import math
from random import random

import torch
from torch import nn, einsum
import torch.nn.functional as F

from functools import partial, wraps
from inspect import isfunction
from collections import namedtuple

from einops import rearrange, repeat, reduce
from einops.layers.torch import Rearrange

from x_transformers.autoregressive_wrapper import AutoregressiveWrapper

# constants

DEFAULT_DIM_HEAD = 64

Intermediates = namedtuple('Intermediates', [
    'pre_softmax_attn',
    'post_softmax_attn'
])

LayerIntermediates = namedtuple('Intermediates', [
    'hiddens',
    'attn_intermediates'
])

# helpers

def exists(val):
    return val is not None

def default(val, d):
    if exists(val):
        return val
    return d() if isfunction(d) else d

def cast_tuple(val, depth):
    return val if isinstance(val, tuple) else (val,) * depth

def maybe(fn):
    @wraps(fn)
    def inner(x, *args, **kwargs):
        if not exists(x):
            return x
        return fn(x, *args, **kwargs)
    return inner

class always():
    def __init__(self, val):
        self.val = val
    def __call__(self, *args, **kwargs):
        return self.val

class not_equals():
    def __init__(self, val):
        self.val = val
    def __call__(self, x, *args, **kwargs):
        return x != self.val

class equals():
    def __init__(self, val):
        self.val = val
    def __call__(self, x, *args, **kwargs):
        return x == self.val

# tensor helpers

def max_neg_value(tensor):
    return -torch.finfo(tensor.dtype).max

def l2norm(t, groups = 1):
    t = rearrange(t, '... (g d) -> ... g d', g = groups)
    t = F.normalize(t, p = 2, dim = -1)
    return rearrange(t, '... g d -> ... (g d)')

def pad_at_dim(t, pad, dim = -1, value = 0.):
    dims_from_right = (- dim - 1) if dim < 0 else (t.ndim - dim - 1)
    zeros = ((0, 0) * dims_from_right)
    return F.pad(t, (*zeros, *pad), value = value)

# init helpers

def init_zero_(layer):
    nn.init.constant_(layer.weight, 0.)
    if exists(layer.bias):
        nn.init.constant_(layer.bias, 0.)

# keyword argument helpers

def pick_and_pop(keys, d):
    values = list(map(lambda key: d.pop(key), keys))
    return dict(zip(keys, values))

def group_dict_by_key(cond, d):
    return_val = [dict(),dict()]
    for key in d.keys():
        match = bool(cond(key))
        ind = int(not match)
        return_val[ind][key] = d[key]
    return (*return_val,)

def string_begins_with(prefix, str):
    return str.startswith(prefix)

def group_by_key_prefix(prefix, d):
    return group_dict_by_key(partial(string_begins_with, prefix), d)

def groupby_prefix_and_trim(prefix, d):
    kwargs_with_prefix, kwargs = group_dict_by_key(partial(string_begins_with, prefix), d)
    kwargs_without_prefix = dict(map(lambda x: (x[0][len(prefix):], x[1]), tuple(kwargs_with_prefix.items())))
    return kwargs_without_prefix, kwargs

# initializations

def deepnorm_init(
    transformer,
    beta,
    module_name_match_list = ['.ff.', '.to_v', '.to_out']
):
    for name, module in transformer.named_modules():
        if type(module) != nn.Linear:
            continue

        needs_beta_gain = any(map(lambda substr: substr in name, module_name_match_list))
        gain = beta if needs_beta_gain else 1
        nn.init.xavier_normal_(module.weight.data, gain = gain)

        if exists(module.bias):
            nn.init.constant_(module.bias.data, 0)

# structured dropout, more effective than traditional attention dropouts

def dropout_seq(seq, mask, dropout):
    b, n, *_, device = *seq.shape, seq.device
    logits = torch.randn(b, n, device = device)

    if exists(mask):
        mask_value = max_neg_value(logits)
        logits = logits.masked_fill(~mask, mask_value)

    keep_prob = 1. - dropout
    num_keep = max(1,  int(keep_prob * n))
    keep_indices = logits.topk(num_keep, dim = 1).indices

    batch_indices = torch.arange(b, device = device)
    batch_indices = rearrange(batch_indices, 'b -> b 1')

    seq = seq[batch_indices, keep_indices]

    if exists(mask):
        seq_counts = mask.sum(dim = -1)
        seq_keep_counts = torch.ceil(seq_counts * keep_prob).int()
        keep_mask = torch.arange(num_keep, device = device) < rearrange(seq_keep_counts, 'b -> b 1')

        mask = mask[batch_indices, keep_indices] & keep_mask

    return seq, mask

# activations

class ReluSquared(nn.Module):
    def forward(self, x):
        return F.relu(x) ** 2

# embedding

class TokenEmbedding(nn.Module):
    def __init__(self, dim, num_tokens, l2norm_embed = False):
        super().__init__()
        self.l2norm_embed = l2norm_embed
        self.emb = nn.Embedding(num_tokens, dim)

    def forward(self, x):
        token_emb = self.emb(x)
        return l2norm(token_emb) if self.l2norm_embed else token_emb

# positional embeddings

class AbsolutePositionalEmbedding(nn.Module):
    def __init__(self, dim, max_seq_len, l2norm_embed = False):
        super().__init__()
        self.scale = dim ** -0.5 if not l2norm_embed else 1.
        self.max_seq_len = max_seq_len
        self.l2norm_embed = l2norm_embed
        self.emb = nn.Embedding(max_seq_len, dim)

    def forward(self, x, pos = None):
        seq_len, device = x.shape[1], x.device
        assert seq_len <= self.max_seq_len, f'you are passing in a sequence length of {seq_len} but your absolute positional embedding has a max sequence length of {self.max_seq_len}'

        if not exists(pos):
            pos = torch.arange(seq_len, device = device)

        pos_emb = self.emb(pos)
        pos_emb = pos_emb * self.scale
        return l2norm(pos_emb) if self.l2norm_embed else pos_emb

class ScaledSinusoidalEmbedding(nn.Module):
    def __init__(self, dim, theta = 10000):
        super().__init__()
        assert (dim % 2) == 0
        self.scale = nn.Parameter(torch.ones(1) * dim ** -0.5)

        half_dim = dim // 2
        freq_seq = torch.arange(half_dim).float() / half_dim
        inv_freq = theta ** -freq_seq
        self.register_buffer('inv_freq', inv_freq, persistent = False)

    def forward(self, x, pos = None):
        seq_len, device = x.shape[1], x.device

        if not exists(pos):
            pos = torch.arange(seq_len, device = device)

        emb = einsum('i, j -> i j', pos, self.inv_freq)
        emb = torch.cat((emb.sin(), emb.cos()), dim = -1)
        return emb * self.scale

class RelativePositionBias(nn.Module):
    def __init__(self, scale, causal = False, num_buckets = 32, max_distance = 128, heads = 8):
        super().__init__()
        self.scale = scale
        self.causal = causal
        self.num_buckets = num_buckets
        self.max_distance = max_distance
        self.relative_attention_bias = nn.Embedding(num_buckets, heads)

