import functools
import math
import torch
from torch import nn, einsum
import torch.nn.functional as F
from functools import partial
from inspect import isfunction
from collections import namedtuple

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

from entmax import entmax15
from torch.utils.checkpoint import checkpoint

from x_transformers.autoregressive_wrapper import AutoregressiveWrapper

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


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


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


def l2norm(t):
    return F.normalize(t, p=2, dim=-1)


# 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


# activations

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


# positional embeddings

class AbsolutePositionalEmbedding(nn.Module):
    def __init__(self, dim, max_seq_len):
        super().__init__()
        self.scale = dim ** -0.5
        self.emb = nn.Embedding(max_seq_len, dim)

    def forward(self, x):
        n = torch.arange(x.shape[1], device=x.device)
        pos_emb = self.emb(n)
        pos_emb = rearrange(pos_emb, 'n d -> () n d')
        return pos_emb * self.scale


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

    def forward(self, x, seq_dim=1, offset=0):
        t = torch.arange(x.shape[seq_dim], device=x.device).type_as(self.inv_freq) + offset
        sinusoid_inp = torch.einsum('i , j -> i j', t, self.inv_freq)
        emb = torch.cat((sinusoid_inp.sin(), sinusoid_inp.cos()), dim=-1)
        return rearrange(emb, 'n d -> () n d')


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(i, 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 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 () ()')
        self.register_buffer('slopes', slopes, persistent=False)
        self.register_buffer('bias', None, persistent=False)

    @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[..., :j]

        bias = torch.arange(j, device=device)
        bias = rearrange(bias, 'j -> () () () j')
        bias = bias * self.slopes

        num_heads_unalibied = h - bias.shape[1]
        bias = F.pad(bias, (0, 0, 0, 0, 0, num_heads_unalibied))

        self.register_buffer('bias', bias, persistent=False)
        return qk_dots + self.bias


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

        self.bidirectional = bidirectional
        if self.bidirectional:
            self.learned_logslopes_future = nn.Parameter(los_slopes)

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

        def get_slopes(param):
            return F.pad(param.exp(), (0, 0, 0, 0, 0, h - param.shape[1]))

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

        if self.bidirectional:
            past_slopes = get_slopes(self.learned_logslopes)
            future_slopes = get_slopes(self.learned_logslopes_future)
            bias = torch.tril(bias * past_slopes) + torch.triu(bias * future_slopes)
        else:
            slopes = get_slopes(self.learned_logslopes)
            bias = bias * slopes

        return qk_dots + bias


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

    def forward(self, max_seq_len, device):
        t = torch.arange(max_seq_len, device=device).type_as(self.inv_freq)
        freqs = torch.einsum('i , j -> i j', t, self.inv_freq)
        emb = torch.cat((freqs, freqs), dim=-1)
        return rearrange(emb, 'n d -> () () n d')


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


# 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 Rezero(nn.Module):
    def __init__(self, fn):
        super().__init__()
        self.fn = fn
        self.g = nn.Parameter(torch.zeros(1))

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

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

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


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

    def forward(self, x):
        norm = torch.norm(x, dim=-1, keepdim=True) * self.scale
        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


class RMSScaleShiftNorm(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))
        self.scale_shift_process = nn.Linear(dim * 2, dim * 2)

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

        ss_emb = self.scale_shift_process(norm_scale_shift_inp)
        scale, shift = torch.chunk(ss_emb, 2, dim=1)
        h = norm * (1 + scale.unsqueeze(1)) + shift.unsqueeze(1)
        return h


# residual and residual gates

class Residual(nn.Module):
    def __init__(self, dim, scale_residual=False):
        super().__init__()
        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

        return x + residual


class GRUGating(nn.Module):
    def __init__(self, dim, scale_residual=False):
        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

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

    return F.pad(t, (0, 0, amount, -amount), 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,
            relu_squared=False,
            post_act_ln=False,
            dropout=0.,
            zero_init_output=False
    ):
        super().__init__()
        inner_dim = int(dim * mult)
        dim_out = default(dim_out, dim)
        activation = ReluSquared() if relu_squared else nn.GELU()

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

        self.net = nn.Sequential(
            project_in,
            nn.LayerNorm(inner_dim) if post_act_ln else nn.Identity(),
            nn.Dropout(dropout),
            nn.Linear(inner_dim, dim_out)
        )

