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{"uid": "1806.01261-543", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Figure 4: Di\u000berent internal GN block con\fgurations. See Section 3.2 for details on the notation,\nand Section 4 for details about each variant. (a) A full GN predicts node, edge, and global output\nattributes based on incoming node, edge, and global attributes. (b) An independent, recurrent\nupdate block takes input and hidden graphs, and the \u001efunctions are RNNs (Sanchez-Gonzalez\net al., 2018). (c) An MPNN (Gilmer et al., 2017) predicts node, edge, and global output attributes\nbased on incoming node, edge, and global attributes. Note that the global prediction does not\ninclude aggregated edges. (d) A NLNN (Wang et al., 2018c) only predicts node output attributes.\n(e) A relation network (Raposo et al., 2017; Santoro et al., 2017) only uses the edge predictions\nto predict global attributes. (f) A Deep Set (Zaheer et al., 2017) bypasses the edge update and\npredicts updated global attributes.\n4.2.1 Message-passing neural network (MPNN)\nGilmer et al. (2017)'s MPNN generalizes a number of previous architectures and can be translated\nnaturally into the GN formalism. Following the MPNN paper's terminology (see Gilmer et al."}


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{"uid": "1806.01261-616", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "5: NLNNs as GNs. A schematic showing how NLNNs (Wang et al., 2018c) are implemented"}


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{"uid": "1806.01261-617", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "by the\u001eeand\u001ae!vunder the GN framework. Typically, NLNNs assume that di\u000berent regions of\nan image (or words in a sentence) correspond to nodes in a fully connected graph, and the attention\nmechanism de\fnes a weighted sum over nodes during the aggregation step.\n\u000ethe readout function, R, plays the role of the GN's \u001eu, but does not take uorE0as input,\nand thus an analog to the GN's \u001ae!uis not required;\n\u000edmaster serves a roughly similar purpose to the GN's u, but is de\fned as an extra node\nconnected to all others, and thus does not in\ruence the edge and global updates directly. It\ncan then be represented in the GN's V.\nFigure 4c shows how an MPNN is structured, according to the GN framework. For details and\nvarious MPNN architectures, see the Appendix.\n4.2.2 Non-local neural networks (NLNN)\nWang et al. (2018c)'s NLNN, which uni\fes various \\intra-/self-/vertex-/graph-attention\" approaches\n(Lin et al., 2017; Vaswani et al., 2017; Hoshen, 2017; Veli\u0014 ckovi\u0013 c et al., 2018; Shaw et al., 2018),"}


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{"uid": "1806.01261-618", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "(Lin et al., 2017; Vaswani et al., 2017; Hoshen, 2017; Veli\u0014 ckovi\u0013 c et al., 2018; Shaw et al., 2018),\ncan also be translated into the GN formalism. The label \\attention\" refers to how the nodes are\nupdated: each node update is based on a weighted sum of (some function of) the node attributes of\nits neighbors, where the weight between a node and one of its neighbors is computed by a scalar\npairwise function between their attributes (and then normalized across neighbors). The published\nNLNN formalism does not explicitly include edges, and instead computes pairwise attention weights\nbetween all nodes. But various NLNN-compliant models, such as the vertex attention interaction\nnetwork (Hoshen, 2017) and graph attention network (Veli\u0014 ckovi\u0013 c et al., 2018), are able to handle\nexplicit edges by e\u000bectively setting to zero the weights between nodes which do not share an edge.\nAs Figures 4d and 5 illustrate, the \u001eeis factored into the scalar pairwise-interaction function\nwhich returns the unnormalized attention term, denoted \u000be(vrk;vsk)=a0\nk, and a vector-valued\nnon-pairwise term, denoted \fe(vsk)=b0"}


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{"uid": "1806.01261-619", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "k, and a vector-valued\nnon-pairwise term, denoted \fe(vsk)=b0\nk. In the\u001ae!vaggregation, the a0\nkterms are normalized\nacross each receiver's edges, b0\nk, and elementwise summed:\n\u001ee(ek;vrk;vsk;u):=fe(vrk;vsk) = ( \u000be(vrk;vsk); \fe(vsk)) = (a0\nk;b0\nk) =e0\nk\n\u001ev\u0000\u0016e0\ni;vi;u\u0001:=fv(\u0016e0\ni)\n\u001ae!v\u0000\nE0\ni\u0001:=1P\nfk:rk=iga0\nkX\nfk:rk=iga0\nkb0\nk\nIn the NLNN paper's terminology (see Wang et al. (2018c), pages 2-4):\n\u000etheirfplays the role of the above \u000b,\n17\n\u000etheirgplays the role of the above \f.\nThis formulation may be helpful for focusing only on those interactions which are most relevant for\nthe downstream task, especially when the input entities were a set, from which a graph was formed\nby adding all possible edges between them."}


created_at: 2023-10-18 12:45:45
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{"uid": "1806.01261-620", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "the downstream task, especially when the input entities were a set, from which a graph was formed\nby adding all possible edges between them.\nVaswani et al. (2017)'s multi-headed self-attention mechanism adds an interesting feature, where\nthe\u001eeand\u001ae!vare implemented by a parallel set of functions, whose results are concatenated\ntogether as the \fnal step of \u001ae!v. This can be interpreted as using typed edges, where the di\u000berent\ntypes index into di\u000berent \u001eecomponent functions, analogous to Li et al. (2016).\nFor details and various NLNN architectures, see the Appendix.\n4.2.3 Other graph network variants\nThe full GN (Equation 2) can be used to predict a full graph, or any subset of (u0;V0;E0), as\noutlined in Section 4.1.1. For example, to predict a global property of a graph, V0andE0can just\nbe ignored. Similarly, if global, node, or edge attributes are unspeci\fed in the inputs, those vectors\ncan be zero-length, i.e., not taken as explicit input arguments. The same idea applies for other GN\nvariants which do not use the full set of mapping ( \u001e) and reduction ( \u001a) functions. For instance,"}


