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Virtuous AI > Graph Neural Networks GNN > Flashcards

Graph Neural Networks GNN Flashcards

1
Q

GNN pooling

A
  • if missing node info, pool edge info, etc…
  • aggregation - usually sum()
  • like global pool is like CNN global average pooling
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2
Q

message passing between parts of graphs

A

pool neighboring info to influence eachothers updated embeddings

  1. gather all neighboring “messages”
  2. aggregate all messages via agg. function (like sum)
  3. messages passed through an update function
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3
Q

XAI GNN Methods

A
  1. Gradient: use gradient as approximation of feature importance
  2. Perturbation: use output variation with respect to the perturbation of input (what attributes need to be kept to reconstruct graph)
  3. Surrogate: train a surrogate model using neighboring areas
  4. Decomposition: decompose prediction into several scores representing importance score
  5. Generation: learn to generate graphs that achieve optimal prediction scores
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4
Q

Perturbation GNN method

A

use output variation with respect to the perturbation of input (what attributes need to be kept to reconstruct graph)

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5
Q

Surrogate GNN method

A

train a surrogate model using neighboring areas

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6
Q

Decomposition GNN method

A

decompose prediction into several scores representing importance score

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7
Q

ordering GNN update

A

can do a weave fashion: node→node(linear), edge→edge(linear), edge→node(edge layer), node→edge(node layer)

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8
Q

global representations

A
  • nodes far apart cannot transfer info (k-layers will propagate at most k-steps)
  • overcome using the master node global context vector connected to all other nodes and edges
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9
Q

multigraphs

A

multi-edge graphs where a pair of nodes can share multiple types of edges

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10
Q

nested graph

A

a hypernode graph where nodes represent a graph

  • useful for representing hierarchical info
  • example - node representing molecules and edges represent interactions if way of transforming
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11
Q

hypergraph

A

edge connected to multiple nodes

  • example - hyper-edge that connects to all nodes in a community
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12
Q

sampling/batching GNN

A
  • poses a problem b/c context matters in sub-selection
  • method 1: to preserve the structure, you could randomly sample uniform num nodes
    • then add neighboring nodes of distance, including their edges
    • each neighborhood is considered a graph and GNN trained on batches of these subgraphs
    • mask to consider node-set
  • method 2: randomly sample a single node, expand its neighborhood to distance k, then pick the other node within the expanded set
    • operations terminated once a certain number of edges or subgraphs constructed
    • constant size neighborhoods, picking the initial node-set, then subsampling a constant num node (e.g. random walk or Metropolis)
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13
Q

4 ways of sampling a graph

A
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14
Q

inductive bias in graphs

A
  • identify patterns in the data and adding modeling components to take advantage of these attributes
  • GNN should preserve explicit relationships (adjacency matrix)
  • GNN should also preserve graph symmetries (permutation invariance)
  • graphs structure great where interactions b/w entities is important
  • GNN should transform on sets → operation order on nodes and edges should not matter
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15
Q

aggregation operation

A
  • want similar inputs providing similar aggregated outputs and vice versa
    • take a variable number of inputs and output the same
  • sum, mean, max, variance
    • mean() is good when you need normalized views
    • max() is good when you want to highlight salient features
    • sum() is a good balance and is used in practice more often
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16
Q

bag of subgraphs

A
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17
Q

graphs dual

A
  • edge and node predictions often reduce to the same problem - “an edge prediction task on a graph G can be phrased as a node-level prediction on Gs dual
  • to obtain Gs dual, convert nodes to edges (and edges to nodes)
  • example - to solve edge classification on G, we can think about doing graph convolutions on Gs dual
18
Q

significance of matrix multiplication on a graph

A
  • applying multiplication multiply times propogates information
  • Example - A^2, all connected nodes continue to receive information as a_i1*
19
Q

graph attention network

A
  • use weighted sum in permutation invariant fashion to communicate info between graph attributes
  • method 1: scalar scoring function that assigns weights based on pairs b/w nodes (how relevant neightboring node is to center node
  • method 2: inner product and nodes are transformed before scoring into query and key vectors via linear map
  • scoring weights can be used as a measure of importance of an edge in relation to a task
20
Q

relationship b/w transformer and GNN

A
  • the transformer models several elements (e.g. tokens) as nodes in a fully connected graph
  • attention mechanism is assigning edge embeddings to each node-pair which are used to compute attention weights
  • the difference - GNN assumes sparse pattern
21
Q

