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All of these improvements were developed by Claude running autonomously over ~2 days using autoresearch. I didn't touch anything - incredible. All tuning was done on d12 but generalized easily to larger models (e.g. d24 in particular). This means we will also get a new "Time to GPT-2" Leaderboard entry, which I will push separately.

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Optimizer & schedule changes:
- Increase unembedding LR 0.004 -> 0.008, weight decay 0.2 -> 0.28
- Per-group Adam betas and weight decay (instead of shared global betas)
- Muon beta2 0.95 -> 0.9, momentum warmup target 0.95 -> 0.97 over 400 steps
- Warmup: ratio-based -> absolute steps (default 40)
- Warmdown ratio 0.5 -> 0.65, final LR fraction 0.0 -> 0.05
- Weight decay schedule: linear -> cosine decay
- Polar express norm factor 1.02 -> 1.01

Architecture & init changes:
- VE gate: channels 32 -> 12, scale range 2x -> 3x, init small positive
- Add post-QK-norm scaling (q,k *= 1.15) for sharper attention
- Embedding init std 1.0 -> 0.8, MLP c_fc init 0.5x smaller
- RoPE base theta 10K -> 100K
- Short attention window: seq_len/2 -> ~seq_len/3 (ceil to 128 tile)
- Logit softcap 20 -> 15
This commit is contained in:
Andrej Karpathy 2026-03-09 20:45:17 +00:00
parent 1076f97059
commit 6ed7d1d82c
3 changed files with 30 additions and 31 deletions
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32
nanochat/gpt.py
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@ -76,7 +76,7 @@ class CausalSelfAttention(nn.Module):
self.c_k = Linear(self.n_embd, self.n_kv_head * self.head_dim, bias=False) self.c_k = Linear(self.n_embd, self.n_kv_head * self.head_dim, bias=False)
self.c_v = Linear(self.n_embd, self.n_kv_head * self.head_dim, bias=False) self.c_v = Linear(self.n_embd, self.n_kv_head * self.head_dim, bias=False)
self.c_proj = Linear(self.n_embd, self.n_embd, bias=False) self.c_proj = Linear(self.n_embd, self.n_embd, bias=False)
self.ve_gate_channels = 32 self.ve_gate_channels = 12
self.ve_gate = Linear(self.ve_gate_channels, self.n_kv_head, bias=False) if has_ve(layer_idx, config.n_layer) else None self.ve_gate = Linear(self.ve_gate_channels, self.n_kv_head, bias=False) if has_ve(layer_idx, config.n_layer) else None
def forward(self, x, ve, cos_sin, window_size, kv_cache): def forward(self, x, ve, cos_sin, window_size, kv_cache):
@ -91,13 +91,15 @@ class CausalSelfAttention(nn.Module):
# Value residual (ResFormer): mix in value embedding with input-dependent gate per head # Value residual (ResFormer): mix in value embedding with input-dependent gate per head
if ve is not None: if ve is not None:
ve = ve.view(B, T, self.n_kv_head, self.head_dim) ve = ve.view(B, T, self.n_kv_head, self.head_dim)
gate = 2 * torch.sigmoid(self.ve_gate(x[..., :self.ve_gate_channels])) # (B, T, n_kv_head), range (0, 2) gate = 3 * torch.sigmoid(self.ve_gate(x[..., :self.ve_gate_channels])) # (B, T, n_kv_head), range (0, 3)
v = v + gate.unsqueeze(-1) * ve v = v + gate.unsqueeze(-1) * ve
# Apply Rotary Embeddings to queries and keys to get relative positional encoding # Apply Rotary Embeddings to queries and keys to get relative positional encoding
cos, sin = cos_sin cos, sin = cos_sin
q, k = apply_rotary_emb(q, cos, sin), apply_rotary_emb(k, cos, sin) q, k = apply_rotary_emb(q, cos, sin), apply_rotary_emb(k, cos, sin)
