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一.引言
二.RoPE 理论
1.RoPE 矩阵形式
2.RoPE 图例形式
3.RoPE 实践分析
三.RoPE 代码分析
1.源码获取
2.源码分析
3.rotary_emb
3.1 __init__
3.2 forward
4.apply_rotary_pos_emb
4.1 rotate_half
4.2 apply_rotary_pos_emb
四.RoPE 代码实现
1.Q/K/V …
目录
一.引言
二.RoPE 理论
1.RoPE 矩阵形式
2.RoPE 图例形式
3.RoPE 实践分析
三.RoPE 代码分析
1.源码获取
2.源码分析
3.rotary_emb
3.1 __init__
3.2 forward
4.apply_rotary_pos_emb
4.1 rotate_half
4.2 apply_rotary_pos_emb
四.RoPE 代码实现
1.Q/K/V States
2.rotary_emd
3.apply_rotray_pos_emd
五.总结 一.引言
LLM - 通俗理解位置编码与 RoPE 一文我们介绍了 RoPE 的理论基础和实现思路下面我们再简单回顾下 RoPE 的实现思路并结合最新 LLM 模型的源代码看下 RoPE 具体是如何实现的。 二.RoPE 理论
1.RoPE 矩阵形式
结合内积的线性叠加性我们可以将 2 维的旋转矩阵 R 推广到多维。相当于在原始 token 的向量上两两截断通过 R 实现旋转操作最后拼接为 R 维向量。犹如我们常用的向量维度都是偶数且是 2 的倍数所以这里针对偶数向量 由于上述 R 矩阵的稀疏性使用矩阵乘法会造成算力的严重浪费所以推荐使用下述线性方式计算 RoPE: 其中 ⊗ 是逐位对应相乘即 Numpy、Tensorflow 等计算框架中的∗运算。从这个实现也可以看到RoPE 可以视为是乘性位置编码的变体将多个二维旋转的叠加 2.RoPE 图例形式
上面将二维旋转矩阵 R 推广到多维旋转矩阵并基于其矩阵特点将稀疏矩阵计算简化至对位相乘通过下图可以更清晰地理解计算过程 因为上面的 是两两表示的所以实际计算中也是将 token 词向量两两分成这也解释了为什么公式里到处是 d/2。其添加位置信息步骤如下
- 遍历每个位置的 token位置为 m范围为 Query / Key 的长度
- 获取对应 token Embeddingdim d
- [2i: 2i1] for i in range(0, d/2) 两两获取向量根据公式计算 θ 并通过 R 进行旋转变换
- 得到新的 Position Encoded Query / Key
- Attention 操作并自动引入 (m-n) 的相对距离信息
从右上角的图中也可以更直观的看到向量旋转的过程。 3.RoPE 实践分析 观察上面的图我们可以看到 RoPE 计算主要分两部分
◆ 旋转角度 θ 这里 theta 完全由 Q、K、V 的向量长度 d 决定即 dim。 ◆ 位置 Position m
位置 m 对应我们的 query 长度实际代码中由 max_position_embeddings 参数决定可以理解为模型支持的最长 query 的长度因此 max 有了m 的范围也就有了。 ◆ Freq 频次矩阵
结合上面的信息针对一个固定了最长 query 长度 m 和向量维度 d 的 LLM我们可以提前将其对应的旋转变换矩阵构造完成 θ 有的地方写 [1, d/2]有的地方范围写 [0, d/2-1]其次位置 Position 有的地方写 [0, m-1]有的写 [1, m]这里写成从 1 开头为了方便大家理解实际代码中会从 0 开始。结合这个 Rd 的变换矩阵分别执行 cos 和 sin便可以得到我们计算所需的全位置全维度的变换矩阵。下面看下代码如何实现。 三.RoPE 代码分析
1.源码获取
开始分析前我们首先需要搞清楚源代码在哪然后再开始分析。InternLM-20B 是最近最新推出的新版大模型我们找最新模型的源码看下对应 RoPE Embedding 部分怎么执行。
◆ Hugging Face
在搜索框搜索对应模型名称。 ◆ InternLM-20B
点击模型的 Files and versions 选项对应的 modeling_xxx.py 即为实现源码。 ◆ modeling_internlm.py
一共 999 行粘过来省的大家再去 HF 上翻了。
# codingutf-8
# Copyright 2022 EleutherAI and the HuggingFace Inc. team. All rights reserved.
#
# This code is based on EleutherAIs GPT-NeoX library and the GPT-NeoX
# and OPT implementations in this library. It has been modified from its
# original forms to accommodate minor architectural differences compared
# to GPT-NeoX and OPT used by the Meta AI team that trained the model.
#
# Licensed under the Apache License, Version 2.0 (the License);
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an AS IS BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.PyTorch InternLM model.
import math
from typing import List, Optional, Tuple, Union
import threading, queueimport torch
import torch.utils.checkpoint
from torch import nn
from torch.nn import BCEWithLogitsLoss, CrossEntropyLoss, MSELossfrom transformers.activations import ACT2FN
from transformers.modeling_outputs import BaseModelOutputWithPast, CausalLMOutputWithPast, SequenceClassifierOutputWithPast
from transformers.modeling_utils import PreTrainedModel
from transformers.generation.streamers import BaseStreamer
from transformers.utils import add_start_docstrings, add_start_docstrings_to_model_forward, logging, replace_return_docstrings
from .configuration_internlm import InternLMConfiglogger logging.get_logger(__name__)_CONFIG_FOR_DOC InternLMConfig# TODO: https://bitddd.blog.csdn.net/article/details/133174206
# Copied from transformers.models.bart.modeling_bart._make_causal_mask
def _make_causal_mask(input_ids_shape: torch.Size, dtype: torch.dtype, device: torch.device, past_key_values_length: int 0
):Make causal mask used for bi-directional self-attention.bsz, tgt_len input_ids_shapemask torch.full((tgt_len, tgt_len), torch.tensor(torch.finfo(dtype).min, devicedevice), devicedevice)mask_cond torch.arange(mask.size(-1), devicedevice)mask.masked_fill_(mask_cond (mask_cond 1).view(mask.size(-1), 1), 0)mask mask.to(dtype)if past_key_values_length 0:mask torch.cat([torch.zeros(tgt_len, past_key_values_length, dtypedtype, devicedevice), mask], dim-1)return mask[None, None, :, :].expand(bsz, 1, tgt_len, tgt_len past_key_values_length)# Copied from transformers.models.bart.modeling_bart._expand_mask
def _expand_mask(mask: torch.Tensor, dtype: torch.dtype, tgt_len: Optional[int] None):Expands attention_mask from [bsz, seq_len] to [bsz, 1, tgt_seq_len, src_seq_len].bsz, src_len mask.size()tgt_len tgt_len if tgt_len is not None else src_lenexpanded_mask mask[:, None, None, :].expand(bsz, 1, tgt_len, src_len).to(dtype)inverted_mask 1.0 - expanded_maskreturn inverted_mask.masked_fill(inverted_mask.to(torch.bool), torch.finfo(dtype).min)class InternLMRMSNorm(nn.Module):def __init__(self, hidden_size, eps1e-6):InternLMRMSNorm is equivalent to T5LayerNormsuper().__init__()self.weight nn.Parameter(torch.ones(hidden_size))self.variance_epsilon epsdef forward(self, hidden_states):variance hidden_states.to(torch.float32).pow(2).mean(-1, keepdimTrue)hidden_states hidden_states * torch.rsqrt(variance self.variance_epsilon)# convert into half-precision if necessaryif self.weight.dtype in [torch.float16, torch.bfloat16]:hidden_states hidden_states.to(self.weight.dtype)return self.weight * hidden_statesclass InternLMRotaryEmbedding(torch.nn.Module):def __init__(self, dim, max_position_embeddings2048, base10000, deviceNone):super().__init__()inv_freq 1.0 / (base ** (torch.arange(0, dim, 2).float().to(device) / dim))self.register_buffer(inv_freq, inv_freq, persistentFalse)# Build here to make torch.jit.trace work.self.max_seq_len_cached max_position_embeddingst torch.arange(self.max_seq_len_cached, deviceself.inv_freq.device, dtypeself.inv_freq.dtype)freqs torch.einsum(i,j-ij, t, self.inv_freq)# Different from paper, but it uses a different permutation in order to obtain the same calculationemb torch.cat((freqs, freqs), dim-1)self.register_buffer(cos_cached, emb.cos()[None, None, :, :], persistentFalse)self.register_buffer(sin_cached, emb.sin()[None, None, :, :], persistentFalse)def forward(self, x, seq_lenNone):# x: [bs, num_attention_heads, seq_len, head_size]# This if block is unlikely to be run after we build sin/cos in __init__. Keep the logic here just in case.if seq_len self.max_seq_len_cached:self.max_seq_len_cached seq_lent torch.arange(self.max_seq_len_cached, devicex.device, dtypeself.inv_freq.dtype)freqs torch.einsum(i,j-ij, t, self.inv_freq)# Different from paper, but it uses a different permutation in order to obtain the same calculationemb torch.cat((freqs, freqs), dim-1).to(x.device)self.register_buffer(cos_cached, emb.cos()[None, None, :, :], persistentFalse)self.register_buffer(sin_cached, emb.sin()[None, None, :, :], persistentFalse)return (self.cos_cached[:, :, :seq_len, ...].to(dtypex.dtype),self.sin_cached[:, :, :seq_len, ...].to(dtypex.dtype),)def rotate_half(x):Rotates half the hidden dims of the input.x1 x[..., : x.shape[-1] // 2]x2 x[..., x.shape[-1] // 2 :]return torch.cat((-x2, x1), dim-1)def apply_rotary_pos_emb(q, k, cos, sin, position_ids):# The first two dimensions of cos and sin are always 1, so we can squeeze them.cos cos.squeeze(1).squeeze(0) # [seq_len, dim]sin sin.squeeze(1).squeeze(0) # [seq_len, dim]cos cos[position_ids].unsqueeze(1) # [bs, 1, seq_len, dim]sin sin[position_ids].unsqueeze(1) # [bs, 1, seq_len, dim]q_embed (q * cos) (rotate_half(q) * sin)k_embed (k * cos) (rotate_half(k) * sin)return q_embed, k_embedclass InternLMMLP(nn.Module):def __init__(self,hidden_size: int,intermediate_size: int,hidden_act: str,):super().