自Meta 发布了开源大模型 llama3 系列，在多个关键基准测试中优于业界 SOTA 模型，并在代码生成任务上全面领先。太强了！10大开源大模型！
此后，开发者们便开始了本地部署和实现，比如 llama3 的中文实现、llama3 的纯 NumPy 实现等。近期，有位名为「Nishant Aklecha」的开发者发布了一个从零开始实现 llama3 的存储库，包括跨多个头的注意力矩阵乘法、位置编码和每个层在内都有非常详细的解释。项目初期就已在 GitHub 上收获了 1.5k 的 star，足可见其含金量！
从零开始实现 llama3
接下来项目作者手把手教你如何从头开始实现 llama3。
https://github.com/naklecha/llama3-from-scratch首先从 Meta 提供的 llama3 模型文件中加载张量。https://llama.meta.com/llama-downloads/
接着是分词器（tokenizer），作者表示没打算自己实现分词器，因而借用了 Andrej Karpathy 的实现方式：https://github.com/karpathy/minbpe
from pathlib import Pathimport tiktokenfrom tiktoken.load import load_tiktoken_bpeimport torchimport jsonimport matplotlib.pyplot as plttokenizer_path = "Meta-Llama-3-8B/tokenizer.model"special_tokens = [ "", "", "", "", "", "",
"", "", "", "", ] + [f"{i}|>" for i in range (5, 256 - 5)] mergeable_ranks = load_tiktoken_bpe (tokenizer_path) tokenizer = tiktoken.Encoding ( name=Path (tokenizer_path).name, pat_str=r"(?i:'s|'t|'re|'ve|'m|'ll|'d)|[^\r\n\p {L}\p {N}]?\p {L}+|\p {N}{1,3}| ?[^\s\p {L}\p {N}]+[\r\n]*|\s*[\r\n]+|\s+(?!\S)|\s+", mergeable_ranks=mergeable_ranks, special_tokens={token: len (mergeable_ranks) + i for i, token in enumerate (special_tokens)},)tokenizer.decode (tokenizer.encode ("hello world!"))
上述步骤完成后，就是读取模型文件了。由于该研究是从头开始实现 llama3，因此代码一次只读取一个张量文件。
model = torch.load ("Meta-Llama-3-8B/consolidated.00.pth")print (json.dumps (list (model.keys ())[:20], indent=4))
[ "tok_embeddings.weight", "layers.0.attention.wq.weight", "layers.0.attention.wk.weight", "layers.0.attention.wv.weight", "layers.0.attention.wo.weight", "layers.0.feed_forward.w1.weight", "layers.0.feed_forward.w3.weight", "layers.0.feed_forward.w2.weight", "layers.0.attention_norm.weight", "layers.0.ffn_norm.weight", "layers.1.attention.wq.weight", "layers.1.attention.wk.weight", "layers.1.attention.wv.weight", "layers.1.attention.wo.weight", "layers.1.feed_forward.w1.weight", "layers.1.feed_forward.w3.weight", "layers.1.feed_forward.w2.weight", "layers.1.attention_norm.weight", "layers.1.ffn_norm.weight", "layers.2.attention.wq.weight"]
with open
("Meta-Llama-3-8B/params.json", "r") as f: config = json.load (f)config
{'dim': 4096, 'n_layers': 32, 'n_heads': 32, 'n_kv_heads': 8, 'vocab_size': 128256, 'multiple_of': 1024, 'ffn_dim_multiplier': 1.3, 'norm_eps': 1e-05, 'rope_theta': 500000.0}
模型有 32 个 transformer 层；
每个多头注意力块有 32 个头。
dim = config ["dim"]n_layers = config ["n_layers"]n_heads = config ["n_heads"]n_kv_heads = config ["n_kv_heads"]vocab_size = config ["vocab_size"]multiple_of = config ["multiple_of"]ffn_dim_multiplier = config ["ffn_dim_multiplier"]norm_eps = config ["norm_eps"]rope_theta = torch.tensor (config ["rope_theta"])