q, k = norm(q), norm(k) # QK norm q, k = norm(q), norm(k) # QK norm
q = q * 1.15 # sharper attention (split scale between Q and K), TODO think through better
k = k * 1.15
# Flash Attention (FA3 on Hopper+, PyTorch SDPA fallback elsewhere) # Flash Attention (FA3 on Hopper+, PyTorch SDPA fallback elsewhere)
# window_size is (left, right) tuple: (N, 0) for causal, (-1, 0) for full context # window_size is (left, right) tuple: (N, 0) for causal, (-1, 0) for full context
@ -208,7 +210,7 @@ class GPT(nn.Module):
""" """
# Embedding and unembedding # Embedding and unembedding
torch.nn.init.normal_(self.transformer.wte.weight, mean=0.0, std=1.0) torch.nn.init.normal_(self.transformer.wte.weight, mean=0.0, std=0.8)
torch.nn.init.normal_(self.lm_head.weight, mean=0.0, std=0.001) torch.nn.init.normal_(self.lm_head.weight, mean=0.0, std=0.001)
# Transformer blocks: uniform init with bound = sqrt(3) * std (same standard deviation as normal) # Transformer blocks: uniform init with bound = sqrt(3) * std (same standard deviation as normal)
@ -219,7 +221,7 @@ class GPT(nn.Module):
torch.nn.init.uniform_(block.attn.c_k.weight, -s, s) torch.nn.init.uniform_(block.attn.c_k.weight, -s, s)
torch.nn.init.uniform_(block.attn.c_v.weight, -s, s) torch.nn.init.uniform_(block.attn.c_v.weight, -s, s)
torch.nn.init.zeros_(block.attn.c_proj.weight) # projections are zero torch.nn.init.zeros_(block.attn.c_proj.weight) # projections are zero
torch.nn.init.uniform_(block.mlp.c_fc.weight, -s, s) torch.nn.init.uniform_(block.mlp.c_fc.weight, -s * 0.5, s * 0.5) # 0.5x init scale for c_fc
torch.nn.init.zeros_(block.mlp.c_proj.weight) torch.nn.init.zeros_(block.mlp.c_proj.weight)
# Per-layer scalars # Per-layer scalars
@ -230,10 +232,10 @@ class GPT(nn.Module):
for ve in self.value_embeds.values(): for ve in self.value_embeds.values():
torch.nn.init.uniform_(ve.weight, -s, s) torch.nn.init.uniform_(ve.weight, -s, s)
# Gate weights init to zero so gates start at sigmoid(0) = 0.5, scaled by 2 -> 1.0 (neutral) # Gate weights init with small positive values so gates start slightly above neutral
for block in self.transformer.h: for block in self.transformer.h:
if block.attn.ve_gate is not None: if block.attn.ve_gate is not None:
torch.nn.init.zeros_(block.attn.ve_gate.weight) torch.nn.init.uniform_(block.attn.ve_gate.weight, 0.0, 0.02)
# Rotary embeddings # Rotary embeddings
head_dim = self.config.n_embd // self.config.n_head head_dim = self.config.n_embd // self.config.n_head
@ -248,7 +250,7 @@ class GPT(nn.Module):
for ve in self.value_embeds.values(): for ve in self.value_embeds.values():
ve.to(dtype=COMPUTE_DTYPE) ve.to(dtype=COMPUTE_DTYPE)
def _precompute_rotary_embeddings(self, seq_len, head_dim, base=10000, device=None): def _precompute_rotary_embeddings(self, seq_len, head_dim, base=100000, device=None):
# TODO: bump base theta more? e.g. 100K is more common more recently # TODO: bump base theta more? e.g. 100K is more common more recently
# autodetect the device from model embeddings # autodetect the device from model embeddings
if device is None: if device is None:
@ -280,7 +282,7 @@ class GPT(nn.Module):
assert all(c in "SL" for c in pattern), f"Invalid window_pattern: {pattern}. Use only S and L." assert all(c in "SL" for c in pattern), f"Invalid window_pattern: {pattern}. Use only S and L."
