1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
|
'use strict';
const DEFAULT_WEIGHT_MAX = 4;
// prototype for network objects
const network_proto = {
connect: function(source, sink, weight) {
return network_connect(this, source, sink, weight);
},
compute: function(inputs, state) {
return network_compute(this, inputs, state);
},
};
// create a new network
export function network(input_count, internal_count, output_count, weight_max = 4) {
const count = input_count + internal_count + output_count;
const n = Object.create(network_proto);
n.input_count = input_count;
n.output_count = output_count;
n.adjacency = new Array(count).fill([]);
n.weight = [];
return Object.freeze(n);
}
// check index is an input
function is_input(n, index) {
return index < n.input_count;
}
// check if index is an output
function is_output(n, index) {
return index >= (n.adjacency.length - n.output_count);
}
// returns a new network with an edge between the given nodes
// with the given weight
function network_connect(n, source, sink, weight) {
if (is_input(n, sink)) {
// inputs cannot be sinks
throw new Error("attempt to use input as sink");
}
if (is_output(n, source)) {
// outputs cannot be sources
throw new Error("attempt to use output as source");
}
const nn = Object.create(network_proto);
nn.input_count = n.input_count;
nn.output_count = n.output_count;
nn.adjacency = n.adjacency.map((row, i) => {
if (i === source && i === sink) {
// self-loop
return [...row, 2];
} else if (i === source) {
return [...row, 1];
} else if (i === sink) {
return [...row, -1];
} else {
return [...row, 0];
}
});
nn.weight = [...n.weight, weight];
return Object.freeze(nn);
}
// gets the indices of the edges incident on the given adjacency list
function incident_edges(n, adj) {
const incident = adj
.map((edge, index) => (edge < 0) || (edge === 2) ? index : null)
.filter(index => index !== null);
console.log(incident);
return incident;
}
// get the indices of the ends of an edge
// in the case of self-loops, both values are the same
function edge_ends(n, edge) {
const ends = n.adjacency
.map((adj, index) => adj[edge] !== 0 ? index : null)
.filter(index => index != null);
ends.sort((a, b) => n.adjacency[a][edge] < n.adjacency[b][edge] ? -1 : 1);
if (ends.length === 1) {
return { source: ends[0], sink: ends[0] };
} else if (ends.length === 2) {
return { source: ends[1], sink: ends[0] };
} else {
throw new Error("something bad happened with the ends");
}
}
// recursively get the value of a node from the input nodes,
// optionally caching the computed values
function get_value(n, index, input, prev, cache) {
if (cache !== undefined && cache[index]) {
return cache[index];
}
if (is_input(n, index)) {
return input[index];
}
const adj = n.adjacency[index];
const incident = incident_edges(n, adj);
const weight = incident.map(x => n.weight[x]);
const sources = incident
.map(x => edge_ends(n, x).source);
const values = sources
.map(x => x === index ? prev[x - n.input_count] : get_value(n, x, input, prev, cache));
console.log(n, index, sources, values);
const sum = values
.reduce((acc, x, i) => acc + (weight[i] * x), 0);
const value = Math.tanh(sum);
// !!! impure caching !!!
if (cache !== undefined) {
cache[index] = value;
}
return value;
}
// compute a network's output and new hidden state
// given the input and previous hidden state
function network_compute(n, input, state) {
// !!! impure caching !!!
const value_cache = {};
const hidden = n.adjacency
.map((x, i) =>
(
(!(is_input(n, i))) &&
(!is_output(n, i))) ? i : null)
.filter(i => i !== null);
const outputs = n.adjacency
.map((x, i) => is_output(n, i) ? i : null)
.filter(i => i !== null);
const output = Object.freeze(
outputs.map(x => get_value(n, x, input, state, value_cache))
);
const newstate = Object.freeze(
hidden.map(x => get_value(n, x, input, state, value_cache))
);
return Object.freeze([output, newstate]);
}
|
