diff options
Diffstat (limited to 'srm/models')
| -rw-r--r-- | srm/models/common.py | 32 | ||||
| -rw-r--r-- | srm/models/hrm/hrm_act_v1.py | 283 | ||||
| -rw-r--r-- | srm/models/layers.py | 157 | ||||
| -rw-r--r-- | srm/models/losses.py | 101 | ||||
| -rw-r--r-- | srm/models/sparse_embedding.py | 132 | ||||
| -rw-r--r-- | srm/models/srm/__init__.py | 0 | ||||
| -rw-r--r-- | srm/models/srm/hrm_orth_v1.py | 376 | ||||
| -rw-r--r-- | srm/models/srm/srm_aol_v1.py | 494 |
8 files changed, 1575 insertions, 0 deletions
diff --git a/srm/models/common.py b/srm/models/common.py new file mode 100644 index 0000000..1a04505 --- /dev/null +++ b/srm/models/common.py @@ -0,0 +1,32 @@ +import math + +import torch +from torch import nn + + +def trunc_normal_init_(tensor: torch.Tensor, std: float = 1.0, lower: float = -2.0, upper: float = 2.0): + # NOTE: PyTorch nn.init.trunc_normal_ is not mathematically correct, the std dev is not actually the std dev of initialized tensor + # This function is a PyTorch version of jax truncated normal init (default init method in flax) + # https://github.com/jax-ml/jax/blob/main/jax/_src/random.py#L807-L848 + # https://github.com/jax-ml/jax/blob/main/jax/_src/nn/initializers.py#L162-L199 + + with torch.no_grad(): + if std == 0: + tensor.zero_() + else: + sqrt2 = math.sqrt(2) + a = math.erf(lower / sqrt2) + b = math.erf(upper / sqrt2) + z = (b - a) / 2 + + c = (2 * math.pi) ** -0.5 + pdf_u = c * math.exp(-0.5 * lower ** 2) + pdf_l = c * math.exp(-0.5 * upper ** 2) + comp_std = std / math.sqrt(1 - (upper * pdf_u - lower * pdf_l) / z - ((pdf_u - pdf_l) / z) ** 2) + + tensor.uniform_(a, b) + tensor.erfinv_() + tensor.mul_(sqrt2 * comp_std) + tensor.clip_(lower * comp_std, upper * comp_std) + + return tensor diff --git a/srm/models/hrm/hrm_act_v1.py b/srm/models/hrm/hrm_act_v1.py new file mode 100644 index 0000000..e91c7d1 --- /dev/null +++ b/srm/models/hrm/hrm_act_v1.py @@ -0,0 +1,283 @@ +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math + +import torch +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel + +from models.common import trunc_normal_init_ +from models.layers import rms_norm, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + + +@dataclass +class HierarchicalReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L: torch.Tensor + + +@dataclass +class HierarchicalReasoningModel_ACTV1Carry: + inner_carry: HierarchicalReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class HierarchicalReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + +class HierarchicalReasoningModel_ACTV1Block(nn.Module): + def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: + super().__init__() + + self.self_attn = Attention( + hidden_size=config.hidden_size, + head_dim=config.hidden_size // config.num_heads, + num_heads=config.num_heads, + num_key_value_heads=config.num_heads, + causal=False + ) + self.mlp = SwiGLU( + hidden_size=config.hidden_size, + expansion=config.expansion, + ) + self.norm_eps = config.rms_norm_eps + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # Post Norm + # Self Attention + hidden_states = rms_norm(hidden_states + self.self_attn(cos_sin=cos_sin, hidden_states=hidden_states), variance_epsilon=self.norm_eps) + # Fully Connected + hidden_states = rms_norm(hidden_states + self.mlp(hidden_states), variance_epsilon=self.norm_eps) + return hidden_states + + +class HierarchicalReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[HierarchicalReasoningModel_ACTV1Block]): + super().__init__() + + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + # Input injection (add) + hidden_states = hidden_states + input_injection + # Layers + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + + return hidden_states + + +class HierarchicalReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + else: + raise NotImplementedError() + + # Reasoning Layers + self.H_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.H_layers)]) + self.L_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + + # Initial states + self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: HierarchicalReasoningModel_ACTV1InnerCarry): + return HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + ) + + def forward(self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + with torch.no_grad(): + z_H, z_L = carry.z_H, carry.z_L + + for _H_step in range(self.config.H_cycles): + for _L_step in range(self.config.L_cycles): + if not ((_H_step == self.config.H_cycles - 1) and (_L_step == self.config.L_cycles - 1)): + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + + if not (_H_step == self.config.H_cycles - 1): + z_H = self.H_level(z_H, z_L, **seq_info) + + assert not z_H.requires_grad and not z_L.requires_grad + + # 1-step grad + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + z_H = self.H_level(z_H, z_L, **seq_info) + + # LM Outputs + new_carry = HierarchicalReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + + # Q head + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) + + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class HierarchicalReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = HierarchicalReasoningModel_ACTV1Config(**config_dict) + self.inner = HierarchicalReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return HierarchicalReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. + + steps=torch.zeros((batch_size, ), dtype=torch.int32), + halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted + + current_data={k: torch.empty_like(v) for k, v in batch.items()} + ) + + def forward(self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + + halted = halted & (new_steps >= min_halt_steps) + + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + next_q_halt_logits, next_q_continue_logits = self.inner(new_inner_carry, new_current_data)[-1] + + outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) + + return HierarchicalReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/srm/models/layers.py b/srm/models/layers.py new file mode 100644 index 0000000..0394744 --- /dev/null +++ b/srm/models/layers.py @@ -0,0 +1,157 @@ +from typing import Tuple + +import torch +from torch import nn +import torch.nn.functional as F + +try: + from flash_attn_interface import flash_attn_func # type: ignore[import] +except ImportError: + # Fallback to FlashAttention 2 + from flash_attn import flash_attn_func # type: ignore[import] + +from models.common import trunc_normal_init_ + + +CosSin = Tuple[torch.Tensor, torch.Tensor] + + +def _find_multiple(a, b): + return (-(a // -b)) * b + + +def rotate_half(x: torch.Tensor): + """Rotates half the hidden dims of the input.""" + x1 = x[..., : x.shape[-1] // 2] + x2 = x[..., x.shape[-1] // 2 :] + return torch.cat((-x2, x1), dim=-1) + + +def apply_rotary_pos_emb(q: torch.Tensor, k: torch.Tensor, cos: torch.Tensor, sin: torch.Tensor): + # q, k: [bs, seq_len, num_heads, head_dim] + # cos, sin: [seq_len, head_dim] + orig_dtype = q.dtype + q = q.to(cos.dtype) + k = k.to(cos.dtype) + + q_embed = (q * cos.unsqueeze(-2)) + (rotate_half(q) * sin.unsqueeze(-2)) + k_embed = (k * cos.unsqueeze(-2)) + (rotate_half(k) * sin.unsqueeze(-2)) + + return q_embed.to(orig_dtype), k_embed.to(orig_dtype) + + +class CastedLinear(nn.Module): + def __init__(self, + in_features: int, + out_features: int, + bias: bool): + super().