2d:null 2e:["$","title",null,{"children":"Graph Sample and Aggregate: GraphSAGE | Ameya Daigavane | Observable"}] 33:T8b8,eqn_display = md` **Next Update (Iteration ${step + 1}):** Equation for Node ${tex`${main_node.name}`}: ${ tex.block` \begin{aligned} ${formatted_main_node_new} &= {f} \left( ${formatted_neighbours_step_1} {${param_col} B^{(${step + 1})}} \times ${formatted_main_node} \right) \\ &= f \left( ${formatted_neighbours_step_2} {${param_col} ${B_curr}} \times ${formatted_main_node_current_features} \right) \\ &= f \left( ${formatted_neighbours_step_3} ${format_feature(B_curr * main_node_current_features)} \right) \\ ${formatted_eqn_step_4} &= \text{ReLU} \left(${formatted_main_node_updated_features_before_f}\right) = ${formatted_main_node_updated_features}. \end{aligned}` } Here, ${tex`f`} is just ${tex`\text{ReLU}`}: ${tex`f(x) = \max(x, 0)`}. Considering the sequence of neighbours as ${tex`[${formatted_neighbour_names}]`}, the ${tex`\text{RNN}`} computes: ${ tex.block` \begin{aligned} \qquad s_0 &= 0. \\ ${formatted_rnn_computation} \end{aligned} ` } The returned aggregated value ${tex`${formatted_rnn_last_state_value}`} is just the last state ${tex`${formatted_rnn_last_state}`} of the ${tex`\text{RNN}`}. Concisely, the initial ${tex`\text{RNN}`} state is ${tex`s_0 = 0`}, and the ${tex`\text{RNN}`} state update equation is: ${ tex.block` \begin{aligned} ${formatted_rnn_computation_concise} \end{aligned} ` } where ${tex`u_t`} is the ${tex`t`}-th neighbour of ${tex`${main_col} ${main_node.name}`} in the considered sequence. In practice, we would consider different permutations of the neighbour sequence, and train the ${tex`\text{RNN}`} to learn the same final aggregated value. This tries to make the ${tex`\text{RNN}`} node-order invariant. Note that the weights ${tex`${param_col} W^{(${step + 1})}`}, ${tex`${param_col} B^{(${step + 1})}`}, ${tex`${param_col} U_s^{(${step + 1})}`} and ${tex`${param_col} U_h^{(${step + 1})}`} are shared across all nodes! `34:T840,network_static = { var height = svg.property("viewBox").baseVal.height; /* Edges. */ var line_g = svg.select("g.edges") var link = line_g.selectAll("line") .attr("class", "edge") .attr("stroke", "gray") .data(graph.links, (d) => (d.source.id)) .join( enter => enter.append("line"), update => update, exit => exit.remove(), ) .call(drag(simulation)); /* Nodes. */ var node_g = svg.select("g.nodes"); var node = node_g.selectAll("g.node") .data(graph.nodes) .join( enter => { enter = enter.append("g") .attr("class", "node"); enter.append("circle") .attr("class", "visible"); enter.append("circle") .attr("class", "invisible"); enter.append("text"); enter.append("g") .attr("class", "node_vector"); return enter; }, update => update, exit => exit.remove(), ) .call(drag(simulation)); var node_circles = node.select("circle.visible") .call(drag(simulation)) .attr("r", 5); var node_invisible_circles = node.select("circle.invisible") .attr("r", 25) .attr("fill", "transparent"); var node_labels = node.select("text") .text((d) => (d.name)) .attr("font-style", "italic") .attr("x", 10) .attr("y", 3) .call(drag(simulation)); return svg.node(); }35:Td7f,network_dynamic = { var node_g = svg.select("g.nodes"); var line_g = svg.select("g.edges") var node = node_g.selectAll("g.node"); var link = line_g.selectAll("line"); /* Node circles. */ var node_circles = node.select("circle.visible") .transition() .duration(500) .attr("fill", (d) => (node_color(d))) .attr("r", (d) => (d.id == main_node_id ? 7 : 5)) /* Node vectors. */ var node_vector_cell_size = 30; var node_vectors = node.select("g.node_vector") var node_vector_rects = node_vectors.selectAll("rect") .data(get_node_features) .join( enter => enter.append("rect"), update => update, exit => exit.remove() ) .attr("fill", "#f5f2eb") .attr("stroke", "gray") .attr("x", 5) .attr("y", (d, i) => (10 + cell_size(d) * i)) .attr("width", (d) => cell_size(d)) .attr("height", (d) => cell_size(d)); var node_vector_text = node_vectors.selectAll("text") .data(get_node_features) .join( enter => enter.append("text"), update => update, exit => exit.remove() ) .attr("text-anchor", "middle") .attr("dominant-baseline", "central") .attr("x", 5) .attr("y", (d, i) => (10 + cell_size(d) * i)) .attr("dx", (d) => 0.5 * cell_size(d)) .attr("dy", (d) => 0.5 * cell_size(d)) .transition() .duration(1000) .text((d) => (+d.toFixed(2))); node.on('click', select_main_node); simulation .nodes(graph.nodes) .on("tick", ticked); simulation.force("link") .links(graph.links); function ticked() { link .attr("x1", function(d) { return