Recipe: propagate_embeddings · Theory: graph signal processing — low-pass filtering on the graph (Stanković et al. 2020, Part II) = SGC/APPNP decoupled propagation · Rail: measurement (does propagation help retrieval?).
Tier 01 produced raw text embeddings. Tier 02 propagates them over the declared citation graph — smoothing each paper’s vector toward its neighbours’. In graph-signal-processing terms this is a low-pass filter on the graph: it attenuates the high-frequency component (idiosyncratic per-paper noise) and keeps the low-frequency component (the shared topic signal a citation cluster agrees on).
The keystone ran one call on the GPU server:
db.propagate_embeddings(
source=papers, embedding_table=embeddings, edge_source=cite_edges,
edge_src_column="src", edge_dst_column="dst",
direction="out", hops=2, weighting="degree_normalized", alpha=0.1,
)and committed the result. This chapter reads it on CPU and measures whether the propagation helped.
from jammi_cookbook import contracts, rails
embeddings = contracts.load_artifact("arxiv.embeddings")
propagated = contracts.load_artifact("arxiv.propagated")
print(f"raw embedding rows: {embeddings.num_rows}")
print(f"propagated embedding rows: {propagated.num_rows}")
print("same dimension preserved: ",
len(embeddings.column("vector")[0]) == len(propagated.column("vector")[0]))raw embedding rows: 4000
propagated embedding rows: 4000
same dimension preserved: TrueThe honest test of a low-pass filter is whether it improves a downstream measurement. We compare same-subject retrieval recall@10 before and after propagation. Both numbers were measured by the keystone on the GPU server (search over each embedding table) and frozen; the delta is the denoising gain.
raw_recall = contracts.golden("arxiv.tier01.recall_at_10").value
prop_recall = contracts.golden("arxiv.tier02.recall_at_10").value
delta = contracts.golden("arxiv.tier02.recall_delta").value
print(f"recall@10 raw: {raw_recall:.3f}")
print(f"recall@10 propagated: {prop_recall:.3f}")
print(f"Δ (denoising gain): {delta:+.3f}")recall@10 raw: 0.538
recall@10 propagated: 0.556
Δ (denoising gain): +0.018Propagation = one low-pass graph filter = one SGC/APPNP layer = the vector-agg over neighbours. One equation, three names, one
propagate_embeddingscall — and theweightingknob is the method choice:
weighting="uniform"= the random-walk operator \(\tilde{D}^{-1}\tilde{A}\) (SGC-flavoured, Wu et al. 2019);weighting="degree_normalized"+alpha= symmetric-normalized propagation with a teleport restart, \((1-\alpha)\hat{A}\,H + \alpha\,X^{(0)}\) — this is APPNP (Gasteiger/Klicpera et al. 2019), which the keystone used;output="jumping_knowledge"= concatenating the signal at every hop.The propagation is deterministic by construction — a fixed
(group, neighbour)f64 fold order, byte-identical across threads, no seeding — so it is the reproducible point on the construct→learn spectrum.
The same low-pass filter runs on Air Routes. The keystone propagated the raw airport embeddings over the declared route graph (the airport↔︎airport flight network) and committed the result; here we read it and measure whether smoothing a node toward its flight-neighbours improves a label-target retrieval.
The keystone ran one call on the GPU server:
db.propagate_embeddings(
source=airports, embedding_table=embeddings, edge_source=route_edges,
edge_src_column="src", edge_dst_column="dst",
direction="undirected", hops=2, weighting="degree_normalized",
)Neptune-contrast. Neptune Analytics ships
pageRank/degree/wccasCALLs over the Air Routes graph; here, propagation-as-low-pass-filter is a Jammi recipe — the same operation over the same route graph, expressed as substrate computation.
air_raw = contracts.load_artifact("air.embeddings")
air_prop = contracts.load_artifact("air.propagated")
print(f"raw airport embedding rows: {air_raw.num_rows}")
print(f"propagated airport embedding rows: {air_prop.num_rows}")
print("same dimension preserved: ",
len(air_raw.column("vector")[0]) == len(air_prop.column("vector")[0]))raw airport embedding rows: 3504
propagated airport embedding rows: 3504
same dimension preserved: TrueThe honest test is a downstream measurement. We compare same-continent retrieval recall@10 before and after propagation. The relevance target is the continent label — independent of the embedding similarity — so a gain is a real denoising result. Continent is near-solved by lat/lon, so this is honestly a teaching label, not a literature benchmark; but the raw→propagated delta over it is a legitimate measured number.
air_raw_recall = contracts.golden("air.tier01.recall_at_10").value
air_prop_recall = contracts.golden("air.tier02.recall_at_10").value
air_delta = contracts.golden("air.tier02.recall_delta").value
print(f"recall@10 raw: {air_raw_recall:.3f}")
print(f"recall@10 propagated: {air_prop_recall:.3f}")
print(f"Δ (denoising gain): {air_delta:+.3f}")recall@10 raw: 0.747
recall@10 propagated: 0.919
Δ (denoising gain): +0.173This is where the Air Routes on-ramp stops (tier 02). Its text is too thin and its label too near-deterministic for a credible learn/predict tier — those live on the ogbn-arxiv keystone above. The on-ramp’s job is done: two graphs constructed and contrasted, a low-pass filter measured, and the tenancy rail made vivid.