__init__() + # Truncated LeCun normal init + self.weight = nn.Parameter( + trunc_normal_init_(torch.empty((out_features, in_features)), std=1.0 / (in_features ** 0.5)) + ) + self.bias = None + if bias: + # Zero init bias + self.bias = nn.Parameter(torch.zeros((out_features, ))) + + def forward(self, input: torch.Tensor) -> torch.Tensor: + return F.linear(input, self.weight.to(input.dtype), bias=self.bias.to(input.dtype) if self.bias is not None else None) + + +class CastedEmbedding(nn.Module): + def __init__(self, + num_embeddings: int, + embedding_dim: int, + init_std: float, + cast_to: torch.dtype): + super().__init__() + self.cast_to = cast_to + + # Truncated LeCun normal init + self.embedding_weight = nn.Parameter( + trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std) + ) + + def forward(self, input: torch.Tensor) -> torch.Tensor: + return F.embedding(input, self.embedding_weight.to(self.cast_to)) + + +class RotaryEmbedding(nn.Module): + def __init__(self, dim, max_position_embeddings, base, device=None): + super().__init__() + + # RoPE + inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2, dtype=torch.float32, device=device) / dim)) + t = torch.arange(max_position_embeddings, dtype=torch.float32, device=device) + freqs = torch.outer(t, inv_freq) + + # Different from paper, but it uses a different permutation in order to obtain the same calculation + emb = torch.cat((freqs, freqs), dim=-1) + self.cos_cached = nn.Buffer(emb.cos(), persistent=False) + self.sin_cached = nn.Buffer(emb.sin(), persistent=False) + + def forward(self): + return self.cos_cached, self.sin_cached + + +class Attention(nn.Module): + def __init__(self, hidden_size, head_dim, num_heads, num_key_value_heads, causal=False): + super().__init__() + + self.hidden_size = hidden_size + self.head_dim = head_dim + self.output_size = head_dim * num_heads + self.num_heads = num_heads + self.num_key_value_heads = num_key_value_heads + self.causal = causal + + self.qkv_proj = CastedLinear(self.hidden_size, (self.num_heads + 2 * self.num_key_value_heads) * self.head_dim, bias=False) + self.o_proj = CastedLinear(self.output_size, self.hidden_size, bias=False) + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + batch_size, seq_len, _ = hidden_states.shape + + # hidden_states: [bs, seq_len, num_heads, head_dim] + qkv = self.qkv_proj(hidden_states) + + # Split head + qkv = qkv.view(batch_size, seq_len, self.num_heads + 2 * self.num_key_value_heads, self.head_dim) + query = qkv[:, :, :self.num_heads] + key = qkv[:, :, self.num_heads: self.num_heads + self.num_key_value_heads] + value = qkv[:, :, self.num_heads + self.num_key_value_heads:] + + # RoPE + if cos_sin is not None: + cos, sin = cos_sin + query, key = apply_rotary_pos_emb(query, key, cos, sin) + + # flash attn + attn_output = flash_attn_func(q=query, k=key, v=value, causal=self.causal) + if isinstance(attn_output, tuple): # fa2 and fa3 compatibility + attn_output = attn_output[0] + + attn_output = attn_output.view(batch_size, seq_len, self.output_size) # type: ignore + return self.o_proj(attn_output) + + +class SwiGLU(nn.Module): + def __init__(self, hidden_size: int, expansion: float): + super().__init__() + inter = _find_multiple(round(expansion * hidden_size * 2 / 3), 256) + + self.gate_up_proj = CastedLinear(hidden_size, inter * 2, bias=False) + self.down_proj = CastedLinear(inter, hidden_size, bias=False) + + def forward(self, x): + gate, up = self.gate_up_proj(x).chunk(2, dim=-1) + return self.down_proj(F.silu(gate) * up) + + +def rms_norm(hidden_states: torch.Tensor, variance_epsilon: float) -> torch.Tensor: + input_dtype = hidden_states.dtype + hidden_states = hidden_states.to(torch.float32) + + variance = hidden_states.square().mean(-1, keepdim=True) + hidden_states = hidden_states * torch.rsqrt(variance + variance_epsilon) + return hidden_states.to(input_dtype) diff --git a/srm/models/losses.py b/srm/models/losses.py new file mode 100644 index 0000000..b3118e7 --- /dev/null +++ b/srm/models/losses.py @@ -0,0 +1,101 @@ +from typing import Any, Tuple, Dict, Sequence, Optional + +import torch +import torch.nn.functional as F +from torch import nn + + +IGNORE_LABEL_ID = -100 + + +def s(x, epsilon=1e-30): + return torch.where( + x<0, + 1/(1-x+ epsilon), + x + 1 + ) + + +def log_stablemax(x, dim=-1): + s_x = s(x) + return torch.log(s_x/torch.sum(s_x, dim=dim, keepdim=True)) + + +def stablemax_cross_entropy(logits, labels, ignore_index: int = -100): + logprobs = log_stablemax(logits.to(torch.float64), dim=-1) + + valid_mask = labels != ignore_index + transformed_labels = torch.where(valid_mask, labels, 0) + prediction_logprobs = torch.gather(logprobs, index=transformed_labels.to(torch.long).unsqueeze(-1), dim=-1).squeeze(-1) + + return -torch.where(valid_mask, prediction_logprobs, 0) + + +def softmax_cross_entropy(logits, labels, ignore_index: int = -100): + # Cast logits to f32 + # Flatten logits + return F.cross_entropy(logits.to(torch.float32).view(-1, logits.shape[-1]), labels.to(torch.long).view(-1), ignore_index=ignore_index, reduction="none").view(labels.shape) + + +class ACTLossHead(nn.Module): + def __init__(self, model: nn.Module, loss_type: str): + super().