Semi-Supervised Classification with Graph Convolutional Networks
2017 · paper · AI and machine learning
Presents a convolutional neural network operating directly on graphs, motivated by an approximation of spectral graph convolutions, for classifying nodes when few labels are available. It scales linearly with edges and outperforms related methods on citation networks and a knowledge graph.
Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.
4 findings
Substance Eq. 1 prints "L_reg = Σ_{i,j} A_ij‖f(X_i) − f(X_j)‖² = f(X)ᵀΔf(X)"; summing over all ordered pairs (i,j) with symmetric A gives 2·f(X)ᵀΔf(X).
- p. 1 Eq. 1
Aij∥f(Xi) −f(Xj)∥2 = f(X)⊤∆f(X)
Only the authors can say what is right here.
Judge's note: Checked Eq. 1 on the page 1 image: the sum is subscripted i,j with no restriction, and A belongs to an undirected graph (so it is symmetric), with Δ = D − A and D_ii = Σ_j A_ij. My own working: Σ_ij A_ij(f_i² − 2f_i f_j + f_j²) = Σ_i d_i f_i² + Σ_j d_j f_j² − 2fᵀAf = 2fᵀ(D−A)f. The equality as printed is therefore off by a factor of 2; it would hold only if the sum ran over unordered pairs, or with a factor 1/2. In the loss the constant can be absorbed into λ, so the practical effect is small.
Second check: another model agreed
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Substance Table 1 gives the NELL label rate as "0.001", but the text says NELL uses "only a single labeled example per class" with 210 classes, and label rate is defined as training labels divided by total nodes: 210/65,755 ≈ 0.0032.
- p. 5 Table 1, NELL row
0.001
- p. 6 Section 5.1, NELL paragraph
only a single labeled example per class in the training set
- p. 5 Section 5.1 label-rate definition
Label rate denotes the number of labeled nodes that are used for training divided by the total number of nodes
Only the authors can say what is right here.
Judge's note: Page 5 defines label rate as the number of labeled training nodes divided by the total number of nodes. Table 1 lists NELL with 65,755 nodes, 210 classes and a rate of 0.001. Page 6 says a single labeled example per class. The other rows agree with 20 labels per class (Citeseer 120/3327 = 0.036, Cora 140/2708 = 0.052, Pubmed 60/19717 = 0.003), but NELL gives about 0.003, not 0.001. Computing over entity nodes only (210/9,891 ≈ 0.021) does not reconcile it either. The table caption says the statistics are as reported in Yang et al. (2016), so the value may be copied from there. Only the authors can say which figure is right.
Second check: another model agreed
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Substance Appendix A.1: the karate club graph "contains 34 nodes, connected by 154 (undirected and unweighted) edges".
- p. 11 Appendix A.1
connected by 154 (undirected and unweighted) edges
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: Zachary's karate club network has 34 nodes and 78 undirected edges. Page 11 prints 154. That is close to twice 78, which suggests each edge was counted in both directions while being described as undirected. 154 undirected edges on 34 nodes would mean an average degree of about 9. Nothing in the files settles the correct count; the authors would need to confirm it.
Second check: another model agreed
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Wording Page 2: "θ′ ∈ R^K is now a vector of Chebyshev coefficients", but Eqs. 4 and 5 sum θ′_k T_k for k = 0 to K, which is K+1 coefficients.
- p. 2 Section 2.1, text after Eq. 4
θ′ ∈ RK is now a vector of Chebyshev coefficients
Judge's note: The page 2 image shows that Eqs. 4 and 5 both run from k=0 to K, and the text declares θ′ ∈ R^K. Counting the indices 0..K gives K+1 entries, so the vector should be in R^(K+1). This is a dimension/notation slip; the method is unaffected.
Second check: another model agreed
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2 minor (typos and the like; most checked by the judge only)
Typo Page 1: "λ is a weighing factor" should read "weighting factor".
- p. 1 Section 1, after Eq. 1
λ is a weighing factor
Judge's note: The page 1 image shows "λ is a weighing factor". λ weights the regularisation term, so 'weighting' is the intended word. This is cosmetic.
Second check: none (judge only)
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Typo The Duvenaud et al. (2015) reference lists "Jorge Iparraguirre, Rafael Bombarell".
- p. 9 References, Duvenaud et al. 2015
Rafael Bombarell
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the co-authors' names are Rafael Gómez-Bombarelli and Jorge Aguilera-Iparraguirre. The page 9 image shows the spelling "Rafael Bombarell" and "Jorge Iparraguirre", so this is not an extraction artefact.
Second check: none (judge only)