GNN XAI

A
  • varies from graph to graph
  • GNNExplainer extracts most relevant subgraph
  • attribution assign ranked importance values to parts of the graph
22
Q

generative graph modeling

A
  • method 1: generate new graphs by sampling from learned distributions or completing a graph given a starting point
  • example - novel molecular graphs with desirable attributes
  • example solution - graphVAE learns connectivity by treating adjacency matrix like an image
  • method 2: build graph sequentially starting w/ a graph and applying addition, subtraction, …. of nodes and edges repeatedly
23
Q

node-order equivariance

A
  • algorithms should not depend on the ordering of the nodes
  • graphs have no inherent ordering present amonst nodes (e.g. contrasting with images with coordinates)
24
Q

problems that can be defined over graphs

A
25
Q

node representation learning

A

map individual neodes to fixed-size real-valued vectors
* generally, compute nodes calculated in iterative process
* each iteration equals a layer in standard ANNs
* params
1. gaph G
2. nodes V
3. edges E
4. node v at k iteration h_v^(k)
5. feature x for node v

26
Q

graph Laplacian

A
  • Laplacian is square (n x n)
    • L = D - A
    • shows up on random walks, spectral cluster, and many more
27
Q

degree of a node

A
  • is the number of edges incident at v
    • D = Sigma_u(A)
28
Q

polynomial of the Laplacian

A
29
Q

polynomial feature vector convolution

A
30
Q

Graph Convolutional Network (GCN)

A
31
Q

Graph Attention Networks (GAT)

A
32
Q

Graph Isomorphic Network (GIN)

A
33
Q

Global Propagation via Embeddings

A
  • graph-level embeddings constructed using pooling tends to ignore underlying topology
  • spectral convolutions do not
34
Q

spectral embedding

A
35
Q

GNNs in Practice

A
  • can update equations using sparse matrix-vector product
  • allows efficient vectorized implementations of GNNs on GPUs
  • can use regularization such as dropout, but methods such as drop edge can boost for many GNNs
36
Q

GNN Pooling Methods

A
  1. SortPool: Sort vertices of the graph to get a fixed-size, and then apply any standard neural network architecture.
  2. DiffPool: Learn to cluster vertices, build a coarser graph over clusters instead of nodes, then apply a GNN over the coarser graph. Repeat until only one cluster is left.
  3. SAGPool: Apply a GNN to learn node scores, then keep only the nodes with the top scores, throwing away the rest. Repeat until only one node is left.
36
Q

GNN Pooling Methods

A
  1. SortPool: Sort vertices of the graph to get a fixed-size, and then apply any standard neural network architecture.
  2. DiffPool: Learn to cluster vertices, build a coarser graph over clusters instead of nodes, then apply a GNN over the coarser graph. Repeat until only one cluster is left.
  3. SAGPool: Apply a GNN to learn node scores, then keep only the nodes with the top scores, throwing away the rest. Repeat until only one node is left.
37
Q

Node Classification

A
  • L(y_v,y^_v)= -∑y_vc log y^_vc
  • L_G = ∑L(y_v,y^_v)/|Labeled(G)|
38
Q

Link Prediction

A
39
Q

Node Clustering

A
  • method 1: train GNN to predict local and global graph properties
  • method 2: random walk like node2vec and DeepWalk: L=∑∑log(exp(zz)/∑exp(zz)
  • or Noise Contrastive Estimation for large graphs

Virtuous AI (12 decks)

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