__init__() + self.model = model + self.loss_fn = globals()[loss_type] + + def initial_carry(self, *args, **kwargs): + return self.model.initial_carry(*args, **kwargs) # type: ignore + + def forward( + self, + return_keys: Sequence[str], + # Model args + **model_kwargs, + ) -> Tuple[Any, torch.Tensor, Dict[str, torch.Tensor], Optional[Dict[str, torch.Tensor]], torch.Tensor]: + # Model logits + # B x SeqLen x D + new_carry, outputs = self.model(**model_kwargs) + labels = new_carry.current_data["labels"] + + # Correctness + with torch.no_grad(): + mask = labels != IGNORE_LABEL_ID + loss_counts = mask.sum(-1) + loss_divisor = loss_counts.clamp_min(1).unsqueeze(-1) # Avoid NaNs in division + + is_correct = mask & (torch.argmax(outputs["logits"], dim=-1) == labels) + seq_is_correct = is_correct.sum(-1) == loss_counts + + # Metrics (halted) + valid_metrics = new_carry.halted & (loss_counts > 0) + metrics = { + "count": valid_metrics.sum(), + + "accuracy": torch.where(valid_metrics, (is_correct.to(torch.float32) / loss_divisor).sum(-1), 0).sum(), + "exact_accuracy": (valid_metrics & seq_is_correct).sum(), + + "q_halt_accuracy": (valid_metrics & ((outputs["q_halt_logits"] >= 0) == seq_is_correct)).sum(), + "steps": torch.where(valid_metrics, new_carry.steps, 0).sum(), + } + + # Losses + # FIXME: Assuming the batch is always full + lm_loss = (self.loss_fn(outputs["logits"], labels, ignore_index=IGNORE_LABEL_ID) / loss_divisor).sum() + q_halt_loss = F.binary_cross_entropy_with_logits(outputs["q_halt_logits"], seq_is_correct.to(outputs["q_halt_logits"].dtype), reduction="sum") + + metrics.update({ + "lm_loss": lm_loss.detach(), + "q_halt_loss": q_halt_loss.detach(), + }) + + # Q continue (bootstrapping target loss) + q_continue_loss = 0 + if "target_q_continue" in outputs: + q_continue_loss = F.binary_cross_entropy_with_logits(outputs["q_continue_logits"], outputs["target_q_continue"], reduction="sum") + + metrics["q_continue_loss"] = q_continue_loss.detach() + + # Filter outputs for return + detached_outputs = {k: outputs[k].detach() for k in return_keys if k in outputs} + + return new_carry, lm_loss + 0.5 * (q_halt_loss + q_continue_loss), metrics, detached_outputs, new_carry.halted.all() diff --git a/srm/models/sparse_embedding.py b/srm/models/sparse_embedding.py new file mode 100644 index 0000000..c701524 --- /dev/null +++ b/srm/models/sparse_embedding.py @@ -0,0 +1,132 @@ +from typing import Union + +import torch +from torch import nn +import torch.distributed as dist +from torch.optim.optimizer import Optimizer, ParamsT + +from models.common import trunc_normal_init_ + + +class CastedSparseEmbedding(nn.Module): + def __init__(self, num_embeddings: int, embedding_dim: int, batch_size: int, init_std: float, cast_to: torch.dtype): + super().__init__() + self.cast_to = cast_to + + # Real Weights + # Truncated LeCun normal init + self.weights = nn.Buffer( + trunc_normal_init_(torch.empty((num_embeddings, embedding_dim)), std=init_std), persistent=True + ) + + # Local weights and IDs + # Local embeddings, with gradient, not persistent + self.local_weights = nn.Buffer(torch.zeros(batch_size, embedding_dim, requires_grad=True), persistent=False) + # Local embedding IDs, not persistent + self.local_ids = nn.Buffer(torch.zeros(batch_size, dtype=torch.int32), persistent=False) + + def forward(self, inputs: torch.Tensor) -> torch.Tensor: + if not self.training: + # Test mode, no gradient + return self.weights[inputs].to(self.cast_to) + + # Training mode, fill puzzle embedding from weights + with torch.no_grad(): + self.local_weights.copy_(self.weights[inputs]) + self.local_ids.copy_(inputs) + + return self.local_weights.to(self.cast_to) + + +class CastedSparseEmbeddingSignSGD_Distributed(Optimizer): + def __init__( + self, + params: ParamsT, + + world_size: int, + lr: Union[float, torch.Tensor] = 1e-3, + weight_decay: float = 1e-2, + ): + if not 0.0 <= lr: + raise ValueError(f"Invalid learning rate: {lr}") + if not 0.0 <= weight_decay: + raise ValueError(f"Invalid weight_decay value: {weight_decay}") + + defaults = dict( + lr=lr, + weight_decay=weight_decay, + world_size=world_size + ) + super().__init__(params, defaults) + + @torch.no_grad + def step(self, closure=None): # type: ignore + for group in self.param_groups: + # Find the sparse embedding weights + local_weights_grad = None + local_ids = None + weights = None + + assert len(group["params"]) == 3 + for p in group["params"]: + if p.requires_grad: + local_weights_grad = p.grad + elif p.ndim == 1: + local_ids = p + elif p.ndim == 2: + weights = p + else: + assert False + + assert local_weights_grad is not None + assert local_ids is not None + assert weights is not None + + # Apply SignSGD + # Adam ≈ SignSGD if gradient is very sparse + _sparse_emb_signsgd_dist( + local_weights_grad, + local_ids, + weights, + + lr=group["lr"], + weight_decay=group["weight_decay"], + world_size=group["world_size"] + ) + + +def _sparse_emb_signsgd_dist( + local_weights_grad: torch.Tensor, + local_ids: torch.Tensor, + weights: torch.Tensor, + + lr: float, + weight_decay: float, + world_size: int +) -> None: + N, D = local_weights_grad.shape + + # All-gather + all_weights_grad = local_weights_grad + all_ids = local_ids + + if world_size > 1: + all_weights_grad = torch.empty((world_size * N, D), dtype=local_weights_grad.dtype, device=local_weights_grad.device) + all_ids = torch.empty(world_size * N, dtype=local_ids.dtype, device=local_ids.device) + + dist.all_gather_into_tensor(all_weights_grad, local_weights_grad) + dist.all_gather_into_tensor(all_ids, local_ids) + + # Unique + grad_ids, inv = all_ids.unique(return_inverse=True) + + grad = torch.zeros((grad_ids.shape[0], D), dtype=all_weights_grad.dtype, device=all_weights_grad.device) + grad.scatter_add_(0, inv.unsqueeze(-1).expand(-1, D), all_weights_grad) + + # SignSGD with decoupled weight decay + p = weights[grad_ids] + + p.mul_(1.0 - lr * weight_decay).add_(torch.sign(grad), alpha=-lr) + + # Write updated slices back + weights[grad_ids] = p diff --git a/srm/models/srm/__init__.py b/srm/models/srm/__init__.py new file mode 100644 index 0000000..e69de29 --- /dev/null +++ b/srm/models/srm/__init__.py diff --git a/srm/models/srm/hrm_orth_v1.py b/srm/models/srm/hrm_orth_v1.py new file mode 100644 index 0000000..65656df --- /dev/null +++ b/srm/models/srm/hrm_orth_v1.py @@ -0,0 +1,376 @@ +"""HRM-Orth v1 — orthogonal patch of HRM per codex round 2 recommendation. + +CORE IDEA (codex Q6 pivot, after pure-orthogonal retract Q1): +Keep HRM's H_level/L_level/ACT structure, just patch the inner Block: + - Attention → cosine-normalized attention (≈ Lipschitz-bounded) + - SwiGLU MLP → CayleyOrth linear + MaxMin + CayleyOrth linear + - rms_norm + add → weighted residual: h_new = (1-σ(w)) · h + σ(w) · f(h) + - "Weak orthogonality": diag(s) scaling with most s≈1, some s∈[0.90, 0.97] for compression + +Per codex Q5 decomp: target +5~+7pp over SRM v1 (0.39 → 0.43-0.46). +Per codex Q3: Cayley used (we have it from srm_aol_v1); Householder would be faster but more impl. +""" +from typing import Tuple, List, Dict, Optional +from dataclasses import dataclass +import math + +import torch +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel + +from models.common import trunc_normal_init_ +from models.layers import rms_norm, SwiGLU, Attention, RotaryEmbedding, CosSin, CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding +from models.srm.srm_aol_v1 import CayleyOrthogonal + + +def maxmin(x: torch.Tensor, group: int = 2) -> torch.Tensor: + """1-Lipschitz norm-preserving activation (Anil et al. 2019 GroupSort). + + Pairs adjacent dims; outputs (min, max) per pair. Permutation a.e. → ||∇|| = 1. + Strictly better than ReLU under norm constraints (no rank-kill). + """ + *prefix, d = x.shape + if d % group != 0: + pad = group - (d % group) + x = F.pad(x, (0, pad)) + d = d + pad + xg = x.reshape(*prefix, d // group, group) + sorted_vals, _ = xg.sort(dim=-1) + return sorted_vals.reshape(*prefix, d) + + +def cosine_attention(q: torch.Tensor, k: torch.Tensor, v: torch.Tensor, + tau: float = 8.0) -> torch.Tensor: + """Cosine-normalized softmax attention. Approximately Lipschitz-bounded + (exact bound depends on tau and value norms — see LipsFormer Qi 2023).""" + q = F.normalize(q, dim=-1) + k = F.normalize(k, dim=-1) + attn = (q @ k.transpose(-2, -1)) * tau + attn = attn.softmax(dim=-1) + return attn @ v + + +class OrthLinear(nn.Module): + """Orthogonal linear layer via Cayley. Allows optional row-scaling diag(s) + where s_i ∈ [s_min, 1] to introduce 'weak orthogonality' (codex Q1 fix). + + If s_min < 1, the operator is contractive in some directions: + Lip = max(s) ≤ 1, det = prod(s) ≤ 1 (weak contraction in compressing modes) + """ + def __init__(self, dim: int, s_min: float = 0.85, learn_scale: bool = True, + init_std_scale: float = 5.0): + super().__init__() + self.Q = CayleyOrthogonal(dim) + # Bump init A by init_std_scale to push Cayley away from identity + with torch.no_grad(): + self.Q.A.mul_(init_std_scale) + self.s_min = s_min + # diag scale: sigmoid -> [s_min, 1] + if learn_scale and s_min < 1.0: + self.log_s_raw = nn.Parameter(torch.zeros(dim)) # init sigmoid(0)=0.5 → scale=(s_min+1)/2 + else: + self.register_buffer("log_s_raw", torch.zeros(dim)) + self.learn_scale = learn_scale + + def scale_diag(self) -> torch.Tensor: + if self.s_min >= 1.0 or not self.learn_scale: + return torch.ones_like(self.log_s_raw) + # Affine map sigmoid → [s_min, 1] + return self.s_min + (1.0 - self.s_min) * torch.sigmoid(self.log_s_raw) + + def forward(self, x: torch.Tensor) -> torch.Tensor: + Q = self.Q() # (d, d) orthogonal + s = self.scale_diag().to(Q.dtype) # (d,) in [s_min, 1] + Qs = Q * s.unsqueeze(0) # rescale columns + return F.linear(x, Qs) + + +@dataclass +class HierarchicalReasoningModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L: torch.Tensor + + +@dataclass +class HierarchicalReasoningModel_ACTV1Carry: + inner_carry: HierarchicalReasoningModel_ACTV1InnerCarry + + steps: torch.Tensor + halted: torch.Tensor + + current_data: Dict[str, torch.Tensor] + + +class HierarchicalReasoningModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + H_cycles: int + L_cycles: int + + H_layers: int + L_layers: int + + # Transformer config + hidden_size: int + expansion: float + num_heads: int + pos_encodings: str + + rms_norm_eps: float = 1e-5 + rope_theta: float = 10000.0 + + # Halting Q-learning config + halt_max_steps: int + halt_exploration_prob: float + + forward_dtype: str = "bfloat16" + + +class HierarchicalReasoningModel_ACTV1Block(nn.Module): + """Orthogonal-patched HRM Block. + + Replaces (attn + SwiGLU + rms_norm) with (cosine attn + Orth-MLP + weighted residual). + The original class name preserved so the ReasoningModule wrapper is unchanged. + """ + def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: + super().__init__() + d = config.hidden_size + s_min = getattr(config, "orth_s_min", 0.85) # v2: 0.95 → 0.85 for real contraction + cosine_tau = getattr(config, "cosine_attn_tau", 1.0) # v2: 8 → 1 for diverse softmax at init + init_std_scale = getattr(config, "orth_init_std_scale", 5.0) + + # Lipschitz-bounded cosine attention: orthogonal Q/K/V/O projections + self.q_proj = OrthLinear(d, s_min=1.0, learn_scale=False, init_std_scale=init_std_scale) + self.k_proj = OrthLinear(d, s_min=1.0, learn_scale=False, init_std_scale=init_std_scale) + self.v_proj = OrthLinear(d, s_min=s_min, learn_scale=True, init_std_scale=init_std_scale) + self.o_proj = OrthLinear(d, s_min=s_min, learn_scale=True, init_std_scale=init_std_scale) + self.cosine_tau = cosine_tau + + # Orth-MLP: OrthLinear -> MaxMin -> OrthLinear (no expansion; uses original d) + self.mlp_in = OrthLinear(d, s_min=s_min, learn_scale=True, init_std_scale=init_std_scale) + self.mlp_out = OrthLinear(d, s_min=s_min, learn_scale=True, init_std_scale=init_std_scale) + + # Weighted residual gates — v2: init logit=+2 → sigmoid=0.88 so block dominates + self.w_attn_logit = nn.Parameter(torch.full((), 2.0)) + self.w_mlp_logit = nn.Parameter(torch.full((), 2.0)) + + def forward(self, cos_sin: CosSin, hidden_states: torch.Tensor) -> torch.Tensor: + # Cosine attention + q = self.q_proj(hidden_states) + k = self.k_proj(hidden_states) + v = self.v_proj(hidden_states) + attn_out = self.o_proj(cosine_attention(q, k, v, tau=self.cosine_tau)) + w_attn = torch.sigmoid(self.w_attn_logit) + hidden_states = (1.0 - w_attn) * hidden_states + w_attn * attn_out + + # Orth-MLP with MaxMin + mlp_out = self.mlp_out(maxmin(self.mlp_in(hidden_states), group=2)) + w_mlp = torch.sigmoid(self.w_mlp_logit) + hidden_states = (1.0 - w_mlp) * hidden_states + w_mlp * mlp_out + return hidden_states + + +class HierarchicalReasoningModel_ACTV1ReasoningModule(nn.Module): + def __init__(self, layers: List[HierarchicalReasoningModel_ACTV1Block]): + super().