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3d7f6c5 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 | """Training tasks for standalone WrinkleBrane evaluation.
Three tasks of increasing difficulty:
1. **Sequence Copy**: Write a random sequence, predict it shifted by one.
Tests basic memory write/read capability.
2. **Associative Recall**: Given key-value pairs followed by a query key,
predict the associated value. Tests selective retrieval.
3. **Synthetic Grammar LM**: Next-token prediction on sequences generated
by a procedural grammar with deterministic and stochastic rules.
Tests whether the model can learn distributional patterns.
All tasks produce ``(input_ids, target_ids)`` pairs suitable for
cross-entropy training with the same model interface.
"""
from __future__ import annotations
from typing import Tuple
import torch
from torch import Tensor
# ---------------------------------------------------------------------------
# Task 1: Sequence Copy
# ---------------------------------------------------------------------------
class SequenceCopyTask:
"""Memorize-and-reproduce task for testing memory write/read.
The model sees a random sequence, then a SEP token, then must
reproduce the sequence from memory:
Input: ``[t_0, t_1, ..., t_{L-1}, SEP, t_0, t_1, ..., t_{L-2}]``
Target: ``[IGN, IGN, ..., IGN, t_0, t_1, ..., t_{L-1}]``
Only the reproduction phase (after SEP) is scored. This directly
tests the model's ability to store tokens in the membrane and
retrieve them in order.
Parameters
----------
vocab_size : int
Number of tokens (including special tokens).
seq_len : int
Length of the random sequence to memorize.
"""
def __init__(
self,
vocab_size: int = 32,
seq_len: int = 8,
):
self.vocab_size = vocab_size
self.seq_len = seq_len
self.sep_token = 0
self.token_offset = 1 # data tokens start at 1
self.ignore_index = -100
def generate_batch(self, batch_size: int) -> Tuple[Tensor, Tensor]:
"""Generate a batch of copy sequences.
Returns
-------
input_ids : Tensor ``[B, 2 * seq_len]``
target_ids : Tensor ``[B, 2 * seq_len]``
First ``seq_len`` positions are ``ignore_index``.
"""
L = self.seq_len
# Random tokens in [token_offset, vocab_size)
tokens = torch.randint(
self.token_offset, self.vocab_size, (batch_size, L),
)
# Input: [t_0, ..., t_{L-1}, SEP, t_0, ..., t_{L-2}]
sep = torch.full((batch_size, 1), self.sep_token, dtype=torch.long)
input_ids = torch.cat([tokens, sep, tokens[:, :-1]], dim=1) # [B, 2L]
# Target: [IGN, ..., IGN, t_0, ..., t_{L-1}]
ignore = torch.full((batch_size, L), self.ignore_index, dtype=torch.long)
target_ids = torch.cat([ignore, tokens], dim=1) # [B, 2L]
return input_ids, target_ids
# ---------------------------------------------------------------------------
# Task 2: Associative Recall
# ---------------------------------------------------------------------------
class AssociativeRecallTask:
"""Generate key-value association sequences.
Format: ``[BOS, k1, v1, k2, v2, ..., SEP, k_query, PAD]``
Target: ``[IGN, IGN, IGN, ..., IGN, IGN, v_query]``
Only the final position's prediction is scored (the value for the
queried key).
Parameters
----------
vocab_size : int
Total vocabulary.
n_pairs : int
Number of key-value pairs per sequence.
"""
def __init__(
self,
vocab_size: int = 32,
n_pairs: int = 4,
):
self.vocab_size = vocab_size
self.n_pairs = n_pairs
# Special tokens
self.bos_token = 0
self.sep_token = 1
self.pad_token = 2
self.token_offset = 3 # data tokens start here
self.ignore_index = -100
def generate_batch(self, batch_size: int) -> Tuple[Tensor, Tensor]:
"""Generate a batch of associative recall sequences.
