PatchTST: ترنسفورمر مبتنی بر وصله برای پیش‌بینی سری‌های زمانی

# backbone.py


```py
"""PatchTST backbone — verbatim from yuqinie98/PatchTST (MIT License).

Only modification: import paths rewritten to this package.
"""

__all__ = ["PatchTST_backbone"]

# Cell
from collections.abc import Callable
from typing import Optional

import numpy as np
import torch
import torch.nn.functional as F
from torch import Tensor, nn

# from collections import OrderedDict
from case_studies.config.patchtst._reference.layers import (
    Transpose,
    get_activation_fn,
    positional_encoding,
)
from case_studies.config.patchtst._reference.revin import RevIN


# Cell
class PatchTST_backbone(nn.Module):
    def __init__(
        self,
        c_in: int,
        context_window: int,
        target_window: int,
        patch_len: int,
        stride: int,
        max_seq_len: int | None = 1024,
        n_layers: int = 3,
        d_model=128,
        n_heads=16,
        d_k: int | None = None,
        d_v: int | None = None,
        d_ff: int = 256,
        norm: str = "BatchNorm",
        attn_dropout: float = 0.0,
        dropout: float = 0.0,
        act: str = "gelu",
        key_padding_mask: bool = "auto",
        padding_var: int | None = None,
        attn_mask: Tensor | None = None,
        res_attention: bool = True,
        pre_norm: bool = False,
        store_attn: bool = False,
        pe: str = "zeros",
        learn_pe: bool = True,
        fc_dropout: float = 0.0,
        head_dropout=0,
        padding_patch=None,
        pretrain_head: bool = False,
        head_type="flatten",
        individual=False,
        revin=True,
        affine=True,
        subtract_last=False,
        verbose: bool = False,
        **kwargs,
    ):

        super().__init__()

        # RevIn
        self.revin = revin
        if self.revin:
            self.revin_layer = RevIN(c_in, affine=affine, subtract_last=subtract_last)

        # Patching
        self.patch_len = patch_len
        self.stride = stride
        self.padding_patch = padding_patch
        patch_num = int((context_window - patch_len) / stride + 1)
        if padding_patch == "end":  # can be modified to general case
            self.padding_patch_layer = nn.ReplicationPad1d((0, stride))
            patch_num += 1

        # Backbone
        self.backbone = TSTiEncoder(
            c_in,
            patch_num=patch_num,
            patch_len=patch_len,
            max_seq_len=max_seq_len,
            n_layers=n_layers,
            d_model=d_model,
            n_heads=n_heads,
            d_k=d_k,
            d_v=d_v,
            d_ff=d_ff,
            attn_dropout=attn_dropout,
            dropout=dropout,
            act=act,
            key_padding_mask=key_padding_mask,
            padding_var=padding_var,
            attn_mask=attn_mask,
            res_attention=res_attention,
            pre_norm=pre_norm,
            store_attn=store_attn,
            pe=pe,
            learn_pe=learn_pe,
            verbose=verbose,
            **kwargs,
        )

        # Head
        self.head_nf = d_model * patch_num
        self.n_vars = c_in
        self.pretrain_head = pretrain_head
        self.head_type = head_type
        self.individual = individual

        if self.pretrain_head:
            self.head = self.create_pretrain_head(
                self.head_nf, c_in, fc_dropout
            )  # custom head passed as a partial func with all its kwargs
        elif head_type == "flatten":
            self.head = Flatten_Head(
                self.individual, self.n_vars, self.head_nf, target_window, head_dropout=head_dropout
            )

    def forward(self, z):  # z: [bs x nvars x seq_len]
        # norm
        if self.revin:
            z = z.permute(0, 2, 1)
            z = self.revin_layer(z, "norm")
            z = z.permute(0, 2, 1)

        # do patching
