502 lines
20 KiB
Python
502 lines
20 KiB
Python
"""
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mHC (Manifold-Constrained Hyper-Connections) — Inference Layer.
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Implements Section 2.2 of the DeepSeek-V4 paper for the forward pass only.
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At inference the Sinkhorn-Knopp constraint has already been enforced during
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training, but B_l is still *dynamically generated* per-token from the input
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residual state. So we still need to:
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1. Project the flattened residual → raw A/B/C parameter values.
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2. Apply sigmoid (A, C) and Sinkhorn-Knopp 20 iters (B).
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3. Mix residual streams.
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The only thing that changes vs training is that we skip the loss and gradient
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through the Sinkhorn projection — the forward arithmetic is identical.
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---------------------------------------------------------------------
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V4-Pro reference dimensions (Section 4.2.1)
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---------------------------------------------------------------------
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d = 7168 hidden dim
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n_hc = 4 hyper-connection expansion factor
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N_proj = 24 fused output of W_pre(4) + W_res(16) + W_post(4)
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K_proj = 4*7168 = 28672 = n_hc * d (flattened residual)
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t_max = 20 Sinkhorn iterations
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---------------------------------------------------------------------
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Kernel dependency
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---------------------------------------------------------------------
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tf32_hc_prenorm_gemm (DeepGEMM, SM90/SM100)
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a: (T, K) BF16 — flattened residual X_flat
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b: (N, K) FP32 — stacked weight [W_pre; W_res; W_post]
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d: (S, T, N) or (T, N) FP32 — raw projection outputs (pre-normalised)
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sqr_sum: (S, T) or (T,) FP32 — Σ a² per token (for RMSNorm denominator)
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num_splits = S (16 recommended for K=28672)
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After the call:
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d = d.sum(0) → (T, N)
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sqr_sum = sqr_sum.sum(0) → (T,)
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rms_scale = sqrt(K / (sqr_sum + eps))
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d_norm = d * rms_scale[:,None] — equivalent to RMSNorm(X_flat) @ W_stacked
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"""
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from __future__ import annotations
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import math
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from dataclasses import dataclass
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from typing import Optional, Tuple
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import torch
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import torch.nn.functional as F
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# ---------------------------------------------------------------------------
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# Try importing DeepGEMM; fall back to plain BF16 matmul if unavailable.
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# ---------------------------------------------------------------------------
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try:
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import deep_gemm
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_HAS_DEEP_GEMM = True
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except ImportError:
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_HAS_DEEP_GEMM = False
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NUM_SPLITS = 16 # K-split count for tf32_hc_prenorm_gemm numerical stability
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EPS_RMSN = 1e-6
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# ---------------------------------------------------------------------------
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# Sinkhorn-Knopp projection (T batched 4×4 matrices, 20 iters)
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# ---------------------------------------------------------------------------
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def sinkhorn_knopp(
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M: torch.Tensor, # (T, n, n) positive (after exp)
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t_max: int = 20,
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) -> torch.Tensor:
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"""
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Project each (n×n) positive matrix onto the Birkhoff polytope
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(doubly stochastic matrices) via alternating row/col normalisation.
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Paper eq. (8): M^(t) = T_r( T_c( M^(t-1) ) )
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where T_r = row-normalise, T_c = col-normalise.
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For n=4 and t_max=20 this is ~160 tiny operations — no kernel needed.
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All ops stay on GPU via standard PyTorch.
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"""
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for _ in range(t_max):
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M = M / (M.sum(dim=-1, keepdim=True) + EPS_RMSN) # T_r (row)
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M = M / (M.sum(dim=-2, keepdim=True) + EPS_RMSN) # T_c (col)
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return M
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# ---------------------------------------------------------------------------
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# Context carried between pre_block and post_block
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# ---------------------------------------------------------------------------
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@dataclass
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class mHCContext:
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"""Holds the per-token mixing matrices computed in pre_block."""
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B_l: torch.Tensor # (T, n_hc, n_hc) doubly stochastic residual transform
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C_l: torch.Tensor # (T, n_hc) output mapping (before unsqueeze)
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# ---------------------------------------------------------------------------
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# mHC layer
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# ---------------------------------------------------------------------------
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class mHCLayer:
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"""
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Wraps one transformer sub-layer (attention *or* MoE) with the mHC
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residual update.
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Typical call pattern per layer:
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x_in, ctx = mhc.pre_block(X_l)
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F_out = transformer_sublayer(x_in) # (T, d)
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X_next = mhc.post_block(X_l, F_out, ctx)
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where X_l has shape (T, n_hc, d) — the expanded residual state.
