HAWKEYE: Seeing One Layer Deeper -- A Cohesion-Aware Structural Channel for Temporal Link Prediction

Jiacheng Ding; Xiaofei Zhang

cs.DBAug 24, 2026

HAWKEYE: Seeing One Layer Deeper -- A Cohesion-Aware Structural Channel for Temporal Link Prediction

Authors: Jiacheng Ding, Xiaofei Zhang

Organizations: Department of Computer Science The University of Memphis Memphis, Tennessee, USA

Abstract

State-of-the-art temporal-link-prediction (TLP) models are, in essence, multi-channel information aggregators: they combine an interaction-history channel, a time-encoding channel, and a structure channel. The first two have been refined relentlessly; the structure channel remains a crude afterthought -- DyGFormer encodes it as a 1--2-bit neighbour-cooccurrence count. We begin with a measurement: on sparse temporal graphs the classical 1-hop common-neighbour signal is near-random (discriminative AUC $\approx 0.50$ ), because two nodes almost never share a direct neighbour; the genuinely discriminative signal lies one hop deeper -- the 2-hop cohesive bridge, whose discAUC reaches 0.73--0.98, on both bipartite and non-bipartite graphs. Motivated by this, we propose HAWKEYE, a cohesion-aware structural channel that incrementally maintains the classical k-family of cohesiveness indicators (degree $\to$ k-core $\to$ k-truss) and forms 2-hop cohesive-bridge features. HAWKEYE is a drop-in replacement for a temporal-graph model's native structure channel, with no change to the backbone. Swapping HAWKEYE into DyGFormer improves test AP/MRR over the cooccurrence channel by +0.6 to +10.8 points across six multi-seed-validated datasets (uci, enron, USLegis, CanParl, reddit, mooc). On the bipartite recommendation benchmark tgbl-subreddit, a 3-seed single-pass struct-only ablation shows HAWKEYE nearly doubling the baseline test MRR (0.103 $\pm$ 0.003 $\to$ 0.204 $\pm$ 0.005, +10.1 points across all three seeds); the streaming pipeline scales to the 67M-edge tgbl-flight in five minutes per pass. We further characterise when it helps: the gain tracks a graph's training-free 2-hop discAUC and vanishes on degenerate or saturated graphs -- a predictable boundary. All code, data, and figure-generation scripts are released.

Figures & tables

Figure 1. Running example (used throughout the paper). In a corporate email network, Alice (

u

) and Bob (

v

) have never emailed each other, so the 1-hop common-neighbour count is

\mathrm{CN}=0

; a cooccurrence-based structure channel sees no signal. Yet two 2-hop paths connect them: Alice–Carol–Dan and Alice–Eve–Grace, where Dan (core

5

) and Grace (core

4

) are Bob’s direct neighbours and Carol, Eve are the length-two intermediaries from Alice. Hawkeye reads exactly these bridges and correctly rates Alice–Bob as a likely next-email pair. Section 3 shows this configuration is the typical informative pair on sparse temporal graphs; Section 4 explains how the cache and the slot encoder make Alice’s, Bob’s, and the intermediaries’ coreness available at query time; and § 5.6 returns to this example in the case study.

TGB benchmarks (streaming discAUC sweep, § 3 setup)
dataset	density / type	1-hop	2-hop	2-hop $\times$ c
tgbl-uci	sparse	0.50	0.76	0.75
tgbl-enron	sparse	0.50	0.73	0.71
tgbl-wiki	sparse	0.50	0.85	0.83
tgbl-subreddit	medium, bipartite	0.50	0.96	0.96
tgbl-coin	denser	0.75	0.77	0.77

Table 1. Discriminability AUC of 1-hop vs. 2-hop structural signals (discAUC

=0.50

is random). 1-hop CN is random on sparse graphs; the 2-hop cohesive bridge is strongly discriminative.

Figure 2. Hawkeye per-batch timing, threaded with the Alice/Bob running example. Gray boxes are CPU work (Cohesion Cache + slot-feature extraction), blue boxes are GPU work (Cohesion Slot Encoder + unchanged DyGFormer). Orange badges P1–P8 mirror the steps of Algorithm 2 ; the orange feedback arrow is the “predict-then-advance” contract that commits the batch’s edges after they have been scored.

component	time	space
adjacency maintenance	$O(1)$ /edge	$O(N{+}M)$
degree update	$O(1)$ /edge	$O(N)$
core-number update	$O(\|S\|)$ /edge	$O(N)$
trussness update (opt.)	up to $O(m^{1.5})$	$O(M)$
2-hop bridge extraction	$O(d_{u}d_{\max})$ /query	$O(d_{\max})$ transient
Cohesion Slot Encoder	$O(d_{\mathrm{feat}}\!\cdot\!\text{ch})$ /slot	$\sim\!10^{3}$ params

Table 2. Per-edge / per-query overhead of Hawkeye over the backbone.

|S|

is the (small) core-affected set;

d_{u},d_{\max}

are degrees.

dataset	source	nodes	edges	$\bar{d}$	type
tgbl-wiki	TGB	$9{,}227$	$157{,}474$	$4.0$	bipartite
tgbl-uci	TGB	$1{,}899$	$59{,}835$	$14.6$	non-bipartite
tgbl-enron	TGB	$184$	$125{,}235$	$24.1$	non-bipartite
tgbl-subreddit	TGB	$10{,}984$	$672{,}447$	$14.3$	bipartite
tgbl-lastfm	TGB	$1{,}980$	$1.29$ M	$156.6$	bipartite
tgbl-review	TGB	$352{,}637$	$4.87$ M	$26.8$	bipartite

Table 3. Dataset statistics used in this paper. Counts are direct from the released edge files.