# Map characters to window sizes # Map characters to window sizes
long_window = config.sequence_len long_window = config.sequence_len
short_window = long_window // 2 short_window = -(-long_window // 3 // 128) * 128 # ceil to FA3 tile size (2048 -> 768)
char_to_window = { char_to_window = {
"L": (long_window, 0), "L": (long_window, 0),
"S": (short_window, 0), "S": (short_window, 0),
@ -353,7 +355,7 @@ class GPT(nn.Module):
'total': total, 'total': total,
} }
def setup_optimizer(self, unembedding_lr=0.004, embedding_lr=0.2, matrix_lr=0.02, weight_decay=0.0, adam_betas=(0.8, 0.95), scalar_lr=0.5): def setup_optimizer(self, unembedding_lr=0.004, embedding_lr=0.2, matrix_lr=0.02, weight_decay=0.0, scalar_lr=0.5):
model_dim = self.config.n_embd model_dim = self.config.n_embd
ddp, rank, local_rank, world_size = get_dist_info() ddp, rank, local_rank, world_size = get_dist_info()
@ -373,10 +375,10 @@ class GPT(nn.Module):
# Build param_groups with all required fields explicit # Build param_groups with all required fields explicit
param_groups = [ param_groups = [
# AdamW groups (embeddings, lm_head, scalars) # AdamW groups (embeddings, lm_head, scalars)
dict(kind='adamw', params=lm_head_params, lr=unembedding_lr * dmodel_lr_scale, betas=adam_betas, eps=1e-10, weight_decay=0.0), dict(kind='adamw', params=lm_head_params, lr=unembedding_lr * dmodel_lr_scale, betas=(0.8, 0.96), eps=1e-10, weight_decay=0.01),
dict(kind='adamw', params=embedding_params, lr=embedding_lr * dmodel_lr_scale, betas=adam_betas, eps=1e-10, weight_decay=0.0), dict(kind='adamw', params=embedding_params, lr=embedding_lr * dmodel_lr_scale, betas=(0.8, 0.995), eps=1e-10, weight_decay=0.001),
dict(kind='adamw', params=value_embeds_params, lr=embedding_lr * dmodel_lr_scale, betas=adam_betas, eps=1e-10, weight_decay=0.0), dict(kind='adamw', params=value_embeds_params, lr=embedding_lr * dmodel_lr_scale * 0.5, betas=(0.8, 0.995), eps=1e-10, weight_decay=0.01),
dict(kind='adamw', params=resid_params, lr=scalar_lr * 0.01, betas=adam_betas, eps=1e-10, weight_decay=0.0), dict(kind='adamw', params=resid_params, lr=scalar_lr * 0.01, betas=(0.8, 0.95), eps=1e-10, weight_decay=0.05),
dict(kind='adamw', params=x0_params, lr=scalar_lr, betas=(0.96, 0.95), eps=1e-10, weight_decay=0.0), # higher beta1 for x0 dict(kind='adamw', params=x0_params, lr=scalar_lr, betas=(0.96, 0.95), eps=1e-10, weight_decay=0.0), # higher beta1 for x0
] ]
# Muon groups (matrix params, grouped by shape for stacking) # Muon groups (matrix params, grouped by shape for stacking)
@ -384,7 +386,7 @@ class GPT(nn.Module):
group_params = [p for p in matrix_params if p.shape == shape] group_params = [p for p in matrix_params if p.shape == shape]
param_groups.append(dict( param_groups.append(dict(
kind='muon', params=group_params, lr=matrix_lr, kind='muon', params=group_params, lr=matrix_lr,
momentum=0.95, ns_steps=5, beta2=0.95, weight_decay=weight_decay, momentum=0.95, ns_steps=5, beta2=0.9, weight_decay=weight_decay,
)) ))
Factory = DistMuonAdamW if ddp else MuonAdamW Factory = DistMuonAdamW if ddp else MuonAdamW
@ -416,7 +418,7 @@ class GPT(nn.Module):
x = norm(x) x = norm(x)
# Forward the lm_head (compute logits) # Forward the lm_head (compute logits)
softcap = 20 # smoothly cap the logits to the range [-softcap, softcap] softcap = 15 # smoothly cap the logits to the range [-softcap, softcap]
logits = self.lm_head(x) # (B, T, padded_vocab_size) <- very big tensor, large amount of memory logits = self.lm_head(x) # (B, T, padded_vocab_size) <- very big tensor, large amount of memory