d.source.x; }) .attr("y1", function(d) { return d.source.y; }) .attr("x2", function(d) { return d.target.x; }) .attr("y2", function(d) { return d.target.y; }); node .attr("transform", function(d) { return "translate(" + d.x + "," + d.y + ")"; }) } function cell_size(d) { return 30 + 5 * (+d.toFixed(2)).toString().length; } function select_main_node(event, d) { mutable main_node_id = d.id; }; function get_node_features(d){ return current_features.find((node) => (node.id == d.id)).features; } function node_color(d) { if(d.id == main_node_id){ return main_col_rgb; } if(main_node_neighbour_ids.includes(d.id)){ return neigh_col_rgb; } return "gray"; } }36:T55d,style = html` `37:T431,function RNN_aggregate(neighbour_features, U_s_step, U_h_step){ function RNN_state_sequence(state_sequence_so_far, new_neighbour_feature){ var prev_state = state_sequence_so_far[state_sequence_so_far.length - 1]; var new_state = post_rnn_func(U_s_step * prev_state + U_h_step * new_neighbour_feature); return state_sequence_so_far.concat([new_state]); } function RNN_state_sequence_pre_nonlinearity(state_sequence_so_far, new_neighbour_feature){ var prev_state = ReLU(state_sequence_so_far[state_sequence_so_far.length - 1]); var new_state_pre_nonlinearity = U_s_step * prev_state + U_h_step * new_neighbour_feature; return state_sequence_so_far.concat([new_state_pre_nonlinearity]); } var rnn_states = neighbour_features.reduce(RNN_state_sequence, [0]); var rnn_states_pre_nonlinearity = neighbour_features.reduce(RNN_state_sequence_pre_nonlinearity, [0]); var aggregated_neighbour_features = rnn_states[rnn_states.length - 1]; return { rnn_states, rnn_states_pre_nonlinearity, aggregated_neighbour_features }; }38:T4de,function compute_features(step){ W_update; B_update; U_s_update; U_h_update; var current_features, aggregated_neighbour_features, updated_features_before_f, updated_features; var features = original_features; for(var curr_step = 0; curr_step <= step; ++curr_step){ current_features = copy(features); aggregated_neighbour_features = compute_aggregated_neighbour_features(features, U_s_arr[curr_step], U_h_arr[curr_step]); updated_features_before_f = update_features(features, W_arr[curr_step], B_arr[curr_step], U_s_arr[curr_step], U_h_arr[curr_step]); updated_features = updated_features_before_f.map((node) => ({ "id": node.id, "features": node.features.map(post_conv_func), })); features = copy(updated_features); } return { "current_features": current_features, "aggregated_neighbour_features": aggregated_neighbour_features, "updated_features_before_f": updated_features_before_f, "updated_features": updated_features, } }39:[] 31:{"id":"25bb95a3e7c6d480","slug":"graph-sample-and-aggregate-graphsage","title":"Graph Sample and Aggregate: GraphSAGE","thumbnail":"2001dc7eaa3b8d2fb395bb7995d305fc88f3e97edc4149fd89e98153f4bf16b9","access_level":"public","create_time":"$D2020-12-03T14:56:47.851Z","update_time":"$D2021-08-18T05:02:31.376Z","view_time":null,"first_public_time":"$D2022-03-03T08:36:21.304Z","has_unpublished_edits":null,"fork":{"id":"9e3484e274ceb382","slug":"graph-convolutional-networks","title":"Graph Convolutional Networks","owner":{"id":"29561bb86c3368e7","login":"ameyasd","name":"Ameya Daigavane"}},"stars":0,"starred":false,"owner":{"type":"team","id":"29561bb86c3368e7","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":"starter_2024"},"version":2603,"publish_version":2603,"role":null,"authored":false,"authors":[{"type":"individual","id":"aa35c1e295926184","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":null}],"members":[{"type":"individual","id":"aa35c1e295926184","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"title":"Graph Sample and Aggregate: GraphSAGE","cells":[{"id":26,"value":"md`\n# Graph Sample and Aggregate: GraphSAGE\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"md`\nAn interactive GraphSAGE model! \nGiven a graph ${tex`G`} with initial node features ${tex`h_v^{(0)}`} at each node ${tex`v`}, the network computes new node features!\n`\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1099,"value":"instructions = md`\n * Choose weights ${tex`W^{(k)}`} and ${tex`B^{(k)}`} with the sliders below.\n * See the update equation for a node by clicking on it.\n * Then, update all nodes' feature values by pressing *Update All Nodes*. Each node will be updated according to its own update equation!\n * Reset to the original feature values by pressing *Reset*.\n * Randomize the graph structure with *Randomize Graph*.\n\nWatch how the update equation changes as you select different nodes and weights!\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":983,"value":"buttons_display = {\n const reset_inp = html``;\n reset_inp.onclick = () => {\n mutable step = 0;\n }\n\n const undo_inp = html``;\n undo_inp.onclick = () => {\n if(step > 0){\n mutable step -= 1;\n }\n }\n\n const update_inp = html``;\n update_inp.onclick = () => {\n mutable step += 1;\n }\n \n const randomize_inp = html``;\n randomize_inp.onclick = () => {\n mutable step = 0;\n randomize_graph();\n }\n\n const combined_div = html`\n \n\n

