History-informed Lagrangian Neural Networks

Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously. Although physics-guided neural networks like Lagrangian Neural Networks (LNNs) guarantee physical plausibility, they generally require complete state inputs and lack adaptability to changing system parameters. To break these limitations, we introduce History-informed Lagrangian Neural Networks (HiLNN). Grounded in the insight that temporal position sequences implicitly encode underlying dynamics, HiLNN employs a recurrent encoder to extract a latent context from history. This context not only reconstructs the unobserved initial velocity but also adaptively modulates the mass matrix, potential energy, and damping coefficients of a structured Lagrangian system. By leveraging a differentiable RK4 rollout scheme, the entire pipeline is optimized end-to-end under multi-step trajectory supervision and energy-consistency regularization. Empirical evaluations across conservative, dissipative, and heterogeneous variable-parameter systems show that HiLNN delivers superior long-term prediction accuracy and maintains precise energy profiles compared to state-of-the-art baselines. The source code is publicly available at https://github.com/yingtian22/History-informed-LNN.

Shackled Dancing: A Bit-Locked Diffusion Algorithm for Lossless and Controllable Image Steganography

Data steganography aims to conceal information within visual content, yet existing spatial- and frequency-domain approaches suffer from trade-offs between security, capacity, and perceptual quality. Recent advances in generative models, particularly diffusion models, offer new avenues for adaptive image synthesis, but integrating precise information embedding into the generative process remains challenging. We introduce Shackled Dancing Diffusion, or SD$^2$, a plug-and-play generative steganography method that combines bit-position locking with diffusion sampling injection to enable controllable information embedding within the generative trajectory. SD$^2$ leverages the expressive power of diffusion models to synthesize diverse carrier images while maintaining full message recovery with $100\%$ accuracy. Our method achieves a favorable balance between randomness and constraint, enhancing robustness against steganalysis without compromising image fidelity. Extensive experiments show that SD$^2$ substantially outperforms prior methods in security, embedding capacity, and stability. This algorithm offers new insights into controllable generation and opens promising directions for secure visual communication.