    @staticmethod
    def _relative_position_bucket(relative_position, causal = True, num_buckets = 32, max_distance = 128):
        ret = 0
        n = -relative_position
        if not causal:
            num_buckets //= 2
            ret += (n < 0).long() * num_buckets
            n = torch.abs(n)
        else:
            n = torch.max(n, torch.zeros_like(n))

        max_exact = num_buckets // 2
        is_small = n < max_exact

        val_if_large = max_exact + (
            torch.log(n.float() / max_exact) / math.log(max_distance / max_exact) * (num_buckets - max_exact)
        ).long()
        val_if_large = torch.min(val_if_large, torch.full_like(val_if_large, num_buckets - 1))

        ret += torch.where(is_small, n, val_if_large)
        return ret

    def forward(self, qk_dots):
        i, j, device = *qk_dots.shape[-2:], qk_dots.device
        q_pos = torch.arange(j - i, j, dtype = torch.long, device = device)
        k_pos = torch.arange(j, dtype = torch.long, device = device)
        rel_pos = k_pos[None, :] - q_pos[:, None]
        rp_bucket = self._relative_position_bucket(rel_pos, causal = self.causal, num_buckets = self.num_buckets, max_distance = self.max_distance)
        values = self.relative_attention_bias(rp_bucket)
        bias = rearrange(values, 'i j h -> h i j')
        return qk_dots + (bias * self.scale)

class DynamicPositionBias(nn.Module):
    def __init__(self, dim, *, heads, depth, log_distance = False, norm = False):
        super().__init__()
        assert depth >= 1, 'depth for dynamic position bias MLP must be greater or equal to 1'
        self.log_distance = log_distance

        self.mlp = nn.ModuleList([])

        self.mlp.append(nn.Sequential(
            nn.Linear(1, dim),
            nn.LayerNorm(dim) if norm else nn.Identity(),
            nn.SiLU()
        ))

        for _ in range(depth - 1):
            self.mlp.append(nn.Sequential(
                nn.Linear(dim, dim),
                nn.LayerNorm(dim) if norm else nn.Identity(),
                nn.SiLU()
            ))

        self.mlp.append(nn.Linear(dim, heads))

    def forward(self, qk_dots):
        n, device, dtype = qk_dots.shape[-1], qk_dots.device, qk_dots.dtype

        # get the (n x n) matrix of distances
        seq_arange = torch.arange(n, device = device)
        context_arange = torch.arange(n, device = device)
        indices = rearrange(seq_arange, 'i -> i 1') - rearrange(context_arange, 'j -> 1 j')
        indices += (n - 1)

        # input to continuous positions MLP
        pos = torch.arange(-n + 1, n, device = device, dtype = dtype)
        pos = rearrange(pos, '... -> ... 1')

        if self.log_distance:
            pos = torch.sign(pos) * torch.log(pos.abs() + 1)  # log of distance is sign(rel_pos) * log(abs(rel_pos) + 1)

        for layer in self.mlp:
            pos = layer(pos)

        # get position biases        
        bias = pos[indices]
        bias = rearrange(bias, 'i j h -> h i j')
        return qk_dots + bias

class AlibiPositionalBias(nn.Module):
    def __init__(self, heads, **kwargs):
        super().__init__()
        self.heads = heads
        slopes = torch.Tensor(self._get_slopes(heads))
        slopes = rearrange(slopes, 'h -> h 1 1')
        self.register_buffer('slopes', slopes, persistent = False)
        self.register_buffer('bias', None, persistent = False)
    
    def get_bias(self, i, j, device):
        i_arange = torch.arange(j - i, j, device = device)
        j_arange = torch.arange(j, device = device)
        bias = -torch.abs(rearrange(j_arange, 'j -> 1 1 j') - rearrange(i_arange, 'i -> 1 i 1'))
        return bias

    @staticmethod
    def _get_slopes(heads):
        def get_slopes_power_of_2(n):
            start = (2**(-2**-(math.log2(n)-3)))
            ratio = start
            return [start*ratio**i for i in range(n)]

        if math.log2(heads).is_integer():
            return get_slopes_power_of_2(heads)

        closest_power_of_2 = 2 ** math.floor(math.log2(heads))
        return get_slopes_power_of_2(closest_power_of_2) + get_slopes_power_of_2(2 * closest_power_of_2)[0::2][:heads-closest_power_of_2]

    def forward(self, qk_dots):
        h, i, j, device = *qk_dots.shape[-3:], qk_dots.device

        if exists(self.bias) and self.bias.shape[-1] >= j:
            return qk_dots + self.bias[..., :i, :j]

        bias = self.get_bias(i, j, device)
        bias = bias * self.slopes

        num_heads_unalibied = h - bias.shape[0]
        bias = pad_at_dim(bias, (0, num_heads_unalibied), dim = 0)
        self.register_buffer('bias', bias, persistent=False)

        return qk_dots + self.bias

class LearnedAlibiPositionalBias(AlibiPositionalBias):
    def __init__(self, heads):
        super().__init__(heads)
        log_slopes = torch.log(self.slopes)
        self.learned_logslopes = nn.Parameter(log_slopes)

    def forward(self, qk_dots):
        h, i, j, device = *qk_dots.shape[-3:], qk_dots.device

        def get_slopes(param):
            return pad_at_dim(param.exp(), (0, h - param.shape[0]), dim = -2)

        if exists(self.bias) and self.bias.shape[-1] >= j:
            bias = self.bias[..., :i, :j]
        else:
            bias = self.get_bias(i, j, device)
            self.register_buffer('bias', bias, persistent=False)

        slopes = get_slopes(self.learned_logslopes)
        bias = bias * slopes

        return qk_dots + bias

class RotaryEmbedding(nn.Module):
    def __init__(
        self,
        dim,
        use_xpos = False,
        scale_base = 512
    ):
        super().__init__()
        inv_freq = 1. / (10000 ** (torch.arange(0, dim, 2).float() / dim))
        self.register_buffer('inv_freq', inv_freq)

        if not use_xpos:
            self.register_buffer('scale', None)
            return

        scale = (torch.arange(0, dim, 2) + 0.4 * dim) / (1.4 * dim)

        self.scale_base = scale_base
        self.register_buffer('scale', scale)

    def forward(self, seq_len, device):
        t = torch.arange(seq_len, device = device).type_as(self.inv_freq)
        freqs = torch.einsum('i , j -> i j', t, self.inv_freq)
        freqs = torch.cat((freqs, freqs), dim = -1)

        if not exists(self.scale):
            return freqs, 1.