接下来的操作是将文本装换为 token，这里作者使用的是 tiktoken 库（一个用于 OpenAI 模型的 BPE tokeniser）。
prompt = "the answer to the ultimate question of life, the universe, and everything is"tokens = [128000] + tokenizer.encode (prompt)print (tokens)tokens = torch.tensor (tokens)prompt_split_as_tokens = [tokenizer.decode ([token.item ()]) for token in tokens]print (prompt_split_as_tokens)
[
128000, 1820, 4320, 311, 279, 17139, 3488, 315, 2324, 11, 279, 15861, 11, 323, 4395, 374, 220]['', 'the', ' answer', ' to', ' the', ' ultimate', ' question', ' of', ' life', ',', ' the', ' universe', ',', ' and', ' everything', ' is', ' ']
embedding_layer = torch.nn.Embedding (vocab_size, dim)embedding_layer.weight.data.copy_(model ["tok_embeddings.weight"])token_embeddings_unnormalized = embedding_layer (tokens).to (torch.bfloat16)token_embeddings_unnormalized.shape
将嵌入进行归一化。该研究使用均方根 RMS 算法进行归一化。不过，在这一步之后，张量形状不会改变，只是值进行了归一化。
# def rms_norm (tensor, norm_weights):# rms = (tensor.pow (2).mean (-1, keepdim=True) + norm_eps)**0.5# return tensor * (norm_weights /rms)def rms_norm (tensor, norm_weights): return (tensor * torch.rsqrt (tensor.pow (2).mean (-1, keepdim=True) + norm_eps)) * norm_weights
构建 transformer 第一层。完成上述准备后，接着是构建 transformer 第一层：从模型文件中访问 layer.0（即第一层），归一化后嵌入维度仍然是 [17x4096] 。
token_embeddings = rms_norm (token_embeddings_unnormalized, model ["layers.0.attention_norm.weight"])token_embeddings.shape
从头开始实现注意力。加载第一层 transformer 的注意力头：
print ( model ["layers.0.attention.wq.weight"].shape, model ["layers.0.attention.wk.weight"].shape, model ["layers.0.attention.wv.weight"].shape, model ["layers.0.attention.wo.weight"].shape)torch.Size ([4096, 4096]) torch.Size ([1024, 4096]) torch.Size ([1024, 4096]) torch.Size ([4096, 4096])
展开查询。展开来自多个注意力头的查询，得到的形状是 [32x128x4096]，这里，32 是 llama3 中注意力头的数量，128 是查询向量的大小，4096 是 token 嵌入的大小。
q_layer0 = model ["layers.0.attention.wq.weight"]head_dim = q_layer0.shape [0] //n_headsq_layer0 = q_layer0.view (n_heads, head_dim, dim)q_layer0.shape
torch.Size ([32, 128, 4096])
从头实现第一层的第一个头。访问第一层的查询权重矩阵，大小是 [128x4096]。
q_layer0_head0 = q_layer0 [0]q_layer0_head0.shape
将查询权重与 token 嵌入相乘，从而得到 token 的查询，在这里你可以看到结果大小是 [17x128]。
q_per_token = torch.matmul (token_embeddings, q_layer0_head0.T)q_per_token.shape
定位编码。现在处于这样一个阶段，即对提示符中的每个 token 都有一个查询向量，但是考虑单个查询向量，我们不知道其提示符中的位置。作者使用了 RoPE（旋转位置嵌入）来解决。
q_per_token_split_into_pairs = q_per_token.float ().view (q_per_token.shape [0], -1, 2)q_per_token_split_into_pairs.shape
在上面的步骤中，该研究将查询向量分成对，并对每对应用旋转角度移位。
zero_to_one_split_into_64_parts = torch.tensor (range (64))/64zero_to_one_split_into_64_parts
tensor ([0.0000, 0.0156, 0.0312, 0.0469, 0.0625, 0.0781, 0.0938, 0.1094, 0.1250, 0.1406, 0.1562, 0.1719, 0.1875, 0.2031, 0.2188, 0.2344, 0.2500, 0.2656, 0.2812, 0.