Returns
-------
input_ids : Tensor ``[B, 2*n_pairs + 3]``
target_ids : Tensor ``[B, 2*n_pairs + 3]``
All positions are ``ignore_index`` except the last.
"""
n = self.n_pairs
data_range = self.vocab_size - self.token_offset
# Generate unique keys and values
keys = torch.randint(
self.token_offset, self.token_offset + data_range // 2,
(batch_size, n),
)
values = torch.randint(
self.token_offset + data_range // 2, self.vocab_size,
(batch_size, n),
)
# Pick a random query index per batch
query_idx = torch.randint(0, n, (batch_size,))
query_keys = keys[torch.arange(batch_size), query_idx]
query_values = values[torch.arange(batch_size), query_idx]
# Build input: [BOS, k1, v1, k2, v2, ..., SEP, k_query, PAD]
seq_len = 2 * n + 3
input_ids = torch.full((batch_size, seq_len), self.pad_token, dtype=torch.long)
input_ids[:, 0] = self.bos_token
for i in range(n):
input_ids[:, 1 + 2 * i] = keys[:, i]
input_ids[:, 2 + 2 * i] = values[:, i]
input_ids[:, 1 + 2 * n] = self.sep_token
input_ids[:, 2 + 2 * n] = query_keys
# Target: ignore all except last position
target_ids = torch.full((batch_size, seq_len), self.ignore_index, dtype=torch.long)
target_ids[:, -1] = query_values
return input_ids, target_ids
# ---------------------------------------------------------------------------
# Task 3: Synthetic Grammar LM
# ---------------------------------------------------------------------------
class SyntheticGrammarTask:
"""Procedural grammar with learnable deterministic and stochastic rules.
Grammar structure:
- Vocabulary: ``vocab_size`` tokens (first 3 reserved for BOS/EOS/PAD)
- Rules are of the form: ``if current token is X, next token is Y``
(deterministic) or ``next is Y1 or Y2 with probabilities p, 1-p``
(stochastic)
- Some tokens trigger deterministic bigram patterns (always A→B)
- Some tokens trigger probabilistic choices (C → D 70% or E 30%)
- Some tokens are "wild" (uniform random next token)
This creates a learnable language with enough structure to test whether
the model captures distributional patterns.
Parameters
----------
vocab_size : int
Total vocabulary including special tokens.
seq_len : int
Sequence length.
deterministic_frac : float
Fraction of tokens with deterministic next-token rules.
stochastic_frac : float
Fraction of tokens with 2-way stochastic rules.
seed : int
RNG seed for rule generation (grammar is fixed, sequences vary).
"""
def __init__(
self,
vocab_size: int = 32,
seq_len: int = 64,
deterministic_frac: float = 0.4,
stochastic_frac: float = 0.3,
seed: int = 42,
):
self.vocab_size = vocab_size
self.seq_len = seq_len
self.bos_token = 0
self.eos_token = 1
self.pad_token = 2
self.token_offset = 3
gen = torch.Generator().manual_seed(seed)
data_tokens = list(range(self.token_offset, vocab_size))
n_data = len(data_tokens)
n_det = int(n_data * deterministic_frac)
n_stoch = int(n_data * stochastic_frac)
# Shuffle to assign rule types
perm = torch.randperm(n_data, generator=gen).tolist()
det_tokens = [data_tokens[i] for i in perm[:n_det]]
stoch_tokens = [data_tokens[i] for i in perm[n_det:n_det + n_stoch]]
# Build rule tables
self.det_rules = {} # token -> next_token
self.stoch_rules = {} # token -> (token_a, token_b, prob_a)
for t in det_tokens:
next_t = data_tokens[torch.randint(0, n_data, (1,), generator=gen).item()]
self.det_rules[t] = next_t
for t in stoch_tokens:
a = data_tokens[torch.randint(0, n_data, (1,), generator=gen).item()]
b = data_tokens[torch.randint(0, n_data, (1,), generator=gen).item()]
while b == a:
b = data_tokens[torch.randint(0, n_data, (1,), generator=gen).item()]
prob_a = 0.3 + 0.4 * torch.rand(1, generator=gen).item() # 0.3-0.7
self.stoch_rules[t] = (a, b, prob_a)
self.wild_tokens = [
t for t in data_tokens
if t not in self.det_rules and t not in self.stoch_rules
]