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The first call at layer 0 should use X_0 initialised via `init_state`.
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"""
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def __init__(
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self,
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hidden_dim: int = 7168,
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n_hc: int = 4,
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t_max_sinkhorn: int = 20,
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device: str = "cuda",
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dtype: torch.dtype = torch.bfloat16,
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):
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self.d = hidden_dim
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self.n_hc = n_hc
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self.K_proj = n_hc * hidden_dim # 28672 for V4-Pro
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self.N_proj = n_hc + n_hc * n_hc + n_hc # 4 + 16 + 4 = 24
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self.t_max = t_max_sinkhorn
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self.device = device
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self.dtype = dtype
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# ── Learnable weights (set via load_weights) ──────────────────
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# Stacked projection: b shape = (N_proj, K_proj) in FP32
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# Stored as separate tensors, fused in forward if DeepGEMM available.
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self.W_pre = self._buf(n_hc, self.K_proj, dtype=torch.float32) # (4, K)
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self.W_res = self._buf(n_hc * n_hc, self.K_proj, dtype=torch.float32) # (16, K)
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self.W_post = self._buf(n_hc, self.K_proj, dtype=torch.float32) # (4, K)
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# Static biases (eq. 3-5, S^pre / S^res / S^post)
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self.S_pre = self._buf(1, n_hc) # (1, 4)
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self.S_res = self._buf(n_hc, n_hc) # (4, 4)
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self.S_post = self._buf(n_hc, 1) # (4, 1)
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# Learnable gating scalars (α), initialised small during training
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# At inference these are just scalars loaded from the checkpoint.
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self.alpha_pre = torch.zeros(1, device=device, dtype=torch.float32)
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self.alpha_res = torch.zeros(1, device=device, dtype=torch.float32)
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self.alpha_post = torch.zeros(1, device=device, dtype=torch.float32)
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# Pre-allocated split buffers (set in _ensure_buffers)
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self._d_split = None # (NUM_SPLITS, max_T, N_proj) FP32
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self._sqr_sum_split = None # (NUM_SPLITS, max_T) FP32
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self._max_T = 0
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# Fused stacked weight for DeepGEMM (built once in _build_stacked)
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self._W_stacked = None # (N_proj, K_proj) FP32
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# ── Construction helpers ──────────────────────────────────────────
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def _buf(self, *shape, dtype=None):
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dt = dtype or self.dtype
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return torch.empty(*shape, dtype=dt, device=self.device)
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def load_weights(
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self,
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W_pre: torch.Tensor, # (n_hc, K) FP32
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W_res: torch.Tensor, # (n_hc², K) FP32
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W_post: torch.Tensor, # (n_hc, K) FP32
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S_pre: torch.Tensor, # (1, n_hc)
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S_res: torch.Tensor, # (n_hc, n_hc)
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S_post: torch.Tensor, # (n_hc, 1)
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alpha_pre: float,
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alpha_res: float,
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alpha_post: float,
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):
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"""
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Load all mHC parameters from the checkpoint.
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The W tensors must be FP32 — they are loaded as FP32 in the prenorm
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GEMM (BF16 input × FP32 weight). Everything else can be BF16 in the
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checkpoint and will be cast here.
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"""
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def _f32(t): return t.to(device=self.device, dtype=torch.float32).contiguous()
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def _cvt(t): return t.to(device=self.device, dtype=self.dtype).contiguous()
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self.W_pre = _f32(W_pre)
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self.W_res = _f32(W_res)
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self.W_post = _f32(W_post)
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self.S_pre = _cvt(S_pre)
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self.S_res = _cvt(S_res)
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self.S_post = _cvt(S_post)
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self.alpha_pre = torch.tensor(alpha_pre, dtype=torch.float32, device=self.device)
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self.alpha_res = torch.tensor(alpha_res, dtype=torch.float32, device=self.device)
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self.alpha_post = torch.tensor(alpha_post, dtype=torch.float32, device=self.device)
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self._W_stacked = None # invalidate cache
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def _build_stacked(self):
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"""Fuse W_pre / W_res / W_post into one (N_proj, K_proj) FP32 tensor."""
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self._W_stacked = torch.cat([self.W_pre, self.W_res, self.W_post], dim=0)
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# Must be K-major (contiguous along K) for DeepGEMM
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self._W_stacked = self._W_stacked.contiguous()
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def _ensure_buffers(self, T: int):
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"""Pre-allocate split buffers if needed (avoids hot-path alloc)."""