        if self.padding_patch == "end":
            z = self.padding_patch_layer(z)
        z = z.unfold(
            dimension=-1, size=self.patch_len, step=self.stride
        )  # z: [bs x nvars x patch_num x patch_len]
        z = z.permute(0, 1, 3, 2)  # z: [bs x nvars x patch_len x patch_num]

        # model
        z = self.backbone(z)  # z: [bs x nvars x d_model x patch_num]
        z = self.head(z)  # z: [bs x nvars x target_window]

        # denorm
        if self.revin:
            z = z.permute(0, 2, 1)
            z = self.revin_layer(z, "denorm")
            z = z.permute(0, 2, 1)
        return z

    def create_pretrain_head(self, head_nf, vars, dropout):
        return nn.Sequential(nn.Dropout(dropout), nn.Conv1d(head_nf, vars, 1))


class Flatten_Head(nn.Module):
    def __init__(self, individual, n_vars, nf, target_window, head_dropout=0):
        super().__init__()

        self.individual = individual
        self.n_vars = n_vars

        if self.individual:
            self.linears = nn.ModuleList()
            self.dropouts = nn.ModuleList()
            self.flattens = nn.ModuleList()
            for i in range(self.n_vars):
                self.flattens.append(nn.Flatten(start_dim=-2))
                self.linears.append(nn.Linear(nf, target_window))
                self.dropouts.append(nn.Dropout(head_dropout))
        else:
            self.flatten = nn.Flatten(start_dim=-2)
            self.linear = nn.Linear(nf, target_window)
            self.dropout = nn.Dropout(head_dropout)

    def forward(self, x):  # x: [bs x nvars x d_model x patch_num]
        if self.individual:
            x_out = []
            for i in range(self.n_vars):
                z = self.flattens[i](x[:, i, :, :])  # z: [bs x d_model * patch_num]
                z = self.linears[i](z)  # z: [bs x target_window]
                z = self.dropouts[i](z)
                x_out.append(z)
            x = torch.stack(x_out, dim=1)  # x: [bs x nvars x target_window]
        else:
            x = self.flatten(x)
            x = self.linear(x)
            x = self.dropout(x)
        return x


class TSTiEncoder(nn.Module):  # i means channel-independent
    def __init__(
        self,
        c_in,
        patch_num,
        patch_len,
        max_seq_len=1024,
        n_layers=3,
        d_model=128,
        n_heads=16,
        d_k=None,
        d_v=None,
        d_ff=256,
        norm="BatchNorm",
        attn_dropout=0.0,
        dropout=0.0,
        act="gelu",
        store_attn=False,
        key_padding_mask="auto",
        padding_var=None,
        attn_mask=None,
        res_attention=True,
        pre_norm=False,
        pe="zeros",
        learn_pe=True,
        verbose=False,
        **kwargs,
    ):

        super().__init__()

        self.patch_num = patch_num
        self.patch_len = patch_len

        # Input encoding
        q_len = patch_num
        self.W_P = nn.Linear(
            patch_len, d_model
        )  # Eq 1: projection of feature vectors onto a d-dim vector space
        self.seq_len = q_len

        # Positional encoding
        self.W_pos = positional_encoding(pe, learn_pe, q_len, d_model)

        # Residual dropout
        self.dropout = nn.Dropout(dropout)

        # Encoder
        self.encoder = TSTEncoder(
            q_len,
            d_model,
            n_heads,
            d_k=d_k,
            d_v=d_v,
            d_ff=d_ff,
            norm=norm,
            attn_dropout=attn_dropout,
            dropout=dropout,
            pre_norm=pre_norm,
            activation=act,
            res_attention=res_attention,
            n_layers=n_layers,
            store_attn=store_attn,
        )

    def forward(self, x) -> Tensor:  # x: [bs x nvars x patch_len x patch_num]

        n_vars = x.shape[1]
        # Input encoding
        x = x.permute(0, 1, 3, 2)  # x: [bs x nvars x patch_num x patch_len]
