KoopmanFlow: Spectrally Decoupled Generative Control Policy via Koopman Structural Bias

Generative Control Policies (GCPs) show immense promise in robotic manipulation but struggle to simultaneously model stable global motions and high-frequency local corrections. While modern architectures extract multi-scale spatial features, their underlying Probability Flow ODEs apply a uniform temporal integration schedule. Compressed to a single step for real-time Receding Horizon Control (RHC), uniform ODE solvers mathematically smooth over sparse, high-frequency transients entangled within low-frequency steady states. To decouple these dynamics without accumulating pipelined errors, we introduce KoopmanFlow, a parameter-efficient generative policy guided by a Koopman-inspired structural inductive bias. Operating in a unified multimodal latent space with visual context, KoopmanFlow bifurcates generation at the terminal stage. Because visual conditioning occurs before spectral decomposition, both branches are visually guided yet temporally specialized. A macroscopic branch anchors slow-varying trajectories via single-step Consistency Training, while a transient branch uses Flow Matching to isolate high-frequency residuals stimulated by sudden visual cues (e.g., contacts or occlusions). Guided by an explicit spectral prior and optimized via a novel asymmetric consistency objective, KoopmanFlow establishes a fused co-training mechanism. This allows the variant branch to absorb localized dynamics without multi-stage error accumulation. Extensive experiments show KoopmanFlow significantly outperforms state-of-the-art baselines in contact-rich tasks requiring agile disturbance rejection. By trading a surplus latency buffer for a richer structural prior, KoopmanFlow achieves superior control fidelity and parameter efficiency within real-time deployment limits.

Cascading Hierarchical Networks with Multi-task Balanced Loss for Fine-grained hashing

With the explosive growth in the number of fine-grained images in the Internet era, it has become a challenging problem to perform fast and efficient retrieval from large-scale fine-grained images. Among the many retrieval methods, hashing methods are widely used due to their high efficiency and small storage space occupation. Fine-grained hashing is more challenging than traditional hashing problems due to the difficulties such as low inter-class variances and high intra-class variances caused by the characteristics of fine-grained images. To improve the retrieval accuracy of fine-grained hashing, we propose a cascaded network to learn compact and highly semantic hash codes, and introduce an attention-guided data augmentation method. We refer to this network as a cascaded hierarchical data augmentation network. We also propose a novel approach to coordinately balance the loss of multi-task learning. We do extensive experiments on some common fine-grained visual classification datasets. The experimental results demonstrate that our proposed method outperforms several state-of-art hashing methods and can effectively improve the accuracy of fine-grained retrieval. The source code is publicly available: https://github.com/kaiba007/FG-CNET.