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{"uid": "1806.01261-621", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "variants which do not use the full set of mapping ( \u001e) and reduction ( \u001a) functions. For instance,\nInteraction Networks (Battaglia et al., 2016; Watters et al., 2017) and the Neural Physics Engine\n(Chang et al., 2017) use a full GN but for the absence of the global to update the edge properties\n(see Appendix for details).\nVarious models, including CommNet (Sukhbaatar et al., 2016), structure2vec (Dai et al., 2016)\n(in the version of (Dai et al., 2017)), and Gated Graph Sequence Neural Networks (Li et al., 2016)\nhave used a \u001eewhich does not directly compute pairwise interactions, but instead ignore the receiver\nnode, operating only on the sender node and in some cases an edge attribute. This can be expressed\nby implementations of \u001eewith the following signatures, such as:\n\u001ee(ek;vrk;vsk;u):=fe(vsk)\nor\u001ee(ek;vrk;vsk;u):=vsk+fe(ek)\nor\u001ee(ek;vrk;vsk;u):=fe(ek;vsk):\nSee the Appendix for further details.\nRelation Networks (Raposo et al., 2017; Santoro et al., 2017) bypass the node update entirely"}


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{"uid": "1806.01261-622", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "See the Appendix for further details.\nRelation Networks (Raposo et al., 2017; Santoro et al., 2017) bypass the node update entirely\nand predict the global output from pooled edge information directly (see also Figure 4e),\n\u001ee(ek;vrk;vsk;u):=fe(vrk;vsk) = NNe([vrk;vsk])\n\u001eu\u0000\n\u0016 e0;\u0016 v0;u\u0001:=fu\u0000\n\u0016 e0\u0001\n= NNu\u0000\n\u0016 e0\u0001\n\u001ae!u\u0000\nE0\u0001:= =X\nke0\nk\nDeep Sets (Zaheer et al., 2017) bypass the edges update completely and predict the global output\nfrom pooled nodes information directly (Figure 4f),\n\u001ev(\u0016ei;vi;u):=fv(vi;u) = NNv([vi;u])\n\u001eu\u0000\n\u0016 e0;\u0016 v0;u\u0001:=fu\u0000\n\u0016 v0\u0001\n= NNu\u0000\n\u0016 v0\u0001\n\u001av!u\u0000\nV0\u0001:= =X\niv0\ni\nPointNet (Qi et al., 2017) use similar update rule, with a max-aggregation for \u001av!uand a two-step\nnode update.\n18\nGM"}


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{"uid": "1806.01261-851", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "(c) Recurrent GN architecture"}


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{"uid": "1806.01261-852", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Figure 6: (a) An example composing multiple GN blocks in sequence to form a GN \\core\". Here,\nthe GN blocks can use shared weights, or they could be independent. (b) The encode-process-decode\narchitecture, which is a common choice for composing GN blocks (see Section 4.3). Here, a GN\nencodes an input graph, which is then processed by a GN core. The output of the core is decoded\nby a third GN block into an output graph, whose nodes, edges, and/or global attributes would be\nused for task-speci\fc purposes. (c) The encode-process-decode architecture applied in a sequential\nsetting in which the core is also unrolled over time (potentially using a GRU or LSTM architecture),\nin addition to being repeated within each time step. Here, merged lines indicate concatenation, and\nsplit lines indicate copying.\n4.3 Composable multi-block architectures\nA key design principle of graph networks is constructing complex architectures by composing GN\nblocks. We de\fned a GN block as always taking a graph comprised of edge, node, and global\nelements as input, and returning a graph with the same constituent elements as output (simply\npassing through the input elements to the output when those elements are not explicitly updated)."}


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{"uid": "1806.01261-853", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "elements as input, and returning a graph with the same constituent elements as output (simply\npassing through the input elements to the output when those elements are not explicitly updated).\nThis graph-to-graph input/output interface ensures that the output of one GN block can be passed\nas input to another, even if their internal con\fgurations are di\u000berent, similar to the tensor-to-tensor\ninterface of the standard deep learning toolkit. In the most basic form, two GN blocks, GN1and\nGN2, can be composed as GN1\u000eGN2by passing the output of the \frst as input to the second:\nG0= GN 2(GN 1(G)).\nArbitrary numbers of GN blocks can be composed, as show in Figure 6a. The blocks can\nbe unshared (di\u000berent functions and/or parameters, analogous to layers of a CNN), GN16=\nGN26=\u0001\u0001\u00016=GNM, or shared (reused functions and parameters, analogous to an unrolled RNN),\nGN1=GN2=\u0001\u0001\u0001=GNM. The white box around the GNcorein Figure 6a represents Mrepeated\ninternal processing sub-steps, with either shared or unshared GN blocks. Shared con\fgurations\nare analogous to message-passing (Gilmer et al., 2017), where the same local update procedure is"}