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

    def forward(self, x):
        return self.net(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,
            collab_heads=False,
            collab_compression=.3,
            sparse_topk=None,
            use_entmax15=False,
            num_mem_kv=0,
            dropout=0.,
            on_attn=False,
            gate_values=False,
            zero_init_output=False,
            max_attend_past=None,
            qk_norm=False,
            scale_init_value=None,
            rel_pos_bias=False,
            rel_pos_num_buckets=32,
            rel_pos_max_distance=128,
    ):
        super().__init__()
        self.scale = dim_head ** -0.5

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

        qk_dim = v_dim = dim_head * heads

        # collaborative heads
        self.collab_heads = collab_heads
        if self.collab_heads:
            qk_dim = int(collab_compression * qk_dim)
            self.collab_mixing = nn.Parameter(torch.randn(heads, qk_dim))

        self.to_q = nn.Linear(dim, qk_dim, bias=False)
        self.to_k = nn.Linear(dim, qk_dim, bias=False)
        self.to_v = nn.Linear(dim, v_dim, bias=False)

        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, v_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
        if qk_norm:
            scale_init_value = default(scale_init_value,
                                       -3)  # if not provided, initialize as though it were sequence length of 1024
            self.scale = nn.Parameter(torch.ones(1, heads, 1, 1) * scale_init_value)

        # talking heads
        self.talking_heads = talking_heads
        if talking_heads:
            self.pre_softmax_proj = nn.Parameter(torch.randn(heads, heads))
            self.post_softmax_proj = nn.Parameter(torch.randn(heads, heads))

        # 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

        # entmax
        self.attn_fn = entmax15 if use_entmax15 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(v_dim, dim * 2), nn.GLU()) if on_attn else nn.Linear(v_dim, dim)

        self.rel_pos_bias = rel_pos_bias
        if rel_pos_bias:
            assert rel_pos_num_buckets <= rel_pos_max_distance, 'number of relative position buckets must be less than the relative position max distance'
            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)

        # 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,
            sinusoidal_emb=None,
            rotary_pos_emb=None,
            prev_attn=None,
            mem=None
    ):
        b, n, _, h, talking_heads, collab_heads, head_scale, scale, device, has_context = *x.shape, self.heads, self.talking_heads, self.collab_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

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

        if exists(sinusoidal_emb):
            # in shortformer, the query would start at a position offset depending on the past cached memory
            offset = k_input.shape[-2] - q_input.shape[-2]
            q_input = q_input + sinusoidal_emb(q_input, offset=offset)
            k_input = k_input + sinusoidal_emb(k_input)

        q = self.to_q(q_input)
        k = self.to_k(k_input)
        v = self.to_v(v_input)

        if not collab_heads:
            q, k, v = map(lambda t: rearrange(t, 'b n (h d) -> b h n d', h=h), (q, k, v))
        else:
            q = einsum('b i d, h d -> b h i d', q, self.collab_mixing)
            k = rearrange(k, 'b n d -> b () n d')
            v = rearrange(v, 'b n (h d) -> b h n d', h=h)

        if exists(rotary_pos_emb) and not has_context:
            l = rotary_pos_emb.shape[-1]
            (ql, qr), (kl, kr), (vl, vr) = map(lambda t: (t[..., :l], t[..., l:]), (q, k, v))
            ql, kl, vl = map(lambda t: apply_rotary_pos_emb(t, rotary_pos_emb), (ql, kl, vl))
            q, k, v = map(lambda t: torch.cat(t, dim=-1), ((ql, qr), (kl, kr), (vl, vr)))

        input_mask = None
        if any(map(exists, (mask, context_mask))):
            q_mask = default(mask, lambda: torch.ones((b, n), device=device).bool())
            k_mask = q_mask if not exists(context) else context_mask
            k_mask = default(k_mask, lambda: torch.ones((b, k.shape[-2]), device=device).bool())
            q_mask = rearrange(q_mask, 'b i -> b () i ()')
            k_mask = rearrange(k_mask, 'b j -> b () () j')
            input_mask = q_mask * k_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 = F.pad(input_mask, (self.num_mem_kv, 0), value=True)

        if collab_heads:
            k = k.expand(-1, h, -1, -1)

        if self.qk_norm:
            q, k = map(l2norm, (q, k))
            scale = 1 / (self.scale.exp().clamp(min=1e-2))