        power = (torch.arange(seq_len, device = device) - (seq_len // 2)) / self.scale_base
        scale = self.scale ** rearrange(power, 'n -> n 1')
        scale = torch.cat((scale, scale), dim = -1)

        return freqs, scale


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(t, freqs, scale = 1):
    seq_len = t.shape[-2]
    freqs = freqs[-seq_len:, :]
    return (t * freqs.cos() * scale) + (rotate_half(t) * freqs.sin() * scale)

# norms

class Scale(nn.Module):
    def __init__(self, value, fn):
        super().__init__()
        self.value = value
        self.fn = fn

    def forward(self, x, **kwargs):
        out = self.fn(x, **kwargs)
        scale_fn = lambda t: t * self.value

        if not isinstance(out, tuple):
            return scale_fn(out)

        return (scale_fn(out[0]), *out[1:])

class ScaleNorm(nn.Module):
    def __init__(self, dim, eps = 1e-5):
        super().__init__()
        self.eps = eps
        self.g = nn.Parameter(torch.ones(1) * (dim ** -0.5))

    def forward(self, x):
        norm = torch.norm(x, dim = -1, keepdim = True)
        return x / norm.clamp(min = self.eps) * self.g

class RMSNorm(nn.Module):
    def __init__(self, dim, eps = 1e-8):
        super().__init__()
        self.scale = dim ** -0.5
        self.eps = eps
        self.g = nn.Parameter(torch.ones(dim))

    def forward(self, x):
        norm = torch.norm(x, dim = -1, keepdim = True) * self.scale
        return x / norm.clamp(min = self.eps) * self.g

# residual and residual gates

class Residual(nn.Module):
    def __init__(self, dim, scale_residual = False, scale_residual_constant = 1.):
        super().__init__()
        self.residual_scale = nn.Parameter(torch.ones(dim)) if scale_residual else None
        self.scale_residual_constant = scale_residual_constant

    def forward(self, x, residual):
        if exists(self.residual_scale):
            residual = residual * self.residual_scale

        if self.scale_residual_constant != 1:
            residual = residual * self.scale_residual_constant

        return x + residual

class GRUGating(nn.Module):
    def __init__(self, dim, scale_residual = False, **kwargs):
        super().__init__()
        self.gru = nn.GRUCell(dim, dim)
        self.residual_scale = nn.Parameter(torch.ones(dim)) if scale_residual else None

    def forward(self, x, residual):
        if exists(self.residual_scale):
            residual = residual * self.residual_scale

        gated_output = self.gru(
            rearrange(x, 'b n d -> (b n) d'),
            rearrange(residual, 'b n d -> (b n) d')
        )

        return gated_output.reshape_as(x)

# token shifting

def shift(t, amount, mask = None):
    if amount == 0:
        return t
    else:
        amount = min(amount, t.shape[1])

    if exists(mask):
        t = t.masked_fill(~mask[..., None], 0.)

    return pad_at_dim(t, (amount, -amount), dim = - 2, value = 0.)

class ShiftTokens(nn.Module):
    def __init__(self, shifts, fn):
        super().__init__()
        self.fn = fn
        self.shifts = tuple(shifts)

    def forward(self, x, **kwargs):
        mask = kwargs.get('mask', None)
        shifts = self.shifts
        segments = len(shifts)
        feats_per_shift = x.shape[-1] // segments
        splitted = x.split(feats_per_shift, dim = -1)
        segments_to_shift, rest = splitted[:segments], splitted[segments:]
        segments_to_shift = list(map(lambda args: shift(*args, mask = mask), zip(segments_to_shift, shifts)))
        x = torch.cat((*segments_to_shift, *rest), dim = -1)
        return self.fn(x, **kwargs)

# feedforward

class GLU(nn.Module):
    def __init__(self, dim_in, dim_out, activation):
        super().__init__()
        self.act = activation
        self.proj = nn.Linear(dim_in, dim_out * 2)

    def forward(self, x):
        x, gate = self.proj(x).chunk(2, dim = -1)
        return x * self.act(gate)

class FeedForward(nn.Module):
    def __init__(
        self,
        dim,
        dim_out = None,
        mult = 4,
        glu = False,
        swish = False,
        relu_squared = False,
        post_act_ln = False,
        dropout = 0.,
        no_bias = False,
        zero_init_output = False
    ):
        super().__init__()
        inner_dim = int(dim * mult)
        dim_out = default(dim_out, dim)

        if relu_squared:
            activation = ReluSquared()
        elif swish:
            activation = nn.SiLU()
        else:
            activation = nn.GELU()

        project_in = nn.Sequential(
            nn.Linear(dim, inner_dim, bias = not no_bias),
            activation
        ) if not glu else GLU(dim, inner_dim, activation)

        self.ff = nn.Sequential(
            project_in,
            nn.LayerNorm(inner_dim) if post_act_ln else nn.Identity(),
            nn.Dropout(dropout),
            nn.Linear(inner_dim, dim_out, bias = not no_bias)
        )

        # init last linear layer to 0
        if zero_init_output:
            init_zero_(self.ff[-1])

    def forward(self, x):
        return self.ff(x)

# attention.

class Attention(nn.Module):
    def __init__(
        self,
        dim,
        dim_head = DEFAULT_DIM_HEAD,
        heads = 8,
        causal = False,
        talking_heads = False,
        head_scale = False,
        sparse_topk = None,
        num_mem_kv = 0,
        dropout = 0.,
        on_attn = False,
        gate_values = False,
        zero_init_output = False,
        max_attend_past = None,
        qk_norm = False,
        qk_norm_groups = 1,
        qk_norm_scale = 10,
        one_kv_head = False,
        shared_kv = False,
        value_dim_head = None,
        tensor_product = False   # https://arxiv.org/abs/2208.06061
    ):
        super().__init__()
        self.scale = dim_head ** -0.5

        self.heads = heads
        self.causal = causal
        self.max_attend_past = max_attend_past

        value_dim_head = default(value_dim_head, dim_head)
        q_dim = k_dim = dim_head * heads
        v_dim = out_dim = value_dim_head * heads

        self.one_kv_head = one_kv_head
        if one_kv_head:
            k_dim = dim_head
            v_dim = value_dim_head
            out_dim = v_dim * heads

        self.to_q = nn.Linear(dim, q_dim, bias = False)
        self.to_k = nn.Linear(dim, k_dim, bias = False)

