RREA¶

relational reflection top performer

Relational Reflection Entity Alignment Xin Mao, Wenting Wang, Yuanbin Wu, Man Lan - CIKM 2020 Paper | models/rrea.py | notebook

Idea in one sentence

The successor of MRAEA: aggregate a neighbour by reflecting it across the hyperplane orthogonal to the relation vector (a norm-preserving Householder reflection), and self-train with turn-based CSLS mutual nearest neighbours.

Architecture¶

%%{init: {'theme':'base','themeVariables':{'fontSize':'14px','fontFamily':'Inter, sans-serif','lineColor':'#7d8590','primaryTextColor':'#e6edf3'}}}%%
flowchart LR
    EF["entity feature"] --> ENC["shared encoder"]
    RF["relation feature"] --> ENC
    ENC --> REF["reflect_r(h_j) = h_j - 2 (h_j . r_hat) r_hat"]
    REF --> ATTN["attention a.[h_i || reflect_r(h_j) || r_hat]"]
    ATTN --> JK["JK concat (depth)"]
    JK --> LOSS["L1 margin loss"]
    JK --> BOOT["turn-based CSLS mutual-NN bootstrap"]
    BOOT -. "pseudo anchors" .-> LOSS
    JK --> EVAL["CSLS"]
    classDef b fill:#3b0764,stroke:#a371f7,stroke-width:2px,color:#f3e8ff;
    class EF,RF,ENC,REF,ATTN,JK,LOSS,BOOT,EVAL b;

Components¶

Relational reflection. When node $i$ aggregates neighbour $j$ via relation $r$, the neighbour is reflected across the hyperplane orthogonal to the unit relation vector $\hat{r}$:

$$\text{reflect}_r(h_j) = h_j - 2\,(h_j \cdot \hat{r})\,\hat{r}$$

a Householder reflection that is norm- and orthogonality-preserving (unlike MRAEA's additive term). - Edge attention $a \cdot [\,h_i \,\|\, \text{reflect}_r(h_j) \,\|\, \hat{r}\,]$, softmax over neighbours (no LeakyReLU). The shared depth-layer encoder is run on an entity-based and a relation-based feature; outputs are concatenated (JK). - Turn-based bootstrap. Between turns, CSLS mutual NN among the unaligned test entities are added as pseudo-anchors. turns: 1 reproduces the basic (non-semi) model.

Results¶

DBP15K zh_en, 30% seed (left-to-right). RREA semi matches/beats the paper - the best in this repo.

	Hit@1	Hit@10	MRR
RREA basic (paper)	0.715	0.929	0.794
This repo (basic)	0.712	0.934	0.793
RREA semi (paper)	0.801	0.948	0.857
This repo (semi)	0.805	0.950	0.859

RREA metrics — Test metrics over training (this repo, zh_en, semi-supervised).

Debugging lessons (the decisive fix)

Match Keras's RMSprop. PyTorch defaults to alpha=0.99; Keras uses rho=0.9, eps=1e-7. Aligning the optimiser added ~2-3 Hit@1 and was the key to reaching the paper.
Reuses MRAEA's graph builder and L1 margin loss - the difference is purely the reflection operator and the optimiser/bootstrap schedule.

References¶

Mao et al., RREA, CIKM 2020.
Mao et al., MRAEA, WSDM 2020.
Lample et al., CSLS, ICLR 2018.