# Pre-compute vectorised lookup tables for fast batch generation.
# rule_type[t]: 0=det, 1=stoch, 2=wild
self._rule_type = torch.full((vocab_size,), 2, dtype=torch.long)
# det_target[t]: deterministic next token (only valid when rule_type==0)
self._det_target = torch.zeros(vocab_size, dtype=torch.long)
# stoch_a[t], stoch_b[t], stoch_p[t]: stochastic rule params
self._stoch_a = torch.zeros(vocab_size, dtype=torch.long)
self._stoch_b = torch.zeros(vocab_size, dtype=torch.long)
self._stoch_p = torch.zeros(vocab_size)
for t, nt in self.det_rules.items():
self._rule_type[t] = 0
self._det_target[t] = nt
for t, (a, b, p) in self.stoch_rules.items():
self._rule_type[t] = 1
self._stoch_a[t] = a
self._stoch_b[t] = b
self._stoch_p[t] = p
def generate_batch(self, batch_size: int) -> Tuple[Tensor, Tensor]:
"""Generate a batch of grammar sequences (vectorised).
Returns
-------
input_ids : Tensor ``[B, seq_len]``
target_ids : Tensor ``[B, seq_len]``
Shifted by one (standard LM target).
"""
B = batch_size
S = self.seq_len + 1 # need one extra for shift
n_data = self.vocab_size - self.token_offset
tokens = torch.empty(B, S, dtype=torch.long)
tokens[:, 0] = self.bos_token
# Random start tokens for the whole batch
current = torch.randint(self.token_offset, self.vocab_size, (B,))
tokens[:, 1] = current
# Pre-sample all random numbers we'll need
rand_vals = torch.rand(B, S)
wild_tokens = torch.randint(self.token_offset, self.vocab_size, (B, S))
for t in range(2, S):
rt = self._rule_type[current] # [B]
det_next = self._det_target[current] # [B]
sa = self._stoch_a[current] # [B]
sb = self._stoch_b[current] # [B]
sp = self._stoch_p[current] # [B]
# Stochastic: pick a if rand < p, else b
stoch_next = torch.where(rand_vals[:, t] < sp, sa, sb)
# Combine: det if rt==0, stoch if rt==1, wild if rt==2
next_tok = torch.where(rt == 0, det_next,
torch.where(rt == 1, stoch_next, wild_tokens[:, t]))
tokens[:, t] = next_tok
current = next_tok
input_ids = tokens[:, :-1].contiguous() # [B, seq_len]
target_ids = tokens[:, 1:].contiguous() # [B, seq_len]
return input_ids, target_ids
# ---------------------------------------------------------------------------
# Evaluation utilities
# ---------------------------------------------------------------------------
def compute_accuracy(
logits: Tensor,
targets: Tensor,
ignore_index: int = -100,
) -> float:
"""Compute token-level accuracy, ignoring padded positions.
Parameters
----------
logits : Tensor ``[B, T, V]``
targets : Tensor ``[B, T]``
ignore_index : int
Target values to ignore.
Returns
-------
float
Accuracy in [0, 1].
"""
preds = logits.argmax(dim=-1) # [B, T]
mask = targets != ignore_index
if mask.sum() == 0:
return 0.0
correct = ((preds == targets) & mask).sum()
return float(correct) / float(mask.sum())
def compute_perplexity(loss: float) -> float:
"""Convert cross-entropy loss to perplexity."""
return math.exp(min(loss, 100)) # clamp to avoid overflow
import math
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