        # shared key / values, for further memory savings during inference
        assert not (shared_kv and value_dim_head != dim_head), 'key and value head dimensions must be equal for shared key / values'
        self.to_v = nn.Linear(dim, v_dim, bias = False) if not shared_kv else None

        # relations projection from tp-attention
        self.to_r = nn.Linear(dim, v_dim, bias = False) if tensor_product else None

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

        # add GLU gating for aggregated values, from alphafold2
        self.to_v_gate = None
        if gate_values:
            self.to_v_gate = nn.Linear(dim, out_dim)
            nn.init.constant_(self.to_v_gate.weight, 0)
            nn.init.constant_(self.to_v_gate.bias, 1)

        # cosine sim attention
        self.qk_norm = qk_norm
        self.qk_norm_groups = qk_norm_groups
        self.qk_norm_scale = qk_norm_scale

        assert (not qk_norm) or (dim_head % qk_norm_groups) == 0, 'dimension per attention head must be divisible by the qk norm groups'
        assert not (qk_norm and (dim_head // qk_norm_groups) <= 2), 'the group dimension may be too small (2 was too small in my tests, but 4 still works, surprisingly)'

        # talking heads
        self.talking_heads = talking_heads
        if talking_heads:
            self.pre_softmax_talking_heads = nn.Conv2d(heads, heads, 1, bias = False)
            self.post_softmax_talking_heads = nn.Conv2d(heads, heads, 1, bias = False)

        # head scaling
        self.head_scale = head_scale
        if head_scale:
            self.head_scale_params = nn.Parameter(torch.ones(1, heads, 1, 1))

        # explicit topk sparse attention
        self.sparse_topk = sparse_topk

        # attention softmax function
        self.attn_fn = partial(F.softmax, dtype = torch.float32) if not qk_norm else F.softmax

        # add memory key / values
        self.num_mem_kv = num_mem_kv
        if num_mem_kv > 0:
            self.mem_k = nn.Parameter(torch.randn(heads, num_mem_kv, dim_head))
            self.mem_v = nn.Parameter(torch.randn(heads, num_mem_kv, dim_head))

        # attention on attention
        self.attn_on_attn = on_attn
        self.to_out = nn.Sequential(nn.Linear(out_dim, dim * 2, bias = False), nn.GLU()) if on_attn else nn.Linear(out_dim, dim, bias = False)

        # init output projection 0
        if zero_init_output:
            init_zero_(self.to_out)

    def forward(
        self,
        x,
        context = None,
        mask = None,
        context_mask = None,
        attn_mask = None,
        rel_pos = None,
        rotary_pos_emb = None,
        prev_attn = None,
        mem = None
    ):
        b, n, _, h, talking_heads, head_scale, scale, device, has_context = *x.shape, self.heads, self.talking_heads, self.head_scale, self.scale, x.device, exists(context)
        kv_input = default(context, x)

        q_input = x
        k_input = kv_input
        v_input = kv_input
        r_input = x

        if exists(mem):
            k_input = torch.cat((mem, k_input), dim = -2)
            v_input = torch.cat((mem, v_input), dim = -2)

        q = self.to_q(q_input)
        k = self.to_k(k_input)
        v = self.to_v(v_input) if exists(self.to_v) else k
        r = self.to_r(r_input) if exists(self.to_r) else None

        q = rearrange(q, 'b n (h d) -> b h n d', h = h)

        if not self.one_kv_head:
            k, v, r = map(lambda t: maybe(rearrange)(t, 'b n (h d) -> b h n d', h = h), (k, v, r))

        if exists(rotary_pos_emb) and not has_context:
            freqs, xpos_scale = rotary_pos_emb
            l = freqs.shape[-1]

            q_xpos_scale, k_xpos_scale = (xpos_scale, xpos_scale ** -1.) if exists(xpos_scale) else (1., 1.)
            (ql, qr), (kl, kr), (vl, vr) = map(lambda t: (t[..., :l], t[..., l:]), (q, k, v))

            ql, kl, vl = map(lambda arg: apply_rotary_pos_emb(arg[0], freqs, arg[1]), ((ql, q_xpos_scale), (kl, k_xpos_scale), (vl, k_xpos_scale)))
            q, k, v = map(lambda t: torch.cat(t, dim = -1), ((ql, qr), (kl, kr), (vl, vr)))

        input_mask = default(context_mask, mask)

        if self.num_mem_kv > 0:
            mem_k, mem_v = map(lambda t: repeat(t, 'h n d -> b h n d', b = b), (self.mem_k, self.mem_v))
            k = torch.cat((mem_k, k), dim = -2)
            v = torch.cat((mem_v, v), dim = -2)

            if exists(input_mask):
                input_mask = pad_at_dim(input_mask, (self.num_mem_kv, 0), dim = -1, value = True)

        if self.qk_norm:
            qk_l2norm = partial(l2norm, groups = self.qk_norm_groups)
            q, k = map(qk_l2norm, (q, k))
            scale = self.qk_norm_scale

        kv_einsum_eq = 'b h j d' if not self.one_kv_head else 'b j d'

        dots = einsum(f'b h i d, {kv_einsum_eq} -> b h i j', q, k) * scale

        mask_value = max_neg_value(dots)

        if exists(prev_attn):
            dots = dots + prev_attn

        pre_softmax_attn = dots.clone()

        if talking_heads:
            dots = self.pre_softmax_talking_heads(dots)

        if exists(rel_pos):
            dots = rel_pos(dots)

        if exists(input_mask):
            input_mask = rearrange(input_mask, 'b j -> b 1 1 j')
            dots = dots.masked_fill(~input_mask, mask_value)
            del input_mask

        if exists(attn_mask):
            assert 2 <= attn_mask.ndim <= 4, 'attention mask must have greater than 2 dimensions but less than or equal to 4'
            if attn_mask.ndim == 2:
                attn_mask = rearrange(attn_mask, 'i j -> 1 1 i j')
            elif attn_mask.ndim == 3:
                attn_mask = rearrange(attn_mask, 'h i j -> 1 h i j')
            dots = dots.masked_fill(~attn_mask, mask_value)

        if exists(self.max_attend_past):
            i, j = dots.shape[-2:]
            range_q = torch.arange(j - i, j, device = device)
            range_k = torch.arange(j, device = device)
            dist = rearrange(range_q, 'i -> 1 1 i 1') - rearrange(range_k, 'j -> 1 1 1 j')
            max_attend_past_mask = dist > self.max_attend_past
            dots = dots.masked_fill(max_attend_past_mask, mask_value)
            del max_attend_past_mask

