"""Train 3 transformers to compare convergence: 1. Chebyshev residual (shallow, 12 layers) 2. Standard residual (shallow, 12 layers) 3. Standard residual (deep, 24 layers, same params via smaller hidden) All trained on same data, same compute budget. """ import torch import torch.nn as nn import torch.nn.functional as F from torch.utils.data import DataLoader, Dataset import math, time, json, os import numpy as np DEVICE = "mps" # Apple Silicon SEED = 42 torch.manual_seed(SEED) np.random.seed(SEED) # === Config === VOCAB = 256 # byte-level for simplicity SEQ_LEN = 128 BATCH = 32 HIDDEN = 256 HEADS = 8 HEAD_DIM = HIDDEN // HEADS N_STEPS = 5000 LR = 3e-4 EVAL_EVERY = 250 # === Dataset: Shakespeare byte-level === class ByteDataset(Dataset): def __init__(self, data, seq_len): self.data = data self.seq_len = seq_len def __len__(self): return len(self.data) - self.seq_len - 1 def __getitem__(self, idx): x = self.data[idx:idx+self.seq_len] y = self.data[idx+1:idx+self.seq_len+1] return torch.tensor(x, dtype=torch.long), torch.tensor(y, dtype=torch.long) # Download Shakespeare DATA_PATH = "/tmp/shakespeare.txt" if not os.path.exists(DATA_PATH): print("Downloading Shakespeare...", flush=True) import urllib.request url = "https://raw.githubusercontent.com/karpathy/char-rnn/master/data/tinyshakespeare/input.txt" urllib.request.urlretrieve(url, DATA_PATH) with open(DATA_PATH, "rb") as f: raw = list(f.read()) split = int(len(raw) * 0.9) train_data = raw[:split] val_data = raw[split:] train_ds = ByteDataset(train_data, SEQ_LEN) val_ds = ByteDataset(val_data, SEQ_LEN) train_dl = DataLoader(train_ds, batch_size=BATCH, shuffle=True, drop_last=True) val_dl = DataLoader(val_ds, batch_size=BATCH, shuffle=False, drop_last=True) print("Data: %d train, %d val tokens" % (len(train_data), len(val_data)), flush=True) # === Attention block === class CausalSelfAttention(nn.Module): def __init__(self, hidden, heads): super().__init__() self.heads = heads self.head_dim = hidden // heads self.qkv = nn.Linear(hidden, 3 * hidden) self.out = nn.Linear(hidden, hidden) def forward(self, x): B, T, C = x.shape qkv = self.qkv(x).reshape(B, T, 3, self.heads, self.head_dim).permute(2, 0, 3, 1, 4) q, k, v = qkv[0], qkv[1], qkv[2] att = (q @ k.transpose(-2, -1)) * (self.head_dim ** -0.5) mask = torch.triu(torch.ones(T, T, device=x.device, dtype=torch.bool), diagonal=1) att = att.masked_fill(mask, float("-inf")) att = F.softmax(att, dim=-1) out = (att @ v).transpose(1, 2).reshape(B, T, C) return self.out(out) # === MLP === class MLP(nn.Module): def __init__(self, hidden): super().__init__() self.fc1 = nn.Linear(hidden, 4 * hidden) self.fc2 = nn.Linear(4 * hidden, hidden) def forward(self, x): return self.fc2(F.gelu(self.fc1(x))) # === Standard Transformer Block === class StandardBlock(nn.Module): def __init__(self, hidden, heads): super().__init__() self.ln1 = nn.LayerNorm(hidden) self.attn = CausalSelfAttention(hidden, heads) self.ln2 = nn.LayerNorm(hidden) self.mlp = MLP(hidden) def forward(self, x): x = x + self.attn(self.ln1(x)) x = x + self.mlp(self.ln2(x)) return x # === Chebyshev Transformer Block === class ChebyshevBlock(nn.Module): """Two-step Chebyshev recurrence: h_{n+1} = 2*f(h_n) - h_{n-1}""" def __init__(self, hidden, heads): super().__init__() self.ln1 = nn.LayerNorm(hidden) self.attn = CausalSelfAttention(hidden, heads) self.ln2 = nn.LayerNorm(hidden) self.mlp = MLP(hidden) # Learnable mixing coefficient (starts at standard residual) self.alpha = nn.Parameter(torch.tensor(0.5)) def forward(self, x, x_prev): # Compute layer output f_x = x + self.attn(self.ln1(x)) f_x = f_x + self.mlp(self.ln2(f_x)) # Chebyshev recurrence: blend between standard and two-step # alpha=0.5 -> standard residual, alpha=1.0 -> full Chebyshev alpha = torch.sigmoid(self.alpha) h_new = (1 + alpha) * f_x - alpha * x_prev return h_new # === Full Models === class StandardTransformer(nn.Module): def __init__(self, vocab, hidden, heads, n_layers): super().__init__() self.embed = nn.Embedding(vocab, hidden) self.pos = nn.Embedding(SEQ_LEN, hidden) self.blocks = nn.ModuleList([StandardBlock(hidden, heads) for _ in range(n_layers)]) self.ln_f = nn.LayerNorm(hidden) self.head = nn.Linear(hidden, vocab, bias=False) self.n_layers = n_layers def forward(self, x): B, T = x.shape h = self.embed(x) + self.pos(torch.arange(T, device=x.device)) for block in self.blocks: h = block(h) return self.head(self.ln_f(h)) class ChebyshevTransformer(nn.Module): def __init__(self, vocab, hidden, heads, n_layers): super().