Generating chemically valid 3D molecules is hindered by discrete bond topology: small local bond errors can cause global failures (valence violations, disconnections, implausible rings), especially for drug-like molecules with long-range constraints. Many unconditional 3D generators emphasize coordinates and then infer bonds or rely on post-processing, leaving topology feasibility weakly controlled. We propose Hierarchy-Guided Latent Topology Flow (HLTF), a planner-executor model that generates bond graphs with 3D coordinates, using a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures. On QM9, HLTF achieves 98.8% atom stability and 92.9% valid-and-unique, improving PoseBusters validity to 94.0% (+0.9 over the strongest reported baseline). On GEOM-DRUGS, HLTF attains 85.5%/85.0% validity/valid-unique-novel without post-processing and 92.2%/91.2% after standardized relaxation, within 0.9 points of the best post-processed baseline. Explicit topology generation also reduces "false-valid" samples that pass RDKit sanitization but fail stricter checks.

However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility)

We further discuss the sample complexity for a desired approximation accuracy.

Neural Information Processing Systems http://nips.cc/

We identify three key challenges when using learned dual variables in a primal-dual algorithm.

When n = 2, the constraint matrixA has E = I2 1>2 and G = 1>2 I2. Now we simplify the matrixAby removing a specific set of redundantrows. Furthermore, the rows of A are categorized into a single set so that the criterion in Proposition 3.2 holds true (thedashed lineintheformulation of Aservesasapartition ofthissingle setintotwosets). We use the proof by contradiction. In particular, assume that problem(10) is a MCF problem whenm 3andn 3,Proposition 3.3 implies that the constraint matrixAisTU.

Bandits, Reinforcement Learning