__init__()self.gate_proj nn.Linear(hidden_size, intermediate_size, biasFalse)self.down_proj nn.Linear(intermediate_size, hidden_size, biasFalse)self.up_proj nn.Linear(hidden_size, intermediate_size, biasFalse)self.act_fn ACT2FN[hidden_act]def forward(self, x):return self.down_proj(self.act_fn(self.gate_proj(x)) * self.up_proj(x))class InternLMAttention(nn.Module):Multi-headed attention from Attention Is All You Need paperdef __init__(self, config: InternLMConfig):super().__init__()self.config configself.hidden_size config.hidden_sizeself.num_heads config.num_attention_headsself.head_dim self.hidden_size // self.num_headsself.max_position_embeddings config.max_position_embeddingsif (self.head_dim * self.num_heads) ! self.hidden_size:raise ValueError(fhidden_size must be divisible by num_heads (got hidden_size: {self.hidden_size}f and num_heads: {self.num_heads}).)self.q_proj nn.Linear(self.hidden_size, self.num_heads * self.head_dim, biasconfig.bias)self.k_proj nn.Linear(self.hidden_size, self.num_heads * self.head_dim, biasconfig.bias)self.v_proj nn.Linear(self.hidden_size, self.num_heads * self.head_dim, biasconfig.bias)self.o_proj nn.Linear(self.num_heads * self.head_dim, self.hidden_size, biasconfig.bias)self.rotary_emb InternLMRotaryEmbedding(self.head_dim, max_position_embeddingsself.max_position_embeddings)def _shape(self, tensor: torch.Tensor, seq_len: int, bsz: int):return tensor.view(bsz, seq_len, self.num_heads, self.head_dim).transpose(1, 2).contiguous()def forward(self,hidden_states: torch.Tensor,attention_mask: Optional[torch.Tensor] None,position_ids: Optional[torch.LongTensor] None,past_key_value: Optional[Tuple[torch.Tensor]] None,output_attentions: bool False,use_cache: bool False,) - Tuple[torch.Tensor, Optional[torch.Tensor], Optional[Tuple[torch.Tensor]]]:bsz, q_len, _ hidden_states.size()query_states self.q_proj(hidden_states).view(bsz, q_len, self.num_heads, self.head_dim).transpose(1, 2)key_states self.k_proj(hidden_states).view(bsz, q_len, self.num_heads, self.head_dim).transpose(1, 2)value_states self.v_proj(hidden_states).view(bsz, q_len, self.num_heads, self.head_dim).transpose(1, 2)kv_seq_len key_states.shape[-2]if past_key_value is not None:kv_seq_len past_key_value[0].shape[-2]cos, sin self.rotary_emb(value_states, seq_lenkv_seq_len)query_states, key_states apply_rotary_pos_emb(query_states, key_states, cos, sin, position_ids)# [bsz, nh, t, hd]if past_key_value is not None:# reuse k, v, self_attentionkey_states torch.cat([past_key_value[0], key_states], dim2)value_states torch.cat([past_key_value[1], value_states], dim2)past_key_value (key_states, value_states) if use_cache else Noneattn_weights torch.matmul(query_states, key_states.transpose(2, 3)) / math.sqrt(self.head_dim)if attn_weights.size() ! (bsz, self.num_heads, q_len, kv_seq_len):raise ValueError(fAttention weights should be of size {(bsz, self.num_heads, q_len, kv_seq_len)}, but isf {attn_weights.size()})if attention_mask is not None:if attention_mask.size() ! (bsz, 1, q_len, kv_seq_len):raise ValueError(fAttention mask should be of size {(bsz, 1, q_len, kv_seq_len)}, but is {attention_mask.size()})attn_weights attn_weights attention_maskattn_weights torch.max(attn_weights, torch.tensor(torch.finfo(attn_weights.dtype).min))# upcast attention to fp32attn_weights nn.functional.softmax(attn_weights, dim-1, dtypetorch.float32).to(query_states.dtype)attn_output torch.matmul(attn_weights, value_states)if attn_output.size() ! (bsz, self.num_heads, q_len, self.head_dim):raise ValueError(fattn_output should be of size {(bsz, self.num_heads, q_len, self.head_dim)}, but isf {attn_output.size()})attn_output attn_output.transpose(1, 2)attn_output attn_output.reshape(bsz, q_len, self.hidden_size)attn_output self.o_proj(attn_output)if not output_attentions:attn_weights Nonereturn attn_output, attn_weights, past_key_valueclass InternLMDecoderLayer(nn.Module):def __init__(self, config: InternLMConfig):super().__init__()self.hidden_size config.hidden_sizeself.self_attn InternLMAttention(configconfig)self.mlp InternLMMLP(hidden_sizeself.hidden_size,intermediate_sizeconfig.intermediate_size,hidden_actconfig.hidden_act,)self.input_layernorm InternLMRMSNorm(config.hidden_size, epsconfig.rms_norm_eps)self.post_attention_layernorm InternLMRMSNorm(config.hidden_size, epsconfig.rms_norm_eps)def forward(self,hidden_states: torch.Tensor,attention_mask: Optional[torch.Tensor] None,position_ids: Optional[torch.LongTensor] None,past_key_value: Optional[Tuple[torch.Tensor]] None,output_attentions: Optional[bool] False,use_cache: Optional[bool] False,) - Tuple[torch.FloatTensor, Optional[Tuple[torch.FloatTensor, torch.FloatTensor]]]:Args:hidden_states (torch.FloatTensor): input to the layer of shape (batch, seq_len, embed_dim)attention_mask (torch.FloatTensor, *optional*): attention mask of size(batch, 1, tgt_len, src_len) where padding elements are indicated by very large negative values.output_attentions (bool, *optional*):Whether or not to return the attentions tensors of all attention layers. See attentions underreturned tensors for more detail.use_cache (bool, *optional*):If set to True, past_key_values key value states are returned and can be used to speed up decoding(see past_key_values).past_key_value (Tuple(torch.FloatTensor), *optional*): cached past key and value projection statesresidual hidden_stateshidden_states self.input_layernorm(hidden_states)# Self Attentionhidden_states, self_attn_weights, present_key_value self.self_attn(hidden_stateshidden_states,attention_maskattention_mask,position_idsposition_ids,past_key_valuepast_key_value,output_attentionsoutput_attentions,use_cacheuse_cache,)hidden_states residual hidden_states# Fully Connectedresidual hidden_stateshidden_states self.post_attention_layernorm(hidden_states)hidden_states self.mlp(hidden_states)hidden_states residual hidden_statesoutputs (hidden_states,)if output_attentions:outputs (self_attn_weights,)if use_cache:outputs (present_key_value,)return outputsINTERNLM_START_DOCSTRING rThis model inherits from [PreTrainedModel]. Check the superclass documentation for the generic methods thelibrary implements for all its model (such as downloading or saving, resizing the input embeddings, pruning headsetc.)This model is also a PyTorch [torch.nn.Module](https://pytorch.org/docs/stable/nn.html#torch.nn.Module) subclass.Use it as a regular PyTorch Module and refer to the PyTorch documentation for all matter related to general usageand behavior.Parameters:config ([InternLMConfig]):Model configuration class with all the parameters of the model. Initializing with a config file does notload the weights associated with the model, only the configuration. Check out the[~PreTrainedModel.from_pretrained] method to load the model weights.