        x = self.W_P(x)  # x: [bs x nvars x patch_num x d_model]

        u = torch.reshape(
            x, (x.shape[0] * x.shape[1], x.shape[2], x.shape[3])
        )  # u: [bs * nvars x patch_num x d_model]
        u = self.dropout(u + self.W_pos)  # u: [bs * nvars x patch_num x d_model]

        # Encoder
        z = self.encoder(u)  # z: [bs * nvars x patch_num x d_model]
        z = torch.reshape(
            z, (-1, n_vars, z.shape[-2], z.shape[-1])
        )  # z: [bs x nvars x patch_num x d_model]
        z = z.permute(0, 1, 3, 2)  # z: [bs x nvars x d_model x patch_num]

        return z


# Cell
class TSTEncoder(nn.Module):
    def __init__(
        self,
        q_len,
        d_model,
        n_heads,
        d_k=None,
        d_v=None,
        d_ff=None,
        norm="BatchNorm",
        attn_dropout=0.0,
        dropout=0.0,
        activation="gelu",
        res_attention=False,
        n_layers=1,
        pre_norm=False,
        store_attn=False,
    ):
        super().__init__()

        self.layers = nn.ModuleList(
            [
                TSTEncoderLayer(
                    q_len,
                    d_model,
                    n_heads=n_heads,
                    d_k=d_k,
                    d_v=d_v,
                    d_ff=d_ff,
                    norm=norm,
                    attn_dropout=attn_dropout,
                    dropout=dropout,
                    activation=activation,
                    res_attention=res_attention,
                    pre_norm=pre_norm,
                    store_attn=store_attn,
                )
                for i in range(n_layers)
            ]
        )
        self.res_attention = res_attention

    def forward(
        self,
        src: Tensor,
        key_padding_mask: Tensor | None = None,
        attn_mask: Tensor | None = None,
    ):
        output = src
        scores = None
        if self.res_attention:
            for mod in self.layers:
                output, scores = mod(
                    output, prev=scores, key_padding_mask=key_padding_mask, attn_mask=attn_mask
                )
            return output
        else:
            for mod in self.layers:
                output = mod(output, key_padding_mask=key_padding_mask, attn_mask=attn_mask)
            return output


class TSTEncoderLayer(nn.Module):
    def __init__(
        self,
        q_len,
        d_model,
        n_heads,
        d_k=None,
        d_v=None,
        d_ff=256,
        store_attn=False,
        norm="BatchNorm",
        attn_dropout=0,
        dropout=0.0,
        bias=True,
        activation="gelu",
        res_attention=False,
        pre_norm=False,
    ):
        super().__init__()
        assert not d_model % n_heads, (
            f"d_model ({d_model}) must be divisible by n_heads ({n_heads})"
        )
        d_k = d_model // n_heads if d_k is None else d_k
        d_v = d_model // n_heads if d_v is None else d_v

        # Multi-Head attention
        self.res_attention = res_attention
        self.self_attn = _MultiheadAttention(
            d_model,
            n_heads,
            d_k,
            d_v,
            attn_dropout=attn_dropout,
            proj_dropout=dropout,
            res_attention=res_attention,
        )

        # Add & Norm
        self.dropout_attn = nn.Dropout(dropout)
        if "batch" in norm.lower():
            self.norm_attn = nn.Sequential(
                Transpose(1, 2), nn.BatchNorm1d(d_model), Transpose(1, 2)
            )
        else:
            self.norm_attn = nn.LayerNorm(d_model)

        # Position-wise Feed-Forward
        self.ff = nn.Sequential(
            nn.Linear(d_model, d_ff, bias=bias),
            get_activation_fn(activation),
            nn.Dropout(dropout),
            nn.Linear(d_ff, d_model, bias=bias),
        )

        # Add & Norm
        self.dropout_ffn = nn.Dropout(dropout)