        dots = einsum('b h i d, b h j d -> 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 = einsum('b h i j, h k -> b k i j', dots, self.pre_softmax_proj).contiguous()

        if self.rel_pos_bias:
            dots = self.rel_pos(dots)

        if exists(input_mask):
            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 -> () () i j')
            elif attn_mask.ndim == 3:
                attn_mask = rearrange(attn_mask, 'h i j -> () h i j')
            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 -> () () i ()') - rearrange(range_k, 'j -> () () () j')
            mask = dist > self.max_attend_past
            dots.masked_fill_(mask, mask_value)
            del mask

        if self.causal:
            i, j = dots.shape[-2:]
            r = torch.arange(i, device=device)
            mask = rearrange(r, 'i -> () () i ()') < rearrange(r, 'j -> () () () j')
            mask = F.pad(mask, (j - i, 0), value=False)
            dots.masked_fill_(mask, mask_value)
            del mask

        if exists(self.sparse_topk) and self.sparse_topk < dots.shape[-1]:
            top, _ = dots.topk(self.sparse_topk, dim=-1)
            vk = top[..., -1].unsqueeze(-1).expand_as(dots)
            mask = dots < vk
            dots.masked_fill_(mask, mask_value)
            del mask

        attn = self.attn_fn(dots, dim=-1)
        post_softmax_attn = attn.clone()

        attn = self.dropout(attn)

        if talking_heads:
            attn = einsum('b h i j, h k -> b k i j', attn, self.post_softmax_proj).contiguous()

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

        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
        )

        return self.to_out(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_rms_scaleshift_norm=False,
            use_rmsnorm=False,
            use_rezero=False,
            alibi_pos_bias=False,
            alibi_num_heads=None,
            alibi_learned=False,
            position_infused_attn=False,
            rotary_pos_emb=False,
            rotary_emb_dim=None,
            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,
            shift_tokens=0,
            sandwich_norm=False,
            use_qk_norm_attn=False,
            qk_norm_attn_seq_len=None,
            zero_init_branch_output=False,
            **kwargs
    ):
        super().__init__()
        ff_kwargs, kwargs = groupby_prefix_and_trim('ff_', kwargs)
        attn_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([])

        rel_pos_bias = 'rel_pos_bias' in attn_kwargs
        self.has_pos_emb = position_infused_attn or rel_pos_bias or rotary_pos_emb
        self.pia_pos_emb = FixedPositionalEmbedding(dim) if position_infused_attn else None

        rotary_emb_dim = max(default(rotary_emb_dim, dim_head // 2), 32)
        self.rotary_pos_emb = RotaryEmbedding(rotary_emb_dim) 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'

        if 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 or not causal else AlibiPositionalBias
            self.rel_pos = alibi_pos_klass(heads=alibi_num_heads, bidirectional=not causal)
        else:
            self.rel_pos = None

        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_class = RMSScaleShiftNorm if use_rms_scaleshift_norm else norm_class
        norm_fn = partial(norm_class, dim)

        norm_fn = nn.Identity if use_rezero else norm_fn
        branch_fn = Rezero if use_rezero else None

        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

        # qk normalization

        if use_qk_norm_attn:
            attn_scale_init_value = -math.log(math.log2(qk_norm_attn_seq_len ** 2 - qk_norm_attn_seq_len)) if exists(
                qk_norm_attn_seq_len) else None
            attn_kwargs = {**attn_kwargs, 'qk_norm': True, 'scale_init_value': attn_scale_init_value}

        # 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)))

        # 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)

            if exists(branch_fn):
                layer = branch_fn(layer)

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

            layer_uses_qk_norm = use_qk_norm_attn and layer_type in ('a', 'c')

            pre_branch_norm = norm_fn() if pre_norm and not layer_uses_qk_norm else None
            post_branch_norm = norm_fn() if sandwich_norm or layer_uses_qk_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
            ]))

    def forward(
            self,
            x,
            context=None,
            full_context=None,  # for passing a list of hidden states from an encoder
            mask=None,
            context_mask=None,
            attn_mask=None,
            mems=None,
            return_hiddens=False,
            norm_scale_shift_inp=None,
    ):

        assert not (self.cross_attend ^ (exists(context) or exists(
            full_context))), 'context must be passed in if cross_attend is set to True'
        assert context is None or full_context is None, 'only one of full_context or context can be provided'