add_start_docstrings(The bare InternLM Model outputting raw hidden-states without any specific head on top.,INTERNLM_START_DOCSTRING,
)
class InternLMPreTrainedModel(PreTrainedModel):config_class InternLMConfigbase_model_prefix modelsupports_gradient_checkpointing True_no_split_modules [InternLMDecoderLayer]_keys_to_ignore_on_load_unexpected [rdecoder\.version]def _init_weights(self, module):std self.config.initializer_rangeif isinstance(module, nn.Linear):module.weight.data.normal_(mean0.0, stdstd)if module.bias is not None:module.bias.data.zero_()elif isinstance(module, nn.Embedding):module.weight.data.normal_(mean0.0, stdstd)if module.padding_idx is not None:module.weight.data[module.padding_idx].zero_()def _set_gradient_checkpointing(self, module, valueFalse):if isinstance(module, InternLMModel):module.gradient_checkpointing valueINTERNLM_INPUTS_DOCSTRING rArgs:input_ids (torch.LongTensor of shape (batch_size, sequence_length)):Indices of input sequence tokens in the vocabulary. Padding will be ignored by default should you provideit.Indices can be obtained using [AutoTokenizer]. See [PreTrainedTokenizer.encode] and[PreTrainedTokenizer.__call__] for details.[What are input IDs?](../glossary#input-ids)attention_mask (torch.Tensor of shape (batch_size, sequence_length), *optional*):Mask to avoid performing attention on padding token indices. Mask values selected in [0, 1]:- 1 for tokens that are **not masked**,- 0 for tokens that are **masked**.[What are attention masks?](../glossary#attention-mask)Indices can be obtained using [AutoTokenizer]. See [PreTrainedTokenizer.encode] and[PreTrainedTokenizer.__call__] for details.If past_key_values is used, optionally only the last decoder_input_ids have to be input (seepast_key_values).If you want to change padding behavior, you should read [modeling_opt._prepare_decoder_attention_mask]and modify to your needs. See diagram 1 in [the paper](https://arxiv.org/abs/1910.13461) for moreinformation on the default strategy.- 1 indicates the head is **not masked**,- 0 indicates the head is **masked**.position_ids (torch.LongTensor of shape (batch_size, sequence_length), *optional*):Indices of positions of each input sequence tokens in the position embeddings. Selected in the range [0,config.n_positions - 1].[What are position IDs?](../glossary#position-ids)past_key_values (tuple(tuple(torch.FloatTensor)), *optional*, returned when use_cacheTrue is passed or when config.use_cacheTrue):Tuple of tuple(torch.FloatTensor) of length config.n_layers, with each tuple having 2 tensors of shape(batch_size, num_heads, sequence_length, embed_size_per_head)) and 2 additional tensors of shape(batch_size, num_heads, encoder_sequence_length, embed_size_per_head).Contains pre-computed hidden-states (key and values in the self-attention blocks and in the cross-attentionblocks) that can be used (see past_key_values input) to speed up sequential decoding.If past_key_values are used, the user can optionally input only the last decoder_input_ids (those thatdont have their past key value states given to this model) of shape (batch_size, 1) instead of alldecoder_input_ids of shape (batch_size, sequence_length).inputs_embeds (torch.FloatTensor of shape (batch_size, sequence_length, hidden_size), *optional*):Optionally, instead of passing input_ids you can choose to directly pass an embedded representation. Thisis useful if you want more control over how to convert input_ids indices into associated vectors than themodels internal embedding lookup matrix.use_cache (bool, *optional*):If set to True, past_key_values key value states are returned and can be used to speed up decoding (seepast_key_values).output_attentions (bool, *optional*):Whether or not to return the attentions tensors of all attention layers. See attentions under returnedtensors for more detail.output_hidden_states (bool, *optional*):Whether or not to return the hidden states of all layers. See hidden_states under returned tensors formore detail.return_dict (bool, *optional*):Whether or not to return a [~utils.ModelOutput] instead of a plain tuple.
add_start_docstrings(The bare InternLM Model outputting raw hidden-states without any specific head on top.,INTERNLM_START_DOCSTRING,
)
class InternLMModel(InternLMPreTrainedModel):Transformer decoder consisting of *config.num_hidden_layers* layers. Each layer is a [InternLMDecoderLayer]Args:config: InternLMConfig_auto_class AutoModeldef __init__(self, config: InternLMConfig):super().__init__(config)self.padding_idx config.pad_token_idself.vocab_size config.vocab_sizeself.embed_tokens nn.Embedding(config.vocab_size, config.hidden_size, self.padding_idx)self.layers nn.ModuleList([InternLMDecoderLayer(config) for _ in range(config.num_hidden_layers)])self.norm InternLMRMSNorm(config.hidden_size, epsconfig.rms_norm_eps)self.gradient_checkpointing False# Initialize weights and apply final processingself.post_init()def get_input_embeddings(self):return self.embed_tokensdef set_input_embeddings(self, value):self.embed_tokens value# Copied from transformers.models.bart.modeling_bart.BartDecoder._prepare_decoder_attention_maskdef _prepare_decoder_attention_mask(self, attention_mask, input_shape, inputs_embeds, past_key_values_length):# create causal mask# [bsz, seq_len] - [bsz, 1, tgt_seq_len, src_seq_len]combined_attention_mask Noneif input_shape[-1] 1:combined_attention_mask _make_causal_mask(input_shape,inputs_embeds.dtype,deviceinputs_embeds.device,past_key_values_lengthpast_key_values_length,)if attention_mask is not None:# [bsz, seq_len] - [bsz, 1, tgt_seq_len, src_seq_len]expanded_attn_mask _expand_mask(attention_mask, inputs_embeds.dtype, tgt_leninput_shape[-1]).to(inputs_embeds.device)combined_attention_mask (expanded_attn_mask if combined_attention_mask is None else expanded_attn_mask combined_attention_mask)return combined_attention_maskadd_start_docstrings_to_model_forward(INTERNLM_INPUTS_DOCSTRING)def