__init__() self.embed = nn.Embedding(vocab, hidden) self.pos = nn.Embedding(SEQ_LEN, hidden) self.blocks = nn.ModuleList([ChebyshevBlock(hidden, heads) for _ in range(n_layers)]) self.ln_f = nn.LayerNorm(hidden) self.head = nn.Linear(hidden, vocab, bias=False) self.n_layers = n_layers def forward(self, x): B, T = x.shape h = self.embed(x) + self.pos(torch.arange(T, device=x.device)) h_prev = h.clone() # initial h_{-1} = h_0 for block in self.blocks: h_new = block(h, h_prev) h_prev = h h = h_new return self.head(self.ln_f(h)) # === Training === def count_params(model): return sum(p.numel() for p in model.parameters()) def evaluate(model, dl): model.eval() total_loss = 0 n = 0 with torch.no_grad(): for xb, yb in dl: xb, yb = xb.to(DEVICE), yb.to(DEVICE) logits = model(xb) loss = F.cross_entropy(logits.view(-1, VOCAB), yb.view(-1)) total_loss += loss.item() n += 1 if n >= 20: break model.train() return total_loss / n def train_model(name, model): model = model.to(DEVICE) params = count_params(model) print("\n%s: %d params (%.2fM), %d layers" % (name, params, params/1e6, model.n_layers), flush=True) opt = torch.optim.AdamW(model.parameters(), lr=LR) scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(opt, N_STEPS) losses = [] val_losses = [] step = 0 t0 = time.perf_counter() while step < N_STEPS: for xb, yb in train_dl: if step >= N_STEPS: break xb, yb = xb.to(DEVICE), yb.to(DEVICE) logits = model(xb) loss = F.cross_entropy(logits.view(-1, VOCAB), yb.view(-1)) opt.zero_grad() loss.backward() torch.nn.utils.clip_grad_norm_(model.parameters(), 1.0) opt.step() scheduler.step() losses.append(loss.item()) step += 1 if step % EVAL_EVERY == 0: vl = evaluate(model, val_dl) val_losses.append((step, vl)) elapsed = time.perf_counter() - t0 print(" step %d/%d: train=%.4f val=%.4f (%.0fs)" % ( step, N_STEPS, np.mean(losses[-100:]), vl, elapsed), flush=True) # Final eval vl = evaluate(model, val_dl) val_losses.append((step, vl)) elapsed = time.perf_counter() - t0 print(" FINAL: val=%.4f, %.0fs, %.1f steps/s" % (vl, elapsed, N_STEPS/elapsed), flush=True) return { "name": name, "params": params, "layers": model.n_layers, "train_losses": losses, "val_losses": val_losses, "time": elapsed, "final_val": vl, } # === Deep standard: SAME hidden, MORE params (2x layers = ~2x params) === HIDDEN_DEEP = HIDDEN # same width HEADS_DEEP = HEADS # same heads print("=" * 60, flush=True) print("CHEBYSHEV vs STANDARD TRANSFORMER COMPARISON", flush=True) print("=" * 60, flush=True) print("Shallow: %d layers, hidden=%d, heads=%d" % (12, HIDDEN, HEADS), flush=True) print("Deep: %d layers, hidden=%d, heads=%d" % (24, HIDDEN_DEEP, HEADS_DEEP), flush=True) print("Steps: %d, Batch: %d, Seq: %d" % (N_STEPS, BATCH, SEQ_LEN), flush=True) # Run all 3 results = [] # 1. Chebyshev shallow model1 = ChebyshevTransformer(VOCAB, HIDDEN, HEADS, 12) r1 = train_model("Chebyshev-12L", model1) results.append(r1) del model1 torch.mps.empty_cache() if hasattr(torch.mps, 'empty_cache') else None # 2. Standard shallow model2 = StandardTransformer(VOCAB, HIDDEN, HEADS, 12) r2 = train_model("Standard-12L", model2) results.append(r2) del model2 torch.mps.empty_cache() if hasattr(torch.mps, 'empty_cache') else None # 3. Standard deep (matched params) model3 = StandardTransformer(VOCAB, HIDDEN_DEEP, HEADS_DEEP, 24) r3 = train_model("Standard-24L", model3) results.append(r3) del model3 # === Summary === print("\n" + "=" * 60, flush=True) print("RESULTS", flush=True) print("=" * 60, flush=True) print("%-20s %8s %6s %10s %10s" % ("Model", "Params", "Layers", "Final Val", "Time"), flush=True) print("-" * 58, flush=True) for r in results: print("%-20s %8d %6d %10.4f %8.0fs" % (r["name"], r["params"], r["layers"], r["final_val"], r["time"]), flush=True) # Convergence comparison: val loss at step 1000, 2500, 5000 print("\nConvergence:", flush=True) print("%-20s %10s %10s %10s" % ("Model", "Step 1000", "Step 2500", "Step 5000"), flush=True) print("-" * 52, flush=True) for r in results: vals = dict(r["val_losses"]) v1k = vals.get(1000, vals.get(750, "N/A")) v25k = vals.get(2500, "N/A") v5k = vals.get(5000, vals.get(4750, "N/A")) print("%-20s %10s %10s %10s" % ( r["name"], "%.4f" % v1k if isinstance(v1k, float) else v1k, "%.4f" % v25k if isinstance(v25k, float) else v25k, "%.4f" % v5k if isinstance(v5k, float) else v5k, ), flush=True) # Save results save = {r["name"]: {"val_losses": r["val_losses"], "params": r["params"], "final_val": r["final_val"], "time": r["time"]} for r in results} with open("/tmp/donkey_cheb_train_results.json", "w") as f: json.dump(save, f, indent=2) print("\nSaved to /tmp/donkey_cheb_train_results.json", flush=True)