmax attention by maintaining a fixed-size recurrent state, but this design requires careful management to preserve useful historical associations and limit interference. The delta rule helps reduce interference through correction of the value associated with each key, but it does not explicitly account for how related value features are distributed across the state. We observe that a state $\boldsymbol{S}\in\mathbb{R}^{d_k\times d_v}$ can be viewed as a bank of $d_k$ addresses storing $d_v$-dimensional values. While a key-side read $\boldsymbol{S}^\top\boldsymbol{k}$ retrieves the value associated with $\boldsymbol{k}$, a value-side read $\boldsymbol{S}\boldsymbol{e}$ aggregates addresses whose stored value features match the selector $\boldsymbol{e}$. Based on this observation, we propose Dual DeltaNet (DDN), which extends Kimi Delta Attention (KDA) with a two-sided delta rule. The key-side delta rule reads with the current key to correct its associated value, while the complementary value-side delta rule reads with selected features of the current value to reorganize the addresses it occupies. We derive a chunkwise parallel training algorithm and a rank-2 recurrence that increases arithmetic intensity during inference. Compared with KDA, GDN-2, and Mamba-3, DDN achieves the strongest overall performance across language modeling, zero-shot downstream tasks, and retrieval, while incurring modest training and inference overhead relative to KDA. Code: https://github.com/ReichtumQian/DualDeltaNet
Bimanual manipulation with dexterous hands has attracted growing attention in research on robotic action models. However, few studies have developed benchmarks specifically tailored for dexterous manipulation, leaving the dexterous manipulation capabilities of existing models insufficiently characterized. In this paper, we present BiDex-100, a simulation benchmark for bimanual dexterous manipulation that combines broad task coverage, multi-dimensional evaluation, and high-DoF hand embodiments. Concretely, the benchmark comprises 106 tasks organized along five capability axes: generalization, instruction following, limited demonstrations, long horizon, and memory. Each task is paired with an out-of-domain variant featuring controlled visual and spatial changes, allowing systematic assessment of robustness. In addition, the benchmark supports two embodiments and provides 8,080 success-validated teleoperated demonstrations, totaling 6.25 million frames. We evaluate seven recent Vision-Language-Action models under a unified protocol, establishing baselines for capability-specific performance, robustness, and data efficiency. The website is available at https://robbyant-research.github.io/BiDex-100/.
Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.1 and Stable Diffusion 3. Despite its remarkable empirical success, the computational and statistical guarantees of iterative rectified flow have remained largely unexplored. We address this problem by studying c-rectified flow, a cost-aware class of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. The ordinary rectified flow can fail to recover the optimal transport coupling: in a Gaussian case study, the iteration converges to the optimal coupling if and only if the source and target covariance matrices commute. More generally, for a Gaussian to log-concave coupling, the ordinary rectified flow can reach a fixed point after one step from independent initialization. In contrast, under suitable regularity and uniform-integrability assumptions, iterative c-rectified flow always converges to the optimal transport coupling. We further establish quantitative one-step contraction and exponential convergence guarantees under projection-stability assumptions for both quadratic and strongly convex displacement costs. Finally, under a Hölder ball assumption, we develop new minimax-optimal score estimation rates and show that, when combined with iterative c-rectified flow, they yield a rate-optimal estimator of the optimal transport for the dimension \(d \ge 3\) and a nearly parametric rate for \(d=1,2\).
Multivariate time series forecasting presents unique challenges because future variables often co-evolve under shared system dynamics. While existing studies mainly focus on cross-variable dependencies in historical observations, dependencies among future values are much less explored. Specifically, modern forecasting models largely follow the Direct Forecasting (DF) paradigm, generating multi-step forecasts with point-wise objectives that do not explicitly constrain cross-variable structure. In this work, we show that the DF objective is mismatched in the presence of cross-variable and lagged dependencies, revealing an objective gap. To address this issue, we propose \textbf{C}ross-\textbf{V}ariable \textbf{Loss} (CvLoss), a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph. CvLoss penalizes inconsistent edge-wise residual differences over forecast patches, encouraging consistency across both synchronous and asynchronous interactions. Our experiments show that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.
We introduce OvisOCR3, a 0.8B model for a broad range of OCR-related tasks. OvisOCR3 unifies document parsing, general OCR, key information extraction (KIE), document figure captioning, and cross-page table reconstruction in a single model. We train the model on real and synthetic data through continued pretraining and use domain-balanced mid-training to balance supervision across tasks with different data volumes and response lengths. Multi-teacher on-policy distillation transfers expertise from five domain-specific 4B teachers into the shared model, followed by mixed-task reinforcement learning with domain-specific rewards. We compare OvisOCR3 with general-purpose vision-language models and specialized OCR models on public and in-house benchmarks covering all five task families. In these comparisons, it achieves an overall score of 96.74 on OmniDocBench v1.6 and the highest overall scores on PureDocBench, Real5-OmniDocBench, and MDPBench. On OCRBench v2, it ranks first, scoring 65.9 and 61.3 on the English and Chinese splits, respectively. It also outperforms the baselines on OCRBench and all four KIE benchmarks. On DocFigCapBench, it achieves the highest localization F1 and a caption score close to that of Qwen3.8-Max. For cross-page tables, it leads in Relation F1 on CrossTabBench and truncated-table TEDS on MPDocBench-Parse. These results demonstrate that a compact 0.8B model can achieve strong performance across diverse OCR-related tasks. OvisOCR3 is available at https://huggingface.co/ATH-MaaS/OvisOCR3.