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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Do Temporal Link Predictors Need Learned Memory? A Smoothed-Count Baseline with a Handful of Parameters

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Chair of Machine Learning for Complex Networks Center for Artificial Intelligence and Data Science (CAIDAS) Julius-Maximilians-Universität Würzburg, DE

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Open paper AskPDF arXiv

Many temporal link predictors summarize past interactions through learned node representations. We examine whether simple counts of recurring interaction patterns can provide competitive predictions without learning these representations. We propose a temporal link predictor based on statistical language modelling. It pools transition and co-occurrence counts across sources to predict links that a source has never formed. We smooth sparse estimates using destination frequencies or Kneser-Ney continuation counts. A shared log-linear rule combines these estimates with popularity, source history, and recency, without node embeddings. In our main evaluation, the model achieves the highest MRR among the compared methods on 7 out of 16 datasets from TGB and TGB-Seq. It also outperforms EdgeBank and Base3 on all 16 datasets and the heuristic family on 14. These gains extend to datasets designed to limit repeated edges. With only 9--13 learned parameters, our model provides a simple and competitive baseline for evaluating future neural temporal link predictors.

Abstract

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