\bar{d}

is the average static degree : distinct neighbours per node over the full stream,

\bar{d}=2|E_{\mathrm{static}}|/|\mathcal{V}|

— the quantity that governs the sparsity mechanism of § 3 (the 1-hop CN degenerates when

\bar{d}\ll\sqrt{|\mathcal{V}|}

). TGB datasets above the rule are used for the main DyGFormer

\,+\,

Hawkeye results; the lower TGB block lists the large-graph datasets used in the scalability experiments (§ 5.4 ); DGB datasets follow the DyGLib ( 35 ) release.

configuration	uci	enron	CanParl	USLegis	mooc	reddit
DyGFormer (none)	$0.838\!\pm\!.001$	$0.771\!\pm\!.007$	$0.680\!\pm\!.045$	$0.715\!\pm\!.005$	$0.797\!\pm\!.001$	$0.966\!\pm\!.000$
DyGFormer (cooccur)	$0.956\!\pm\!.000$	$0.917\!\pm\!.000$	$0.708\!\pm\!.008$	$0.719\!\pm\!.001$	$0.857\!\pm\!.001$	$\mathbf{0.975\!\pm\!.014}$
DyGFormer ( $+$ Hawkeye )	$0.942\!\pm\!.004$	$0.924\!\pm\!.001$	$0.816\!\pm\!.001$	$0.768\!\pm\!.004$	$0.915\!\pm\!.007$	$0.974\!\pm\!.014$
DyGFormer ( $\oplus$ Hawkeye )	$\mathbf{0.962\!\pm\!.001}$	$\mathbf{0.930\!\pm\!.001}$	$\mathbf{0.821\!\pm\!.002}$	$\mathbf{0.770\!\pm\!.003}$	$\mathbf{0.917\!\pm\!.003}$	$0.966\!\pm\!.000$

Table 4. Structure-channel swap-in on DyGFormer (DGB protocol, test AP). All entries 3-seed mean

\pm

std under the current code. Bold : best per dataset. tgbl-wiki (TGB MRR) is reported separately in Table 6 .

dataset	edges	baseline	with Hawkeye	gain
tgbl-subreddit	672K	$0.103\!\pm\!.003$	$\mathbf{0.204\!\pm\!.005}$	$\mathbf{+10.1}^{\bigstar}$
tgbl-review	$4.87$ M	$0.283\!\pm\!.002$	$0.275^{\,1}$	$-0.8$
tgbl-lastfm	$1.29$ M	$0.008$	$0.007$	$\approx 0$

Table 5. Large-graph effectiveness. Single-pass struct-only training, 1 h cap. “Baseline” uses degree only with no pairwise computation; “with Hawkeye ” adds

k

-core and the 2-hop cohesive bridge. Gain is in test-MRR points.

method	test MRR
TGN †	0.396
TGAT	0.508
DyGFormer (none)	0.537
GraphMixer	0.549
EdgeBank †	0.571
DyGFormer (cooccur)	0.779

Table 6. Comparison on tgbl-wiki (test MRR). † cited from the TGB leaderboard / original papers.

Figure 3. Per-dataset Hawkeye swap-in gain over the DyGFormer (cooccur) baseline (test AP for DGB, test MRR for wiki );

\bigstar

= 3-seed validated (std

\leq 0.011

). Double-digit gains on CanParl (

+10.8

) and tgbl-subreddit (

+10.1

), mid single-digit on mooc (

+5.8

) and USLegis (

+4.8

), small but consistent on sparse uci / enron ; on saturated reddit and degenerate tgbl-lastfm the gain correctly vanishes, tracking the training-free 2-hop discAUC predictor (§ 3 ).

dataset	2-hop discAUC	Hawkeye gain (pts)
reddit	$\mathbf{0.98}$	$\approx 0$ (cooccur sat.) ★
tgbl-subreddit	$\mathbf{0.96}$	$\mathbf{+10.1}^{\bigstar}$
mooc	$\mathbf{0.94}$	$\mathbf{+5.8}^{\bigstar}$
tgbl-wiki	$0.85$	$+2.8$ (legacy)
tgbl-uci	$0.76$	$+0.6^{\bigstar}$
tgbl-enron	$0.73$	$+1.3^{\bigstar}$

Table 7. Training-free 2-hop discAUC (Table 1 ) vs. measured Hawkeye gain. Direct in the sparse/bipartite regimes; in the near-complete regime ( CanParl , USLegis ) the raw 2-hop count saturates but the trained, core-weighted Hawkeye still wins. ★ 3-seed mean

\pm

std. tgbl-coin and UNvote have discAUC only (no trained gain) and are omitted.

Strategy	uci	mooc	reddit
baseline	$1.00\times$	$1.00\times$	$1.00\times$
pinned $+$ async	$1.11\times$	$1.00\times$	$1.04\times$
prefetcher	$1.21\times$	$1.03\times$	$1.07\times$
prefetch $\times 2$	$1.08\times$	$1.00\times$	$1.15\times$
precompute	$\mathbf{3.47\times}$	$\mathbf{3.04\times}$	$\mathbf{3.16\times}$

Table 8. Wall-clock speedup over the sequential baseline (three simulated epochs of

50

batches). Only precompute is universally robust.

configuration	time / epoch (s)	overhead
DyGFormer (none, no struct.)	5.4	$-76\%$
DyGFormer (cooccur, baseline)	22.4	reference
DyGFormer $+$ Hawkeye (gev, replace)	40.2	$+79\%$
DyGFormer $\oplus$ Hawkeye (both, add)	57.1	$+154\%$

Table 9. Measured per-epoch wall time on uci (3-seed mean). Overhead is relative to the DyGFormer baseline (cooccur).

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