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if T <= self._max_T:
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return
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self._d_split = torch.empty(
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NUM_SPLITS, T, self.N_proj, dtype=torch.float32, device=self.device
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)
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self._sqr_sum_split = torch.empty(
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NUM_SPLITS, T, dtype=torch.float32, device=self.device
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)
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self._max_T = T
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# ── Forward ──────────────────────────────────────────────────────
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def _project_and_rms(self, X_flat: torch.Tensor) -> torch.Tensor:
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"""
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Compute RMSNorm(X_flat) @ W_stacked.T → (T, N_proj) FP32.
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Uses tf32_hc_prenorm_gemm when DeepGEMM is available for fused
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GEMM + squared-sum accumulation. Falls back to plain BF16 matmul.
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X_flat: (T, K_proj) BF16
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"""
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T = X_flat.shape[0]
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K = self.K_proj
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if _HAS_DEEP_GEMM:
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if self._W_stacked is None:
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self._build_stacked()
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self._ensure_buffers(T)
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d_s = self._d_split[:, :T, :] # view, no copy
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ss_s = self._sqr_sum_split[:, :T]
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# a: (T, K) BF16 b: (N, K) FP32 → d_s: (S, T, N), ss_s: (S, T)
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# Both d and sqr_sum are OUTPUT tensors (written by the kernel).
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deep_gemm.tf32_hc_prenorm_gemm(
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X_flat.contiguous(), # a
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self._W_stacked, # b (N, K) FP32
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d_s, # d (S, T, N)
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ss_s, # sqr_sum (S, T)
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num_splits=NUM_SPLITS,
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)
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d_out = d_s.sum(dim=0) # (T, N)
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sqr_sum = ss_s.sum(dim=0) # (T,)
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else:
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# Fallback: BF16 matmul + manual squared sum
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if self._W_stacked is None:
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self._build_stacked()
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x_f32 = X_flat.float()
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d_out = x_f32 @ self._W_stacked.T # (T, N)
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sqr_sum = x_f32.pow(2).sum(dim=-1) # (T,)
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# RMSNorm scale: multiply raw GEMM output by rsqrt(mean(x²))
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# mean(x²) = sqr_sum / K → scale = sqrt(K / sqr_sum)
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rms_scale = torch.sqrt(K / (sqr_sum + EPS_RMSN)) # (T,)
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return (d_out * rms_scale.unsqueeze(-1)).to(self.dtype) # (T, N) in BF16
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def _dynamic_params(
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self, X_l: torch.Tensor
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) -> Tuple[torch.Tensor, torch.Tensor, torch.Tensor]:
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"""
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Compute per-token A_l, B_l, C_l from the current residual state.
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X_l: (T, n_hc, d)
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Returns:
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A_l: (T, n_hc) sigmoid-constrained input mapping
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B_l: (T, n_hc, n_hc) doubly-stochastic residual transform
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C_l: (T, n_hc) 2*sigmoid-constrained output mapping
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"""
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T, n, d = X_l.shape
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assert n == self.n_hc and d == self.d
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# Flatten: (T, n_hc*d)
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X_flat = X_l.reshape(T, self.K_proj).to(self.dtype)
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# Fused RMSNorm projection: (T, N_proj)
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proj = self._project_and_rms(X_flat).float() # keep FP32 for precision
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# Split into raw A / B / C
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i0, i1, i2, i3 = 0, self.n_hc, self.n_hc + self.n_hc**2, self.N_proj
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A_raw = proj[:, i0:i1] # (T, n_hc)
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B_raw = proj[:, i1:i2] # (T, n_hc²)
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C_raw = proj[:, i2:i3] # (T, n_hc)
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# Add static biases and scale by learned gating factors (eq. 3-5)
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S_pre = self.S_pre.float() # (1, n_hc)
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S_res = self.S_res.float() # (n_hc, n_hc)
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S_post = self.S_post.float() # (n_hc, 1)
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A_tilde = self.alpha_pre * A_raw + S_pre # (T, n_hc)
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B_tilde = self.alpha_res * B_raw + S_res.flatten().unsqueeze(0) # (T, n_hc²)
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C_tilde = self.alpha_post * C_raw + S_post.flatten().unsqueeze(0) # (T, n_hc)
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# Apply constraints (paper eqs. 6-8)
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A_l = torch.sigmoid(A_tilde) # (T, n_hc)
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C_l = 2.0 * torch.sigmoid(C_tilde) # (T, n_hc)
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# B_l: exp → Sinkhorn-Knopp → doubly stochastic
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B_exp = torch.exp(B_tilde).reshape(T, self.n_hc, self.n_hc)
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B_l = sinkhorn_knopp(B_exp, t_max=self.t_max) # (T, n_hc, n_hc)
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# Keep B_l in FP32 — the (T,4,4) bmm precision matters more than memory.