        if "batch" in norm.lower():
            self.norm_ffn = nn.Sequential(Transpose(1, 2), nn.BatchNorm1d(d_model), Transpose(1, 2))
        else:
            self.norm_ffn = nn.LayerNorm(d_model)

        self.pre_norm = pre_norm
        self.store_attn = store_attn

    def forward(
        self,
        src: Tensor,
        prev: Tensor | None = None,
        key_padding_mask: Tensor | None = None,
        attn_mask: Tensor | None = None,
    ) -> Tensor:

        # Multi-Head attention sublayer
        if self.pre_norm:
            src = self.norm_attn(src)
        ## Multi-Head attention
        if self.res_attention:
            src2, attn, scores = self.self_attn(
                src, src, src, prev, key_padding_mask=key_padding_mask, attn_mask=attn_mask
            )
        else:
            src2, attn = self.self_attn(
                src, src, src, key_padding_mask=key_padding_mask, attn_mask=attn_mask
            )
        if self.store_attn:
            self.attn = attn
        ## Add & Norm
        src = src + self.dropout_attn(src2)  # Add: residual connection with residual dropout
        if not self.pre_norm:
            src = self.norm_attn(src)

        # Feed-forward sublayer
        if self.pre_norm:
            src = self.norm_ffn(src)
        ## Position-wise Feed-Forward
        src2 = self.ff(src)
        ## Add & Norm
        src = src + self.dropout_ffn(src2)  # Add: residual connection with residual dropout
        if not self.pre_norm:
            src = self.norm_ffn(src)

        if self.res_attention:
            return src, scores
        else:
            return src


class _MultiheadAttention(nn.Module):
    def __init__(
        self,
        d_model,
        n_heads,
        d_k=None,
        d_v=None,
        res_attention=False,
        attn_dropout=0.0,
        proj_dropout=0.0,
        qkv_bias=True,
        lsa=False,
    ):
        """Multi Head Attention Layer
        Input shape:
            Q:       [batch_size (bs) x max_q_len x d_model]
            K, V:    [batch_size (bs) x q_len x d_model]
            mask:    [q_len x q_len]
        """
        super().__init__()
        d_k = d_model // n_heads if d_k is None else d_k
        d_v = d_model // n_heads if d_v is None else d_v

        self.n_heads, self.d_k, self.d_v = n_heads, d_k, d_v

        self.W_Q = nn.Linear(d_model, d_k * n_heads, bias=qkv_bias)
        self.W_K = nn.Linear(d_model, d_k * n_heads, bias=qkv_bias)
        self.W_V = nn.Linear(d_model, d_v * n_heads, bias=qkv_bias)

        # Scaled Dot-Product Attention (multiple heads)
        self.res_attention = res_attention
        self.sdp_attn = _ScaledDotProductAttention(
            d_model, n_heads, attn_dropout=attn_dropout, res_attention=self.res_attention, lsa=lsa
        )

        # Poject output
        self.to_out = nn.Sequential(nn.Linear(n_heads * d_v, d_model), nn.Dropout(proj_dropout))

    def forward(
        self,
        Q: Tensor,
        K: Tensor | None = None,
        V: Tensor | None = None,
        prev: Tensor | None = None,
        key_padding_mask: Tensor | None = None,
        attn_mask: Tensor | None = None,
    ):

        bs = Q.size(0)
        if K is None:
            K = Q
        if V is None:
            V = Q

        # Linear (+ split in multiple heads)
        q_s = (
            self.W_Q(Q).view(bs, -1, self.n_heads, self.d_k).transpose(1, 2)
        )  # q_s    : [bs x n_heads x max_q_len x d_k]
        k_s = (
            self.W_K(K).view(bs, -1, self.n_heads, self.d_k).permute(0, 2, 3, 1)
        )  # k_s    : [bs x n_heads x d_k x q_len] - transpose(1,2) + transpose(2,3)
        v_s = (
            self.W_V(V).view(bs, -1, self.n_heads, self.d_v).transpose(1, 2)
        )  # v_s    : [bs x n_heads x q_len x d_v]

        # Apply Scaled Dot-Product Attention (multiple heads)
        if self.res_attention:
            output, attn_weights, attn_scores = self.sdp_attn(
                q_s, k_s, v_s, prev=prev, key_padding_mask=key_padding_mask, attn_mask=attn_mask
            )
        else:
            output, attn_weights = self.sdp_attn(
                q_s, k_s, v_s, key_padding_mask=key_padding_mask, attn_mask=attn_mask
            )
        # output: [bs x n_heads x q_len x d_v], attn: [bs x n_heads x q_len x q_len], scores: [bs x n_heads x max_q_len x q_len]

        # back to the original inputs dimensions
        output = (
            output.transpose(1, 2).contiguous().view(bs, -1, self.n_heads * self.d_v)
        )  # output: [bs x q_len x n_heads * d_v]
        output = self.to_out(output)

        if self.res_attention:
            return output, attn_weights, attn_scores
        else:
            return output, attn_weights


class _ScaledDotProductAttention(nn.Module):
    r"""Scaled Dot-Product Attention module (Attention is all you need by Vaswani et al., 2017) with optional residual attention from previous layer
    (Realformer: Transformer likes residual attention by He et al, 2020) and locality self sttention (Vision Transformer for Small-Size Datasets
    by Lee et al, 2021)"""

    def __init__(self, d_model, n_heads, attn_dropout=0.0, res_attention=False, lsa=False):
        super().__init__()
        self.attn_dropout = nn.Dropout(attn_dropout)
        self.res_attention = res_attention
        head_dim = d_model // n_heads
        self.scale = nn.Parameter(torch.tensor(head_dim**-0.5), requires_grad=lsa)
        self.lsa = lsa

    def forward(
        self,
        q: Tensor,
        k: Tensor,
        v: Tensor,
        prev: Tensor | None = None,
        key_padding_mask: Tensor | None = None,
        attn_mask: Tensor | None = None,
    ):
        """
        Input shape:
            q               : [bs x n_heads x max_q_len x d_k]
            k               : [bs x n_heads x d_k x seq_len]
            v               : [bs x n_heads x seq_len x d_v]
            prev            : [bs x n_heads x q_len x seq_len]
            key_padding_mask: [bs x seq_len]
            attn_mask       : [1 x seq_len x seq_len]
        Output shape:
            output:  [bs x n_heads x q_len x d_v]
            attn   : [bs x n_heads x q_len x seq_len]
            scores : [bs x n_heads x q_len x seq_len]
        """

        # Scaled MatMul (q, k) - similarity scores for all pairs of positions in an input sequence
        attn_scores = (
            torch.matmul(q, k) * self.scale
        )  # attn_scores : [bs x n_heads x max_q_len x q_len]

        # Add pre-softmax attention scores from the previous layer (optional)
        if prev is not None:
            attn_scores = attn_scores + prev

        # Attention mask (optional)
        if (
            attn_mask is not None
        ):  # attn_mask with shape [q_len x seq_len] - only used when q_len == seq_len
            if attn_mask.dtype == torch.bool:
                attn_scores.masked_fill_(attn_mask, -np.inf)
            else:
                attn_scores += attn_mask

        # Key padding mask (optional)
        if (
            key_padding_mask is not None
        ):  # mask with shape [bs x q_len] (only when max_w_len == q_len)
            attn_scores.masked_fill_(key_padding_mask.unsqueeze(1).unsqueeze(2), -np.inf)

        # normalize the attention weights
        attn_weights = F.softmax(
            attn_scores, dim=-1
        )  # attn_weights   : [bs x n_heads x max_q_len x q_len]
        attn_weights = self.attn_dropout(attn_weights)

        # compute the new values given the attention weights
        output = torch.matmul(attn_weights, v)  # output: [bs x n_heads x max_q_len x d_v]

        if self.res_attention:
            return output, attn_weights, attn_scores
        else:
            return output, attn_weights

```