logits = logits[..., :self.config.vocab_size] # slice to remove padding logits = logits[..., :self.config.vocab_size] # slice to remove padding
logits = logits.float() # switch to fp32 for logit softcap and loss computation logits = logits.float() # switch to fp32 for logit softcap and loss computation

2
nanochat/optim.py
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@ -113,7 +113,7 @@ def muon_step_fused(
# Polar express # Polar express
X = g.bfloat16() X = g.bfloat16()
X = X / (X.norm(dim=(-2, -1), keepdim=True) * 1.02 + 1e-6) X = X / (X.norm(dim=(-2, -1), keepdim=True) * 1.01 + 1e-6)
if g.size(-2) > g.size(-1): # Tall matrix if g.size(-2) > g.size(-1): # Tall matrix
for a, b, c in polar_express_coeffs[:ns_steps]: for a, b, c in polar_express_coeffs[:ns_steps]:
A = X.mT @ X A = X.mT @ X

27
scripts/base_train.py
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@ -60,15 +60,13 @@ parser.add_argument("--target-param-data-ratio", type=float, default=10.5, help=
parser.add_argument("--device-batch-size", type=int, default=32, help="per-device batch size. good number to reduce to 16,8,4,... if you OOM on VRAM.") parser.add_argument("--device-batch-size", type=int, default=32, help="per-device batch size. good number to reduce to 16,8,4,... if you OOM on VRAM.")
parser.add_argument("--total-batch-size", type=int, default=-1, help="total batch size in tokens. decent numbers are e.g. 524288. (-1 = auto-compute optimal)") parser.add_argument("--total-batch-size", type=int, default=-1, help="total batch size in tokens. decent numbers are e.g. 524288. (-1 = auto-compute optimal)")
parser.add_argument("--embedding-lr", type=float, default=0.3, help="learning rate for embedding parameters (Adam)") parser.add_argument("--embedding-lr", type=float, default=0.3, help="learning rate for embedding parameters (Adam)")
parser.add_argument("--unembedding-lr", type=float, default=0.004, help="learning rate for unembedding parameters (Adam)") parser.add_argument("--unembedding-lr", type=float, default=0.008, help="learning rate for unembedding parameters (Adam)")
parser.add_argument("--weight-decay", type=float, default=0.2, help="cautious weight decay for the Muon optimizer (for weights)") parser.add_argument("--weight-decay", type=float, default=0.28, help="cautious weight decay for the Muon optimizer (for weights)")
parser.add_argument("--matrix-lr", type=float, default=0.02, help="learning rate for matrix parameters (Muon)") parser.add_argument("--matrix-lr", type=float, default=0.02, help="learning rate for matrix parameters (Muon)")
parser.add_argument("--scalar-lr", type=float, default=0.5, help="learning rate for scalars (resid_lambdas, x0_lambdas)") parser.add_argument("--scalar-lr", type=float, default=0.5, help="learning rate for scalars (resid_lambdas, x0_lambdas)")
parser.add_argument("--adam-beta1", type=float, default=0.8, help="Adam beta1 for embedding/unembedding") parser.add_argument("--warmup-steps", type=int, default=40, help="number of steps for LR warmup")
parser.add_argument("--adam-beta2", type=float, default=0.95, help="Adam beta2 for embedding/unembedding") parser.add_argument("--warmdown-ratio", type=float, default=0.65, help="ratio of iterations for LR warmdown")
parser.add_argument("--warmup-ratio", type=float, default=0.0, help="ratio of iterations for LR warmup") parser.add_argument("--final-lr-frac", type=float, default=0.05, help="final LR as fraction of initial LR")
parser.add_argument("--warmdown-ratio", type=float, default=0.5, help="ratio of iterations for LR warmdown")
parser.add_argument("--final-lr-frac", type=float, default=0.0, help="final LR as fraction of initial LR")