\n ${reset_inp}\n ${undo_inp}\n ${update_inp}\n ${randomize_inp}\n

\n `;\n return combined_div;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1682,"value":"main_div = {\n return html`\n ${style}\n

\n ${step == 0 ? \"Initial Graph\" : \"Graph after Iteration \" + step.toString()}\n

\n Parameters for Next Update\n

\n ${W_slider}\n ${B_slider}\n ${U_s_slider}\n ${U_h_slider}\n

\n \n

\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2143,"value":"simulation = {\n var height = svg.property(\"viewBox\").baseVal.height;\n return d3.forceSimulation()\n .force(\"link\", d3.forceLink().id(d => d.id).strength(0.01))\n .force(\"charge\", d3.forceManyBody().strength(-100))\n .force(\"center\", d3.forceCenter(width / 2, height / 2));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":754,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2588,"value":"formatted_rnn_computation_concise = `s_{t} &= \\\\text{ReLU}\\\\left({${param_col} U_s} s_{t - 1} + {${param_col} U_h} h_{u_t}^{(${step})}\\\\right) \\\\\\\\ &= \\\\text{ReLU}\\\\left({${param_col} ${U_s_curr}} \\ s_{t - 1} + {${param_col} ${U_h_curr}} \\ h_{u_t}^{(${step})}\\\\right).`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2452,"value":"formatted_rnn_computation = main_node_neighbours.map(\n (neighbour, t) => \n `s_{` + (t + 1).toString() + `}`+\n `&= \\\\text{ReLU}\\\\left({${param_col} U_s} s_{${t}} + {${param_col} U_h} {${neigh_col} h_{${neighbour.name}}^{(${step})}}\\\\right)` +\n ` = \\\\text{ReLU}\\\\left(\n {${param_col} ${U_s_curr}}\n \\\\times ${format_feature(main_node_rnn_states[t])} + \n {${param_col} ${U_h_curr}} \n \\\\times {${neigh_col} ${format_feature(main_node_neighbours_values[t])}} \\\\right)` +\n ` = \\\\text{ReLU}\\\\left(${format_feature(main_node_rnn_states_pre_nonlinearity[t + 1])}\\\\right)` +\n ` = ${format_feature(main_node_rnn_states[t + 1])}.`\n).join(` \\\\\\\\ `)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2542,"value":"formatted_rnn_last_state_value = \n`${neigh_col} ${format_feature(main_node_rnn_states[main_node_neighbours.length])}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2549,"value":"formatted_rnn_last_state = \n`s_{${main_node_neighbours.length}}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":38,"value":"md`\n# Appendix\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1882,"value":"md`\n### Visualization\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":383,"value":"svg = {\n var height = 500;\n var svg = d3.select(main_div).select(\"svg\")\n .attr(\"viewBox\", [width/3, 0, width/3, height])\n .attr(\"width\", width)\n .attr(\"height\", height);\n let line_g = svg.append(\"g\")\n .attr(\"class\", \"edges\")\n .attr(\"stroke\", \"gray\");\n let node_g = svg.append(\"g\")\n .attr(\"class\", \"nodes\");\n return svg;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2579,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2009,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1256,"value":"md`\n### Inputs\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":81,"value":"mutable graph = {\n return {\n \"nodes\": [\n { \"id\": 1, \"name\": \"A\", \"features\": [6] },\n { \"id\": 2, \"name\": \"B\", \"features\": [2] },\n { \"id\": 3, \"name\": \"C\", \"features\": [-10] },\n { \"id\": 4, \"name\": \"D\", \"features\": [1] },\n { \"id\": 5, \"name\": \"E\", \"features\": [3] },\n ],\n \"links\": [\n { \"source\": 2, \"target\": 5 },\n { \"source\": 1, \"target\": 3 },\n { \"source\": 4, \"target\": 5 },\n { \"source\": 5, \"target\": 1 },\n ]\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1528,"value":"post_conv_func = ReLU","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2509,"value":"post_rnn_func = ReLU","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":926,"value":"function ReLU(x){\n return x > 0 ? x : 0; // ReLU!