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{"uid": "1806.01261-854", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "are analogous to message-passing (Gilmer et al., 2017), where the same local update procedure is\napplied iteratively to propagate information across the structure (Figure 7). If we exclude the global\nu(which aggregates information from across the nodes and edges), the information that a node\nhas access to after msteps of propagation is determined by the set of nodes and edges that are at\nmostmhops away. This can be interpreted as breaking down a complex computation into smaller\nelementary steps. The steps can also be used to capture sequentiality in time. In our ball-spring\nexample, if each propagation step predicts the physical dynamics over one time step of duration \u0001 t,\nthen theMpropagation steps result in a total simulation time of, M\u0001\u0001t.\nA common architecture design is what we call the encode-process-decode con\fguration (Hamrick\net al. (2018); also see Figure 6ba): an input graph, Ginpis transformed into a latent representation,\nG0, by an encoder, GNenc; a shared core block, GNcore, is applied Mtimes to return GM; and\n\fnally an output graph, Gout, is decoded by GNdec. For example, in our running example, the\nencoder might compute the initial forces and interaction energies between the balls, the core might\n19\nm=0"}


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{"uid": "1806.01261-964", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "7: Example of message passing. Each row highlights the information that di\u000buses through"}


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{"uid": "1806.01261-965", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "the graph starting from a particular node. In the top row, the node of interest is in the upper\nright; in the bottom row, the node of interest is in the bottom right. Shaded nodes indicate how far\ninformation from the original node can travel in msteps of message passing; bolded edges indicate\nwhich edges that information has the potential to travel across. Note that during the full message\npassing procedure, this propagation of information happens simultaneously for all nodes and edges\nin the graph (not just the two shown here).\napply an elementary dynamics update, and the decoder might read out the \fnal positions from the\nupdated graph state.\nSimilar to the encode-process-decode design, recurrent GN-based architectures can be built by\nmaintaining a hidden graph, Gt\nhid, taking as input an observed graph, Gt\ninp, and returning an output\ngraph,Gt\nout, on each step (see Figure 6c). This type of architecture can be particularly useful for\npredicting sequences of graphs, such as predicting the trajectory of a dynamical system over time\n(e.g. Sanchez-Gonzalez et al., 2018). The encoded graph, output by GNenc, must have the same\nstructure as Gt\nhid, and they can be easily combined by concatenating their corresponding ek,vi,"}


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{"uid": "1806.01261-966", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "structure as Gt\nhid, and they can be easily combined by concatenating their corresponding ek,vi,\nanduvectors (where the upward arrow merges into the left-hand horizontal arrow in Figure 6c),\nbefore being passed to GNcore. For the output, the Gt\nhidis copied (where the right-hand horizontal\narrow splits into the downward arrow in Figure 6c) and decoded by GNdec. This design reuses GN\nblocks in several ways: GNenc,GNdec, and GNcoreare shared across each step, t; and within each\nstep, GN coremay perform multiple shared sub-steps.\nVarious other techniques for designing GN-based architectures can be useful. Graph skip\nconnections, for example, would concatenate a GN block's input graph, Gm, with its output graph,\nGm+1, before proceeding to further computations. Merging and smoothing input and hidden graph\ninformation, as in Figure 6c, can use LSTM- or GRU-style gating schemes, instead of simple\nconcatenation (Li et al., 2016). Or distinct, recurrent GN blocks (e.g. Figure 4b) can be composed\nbefore and/or after other GN blocks, to improve stability in the representations over multiple\npropagation steps (Sanchez-Gonzalez et al., 2018)."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-967", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "before and/or after other GN blocks, to improve stability in the representations over multiple\npropagation steps (Sanchez-Gonzalez et al., 2018).\n4.4 Implementing graph networks in code\nSimilar to CNNs (see Figure 1), which are naturally parallelizable (e.g. on GPUs), GNs have a\nnatural parallel structure: since the \u001eeand\u001evfunctions in Equation 1 are shared over the edges\nand nodes, respectively, they can be computed in parallel. In practice, this means that with respect\n20\nBox 4: Graph Nets open-source software library: github.com/deepmind/graph nets\nWe have released an open-source library for building GNs in Tensor\row/Sonnet. It includes\ndemos of how to create, manipulate, and train GNs to reason about graph-structured data, on\na shortest path-\fnding task, a sorting task, and a physical prediction task. Each demo uses the\nsame GN architecture, which highlights the \rexibility of the approach.\nShortest path demo: tinyurl.com/gn-shortest-path-demo\nThis demo creates random graphs, and trains a GN to label the nodes and edges on the shortest\npath between any two nodes. Over a sequence of message-passing steps (as depicted by each"}


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{"uid": "1806.01261-968", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "This demo creates random graphs, and trains a GN to label the nodes and edges on the shortest\npath between any two nodes. Over a sequence of message-passing steps (as depicted by each\nstep's plot), the model re\fnes its prediction of the shortest path.\nSort demo: tinyurl.com/gn-sort-demo\nThis demo creates lists of random numbers, and trains a GN to sort the list. After a sequence\nof message-passing steps, the model makes an accurate prediction of which elements (columns\nin the \fgure) come next after each other (rows).\nPhysics demo: tinyurl.com/gn-physics-demo\nThis demo creates random mass-spring physical systems, and trains a GN to predict the state of\nthe system on the next timestep. The model's next-step predictions can be fed back in as input\nto create a rollout of a future trajectory. Each subplot below shows the true and predicted\nmass-spring system states over 50 timesteps. This is similar to the model and experiments in\n(Battaglia et al., 2016)'s \\interaction networks\".\n21\nto\u001eeand\u001ev, the nodes and edges can be treated like the batch dimension in typical mini-batch\ntraining regimes. Moreover, several graphs can be naturally batched together by treating them as"}