        if self.causal:
            i, j = dots.shape[-2:]
            causal_mask = torch.ones((i, j), dtype = torch.bool, device = device).triu(j - i + 1)
            dots = dots.masked_fill(causal_mask, mask_value)
            del causal_mask

        if exists(self.sparse_topk) and self.sparse_topk < dots.shape[-1]:
            top, _ = dots.topk(self.sparse_topk, dim = -1)
            vk = rearrange(top[..., -1], '... -> ... 1')
            sparse_topk_mask = dots < vk
            dots = dots.masked_fill(sparse_topk_mask, mask_value)
            del sparse_topk_mask

        dtype = dots.dtype

        attn = self.attn_fn(dots, dim = -1)
        attn = attn.type(dtype)

        post_softmax_attn = attn.clone()

        attn = self.dropout(attn)

        if talking_heads:
            attn = self.post_softmax_talking_heads(attn)

        out = einsum(f'b h i j, {kv_einsum_eq} -> b h i d', attn, v)

        if exists(r):
            # https://arxiv.org/abs/2208.06061 proposes to add a residual for better gradients
            out = out * r + out

        if head_scale:
            out = out * self.head_scale_params

        out = rearrange(out, 'b h n d -> b n (h d)')

        if exists(self.to_v_gate):
            gates = self.to_v_gate(x)
            out = out * gates.sigmoid()

        intermediates = Intermediates(
            pre_softmax_attn = pre_softmax_attn,
            post_softmax_attn = post_softmax_attn
        )

        out = self.to_out(out)

        if exists(mask):
            mask = rearrange(mask, 'b n -> b n 1')
            out = out.masked_fill(~mask, 0.)

        return out, intermediates

class AttentionLayers(nn.Module):
    def __init__(
        self,
        dim,
        depth,
        heads = 8,
        causal = False,
        cross_attend = False,
        only_cross = False,
        use_scalenorm = False,
        use_rmsnorm = False,
        alibi_pos_bias = False,
        alibi_num_heads = None,
        alibi_learned = False,
        rel_pos_bias = False,
        rel_pos_num_buckets = 32,
        rel_pos_max_distance = 128,
        dynamic_pos_bias = False,
        dynamic_pos_bias_log_distance = False,
        dynamic_pos_bias_mlp_depth = 2,
        dynamic_pos_bias_norm = False,
        rotary_pos_emb = False,
        rotary_emb_dim = None,
        rotary_xpos = False,
        rotary_xpos_scale_base = 512,
        custom_layers = None,
        sandwich_coef = None,
        par_ratio = None,
        residual_attn = False,
        cross_residual_attn = False,
        macaron = False,
        pre_norm = True,
        gate_residual = False,
        scale_residual = False,
        scale_residual_constant = 1.,
        deepnorm = False,
        shift_tokens = 0,
        sandwich_norm = False,
        zero_init_branch_output = False,
        layer_dropout = 0.,
        cross_attn_tokens_dropout = 0.,
        **kwargs
    ):
        super().__init__()
        rotary_pos_emb = rotary_pos_emb or rotary_xpos

        ff_kwargs, kwargs = groupby_prefix_and_trim('ff_', kwargs)
        attn_kwargs, kwargs = groupby_prefix_and_trim('attn_', kwargs)

        dim_head = attn_kwargs.get('dim_head', DEFAULT_DIM_HEAD)

        self.dim = dim
        self.depth = depth
        self.layers = nn.ModuleList([])

        self.has_pos_emb = rel_pos_bias or rotary_pos_emb

        rotary_emb_dim = max(default(rotary_emb_dim, dim_head // 2), 32)

        assert not (rotary_xpos and not causal), 'rotary xpos is not compatible with bidirectional attention'
        self.rotary_pos_emb = RotaryEmbedding(rotary_emb_dim, use_xpos = rotary_xpos, scale_base = rotary_xpos_scale_base) if rotary_pos_emb else None

        assert not (alibi_pos_bias and rel_pos_bias), 'you can only choose Alibi positional bias or T5 relative positional bias, not both'
        assert rel_pos_num_buckets <= rel_pos_max_distance, 'number of relative position buckets must be less than the relative position max distance'

        # relative positional bias

        self.rel_pos = None
        if rel_pos_bias:
            self.rel_pos = RelativePositionBias(scale = dim_head ** 0.5, causal = causal, heads = heads, num_buckets = rel_pos_num_buckets, max_distance = rel_pos_max_distance)
        elif dynamic_pos_bias:
            self.rel_pos = DynamicPositionBias(dim = dim // 4, heads = heads, log_distance = dynamic_pos_bias_log_distance, depth = dynamic_pos_bias_mlp_depth, norm = dynamic_pos_bias_norm)
        elif alibi_pos_bias:
            alibi_num_heads = default(alibi_num_heads, heads)
            assert alibi_num_heads <= heads, 'number of ALiBi heads must be less than the total number of heads'
            alibi_pos_klass = LearnedAlibiPositionalBias if alibi_learned else AlibiPositionalBias
            self.rel_pos = alibi_pos_klass(heads = alibi_num_heads)

        # determine deepnorm and residual scale

        if deepnorm:
            assert scale_residual_constant == 1, 'scale residual constant is being overridden by deep norm settings'
            pre_norm = sandwich_norm = False
            scale_residual = True
            scale_residual_constant = (2 * depth) ** 0.25

        assert not (not pre_norm and sandwich_norm), 'sandwich norm cannot be used when not using prenorm'
        self.pre_norm = pre_norm
        self.sandwich_norm = sandwich_norm

        self.residual_attn = residual_attn
        self.cross_residual_attn = cross_residual_attn
        self.cross_attend = cross_attend

        norm_class = ScaleNorm if use_scalenorm else nn.LayerNorm
        norm_class = RMSNorm if use_rmsnorm else norm_class
        norm_fn = partial(norm_class, dim)

        if cross_attend and not only_cross:
            default_block = ('a', 'c', 'f')
        elif cross_attend and only_cross:
            default_block = ('c', 'f')
        else:
            default_block = ('a', 'f')

        if macaron:
            default_block = ('f',) + default_block

        # zero init

        if zero_init_branch_output:
            attn_kwargs = {**attn_kwargs, 'zero_init_output':  True}
            ff_kwargs = {**ff_kwargs, 'zero_init_output':  True}

