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GLADIUS v2.0 — Hybrid Attention (SLA2-inspired)
The core attention mechanism: α-blended softmax + linear attention.
Linear path: O(n) — cheap background awareness of all tokens.
Softmax path: O(n·k) — precise attention for important token pairs.
α: Per-token, learned. High when precision matters, low for routine.
This is the SLA2 principle applied to GLADIUS:
O = α ⊙ softmax_attention(Q, K_important, V) + (1-α) ⊙ linear_attention(Q, K_all, V)
Reference: Ali's SLA2 attention pipeline diagram (ali-ref/img-09.jpg)
"""
import torch
import torch.nn as nn
import torch.nn.functional as F
import math
from .config import KernelConfig
class RoPE(nn.Module):
"""Rotary Position Embeddings (Su et al., 2021).
Applied to Q and K before attention computation.
Does not interfere with our additive temporal encoding
(they operate in different subspaces — RoPE is rotational,
time encoding is additive).
"""
def __init__(self, head_dim: int, max_seq_len: int = 2048):
super().__init__()
# Precompute frequency bands
inv_freq = 1.0 / (10000 ** (torch.arange(0, head_dim, 2).float() / head_dim))
self.register_buffer('inv_freq', inv_freq)
# Precompute rotation matrices for max_seq_len
t = torch.arange(max_seq_len).float()
freqs = torch.einsum('i,j->ij', t, inv_freq)
emb = torch.cat([freqs, freqs], dim=-1)
self.register_buffer('cos_cached', emb.cos())
self.register_buffer('sin_cached', emb.sin())
def forward(self, x: torch.Tensor, seq_len: int) -> torch.Tensor:
"""Apply rotary embeddings. x: (batch, heads, seq, head_dim)"""
cos = self.cos_cached[:seq_len].unsqueeze(0).unsqueeze(0)
sin = self.sin_cached[:seq_len].unsqueeze(0).unsqueeze(0)
return (x * cos) + (self._rotate_half(x) * sin)
@staticmethod
def _rotate_half(x: torch.Tensor) -> torch.Tensor:
x1, x2 = x.chunk(2, dim=-1)
return torch.cat([-x2, x1], dim=-1)
class HybridAttention(nn.Module):
"""
SLA2-inspired hybrid attention.
Every token gets linear attention (cheap, global context).
Important tokens ALSO get softmax attention (expensive, precise).
The blend ratio α is learned per-token.
argmax_attention: α = argmax_{blend} S(blend | hidden_state)
"""
def __init__(self, config: KernelConfig, layer_idx: int = 0):
super().__init__()
self.config = config
self.layer_idx = layer_idx
self.num_heads = config.num_heads
self.head_dim = config.head_dim
self.hidden_dim = config.hidden_dim
# Projections
self.q_proj = nn.Linear(config.hidden_dim, config.hidden_dim, bias=False)
self.k_proj = nn.Linear(config.hidden_dim, config.hidden_dim, bias=False)
self.v_proj = nn.Linear(config.hidden_dim, config.hidden_dim, bias=False)
self.o_proj = nn.Linear(config.hidden_dim, config.hidden_dim, bias=False)
# Learned blend ratio: per-head α router
# Input: hidden state → Output: per-head scalar in [0, 1]
self.alpha_router = nn.Sequential(
nn.Linear(config.hidden_dim, config.num_heads),
nn.Sigmoid()
)
# RoPE
self.rope = RoPE(config.head_dim, config.max_seq_len)