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{"uid": "1806.01261-969", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "training regimes. Moreover, several graphs can be naturally batched together by treating them as\ndisjoint components of a larger graph. With some additional bookkeeping, this allows batching\ntogether the computations made on several independent graphs.\nReusing\u001eeand\u001evalso improves GNs' sample e\u000eciency. Again, analogous to a convolutional\nkernel, the number of samples which are used to optimize a GN's \u001eeand\u001evfunctions is the number\nof edges and nodes, respectively, across all training graphs. For example, in the balls example\nfrom Sec. 3.2, a scene with four balls which are all connected by springs will provide twelve (4 \u00023)\nexamples of the contact interaction between them.\nWe have released an open-source software library for building GNs, which can be found here:\ngithub.com/deepmind/graph nets . See Box 4 for an overview.\n4.5 Summary\nIn this section, we have discussed the design principles behind graph networks: \rexible representations, con\fgurable within-block structure, and composable multi-block architectures. These three\ndesign principles combine in our framework which is extremely \rexible and applicable to a wide range\nof domains ranging from perception, language, and symbolic reasoning. And, as we will see in the"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3c4-6db4-11ee-8587-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-970", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "design principles combine in our framework which is extremely \rexible and applicable to a wide range\nof domains ranging from perception, language, and symbolic reasoning. And, as we will see in the\nremainder of this paper, the strong relational inductive bias possessed by graph networks supports\ncombinatorial generalization, thus making it a powerful tool both in terms of implementation and\ntheory.\n5 Discussion\nIn this paper, we analyzed the extent to which relational inductive bias exists in deep learning\narchitectures like MLPs, CNNs, and RNNs, and concluded that while CNNs and RNNs do contain\nrelational inductive biases, they cannot naturally handle more structured representations such as\nsets or graphs. We advocated for building stronger relational inductive biases into deep learning\narchitectures by highlighting an underused deep learning building block called a graph network ,\nwhich performs computations over graph-structured data. Our graph network framework uni\fes\nexisting approaches that also operate over graphs, and provides a straightforward interface for\nassembling graph networks into complex, sophisticated architectures.\n5.1 Combinatorial generalization in graph networks\nThe structure of GNs naturally supports combinatorial generalization because they do not perform\ncomputations strictly at the system level, but also apply shared computations across the entities and"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3c5-6db4-11ee-9a93-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-971", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "The structure of GNs naturally supports combinatorial generalization because they do not perform\ncomputations strictly at the system level, but also apply shared computations across the entities and\nacross the relations as well. This allows never-before-seen systems to be reasoned about, because\nthey are built from familiar components, in a way that re\rects von Humboldt's \\in\fnite use of \fnite\nmeans\" (Humboldt, 1836; Chomsky, 1965).\nA number of studies have explored GNs' capacity for combinatorial generalization. Battaglia\net al. (2016) found that GNs trained to make one-step physical state predictions could simulate\nthousands of future time steps, and also exhibit accurate zero-shot transfer to physical systems\nwith double, or half, the number of entities experienced during training. Sanchez-Gonzalez et al.\n(2018) found similar results in more complex physical control settings, including that GNs trained as\nforward models on simulated multi-joint agents could generalize to agents with new numbers of joints.\nHamrick et al. (2018) and Wang et al. (2018b) each found that GN-based decision-making policies\ncould transfer to novel numbers of entities as well. In combinatorial optimization problems, Bello\n22"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3c6-6db4-11ee-8ddd-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-972", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "could transfer to novel numbers of entities as well. In combinatorial optimization problems, Bello\n22\net al. (2016); Nowak et al. (2017); Dai et al. (2017); Kool and Welling (2018) showed that GNs could\ngeneralize well to problems of much di\u000berent sizes than they had been trained on. Similarly, Toyer\net al. (2017) showed generalization to di\u000berent sizes of planning problems, and Hamilton et al. (2017)\nshowed generalization to producing useful node embeddings for previously unseen data. On boolean\nSAT problems, Selsam et al. (2018) demonstrated generalization both to di\u000berent problem sizes and\nacross problem distributions: their model retained good performance upon strongly modifying the\ndistribution of the input graphs and its typical local structure.\nThese striking examples of combinatorial generalization are not entirely surprising, given GNs'\nentity- and relation-centric organization, but nonetheless provide important support for the view\nthat embracing explicit structure and \rexible learning is a viable approach toward realizing better\nsample e\u000eciency and generalization in modern AI.\n5.2 Limitations of graph networks\nOne limitation of GNs' and MPNNs' form of learned message-passing (Shervashidze et al., 2011)"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3c7-6db4-11ee-83b6-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-973", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "5.2 Limitations of graph networks\nOne limitation of GNs' and MPNNs' form of learned message-passing (Shervashidze et al., 2011)\nis that it cannot be guaranteed to solve some classes of problems, such as discriminating between\ncertain non-isomorphic graphs. Kondor et al. (2018) suggested that covariance7(Cohen and Welling,\n2016; Kondor and Trivedi, 2018), rather than invariance to permutations of the nodes and edges\nis preferable, and proposed \\covariant compositional networks\" which can preserve structural\ninformation, and allow it to be ignored only if desired.\nMore generally, while graphs are a powerful way of representing structure information, they\nhave limits. For example, notions like recursion, control \row, and conditional iteration are not\nstraightforward to represent with graphs, and, minimally, require additional assumptions (e.g., in\ninterpreting abstract syntax trees). Programs and more \\computer-like\" processing can o\u000ber greater\nrepresentational and computational expressivity with respect to these notions, and some have argued\nthey are an important component of human cognition (Tenenbaum et al., 2011; Lake et al., 2015;\nGoodman et al., 2015).\n5.3 Open questions\nAlthough we are excited about the potential impacts that graph networks can have, we caution that"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3c8-6db4-11ee-a343-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-974", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Goodman et al., 2015).\n5.3 Open questions\nAlthough we are excited about the potential impacts that graph networks can have, we caution that\nthese models are only one step forward. Realizing the full potential of graph networks will likely be\nfar more challenging than organizing their behavior under one framework, and indeed, there are a\nnumber of unanswered questions regarding the best ways to use graph networks.\nOne pressing question is: where do the graphs come from that graph networks operate over?\nOne of the hallmarks of deep learning has been its ability to perform complex computations over\nraw sensory data, such as images and text, yet it is unclear the best ways to convert sensory data\ninto more structured representations like graphs. One approach (which we have already discussed)\nassumes a fully connected graph structure between spatial or linguistic entities, such as in the\nliterature on self-attention (Vaswani et al., 2017; Wang et al., 2018c). However, such representations\nmay not correspond exactly to the \\true\" entities (e.g., convolutional features do not directly\ncorrespond to objects in a scene). Moreover, many underlying graph structures are much more\nsparse than a fully connected graph, and it is an open question how to induce this sparsity. Several\nlines of active research are exploring these issues (Watters et al., 2017; van Steenkiste et al., 2018;"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3c9-6db4-11ee-a106-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-975", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "lines of active research are exploring these issues (Watters et al., 2017; van Steenkiste et al., 2018;\nLi et al., 2018; Kipf et al., 2018) but as of yet there is no single method which can reliably extract\ndiscrete entities from sensory data. Developing such a method is an exciting challenge for future\n7Covariance means, roughly, that the activations vary in a predictable way as a function of the ordering of the\nincoming edges.