forward(self,input_ids: torch.LongTensor None,attention_mask: Optional[torch.Tensor] None,position_ids: Optional[torch.LongTensor] None,past_key_values: Optional[List[torch.FloatTensor]] None,inputs_embeds: Optional[torch.FloatTensor] None,use_cache: Optional[bool] None,output_attentions: Optional[bool] None,output_hidden_states: Optional[bool] None,return_dict: Optional[bool] None,) - Union[Tuple, BaseModelOutputWithPast]:output_attentions output_attentions if output_attentions is not None else self.config.output_attentionsoutput_hidden_states (output_hidden_states if output_hidden_states is not None else self.config.output_hidden_states)use_cache use_cache if use_cache is not None else self.config.use_cachereturn_dict return_dict if return_dict is not None else self.config.use_return_dict# retrieve input_ids and inputs_embedsif input_ids is not None and inputs_embeds is not None:raise ValueError(You cannot specify both decoder_input_ids and decoder_inputs_embeds at the same time)elif input_ids is not None:batch_size, seq_length input_ids.shapeelif inputs_embeds is not None:batch_size, seq_length, _ inputs_embeds.shapeelse:raise ValueError(You have to specify either decoder_input_ids or decoder_inputs_embeds)seq_length_with_past seq_lengthpast_key_values_length 0if past_key_values is not None:past_key_values_length past_key_values[0][0].shape[2]seq_length_with_past seq_length_with_past past_key_values_lengthif position_ids is None:device input_ids.device if input_ids is not None else inputs_embeds.deviceposition_ids torch.arange(past_key_values_length, seq_length past_key_values_length, dtypetorch.long, devicedevice)position_ids position_ids.unsqueeze(0).view(-1, seq_length)else:position_ids position_ids.view(-1, seq_length).long()if inputs_embeds is None:inputs_embeds self.embed_tokens(input_ids)# embed positionsif attention_mask is None:attention_mask torch.ones((batch_size, seq_length_with_past), dtypetorch.bool, deviceinputs_embeds.device)attention_mask self._prepare_decoder_attention_mask(attention_mask, (batch_size, seq_length), inputs_embeds, past_key_values_length)hidden_states inputs_embedsif self.gradient_checkpointing and self.training:if use_cache:logger.warning_once(use_cacheTrue is incompatible with gradient checkpointing. Setting use_cacheFalse...)use_cache False# decoder layersall_hidden_states () if output_hidden_states else Noneall_self_attns () if output_attentions else Nonenext_decoder_cache () if use_cache else Nonefor idx, decoder_layer in enumerate(self.layers):if output_hidden_states:all_hidden_states (hidden_states,)past_key_value past_key_values[idx] if past_key_values is not None else Noneif self.gradient_checkpointing and self.training:def create_custom_forward(module):def custom_forward(*inputs):# None for past_key_valuereturn module(*inputs, output_attentions, None)return custom_forwardlayer_outputs torch.utils.checkpoint.checkpoint(create_custom_forward(decoder_layer),hidden_states,attention_mask,position_ids,None,)else:layer_outputs decoder_layer(hidden_states,attention_maskattention_mask,position_idsposition_ids,past_key_valuepast_key_value,output_attentionsoutput_attentions,use_cacheuse_cache,)hidden_states layer_outputs[0]if use_cache:next_decoder_cache (layer_outputs[2 if output_attentions else 1],)if output_attentions:all_self_attns (layer_outputs[1],)hidden_states self.norm(hidden_states)# add hidden states from the last decoder layerif output_hidden_states:all_hidden_states (hidden_states,)next_cache next_decoder_cache if use_cache else Noneif not return_dict:return tuple(v for v in [hidden_states, next_cache, all_hidden_states, all_self_attns] if v is not None)return BaseModelOutputWithPast(last_hidden_statehidden_states,past_key_valuesnext_cache,hidden_statesall_hidden_states,attentionsall_self_attns,)class InternLMForCausalLM(InternLMPreTrainedModel):_auto_class AutoModelForCausalLMdef __init__(self, config):super().__init__(config)self.model InternLMModel(config)self.lm_head nn.Linear(config.hidden_size, config.vocab_size, biasFalse)# Initialize weights and apply final processingself.post_init()def get_input_embeddings(self):return self.model.embed_tokensdef set_input_embeddings(self, value):self.model.embed_tokens valuedef get_output_embeddings(self):return self.lm_headdef set_output_embeddings(self, new_embeddings):self.lm_head new_embeddingsdef set_decoder(self, decoder):self.model decoderdef get_decoder(self):return self.modeladd_start_docstrings_to_model_forward(INTERNLM_INPUTS_DOCSTRING)replace_return_docstrings(output_typeCausalLMOutputWithPast, config_class_CONFIG_FOR_DOC)def forward(self,input_ids: torch.LongTensor None,attention_mask: Optional[torch.Tensor] None,position_ids: Optional[torch.LongTensor] None,past_key_values: Optional[List[torch.FloatTensor]] None,inputs_embeds: Optional[torch.FloatTensor] None,labels: Optional[torch.LongTensor] None,use_cache: Optional[bool] None,output_attentions: Optional[bool] None,output_hidden_states: Optional[bool] None,return_dict: Optional[bool] None,) - Union[Tuple, CausalLMOutputWithPast]:rArgs:labels (torch.LongTensor of shape (batch_size, sequence_length), *optional*):Labels for computing the masked language modeling loss. Indices should either be in [0, ...,config.vocab_size] or -100 (see input_ids docstring). Tokens with indices set to -100 are ignored(masked), the loss is only computed for the tokens with labels in [0, ..., config.vocab_size].Returns:Example:python from transformers import AutoTokenizer, InternLMForCausalLM model InternLMForCausalLM.from_pretrained(PATH_TO_CONVERTED_WEIGHTS) tokenizer AutoTokenizer.from_pretrained(PATH_TO_CONVERTED_TOKENIZER) prompt Hey, are you consciours? Can you talk to me? inputs tokenizer(prompt, return_tensorspt) # Generate generate_ids model.generate(inputs.input_ids, max_length30) tokenizer.batch_decode(generate_ids, skip_special_tokensTrue, clean_up_tokenization_spacesFalse)[0]Hey, are you consciours? Can you talk to me?