import torch import torch.nn.functional as F from einops import rearrange from torch import einsum, matmul, nn # normalization # they use layernorm without bias, something that pytorch does not offer class LayerNorm(nn.Module): def __init__(self, dim, eps=1e-5): super().__init__() self.eps = eps self.gamma = nn.Parameter(torch.ones(dim)) self.register_buffer("beta", torch.zeros(dim)) def forward(self, x): return F.layer_norm(x, x.shape[-1:], self.gamma, self.beta) # parallel with residual # discovered by Wang et al + EleutherAI from GPT-J fame class ParallelResidual(nn.Module): def __init__(self, *fns): super().__init__() self.fns = nn.ModuleList(fns) def forward(self, x): return x + sum([fn(x) for fn in self.fns]) # rotary positional embedding # https://arxiv.org/abs/2104.09864 class RotaryEmbedding(nn.Module): def __init__(self, dim): super().__init__() inv_freq = 1.0 / (10000**(torch.arange(0, dim, 2).float() / dim)) self.register_buffer("inv_freq", inv_freq) def forward(self, max_seq_len, *, device): seq = torch.arange(max_seq_len, device=device) #freqs = einsum("i , j -> i j", seq.type_as(self.inv_freq), self.inv_freq) #freqs = torch.outer(seq.type_as(self.inv_freq), self.inv_freq) i, j = len(seq.type_as(self.inv_freq)), len(self.inv_freq) freqs = matmul(seq.type_as(self.inv_freq).reshape(i, 1), self.inv_freq.reshape(1, j)) return torch.cat((freqs, freqs), dim=-1) def rotate_half(x): x = rearrange(x, "... (j d) -> ... j d", j=2) x1, x2 = x.unbind(dim=-2) return torch.cat((-x2, x1), dim=-1) def apply_rotary_pos_emb(pos, t): return (t * pos.cos()) + (rotate_half(t) * pos.sin()) # feedforward # classic Noam Shazeer paper, except here they use SwiGLU instead of the more popular GEGLU # https://arxiv.org/abs/2002.05202 class SwiGLU(nn.Module): def forward(self, x): x, gate = x.chunk(2, dim=-1) return F.silu(gate) * x def FeedForward(dim, mult=4): inner_dim = int(dim * mult) return nn.Sequential( LayerNorm(dim), nn.Linear(dim, inner_dim * 2, bias=False), SwiGLU(), nn.Linear(inner_dim, dim, bias=False), ) # attention class Attention(nn.Module): def __init__(self, dim, dim_head=64, heads=8): super().__init__() inner_dim = dim_head * heads self.norm = LayerNorm(dim) self.heads = heads self.scale = dim_head**-0.5 self.rotary_emb = RotaryEmbedding(dim_head) self.to_q = nn.Linear(dim, inner_dim, bias=False) self.to_kv = nn.Linear(dim, dim_head * 2, bias=False) self.to_out = nn.Linear(inner_dim, dim, bias=False) # for caching causal mask and rotary embeddings self.register_buffer("mask", None, persistent=False) self.register_buffer("pos_emb", None, persistent=False) def get_mask(self, n, device): if self.mask is not None and self.mask.shape[-1] >= n: return self.mask[:n, :n] mask = torch.ones((n, n), device=device, dtype=torch.bool).triu(1) self.register_buffer("mask", mask, persistent=False) return mask def get_rotary_embedding(self, n, device): if self.pos_emb is not None and self.pos_emb.shape[-2] >= n: return self.pos_emb[:n] pos_emb = self.rotary_emb(n, device=device) self.register_buffer("position", pos_emb, persistent=False) return pos_emb def forward(self, x): """ einstein notation b - batch h - heads n, i, j - sequence length (base sequence length, source, target) d - feature dimension """ n, device, h = x.shape[1], x.device, self.heads # pre layernorm x = self.norm(x) # queries, keys, values q, k, v = (self.to_q(x), *self.to_kv(x).chunk(2, dim=-1)) # split heads # they use multi-query single-key-value attention, yet another Noam Shazeer paper # they found no performance loss past a certain scale, and more efficient decoding obviously # https://arxiv.org/abs/1911.02150 q = rearrange(q, "b n (h d) -> b h n d", h=h) # rotary embeddings positions = self.get_rotary_embedding(n, device) q, k = map(lambda t: apply_rotary_pos_emb(positions, t), (q, k)) # scale q = q * self.scale b, h, i, d, j = q.size(0), q.size(1), q.size(2), q.size(3), k.size(1) # similarity #sim = einsum("b h i d, b j d -> b h i j", q, k) sim = matmul(q.reshape(b, h * i, d), k.transpose(1, 2)) sim = sim.reshape(b, h, i, j) # causal mask causal_mask = self.get_mask(n, device) sim = sim.masked_fill(causal_mask, -torch.finfo(sim.dtype).max) # attention sim = sim - sim.amax(dim=-1, keepdim=True).detach() attn = sim.softmax(dim=-1) b_, h_, i_, j_, d_ = attn.size(0), attn.size(1), attn.size(2), attn.size(3), v.size(2) # aggregate values #out = einsum("b h i j, b j d -> b h i d", attn, v) out = matmul(attn.reshape(b_, h_ * i_, j_), v) out = out.reshape(b_, h_, i_, d_) # merge heads out = rearrange(out, "b h n d -> b n (h d)") return self.to_out(out) # transformer def PaLM(*, dim, num_tokens, depth, dim_head=64, heads=8, ff_mult=4): net = nn.Sequential( nn.Embedding(num_tokens, dim), *[ ParallelResidual( Attention(dim=dim, dim_head=dim_head, heads=heads), FeedForward(dim=dim, mult=ff_mult), ) for _ in range(depth) ], LayerNorm(dim), nn.Linear(dim, num_tokens, bias=False)) # they used embedding weight tied projection out to logits, not common, but works net[-1].weight = net[0].weight nn.init.normal_(net[0].weight, std=0.02) return net