\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":989,"value":"mutable step = 0;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":672,"value":"W_curr = Generators.input(W_slider)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1856,"value":"mutable W_arr = Array(100).fill(1);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":683,"value":"U_s_curr = Generators.input(U_s_slider)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1857,"value":"mutable U_s_arr = Array(100).fill(1);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2303,"value":"U_h_curr = Generators.input(U_h_slider)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2305,"value":"mutable U_h_arr = Array(100).fill(1);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2318,"value":"B_curr = Generators.input(B_slider)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2322,"value":"mutable B_arr = Array(100).fill(1);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1860,"value":"W_update = {\n mutable W_arr[step] = W_curr;\n mutable W_arr = mutable W_arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1863,"value":"U_s_update = {\n mutable U_s_arr[step] = U_s_curr;\n mutable U_s_arr = mutable U_s_arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2307,"value":"U_h_update = {\n mutable U_h_arr[step] = U_h_curr;\n mutable U_h_arr = mutable U_h_arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2327,"value":"B_update = {\n mutable B_arr[step] = B_curr;\n mutable B_arr = mutable B_arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1778,"value":"W_slider = slider({\n min: -10,\n max: 10, \n step: 0.1,\n value: this ? this.input.value : 1,\n title: tex`W^{(${step + 1})}`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2320,"value":"B_slider = slider({\n min: -10,\n max: 10, \n step: 0.1,\n value: this ? this.input.value : 1,\n title: tex`B^{(${step + 1})}`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1783,"value":"U_s_slider = slider({\n min: -10,\n max: 10, \n step: 0.1,\n value: this ? this.input.value : 1,\n title: tex`U_s^{(${step + 1})}`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2296,"value":"U_h_slider = slider({\n min: -10,\n max: 10, \n step: 0.1,\n value: this ? this.input.value : 1,\n title: tex`U_h^{(${step + 1})}`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1253,"value":"md`\n### Features\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2341,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2365,"value":"function compute_aggregated_neighbour_features(features, U_s_step, U_h_step){\n return features.map((node) => {\n const neighbour_features = get_neighbours_features(features, node.id);\n const { \n aggregated_neighbour_features,\n rnn_states,\n rnn_states_pre_nonlinearity,\n } = RNN_aggregate(neighbour_features, U_s_step, U_h_step);\n \n return {\n \"id\": node.id,\n \"aggregated_neighbour_features\": aggregated_neighbour_features,\n \"rnn_states\": rnn_states,\n \"rnn_states_pre_nonlinearity\": rnn_states_pre_nonlinearity,\n }\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1531,"value":"function update_features(features, W_step, B_step, U_s_step, U_h_step){\n return features.map((node) => {\n const neighbour_features = get_neighbours_features(features, node.id);\n \n var neighbour_features_aggregrated;\n if(neighbour_features.length > 0){\n neighbour_features_aggregrated = RNN_aggregate(neighbour_features,\n U_s_step, U_h_step).aggregated_neighbour_features;\n } else {\n neighbour_features_aggregrated = 0;\n }\n\n var node_updated_features_before_f = math.add(math.multiply(W_step, neighbour_features_aggregrated),\n math.multiply(B_step, node.features));\n\n if(!(node_updated_features_before_f instanceof Array)){\n node_updated_features_before_f = [node_updated_features_before_f]\n }\n\n return {\n \"id\": node.id,\n \"features\": node_updated_features_before_f,\n }\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1524,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1941,"value":"all_features = compute_features(step);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1062,"value":"mutable original_features = copy(graph.nodes.map((node) => ({\n \"id\": node.id,\n \"features\": node.features,\n})));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1534,"value":"current_features = all_features.current_features;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1539,"value":"updated_features_before_f = all_features.updated_features_before_f;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1544,"value":"updated_features = all_features.updated_features;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2386,"value":"aggregated_neighbour_features = all_features.aggregated_neighbour_features","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1242,"value":"md`\n### Graph Utils\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1456,"value":"function randomize_graph() {\n\n /* Remove old nodes. */\n const num_nodes = Math.max(4, Math.round(10 * Math.random()));\n graph.nodes = [];\n\n /* Add nodes. */\n for(var id = 1; id <= num_nodes; ++id){\n var feature = [-5 + Math.round(10 * Math.random())];\n var name = String.fromCharCode(64 + id);\n \n graph.nodes.push({\n \"id\": id,\n \"features\": feature,\n \"name\": name,\n })\n }\n\n /* Remove old edges. */\n graph.links = [];\n\n /* Add edges. */\n const p = Math.max(0.5, Math.random());\n for(var id1 = 1; id1 <= num_nodes; ++id1){\n for(var id2 = id1 + 1; id2 <= num_nodes; ++id2){\n if(Math.random() <= p){\n graph.links.push({\n \"source\": id1,\n \"target\": id2,\n })\n }\n }\n }\n \n mutable original_features = copy(graph.nodes.map((node) => ({\n \"id\": node.id,\n \"features\": node.features,\n })));\n \n mutable main_node_id = 1;\n} ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1259,"value":"function assign_to_graph(features){\n graph.nodes.forEach(\n (node) => node.features = (features.find((orig_node) => (node.id == orig_node.id))).features\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1162,"value":"function get_neighbour_ids(node_id){\n return get_links(node_id).map((edge) => {\n if(edge.source.id != undefined){\n if(edge.source.id != node_id){\n return edge.source.id;\n } else {\n return edge.target.id;\n }\n }\n else {\n if(edge.source != node_id){\n return edge.source;\n } else {\n return edge.target;\n }\n }\n }).filter(unique);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1158,"value":"function get_links(node_id){\n return graph.links.filter((edge) => (edge.target.id == node_id || edge.target == node_id ||\n edge.source.id == node_id || edge.source == node_id));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1171,"value":"function get_neighbours(node_id){\n return get_neighbour_ids(node_id).map((id) => graph.nodes.find((element) => (element.id == id))).sort(\n (el1, el2) => {\n if(el1.name < el2.name){\n return -1;\n }\n \n if(el1.name > el2.name){\n return 1;\n }\n \n return 0;\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2394,"value":"function get_neighbours_features(features, node_id){\n const neighbour_ids = get_neighbours(node_id).map((o_node) => (o_node.id));\n const neighbour_features = neighbour_ids.map(\n (id) => (features.find((node) => (node.id == id)).features)\n );\n return neighbour_features;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1236,"value":"md`\n### Main Node Quantities\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":536,"value":"mutable main_node_id = 1;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":538,"value":"main_node = graph.nodes.find((node) => (node.id == main_node_id));","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":541,"value":"main_node_links = get_links(main_node_id);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":817,"value":"main_node_neighbour_ids = get_neighbour_ids(main_node_id);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":820,"value":"main_node_neighbours = get_neighbours(main_node_id);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1302,"value":"main_node_num_neighbours = main_node_neighbour_ids.length","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":529,"value":"main_node_current_features = current_features.find((node) => (node.id == main_node_id)).features;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":519,"value":"main_node_updated_features_before_f = updated_features_before_f.find((node) => (node.id == main_node_id)).features","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":923,"value":"main_node_updated_features = main_node_updated_features_before_f.map(ReLU)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2490,"value":"main_node_neighbours_values = main_node_neighbours.map(\n (neighbour) => current_features.find((node) => (node.id == neighbour.id)).features\n);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1363,"value":"main_node_neighbours_values_agg = aggregated_neighbour_features.find(\n (node) => (node.id == main_node_id)\n).aggregated_neighbour_features;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2462,"value":"main_node_rnn_states = aggregated_neighbour_features.find(\n (node) => (node.id == main_node_id)\n).rnn_states;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2516,"value":"main_node_rnn_states_pre_nonlinearity = aggregated_neighbour_features.find(\n (node) => (node.id == main_node_id)\n).rnn_states_pre_nonlinearity;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1232,"value":"md`\n### Formatters\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2015,"value":"formatted_main_node = \"{\" + main_col + \"h_\\{\" + main_node.name + \"\\}^{(\" + step.toString() + \")}}\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2055,"value":"formatted_main_node_new = \"{\" + main_col + \"h_\\{\" + main_node.name + \"\\}^{(\" + (step + 1).toString() + \")}}\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1030,"value":"formatted_main_node_current_features = \"{\" + main_col + format_feature(main_node_current_features) + \"}\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1032,"value":"formatted_main_node_updated_features = {\n step;\n return format_feature(main_node_updated_features);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1036,"value":"formatted_main_node_updated_features_before_f = format_feature(main_node_updated_features_before_f)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2438,"value":"formatted_neighbour_names = main_node_neighbours.map((neighbour) => \n\"{\" + neigh_col + neighbour.name.toString() + \"}\").join(\" , \")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":800,"value":"formatted_neighbours = main_node_neighbours.map((neighbour) => \n\"{\" + neigh_col + \"h_{\" + neighbour.name.toString() + \"}^{(\" + step + \")}}\").join(\" , \")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2153,"value":"formatted_neighbours_step_1 = main_node_neighbours.length > 0 ?\n`{${param_col} W^{(${step + 1})}} \\\\times \\\\text{RNN}\\\\left[${formatted_neighbours}\\\\right] + ` : ``;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2161,"value":"formatted_neighbours_step_2 = main_node_neighbours.length > 0 ?\n`{${param_col} ${W_curr}} \\\\times ${formatted_neighbours_values_agg} + ` : ``;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2167,"value":"formatted_neighbours_step_3 = main_node_neighbours.length > 0 ?\n`${format_feature(W_curr * main_node_neighbours_values_agg)} + `: ``; ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2236,"value":"formatted_eqn_step_4 = main_node_neighbours.length > 0 ?\n`&= f \\\\left(${formatted_main_node_updated_features_before_f} \\\\right) \\\\\\\\` : ``;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":840,"value":"formatted_neighbours_values_agg = \n\"{\" + neigh_col +\nformat_feature(main_node_neighbours_values_agg) +\n\"}\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1038,"value":"function format_feature(feat){\n var val;\n if(feat instanceof Array){\n val = feat[0];\n } else {\n val = feat;\n }\n return (+val.toFixed(2)).toString();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1239,"value":"md`\n### Miscellaneous\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":343,"value":"function copy(aObject) {\n if (!aObject) {\n return aObject;\n }\n\n var v;\n var bObject = Array.isArray(aObject) ? [] : {};\n for (const k in aObject) {\n v = aObject[k];\n bObject[k] = (typeof v === \"object\") ? copy(v) : v;\n }\n\n return bObject;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":867,"value":"function unique (elem, pos,arr) {\n return arr.indexOf(elem) == pos;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":656,"value":"drag = simulation => {\n \n function dragstarted(event) {\n if (!event.active) simulation.alphaTarget(0.3).restart();\n event.subject.fx = event.subject.x;\n event.subject.fy = event.subject.y;\n }\n \n function dragged(event) {\n event.subject.fx = event.x;\n event.subject.fy = event.y;\n }\n \n function dragended(event) {\n if (!event.active) simulation.alphaTarget(0);\n event.subject.fx = null;\n event.subject.fy = null;\n }\n \n return d3.drag()\n .on(\"start\", dragstarted)\n .on(\"drag\", dragged)\n .on(\"end\", dragended);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1206,"value":"md`\n### Imports\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2095,"value":"import {param_col, neigh_col, neigh_col_rgb, main_col, main_col_rgb} from \"@ameyasd/gnn-styles\";","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1124,"value":"import {slider} from \"@jashkenas/inputs\";","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"d3 = require('d3@6')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":240,"value":"math = require('mathjs@7.6.0/dist/math.min.js')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W39","stdlib":"1","titling":"auto"}} 32:"$31:body"