2d:null 2e:["$","title",null,{"children":"Graph Attention Networks | Ameya Daigavane | Observable"}] 33:T702,eqn_display = md` **Next Update (Iteration ${step + 1}):** Equation for Node ${tex`${main_node.name}`}: ${ tex.block` \begin{aligned} ${formatted_main_node_new} &= f \left({${param_col} W^{(${step + 1})}} \times \left(${formatted_self_and_neighbours} \right) \right) \\ &= f \left({${param_col} W^{(${step + 1})}} \times \left(${formatted_self_and_neighbours_partial} \right) \right) \\ &= f \left({${param_col} W^{(${step + 1})}} \times \big(${formatted_self_and_neighbours_partial_more}\big) \right) \\ &= f \left({${param_col} W^{(${step + 1})}} \times \big(${formatted_self_and_neighbours_partial_even_more} \big) \right) \\ &= f \left({${param_col} ${W_curr}} \times \left(${formatted_self_and_neighbours_evaluated} \right) \right) \\ &= f \left(${formatted_main_node_updated_features_before_f}\right) \\ &= \text{ReLU} \left(${formatted_main_node_updated_features_before_f}\right) = ${formatted_main_node_updated_features}. \end{aligned}` } with attention weights ${tex`\alpha_{${main_node.name}}`} computed as: ${ tex.block` \begin{aligned} ${formatted_self_and_neighbours_attentions_normalized_annotated} \end{aligned} ` } where the unnormalized attention weights ${tex`e_{${main_node.name}}`} are given by: ${ tex.block` \begin{aligned} ${formatted_attention_unnormalized} \\ \end{aligned} ` } We have omitted the superscripts on the attention weights for clarity. Here, ${tex`f`} is just ${tex`\text{ReLU}`}: ${tex`f(x) = \max(x, 0)`}. Note that the weights ${tex`${param_col} W^{(${step + 1})}`} and ${tex`${param_col} A_{W}^{(${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:T4d6,style = html` `37:T541,function compute_attention_weights_helper(self_features, self_and_neighbour_features, W_step, A_step){ var self_and_neighbour_attentions = self_and_neighbour_features.map( (o_features) => attention_mech(A_step, W_step * self_features, W_step * o_features) ); var self_and_neighbour_attentions_logged_pre_nonlinearity = self_and_neighbour_features.map( (o_features) => attention_mech_pre_nonlinearity(A_step, W_step * self_features, W_step * o_features) ); var self_and_neighbour_attentions_logged = copy(self_and_neighbour_attentions); /* For numerical stability. */ var max_weight = math.max(self_and_neighbour_attentions); self_and_neighbour_attentions = self_and_neighbour_attentions.map( (attention_weight) => math.exp(attention_weight - max_weight) ); var self_and_neighbour_attentions_unnormalized = copy(self_and_neighbour_attentions); var self_and_neighbour_attentions_sum = math.sum(self_and_neighbour_attentions); self_and_neighbour_attentions = self_and_neighbour_attentions.map( (attention_weight) => (attention_weight / self_and_neighbour_attentions_sum) ); return { self_and_neighbour_attentions, self_and_neighbour_attentions_logged_pre_nonlinearity, self_and_neighbour_attentions_logged, self_and_neighbour_attentions_unnormalized }; }38:T455,function compute_attention_weights(features, W_step, A_step){ return features.map((node) => { const self_features = node.features; const self_and_neighbour_ids = get_self_and_neighbour_ids(node.id); const self_and_neighbour_features = self_and_neighbour_ids.map( (id) => (features.find((node) => (node.id == id)).features) ); const { self_and_neighbour_attentions, self_and_neighbour_attentions_logged_pre_nonlinearity, self_and_neighbour_attentions_logged, self_and_neighbour_attentions_unnormalized, } = compute_attention_weights_helper(self_features, self_and_neighbour_features, W_step, A_step); return { "id": node.id, "attention_weights": self_and_neighbour_attentions, "attention_weights_unnormalized": self_and_neighbour_attentions_unnormalized, "attention_weights_logged": self_and_neighbour_attentions_logged, "attention_weights_logged_pre_nonlinearity": self_and_neighbour_attentions_logged_pre_nonlinearity, } }); }39:T4ca,function update_features(features, W_step, A_step){ return features.map((node) => { const self_features = features.find((o_node) => (o_node.id == node.id)).features; const self_and_neighbour_ids = get_self_and_neighbour_ids(node.id); const self_and_neighbour_features = self_and_neighbour_ids.map( (id) => (features.find((node) => (node.id == id)).features) ); var { self_and_neighbour_attentions } = compute_attention_weights_helper(self_features, self_and_neighbour_features, W_step, A_step); var self_and_neighbour_features_aggregated = math.multiply(self_and_neighbour_attentions, self_and_neighbour_features); var node_updated_features_before_f = math.multiply(W_step, self_and_neighbour_features_aggregated); if(!