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

        mems = mems.copy() if exists(mems) else [None] * self.num_attn_layers
        norm_args = {}
        if exists(norm_scale_shift_inp):
            norm_args['norm_scale_shift_inp'] = norm_scale_shift_inp

        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)

        cross_attn_count = 0
        for ind, (layer_type, (norm, block, residual_fn)) in enumerate(zip(self.layer_types, self.layers)):
            if layer_type == 'a':
                layer_mem = mems.pop(0) if mems else None

            residual = x

            pre_branch_norm, post_branch_norm, post_main_norm = norm

            if exists(pre_branch_norm):
                x = pre_branch_norm(x, **norm_args)

            if layer_type == 'a':
                out, inter = checkpoint(block, x, None, mask, None, attn_mask, self.pia_pos_emb, rotary_pos_emb,
                                        prev_attn, layer_mem)
            elif layer_type == 'c':
                if exists(full_context):
                    out, inter = checkpoint(block, x, full_context[cross_attn_count], mask, context_mask, None, None,
                                            None, prev_attn)
                else:
                    out, inter = checkpoint(block, x, context, mask, context_mask, None, None, None, prev_attn)
            elif layer_type == 'f':
                out = checkpoint(block, x)

            if exists(post_branch_norm):
                out = post_branch_norm(out, **norm_args)

            x = residual_fn(out, residual)

            if layer_type in ('a', 'c'):
                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, **norm_args)

            if layer_type == 'c':
                cross_attn_count += 1

            if layer_type == 'f':
                hiddens.append(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,
            num_classes=None,
            dropout=0.,
            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 = 3 * 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.cls_token = nn.Parameter(torch.randn(1, 1, dim))
        self.dropout = nn.Dropout(emb_dropout)

        self.attn_layers = attn_layers
        self.norm = nn.LayerNorm(dim)
        self.mlp_head = FeedForward(dim, dim_out=num_classes, dropout=dropout) if exists(num_classes) else None

    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)
        b, n, _ = x.shape

        cls_tokens = repeat(self.cls_token, '() n d -> b n d', b=b)
        x = torch.cat((cls_tokens, x), dim=1)
        x = x + self.pos_embedding[:, :(n + 1)]
        x = self.dropout(x)

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

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

        return self.mlp_head(x[:, 0])


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.,
            num_memory_tokens=None,
            tie_embedding=False,
            use_pos_emb=True
    ):
        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.max_seq_len = max_seq_len
        self.max_mem_len = max_mem_len
        self.shift_mem_down = shift_mem_down

        self.token_emb = nn.Embedding(num_tokens, emb_dim)
        self.pos_emb = AbsolutePositionalEmbedding(emb_dim, max_seq_len) if (
                    use_pos_emb and not attn_layers.has_pos_emb) else always(0)
        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_()

        self.to_logits = nn.Linear(dim, num_tokens) 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):
        nn.init.kaiming_normal_(self.token_emb.weight)

    def forward(
            self,
            x,
            return_embeddings=False,
            mask=None,
            return_hiddens=False,
            return_attn=False,
            mems=None,
            **kwargs
    ):
        b, n, device, num_mem = *x.shape, x.device, self.num_memory_tokens
        x = self.token_emb(x)
        x = x + self.pos_emb(x)
        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 = F.pad(mask, (num_mem, 0), 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]

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

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

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

        if return_hiddens:
            hiddens = intermediates.hiddens
            return out, hiddens

        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,
            emb_dropout=0.,
            use_pos_emb=True
    ):
        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

        self.pos_emb = AbsolutePositionalEmbedding(dim, max_seq_len) if (
                    use_pos_emb and not attn_layers.has_pos_emb) else always(0)
        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,
            mask=None,
            return_attn=False,
            mems=None,
            **kwargs
    ):
        b, n, _, device = *x.shape, x.device

        x = self.project_in(x)
        x = x + self.pos_emb(x)
        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_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,
            **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)
        enc_transformer_kwargs['use_pos_emb'] = enc_kwargs.pop('use_pos_emb', True)

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

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

        self.decoder = AutoregressiveWrapper(self.decoder)

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

    def forward(self, src, tgt, src_mask=None, tgt_mask=None, src_attn_mask=None):
        enc = self.encoder(src, mask=src_mask, attn_mask=src_attn_mask, return_embeddings=True)
        out = self.decoder(tgt, context=enc, mask=tgt_mask, context_mask=src_mask)
        return out