__init__() + + self.layers = torch.nn.ModuleList(layers) + + def forward(self, hidden_states: torch.Tensor, input_injection: torch.Tensor, **kwargs) -> torch.Tensor: + # Input injection (add) + hidden_states = hidden_states + input_injection + # Layers + for layer in self.layers: + hidden_states = layer(hidden_states=hidden_states, **kwargs) + + return hidden_states + + +class HierarchicalReasoningModel_ACTV1_Inner(nn.Module): + def __init__(self, config: HierarchicalReasoningModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, self.config.forward_dtype) + + # I/O + self.embed_scale = math.sqrt(self.config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(self.config.vocab_size, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(self.config.hidden_size, self.config.vocab_size, bias=False) + self.q_head = CastedLinear(self.config.hidden_size, 2, bias=True) + + self.puzzle_emb_len = -(self.config.puzzle_emb_ndim // -self.config.hidden_size) # ceil div + if self.config.puzzle_emb_ndim > 0: + # Zero init puzzle embeddings + self.puzzle_emb = CastedSparseEmbedding(self.config.num_puzzle_identifiers, self.config.puzzle_emb_ndim, + batch_size=self.config.batch_size, init_std=0, cast_to=self.forward_dtype) + + # LM Blocks + if self.config.pos_encodings == "rope": + self.rotary_emb = RotaryEmbedding(dim=self.config.hidden_size // self.config.num_heads, + max_position_embeddings=self.config.seq_len + self.puzzle_emb_len, + base=self.config.rope_theta) + elif self.config.pos_encodings == "learned": + self.embed_pos = CastedEmbedding(self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, init_std=embed_init_std, cast_to=self.forward_dtype) + else: + raise NotImplementedError() + + # Reasoning Layers + self.H_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.H_layers)]) + self.L_level = HierarchicalReasoningModel_ACTV1ReasoningModule(layers=[HierarchicalReasoningModel_ACTV1Block(self.config) for _i in range(self.config.L_layers)]) + + # Initial states + self.H_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + self.L_init = nn.Buffer(trunc_normal_init_(torch.empty(self.config.hidden_size, dtype=self.forward_dtype), std=1), persistent=True) + + # Q head special init + # Init Q to (almost) zero for faster learning during bootstrapping + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) # type: ignore + + def _input_embeddings(self, input: torch.Tensor, puzzle_identifiers: torch.Tensor): + # Token embedding + embedding = self.embed_tokens(input.to(torch.int32)) + + # Puzzle embeddings + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_identifiers) + + pad_count = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad_count > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad_count)) + + embedding = torch.cat((puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size), embedding), dim=-2) + + # Position embeddings + if self.config.pos_encodings == "learned": + # scale by 1/sqrt(2) to maintain forward variance + embedding = 0.707106781 * (embedding + self.embed_pos.embedding_weight.to(self.forward_dtype)) + + # Scale + return self.embed_scale * embedding + + def empty_carry(self, batch_size: int): + return HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + z_L=torch.empty(batch_size, self.config.seq_len + self.puzzle_emb_len, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, carry: HierarchicalReasoningModel_ACTV1InnerCarry): + return HierarchicalReasoningModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + ) + + def forward(self, carry: HierarchicalReasoningModel_ACTV1InnerCarry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + seq_info = dict( + cos_sin=self.rotary_emb() if hasattr(self, "rotary_emb") else None, + ) + + # Input encoding + input_embeddings = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # Forward iterations + with torch.no_grad(): + z_H, z_L = carry.z_H, carry.z_L + + for _H_step in range(self.config.H_cycles): + for _L_step in range(self.config.L_cycles): + if not ((_H_step == self.config.H_cycles - 1) and (_L_step == self.config.L_cycles - 1)): + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + + if not (_H_step == self.config.H_cycles - 1): + z_H = self.H_level(z_H, z_L, **seq_info) + + assert not z_H.requires_grad and not z_L.requires_grad + + # 1-step grad + z_L = self.L_level(z_L, z_H + input_embeddings, **seq_info) + z_H = self.H_level(z_H, z_L, **seq_info) + + # LM Outputs + new_carry = HierarchicalReasoningModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) # New carry no grad + output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + + # Q head + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) + + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class HierarchicalReasoningModel_ACTV1(nn.Module): + """ACT wrapper.""" + + def __init__(self, config_dict: dict): + super().__init__() + self.config = HierarchicalReasoningModel_ACTV1Config(**config_dict) + self.inner = HierarchicalReasoningModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]): + batch_size = batch["inputs"].shape[0] + + return HierarchicalReasoningModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(batch_size), # Empty is expected, it will be reseted in first pass as all sequences are halted. + + steps=torch.zeros((batch_size, ), dtype=torch.int32), + halted=torch.ones((batch_size, ), dtype=torch.bool), # Default to halted + + current_data={k: torch.empty_like(v) for k, v in batch.items()} + ) + + def forward(self, carry: HierarchicalReasoningModel_ACTV1Carry, batch: Dict[str, torch.Tensor]) -> Tuple[HierarchicalReasoningModel_ACTV1Carry, Dict[str, torch.Tensor]]: + # Update data, carry (removing halted sequences) + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + + new_steps = torch.where(carry.halted, 0, carry.steps) + + new_current_data = {k: torch.where(carry.halted.view((-1, ) + (1, ) * (batch[k].ndim - 1)), batch[k], v) for k, v in carry.current_data.items()} + + # Forward inner model + new_inner_carry, logits, (q_halt_logits, q_continue_logits) = self.inner(new_inner_carry, new_current_data) + + outputs = { + "logits": logits, + "q_halt_logits": q_halt_logits, + "q_continue_logits": q_continue_logits + } + + with torch.no_grad(): + # Step + new_steps = new_steps + 1 + is_last_step = new_steps >= self.config.halt_max_steps + + halted = is_last_step + + # if training, and ACT is enabled + if self.training and (self.config.halt_max_steps > 1): + # Halt signal + # NOTE: During evaluation, always use max steps, this is to guarantee the same halting steps inside a batch for batching purposes + halted = halted | (q_halt_logits > q_continue_logits) + + # Exploration + min_halt_steps = (torch.rand_like(q_halt_logits) < self.config.halt_exploration_prob) * torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + + halted = halted & (new_steps >= min_halt_steps) + + # Compute target Q + # NOTE: No replay buffer and target networks for computing target Q-value. + # As batch_size is large, there're many parallel envs. + # Similar concept as PQN https://arxiv.org/abs/2407.04811 + next_q_halt_logits, next_q_continue_logits = self.inner(new_inner_carry, new_current_data)[-1] + + outputs["target_q_continue"] = torch.sigmoid(torch.where(is_last_step, next_q_halt_logits, torch.maximum(next_q_halt_logits, next_q_continue_logits))) + + return HierarchicalReasoningModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs diff --git a/srm/models/srm/srm_aol_v1.py b/srm/models/srm/srm_aol_v1.py new file mode 100644 index 0000000..c4e2719 --- /dev/null +++ b/srm/models/srm/srm_aol_v1.py @@ -0,0 +1,494 @@ +"""SRM-Joint-AOL v1 — Stable Recursive Model (forked from hrm_act_v1.py). + +Replaces HRM's separate H_level / L_level transformer stacks with ONE joint +operator T on state z = (h, l) that is provably contractive under weighted +P-norm ||z||²_P = ||h||² + η||l||² with Lipschitz constant ≤ κ ∈ (0.85, 0.95). + +Key replacement vs HRM: +- HierarchicalReasoningModel_ACTV1Block (attn + SwiGLU) + → StableRecursionModel_ACTV1Block (joint SRM step on (h, l)) +- ReasoningModule wraps n_iters joint updates instead of separate H/L cycles. + +Lipschitz analysis (per step, in P-norm): + Lip_P(T) ≤ (1-α) + α · κ < 1 + ⇒ joint top-1 Lyapunov per micro-step: λ_1 ≤ log((1-α) + α·κ) < 0 + +ARCHITECTURE (one joint step): + z = concat(h + b_in_h(x), √η · (l + b_in_l(x))) # join with input bias + ψ = AOL_Block(z) # Lip_P(ψ) ≤ 1 + ψ_h, ψ_l_scaled = split(ψ); ψ_l = ψ_l_scaled / √η + Az_h = a_HH·ψ_h + a_HL·(U_HL·ψ_l) # gain row sum ≤ κ + Az_l = a_LH·(U_LH·ψ_h) + a_LL·ψ_l + h_new = (1-α)·h + α·Az_h + b_out_h(x) + l_new = (1-α)·l + α·Az_l + b_out_l(x) + +REUSED FROM HRM: +- ACT framework (q_head, halt logic) +- CastedEmbedding/CastedLinear (bf16-safe linears) +- CastedSparseEmbedding (puzzle_emb) +- 1-step grad / DEQ-style truncation +""" +from typing import Tuple, Dict +from dataclasses import dataclass +import math + +import torch +import torch.nn.functional as F +from torch import nn +from pydantic import BaseModel + +from models.common import trunc_normal_init_ +from models.layers import CastedEmbedding, CastedLinear +from models.sparse_embedding import CastedSparseEmbedding + + +# ============================================================================= +# Approximately 1-Lipschitz primitives +# Normalization (AOL) and orthogonalization (Cayley) are computed in float32, +# then cast to forward dtype (bf16 by default). The bound is *exact in fp32* +# but only approximate after cast — bf16 rounding introduces a small error +# that accumulates over n_aol_layers matmuls. Empirically the margin to the +# theoretical κ-bound is large (~5×), so this is fine in practice, but the +# guarantee is not strict. For applications where strictness matters, run +# the bounded operators in float32. +# ============================================================================= + +class AOLLinear(nn.Module): + """≤1-Lipschitz linear layer via AOL (Prach & Lampert 2022) rescaling. + + Given W ∈ R^(out × in), let A = W^T W (symmetric PSD). + Define D_jj = 1 / √(Σ_i |A_ij| + eps); set W̃ = W · diag(D). + Then ||W̃ x||_2 ≤ ||x||_2 in float32 (Prach & Lampert Theorem 1). + Bound is approximate (not exact) under bf16 due to rounding in W·diag(D) + and the subsequent matmul. Bias is unconstrained (shift only, doesn't + affect Lipschitz w.r.t. input). + """ + def __init__(self, in_dim: int, out_dim: int, bias: bool = True, + cast_to: torch.dtype = torch.bfloat16, eps: float = 1e-6): + super().__init__() + std = 1.0 / math.sqrt(in_dim) + self.W = nn.Parameter(torch.randn(out_dim, in_dim) * std) + self.b = nn.Parameter(torch.zeros(out_dim)) if bias else None + self.cast_to = cast_to + self.eps = eps + + def normalized_weight(self) -> torch.Tensor: + W32 = self.W.float() + WTW = W32.t() @ W32 + col_abs_sum = WTW.abs().sum(dim=0) + scale = torch.rsqrt(col_abs_sum + self.eps) + return (W32 * scale.unsqueeze(0)).to(self.cast_to) + + def forward(self, x: torch.Tensor) -> torch.Tensor: + W = self.normalized_weight() + out = F.linear(x, W) + if self.b is not None: + out = out + self.b.to(out.dtype) + return out + + +class AOLBlock(nn.Module): + """Stack of AOLLinear with 1-Lipschitz activation (ReLU) between layers. + + Composition of 1-Lipschitz maps is 1-Lipschitz. SiLU/GELU NOT allowed + (max derivative > 1 would break the bound). + """ + def __init__(self, dim: int, n_layers: int = 2, cast_to: torch.dtype = torch.bfloat16): + super().__init__() + assert n_layers >= 1 + self.layers = nn.ModuleList([ + AOLLinear(dim, dim, bias=True, cast_to=cast_to) for _ in range(n_layers) + ]) + + def forward(self, x: torch.Tensor) -> torch.Tensor: + for i, layer in enumerate(self.layers): + x = layer(x) + if i < len(self.layers) - 1: + x = F.relu(x) + return x + + +class CayleyOrthogonal(nn.Module): + """Approximately orthogonal Q ∈ R^(d × d) via Cayley transform. + + Q = (I + S)^{-1}(I - S) where S = (A - A^T)/2 is skew-symmetric. + Since (I+S) and (I-S) commute (both polynomials in S), the form is also + Q = (I - S)(I + S)^{-1}. Q^T Q = I exactly in float32 — approximate + after cast to bf16. Solve done in float32 for numerical stability. + NOTE: torch.linalg.solve may not be fullgraph-compile friendly. Test + before enabling torch.compile / FSDP. + """ + def __init__(self, dim: int, cast_to: torch.dtype = torch.bfloat16): + super().__init__() + self.A = nn.Parameter(torch.randn(dim, dim) * (1.0 / math.sqrt(dim))) + self.dim = dim + self.cast_to = cast_to + self.register_buffer("I", torch.eye(dim), persistent=False) + + def forward(self) -> torch.Tensor: + A32 = self.A.float() + S = 0.5 * (A32 - A32.t()) + I = self.I.float() + Q = torch.linalg.solve(I + S, I - S) + return Q.to(self.cast_to) + + +class BlockGain(nn.Module): + """Block gain matrix A with row sums ≤ κ under weighted P-norm. + + H row entries (P-normalized): [a_HH, √η · a_HL], sum = κ + L row entries (P-normalized): [(1/√η) · a_LH, a_LL], sum = κ + Parameterized via softmax × κ ⇒ exact equality (saturation). + """ + def __init__(self, kappa: float = 0.9, eta: float = 1.0, init_diag: float = 3.0): + super().__init__() + self.kappa = kappa + self.eta = eta + # init_diag=3.0 → softmax([3, 0]) ≈ [0.953, 0.047] ⇒ ~5% cross-coupling at start + # (init_diag=1.0 was too weak — gave 27% cross-coupling; init_diag=3.0 truly minimal) + self.logits_H = nn.Parameter(torch.tensor([init_diag, 0.0])) + self.logits_L = nn.Parameter(torch.tensor([0.0, init_diag])) + + def forward(self) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]: + sqrt_eta = math.sqrt(self.eta) + gH = self.kappa * F.softmax(self.logits_H.float(), dim=0) + a_HH, a_HL_scaled = gH[0], gH[1] + a_HL = a_HL_scaled / sqrt_eta + gL = self.kappa * F.softmax(self.logits_L.float(), dim=0) + a_LH_scaled, a_LL = gL[0], gL[1] + a_LH = a_LH_scaled * sqrt_eta + return a_HH, a_HL, a_LH, a_LL + + +class AOLTokenMixer(nn.Module): + """1-Lipschitz mixing across token (seq) and channel dims via AOL. + + Pipeline for x of shape (B, seq, dim): + 1) Channel mix (AOL across `dim`) + 2) ReLU + 3) Token mix (AOL across `seq`, applied after transpose) + 4) ReLU + Composition of 1-Lipschitz maps ⇒ Lip ≤ 1. + """ + def __init__(self, seq_len: int, dim: int, n_layers: int = 1, + cast_to: torch.dtype = torch.bfloat16): + super().