File size: 5,076 Bytes
4754707 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 | """v56: Top-K attention with strict ±1 everywhere.
Gumbel hard-argmax (v16/v17) forces each query to attend to EXACTLY ONE past
position — a crushing expressivity constraint. Top-K relaxes this to K
positions (K > 1) while keeping every activation strictly ±1:
scores = Q @ K^T (integer popcount) minus ALiBi
causal mask
top-K per query → indices + gather
O = sign_ste(sum of gathered V's) # integer sum of K ±1 vectors, signed
Differentiability: top-K is non-differentiable. We use a soft-hard trick: the
forward produces hard top-K gather; the backward flows through the scores with
straight-through on the top-K set. Implemented by adding a soft-softmax surrogate
for gradient + hard top-K for forward.
Config: v17 shape (d=512, L=4, d_ff=192, 5.52M). K=4.
"""
import math
import torch
import torch.nn as nn
import torch.nn.functional as F
from model import sign_ste, BitLinear, BitFFN, BinaryEmbedding
class TopKBinaryAttention(nn.Module):
def __init__(self, d_model, n_heads, top_k=4):
super().__init__()
assert d_model % n_heads == 0
self.d_model = d_model
self.n_heads = n_heads
self.head_dim = d_model // n_heads
self.top_k = top_k
self.q_proj = BitLinear(d_model, d_model)
self.k_proj = BitLinear(d_model, d_model)
self.v_proj = BitLinear(d_model, d_model)
self.o_proj = BitLinear(d_model, d_model)
slopes = torch.tensor([1 << i for i in range(n_heads)], dtype=torch.long)
self.register_buffer('alibi_slopes_int', slopes)
def forward(self, x):
B, T, D = x.shape
H, Dh, K = self.n_heads, self.head_dim, self.top_k
Q = self.q_proj(x).view(B, T, H, Dh).transpose(1, 2)
K_ = self.k_proj(x).view(B, T, H, Dh).transpose(1, 2)
V = self.v_proj(x).view(B, T, H, Dh).transpose(1, 2)
scores = torch.matmul(Q, K_.transpose(-2, -1))
pos = torch.arange(T, device=x.device)
dist = (pos.unsqueeze(0) - pos.unsqueeze(1)).abs()
alibi = self.alibi_slopes_int.view(1, H, 1, 1).to(scores.dtype) \
* dist.view(1, 1, T, T).to(scores.dtype)
scores = scores - alibi
mask = torch.triu(torch.ones(T, T, device=x.device, dtype=torch.bool), diagonal=1)
scores = scores.masked_fill(mask, -1e9)
# Soft-hard top-K:
# - hard: pick top-K, one-hot mask
# - soft: softmax over scores for gradient
eff_k = min(K, T)
top_vals, top_idx = scores.topk(eff_k, dim=-1) # (B, H, T, K)
# hard attention mask
hard_A = torch.zeros_like(scores)
hard_A.scatter_(-1, top_idx, 1.0)
# soft softmax (normalized) for backward path
soft_A = F.softmax(scores, dim=-1)
A = soft_A + (hard_A - soft_A).detach() # STE: forward=hard, backward=soft
# Sum of K ±1 V's per query → sign
O = torch.matmul(A, V) # (B, H, T, Dh) integer in [-K, K]
O = sign_ste(O) # ±1
O = O.transpose(1, 2).contiguous().view(B, T, D)
return self.o_proj(O)
class BitBlockV56(nn.Module):
def __init__(self, d_model, n_heads, d_ff, top_k=4):
super().__init__()
self.attn = TopKBinaryAttention(d_model, n_heads, top_k=top_k)
self.ffn = BitFFN(d_model, d_ff)
def forward(self, x):
a = self.attn(x)
f = self.ffn(x)
return sign_ste(x + a + f) # strict ±1 residual
class BitLMv56(nn.Module):
def __init__(self, vocab_size=128, d_model=512, n_layers=4, n_heads=8,
d_ff=192, top_k=4, max_seq_len=256):
super().__init__()
self.vocab_size = vocab_size
self.d_model = d_model
self.n_layers = n_layers
self.max_seq_len = max_seq_len
self.top_k = top_k
self.embed = BinaryEmbedding(vocab_size, d_model)
self.blocks = nn.ModuleList([
BitBlockV56(d_model, n_heads, d_ff, top_k=top_k) for _ in range(n_layers)
])
self.out_codebook = nn.Parameter(torch.randn(vocab_size, d_model) * 0.02)
self.logit_scale = nn.Parameter(torch.tensor(1.0 / math.sqrt(d_model)))
self.out_bias = nn.Parameter(torch.zeros(vocab_size))
def forward(self, idx, targets=None):
x = self.embed(idx)
for blk in self.blocks:
x = blk(x)
W_out = sign_ste(self.out_codebook)
scores = torch.matmul(x, W_out.t())
logits = scores * self.logit_scale + self.out_bias
loss = None
if targets is not None:
loss = F.cross_entropy(logits.view(-1, self.vocab_size), targets.view(-1))
return logits, loss
if __name__ == '__main__':
m = BitLMv56(d_model=512, n_layers=4, d_ff=192, top_k=4)
n = sum(p.numel() for p in m.parameters())
print(f'v56 top-4 attn: {n:,} ({n/1e6:.3f}M)')
x = torch.randint(0, 128, (2, 64))
y = torch.randint(0, 128, (2, 64))
logits, loss = m(x, y)
loss.backward()
print(f'loss={loss.item():.3f}, backward OK')
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