        # calculate layer block order

        if exists(custom_layers):
            layer_types = custom_layers
        elif exists(par_ratio):
            par_depth = depth * len(default_block)
            assert 1 < par_ratio <= par_depth, 'par ratio out of range'
            default_block = tuple(filter(not_equals('f'), default_block))
            par_attn  = par_depth // par_ratio
            depth_cut = par_depth * 2 // 3  # 2 / 3 attention layer cutoff suggested by PAR paper
            par_width = (depth_cut + depth_cut // par_attn) // par_attn
            assert len(default_block) <= par_width, 'default block is too large for par_ratio'
            par_block = default_block + ('f',) * (par_width - len(default_block))
            par_head = par_block * par_attn
            layer_types = par_head + ('f',) * (par_depth - len(par_head))
        elif exists(sandwich_coef):
            assert sandwich_coef > 0 and sandwich_coef <= depth, 'sandwich coefficient should be less than the depth'
            layer_types = ('a',) * sandwich_coef + default_block * (depth - sandwich_coef) + ('f',) * sandwich_coef
        else:
            layer_types = default_block * depth

        self.layer_types = layer_types
        self.num_attn_layers = len(list(filter(equals('a'), layer_types)))

        # stochastic depth

        self.layer_dropouts = cast_tuple(layer_dropout, len(layer_types))

        # structured dropout for cross attending

        self.cross_attn_tokens_dropout = cross_attn_tokens_dropout

        # calculate token shifting

        shift_tokens = cast_tuple(shift_tokens, len(layer_types))

        # iterate and construct layers

        for ind, (layer_type, layer_shift_tokens) in enumerate(zip(self.layer_types, shift_tokens)):
            is_last_layer = ind == (len(self.layer_types) - 1)

            if layer_type == 'a':
                layer = Attention(dim, heads = heads, causal = causal, **attn_kwargs)
            elif layer_type == 'c':
                layer = Attention(dim, heads = heads, **attn_kwargs)
            elif layer_type == 'f':
                layer = FeedForward(dim, **ff_kwargs)
                layer = layer if not macaron else Scale(0.5, layer)
            else:
                raise Exception(f'invalid layer type {layer_type}')

            if layer_shift_tokens > 0:
                shift_range_upper = layer_shift_tokens + 1
                shift_range_lower = -layer_shift_tokens if not causal else 0
                layer = ShiftTokens(range(shift_range_lower, shift_range_upper), layer)

            residual_fn = GRUGating if gate_residual else Residual
            residual = residual_fn(dim, scale_residual = scale_residual, scale_residual_constant = scale_residual_constant)

            pre_branch_norm = norm_fn() if pre_norm else None
            post_branch_norm = norm_fn() if sandwich_norm else None
            post_main_norm = norm_fn() if not pre_norm and not is_last_layer else None

            norms = nn.ModuleList([
                pre_branch_norm,
                post_branch_norm,
                post_main_norm
            ])

            self.layers.append(nn.ModuleList([
                norms,
                layer,
                residual
            ]))

        if deepnorm:
            init_gain = (8 * depth) ** -0.25
            deepnorm_init(self, init_gain)

    def forward(
        self,
        x,
        context = None,
        mask = None,
        context_mask = None,
        attn_mask = None,
        self_attn_context_mask = None,
        mems = None,
        return_hiddens = False
    ):
        assert not (self.cross_attend ^ exists(context)), 'context must be passed in if cross_attend is set to True'

        hiddens = []
        intermediates = []
        prev_attn = None
        prev_cross_attn = None

        mems = mems.copy() if exists(mems) else [None] * self.num_attn_layers

        rotary_pos_emb = None
        if exists(self.rotary_pos_emb):
            max_rotary_emb_length = max(list(map(lambda m: (m.shape[1] if exists(m) else 0) + x.shape[1], mems)))
            rotary_pos_emb = self.rotary_pos_emb(max_rotary_emb_length, x.device)

        for ind, (layer_type, (norm, block, residual_fn), layer_dropout) in enumerate(zip(self.layer_types, self.layers, self.layer_dropouts)):
            is_last = ind == (len(self.layers) - 1)

            if self.training and layer_dropout > 0. and random() < layer_dropout:
                continue

            if layer_type == 'a':
                if return_hiddens:
                    hiddens.append(x)
                layer_mem = mems.pop(0) if mems else None

            if layer_type == 'c':
                if self.training and self.cross_attn_tokens_dropout > 0.:
                    context, context_mask = dropout_seq(context, context_mask, self.cross_attn_tokens_dropout)

            residual = x

            pre_branch_norm, post_branch_norm, post_main_norm = norm

            if exists(pre_branch_norm):
                x = pre_branch_norm(x)

            if layer_type == 'a':
                out, inter = block(x, mask = mask, context_mask = self_attn_context_mask, attn_mask = attn_mask, rel_pos = self.rel_pos, rotary_pos_emb = rotary_pos_emb, prev_attn = prev_attn, mem = layer_mem)
            elif layer_type == 'c':
                out, inter = block(x, context = context, mask = mask, context_mask = context_mask, prev_attn = prev_cross_attn)
            elif layer_type == 'f':
                out = block(x)

            if exists(post_branch_norm):
                out = post_branch_norm(out)

            x = residual_fn(out, residual)

            if layer_type in ('a', 'c') and return_hiddens:
                intermediates.append(inter)

            if layer_type == 'a' and self.residual_attn:
                prev_attn = inter.pre_softmax_attn
            elif layer_type == 'c' and self.cross_residual_attn:
                prev_cross_attn = inter.pre_softmax_attn

            if exists(post_main_norm):
                x = post_main_norm(x)

        if return_hiddens:
            intermediates = LayerIntermediates(
                hiddens = hiddens,
                attn_intermediates = intermediates
            )

            return x, intermediates

        return x

class Encoder(AttentionLayers):
    def __init__(self, **kwargs):
        assert 'causal' not in kwargs, 'cannot set causality on encoder'
        super().__init__(causal = False, **kwargs)

class Decoder(AttentionLayers):
    def __init__(self, **kwargs):
        assert 'causal' not in kwargs, 'cannot set causality on decoder'
        super().__init__(causal = True, **kwargs)

class CrossAttender(AttentionLayers):
    def __init__(self, **kwargs):
        super().__init__(cross_attend = True, only_cross = True, **kwargs)

class ViTransformerWrapper(nn.Module):
    def __init__(
        self,
        *,
        image_size,
        patch_size,
        attn_layers,
        channels = 3,
        num_classes = None,
        dropout = 0.,
        post_emb_norm = False,
        emb_dropout = 0.
    ):
        super().__init__()
        assert isinstance(attn_layers, Encoder), 'attention layers must be an Encoder'
        assert image_size % patch_size == 0, 'image dimensions must be divisible by the patch size'
        dim = attn_layers.dim
        num_patches = (image_size // patch_size) ** 2
        patch_dim = channels * patch_size ** 2