\n23\nresearch, and once solved will likely open the door for much more powerful and \rexible reasoning\nalgorithms.\nA related question is how to adaptively modify graph structures during the course of computation.\nFor example, if an object fractures into multiple pieces, a node representing that object also ought\nto split into multiple nodes. Similarly, it might be useful to only represent edges between objects\nthat are in contact, thus requiring the ability to add or remove edges depending on context. The\nquestion of how to support this type of adaptivity is also actively being researched, and in particular,\nsome of the methods used for identifying the underlying structure of a graph may be applicable (e.g.\nLi et al., 2018; Kipf et al., 2018).\nHuman cognition makes the strong assumption that the world is composed of objects and"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3ca-6db4-11ee-8689-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-976", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Li et al., 2018; Kipf et al., 2018).\nHuman cognition makes the strong assumption that the world is composed of objects and\nrelations (Spelke and Kinzler, 2007), and because GNs make a similar assumption, their behavior\ntends to be more interpretable. The entities and relations that GNs operate over often correspond\nto things that humans understand (such as physical objects), thus supporting more interpretable\nanalysis and visualization (e.g., as in Selsam et al., 2018). An interesting direction for future work\nis to further explore the interpretability of the behavior of graph networks.\n5.4 Integrative approaches for learning and structure\nWhile our focus here has been on graphs, one takeaway from this paper is less about graphs\nthemselves and more about the approach of blending powerful deep learning approaches with\nstructured representations. We are excited by related approaches which have explored this idea for\nother types of structured representations and computations, such as linguistic trees (Socher et al.,\n2011a,b, 2012, 2013; Tai et al., 2015; Andreas et al., 2016), partial tree traversals in a state-action\ngraph (Guez et al., 2018; Farquhar et al., 2018), hierarchical action policies (Andreas et al., 2017),"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3cb-6db4-11ee-a2d2-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-977", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "graph (Guez et al., 2018; Farquhar et al., 2018), hierarchical action policies (Andreas et al., 2017),\nmulti-agent communication channels (Foerster et al., 2016), \\capsules\" (Sabour et al., 2017), and\nprograms (Parisotto et al., 2017). Other methods have attempted to capture di\u000berent types of\nstructure by mimicking key hardware and software components in computers and how they transfer\ninformation between each other, such as persistent slotted storage, registers, memory I/O controllers,\nstacks, and queues (e.g. Dyer et al., 2015; Grefenstette et al., 2015; Joulin and Mikolov, 2015;\nSukhbaatar et al., 2015; Kurach et al., 2016; Graves et al., 2016).\n5.5 Conclusion\nRecent advances in AI, propelled by deep learning, have been transformative across many important\ndomains. Despite this, a vast gap between human and machine intelligence remains, especially with\nrespect to e\u000ecient, generalizable learning. We argue for making combinatorial generalization a top\npriority for AI, and advocate for embracing integrative approaches which draw on ideas from human\ncognition, traditional computer science, standard engineering practice, and modern deep learning.\nHere we explored \rexible learning-based approaches which implement strong relational inductive"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3cc-6db4-11ee-bb42-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-978", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "cognition, traditional computer science, standard engineering practice, and modern deep learning.\nHere we explored \rexible learning-based approaches which implement strong relational inductive\nbiases to capitalize on explicitly structured representations and computations, and presented a\nframework called graph networks , which generalize and extend various recent approaches for neural\nnetworks applied to graphs. Graph networks are designed to promote building complex architectures\nusing customizable graph-to-graph building blocks, and their relational inductive biases promote\ncombinatorial generalization and improved sample e\u000eciency over other standard machine learning\nbuilding blocks.\nDespite their bene\fts and potential, however, learnable models which operate on graphs are\nonly a stepping stone on the path toward human-like intelligence. We are optimistic about a\nnumber of other relevant, and perhaps underappreciated, research directions, including marrying\n24\nlearning-based approaches with programs (Ritchie et al., 2016; Andreas et al., 2016; Gaunt et al.,\n2016; Evans and Grefenstette, 2018; Evans et al., 2018), developing model-based approaches with an\nemphasis on abstraction (Kansky et al., 2017; Konidaris et al., 2018; Zhang et al., 2018; Hay et al.,\n2018), investing more heavily in meta-learning (Wang et al., 2016, 2018a; Finn et al., 2017), and"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3cd-6db4-11ee-afa0-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-979", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "2018), investing more heavily in meta-learning (Wang et al., 2016, 2018a; Finn et al., 2017), and\nexploring multi-agent learning and interaction as a key catalyst for advanced intelligence (Nowak,\n2006; Ohtsuki et al., 2006). These directions each involve rich notions of entities, relations, and\ncombinatorial generalization, and can potentially bene\ft, and bene\ft from, greater interaction with\napproaches for learning relational reasoning over explicitly structured representations.\nAcknowledgements\nWe thank Tobias Pfa\u000b, Danilo Rezende, Nando de Freitas, Murray Shanahan, Thore Graepel, John\nJumper, Demis Hassabis, and the broader DeepMind and Google communities for valuable feedback\nand support.\nReferences\nAllamanis, M., Brockschmidt, M., and Khademi, M. (2018). Learning to represent programs with\ngraphs. In Proceedings of the International Conference on Learning Representations (ICLR) .\nAllamanis, M., Chanthirasegaran, P., Kohli, P., and Sutton, C. (2017). Learning continuous\nsemantic representations of symbolic expressions. In Proceedings of the International Conference\non Machine Learning (ICML) .\nAnderson, J. R. (1982). Acquisition of cognitive skill. Psychological Review , 89(4):369."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3ce-6db4-11ee-8bc5-00155d3fea2c
encoding: FLOAT32
metadata:
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topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3cf-6db4-11ee-82b3-00155d3fea2c
encoding: FLOAT32
metadata:
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topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3d0-6db4-11ee-88d5-00155d3fea2c
encoding: FLOAT32
metadata:
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id: 2d1bd3d1-6db4-11ee-9a24-00155d3fea2c
encoding: FLOAT32
metadata:
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3d3-6db4-11ee-a650-00155d3fea2c
encoding: FLOAT32
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3d4-6db4-11ee-aa7d-00155d3fea2c
encoding: FLOAT32
metadata:
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topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3d5-6db4-11ee-93f0-00155d3fea2c
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{"uid": "1806.01261-987", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Elman, J. L. (1991). Distributed representations, simple recurrent networks, and grammatical\nstructure. Machine Learning , 7(2-3):195{225.\nEslami, S. A., Heess, N., Weber, T., Tassa, Y., Szepesvari, D., Hinton, G. E., et al. (2016). Attend,\ninfer, repeat: Fast scene understanding with generative models. In Advances in Neural Information\nProcessing Systems , pages 3225{3233.\nEvans, R. and Grefenstette, E. (2018). Learning explanatory rules from noisy data. Journal of\nArti\fcial Intelligence Research , 61:1{64.\nEvans, R., Saxton, D., Amos, D., Kohli, P., and Grefenstette, E. (2018). Can neural networks\nunderstand logical entailment? In Proceedings of the International Conference on Learning\nRepresentations (ICLR) .\nFarquhar, G., Rockt\u007f aschel, T., Igl, M., and Whiteson, S. (2018). TreeQN and ATreeC: Di\u000berentiable\ntree planning for deep reinforcement learning. In Proceedings of the International Conference on\nLearning Representations (ICLR) ."}