__init__() + self.channel_mix = AOLBlock(dim=dim, n_layers=n_layers, cast_to=cast_to) + self.token_mix = AOLBlock(dim=seq_len, n_layers=n_layers, cast_to=cast_to) + + def forward(self, x: torch.Tensor) -> torch.Tensor: + y = self.channel_mix(x) + y = F.relu(y) + y = y.transpose(-2, -1) # (B, dim, seq) + y = self.token_mix(y) + y = y.transpose(-2, -1) # (B, seq, dim) + return y + + +# ============================================================================= +# Carry types and config +# ============================================================================= + +@dataclass +class StableRecursionModel_ACTV1InnerCarry: + z_H: torch.Tensor + z_L: torch.Tensor + + +@dataclass +class StableRecursionModel_ACTV1Carry: + inner_carry: StableRecursionModel_ACTV1InnerCarry + steps: torch.Tensor + halted: torch.Tensor + current_data: Dict[str, torch.Tensor] + + +class StableRecursionModel_ACTV1Config(BaseModel): + batch_size: int + seq_len: int + puzzle_emb_ndim: int = 0 + num_puzzle_identifiers: int + vocab_size: int + + # SRM-specific + n_iters: int = 12 # joint micro-steps per ACT step + n_aol_layers: int = 2 # depth of ψ AOL block + kappa: float = 0.9 + eta: float = 1.0 + alpha: float = 1.0 + + # Shared with HRM + hidden_size: int + halt_max_steps: int + halt_exploration_prob: float = 0.1 + forward_dtype: str = "bfloat16" + + +# ============================================================================= +# SRM joint step (replaces HRM's H/L transformer blocks) +# ============================================================================= + +class StableRecursionModel_ACTV1Block(nn.Module): + """One SRM joint step on (h, l). Per-step Lip_P ≤ (1-α) + α·κ < 1.""" + def __init__(self, config: StableRecursionModel_ACTV1Config, seq_full: int) -> None: + super().__init__() + self.config = config + self.hidden_size = config.hidden_size + self.kappa = config.kappa + self.eta = config.eta + self.alpha = config.alpha + cast = getattr(torch, config.forward_dtype) + + joint_dim = 2 * config.hidden_size + self.psi = AOLTokenMixer(seq_len=seq_full, dim=joint_dim, + n_layers=config.n_aol_layers, cast_to=cast) + self.gain = BlockGain(kappa=config.kappa, eta=config.eta) + self.U_HL = CayleyOrthogonal(config.hidden_size, cast_to=cast) + self.U_LH = CayleyOrthogonal(config.hidden_size, cast_to=cast) + + # Input biases — unconstrained (only affect Lip w.r.t. x, not w.r.t. z; + # x is fixed across recursion so doesn't affect Lyapunov) + self.bias_in_h = CastedLinear(config.hidden_size, config.hidden_size, bias=True) + self.bias_in_l = CastedLinear(config.hidden_size, config.hidden_size, bias=True) + self.bias_out_h = CastedLinear(config.hidden_size, config.hidden_size, bias=True) + self.bias_out_l = CastedLinear(config.hidden_size, config.hidden_size, bias=True) + + def forward(self, h: torch.Tensor, l: torch.Tensor, input_emb: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]: + sqrt_eta = math.sqrt(self.eta) + + # 1. Join with input bias + h_in = h + self.bias_in_h(input_emb) + l_in = l + self.bias_in_l(input_emb) + z = torch.cat([h_in, sqrt_eta * l_in], dim=-1) # (B, seq, 2h) + + # 2. 1-Lipschitz feature map ψ + psi = self.psi(z) + psi_h, psi_l_scaled = psi.chunk(2, dim=-1) + psi_l = psi_l_scaled / sqrt_eta + + # 3. Block-gain matrix A (κ-bounded row sums) + a_HH, a_HL, a_LH, a_LL = self.gain() + U_HL = self.U_HL() + U_LH = self.U_LH() + psi_l_mix = F.linear(psi_l, U_HL) # ≡ psi_l @ U_HL.T + psi_h_mix = F.linear(psi_h, U_LH) + Az_h = a_HH * psi_h + a_HL * psi_l_mix + Az_l = a_LH * psi_h_mix + a_LL * psi_l + + # 4. Damped update + output bias + h_new = (1.0 - self.alpha) * h + self.alpha * Az_h + self.bias_out_h(input_emb) + l_new = (1.0 - self.alpha) * l + self.alpha * Az_l + self.bias_out_l(input_emb) + return h_new, l_new + + +# ============================================================================= +# Inner model + ACT wrapper (matches HRM_ACTV1 interface) +# ============================================================================= + +class StableRecursionModel_ACTV1_Inner(nn.Module): + def __init__(self, config: StableRecursionModel_ACTV1Config) -> None: + super().__init__() + self.config = config + self.forward_dtype = getattr(torch, config.forward_dtype) + + self.embed_scale = math.sqrt(config.hidden_size) + embed_init_std = 1.0 / self.embed_scale + + self.embed_tokens = CastedEmbedding(config.vocab_size, config.hidden_size, + init_std=embed_init_std, cast_to=self.forward_dtype) + self.lm_head = CastedLinear(config.hidden_size, config.vocab_size, bias=False) + self.q_head = CastedLinear(config.hidden_size, 2, bias=True) + with torch.no_grad(): + self.q_head.weight.zero_() + self.q_head.bias.fill_(-5) + + self.puzzle_emb_len = -(config.puzzle_emb_ndim // -config.hidden_size) + if config.puzzle_emb_ndim > 0: + self.puzzle_emb = CastedSparseEmbedding( + config.num_puzzle_identifiers, config.puzzle_emb_ndim, + batch_size=config.batch_size, init_std=0, cast_to=self.forward_dtype, + ) + seq_full = config.seq_len + self.puzzle_emb_len + + # Single tied SRM block used n_iters times per ACT step + self.srm_block = StableRecursionModel_ACTV1Block(config, seq_full=seq_full) + + self.H_init = nn.Buffer( + trunc_normal_init_(torch.empty(config.hidden_size, dtype=self.forward_dtype), std=1), + persistent=True, + ) + self.L_init = nn.Buffer( + trunc_normal_init_(torch.empty(config.hidden_size, dtype=self.forward_dtype), std=1), + persistent=True, + ) + + def _input_embeddings(self, input_ids: torch.Tensor, puzzle_ids: torch.Tensor) -> torch.Tensor: + emb = self.embed_tokens(input_ids.to(torch.int32)) + if self.config.puzzle_emb_ndim > 0: + puzzle_embedding = self.puzzle_emb(puzzle_ids) + pad = self.puzzle_emb_len * self.config.hidden_size - puzzle_embedding.shape[-1] + if pad > 0: + puzzle_embedding = F.pad(puzzle_embedding, (0, pad)) + puzzle_embedding = puzzle_embedding.view(-1, self.puzzle_emb_len, self.config.hidden_size) + emb = torch.cat((puzzle_embedding, emb), dim=-2) + return self.embed_scale * emb + + def empty_carry(self, batch_size: int) -> StableRecursionModel_ACTV1InnerCarry: + seq_full = self.config.seq_len + self.puzzle_emb_len + return