\nIm not consciours, but I can talk to you.output_attentions output_attentions if output_attentions is not None else self.config.output_attentionsoutput_hidden_states (output_hidden_states if output_hidden_states is not None else self.config.output_hidden_states)return_dict return_dict if return_dict is not None else self.config.use_return_dict# decoder outputs consists of (dec_features, layer_state, dec_hidden, dec_attn)outputs self.model(input_idsinput_ids,attention_maskattention_mask,position_idsposition_ids,past_key_valuespast_key_values,inputs_embedsinputs_embeds,use_cacheuse_cache,output_attentionsoutput_attentions,output_hidden_statesoutput_hidden_states,return_dictreturn_dict,)hidden_states outputs[0]logits self.lm_head(hidden_states)loss Noneif labels is not None:# Shift so that tokens n predict nshift_logits logits[..., :-1, :].contiguous()shift_labels labels[..., 1:].contiguous()# Flatten the tokensloss_fct CrossEntropyLoss()shift_logits shift_logits.view(-1, self.config.vocab_size)shift_labels shift_labels.view(-1)# Enable model parallelismshift_labels shift_labels.to(shift_logits.device)loss loss_fct(shift_logits, shift_labels)if not return_dict:output (logits,) outputs[1:]return (loss,) output if loss is not None else outputreturn CausalLMOutputWithPast(lossloss,logitslogits,past_key_valuesoutputs.past_key_values,hidden_statesoutputs.hidden_states,attentionsoutputs.attentions,)def prepare_inputs_for_generation(self, input_ids, past_key_valuesNone, attention_maskNone, inputs_embedsNone, **kwargs):if past_key_values:input_ids input_ids[:, -1:]position_ids kwargs.get(position_ids, None)if attention_mask is not None and position_ids is None:# create position_ids on the fly for batch generationposition_ids attention_mask.long().cumsum(-1) - 1position_ids.masked_fill_(attention_mask 0, 1)if past_key_values:position_ids position_ids[:, -1].unsqueeze(-1)# if inputs_embeds are passed, we only want to use them in the 1st generation stepif inputs_embeds is not None and past_key_values is None:model_inputs {inputs_embeds: inputs_embeds}else:model_inputs {input_ids: input_ids}model_inputs.update({position_ids: position_ids,past_key_values: past_key_values,use_cache: kwargs.get(use_cache),attention_mask: attention_mask,})return model_inputsstaticmethoddef _reorder_cache(past_key_values, beam_idx):reordered_past ()for layer_past in past_key_values:reordered_past (tuple(past_state.index_select(0, beam_idx) for past_state in layer_past),)return reordered_pastdef build_inputs(self, tokenizer, query: str, history: List[Tuple[str, str]] []):prompt for record in history:prompt fs|User|:{record[0]}eoh\n|Bot|:{record[1]}eoa\nif len(prompt) 0:prompt sprompt f|User|:{query}eoh\n|Bot|:return tokenizer([prompt], return_tensorspt)torch.no_grad()def chat(self, tokenizer, query: str,history: List[Tuple[str, str]] [], streamer: Optional[BaseStreamer] None,max_new_tokens: int 1024,do_sample: bool True,temperature: float 0.8,top_p: float 0.8,**kwargs):inputs self.build_inputs(tokenizer, query, history)inputs {k: v.to(self.device) for k, v in inputs.items() if torch.is_tensor(v)}outputs self.generate(**inputs, streamerstreamer, max_new_tokensmax_new_tokens, do_sampledo_sample, temperaturetemperature, top_ptop_p, **kwargs)outputs outputs[0].cpu().tolist()[len(inputs[input_ids][0]):]response tokenizer.decode(outputs, skip_special_tokensTrue)response response.split(eoa)[0]history history [(query, response)]return response, historytorch.no_grad()def stream_chat(self, tokenizer,query: str,history: List[Tuple[str, str]] [], max_new_tokens: int 1024,do_sample: bool True,temperature: float 0.8,top_p: float 0.8,**kwargs):Return a generator in format: (response, history)Eg.(你好有什么可以帮助您的吗, [(你好, 你好有什么可以帮助您的吗)])(你好有什么可以帮助您的吗, [(你好, 你好有什么可以帮助您的吗)])response_queue queue.Queue(maxsize20)class ChatStreamer(BaseStreamer):def __init__(self, tokenizer) - None:super().__init__()self.tokenizer tokenizerself.queue response_queueself.query queryself.history historyself.response self.received_inputs Falseself.queue.put((self.response, history [(self.query, self.response)]))def put(self, value):if len(value.shape) 1 and value.shape[0] 1:raise ValueError(ChatStreamer only supports batch size 1)elif len(value.shape) 1:value value[0]if not self.received_inputs:# The first received value is input_ids, ignore hereself.received_inputs Truereturntoken self.tokenizer.decode([value[-1]], skip_special_tokensTrue)if token.strip() ! eoa:self.response self.response tokenhistory self.history [(self.query, self.response)]self.queue.put((self.response, history))def end(self):self.queue.put(None)def stream_producer():return self.chat(tokenizertokenizer,queryquery,streamerChatStreamer(tokenizertokenizer),historyhistory, max_new_tokensmax_new_tokens,do_sampledo_sample,temperaturetemperature,top_ptop_p,**kwargs)def consumer():producer threading.Thread(targetstream_producer)producer.start()while True:res response_queue.get()if res is None:returnyield resreturn consumer()add_start_docstrings(The InternLM Model transformer with a sequence classification head on top (linear layer).[InternLMForSequenceClassification] uses the last token in order to do the classification, as other causal models(e.g. GPT-2) do.Since it does classification on the last token, it requires to know the position of the last token. If apad_token_id is defined in the configuration, it finds the last token that is not a padding token in each row. Ifno pad_token_id is defined, it simply takes the last value in each row of the batch. Since it cannot guess thepadding tokens when inputs_embeds are passed instead of input_ids, it does the same (take the last value ineach row of the batch).,INTERNLM_START_DOCSTRING,
)
