Message Passing Across the Diagnostic Constellation

The mathematics of how Kronos propagates information between physically related sensors, and why attention weights track the plasma state.

The message-passing update

A GNN layer updates each node representation h_i by aggregating messages from its neighborhood N(i). Kronos uses an attention-weighted aggregation so that the influence of neighbor j on node i scales with how physically relevant j is right now:

# attention-weighted message passing (per layer l)
#   alpha_ij  attention from edge/geometry features
#   a         learnable attention vector; W  linear map
e_ij   = LeakyReLU( a @ concat(W@h_i, W@h_j, edge_ij) )
alpha  = softmax_over_neighbors(e_ij)
h_i_l1 = sigma( sum_j alpha_ij * (W @ h_j) )

Stacking L layers lets information travel up to L hops across the constellation, so a neutron-flux node can be informed by a Thomson-scattering node several edges away if the intervening flux-surface links justify it. Three to four layers are sufficient for the breeder graph; beyond that, over-smoothing washes out node-specific detail.

Attention as physical relevance

The attention weight alpha_ij is not a black box. During a breeder ELM-free negative-triangularity discharge, the coils on the outboard midplane where MHD activity concentrates receive higher attention among themselves; during a burner plug-density excursion, the end-cell diagnostics dominate. Inspecting alpha therefore doubles as an interpretability tool: operators can see which sensors the model is leaning on, and validation checks that those are the physically sensible ones.

Temporal state

Each node also carries a gated recurrent state so the graph is spatio-temporal: message passing handles the spatial structure at one instant, and the gated update carries information across the sub-microsecond-sampled time series L2 provides. This lets the network distinguish a genuine physical transient (coherent across neighbors and time) from single-channel noise (incoherent), which is the same discrimination the anomaly ensemble needs upstream of quench detection.