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# A_l and C_l are cast to dtype for the input/output mixing multiplies.
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return A_l.to(self.dtype), B_l, C_l.to(self.dtype)
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# ----------------------------------------------------------------
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# Public API: pre_block / post_block
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# ----------------------------------------------------------------
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def pre_block(
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self,
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X_l: torch.Tensor, # (T, n_hc, d) BF16
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) -> Tuple[torch.Tensor, mHCContext]:
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"""
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Compute dynamic mixing params and extract the layer input.
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Returns:
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x_in: (T, d) BF16 — the actual input to pass to the sub-layer
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ctx: mHCContext — {B_l, C_l} to be passed to post_block
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"""
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A_l, B_l, C_l = self._dynamic_params(X_l)
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# Layer input: x_in = A_l @ X_l (per token, weighted sum of streams)
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# A_l: (T, n_hc) X_l: (T, n_hc, d)
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# → (T, 1, n_hc) bmm (T, n_hc, d) = (T, 1, d) → squeeze
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x_in = torch.bmm(A_l.unsqueeze(1), X_l).squeeze(1) # (T, d)
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return x_in, mHCContext(B_l=B_l, C_l=C_l)
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def post_block(
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self,
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X_l: torch.Tensor, # (T, n_hc, d) BF16 — residual state BEFORE sub-layer
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F_out: torch.Tensor, # (T, d) BF16 — sub-layer output
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ctx: mHCContext,
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) -> torch.Tensor:
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"""
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Apply the mHC residual update (eq. 1):
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X_{l+1} = B_l @ X_l + C_l ⊗ F_out
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Returns:
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X_next: (T, n_hc, d) BF16
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"""
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# B_l is FP32, X_l is BF16 — bmm upcasts automatically in PyTorch.
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BX = torch.bmm(ctx.B_l, X_l.float())
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CF = ctx.C_l.unsqueeze(-1) * F_out.unsqueeze(1) # (T, n_hc, d)
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return (BX + CF.float()).to(self.dtype) # (T, n_hc, d)
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# ----------------------------------------------------------------
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# Utility
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# ----------------------------------------------------------------
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@staticmethod
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def init_state(
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embeddings: torch.Tensor, # (T, d) BF16 — token embeddings
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n_hc: int = 4,
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) -> torch.Tensor:
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"""
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Initialise X_0 for the first layer.
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The paper figure shows the embedding feeding into the first
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Residual Mixing. We broadcast the embedding across all n_hc
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residual streams as the simplest valid initialisation.
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Returns: (T, n_hc, d) BF16
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"""
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return embeddings.unsqueeze(1).expand(-1, n_hc, -1).clone()
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@staticmethod
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def read_out(X_L: torch.Tensor) -> torch.Tensor:
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"""
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Extract the final hidden state from the last residual state.
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Convention: stream 0 is the primary output stream (standard choice
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for HC models — the first stream carries the main residual).
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Returns: (T, d) BF16
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"""
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return X_L[:, 0, :]
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# ---------------------------------------------------------------------------
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# Quick smoke test
