"""Tiny arithmetic LM — from-scratch GPT, digit-level vocab, SFT on generated data. Single file, no deps beyond torch+numpy. Runs unchanged on local CPU (dry-run preset) and Kaggle T4 (sweep preset). Format experiment (Phase 0b picks the winner): l2r : "47+68=\n115\n" answer left-to-right rtl : "47+68=\n511\n" answer right-to-left (carry-friendly) cot : "47+68=\n7+8=15,4+6+1=11,115\n" digit-wise steps, comma-separated, answer = last comma-field. Single trailing newline keeps eval-stopping trivial (generate until first '\n'). """ import argparse, json, math, os, random, time from pathlib import Path import numpy as np import torch import torch.nn as nn import torch.nn.functional as F # ---------------------------------------------------------------- tokenizer VOCAB = list("0123456789+-=\n,") + [""] TOK = {c: i for i, c in enumerate(VOCAB)} PAD = TOK[""] V = len(VOCAB) # 16 def enc(s): return [TOK[c] for c in s] def dec(ids): return "".join(VOCAB[i] for i in ids) # ---------------------------------------------------------------- data def sample_pair(rng, digits): lo, hi = (0, 9) if digits == 1 else (10 ** (digits - 1), 10 ** digits - 1) return rng.randint(lo, hi), rng.randint(lo, hi) def format_problem(a, b, ans, fmt): if fmt == "l2r": return f"{a}+{b}=\n{ans}\n" if fmt == "rtl": return f"{a}+{b}=\n{str(ans)[::-1]}\n" if fmt == "cot": sa, sb = str(a), str(b) n = max(len(sa), len(sb)) sa, sb = sa.rjust(n, "0"), sb.rjust(n, "0") steps, carry = [], 0 for i in range(n - 1, -1, -1): d1, d2 = int(sa[i]), int(sb[i]) s = d1 + d2 + carry steps.append(f"{d1}+{d2}" + (f"+{carry}" if carry else "") + f"={s}") carry = s // 10 return f"{a}+{b}=\n{','.join(steps)},{ans}\n" raise ValueError(fmt) def parse_answer(completion, fmt): """completion = generated text after the prompt, before stopping.""" line = completion.split("\n")[0].strip() if not line: return None if fmt == "rtl": return line[::-1] if fmt == "cot": return line.split(",")[-1] return line def max_new_for(fmt, digits=4): # cot completion ≈ 9 chars/step + answer; l2r/rtl ≈ answer + newline return {"l2r": digits + 4, "rtl": digits + 4, "cot": 10 * digits + 12}[fmt] def make_stream(seed, digits, fmt, eval_set, budget_tokens): """Generator of token-id chunks; rejects problems in eval_set (guarantees zero train/eval contamination by construction). Yields one problem's ids per chunk; constant memory at any budget.""" py_rng = random.Random(seed) n = 0 while n < budget_tokens: a, b = sample_pair(py_rng, digits) if (a, b) in eval_set: continue text = format_problem(a, b, a + b, fmt) n += len(text) yield enc(text) def make_eval_set(seed, digits, n_problems, exclude=None): """Fixed held-out problems. exclude: set of (a,b) pairs to never return (used to keep the tuning-eval and final-eval sets disjoint). Attempts-guarded: for tiny digit spaces (1-digit = 100 pairs) it returns what exists instead of looping forever.""" rng = random.Random(seed) exclude = exclude or set() seen, out, attempts = set(), [], 0 while len(out) < n_problems and attempts < n_problems * 100 + 10_000: attempts += 1 a, b = sample_pair(rng, digits) if (a, b) in seen or (a, b) in exclude: continue seen.add((a, b)) out.append((a, b)) return out # ---------------------------------------------------------------- model class Block(nn.Module): def __init__(self, d, H): super().__init__() self.ln1 = nn.LayerNorm(d) self.qkv = nn.Linear(d, 3 * d) self.proj = nn.Linear(d, d) self.ln2 = nn.LayerNorm(d) self.mlp = nn.Sequential(nn.Linear(d, 4 * d), nn.GELU(), nn.Linear(4 * d, d)) self.H = H def forward(self, x, mask): h = self.ln1(x) q, k, v = self.qkv(h).chunk(3, -1) B, T, d = q.shape hd = d // self.H q = q.view(B, T, self.H, hd).transpose(1, 2) k = k.view(B, T, self.H, hd).transpose(1, 2) v = v.view(B, T, self.H, hd).transpose(1, 2) a = F.scaled_dot_product_attention(q, k, v, attn_mask=mask, is_causal=mask is None) a = a.transpose(1, 2).reshape(B, T, d) x = x + self.proj(a) x = x + self.mlp(self.ln2(x)) return x class TinyGPT(nn.Module): def __init__(self, d, L, H, ctx=64): super().