class InternLMForSequenceClassification(InternLMPreTrainedModel):_keys_to_ignore_on_load_missing [rlm_head.weight]def __init__(self, config):super().__init__(config)self.num_labels config.num_labelsself.model InternLMModel(config)self.score nn.Linear(config.hidden_size, self.num_labels, biasFalse)# Initialize weights and apply final processingself.post_init()def get_input_embeddings(self):return self.model.embed_tokensdef set_input_embeddings(self, value):self.model.embed_tokens valueadd_start_docstrings_to_model_forward(INTERNLM_INPUTS_DOCSTRING)def forward(self,input_ids: torch.LongTensor None,attention_mask: Optional[torch.Tensor] None,position_ids: Optional[torch.LongTensor] None,past_key_values: Optional[List[torch.FloatTensor]] None,inputs_embeds: Optional[torch.FloatTensor] None,labels: Optional[torch.LongTensor] None,use_cache: Optional[bool] None,output_attentions: Optional[bool] None,output_hidden_states: Optional[bool] None,return_dict: Optional[bool] None,) - Union[Tuple, SequenceClassifierOutputWithPast]:rlabels (torch.LongTensor of shape (batch_size,), *optional*):Labels for computing the sequence classification/regression loss. Indices should be in [0, ...,config.num_labels - 1]. If config.num_labels 1 a regression loss is computed (Mean-Square loss), Ifconfig.num_labels 1 a classification loss is computed (Cross-Entropy).return_dict return_dict if return_dict is not None else self.config.use_return_dicttransformer_outputs self.model(input_ids,attention_maskattention_mask,position_idsposition_ids,past_key_valuespast_key_values,inputs_embedsinputs_embeds,use_cacheuse_cache,output_attentionsoutput_attentions,output_hidden_statesoutput_hidden_states,return_dictreturn_dict,)hidden_states transformer_outputs[0]logits self.score(hidden_states)if input_ids is not None:batch_size input_ids.shape[0]else:batch_size inputs_embeds.shape[0]if self.config.pad_token_id is None and batch_size ! 1:raise ValueError(Cannot handle batch sizes 1 if no padding token is defined.)if self.config.pad_token_id is None:sequence_lengths -1else:if input_ids is not None:sequence_lengths (torch.ne(input_ids, self.config.pad_token_id).sum(-1) - 1).to(logits.device)else:sequence_lengths -1pooled_logits logits[torch.arange(batch_size, devicelogits.device), sequence_lengths]loss Noneif labels is not None:labels labels.to(logits.device)if self.config.problem_type is None:if self.num_labels 1:self.config.problem_type regressionelif self.num_labels 1 and (labels.dtype torch.long or labels.dtype torch.int):self.config.problem_type single_label_classificationelse:self.config.problem_type multi_label_classificationif self.config.problem_type regression:loss_fct MSELoss()if self.num_labels 1:loss loss_fct(pooled_logits.squeeze(), labels.squeeze())else:loss loss_fct(pooled_logits, labels)elif self.config.problem_type single_label_classification:loss_fct CrossEntropyLoss()loss loss_fct(pooled_logits.view(-1, self.num_labels), labels.view(-1))elif self.config.problem_type multi_label_classification:loss_fct BCEWithLogitsLoss()loss loss_fct(pooled_logits, labels)if not return_dict:output (pooled_logits,) transformer_outputs[1:]return ((loss,) output) if loss is not None else outputreturn SequenceClassifierOutputWithPast(lossloss,logitspooled_logits,past_key_valuestransformer_outputs.past_key_values,hidden_statestransformer_outputs.hidden_states,attentionstransformer_outputs.attentions,) 2.源码分析
这里 modeling_xxx.py 里除了我们提到的 RoPE 位置编码的实现过程还有前面提到的归一化函数 RMSNormalMLP 的多个 proj激活函数 SiLU 等等。有兴趣的同学可以有选择的阅读其他部分的代码加深对大模型实现过程的认识。言归症状先找到 RoPE 的调用位置L199-L207对应 Class InternLMAttention 注意力层的 forward 前向传递部分 query、key、value 获取可以理解为从 Embedding 层 lookup 获取向量除此之外还有两个方法
◆ rotary_emb
rotary_emb 对应 InternLMRotaryEmbedding 层其中内置 init 初始化方法和 forward 前向调用这个方法负责生成我们上面实践分析中提到的 cos 和 sin。 ◆ apply_rotary_pos_emb
该方法用于将旋转编码应用到 k、v 上内部还用到了 rotate_half 的辅助函数。 3.rotary_emb
rotary_emb 继承 torch.nn.Module 实现了 InternLMRotaryEmbedding其中包含 init 和 forward 前向计算的方法下面看下两个方法的实现步骤。
3.1 __init__ ◆ 参数分析
首先看 InternLMRotaryEmbedding init 方法的四个参数:
dim - 向量维度
max_position_embedding - 最大位置向量其实就是我们上面分析的最大的 position: m
base - 计算 θ 的底数是 base默认取 10000和论文的公式是一致的
device - 设备这个参数目前对我们代码理解没有影响所以后续会取 None ◆ 构造 θ 全集
下面我们逐行执行代码这里取向量维度 dim8底数 base10000设备 deviceNone。 dim 8base 10000device None# 根据概率计算θ, dim/2个θinv_freq 1.0 / (base ** (torch.arange(0, dim, 2).float().to(device) / dim)) 这里就是根据维度 d 将所有的 θ 得到由于是将向量两两旋转应用 RoPE所以共有 d/2 个 θ所以下面会得到 8/2 4 个 θ即 inv_freq
tensor([1.0000, 0.1000, 0.0100, 0.0010])◆ 扩展至 m x d/2 inv_freq_cached inv_freqmax_seq_len_cached max_position_embeddingst torch.arange(max_seq_len_cached, devicedevice, dtypeinv_freq.dtype)freqs torch.einsum(i,j-ij, t, inv_freq)
这里 max_seq_len_cache 即为 max_position_embeddings 即为最大位置我们可以到代码的 config.py 文件中查看该配置此处 max_position_embeddings 的值为 4096 arange 根据 max_position_embeddings 的 4096 生成对应的 Tensor
tensor([0.0000e00, 1.0000e00, 2.0000e00, ..., 4.0660e03, 4.0670e03, 4.0680e03])
而 torch.einsum 则是通过爱因斯坦求和约定将 arange Tensor 与 θ Tensor 进行合并生成 4096 x d/2 的初始旋转矩阵也就是下面这个 Rd 这里 inv_freq.shape [4]t.shape [4096]enisum 乘法后维度为 torch.Size([4069, 4])。关于 enisum 的使用之前也出了示例大家可以参考: 深度学习矩阵乘法大全。 ◆ R 旋转矩阵扩展
emb torch.cat((freqs, freqs), dim-1)
self.register_buffer(cos_cached, emb.cos()[None, None, :, :], persistentFalse)
self.register_buffer(sin_cached, emb.sin()[None, None, :, :], persistentFalse) 这里将提前计算的 freq 矩阵叠加得到 m x d 的旋转矩阵
[θ1,θ2,θ3,θ4] [4069, 4] x 2 - [θ1,θ2,θ3,θ4,θ1,θ2,θ3,θ4] torch.Size([4069, 8]) 扩展一倍也很好理解因为每个位置的 θ 需要对应两个 dim 的向量值。最后将扩展后的矩阵分别执行 cos 和 sin 即得到可用的旋转矩阵。而 [None, None, :, :] 的操作则是为了匹配原始 query、key 和 value 的维度。
- cos - sin 3.2 forward 仔细观察 forward 函数这里对于输入的 Tensor x仅获取其对应 device 和 dtype。而且可以注意到其实现逻辑与 __init__ 一致只是只是新增了判断 seq_len max_seq_len_cache 的情况将 max_seq_len_cache 的长度 m 提高不过按照官方的注释 # 在__init__中构建sin/cos之后这个if块不太可能运行。把逻辑放在这里以防万一
# This if block is unlikely to be run after we build sin/cos in __init__. Keep the logic here just in case.
所以调用 forward 函数可以理解为直接获取 init 函数中的 cos 和 sin 的旋转矩阵唯一做的就是转换其 dtype 与当前传入的 Tensor x 保持类型一致观察 config 我们可以看到 InternLM 使用的类型为 bfloat16。最终 [:, :, :seq_len, ...] 取与当前 seq_len 匹配的矩阵防止多余的空间和计算资源浪费此时 cos 和 sin 的维度为:
torch.Size([1, 1, 4069, 8]) 4.apply_rotary_pos_emb