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{"uid": "1806.01261-1005", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "quadratic assignment with graph neural networks. In Proceedings of the Principled Approaches to\nDeep Learning Workshop (PADL) at the International Conference of Machine Learning (ICML) .\nNowak, M. A. (2006). Five rules for the evolution of cooperation. science , 314(5805):1560{1563.\nOhtsuki, H., Hauert, C., Lieberman, E., and Nowak, M. A. (2006). A simple rule for the evolution\nof cooperation on graphs and social networks. Nature , 441(7092):502.\n32\nO~ noro-Rubio, D., Niepert, M., Garc\u0013 \u0010a-Dur\u0013 an, A., Gonz\u0013 alez-S\u0013 anchez, R., and L\u0013 opez-Sastre,\nR. J. (2017). Representation learning for visual-relational knowledge graphs. arXiv preprint\narXiv:1709.02314 .\nParisotto, E., Mohamed, A.-r., Singh, R., Li, L., Zhou, D., and Kohli, P. (2017). Neuro-symbolic\nprogram synthesis. In Proceedings of the International Conference on Learning Representations\n(ICLR) ."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-1008", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "and impaired word reading: computational principles in quasi-regular domains. Psychological\nReview , 103(1):56.\nPollack, J. B. (1990). Recursive distributed representations. Arti\fcial Intelligence , 46(1-2):77{105.\nQi, C. R., Su, H., Mo, K., and Guibas, L. J. (2017). Pointnet: Deep learning on point sets for 3d\nclassi\fcation and segmentation. In Proceedings of the IEEE Conference on Computer Vision and\nPattern Recognition (CVPR) .\nRaposo, D., Santoro, A., Barrett, D., Pascanu, R., Lillicrap, T., and Battaglia, P. (2017). Discovering\nobjects and their relations from entangled scene representations. In Workshops at the International\nConference on Learning Representations (ICLR) .\n33\nReed, S. and De Freitas, N. (2016). Neural programmer-interpreters. In Proceedings of the\nInternational Conference on Learning Representations (ICLR) .\nRitchie, D., Horsfall, P., and Goodman, N. D. (2016). Deep amortized inference for probabilistic\nprograms. arXiv preprint arXiv:1610.05735 ."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f1-6db4-11ee-bcec-00155d3fea2c
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{"uid": "1806.01261-1015", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "InAdvances in Neural Information Processing Systems , pages 3104{3112.\nSzegedy, C., Io\u000be, S., Vanhoucke, V., and Alemi, A. A. (2017). Inception-v4, inception-resnet\nand the impact of residual connections on learning. In Proceedings of the AAAI Conference on\nArti\fcial Intelligence (AAAI) , volume 4, page 12.\nTai, K. S., Socher, R., and Manning, C. D. (2015). Improved semantic representations from\ntree-structured long short-term memory networks. In Proceedings of the Annual Meeting of the\nAssociation for Computational Linguistics (ACL) .\nTang, J., Qu, M., Wang, M., Zhang, M., Yan, J., and Mei, Q. (2015). Line: Large-scale information\nnetwork embedding. In Proceedings of the 24th International Conference on World Wide Web ,\npages 1067{1077. International World Wide Web Conferences Steering Committee.\nTenenbaum, J. B., Gri\u000eths, T. L., and Kemp, C. (2006). Theory-based bayesian models of inductive\nlearning and reasoning. Trends in Cognitive Sciences , 10(7):309{318.\n35"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f3-6db4-11ee-8751-00155d3fea2c
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{"uid": "1806.01261-1017", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "maximization: Unsupervised discovery of objects and their interactions. Proceedings of the\nInternational Conference on Learning Representations (ICLR) .\nVaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., and\nPolosukhin, I. (2017). Attention is all you need. In Advances in Neural Information Processing\nSystems .\nVeli\u0014 ckovi\u0013 c, P., Cucurull, G., Casanova, A., Romero, A., Li\u0012 o, P., and Bengio, Y. (2018). Graph\nattention networks. In Proceedings of the International Conference on Learning Representations\n(ICLR) .\nWang, J. X., Kurth-Nelson, Z., Kumaran, D., Tirumala, D., Soyer, H., Leibo, J. Z., Hassabis, D.,\nand Botvinick, M. (2018a). Prefrontal cortex as a meta-reinforcement learning system. Nature\nneuroscience , page 1.\nWang, J. X., Kurth-Nelson, Z., Tirumala, D., Soyer, H., Leibo, J. Z., Munos, R., Blundell, C.,"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
