code/policy_models/module/transformers/position_embeddings.py

from matplotlib.pyplot import cla
import torch
import torch.nn as nn
import torch.nn.functional as F
import einops

from math import pi, log

import torch
from torch import nn, einsum

from einops import rearrange, repeat


from torch.distributions import Categorical

from typing import Optional, Tuple

import logging
import math 
from typing import Optional

import torch
import torch.nn as nn
from torch.nn import functional as F
from omegaconf import DictConfig
import einops

# code imported from https://github.com/lucidrains/x-transformers
# Rot Embedding copied from https://github.com/lucidrains/rotary-embedding-torch/tree/main
# helper functions

def exists(val):
    return val is not None

def broadcat(tensors, dim = -1):
    num_tensors = len(tensors)
    shape_lens = set(list(map(lambda t: len(t.shape), tensors)))
    assert len(shape_lens) == 1, 'tensors must all have the same number of dimensions'
    shape_len = list(shape_lens)[0]

    dim = (dim + shape_len) if dim < 0 else dim
    dims = list(zip(*map(lambda t: list(t.shape), tensors)))

    expandable_dims = [(i, val) for i, val in enumerate(dims) if i != dim]
    assert all([*map(lambda t: len(set(t[1])) <= 2, expandable_dims)]), 'invalid dimensions for broadcastable concatentation'
    max_dims = list(map(lambda t: (t[0], max(t[1])), expandable_dims))
    expanded_dims = list(map(lambda t: (t[0], (t[1],) * num_tensors), max_dims))
    expanded_dims.insert(dim, (dim, dims[dim]))
    expandable_shapes = list(zip(*map(lambda t: t[1], expanded_dims)))
    tensors = list(map(lambda t: t[0].expand(*t[1]), zip(tensors, expandable_shapes)))
    return torch.cat(tensors, dim = dim)

# rotary embedding helper functions

def rotate_half(x):
    x = rearrange(x, '... (d r) -> ... d r', r = 2)
    x1, x2 = x.unbind(dim = -1)
    x = torch.stack((-x2, x1), dim = -1)
    return rearrange(x, '... d r -> ... (d r)')

def apply_rotary_emb(freqs, t, start_index = 0, scale = 1.):
    freqs = freqs.to(t)
    rot_dim = freqs.shape[-1]
    end_index = start_index + rot_dim
    assert rot_dim <= t.shape[-1], f'feature dimension {t.shape[-1]} is not of sufficient size to rotate in all the positions {rot_dim}'
    t_left, t, t_right = t[..., :start_index], t[..., start_index:end_index], t[..., end_index:]
    t = (t * freqs.cos() * scale) + (rotate_half(t) * freqs.sin() * scale)
    return torch.cat((t_left, t, t_right), dim = -1)

# learned rotation helpers

def apply_learned_rotations(rotations, t, start_index = 0, freq_ranges = None):
    if exists(freq_ranges):
        rotations = einsum('..., f -> ... f', rotations, freq_ranges)
        rotations = rearrange(rotations, '... r f -> ... (r f)')

    rotations = repeat(rotations, '... n -> ... (n r)', r = 2)
    return apply_rotary_emb(rotations, t, start_index = start_index)

# classes

class RotaryEmbedding(nn.Module):
    def __init__(
        self,
        dim,
        custom_freqs = None,
        freqs_for = 'lang',
        theta = 10000,
        max_freq = 10,
        num_freqs = 1,
        learned_freq = False,
        use_xpos = False,
        xpos_scale_base = 512,
        interpolate_factor = 1.,
        theta_rescale_factor = 1.
    ):
        super().__init__()
        # proposed by reddit user bloc97, to rescale rotary embeddings to longer sequence length without fine-tuning
        # has some connection to NTK literature
        # https://www.reddit.com/r/LocalLLaMA/comments/14lz7j5/ntkaware_scaled_rope_allows_llama_models_to_have/
        theta *= theta_rescale_factor ** (dim / (dim - 2))

        if exists(custom_freqs):
            freqs = custom_freqs
        elif freqs_for == 'lang':
            freqs = 1. / (theta ** (torch.arange(0, dim, 2)[:(dim // 2)].float() / dim))
        elif freqs_for == 'pixel':
            freqs = torch.linspace(1., max_freq / 2, dim // 2) * pi
        elif freqs_for == 'constant':
            freqs = torch.ones(num_freqs).float()
        else:
            raise ValueError(f'unknown modality {freqs_for}')

        self.cache = dict()
        self.cache_scale = dict()
        self.freqs = nn.Parameter(freqs, requires_grad = learned_freq)

        # interpolation factors

        assert interpolate_factor >= 1.
        self.interpolate_factor = interpolate_factor

        # xpos

        self.use_xpos = use_xpos
        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 = xpos_scale_base
        self.register_buffer('scale', scale)

    def get_seq_pos(self, seq_len, device, dtype, offset = 0):
        return (torch.arange(seq_len, device = device, dtype = dtype) + offset) / self.interpolate_factor

    def rotate_queries_or_keys(self, t, seq_dim = -2, offset = 0):
        assert not self.use_xpos, 'you must use `.rotate_queries_and_keys` method instead and pass in both queries and keys, for length extrapolatable rotary embeddings'
        device, dtype, seq_len = t.device, t.dtype, t.shape[seq_dim]
        freqs = self.forward(lambda: self.get_seq_pos(seq_len, device = device, dtype = dtype, offset = offset), cache_key = f'freqs:{seq_len}|offset:{offset}')
        return apply_rotary_emb(freqs, t)

    def rotate_queries_and_keys(self, q, k, seq_dim = -2):
        assert self.use_xpos
        device, dtype, seq_len = q.device, q.dtype, q.shape[seq_dim]
        seq = self.get_seq_pos(seq_len, dtype = dtype, device = device)
        freqs = self.forward(lambda: seq, cache_key = f'freqs:{seq_len}')
        scale = self.get_scale(lambda: seq, cache_key = f'scale:{seq_len}').to(dtype)
        rotated_q = apply_rotary_emb(freqs, q, scale = scale)
        rotated_k = apply_rotary_emb(freqs, k, scale = scale ** -1)
        return rotated_q, rotated_k

    def get_scale(self, t, cache_key = None):
        assert self.use_xpos

        if exists(cache_key) and cache_key in self.cache:
            return self.cache[cache_key]

        if callable(t):
            t = t()

        scale = 1.
        if self.use_xpos:
            power = (t - len(t) // 2) / self.scale_base
            scale = self.scale ** rearrange(power, 'n -> n 1')
            scale = torch.cat((scale, scale), dim = -1)

        if exists(cache_key):
            self.cache[cache_key] = scale

        return scale

    def forward(self, t, cache_key = None):
        if exists(cache_key) and cache_key in self.cache:
            return self.cache[cache_key]

        if callable(t):
            t = t()

        freqs = self.freqs

        freqs = torch.einsum('..., f -> ... f', t.type(freqs.dtype), freqs)
        freqs = repeat(freqs, '... n -> ... (n r)', r = 2)

        if exists(cache_key):
            self.cache[cache_key] = freqs

        return freqs
# norms

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

    @property
    def device(self):
        return next(self.parameters()).device

    def forward(self, i, j):
        device = self.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 = einops.rearrange(values, 'i j h -> h i j')
        return 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 None,
            nn.SiLU()
        ))

        for _ in range(depth - 1):
            self.mlp.append(nn.Sequential(
                nn.Linear(dim, dim),
                nn.LayerNorm(dim) if norm else None,
                nn.SiLU()
            ))

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