该方法用于将 cos、sin 的旋转矩阵应用到原始的 query 和 key 向量上这样在 Attention 内积时就会为 query 和 key 引入位置信息其中还涉及到了辅助函数 ratate_half 用于调整向量位置。
4.1 rotate_half 这个函数很好理解就是将原始向量从中间劈开分为 A、B 两份然后拼接为 [-B, A] 的状态
v1: [q0,q1,q2,q3,q4,q5,q6,q7] - [-q4,-q5,-q6,-q7,q0,q1,q2,q3] 4.2 apply_rotary_pos_emb 这个方法对照着前面矩阵形式里的公式就很好理解了首先 lookup 获取对应位置的 cosmθ 和 sinmθ 值然后分别计算前面的 cos 部分再计算后面的 sinθ * rotate_half 部分。 不过按照代码的逻辑rotate_half 后计算结果似乎与上图不匹配: # v1: [q0,q1,q2,q3,q4,q5,q6,q7] - [-q4,-q5,-q6,-q7,q0,q1,q2,q3]# [cosθ1, cosθ2, cosθ3, cosθ4, cosθ1, cosθ2, cosθ3, cosθ4]# [sinθ1, sinθ2, sinθ3, sinθ4, sinθ1, sinθ2, sinθ3, sinθ4]
cos 部分不影响两两与对应 θ 相乘即可出问题部分是 sin 计算这里按照 rotate_half 翻转后对应的向量 4,5,6,7 部分变负但是矩阵中应该是 1,3,5,7 变负这里暂时没有搞清楚原因但是大体的计算流程是与示意图匹配的。博主这里参考剑神论文给的代码稍微修改了一下 rotate_half 函数修改后可以达到正确的 cos、sin 计算
def rotate_half_v2(x):x1 x[..., ::2]x2 x[..., 1::2]return torch.cat((-x2, x1), dim-1)
使用该旋转函数后sin 计算逻辑正常 # v2: [q0,q1,q2,q3,q4,q5,q6,q7] - [-q1,-q3,-q5,-q7,q0,q2,q4,q6]# [cosθ1, cosθ2, cosθ3, cosθ4, cosθ1, cosθ2, cosθ3, cosθ4]# [sinθ1, sinθ2, sinθ3, sinθ4, sinθ1, sinθ2, sinθ3, sinθ4] 四.RoPE 代码实现 原始代码如上我们只需自己构造 query、key、value states 和 position_ids 即可跑通流程。
1.Q/K/V States Q/K/V 对应维度为 [bsz, seq_len, num_heads, head_dim]transpose 将 seq_len 和 num_heads 的维度调换了得到的 states 维度为 [bsz, num_heads, seq_len, head_dim]。这个变换是为了将 seq_len x head_dim 4096 x 8 挪到一起方便后面的 ⊗ 对位相乘。 # Query、Key、Value 信息batch_size 2query_length 10num_heads 4head_dim 8past_key_value None# 获取 Query、Key、Value Matrixquery_states torch.rand(batch_size, query_length, num_heads, head_dim).transpose(1, 2)key_states torch.rand(batch_size, query_length, num_heads, head_dim).transpose(1, 2)value_states torch.rand(batch_size, query_length, num_heads, head_dim).transpose(1, 2)
随机初始化后的 states 维度为: torch.Size([2, 4, 10, 8])这里使用 torch.rand 随机生成并展示 query_states
tensor([[[[2.9183e-01, 5.9775e-02, 3.5425e-01, 2.7915e-01, 5.2601e-01,8.3887e-01, 3.3162e-01, 1.3850e-01],[2.8997e-01, 1.5348e-01, 6.1809e-01, 6.7418e-01, 2.4923e-02,3.9746e-01, 7.3853e-01, 3.4693e-02],[4.1272e-01, 8.2844e-01, 3.2101e-01, 9.3669e-01, 9.9066e-01,7.3192e-01, 4.9623e-01, 3.6537e-01],[9.3123e-01, 6.0658e-01, 5.1689e-02, 4.8995e-01, 8.3494e-01,9.5322e-01, 4.4755e-01, 4.6204e-01],[2.2266e-01, 7.8899e-01, 3.1150e-01, 8.6672e-01, 5.7448e-01,1.8205e-02, 1.4669e-01, 1.4783e-01],[2.3940e-01, 8.3407e-01, 2.4727e-01, 4.8705e-02, 7.4942e-01,3.3560e-01, 5.5196e-01, 9.0414e-01],[5.7593e-01, 3.1633e-01, 1.8330e-01, 7.7621e-01, 5.8697e-01,1.8219e-01, 8.6412e-01, 4.4979e-02],[7.9487e-01, 2.2888e-02, 7.1163e-01, 1.7849e-01, 5.7600e-01,8.9930e-01, 3.5231e-01, 1.5648e-01],[5.2896e-02, 3.2068e-01, 7.3980e-01, 7.7020e-01, 4.4519e-01,7.1207e-01, 2.2424e-01, 1.2025e-01],[6.8193e-01, 4.9851e-01, 1.0965e-02, 1.3012e-02, 8.7816e-01,8.8564e-01, 5.6333e-01, 8.6411e-01]],[[6.8500e-01, 7.0738e-01, 2.9308e-01, 9.2951e-01, 6.1441e-02,3.6203e-02, 6.3757e-01, 4.7221e-01],[4.3020e-01, 5.7936e-01, 5.8797e-01, 5.2842e-01, 2.1757e-01,8.2139e-01, 8.1286e-01, 5.1831e-01],[5.0025e-01, 4.9856e-01, 8.6077e-01, 4.8580e-01, 6.7289e-01,1.6959e-01, 9.1899e-01, 7.0452e-02],[6.8620e-01, 5.9861e-01, 6.1024e-01, 9.4969e-01, 8.7641e-01,2.1290e-01, 2.9642e-01, 6.4476e-01],[4.0705e-02, 3.1697e-02, 9.2447e-01, 6.6854e-02, 2.7703e-01,1.0916e-01, 1.8328e-01, 8.0773e-01],[7.6717e-02, 3.4182e-01, 8.6993e-01, 3.9317e-01, 5.4155e-01,9.5709e-01, 3.4793e-01, 7.6505e-01],[8.4284e-01, 7.8279e-01, 3.6731e-01, 8.2489e-01, 7.0346e-01,9.5639e-01, 8.0766e-01, 9.2304e-01],[7.2185e-01, 2.5139e-01, 4.0992e-01, 2.3913e-01, 9.5667e-01,8.7461e-01, 5.1859e-02, 6.5691e-01],[5.9603e-01, 5.5759e-01, 6.1473e-01, 4.7875e-01, 7.2805e-01,7.7380e-02, 1.4822e-01, 4.0581e-01],[8.4941e-01, 5.4692e-01, 1.9650e-01, 7.9873e-01, 4.7650e-01,4.1342e-01, 5.8423e-01, 4.6351e-02]],[[6.4038e-01, 9.8298e-01, 3.1733e-01, 9.0533e-01, 5.8110e-01,4.9543e-01, 2.5562e-01, 9.5430e-01],[8.4416e-01, 1.5592e-01, 5.0446e-01, 9.4544e-01, 7.0241e-01,1.1321e-01, 9.0690e-01, 5.6367e-01],[6.8041e-01, 4.5696e-01, 8.0091e-01, 6.6836e-01, 3.1932e-01,2.5314e-02, 4.5553e-01, 3.2404e-03],[8.5800e-01, 6.9543e-01, 7.2294e-01, 1.3468e-01, 2.9467e-01,4.5119e-01, 6.0176e-01, 5.9708e-01],[4.7581e-01, 9.5652e-01, 3.6950e-01, 8.5315e-01, 1.5493e-01,4.5351e-01, 5.5274e-02, 3.9174e-01],[6.7330e-01, 4.2024e-01, 4.5872e-01, 3.6176e-01, 5.6271e-01,7.4545e-01, 1.9587e-01, 9.3089e-01],[3.6712e-01, 7.1372e-01, 1.8244e-01, 9.1078e-01, 1.4220e-01,9.6800e-01, 2.0999e-01, 2.3815e-01],[6.0856e-01, 5.5768e-01, 4.7132e-01, 5.1918e-01, 8.2279e-01,5.6378e-01, 6.5475e-01, 8.8963e-01],[4.7355e-01, 8.9392e-01, 5.2195e-01, 9.9627e-01, 7.1131e-01,9.4066e-01, 9.6293e-01, 2.1514e-01],[6.6799e-01, 1.5106e-03, 1.0987e-01, 7.2399e-01, 5.0414e-01,2.2703e-01, 2.2963e-01, 3.0123e-01]],[[3.4204e-01, 5.2402e-01, 5.7015e-01, 2.3358e-02, 8.8628e-01,7.8516e-01, 3.6371e-01, 8.4997e-01],[1.8298e-01, 3.5044e-01, 2.1751e-01, 2.5430e-01, 1.2984e-01,1.5158e-01, 4.8908e-01, 9.8046e-01],[4.0914e-01, 9.2517e-01, 6.0098e-02, 4.6138e-01, 3.2282e-01,3.6191e-01, 3.0836e-01, 2.8638e-01],[3.8517e-01, 7.4692e-01, 8.9863e-01, 2.7790e-02, 3.9417e-01,9.2557e-01, 9.2542e-01, 7.1499e-01],[8.0929e-01, 8.2430e-01, 7.7641e-01, 4.4017e-01, 9.4351e-01,8.4430e-01, 3.9162e-01, 4.7323e-01],[4.4801e-02, 1.0588e-01, 2.5283e-01, 2.9120e-01, 8.0959e-01,6.7210e-01, 6.3844e-01, 2.8742e-01],[7.6291e-01, 7.9657e-01, 3.8156e-01, 8.2935e-01, 2.1237e-01,6.5650e-01, 7.8452e-01, 2.8097e-01],[2.0586e-01, 7.0199e-01, 5.1598e-01, 1.3107e-01, 7.8793e-01,1.1133e-01, 4.1328e-01, 1.5066e-01],[2.1346e-01, 4.1860e-01, 2.8186e-01, 6.9559e-03, 3.1852e-01,7.0937e-01, 8.8809e-01, 7.5510e-01],[9.1850e-01, 6.2456e-01, 9.4854e-01, 2.2026e-01, 8.4640e-01,4.0601e-02, 7.9473e-01, 8.2286e-01]]],[[[2.8326e-01, 9.0059e-01, 9.3148e-01, 4.2370e-01, 2.5814e-01,6.6909e-01, 1.0928e-02, 3.9296e-01],[5.1192e-01, 7.1407e-01, 8.8236e-01, 3.7678e-01, 2.2305e-01,3.1705e-01, 6.3382e-01, 7.9083e-01],[8.0426e-01, 5.3209e-01, 2.9103e-01, 1.0520e-02, 6.4828e-01,7.5650e-01, 4.3391e-01, 1.9701e-01],[6.4033e-01, 9.4359e-01, 