Hyunmog Kim

Hyunmog Kim

We introduce a spectral-injection diagnostic for measuring which angular frequencies a trained equivariant force-field backbone preserves: inject a controlled angular-frequency perturbation into a molecular force field, attach a lightweight Spectral Prediction Network (SPN) to the frozen backbone, and read off which frequencies are recoverable. On aspirin, a quadratic SPN attached to an L = 2 NequIP backbone recovers the boundary signal at l = 4 but collapses at l = 5: a 11.7x cliff at the predicted drL boundary, with p dropping from 0.913 to 0.078. The same boundary-vs-above contrast persists across n = 4 independently trained backbones (raw-gain delta contrast, hierarchical cluster bootstrap) and is corroborated by a denominator-free injected-residual metric (R2_inj(4) = 0.374 versus R2_inj(5) = 0.006). A finite-degree span theorem calibrates the diagnostic: for a single marked direction, degree-d polynomials of degree-L spherical-harmonic features span exactly H less than or equal to dL with multiplicity-one saturation at the boundary (scoped to single-direction degree-bounded probes, not a function-class upper bound on multi-atom MPNNs). A synthetic C5 calibration plus capacity, activation, and cross-architecture controls rule out parameter count alone as the explanation.

Hyunmog Kim

EDA problems are graph-structured, but not all graph-structured problems call for the same GNN computation. We argue that successful GNN-for-EDA methods are those whose propagation, aggregation, and supervision align with the native algebra of the target task. Concretely: static timing analysis is a max-plus/min-plus recurrence on a topologically ordered DAG, structurally aligned with asynchronous DAG-GNNs; placement is governed by hypergraph wirelength and density penalties and is exploited by differentiable placers rather than by message-passing GNNs alone; routing congestion is a sparse demand-supply field over a layout grid; switching-activity propagation is a probabilistic recurrence on a directed netlist; IR drop is a linear system on the power-delivery network; and analog symmetry extraction is a discrete constraint-prediction problem on schematic graphs. Through these task-by-task alignments we (i) review the GNN architectural toolkit relevant to circuits, (ii) formalize how circuit graphs differ from generic graphs (directed, heterogeneous, multi-scale, with sequential and clock structure), (iii) characterize where current methods succeed and where the algebra-architecture mismatch limits them, and (iv) identify failure modes--stage leakage, proxy-to-signoff gap, calibration, and design-distribution shift--that we believe are likely to dominate the next phase of work. We position the paper as a GNN-for-EDA, task-aligned analysis rather than a comprehensive AI-for-chip-design survey. Continuous SE(3)-equivariant geometric GNNs are usually mismatched to Manhattan digital layout, and LLM-for-RTL, HLS, and RL/diffusion-based topology generation are outside our scope.