StableRecursionModel_ACTV1InnerCarry( + z_H=torch.empty(batch_size, seq_full, self.config.hidden_size, dtype=self.forward_dtype), + z_L=torch.empty(batch_size, seq_full, self.config.hidden_size, dtype=self.forward_dtype), + ) + + def reset_carry(self, reset_flag: torch.Tensor, + carry: StableRecursionModel_ACTV1InnerCarry) -> StableRecursionModel_ACTV1InnerCarry: + return StableRecursionModel_ACTV1InnerCarry( + z_H=torch.where(reset_flag.view(-1, 1, 1), self.H_init, carry.z_H), + z_L=torch.where(reset_flag.view(-1, 1, 1), self.L_init, carry.z_L), + ) + + def forward(self, carry: StableRecursionModel_ACTV1InnerCarry, + batch: Dict[str, torch.Tensor]) -> Tuple[StableRecursionModel_ACTV1InnerCarry, torch.Tensor, Tuple[torch.Tensor, torch.Tensor]]: + input_emb = self._input_embeddings(batch["inputs"], batch["puzzle_identifiers"]) + + # n_iters - 1 no-grad iterations + 1 grad iteration (HRM-style DEQ truncation) + with torch.no_grad(): + z_H, z_L = carry.z_H, carry.z_L + for _ in range(self.config.n_iters - 1): + z_H, z_L = self.srm_block(z_H, z_L, input_emb) + assert not z_H.requires_grad and not z_L.requires_grad + + z_H, z_L = self.srm_block(z_H, z_L, input_emb) + + new_carry = StableRecursionModel_ACTV1InnerCarry(z_H=z_H.detach(), z_L=z_L.detach()) + output = self.lm_head(z_H)[:, self.puzzle_emb_len:] + q_logits = self.q_head(z_H[:, 0]).to(torch.float32) + return new_carry, output, (q_logits[..., 0], q_logits[..., 1]) + + +class StableRecursionModel_ACTV1(nn.Module): + """ACT wrapper — mirrors HierarchicalReasoningModel_ACTV1 1-to-1.""" + def __init__(self, config_dict: dict): + super().__init__() + self.config = StableRecursionModel_ACTV1Config(**config_dict) + self.inner = StableRecursionModel_ACTV1_Inner(self.config) + + @property + def puzzle_emb(self): + return self.inner.puzzle_emb + + def initial_carry(self, batch: Dict[str, torch.Tensor]) -> StableRecursionModel_ACTV1Carry: + B = batch["inputs"].shape[0] + return StableRecursionModel_ACTV1Carry( + inner_carry=self.inner.empty_carry(B), + steps=torch.zeros((B,), dtype=torch.int32), + halted=torch.ones((B,), dtype=torch.bool), + current_data={k: torch.empty_like(v) for k, v in batch.items()}, + ) + + def forward(self, carry: StableRecursionModel_ACTV1Carry, + batch: Dict[str, torch.Tensor]) -> Tuple[StableRecursionModel_ACTV1Carry, Dict[str, torch.Tensor]]: + new_inner_carry = self.inner.reset_carry(carry.halted, carry.inner_carry) + new_steps = torch.where(carry.halted, 0, carry.steps) + new_current_data = { + k: torch.where(carry.halted.view((-1,) + (1,) * (batch[k].ndim - 1)), batch[k], v) + for k, v in carry.current_data.items() + } + + new_inner_carry, logits, (q_halt, q_continue) = self.inner(new_inner_carry, new_current_data) + outputs = {"logits": logits, "q_halt_logits": q_halt, "q_continue_logits": q_continue} + + with torch.no_grad(): + new_steps = new_steps + 1 + is_last = new_steps >= self.config.halt_max_steps + halted = is_last + + if self.training and self.config.halt_max_steps > 1: + halted = halted | (q_halt > q_continue) + min_halt = (torch.rand_like(q_halt) < self.config.halt_exploration_prob) * \ + torch.randint_like(new_steps, low=2, high=self.config.halt_max_steps + 1) + halted = halted & (new_steps >= min_halt) + + next_q_halt, next_q_continue = self.inner(new_inner_carry, new_current_data)[-1] + outputs["target_q_continue"] = torch.sigmoid( + torch.where(is_last, next_q_halt, torch.maximum(next_q_halt, next_q_continue)) + ) + + return StableRecursionModel_ACTV1Carry(new_inner_carry, new_steps, halted, new_current_data), outputs + + +# ============================================================================= +# Empirical Lipschitz diagnostic +# ============================================================================= + +@torch.no_grad() +def measure_lipschitz_constant(inner: StableRecursionModel_ACTV1_Inner, + sample_batch: Dict[str, torch.Tensor], + n_probes: int = 64, eps: float = 1e-3) -> Dict[str, float]: + """Estimate Lip_P of srm_block via random perturbations. + + Returns ratio ||T(z+δ) - T(z)||_P / ||δ||_P. Should be ≤ (1-α) + α·κ. + """ + cfg = inner.config + B = sample_batch["inputs"].shape[0] + seq_full = cfg.seq_len + inner.puzzle_emb_len + h = inner.H_init.unsqueeze(0).expand(B, seq_full, cfg.hidden_size).to(inner.forward_dtype).clone() + l = inner.L_init.unsqueeze(0).expand(B, seq_full, cfg.hidden_size).to(inner.forward_dtype).clone() + input_emb = inner._input_embeddings(sample_batch["inputs"], sample_batch["puzzle_identifiers"]) + h_new, l_new = inner.srm_block(h, l, input_emb) + + ratios = [] + for _ in range(n_probes): + dh = torch.randn_like(h) * eps + dl = torch.randn_like(l) * eps + h_p, l_p = inner.srm_block(h + dh, l + dl, input_emb) + d_in_h = dh.float().flatten(1).pow(2).sum(1) + d_in_l = dl.float().flatten(1).pow(2).sum(1) + d_in_P = (d_in_h + cfg.eta * d_in_l).sqrt() + d_out_h = (h_p - h_new).float().flatten(1).pow(2).sum(1) + d_out_l = (l_p - l_new).float().flatten(1).pow(2).sum(1) + d_out_P = (d_out_h + cfg.eta * d_out_l).sqrt() + ratios.append((d_out_P / d_in_P.clamp_min(1e-12)).cpu()) + R = torch.cat(ratios) + bound = (1 - cfg.alpha) + cfg.alpha * cfg.kappa + return { + "lip_emp_mean": float(R.mean()), + "lip_emp_max": float(R.max()), + "lip_emp_99p": float(R.quantile(0.99)), + "lip_theoretical_bound": float(bound), + "passes_bound": bool(R.max() <= bound * 1.05), + } + + +if __name__ == "__main__": + cfg = dict( + batch_size=4, seq_len=81, vocab_size=11, + num_puzzle_identifiers=1, puzzle_emb_ndim=512, + hidden_size=256, n_iters=6, n_aol_layers=2, + kappa=0.9, eta=1.0, alpha=1.0, + halt_max_steps=4, halt_exploration_prob=0.1, + forward_dtype="bfloat16", + ) + model = StableRecursionModel_ACTV1(cfg).cuda() + print(f"params={sum(p.numel() for p in model.parameters()):,}") + + batch = { + "inputs": torch.randint(0, 11, (4, 81), dtype=torch.int32).cuda(), + "labels": torch.randint(0, 11, (4, 81), dtype=torch.int32).cuda(), + "puzzle_identifiers": torch.zeros(4, dtype=torch.int32).cuda(), + } + carry = model.initial_carry(batch) + carry.inner_carry.z_H = carry.inner_carry.z_H.cuda() + carry.inner_carry.z_L = carry.inner_carry.z_L.cuda() + carry.steps = carry.steps.cuda() + carry.halted = carry.halted.cuda() + for k in carry.current_data: + carry.current_data[k] = batch[k] + + model.eval() + new_carry, out = model(carry, batch) + print(f"forward OK | logits={out['logits'].shape}") + + lip = measure_lipschitz_constant(model.inner, batch, n_probes=32) + print(f"Lipschitz check: emp_max={lip['lip_emp_max']:.4f} bound={lip['lip_theoretical_bound']:.4f} " + f"passes={lip['passes_bound']} emp_mean={lip['lip_emp_mean']:.4f}") |