5 import torch, torchvision
8 from torch.nn import functional as F
10 ######################################################################
14 def generate_sequences(self, nb):
17 def seq2str(self, seq):
18 return "[NOT IMPLEMENTED]"
20 def compute_nb_correct(self, input, ar_mask, result):
21 nb_total = ar_mask.sum().item()
22 nb_correct = ((result == input).long() * ar_mask).sum().item()
23 return nb_total, nb_correct
29 class ProblemDegradation(Problem):
30 def __init__(self, nb_state_tokens=5, nb_time_steps=12, value_max=25, hard=False):
31 assert value_max // nb_state_tokens >= 2
32 self.nb_state_tokens = nb_state_tokens
33 self.nb_time_steps = nb_time_steps
34 self.value_max = value_max
37 def generate_sequences(self, nb):
39 torch.rand(nb, self.nb_state_tokens).sort(dim=-1).indices == 0
40 ).long() * self.value_max
43 for t in range(self.nb_time_steps - 1):
44 v = (torch.rand(x.size()).sort(dim=-1).indices + 1) * (x >= 2).long()
45 u = (v.max(dim=-1, keepdim=True).values == v).long()
48 .minimum(2 + torch.randint(self.value_max // 4 - 2, x.size()))
49 .sum(dim=-1, keepdim=True)
51 m = 1 + ((n - 1) * torch.rand(n.size())).long()
54 + m * u.roll(shifts=-1, dims=-1)
56 + (n - m) * u.roll(shifts=1, dims=-1)
63 seq = torch.cat(seq, dim=1)
64 return seq, seq.new_full(seq.size(), 1, dtype=torch.int64)
66 def compute_nb_correct(self, input, ar_mask, result):
67 nb_total = result.size(0)
69 e = result.new_zeros(self.nb_state_tokens)
72 states = list(seq.split(self.nb_state_tokens))
77 j = d.sort(descending=True).indices[0]
80 if (d - e).abs().sum() == 0:
82 for k in range(len(states) - 1):
83 d = states[k + 1] - states[k]
84 j = d.sort(descending=False).indices[0]
87 or d[j] > self.value_max // 4
88 or d[(j + 1) % e.size(0)] <= 0
89 or d[(j + 1) % e.size(0)] >= -d[j]
95 e[(j + 1) % e.size(0)] = d[(j + 1) % e.size(0)]
96 e[(j - 1) % e.size(0)] = -d[(j + 1) % e.size(0)] - d[j]
97 if (d - e).abs().sum() > 0:
102 return nb_total, nb_correct
104 def seq2str(self, seq):
106 [" ".join([f"{x:02d}" for x in s]) for s in seq.split(self.nb_state_tokens)]
113 class ProblemTwoTargets(Problem):
114 def __init__(self, len_total=10, len_targets=3):
115 assert len_targets >= 3
116 assert len_total >= 3 * len_targets - 1
117 self.len_total = len_total
118 self.len_targets = len_targets
120 def generate_sequences(self, nb):
121 k = torch.arange(self.len_total)[None, :]
122 s = torch.randint(10, (nb, self.len_total))
123 l = torch.rand(nb, self.len_total)
124 l = l * (k <= self.len_total - self.len_targets).long()
125 k1 = l.argmax(dim=1, keepdim=True)
126 m = (k != k1).long() * (k != k1 + self.len_targets - 1).long()
127 s = s * m + 10 * (1 - m)
130 - (k + self.len_targets - 1 >= k1).long()
131 * (k < k1 + self.len_targets).long()
133 k2 = l.argmax(dim=1, keepdim=True)
134 m = (k != k2).long() * (k != k2 + self.len_targets - 1).long()
135 s = s * m + 11 * (1 - m)
136 a1 = s.gather(dim=1, index=k1 + 1 + torch.arange(self.len_targets - 2)[None, :])
137 a2 = s.gather(dim=1, index=k2 + 1 + torch.arange(self.len_targets - 2)[None, :])
138 sequences = torch.cat(
141 torch.full((nb, 1), 12),
143 torch.full((nb, 1), 12),
145 torch.full((nb, 1), 12),
149 ar_mask = (sequences == 12).long()
150 ar_mask = (ar_mask.cumsum(1) - ar_mask).clamp(max=1)