2.6629e-01, 5.5410e-01, 8.4910e-01,7.3342e-01, 1.4064e-01, 8.7489e-01],[1.7254e-01, 9.6152e-01, 3.8131e-01, 3.8041e-01, 6.3002e-01,7.7604e-01, 2.7887e-01, 6.7200e-01],[2.0756e-01, 7.8653e-01, 4.6171e-01, 4.1734e-01, 5.7438e-01,3.6887e-01, 2.0821e-01, 9.6894e-01],[7.8206e-01, 3.9417e-01, 1.6260e-01, 7.2534e-01, 7.5993e-02,9.3412e-01, 7.7624e-02, 9.3928e-01],[9.7513e-02, 6.1370e-01, 5.7725e-01, 3.4250e-01, 1.1776e-01,5.8991e-01, 3.6010e-01, 1.5810e-01],[9.6534e-03, 3.0747e-01, 5.6363e-01, 2.5881e-01, 3.7878e-01,4.2585e-01, 4.9041e-01, 7.6013e-01],[4.1924e-01, 1.4514e-01, 6.4527e-01, 9.7834e-01, 6.0451e-01,7.6843e-01, 4.1792e-01, 8.4611e-01]],[[2.4590e-01, 3.4102e-01, 6.0761e-01, 3.9460e-01, 4.5805e-01,7.6451e-01, 2.3557e-03, 5.7520e-01],[2.5920e-01, 9.7934e-01, 3.2950e-01, 7.1681e-01, 2.3382e-01,1.1517e-01, 6.4881e-01, 9.3044e-01],[5.1903e-03, 4.7432e-01, 7.3803e-01, 8.9230e-03, 6.6601e-01,6.7898e-02, 5.2286e-01, 9.1362e-01],[5.5971e-01, 7.1264e-01, 5.3499e-01, 2.8207e-02, 6.8861e-01,5.3159e-01, 2.0791e-01, 3.0657e-01],[4.5751e-01, 7.7627e-01, 4.8192e-01, 1.3568e-01, 2.0047e-01,4.8248e-02, 4.4249e-01, 6.4919e-01],[4.0007e-01, 6.7373e-01, 8.6021e-01, 3.7193e-01, 3.9114e-01,6.1232e-01, 3.7100e-01, 8.6428e-01],[3.8925e-01, 5.3274e-01, 2.7094e-01, 4.5749e-01, 4.0679e-01,4.0885e-01, 8.1395e-01, 9.3831e-01],[8.5813e-03, 4.6552e-01, 4.2767e-01, 3.5360e-01, 2.9415e-01,9.4150e-01, 6.7335e-01, 4.2026e-02],[6.9338e-01, 5.0140e-01, 7.2334e-01, 3.3677e-01, 7.4549e-01,6.3400e-01, 8.9057e-01, 7.8879e-01],[8.0550e-01, 2.5435e-01, 9.1497e-01, 9.2267e-01, 7.1124e-01,7.9191e-01, 6.8408e-01, 6.8683e-01]],[[5.0144e-02, 7.6259e-01, 6.7326e-01, 9.8079e-01, 1.1124e-01,4.2291e-01, 1.8365e-02, 4.4412e-01],[5.4025e-01, 1.1574e-01, 6.8358e-01, 1.4154e-01, 7.2759e-01,3.1403e-01, 7.0689e-01, 1.6075e-02],[3.3388e-01, 7.9689e-01, 1.0852e-02, 9.4362e-01, 7.6169e-01,8.1700e-01, 4.6899e-01, 3.6307e-01],[1.8781e-01, 6.3930e-01, 6.3530e-02, 2.2288e-01, 5.0376e-01,5.7084e-01, 6.6219e-01, 6.0037e-01],[9.1527e-01, 8.0093e-01, 1.0186e-01, 4.6437e-01, 3.7368e-01,9.9534e-01, 5.6913e-01, 5.1303e-01],[5.9391e-01, 6.7338e-01, 9.4407e-01, 5.5762e-01, 5.8258e-01,1.8335e-02, 4.0466e-01, 1.5728e-01],[5.5420e-02, 8.7254e-01, 4.2972e-01, 7.3742e-01, 4.0287e-01,9.8190e-01, 2.8029e-01, 4.3533e-01],[3.2755e-01, 6.7667e-01, 5.8706e-01, 2.0986e-01, 9.5659e-01,7.9053e-01, 7.8864e-01, 9.1482e-02],[5.7617e-01, 7.2545e-02, 9.7183e-01, 6.0007e-01, 6.8718e-01,9.3688e-01, 7.3142e-01, 3.5678e-01],[7.1092e-01, 9.9054e-01, 6.8759e-01, 9.4545e-04, 7.7356e-01,3.8864e-01, 3.4851e-01, 7.0661e-01]],[[8.3643e-01, 5.9542e-01, 2.8547e-01, 4.0909e-01, 4.0864e-01,6.4102e-01, 6.2927e-01, 7.0807e-01],[2.2826e-01, 3.7989e-01, 4.4519e-01, 9.7904e-01, 2.2382e-01,5.0949e-01, 6.7909e-01, 4.7000e-01],[6.3309e-01, 5.1963e-01, 3.8026e-01, 6.9920e-01, 3.8465e-01,2.5132e-01, 4.9886e-01, 4.6673e-01],[9.5898e-01, 8.0877e-01, 6.4463e-01, 7.9780e-01, 7.6710e-01,1.4926e-01, 8.9849e-01, 4.8631e-01],[7.8407e-01, 1.0189e-01, 9.9365e-01, 9.5311e-01, 4.6489e-01,6.7042e-01, 1.6722e-01, 7.3440e-01],[5.4366e-01, 4.0804e-01, 2.1323e-01, 1.5707e-01, 3.4207e-01,2.5938e-01, 6.3546e-01, 7.6161e-01],[8.2502e-01, 6.5296e-01, 5.5894e-01, 6.8899e-01, 7.9576e-01,2.8821e-01, 5.0587e-01, 7.1531e-01],[7.5482e-02, 7.7817e-01, 8.5415e-01, 8.1673e-01, 7.6846e-01,6.3890e-01, 3.5124e-01, 9.1766e-01],[6.8266e-01, 8.7167e-01, 1.1057e-01, 5.7511e-01, 1.4933e-01,1.3559e-01, 1.2099e-01, 5.2032e-01],[7.0112e-01, 1.2467e-01, 3.8753e-01, 8.5428e-01, 2.8684e-01,6.2195e-01, 6.6607e-01, 1.9613e-01]]]]) 2.rotary_emd
past_key_value 这个参数之前分析过这里直接置为 None 不再额外操作。rotary_emd 在代码中是通过 InternLMRotaryEmbedding 类初始化的 这里我们也仿造源码中的初始化方式其中 max_position_embeddings 4069这里再啰嗦一下4069 就是 position 里对应的 max m 即最大位置kv_seq_len 这里为了方便展示选取了 10。 # 补齐 past_key_valuekv_seq_len key_states.shape[-2]if past_key_value is not None:kv_seq_len past_key_value[0].shape[-2]max_position_embeddings 4069rotary_emb InternLMRotaryEmbedding(head_dim, max_position_embeddingsmax_position_embeddings)cos, sin rotary_emb(value_states, seq_lenkv_seq_len)这里传入的 value_states 经过上面的分析rotary_emb 只使用了其 device 和 dtype然后得到对应 m x d 的 cos、sin 矩阵由于是将 2 个 inv_freq concat 拼接而成所以前后是一样的
◆ Cos ◆ Sin 3.apply_rotray_pos_emd
这里把 rotate_half 函数切换为 rotate_half_v2
def apply_rotary_pos_emb(q, k, cos, sin, position_ids):# The first two dimensions of cos and sin are always 1, so we can squeeze them.cos cos.squeeze(1).squeeze(0) # [seq_len, dim]sin sin.squeeze(1).squeeze(0) # [seq_len, dim]cos cos[position_ids].unsqueeze(1) # [bs, 1, seq_len, dim]sin sin[position_ids].unsqueeze(1) # [bs, 1, seq_len, dim]q_embed (q * cos) (rotate_half_v2(q) * sin)k_embed (k * cos) (rotate_half_v2(k) * sin)return q_embed, k_embed
截止目前 q、k、cos、sin 都已经得到只需要得到 position_ids 即可
position_ids torch.tensor(list(range(0, kv_seq_len))).unsqueeze(0).repeat(batch_size, 1)
q, k query_states, key_states
q_embed, k_embed apply_rotary_pos_emb(q, k, cos, sin, position_ids)
其中 position_ids 需要进行 repeat 操作才能满足当前 bsz
tensor([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]])
最后得到的 q_emded、k_emded 维度为: torch.Size([2, 4, 10, 8])对应前面的信息 batch_size 2query_length 10num_heads 4head_dim 8
即 [bsz, num_heads, query_length, head_dim]。 五.总结
国庆前前后后大概花了一周从理论到实践从复数、旋转正交到最后的对位相乘对 RoPE 旋转编码有了一定认识还是感慨大佬的理论和实践能力能够将数学真正应用到实践中。继续努力学习 ing ... 后续有机会把 MLP 这些也捣鼓捣鼓。 ◆ 后记
源码中还多次用到了 resister_buffer 函数:
self.register_buffer(inv_freq, inv_freq, persistentFalse)
register_buffer 是 PyTorch 中的一个函数。在 PyTorch 中这个函数用于将 CPU 中的内存块注册为 PyTorch 中的 Buffer用于在 GPU 或其他设备上存储数据。persistent 参数决定了这个 Buffer 是否会在所有新的向前和向后传递中保留其值。
persistent True
如果 persistent 参数被设置为 True那么 Buffer 的内容将不会被梯度计算影响也不会因为在计算新的前向传递时清除旧的 Buffer 内容。这意味着该 Buffer 会在每次新的前向或后向传递时都保持其值。
persistent False
如果 persistent 参数 False那么这个 Buffer 仅在当前训练迭代中存在在开始新的迭代或者优化器更新后会被清空。换句话说persistent 参数 False 意味着这个 Buffer 的内容不会持久存在而是会在每次新的前向或后向传递时被重新计算和更新。
这里参数置为 False 我想着是不是因为每一个 batch 的样本 seq_len 不一致所以需要每次重新计算所以没有进行持久化。其次 register_buffer 就像是 map 构造了 kv 对的缓存供 RoPE 在当前计算中使用。
