Graph-based collaborative filtering has advanced by modeling higher-order interactions, yet performance remains constrained by underlying geometric assumptions and propagation schemes. User-item interaction graphs typically exhibit pronounced topological heterogeneity, whereas existing methods rely on a fixed, homogeneous geometry and employ tangent space aggregation. To address these fundamental limitations, this paper introduces Adaptive Geometric Collaborative Filtering (AGCF), a novel method rooted in Hamiltonian dynamics, which reframes representation learning as a physical process evolving on a time-varying manifold. AGCF is distinguished by an integrated design comprising: (1) a learnable, node-dependent Riemannian metric that construct a continuous heterogeneous manifold aligned with local topology; (2) unified dynamic trajectories that achieve intrinsic propagation without tangent space approximations; (3) a channel-wise metric that captures semantic anisotropy in the feature space. We rigorously prove global existence and uniqueness of the induced dynamics and explain the mechanism enabling long-range information propagation. Extensive experiments on five benchmark datasets show consistent gains over representative baselines.

The application of Reinforcement Learning (RL) in Electronic Design Automation (EDA), particularly for chip placement, has attracted considerable attention in recent years. While existing machine learning (ML)-based approaches have achieved notable progress, they predominantly focus on generating optimal layouts in a single attempt, often producing solutions that require subsequent refinement. To address this limitation, we propose RollPlace, a novel and generalized macro placement framework. RollPlace adopts a two-stage optimization strategy: generating initial placement solutions via machine learning methods or heuristic-based strategies, and refining these layouts efficiently by adjusting specific macros derived from the initial stage. This strategy circumvents the sequential generation constraints inherent in traditional RL-based placement methods. Furthermore, RollPlace seamlessly integrates Monte Carlo Tree Search (MCTS) to balance exploration and exploitation, and employs a rollout mechanism for efficient local search. Extensive experiments on the ISPD 2005 benchmark demonstrate that RollPlace outperforms state-of-the-art methods. Additionally, end-to-end experimental results based on OpenROAD across 19 benchmarks show that RollPlace excels in multiple metrics. The proposed framework offers a robust and scalable solution for addressing the growing complexity of modern chip design challenges.