parser.add_argument("--resume-from-step", type=int, default=-1, help="resume training from this step (-1 = disable)") parser.add_argument("--resume-from-step", type=int, default=-1, help="resume training from this step (-1 = disable)")
# Evaluation # Evaluation
parser.add_argument("--eval-every", type=int, default=250, help="evaluate val bpb every N steps (-1 = disable)") parser.add_argument("--eval-every", type=int, default=250, help="evaluate val bpb every N steps (-1 = disable)")
@ -311,7 +309,6 @@ optimizer = model.setup_optimizer(
unembedding_lr=args.unembedding_lr * batch_lr_scale, unembedding_lr=args.unembedding_lr * batch_lr_scale,
embedding_lr=args.embedding_lr * batch_lr_scale, embedding_lr=args.embedding_lr * batch_lr_scale,
scalar_lr=args.scalar_lr * batch_lr_scale, scalar_lr=args.scalar_lr * batch_lr_scale,
adam_betas=(args.adam_beta1, args.adam_beta2),
# Muon hyperparameters # Muon hyperparameters
matrix_lr=args.matrix_lr * batch_lr_scale, matrix_lr=args.matrix_lr * batch_lr_scale,
weight_decay=weight_decay_scaled, weight_decay=weight_decay_scaled,
@ -360,7 +357,7 @@ print0(f"Total training FLOPs estimate: {num_flops_per_token * total_tokens:e}")
# Learning rate schedule (linear warmup, constant, linear warmdown) # Learning rate schedule (linear warmup, constant, linear warmdown)
def get_lr_multiplier(it): def get_lr_multiplier(it):
warmup_iters = round(args.warmup_ratio * num_iterations) warmup_iters = args.warmup_steps
warmdown_iters = round(args.warmdown_ratio * num_iterations) warmdown_iters = round(args.warmdown_ratio * num_iterations)
if it < warmup_iters: if it < warmup_iters:
return (it + 1) / warmup_iters return (it + 1) / warmup_iters
@ -370,15 +367,15 @@ def get_lr_multiplier(it):
progress = (num_iterations - it) / warmdown_iters progress = (num_iterations - it) / warmdown_iters
return progress * 1.0 + (1 - progress) * args.final_lr_frac return progress * 1.0 + (1 - progress) * args.final_lr_frac
# Momentum scheduler for Muon optimizer (warms up to 0.95 over the first 300 steps) # Momentum scheduler for Muon optimizer (warms up to 0.97 over the first 400 steps)
def get_muon_momentum(it): def get_muon_momentum(it):
frac = min(it / 300, 1) frac = min(it / 400, 1)
momentum = (1 - frac) * 0.85 + frac * 0.95 momentum = (1 - frac) * 0.85 + frac * 0.97
return momentum return momentum
# Weight decay scheduler for Muon optimizer (linearly decays to zero over the course of training) # Weight decay scheduler for Muon optimizer (cosine decay to zero over the course of training)
def get_weight_decay(it): def get_weight_decay(it):
return weight_decay_scaled * (1 - it / num_iterations) return weight_decay_scaled * 0.5 * (1 + math.cos(math.pi * it / num_iterations))
# ----------------------------------------------------------------------------- # -----------------------------------------------------------------------------
# Training loop # Training loop
@ -605,7 +602,7 @@ get_report().log(section="Base model training", data=[
"Number of training tokens": total_tokens, "Number of training tokens": total_tokens,
"Tokens : Scaling params ratio": total_batch_size * num_iterations / num_scaling_params, "Tokens : Scaling params ratio": total_batch_size * num_iterations / num_scaling_params,
"DDP world size": ddp_world_size, "DDP world size": ddp_world_size,
"warmup_ratio": args.warmup_ratio, "warmup_steps": args.warmup_steps,
"warmdown_ratio": args.warmdown_ratio, "warmdown_ratio": args.warmdown_ratio,
"final_lr_frac": args.final_lr_frac, "final_lr_frac": args.final_lr_frac,
}, },