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{"uid": "1806.01261-1018", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Kumaran, D., and Botvinick, M. (2016). Learning to reinforcement learn. arXiv preprint\narXiv:1611.05763 .\nWang, T., Liao, R., Ba, J., and Fidler, S. (2018b). Nervenet: Learning structured policy with graph\nneural networks. In Proceedings of the International Conference on Learning Representations\n(ICLR) .\nWang, X., Girshick, R., Gupta, A., and He, K. (2018c). Non-local neural networks. In Proceedings\nof the Conference on Computer Vision and Pattern Recognition (CVPR) .\nWang, Y., Sun, Y., Liu, Z., Sarma, S. E., Bronstein, M. M., and Solomon, J. M. (2018d). Dynamic\ngraph cnn for learning on point clouds. arXiv preprint arXiv:1801.07829 .\nWatters, N., Zoran, D., Weber, T., Battaglia, P., Pascanu, R., and Tacchetti, A. (2017). Visual\ninteraction networks: Learning a physics simulator from video. In Advances in Neural Information\nProcessing Systems , pages 4542{4550."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f5-6db4-11ee-b256-00155d3fea2c
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{"uid": "1806.01261-1019", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "interaction networks: Learning a physics simulator from video. In Advances in Neural Information\nProcessing Systems , pages 4542{4550.\nWu, J., Lu, E., Kohli, P., Freeman, B., and Tenenbaum, J. (2017). Learning to see physics via\nvisual de-animation. In Advances in Neural Information Processing Systems , pages 152{163.\nYoon, K., Liao, R., Xiong, Y., Zhang, L., Fetaya, E., Urtasun, R., Zemel, R., and Pitkow, X.\n(2018). Inference in probabilistic graphical models by graph neural networks. In Workshops at\nthe International Conference on Learning Representations (ICLR) .\nYou, J., Ying, R., Ren, X., Hamilton, W. L., and Leskovec, J. (2018). GraphRNN: A deep generative\nmodel for graphs. arXiv preprint arXiv:1802.08773 .\n36\nYuille, A. L. and Liu, C. (2018). Deep nets: What have they ever done for vision? arXiv preprint\narXiv:1805.04025 ."}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f6-6db4-11ee-af00-00155d3fea2c
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{"uid": "1806.01261-1020", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "arXiv:1805.04025 .\nZaheer, M., Kottur, S., Ravanbakhsh, S., Poczos, B., Salakhutdinov, R. R., and Smola, A. J. (2017).\nDeep sets. In Advances in Neural Information Processing Systems , pages 3394{3404.\nZambaldi, V., Raposo, D., Santoro, A., Bapst, V., Li, Y., Babuschkin, I., Tuyls, K., Reichert, D.,\nLillicrap, T., Lockhart, E., Shanahan, M., Langston, V., Pascanu, R., Botvinick, M., Vinyals, O.,\nand Battaglia, P. (2018). Relational deep reinforcement learning. arXiv preprint arXiv .\nZhang, A., Lerer, A., Sukhbaatar, S., Fergus, R., and Szlam, A. (2018). Composable planning with\nattributes. arXiv preprint arXiv:1803.00512 .\nZ\u007f ugner, D., Akbarnejad, A., and G\u007f unnemann, S. (2018). Adversarial Attacks on Neural Networks"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f7-6db4-11ee-9d43-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-1021", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "Z\u007f ugner, D., Akbarnejad, A., and G\u007f unnemann, S. (2018). Adversarial Attacks on Neural Networks\nfor Graph Data. arXiv preprint arXiv:1805.07984 .\n37\nAppendix: Formulations of additional models\nIn this appendix we give more examples of how published networks can \ft in the frame de\fned by\nEquation 1.\nInteraction networks\nInteraction Networks (Battaglia et al., 2016; Watters et al., 2017) and the Neural Physics Engine\nChang et al. (2017) use a full GN but for the absence of the global to update the edge properties:\n\u001ee(ek;vrk;vsk;u):=fe(ek;vrk;vsk) = NNe([ek;vrk;vsk])\n\u001ev\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi;u\u0001\n= NNv\u0000\n[\u0016 e0\ni;vi;u]\u0001\n\u001ae!v\u0000\nE0\ni\u0001:= =X\nfk:rk=ige0\nk\nThat work also included an extension to the above formulation which output global, rather than\nper-node, predictions:"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f8-6db4-11ee-956b-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-1022", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "fk:rk=ige0\nk\nThat work also included an extension to the above formulation which output global, rather than\nper-node, predictions:\n\u001ee(ek;vrk;vsk;u):=fe(ek;vrk;vsk) = NNe([ek;vrk;vsk])\n\u001ev\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi;u\u0001\n= NNv\u0000\n[\u0016 e0\ni;vi;u]\u0001\n\u001eu\u0000\n\u0016 e0;\u0016 v0;u\u0001:=fu\u0000\n\u0016 v0;u\u0001\n= NNu\u0000\n[\u0016 v0;u]\u0001\n\u001av!g\u0000\nV0\u0001:= =X\niv0\ni\nNon-pairwise interactions\nGated Graph Sequence Neural Networks (GGS-NN) (Li et al., 2016) use a slightly generalized\nformulation where each edge has an attached type tk2f1;::;Tg, and the updates are:\n\u001ee((ek;tk);vrk;vsk;u):=fe(ek;vsk) = NNe;tk(vsk)\n\u001ev\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi\u0001"}