151 return sequences, ar_mask
153 def seq2str(self, seq):
154 return "".join("0123456789-+|"[x.item()] for x in seq)
160 class ProblemByHeart(Problem):
161 def __init__(self, nb_sentences=100, len_prompt=8, len_result=8):
162 self.seq = torch.randint(10, (nb_sentences, len_prompt + 1 + len_result))
163 self.seq[:, len_prompt] = 10
165 def generate_sequences(self, nb):
166 sequences = self.seq[torch.randint(self.seq.size(0), (nb,))]
167 ar_mask = (sequences == 10).long()
168 ar_mask = (ar_mask.cumsum(1) - ar_mask).clamp(max=1)
169 return sequences, ar_mask
171 def seq2str(self, seq):
172 return "".join("0123456789|"[x.item()] for x in seq)
178 class ProblemLearnOperator(Problem):
179 def __init__(self, nb_operators=100, len_source=6, len_result=9):
180 self.len_source = len_source
181 self.len_result = len_result
182 self.len_nb_operator = int(math.log(nb_operators) / math.log(10)) + 1
183 self.operators = F.one_hot(
184 torch.rand(nb_operators, len_result, len_source).argmax(-1),
185 num_classes=len_source,
188 def generate_sequences(self, nb):
189 nb_operators = torch.randint(self.operators.size(0), (nb,))
190 operators = self.operators[nb_operators]
192 nb_operators[:, None]
193 // 10 ** torch.arange(self.len_nb_operator - 1, -1, -1)
195 marker1 = torch.full((nb, 1), 10)
196 source = torch.rand(nb, 10).sort(dim=1).indices[:, : self.len_source]
197 marker2 = torch.full((nb, 1), 11)
198 result = operators.bmm(source[:, :, None]).squeeze(-1)
199 sequences = torch.cat((nb_operators, marker1, source, marker2, result), 1)
200 ar_mask = (sequences == 11).long()
201 ar_mask = (ar_mask.cumsum(1) - ar_mask).clamp(max=1)
202 return sequences, ar_mask
204 def seq2str(self, seq):
205 return "".join("0123456789|>"[x.item()] for x in seq)
211 class ProblemGuessOperator(Problem):
212 def __init__(self, len_source=5, len_result=8):
213 self.len_source = len_source
214 self.len_result = len_result
216 def generate_sequences(self, nb):
217 operators = F.one_hot(
218 torch.rand(nb, self.len_result, self.len_source).argmax(-1),
219 num_classes=self.len_source,
221 source1 = torch.rand(nb, 10).sort(dim=1).indices[:, : self.len_source]
222 marker1 = torch.full((nb, 1), 10)
223 result1 = operators.bmm(source1[:, :, None]).squeeze(-1)
224 marker2 = torch.full((nb, 1), 11)
225 source2 = torch.randint(10, (nb, self.len_source))
226 marker3 = torch.full((nb, 1), 12)
227 result2 = operators.bmm(source2[:, :, None]).squeeze(-1)
229 sequences = torch.cat(
230 (source1, marker1, result1, marker2, source2, marker3, result2), 1
232 ar_mask = (sequences == 12).long()
233 ar_mask = (ar_mask.cumsum(1) - ar_mask).clamp(max=1)
234 return sequences, ar_mask
236 def seq2str(self, seq):
237 return "".join("0123456789>|~"[x.item()] for x in seq)
243 class ProblemAddition(Problem):
244 def __init__(self, nb_digits=10, zero_padded=False, inverted_result=False):
245 self.nb_digits = nb_digits
246 self.zero_padded = zero_padded
247 self.inverted_result = inverted_result
248 self.char2id = dict([(c, n) for n, c in enumerate("0123456789+=$")])
249 self.id2char = dict([(n, c) for c, n in self.char2id.items()])
251 def tensorize(self, strings):
252 len_max = max([len(x) for x in strings])
257 [self.char2id[c] for c in s + "$" * (len_max - len(s))]
265 def generate_sequences(self, nb):