(node_updated_features_before_f instanceof Array)){ node_updated_features_before_f = [node_updated_features_before_f] } return { "id": node.id, "features": node_updated_features_before_f, } }); }3a:T4e2,formatted_attention_unnormalized = main_node_self_and_neighbours.map( (node, index) => "e_{" + main_node.name + node.name + "}" + " &= " + "\\text{ReLU}\\left(" + "{" + param_col + "A_{W}^\{(" + (step + 1).toString() + ")\}} \\left(" + "{" + param_col + "W^\{(" + (step + 1).toString() + ")\}}" + "{" + main_col + " h_{" + main_node.name + "}^{(" + step.toString() + ")}}" + " + " + "{" + param_col + "W^\{(" + (step + 1).toString() + ")\}}" + "{" + ((node.id == main_node.id) ? main_col : neigh_col) + " h_{" + node.name + "}^{(" + step.toString() + ")}} \\right)" + "\\right)" + " = " + "\\text{ReLU}\\left(" + "{" + param_col + A_curr + "}\\left(" + "{" + param_col + W_curr + "}" + "\\times " + "{" + main_col + formatted_main_node_current_features + "}" + " + " + "{" + param_col + W_curr + "}" + " \\times " + "{" + (node.id == main_node_id ? main_col: neigh_col) + format_feature(main_node_self_and_neighbours_values[index]) + "}" + "\\right)" + "\\right)" + " = " + "\\text{ReLU}\\left(" + format_feature(main_node_attentions_logged_pre_nonlinearity[index]) + "\\right)" + " = " + format_feature(main_node_attentions_logged[index]) + "." ).join(" \\\\ ")3b:[] 31:{"id":"99786291352ae172","slug":"graph-attention-networks","title":"Graph Attention Networks","thumbnail":"1eca58041c873f3e5dcc2e7534cda6d185575a53f5c1898743931af99f3b826c","access_level":"public","create_time":"$D2020-11-12T09:21:07.258Z","update_time":"$D2021-06-29T14:57:45.600Z","view_time":null,"first_public_time":"$D2022-03-03T08:36:37.874Z","has_unpublished_edits":null,"fork":{"id":"9e3484e274ceb382","slug":"graph-convolutional-networks","title":"Graph Convolutional Networks","owner":{"id":"29561bb86c3368e7","login":"ameyasd","name":"Ameya Daigavane"}},"stars":2,"starred":false,"owner":{"type":"team","id":"29561bb86c3368e7","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":"starter_2024"},"version":2491,"publish_version":2491,"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":8,"collection":null,"type":"notebook","body":{"title":"Graph Attention Networks","cells":[{"id":26,"value":"md`\n# Graph Attention Networks\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":32,"value":"md`\nAn interactive graph attention network! \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 ${A_slider}\n

\n \n

\n`;\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":"$undefined"},{"id":38,"value":"md`\n# Appendix\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2446,"value":"simulation = {\n var height = svg.property(\"viewBox\").baseVal.height;\n return d3.forceSimulation()\n .force(\"link\", d3.forceLink().id(d => d.id).strength(0.01))\n .force(\"charge\", d3.forceManyBody().strength(-100))\n .force(\"center\", d3.forceCenter(width / 2, height / 2));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2486,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2013,"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":"$undefined"},{"id":926,"value":"function ReLU(x){\n return x > 0 ? x : 0; // ReLU!