Vision–language–action (VLA) models often suffer from limited robustness in long-horizon manipulation tasks—where robots must execute extended sequences of actions over multiple time steps to achieve complex goals—due to their inability to explicitly exploit structural symmetries and to react adaptively when such symmetries are violated by environmental uncertainty. To address this limitation, this paper proposes PI-VLA, a symmetry-aware predictive and interactive VLA framework for robust robotic manipulation. PI-VLA is built upon three key symmetry-driven principles. First, a Cognitive–Motor Synergy (CMS) module jointly generates discrete and continuous action chunks together with predictive world-model features in a single forward pass, enforcing cross-modal action consistency as an implicit symmetry constraint across heterogeneous action representations. Second, a unified training objective integrates imitation learning, reinforcement learning, and state prediction, encouraging invariance to task-relevant transformations while enabling adaptive symmetry breaking when long-horizon deviations emerge. Third, an Active Uncertainty-Resolving Decider (AURD) explicitly monitors action consensus discrepancies and state prediction errors as symmetry-breaking signals, dynamically adjusting the execution horizon through closed-loop replanning. Extensive experiments on long-horizon benchmarks demonstrate that PI-VLA achieves state-of-the-art performance, attaining a 73.2% average success rate on the LIBERO benchmark (with particularly strong gains on the Long-Horizon suite) and an 88.3% success rate in real-world manipulation tasks under visual distractions and unseen conditions. Ablation studies confirm that symmetry-aware action consensus and uncertainty-triggered replanning are critical to robust execution. These results establish PI-VLA as a principled framework that leverages symmetry preservation and controlled symmetry breaking to enable reliable and interactive robotic manipulation.

Current patent claim generation systems face three fundamental limitations: poor cross-jurisdictional generalization, inadequate semantic relationship modeling between claims and prior art, and unreliable quality assessment. We introduce a novel three-stage framework that addresses these challenges through relationship-aware similarity analysis, domain-adaptive claim generation, and unified quality assessment. Our approach employs multi-head attention with eight specialized heads for explicit relationship modeling, integrates curriculum learning with dynamic LoRA adapter selection across five patent domains, and implements cross-attention mechanisms between evaluation aspects for comprehensive quality assessment. Extensive experiments on USPTO HUPD dataset, EPO patent collections, and Patent-CE benchmark demonstrate substantial improvements: 7.6-point ROUGE-L gain over GPT-4o, 8.3\% BERTScore enhancement over Llama-3.1-8B, and 0.847 correlation with human experts compared to 0.623 for separate evaluation models. Our method maintains 89.4\% cross-jurisdictional performance retention versus 76.2\% for baselines, establishing a comprehensive solution for automated patent prosecution workflows.

Vision–language–action (VLA) models often suffer from limited robustness in long-horizon manipulation tasks due to their inability to explicitly exploit structural symmetries and to react adaptively when such symmetries are violated by environmental uncertainty. To address this limitation, this paper proposes PI-VLA, a symmetry-aware predictive and interactive VLA framework for robust robotic manipulation. PI-VLA is built upon three key symmetry-driven principles. First, a Cognitive–Motor Synergy (CMS) module jointly generates discrete and continuous action chunks together with predictive world-model features in a single forward pass, enforcing cross-modal action consistency as an implicit symmetry constraint across heterogeneous action representations. Second, a unified training objective integrates imitation learning, reinforcement learning, and state prediction, encouraging invariance to task-relevant transformations while enabling adaptive symmetry breaking when long-horizon deviations emerge. Third, an Active Uncertainty-Resolving Decider (AURD) explicitly monitors action-consensus discrepancies and state prediction errors as symmetry-breaking signals, dynamically adjusting the execution horizon through closed-loop replanning. Extensive experiments demonstrate that PI-VLA achieves state-of-the-art performance, attaining a 73.2% average success rate on the LIBERO benchmark and an 88.3% success rate in real-world manipulation tasks under visual distractions and unseen conditions. Ablation studies confirm that symmetry-aware action consensus and uncertainty-triggered replanning are critical to robust execution. These results establish PI-VLA as a principled framework that leverages symmetry preservation and controlled symmetry breaking to enable reliable and interactive robotic manipulation.

Regular graphs are classical symmetric structures in graph theory, where each vertex has identical degree and the overall topology often exhibits strong automorphism properties. However, practical systems frequently require heterogeneous constraints, which can be modeled by introducing vertex colorings and non-uniform degree requirements, leading to controlled symmetry breaking. In this paper, we investigate two-tone factors in edge-connected regular graphs and claw-free cubic graphs under arbitrary red-blue vertex colorings. Using the framework of parity (g,f)-factors, we establish two main existence results. First, we prove that every λ-edge connected r-regular graph admits a two-tone ({k},{k,k+2})-factor for any coloring, provided that r/λ⩽k⩽r−r/λ, k⩽r−2, and k|G| is even. Second, we show that every 3-edge connected claw-free cubic graph admits a two-tone ({0,1},{2,3})-factor regardless of the coloring configuration. Beyond existence, we provide a constructive algorithm by reducing the parity factor problem to an exact f-factor problem and further to a perfect matching problem via vertex-splitting techniques. We rigorously justify the correctness of this reduction and show that the desired factor can be computed in polynomial time. From a structural perspective, our results reveal that edge-connectivity serves as a stabilizing mechanism that preserves parity feasibility under arbitrary color-induced perturbations, while claw-free constraints enforce local density that prevents parity imbalance. This provides a symmetry-based interpretation of two-tone factors as a balance between global regularity and local asymmetry. These findings contribute to both the theoretical development of factor theory and its algorithmic realization, with potential implications for deterministic network design and resource allocation in structured systems.