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# ---------------------------------------------------------------------------
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if __name__ == "__main__":
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import sys
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torch.manual_seed(0)
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device = "cuda" if torch.cuda.is_available() else "cpu"
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dtype = torch.bfloat16
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D, N_HC = 7168, 4
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K = N_HC * D # 28672
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N_PROJ = N_HC + N_HC ** 2 + N_HC # 24
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mhc = mHCLayer(hidden_dim=D, n_hc=N_HC, device=device, dtype=dtype)
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# Random weights matching the expected shapes
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mhc.load_weights(
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W_pre = torch.randn(N_HC, K, dtype=torch.float32),
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W_res = torch.randn(N_HC**2, K, dtype=torch.float32),
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W_post = torch.randn(N_HC, K, dtype=torch.float32),
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S_pre = torch.zeros(1, N_HC, dtype=dtype),
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S_res = torch.eye(N_HC, dtype=dtype), # identity: pure residual
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S_post = torch.zeros(N_HC, 1, dtype=dtype),
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alpha_pre = 0.01,
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alpha_res = 0.01,
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alpha_post = 0.01,
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)
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T = 4 # 4 tokens
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# ── Forward pass ────────────────────────────────────────────────
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embeddings = torch.randn(T, D, dtype=dtype, device=device)
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X = mHCLayer.init_state(embeddings, n_hc=N_HC)
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print(f"X_0: {X.shape} (T={T}, n_hc={N_HC}, d={D})")
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# Simulate a 2-layer stack
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for layer_idx in range(2):
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x_in, ctx = mhc.pre_block(X)
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print(f"\nLayer {layer_idx}:")
|
||
print(f" x_in (to sub-layer): {x_in.shape}")
|
||
print(f" B_l: {ctx.B_l.shape}")
|
||
print(f" C_l: {ctx.C_l.shape}")
|
||
|
||
# Dummy sub-layer: identity (for testing the mHC mechanics)
|
||
F_out = x_in
|
||
|
||
X = mhc.post_block(X, F_out, ctx)
|
||
print(f" X_next: {X.shape}")
|
||
|
||
hidden = mHCLayer.read_out(X)
|
||
print(f"\nFinal hidden: {hidden.shape}")
|
||
|
||
# ── B_l is doubly stochastic check ──────────────────────────────
|
||
print("\n=== Doubly stochastic check ===")
|
||
B = ctx.B_l # (T, 4, 4) — FP32 from Sinkhorn
|
||
row_sums = B.sum(dim=-1) # (T, 4) — should all be ~1
|
||
col_sums = B.sum(dim=-2) # (T, 4) — should all be ~1
|
||
print(f" row sum range: [{row_sums.min():.6f}, {row_sums.max():.6f}] (want ≈ 1.0)")
|
||
print(f" col sum range: [{col_sums.min():.6f}, {col_sums.max():.6f}] (want ≈ 1.0)")
|
||
assert (row_sums - 1).abs().max() < 1e-3, "B_l rows do not sum to 1"
|
||
assert (col_sums - 1).abs().max() < 1e-3, "B_l cols do not sum to 1"
|
||
print(" PASSED")
|
||
|
||
# ── A_l and C_l are bounded ──────────────────────────────────────
|
||
# (Re-run dynamic params to expose A_l for checking)
|
||
A_l, B_l2, C_l = mhc._dynamic_params(X)
|
||
print(f"\n=== A_l ∈ (0,1) check ===")
|
||
print(f" A_l range: [{A_l.min():.4f}, {A_l.max():.4f}] (want ∈ (0,1))")
|
||
assert A_l.min() > 0 and A_l.max() < 1, "A_l out of sigmoid range"
|
||
print(" PASSED")
|
||
print(f"\n=== C_l ∈ (0,2) check ===")
|
||
print(f" C_l range: [{C_l.min():.4f}, {C_l.max():.4f}] (want ∈ (0,2))")
|
||
assert C_l.min() > 0 and C_l.max() < 2, "C_l out of 2*sigmoid range"
|
||
print(" PASSED")
|
||
|
||
# ── Consistency: S_res = identity → B_l ≈ doubly-stochastic I ───
|
||
print("\n=== S_res=I, alpha_res≈0 → B_l ≈ uniform matrix ===")
|
||
# With S_res = I and alpha_res ≈ 0:
|
||
# B_tilde ≈ I → exp(I) → Sinkhorn of exp(I)
|
||
# exp(I) is diag-dominant; after Sinkhorn it converges to a doubly stochastic matrix.
|
||
# We just check doubly-stochastic property is preserved (already checked above).
|
||
print(" Already verified via doubly stochastic check above.")
|
||
|
||
# ── Equivalence: T=1 decode vs T=N prefill ──────────────────────
|
||
print("\n=== Token-by-token decode == batch prefill ===")
|
||
T_big = 8
|
||
h_big = torch.randn(T_big, D, dtype=dtype, device=device)
|
||
X_batch = mHCLayer.init_state(h_big, n_hc=N_HC)
|
||
|
||
# Batch
|
||
x_in_batch, ctx_batch = mhc.pre_block(X_batch)
|
||
|
||
# Token by token
|
||
x_in_tokens = []
|
||
for t in range(T_big):
|
||
X_t = X_batch[t:t+1] # (1, n_hc, d)
|
||
x_in_t, _ = mhc.pre_block(X_t)
|
||
x_in_tokens.append(x_in_t)
|
||
x_in_seq = torch.cat(x_in_tokens, dim=0) # (T_big, d)
|
||
|
||
diff = (x_in_batch - x_in_seq).abs().max().item()
|
||
print(f" max |batch - sequential| on x_in: {diff:.6f}")
|
||
assert diff < 1e-2, f"Mismatch too large: {diff}"
|
||
print(" PASSED")
|
||
|
||
print("\nAll checks done.")
|
||
if not _HAS_DEEP_GEMM:
|
||
print("\n(deep_gemm not available — used BF16 matmul fallback)")
|