\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":1860,"value":"W_update = {\n mutable W_arr[step] = W_curr;\n mutable W_arr = mutable W_arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2050,"value":"A_curr = Generators.input(A_slider);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2052,"value":"mutable A_arr = Array(100).fill(1);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2048,"value":"A_update = {\n mutable A_arr[step] = A_curr;\n mutable A_arr = mutable A_arr;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2454,"value":"function attention_mech_pre_nonlinearity(A, feat_i, feat_j){\n return math.multiply(A, feat_i + feat_j);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2029,"value":"function attention_mech(A, feat_i, feat_j){\n return ReLU(attention_mech_pre_nonlinearity(A, feat_i, feat_j));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2090,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2082,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1531,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1524,"value":"function compute_features(step){\n W_update; A_update;\n\n var current_features, attention_weights, updated_features_before_f, updated_features;\n \n var features = original_features;\n for(var curr_step = 0; curr_step <= step; ++curr_step){ \n current_features = copy(features);\n attention_weights = compute_attention_weights(features, W_arr[curr_step], A_arr[curr_step]);\n updated_features_before_f = update_features(features, W_arr[curr_step], A_arr[curr_step]);\n updated_features = updated_features_before_f.map((node) => ({\n \"id\": node.id,\n \"features\": node.features.map(post_conv_func),\n }));\n\n features = copy(updated_features);\n }\n \n return {\n \"current_features\": current_features,\n \"updated_features_before_f\": updated_features_before_f,\n \"updated_features\": updated_features,\n \"attention_weights\": attention_weights,\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2084,"value":"attention_weights = all_features.attention_weights","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":1456,"value":"function randomize_graph() {\n\n /* Remove old nodes. */\n const num_nodes = Math.max(4, Math.round(8 * Math.random()));\n graph.nodes = [];\n\n /* Add nodes. */\n for(var id = 1; id <= num_nodes; ++id){\n var feature = [-5 + Math.round(10 * Math.random())];\n var name = String.fromCharCode(64 + id);\n \n graph.nodes.push({\n \"id\": id,\n \"features\": feature,\n \"name\": name,\n })\n }\n\n /* Remove old edges. */\n graph.links = [];\n\n /* Add edges. */\n const p = Math.max(0.5, Math.random());\n for(var id1 = 1; id1 <= num_nodes; ++id1){\n for(var id2 = id1 + 1; id2 <= num_nodes; ++id2){\n if(Math.random() <= p){\n graph.links.push({\n \"source\": id1,\n \"target\": id2,\n })\n }\n }\n }\n \n mutable original_features = copy(graph.nodes.map((node) => ({\n \"id\": node.id,\n \"features\": node.features,\n })));\n \n mutable main_node_id = 1;\n} ","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2179,"value":"function get_self_and_neighbour_ids(node_id){\n return get_neighbours(node_id).map((o_node) => (o_node.id)).concat([node_id]);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":1236,"value":"md`\n### Main Node Quantities\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2110,"value":"main_node_self_and_neighbours = main_node_neighbours.concat(main_node);","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2103,"value":"main_node_attentions = attention_weights.find(\n (node) => (node.id == main_node_id)\n).attention_weights;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2216,"value":"main_node_attentions_unnormalized = attention_weights.find(\n (node) => (node.id == main_node_id)\n).attention_weights_unnormalized;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2226,"value":"main_node_attentions_logged = attention_weights.find(\n (node) => (node.id == main_node_id)\n).attention_weights_logged","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2467,"value":"main_node_attentions_logged_pre_nonlinearity = attention_weights.find(\n (node) => (node.id == main_node_id)\n).attention_weights_logged_pre_nonlinearity;","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1363,"value":"main_node_self_and_neighbours_values = main_node_self_and_neighbours.map(\n (neighbour) => current_features.find((node) => (node.id == neighbour.id)).features\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2137,"value":"main_node_self_and_neighbours_values_agg = math.multiply(main_node_attentions, main_node_self_and_neighbours_values)","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2361,"value":"formatted_main_node_new = \"{\" + main_col + \"h_\\{\" + main_node.name + \"\\}^{(\" + (step + 1).toString() + \")}}\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1030,"value":"formatted_main_node_current_features = format_feature(main_node_current_features)","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":800,"value":"formatted_self_and_neighbours = main_node_self_and_neighbours.map(\n (node) =>\n \"\\\\alpha_\\{\" + main_node.name + node.name + \"\\} \\\\times {\" + \n ((node.id == main_node.id) ? main_col : neigh_col) + \n \"h_\\{\" + node.name.toString() + \"\\}^{(\" + step + \")}}\"\n).join(\" + \")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2114,"value":"formatted_self_and_neighbours_partial = main_node_self_and_neighbours.map(\n (node, index) => \n format_feature(main_node_attentions[index]) + \" \\\\times \" + \"{\" + \n ((node.id == main_node.id) ? main_col : neigh_col) + \n \"h_\\{\" + node.name.toString() + \"\\}^{(\" + step + \")}}\"\n).join(\" + \")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2152,"value":"formatted_self_and_neighbours_partial_more = main_node_self_and_neighbours.map(\n (node, index) => \n format_feature(main_node_attentions[index]) + \" \\\\times \" + \"{\" +\n ((node.id == main_node.id) ? main_col : neigh_col) + \n format_feature(main_node_self_and_neighbours_values[index]) + \"}\"\n).join(\" + \")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2127,"value":"formatted_self_and_neighbours_partial_even_more = main_node_self_and_neighbours_values.map(\n (val, index) => format_feature(main_node_attentions[index] * val)\n).join(\" + \")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":840,"value":"formatted_self_and_neighbours_evaluated = format_feature(main_node_self_and_neighbours_values_agg)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2232,"value":"formatted_self_and_neighbours_attentions = main_node_attentions_logged.map(\n (weight) => \"\\\\exp\\{(\" + format_feature(weight) + \")\\}\"\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2262,"value":"formatted_self_and_neighbours_attentions_names = main_node_self_and_neighbours.map(\n (node) => \"\\\\exp\\{(\" + \"e_\\{\" + main_node.name.toString() + node.name.toString() + \"\\}\" + \")\\}\"\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2294,"value":"formatted_self_and_neighbours_attentions_names_normalized = formatted_self_and_neighbours_attentions_names.map(\n (formatted) => \"\\\\frac\\{\" + formatted + \"\\}\\{\" + formatted_self_and_neighbours_attentions_names.join(\" + \") + \"\\}\"\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2289,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2236,"value":"formatted_self_and_neighbours_attentions_normalized = formatted_self_and_neighbours_attentions.map(\n (formatted) => \"\\\\frac\\{\" + formatted + \"\\}\\{\" + formatted_self_and_neighbours_attentions.join(\" + \") + \"\\}\"\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2249,"value":"formatted_self_and_neighbours_attentions_normalized_annotated = formatted_self_and_neighbours_attentions_normalized.map(\n (formatted, index) =>\n \"\\\\alpha_\\{\" + main_node.name + main_node_self_and_neighbours[index].name + \"\\} = \" +\n formatted_self_and_neighbours_attentions_names_normalized[index] + \" &\\\\approx \" +\n format_feature(main_node_attentions[index]) +\n \".\"\n).join(\" \\\\\\\\ \")","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":2374,"value":"import {param_col, neigh_col, neigh_col_rgb, main_col, main_col_rgb} from \"@ameyasd/gnn-styles\";","pinned":false,"hidden":false,"mode":"ojs","author":"$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":"$undefined"},{"id":1778,"value":"W_slider = slider({\n min: -10,\n max: 10, \n step: 0.1,\n value: this ? this.input.value : 1,\n title: tex`W^{(${step + 1})}`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1783,"value":"A_slider = slider({\n min: -1,\n max: 1, \n step: 0.01,\n value: this ? this.input.value : 1,\n title: tex`A_W^{(${step + 1})}`, \n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W3b","stdlib":"1","titling":"auto"}} 32:"$31:body"