__init__() self.emb = nn.Embedding(V, d) self.pos = nn.Embedding(ctx, d) self.blocks = nn.ModuleList(Block(d, H) for _ in range(L)) self.ln = nn.LayerNorm(d) self.head = nn.Linear(d, V, bias=False) self.apply(self._init) @staticmethod def _init(m): if isinstance(m, (nn.Linear, nn.Embedding)): nn.init.normal_(m.weight, std=0.02) if isinstance(m, nn.Linear) and m.bias is not None: nn.init.zeros_(m.bias) def forward(self, idx): B, T = idx.shape p = torch.arange(T, device=idx.device) x = self.emb(idx) + self.pos(p)[None] for b in self.blocks: x = b(x, None) return self.head(self.ln(x)) SIZES = { "1m": dict(d=128, L=4, H=4), # ~1.07M "5m": dict(d=192, L=8, H=6), # ~4.76M "8m": dict(d=256, L=8, H=8), # ~8.45M } def count_params(m): return sum(p.numel() for p in m.parameters()) # ---------------------------------------------------------------- eval @torch.no_grad() def evaluate(model, eval_pairs, fmt, device, batch=256, digits=4, return_trunc=False): """Greedy decode, strict exact-match. Returns (acc, n_correct, examples) or (..., trunc_frac) when return_trunc=True — trunc_frac = fraction of generations that hit the length cap without emitting a newline (needed when evaluating beyond trained sequence lengths, where truncation can silently masquerade as model failure).""" model.eval() mx = max_new_for(fmt, digits) prompts = [f"{a}+{b}=\n" for a, b in eval_pairs] golds = [str(a + b) for a, b in eval_pairs] correct, wrong_ex = 0, [] truncated = 0 for i in range(0, len(prompts), batch): pb = prompts[i:i + batch] gb = golds[i:i + batch] ids = torch.tensor([enc(p) for p in pb], device=device) done = torch.zeros(len(pb), dtype=torch.bool, device=device) for _ in range(mx): if ids.shape[1] >= model.pos.num_embeddings - 1: break # hard stop at positional-embedding limit; never crash logits = model(ids) nxt = logits[:, -1].argmax(-1, keepdim=True) ids = torch.cat([ids, nxt], 1) done |= (nxt.squeeze(1) == TOK["\n"]) if done.all(): break truncated += int((~done).sum()) for j, (p, g) in enumerate(zip(pb, gb)): gen = ids[j, len(p):].tolist() comp = [] for t in gen: if t == TOK["\n"]: break comp.append(t) pred = parse_answer(dec(comp), fmt) if pred == g: correct += 1 elif len(wrong_ex) < 5: wrong_ex.append((p.replace("\n", "\\n"), dec(comp).replace("\n", "\\n"), g)) model.train() if return_trunc: return correct / len(prompts), correct, wrong_ex, truncated / len(prompts) return correct / len(prompts), correct, wrong_ex # ---------------------------------------------------------------- train def train(args): device = "cuda" if torch.cuda.is_available() and not args.local else "cpu" torch.manual_seed(args.seed) rng = random.Random(args.seed) cfg = SIZES[args.size] ctx = 64 model = TinyGPT(cfg["d"], cfg["L"], cfg["H"], ctx).to(device) n_params = count_params(model) eval_pairs = make_eval_set(args.seed + 999, args.digits, args.eval_n) eval_keys = set(eval_pairs) # final eval set created UPFRONT and excluded from training by construction: # the stream must never see any problem in either eval set. final_pairs = make_eval_set(args.seed + 12345, args.digits, args.eval_final_n, exclude=eval_keys) final_keys = set(final_pairs) train_reject = eval_keys | final_keys assert not (final_keys & eval_keys), "final eval overlaps tuning eval!" B, T = args.batch, ctx steps = args.tokens // (B * T) opt = torch.optim.AdamW(model.parameters(), lr=args.lr, betas=(0.9, 0.95), weight_decay=0.1) warm = max(1, int(0.05 * steps)) sched = torch.optim.lr_scheduler.LambdaLR( opt, lambda s: s / warm if s < warm else 0.1 + 0.9 * 0.5 * (1 + math.cos(math.pi * (s - warm) / max(1, steps - warm)))) stream = make_stream(args.seed, args.digits, args.fmt, train_reject, steps * B * (T + 1) + 4096) buf = [] out = Path(args.out) out.mkdir(parents=True, exist_ok=True) log_f = open(out / "curve.csv", "w") log_f.write("step,loss,lr,eval_acc,elapsed_s,tok_per_s\n") eval_every = max(20, steps // args.eval_points) best_acc, best_step = -1.0, -1 t0 = time.time() tok_count = 0 for step in range(1, steps + 1): while len(buf) < B * (T + 1): buf.extend(next(stream)) batch = torch.tensor(buf[: B * (T + 1)], device=device).view(B, T + 1) buf = buf[B * (T + 1):] x, y = batch[:, :-1], batch[:, 1:] logits = model(x) loss = F.cross_entropy(logits.view(-1, V), y.reshape(-1)) opt.zero_grad() loss.backward() torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0) opt.step() sched.step() tok_count += B * T if step % eval_every == 0 or step == steps: acc, nc, wrong = evaluate(model, eval_pairs[: args.eval_n], args.fmt, device, digits=args.digits) el = time.time() - t0 tps = tok_count / el lr_now = opt.param_groups[0]["lr"] log_f.write(f"{step},{loss.item():.4f},{lr_now:.2e},{acc:.4f},{el:.1f},{tps:.0f}\n") log_f.flush() print(f"[{args.tag}] step {step}/{steps} loss {loss.item():.4f} eval_acc {acc:.4f} " f"({el/60:.1f} min, {tps:.0f} tok/s)", flush=True) if wrong: print(f" sample wrong: {wrong[0]}", flush=True) if acc > best_acc: best_acc, best_step = acc, step torch.save({"model": model.state_dict(), "cfg": cfg, "args": vars(args)}, out / "best.pt") torch.save({"model": model.state_dict(), "cfg": cfg, "args": vars(args)}, out / "final.pt") # final eval on the pre-built held-out set (n=eval_final_n) model.load_state_dict(torch.load(out / "best.pt", map_location=device)["model"]) acc_best, _, wrong_best = evaluate(model, final_pairs, args.fmt, device, digits=args.digits) summary = { "tag": args.tag, "size": args.size, "params": n_params, "fmt": args.fmt, "digits": args.digits, "train_tokens": args.tokens, "best_tuning_acc": best_acc, "best_step": best_step, "final_bestckpt_acc": acc_best, "eval_n": args.eval_final_n, "wall_min": (time.time() - t0) / 60, "device": device, "wrong_examples": wrong_best[:10], } (out / "summary.json").write_text(json.dumps(summary, indent=2)) print(f"[{args.tag}] DONE best_tuning={best_acc:.4f} final(n={args.eval_final_n})={acc_best:.4f}", flush=True) return summary PRESETS = { # local dry-run: tiny everything, catches bugs for zero GPU cost "local": dict(tokens=50_000, eval_n=30, eval_final_n=50, eval_points=3, batch=32, lr=1e-3), # real runs "sweep": dict(tokens=10_000_000, eval_n=1000, eval_final_n=5000, eval_points=10, batch=128, lr=6e-4), } if __name__ == "__main__": ap = argparse.ArgumentParser() ap.add_argument("--size", choices=list(SIZES), required=True) ap.add_argument("--fmt", choices=["l2r", "rtl", "cot"], required=True) ap.add_argument("--digits", type=int, default=4) ap.add_argument("--tokens", type=int, default=None) ap.add_argument("--lr", type=float, default=None) ap.add_argument("--batch", type=int, default=None) ap.add_argument("--eval_n", type=int, default=None) ap.add_argument("--eval_final_n", type=int, default=None) ap.add_argument("--eval_points", type=int, default=None) ap.add_argument("--seed", type=int, default=0) ap.add_argument("--preset", choices=list(PRESETS), default="sweep") ap.add_argument("--local", action="store_true", help="force CPU even if cuda exists") ap.add_argument("--out", default=None) ap.add_argument("--tag", default=None) a = ap.parse_args() for k, v in PRESETS[a.preset].items(): if getattr(a, k) is None: setattr(a, k, v) a.tag = a.tag or f"{a.size}_{a.fmt}_{a.digits}d_{a.tokens//1000}k" a.out = a.out or f"runs/{a.tag}" if torch.cuda.is_available() and not a.local: torch.backends.cuda.matmul.allow_tf32 = True print(json.dumps({k: v for k, v in vars(a).items()}, indent=2), flush=True) train(a)