        self.patch_size = patch_size

        self.pos_embedding = nn.Parameter(torch.randn(1, num_patches + 1, dim))
        self.patch_to_embedding = nn.Linear(patch_dim, dim)
        self.post_emb_norm = nn.LayerNorm(dim) if post_emb_norm else nn.Identity()
        self.dropout = nn.Dropout(emb_dropout)

        self.attn_layers = attn_layers
        self.norm = nn.LayerNorm(dim)
        self.mlp_head = nn.Linear(dim, num_classes) if exists(num_classes) else nn.Identity()

    def forward(
        self,
        img,
        return_embeddings = False
    ):
        p = self.patch_size

        x = rearrange(img, 'b c (h p1) (w p2) -> b (h w) (p1 p2 c)', p1 = p, p2 = p)
        x = self.patch_to_embedding(x)
        n = x.shape[1]

        x = x + self.pos_embedding[:, :n]

        x = self.post_emb_norm(x)
        x = self.dropout(x)

        x = self.attn_layers(x)
        x = self.norm(x)

        if not exists(self.mlp_head) or return_embeddings:
            return x

        x = x.mean(dim = -2)
        return self.mlp_head(x)

class TransformerWrapper(nn.Module):
    def __init__(
        self,
        *,
        num_tokens,
        max_seq_len,
        attn_layers,
        emb_dim = None,
        max_mem_len = 0.,
        shift_mem_down = 0,
        emb_dropout = 0.,
        post_emb_norm = False,
        num_memory_tokens = None,
        tie_embedding = False,
        logits_dim = None,
        use_abs_pos_emb = True,
        scaled_sinu_pos_emb = False,
        l2norm_embed = False,
        emb_frac_gradient = 1. # GLM-130B and Cogview successfully used this, set at 0.1
    ):
        super().__init__()
        assert isinstance(attn_layers, AttentionLayers), 'attention layers must be one of Encoder or Decoder'

        dim = attn_layers.dim
        emb_dim = default(emb_dim, dim)
        self.emb_dim = emb_dim

        self.max_seq_len = max_seq_len
        self.max_mem_len = max_mem_len
        self.shift_mem_down = shift_mem_down

        self.l2norm_embed = l2norm_embed
        self.token_emb = TokenEmbedding(emb_dim, num_tokens, l2norm_embed = l2norm_embed)

        if not (use_abs_pos_emb and not attn_layers.has_pos_emb):
            self.pos_emb = always(0)
        elif scaled_sinu_pos_emb:
            self.pos_emb = ScaledSinusoidalEmbedding(emb_dim)
        else:
            self.pos_emb = AbsolutePositionalEmbedding(emb_dim, max_seq_len, l2norm_embed = l2norm_embed)

        self.emb_frac_gradient = emb_frac_gradient # fraction of the gradient that should go to the embedding, https://arxiv.org/abs/2105.13290

        self.post_emb_norm = nn.LayerNorm(emb_dim) if post_emb_norm else nn.Identity()
        self.emb_dropout = nn.Dropout(emb_dropout)

        self.project_emb = nn.Linear(emb_dim, dim) if emb_dim != dim else nn.Identity()
        self.attn_layers = attn_layers
        self.norm = nn.LayerNorm(dim)

        self.init_()

        logits_dim = default(logits_dim, num_tokens)
        self.to_logits = nn.Linear(dim, logits_dim) if not tie_embedding else lambda t: t @ self.token_emb.weight.t()

        # memory tokens (like [cls]) from Memory Transformers paper
        num_memory_tokens = default(num_memory_tokens, 0)
        self.num_memory_tokens = num_memory_tokens
        if num_memory_tokens > 0:
            self.memory_tokens = nn.Parameter(torch.randn(num_memory_tokens, dim))

    def init_(self):
        if self.l2norm_embed:
            nn.init.normal_(self.token_emb.emb.weight, std = 1e-5)
            if not isinstance(self.pos_emb, always):
                nn.init.normal_(self.pos_emb.emb.weight, std = 1e-5)
            return

        nn.init.kaiming_normal_(self.token_emb.emb.weight)

    def forward(
        self,
        x,
        return_embeddings = False,
        return_logits_and_embeddings = False,
        return_intermediates = False,
        mask = None,
        return_mems = False,
        return_attn = False,
        mems = None,
        pos = None,
        prepend_embeds = None,
        sum_embeds = None,
        **kwargs
    ):
        b, n, device, num_mem, emb_frac_gradient = *x.shape, x.device, self.num_memory_tokens, self.emb_frac_gradient
        return_hiddens = return_mems | return_attn

        # absolute positional embedding

        external_pos_emb = exists(pos) and pos.dtype != torch.long
        pos_emb = self.pos_emb(x, pos = pos) if not external_pos_emb else pos
        x = self.token_emb(x) + pos_emb

        # for summing embeddings passed externally - needs this for self-conditioning in non-autoregressive training

        if exists(sum_embeds):
            x = x + sum_embeds

        # post embedding norm, purportedly leads to greater stabilization

        x = self.post_emb_norm(x)

        # whether to append embeds, as in PaLI, for image embeddings

        if exists(prepend_embeds):
            prepend_seq, prepend_dim = prepend_embeds.shape[1:]
            assert prepend_dim == x.shape[-1], 'prepended embeddings need to have same dimensions as text model dimensions'

            x = torch.cat((prepend_embeds, x), dim = -2)

        # whether to reduce the gradient going to the embedding, from cogview paper, corroborated by GLM-130B model

        if emb_frac_gradient < 1:
            assert emb_frac_gradient > 0
            x = x * emb_frac_gradient + x.detach() * (1 - emb_frac_gradient)

        # embedding dropout

        x = self.emb_dropout(x)

        x = self.project_emb(x)

        if num_mem > 0:
            mem = repeat(self.memory_tokens, 'n d -> b n d', b = b)
            x = torch.cat((mem, x), dim = 1)

