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.

Crude oil prices exhibit complex dynamics---such as volatility clustering, asymmetric temporal dependencies, and nonlinear responses to geopolitical and economic shocks---that pose challenges to accurate forecasting. To address this, we propose a hybrid model, GBK-Net, which integrates three complementary components: GARCH for modeling time-varying volatility, BiLSTM for capturing bidirectional temporal dependencies, and Kolmogorov-Arnold Network (KAN) for refining nonlinear relationships. Empirical validation is conducted on 39 years of daily WTI crude oil prices (1986--2025), covering major events such as the 2008 financial crisis and the COVID--19 pandemic. Comparative experiments against benchmark models---including GARCH, EGARCH, LSTM, and CNN--LSTM--KAN---demonstrate that GBK-Net achieves the lowest prediction error (RMSE = 2.49; R² = 0.981), with statistical tests confirming its superiority. We also benchmark nested specifications using approximately unbiased tests [1]. This work contributes a robust forecasting tool for energy economics, with implications for strategic planning, risk hedging, and financial decision-making in volatile energy markets. Unless otherwise noted, we model and evaluate on shifted log-returns to accommodate the 2020 negative-price episode; results using arithmetic returns are reported as robustness checks in the Appendix.