268 a, b = torch.randint(10**self.nb_digits, (2,))
270 a, b, c = str(a.item()), str(b.item()), str(c.item())
272 a = "0" * (self.nb_digits - len(a)) + a
273 b = "0" * (self.nb_digits - len(b)) + b
274 c = "0" * (self.nb_digits + 1 - len(c)) + c
275 if self.inverted_result:
277 sequences.append(f"{a}+{b}={c}$")
279 sequences = self.tensorize(sequences)
280 ar_mask = (sequences == self.char2id["="]).long()
281 ar_mask = (ar_mask.cumsum(1) - ar_mask).clamp(max=1)
282 return sequences, ar_mask
284 def seq2str(self, seq):
285 return "".join(self.id2char[x.item()] for x in seq)
291 class ProblemMixing(Problem):
293 self, height=4, width=4, nb_time_steps=9, hard=False, random_start=True
297 self.nb_time_steps = nb_time_steps
299 self.random_start = random_start
301 def start_random(self, nb):
302 y = torch.arange(self.height * self.width).reshape(1, -1).expand(nb, -1)
304 if self.random_start:
306 torch.arange(self.height)
308 .expand(nb, self.height, self.width)
311 torch.arange(self.width)
313 .expand(nb, self.height, self.width)
316 ri = torch.randint(self.height, (nb,)).reshape(nb, 1, 1)
317 rj = torch.randint(self.width, (nb,)).reshape(nb, 1, 1)
319 m = 1 - torch.logical_or(i == ri, j == rj).long().flatten(1)
321 y = y * m + self.height * self.width * (1 - m)
323 y = y.reshape(nb, self.height, self.width)
327 def start_error(self, x):
328 i = torch.arange(self.height, device=x.device).reshape(1, -1, 1).expand_as(x)
329 j = torch.arange(self.width, device=x.device).reshape(1, 1, -1).expand_as(x)
332 (x == self.height * self.width).long().sum(dim=-1).argmax(-1).view(-1, 1, 1)
335 (x == self.height * self.width).long().sum(dim=-2).argmax(-1).view(-1, 1, 1)
338 m = 1 - torch.logical_or(i == ri, j == rj).long().flatten(1)
341 u = torch.arange(self.height * self.width, device=x.device).reshape(1, -1)
343 d = (x - (m * u + (1 - m) * self.height * self.width)).abs().sum(-1)
349 .expand(-1, self.height * 2 + self.width * 2, -1, -1)
354 for i in range(self.height):
355 y[:, k, i, :] = y[:, k, i, :].roll(dims=-1, shifts=-1)
357 y[:, k, i, :] = y[:, k, i, :].roll(dims=-1, shifts=1)
360 for j in range(self.width):
361 y[:, k, :, j] = y[:, k, :, j].roll(dims=-1, shifts=-1)
363 y[:, k, :, j] = y[:, k, :, j].roll(dims=-1, shifts=1)
368 def generate_sequences(self, nb):
369 x = self.start_random(nb)
373 for t in range(self.nb_time_steps - 1):
375 x = y[torch.arange(nb), torch.randint(y.size(1), (nb,))]
376 seq.append(x.flatten(1))
381 seq = torch.cat(seq, dim=1)
382 return seq, seq.new_full(seq.size(), 1, dtype=torch.int64)
384 def compute_nb_correct(self, input, ar_mask, result):
386 x.reshape(result.size(0), self.height, self.width)
387 for x in result.split(self.height * self.width, dim=1)
394 d = self.start_error(x)
396 for t in range(self.nb_time_steps - 1):
397 x0, x = a[t], a[t + 1]
399 d = d + (x[:, None] - y).abs().sum((-1, -2)).min(dim=-1).values
401 nb_total, nb_correct = result.size(0), (d == 0).long().sum().item()
403 return nb_total, nb_correct
405 def seq2str(self, seq):
412 f"{x:02d}" if x < self.height * self.width else "**"
416 for s in r.split(self.width)
419 for r in seq.split(self.height * self.width)
426 if __name__ == "__main__":
428 s, m = p.generate_sequences(10000)
431 print(p.compute_nb_correct(None, None, s))