# QK-Clip: softcap for attention logit stability (Gemma 2 / Kimi K2)
# Smooth capping: logits = cap * tanh(logits / cap)
# Prevents attention logit explosion at scale. None = disabled (backward-compatible).
self.qk_softcap = getattr(config, 'qk_softcap', None)
# Linear attention feature map: elu(x) + 1 (Katharopoulos et al., 2020)
# Makes dot products non-negative for valid linear attention
self._init_weights()
def _init_weights(self):
for proj in [self.q_proj, self.k_proj, self.v_proj, self.o_proj]:
nn.init.normal_(proj.weight, std=0.02)
# Initialize alpha toward 0.5 (balanced blend)
nn.init.zeros_(self.alpha_router[0].bias)
def forward(
self,
x: torch.Tensor,
mask: torch.Tensor | None = None,
memory_keys: torch.Tensor | None = None,
memory_values: torch.Tensor | None = None,
) -> torch.Tensor:
"""
Args:
x: (batch, seq_len, hidden_dim)
mask: (batch, 1, seq_len, seq_len) causal mask
memory_keys: Optional hot memory keys to attend over
memory_values: Optional hot memory values
Returns:
(batch, seq_len, hidden_dim)
"""
B, S, D = x.shape
# Project to multi-head
Q = self.q_proj(x).view(B, S, self.num_heads, self.head_dim).transpose(1, 2)
K = self.k_proj(x).view(B, S, self.num_heads, self.head_dim).transpose(1, 2)
V = self.v_proj(x).view(B, S, self.num_heads, self.head_dim).transpose(1, 2)
# Apply RoPE to Q and K
Q = self.rope(Q, S)
K = self.rope(K, S)
# === Linear Attention Path (O(n)) ===
# Feature map: elu(x) + 1 → non-negative
Q_lin = F.elu(Q) + 1 # (B, H, S, D)
K_lin = F.elu(K) + 1
# Causal linear attention via cumulative sum
# KV = K_lin^T @ V accumulated causally
# For simplicity in skeleton, use full (non-causal) linear attention
# TODO: Replace with causal linear attention for autoregressive generation
KV_lin = torch.matmul(K_lin.transpose(-2, -1), V) # (B, H, D, D)
Z_lin = K_lin.transpose(-2, -1).sum(dim=-1, keepdim=True) # normalizer
O_linear = torch.matmul(Q_lin, KV_lin) / (torch.matmul(Q_lin, Z_lin) + 1e-6)
# === Softmax Attention Path (O(n²) but precise) ===
scores = torch.matmul(Q, K.transpose(-2, -1)) / math.sqrt(self.head_dim)
# QK-Clip: prevent attention logit explosion (Gemma 2 / Kimi K2 style)
if self.qk_softcap is not None and self.qk_softcap > 0:
scores = self.qk_softcap * torch.tanh(scores / self.qk_softcap)
if mask is not None:
scores = scores.masked_fill(mask == 0, float('-inf'))
attn_weights = F.softmax(scores, dim=-1)
O_softmax = torch.matmul(attn_weights, V)
# === Blend ===
# α per-token, per-head: (B, S, num_heads) → (B, num_heads, S, 1)
alpha = self.alpha_router(x) # (B, S, H)
alpha = alpha.permute(0, 2, 1).unsqueeze(-1) # (B, H, S, 1)
O = alpha * O_softmax + (1 - alpha) * O_linear
# Reshape back
O = O.transpose(1, 2).contiguous().view(B, S, D)
return self.o_proj(O)
class SwiGLU(nn.Module):
"""SwiGLU FFN block (Shazeer, 2020). Used in LLaMA, Mistral, etc."""
def __init__(self, config: KernelConfig):
super().__init__()
self.gate_proj = nn.Linear(config.hidden_dim, config.ffn_dim, bias=False)
self.up_proj = nn.Linear(config.hidden_dim, config.ffn_dim, bias=False)
self.down_proj = nn.Linear(config.ffn_dim, config.hidden_dim, bias=False)
self._init_weights()
def _init_weights(self):
for proj in [self.gate_proj, self.up_proj, self.down_proj]:
nn.init.normal_(proj.weight, std=0.02)
def forward(self, x: torch.Tensor) -> torch.Tensor:
return self.down_proj(F.silu(self.gate_proj(x)) * self.up_proj(x))
class RMSNorm(nn.Module):
"""Root Mean Square Layer Normalization (Zhang & Sennrich, 2019)."""
def __init__(self, dim: int, eps: float = 1e-6):
super().__init__()
self.weight = nn.Parameter(torch.ones(dim))
self.eps = eps
def forward(self, x: torch.Tensor) -> torch.Tensor:
norm = torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + self.eps)
return x * norm * self.weight
class TransformerLayer(nn.Module):
"""Single transformer layer: RMSNorm → HybridAttn → RMSNorm → SwiGLU."""
def __init__(self, config: KernelConfig, layer_idx: int = 0):
super().__init__()
self.attention = HybridAttention(config, layer_idx)
self.ffn = SwiGLU(config)
self.attn_norm = RMSNorm(config.hidden_dim)
self.ffn_norm = RMSNorm(config.hidden_dim)
def forward(
self,
x: torch.Tensor,
mask: torch.Tensor | None = None,
) -> torch.Tensor:
# Pre-norm residual connections
x = x + self.attention(self.attn_norm(x), mask=mask)
x = x + self.ffn(self.ffn_norm(x))
return x
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