created_at: 2023-10-18 12:45:45
topic: persistent://default/default/052498be-6b77-431d-a531-3048a38fd9e3
id: 2d1bd3f9-6db4-11ee-92c0-00155d3fea2c
encoding: FLOAT32
metadata:
{"uid": "1806.01261-1023", "title": "Relational inductive biases, deep learning, and graph networks", "source": "http://arxiv.org/pdf/1806.01261", "start_index": 0, "chroma:document": "v\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi\u0001\n= NNv\u0000\n[\u0016 e0\ni;vi]\u0001\n\u001ae!v\u0000\nE0\ni\u0001:= =X\nfk:rk=ige0\nk\nThese updates are applied recurrently (the NNvis a GRU (Cho et al., 2014)), followed by a global\ndecoder which computes a weighted sum of embedded \fnal node states. Here each NNe;tkis a neural\nnetwork with speci\fc parameters.\nCommNet (Sukhbaatar et al., 2016) (in the slightly more general form described by (Hoshen,\n2017)) uses:\n\u001ee(ek;vrk;vsk;u):=fe(vsk) = NN e(vsk)\n\u001ev\u0000\n\u0016 e0\ni;vi;u\u0001:=fv\u0000\n\u0016 e0\ni;vi\u0001\n= NNv\u0000\n[\u0016 e0\ni;NNv0(vi)]\u0001\n\u001ae!v\u0000\nE0\ni\u0001:= =1\njE0\nijX\nfk:rk=ige0\nk\n38\nAttention-based approaches"}