            # auto-handle masking after appending memory tokens
            if exists(mask):
                mask = pad_at_dim(mask, (num_mem, 0), dim = -1, value = True)

        if self.shift_mem_down and exists(mems):
            mems_l, mems_r = mems[:self.shift_mem_down], mems[self.shift_mem_down:]
            mems = [*mems_r, *mems_l]

        if return_hiddens:
            x, intermediates = self.attn_layers(x, mask = mask, mems = mems, return_hiddens = True, **kwargs)
        else:
            x = self.attn_layers(x, mask = mask, mems = mems, **kwargs)

        x = self.norm(x)

        mem, x = x[:, :num_mem], x[:, num_mem:]

        if return_logits_and_embeddings:
            out = (self.to_logits(x), x)
        elif return_embeddings:
            out = x
        else:
            out = self.to_logits(x)

        if return_intermediates:
            return out, intermediates

        if return_mems:
            hiddens = intermediates.hiddens
            new_mems = list(map(lambda pair: torch.cat(pair, dim = -2), zip(mems, hiddens))) if exists(mems) else hiddens
            new_mems = list(map(lambda t: t[..., -self.max_mem_len:, :].detach(), new_mems))
            return out, new_mems

        if return_attn:
            attn_maps = list(map(lambda t: t.post_softmax_attn, intermediates.attn_intermediates))
            return out, attn_maps

        return out

class ContinuousTransformerWrapper(nn.Module):
    def __init__(
        self,
        *,
        max_seq_len,
        attn_layers,
        dim_in = None,
        dim_out = None,
        emb_dim = None,
        post_emb_norm = False,
        emb_dropout = 0.,
        use_abs_pos_emb = True,
        scaled_sinu_pos_emb = False
    ):
        super().__init__()
        assert isinstance(attn_layers, AttentionLayers), 'attention layers must be one of Encoder or Decoder'

        dim = attn_layers.dim

        self.max_seq_len = max_seq_len

        if not (use_abs_pos_emb and not attn_layers.has_pos_emb):
            self.pos_emb = always(0)
        elif scaled_sinu_pos_emb:
            self.pos_emb = ScaledSinusoidalEmbedding(dim)
        else:
            self.pos_emb = AbsolutePositionalEmbedding(dim, max_seq_len)

        self.post_emb_norm = nn.LayerNorm(dim) if post_emb_norm else nn.Identity()
        self.emb_dropout = nn.Dropout(emb_dropout)

        self.project_in = nn.Linear(dim_in, dim) if exists(dim_in) else nn.Identity()

        self.attn_layers = attn_layers
        self.norm = nn.LayerNorm(dim)

        self.project_out = nn.Linear(dim, dim_out) if exists(dim_out) else nn.Identity()

    def forward(
        self,
        x,
        return_embeddings = False,
        return_intermediates = False,
        mask = None,
        return_attn = False,
        mems = None,
        pos = None,
        prepend_embeds = None,
        **kwargs
    ):
        x = self.project_in(x)
        x = x + self.pos_emb(x, pos = pos)

        x = self.post_emb_norm(x)

        # whether to append embeds, as in PaLI, for image embeddings

        if exists(prepend_embeds):
            _, prepend_dim = prepend_embeds.shape[1:]
            assert prepend_dim == x.shape[-1], 'prepended embeddings need to have same dimensions as model dimensions'

            x = torch.cat((prepend_embeds, x), dim = -2)

        x = self.emb_dropout(x)

        x, intermediates = self.attn_layers(x, mask = mask, mems = mems, return_hiddens = True, **kwargs)
        x = self.norm(x)

        out = self.project_out(x) if not return_embeddings else x

        if return_intermediates:
            return out, intermediates

        if return_attn:
            attn_maps = list(map(lambda t: t.post_softmax_attn, intermediates.attn_intermediates))
            return out, attn_maps

        return out

class XTransformer(nn.Module):
    def __init__(
        self,
        *,
        dim,
        tie_token_emb = False,
        ignore_index = -100,
        pad_value = 0,
        deepnorm = False,
        cross_attn_tokens_dropout = 0.,
        **kwargs
    ):
        super().__init__()
        enc_kwargs, kwargs = groupby_prefix_and_trim('enc_', kwargs)
        dec_kwargs, kwargs = groupby_prefix_and_trim('dec_', kwargs)

        assert 'dim' not in enc_kwargs and 'dim' not in dec_kwargs, 'dimension of either encoder or decoder must be set with `dim` keyword'
        enc_transformer_kwargs = pick_and_pop(['num_tokens', 'max_seq_len'], enc_kwargs)
        enc_transformer_kwargs['emb_dropout'] = enc_kwargs.pop('emb_dropout', 0)
        enc_transformer_kwargs['num_memory_tokens'] = enc_kwargs.pop('num_memory_tokens', None)

        dec_transformer_kwargs = pick_and_pop(['num_tokens', 'max_seq_len'], dec_kwargs)
        dec_transformer_kwargs['emb_dropout'] = dec_kwargs.pop('emb_dropout', 0)

        self.cross_attn_tokens_dropout = cross_attn_tokens_dropout  # how many tokens from the encoder to dropout when cross attending from decoder - seen in a couple papers, including Perceiver AR - this will also be very effective regularization when cross attending to very long memories

        if deepnorm:
            enc_kwargs['scale_residual'] = True
            dec_kwargs['scale_residual'] = True

            enc_depth = enc_kwargs['depth']
            dec_depth = dec_kwargs['depth']

            enc_kwargs['scale_residual_constant'] = 0.81 * ((enc_depth ** 4) * dec_depth) ** .0625
            dec_kwargs['scale_residual_constant'] = (3 * dec_depth) ** 0.25

        self.encoder = TransformerWrapper(
            **enc_transformer_kwargs,
            attn_layers = Encoder(dim = dim, **enc_kwargs)
        )

        self.decoder = TransformerWrapper(
            **dec_transformer_kwargs,
            attn_layers = Decoder(dim = dim, cross_attend = True, **dec_kwargs)
        )

        if deepnorm:
            deepnorm_init(self.encoder, 0.87 * ((enc_depth ** 4) * dec_depth) ** -0.0625)
            deepnorm_init(self.decoder, (12 * dec_depth) ** -0.25)

        if tie_token_emb:
            self.decoder.token_emb = self.encoder.token_emb

        self.decoder = AutoregressiveWrapper(self.decoder, ignore_index=ignore_index, pad_value=pad_value)

    @torch.no_grad()
    def generate(self, seq_in, seq_out_start, seq_len, mask = None, attn_mask = None, **kwargs):
        encodings = self.encoder(seq_in, mask = mask, attn_mask = attn_mask, return_embeddings = True)
        return self.decoder.generate(seq_out_start, seq_len, context = encodings, context_mask = mask, **kwargs)

    def forward(self, src, tgt, mask = None, attn_mask = None, src_prepend_embeds = None):

        if exists(src_prepend_embeds) and exists(mask):
            mask = pad_at_dim(mask, (src_prepend_embeds.shape[-2], 0), dim = -1, value = True)

        enc = self.encoder(src, mask = mask, attn_mask = attn_mask, prepend_embeds = src_prepend_embeds, return_embeddings = True)

        if self.training and self.cross_attn_tokens_dropout > 0:
            enc, mask = dropout_seq(enc, mask, self.cross_attn_tokens_dropout)

        out = self.decoder(tgt, context = enc, context_mask = mask)
        return out
