topos 0.13.0

An autodiff compiler stack in Rust.
Documentation 
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
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297

use std::thread;

use crate::{Parameters, Tape, Tensor};

#[test]
fn sealing_preserves_the_recorded_length() {
    let tape = Tape::new();
    tape.parameter(1.5_f64);
    tape.leaf(2.0);
    let recorded = tape.len();
    let network = tape.into_network();
    assert!(!network.is_empty());
    assert_eq!(network.len(), recorded);
}

#[test]
fn forward_reads_parameters_from_the_callers_state() {
    let tape = Tape::new();
    let parameter = tape.parameter(1.5_f64);
    let input = tape.leaf(2.0);
    let output = (parameter * input).symbol();
    let network = tape.into_network();

    let parameters = network.parameters();
    assert_eq!(network.forward(&parameters, []).of(output).scalar(), 3.0);
}

#[test]
fn input_defaults_flow_through_forward() {
    let tape = Tape::new();
    let input = tape.input(3.0_f64);
    let doubled = (input * 2.0).symbol();
    let network = tape.into_network();
    let parameters = network.parameters();
    assert_eq!(network.forward(&parameters, []).of(doubled).scalar(), 6.0);
}

#[test]
fn feeds_override_inputs_per_run() {
    let tape = Tape::new();
    let input = tape.input(1.0_f64);
    let doubled = (input * 2.0).symbol();
    let input = input.symbol();
    let network = tape.into_network();
    let parameters = network.parameters();

    let fed = network.forward(&parameters, [(input, 10.0.into())]);
    assert_eq!(fed.of(doubled).scalar(), 20.0);

    // Feeds are run-local: an unfed forward returns to the default,
    // which lives in the spec untouched.
    assert_eq!(network.forward(&parameters, []).of(doubled).scalar(), 2.0);
}

#[test]
#[should_panic(expected = "only inputs can be fed")]
fn feeds_reject_non_inputs() {
    let tape = Tape::new();
    let constant = tape.leaf(1.0_f64).symbol();
    let network = tape.into_network();
    network.forward(&network.parameters(), [(constant, 2.0.into())]);
}

#[test]
#[should_panic(expected = "symbol belongs to a different network")]
fn feeds_reject_foreign_symbols() {
    let tape = Tape::<f64>::new();
    let network = tape.into_network();
    let foreign = Tape::new().input(1.0_f64).symbol();
    network.forward(&network.parameters(), [(foreign, 2.0.into())]);
}

#[test]
#[should_panic(expected = "parameters belong to a different network")]
fn forward_rejects_foreign_parameters() {
    let tape = Tape::new();
    tape.parameter(1.0_f64);
    let network = tape.into_network();

    let other = Tape::new();
    other.parameter(1.0_f64);
    let foreign = other.into_network().parameters();
    network.forward(&foreign, []);
}

#[test]
fn concurrent_forwards_share_one_network_and_state() {
    let tape = Tape::new();
    let input = tape.input(0.0_f64);
    let squared = (input * input).symbol();
    let input = input.symbol();
    let network = tape.into_network();
    let parameters = network.parameters();

    thread::scope(|scope| {
        for fed in [2.0, 3.0, 4.0] {
            let network = &network;
            let parameters = &parameters;
            scope.spawn(move || {
                let run = network.forward(parameters, [(input, fed.into())]);
                assert_eq!(run.of(squared).scalar(), fed * fed);
            });
        }
    });
}

#[test]
fn training_steps_state_without_touching_the_network() {
    let tape = Tape::new();
    let weight = tape.parameter(0.0_f64);
    let bias = tape.parameter(0.0);
    let input = tape.input(0.0);
    let target = tape.input(0.0);
    let error = weight * input + bias - target;
    let loss = (error * error).symbol();
    let (weight, bias) = (weight.symbol(), bias.symbol());
    let (input, target) = (input.symbol(), target.symbol());
    let network = tape.into_network();
    let recorded = network.len();

    let samples = [(1.0, 3.0), (2.0, 5.0), (3.0, 7.0)];
    let mut parameters = network.parameters();
    for step in 0..600 {
        let (sample_input, sample_target) = samples[step % samples.len()];
        let run = network.forward(
            &parameters,
            [(input, sample_input.into()), (target, sample_target.into())],
        );
        let gradients = run.backward(loss).parameters(&parameters);
        parameters = parameters.step(&gradients, |parameter, gradient| {
            parameter.clone() - gradient.clone() * Tensor::from(0.05)
        });
    }

    assert_eq!(network.len(), recorded);
    assert!((parameters.of(weight).scalar() - 2.0).abs() < 1e-3);
    assert!((parameters.of(bias).scalar() - 1.0).abs() < 1e-3);
}

#[test]
fn gradient_descent_converges() {
    let tape = Tape::new();
    let parameter = tape.parameter(0.0_f64);
    let target = tape.leaf(3.0);
    let error = parameter - target;
    let loss = (error * error).symbol();
    let parameter = parameter.symbol();
    let network = tape.into_network();

    let mut parameters = network.parameters();
    for _ in 0..30 {
        let gradients = network
            .forward(&parameters, [])
            .backward(loss)
            .parameters(&parameters);
        parameters = parameters.step(&gradients, |parameter, gradient| {
            parameter.clone() - gradient.clone() * Tensor::from(0.3)
        });
    }
    assert!((parameters.of(parameter).scalar() - 3.0).abs() < 1e-6);
}

