"""Datasets: text8 for language modelling, plus dependency-controlled probes. text8 is the standard small-scale benchmark for discrete diffusion language models (D3PM, SEDD, MDLM all report bits-per-character on it), which is what makes a from-scratch comparison meaningful. The probes exist because text8 alone cannot isolate the phenomenon we study. Parallel decoding fails when simultaneously-revealed tokens depend on each other, so we need tasks where that dependence is a knob rather than a property of English. """ import os import numpy as np TEXT8_URL = "http://mattmahoney.net/dc/text8.zip" # text8 is lowercase letters plus space: a 27-symbol alphabet, no tokenizer. ALPHABET = " abcdefghijklmnopqrstuvwxyz" SPECIALS = ["[MASK]", "[PAD]"] class CharTokenizer: def __init__(self): self.itos = SPECIALS + list(ALPHABET) self.stoi = {c: i for i, c in enumerate(self.itos)} self.mask = self.stoi["[MASK]"] self.pad = self.stoi["[PAD]"] def __len__(self): return len(self.itos) def encode(self, s): return [self.stoi[c] for c in s if c in self.stoi] def decode(self, ids): return "".join(self.itos[i] for i in ids) def load_text8(root, seq_len=256): """Standard 90M/5M/5M character split used throughout the literature.""" raw = os.path.join(root, "text8") if not os.path.exists(raw): os.makedirs(root, exist_ok=True) import zipfile, io, requests # only needed on first download r = requests.get(TEXT8_URL, timeout=300) r.raise_for_status() with zipfile.ZipFile(io.BytesIO(r.content)) as z: z.extract("text8", root) text = open(raw).read() assert len(text) == 100_000_000, f"unexpected text8 length {len(text)}" tok = CharTokenizer() cache = os.path.join(root, "text8.npy") if os.path.exists(cache): ids = np.load(cache) else: ids = np.array(tok.encode(text), dtype=np.uint8) np.save(cache, ids) tr, va = ids[:90_000_000], ids[90_000_000:95_000_000] te = ids[95_000_000:] def chunk(a): n = len(a) // seq_len return a[: n * seq_len].reshape(n, seq_len).astype(np.int64) return chunk(tr), chunk(va), chunk(te), tok # --------------------------------------------------------------------------- # Dependency-controlled probes. # # Each item is a sequence whose tokens must agree with each other. `coupling` # sets how many positions are bound together, which is the exact quantity that # breaks parallel decoding: revealing two mutually-dependent positions in one # step forces the model to guess them independently. # --------------------------------------------------------------------------- def build_probe(n, seq_len, coupling, seed=0, task="copy"): """ copy : second half must equal the first half. Each answer position is fixed by one context position, so answer positions are mutually INDEPENDENT given the context - parallel decoding should be safe. agree : within each group of `coupling` positions all tokens must be equal AND adjacent groups must differ. The value of a group is free, so its members are mutually DEPENDENT: revealing two of them in one step is a 1/V coin flip. This is the failure mode, isolated. parity : groups are a run of bits whose last element is the XOR of the rest, with adjacent groups forced to differ, so the group is jointly constrained without any member being determined alone. The adjacent-groups-differ rule matters: without it a model that emits one constant token everywhere satisfies "all members agree" perfectly, and an untrained model scores 100% at maximum parallelism. That degenerate solution made the first version of this metric meaningless. """ tok = CharTokenizer() rng = np.random.default_rng(seed) V = 2 + 26 # specials + letters lo, hi = 2, V # sample letters only X = np.zeros((n, seq_len), dtype=np.int64) for i in range(n): if task == "copy": half = seq_len // 2 src = rng.integers(lo, hi, size=half) X[i, :half] = src X[i, half:half * 2] = src elif task == "agree": g, prev = coupling, -1 for s in range(0, seq_len, g): v = int(rng.integers(lo, hi)) while v == prev: # adjacent groups must differ v = int(rng.integers(lo, hi)) X[i, s:s + g] = v prev = v elif task == "parity": g, prev = coupling, None for s in range(0, seq_len, g): end = min(s + g, seq_len) if end - s < 2: X[i, s:end] = lo continue while True: bits = list(rng.integers(0, 2, size=end - s - 1)) vals = bits + [int(sum(bits) % 2)] if vals != prev: # adjacent groups must differ break X[i, s:end] = [lo + v for v in vals] prev = vals else: raise ValueError(task) return X, tok # --------------------------------------------------------------------------- # Addition: the canonical UNIQUE-answer task with chained inter-token # dependence. Given the operands the answer is fully determined, so every # position's true marginal is a point mass and parallel decoding faces no # information-theoretic barrier - unlike `agree`/`parity`, where the value is # genuinely free and the bound is unbeatable. What remains is a computation # problem: digit i needs the carry out of digit i-1, and sequential decoding # amortises that chain across passes while parallel decoding must fit it inside # one fixed-depth forward pass. # --------------------------------------------------------------------------- DIGITS10 = "0123456789" class AddTokenizer: def __init__(self): self.itos = ["[MASK]", "[PAD]", "+", "="] + list(DIGITS10) self.stoi = {c: i for i, c in enumerate(self.itos)} self.mask = self.stoi["[MASK]"] self.pad = self.stoi["[PAD]"] def __len__(self): return len(self.itos) def build_addition(n, digits, seq_len, seed=0, exact=False): """Returns (X, answer_mask, tok). Layout: operand a, '+', operand b, '=', then the answer written units-first. `answer_mask` marks the positions the model must produce; the prompt is always visible, so the task is conditional and the answer unique. """ tok = AddTokenizer() rng = np.random.default_rng(seed) X = np.full((n, seq_len), tok.pad, dtype=np.int64) A = np.zeros((n, seq_len), dtype=bool) for i in range(n): d = digits if exact else int(rng.integers(1, digits + 1)) def draw(nd): ds = rng.integers(0, 10, size=nd) if nd > 1 and ds[0] == 0: ds[0] = rng.integers(1, 10) return "".join(str(int(v)) for v in ds) pa, pb = draw(d), draw(d) s = str(int(pa) + int(pb))[::-1] # units first seq = list(pa) + ["+"] + list(pb) + ["="] + list(s) if len(seq) > seq_len: raise ValueError(f"seq_len {seq_len} too small for {d} digits") ids = [tok.stoi[c] for c in seq] X[i, : len(ids)] = ids A[i, len(pa) + len(pb) + 2: len(ids)] = True # answer positions only return X, A, tok