#[test]
fn momentum_descent_converges() {
    let tape = Tape::new();
    let parameter = tape.parameter(0.0_f64);
    let target = tape.leaf(3.0);
    let error = parameter - target;
    let loss = (error * error).symbol();
    let parameter = parameter.symbol();
    let network = tape.into_network();

    let mut parameters = network.parameters();
    let mut velocity: Option<Parameters<f64>> = None;
    for _ in 0..40 {
        let gradients = network
            .forward(&parameters, [])
            .backward(loss)
            .parameters(&parameters);
        let step = match velocity {
            Some(previous) => previous.scale(&0.5.into()) + gradients,
            None => gradients,
        };
        parameters = parameters.step(&step, |parameter, direction| {
            parameter.clone() - direction.clone() * Tensor::from(0.1)
        });
        velocity = Some(step);
    }
    assert!((parameters.of(parameter).scalar() - 3.0).abs() < 1e-3);
}

#[test]
fn forward_for_evaluates_only_the_ancestor_closure() {
    let tape: Tape<f64> = Tape::new();
    let x = tape.leaf(Tensor::new([2], [2.0_f64, 3.0]));
    let wanted = (x * x).sum().symbol();
    let _unwanted = (x + x).sum();
    let x = x.symbol();
    let network = tape.into_network();
    let parameters = network.parameters();

    let run = network.entry([wanted]).interpret(&parameters, []);
    assert_eq!(run.of(wanted).to_vec(), &[13.0]);

    // The sliced gradients match the full ones exactly.
    let sliced = run.backward(wanted);
    let full = network.forward(&parameters, []).backward(wanted);
    assert_eq!(sliced.of(x).to_vec(), full.of(x).to_vec());
}

#[test]
#[should_panic(expected = "not computed by this target-sliced run")]
fn sliced_reads_outside_the_closure_are_rejected() {
    let tape = Tape::new();
    let x = tape.leaf(2.0_f64);
    let wanted = (x * x).symbol();
    let unwanted = (x + x).symbol();
    let network = tape.into_network();

    let run = network.entry([wanted]).interpret(&network.parameters(), []);
    run.of(unwanted);
}

#[test]
#[should_panic(expected = "not computed by this target-sliced run")]
fn sliced_backward_outside_the_closure_is_rejected() {
    let tape = Tape::new();
    let x = tape.leaf(2.0_f64);
    let wanted = (x * x).symbol();
    let unwanted = (x + x).symbol();
    let network = tape.into_network();

    let run = network.entry([wanted]).interpret(&network.parameters(), []);
    run.backward(unwanted);
}

#[test]
fn forward_for_binds_feeds_like_forward() {
    let tape = Tape::new();
    let x = tape.input(Tensor::new([2], [0.0_f64, 0.0]));
    let doubled = (x * Tensor::new([2], [2.0, 2.0])).symbol();
    let x = x.symbol();
    let network = tape.into_network();

    let run = network
        .entry([doubled])
        .interpret(&network.parameters(), [(x, Tensor::new([2], [4.0, 5.0]))]);
    assert_eq!(run.of(doubled).to_vec(), &[8.0, 10.0]);
}

#[test]
fn sliced_gradients_step_parameters_like_full_gradients() {
    // Two expressions share one recording; slicing to the first must
    // step its parameter exactly as a full run does, while the second
    // expression's parameter receives its true gradient — zero — and
    // stays put.
    let tape = Tape::new();
    let first = tape.parameter(Tensor::new([2], [1.0_f64, 2.0]));
    let second = tape.parameter(Tensor::new([2], [5.0, 6.0]));
    let first_loss = (first * first).sum().symbol();
    let _second_loss = (second * second).sum();
    let (first, second) = (first.symbol(), second.symbol());
    let network = tape.into_network();

    let parameters = network.parameters();
    let run = network.entry([first_loss]).interpret(&parameters, []);
    let gradients = run.backward(first_loss).parameters(&parameters);
    let stepped = parameters.step(&gradients, |parameter: &Tensor<f64>, gradient| {
        parameter.clone() - gradient.clone()
    });

    // `d(sum(w^2))/dw = 2w`, so the first parameter steps by `-2w`.
    assert_eq!(stepped.of(first).to_vec(), &[-1.0, -2.0]);
    assert_eq!(stepped.of(second).to_vec(), &[5.0, 6.0]);
}

#[test]
fn reopened_networks_serve_old_runs_and_new_expressions() {
    let tape = Tape::new();
    let weight = tape.parameter(2.0_f64);
    let squared = (weight * weight).symbol();
    let weight = weight.symbol();
    let network = tape.into_network();
    let parameters = network.parameters();
    let run = network.forward(&parameters, []);
    assert_eq!(run.of(squared).scalar(), 4.0);

    // Linear extension: reopen, record, reseal. The old run keeps
    // answering, and the extended spec serves the new expression.
    let tape = network.into_tape();
    let cubed = (tape.resolve(squared) * tape.resolve(weight)).symbol();
    let network = tape.into_network();
    let parameters = parameters.carried(&network);

    assert_eq!(run.of(squared).scalar(), 4.0);
    assert_eq!(network.forward(&parameters, []).of(cubed).scalar(), 8.0);
}