2969, 0.3125, 0.3281, 0.3438, 0.3594, 0.3750, 0.3906, 0.4062, 0.4219, 0.4375, 0.4531, 0.4688, 0.4844, 0.5000, 0.5156, 0.5312, 0.5469, 0.5625, 0.5781, 0.5938, 0.6094, 0.6250, 0.6406, 0.6562, 0.6719, 0.6875, 0.7031, 0.7188, 0.7344, 0.7500, 0.7656, 0.7812, 0.7969, 0.8125, 0.8281, 0.8438, 0.8594, 0.8750, 0.8906, 0.9062, 0.9219, 0.9375, 0.9531, 0.9688, 0.9844])
freqs = 1.0 / (rope_theta ** zero_to_one_split_into_64_parts)freqs
tensor ([1.0000e+00, 8.1462e-01, 6.6360e-01, 5.4058e-01, 4.4037e-01, 3.5873e-01, 2.9223e-01, 2.3805e-01, 1.9392e-01, 1.5797e-01, 1.2869e-01, 1.0483e-01, 8.5397e-02, 6.9566e-02, 5.6670e-02, 4.6164e-02, 3.7606e-02,
3.0635e-02, 2.4955e-02, 2.0329e-02, 1.6560e-02, 1.3490e-02, 1.0990e-02, 8.9523e-03, 7.2927e-03, 5.9407e-03, 4.8394e-03, 3.9423e-03, 3.2114e-03, 2.6161e-03, 2.1311e-03, 1.7360e-03, 1.4142e-03, 1.1520e-03, 9.3847e-04, 7.6450e-04, 6.2277e-04, 5.0732e-04, 4.1327e-04, 3.3666e-04, 2.7425e-04, 2.2341e-04, 1.8199e-04, 1.4825e-04, 1.2077e-04, 9.8381e-05, 8.0143e-05, 6.5286e-05, 5.3183e-05, 4.3324e-05, 3.5292e-05, 2.8750e-05, 2.3420e-05, 1.9078e-05, 1.5542e-05, 1.2660e-05, 1.0313e-05, 8.4015e-06, 6.8440e-06, 5.5752e-06, 4.5417e-06, 3.6997e-06, 3.0139e-06, 2.4551e-06])
freqs_for_each_token = torch.outer (torch.arange (17), freqs)freqs_cis = torch.polar (torch.ones_like (freqs_for_each_token), freqs_for_each_token)freqs_cis.shape# viewing tjhe third row of freqs_cisvalue = freqs_cis [3]plt.figure ()for i, element in enumerate (value [:17]): plt.plot ([0, element.real], [0, element.imag], color='blue', linewidth=1, label=f"Index: {i}")
plt.annotate (f"{i}", xy=(element.real, element.imag), color='red') plt.xlabel ('Real') plt.ylabel ('Imaginary') plt.title ('Plot of one row of freqs_cis') plt.show ()
q_per_token_as_complex_numbers = torch.view_as_complex (q_per_token_split_into_pairs)q_per_token_as_complex_numbers.shape
q_per_token_as_complex_numbers_rotated = q_per_token_as_complex_numbers * freqs_cisq_per_token_as_complex_numbers_rotated.shape
q_per_token_split_into_pairs_rotated = torch.view_as_real (q_per_token_as_complex_numbers_rotated)q_per_token_split_into_pairs_rotated.shape
现在有了一个新的查询向量 (旋转查询向量)，形状为 [17x128]，其中 17 是 token 数量，128 是查询向量的维度。q_per_token_rotated = q_per_token_split_into_pairs_rotated.view (q_per_token.shape)q_per_token_rotated.shape
键（几乎和查询一样），键也生成维度为 128 的键向量。键的权重只有查询的 1/4，这是因为键的权重在 4 个头之间共享，以减少所需的计算量，键也会被旋转以添加位置信息，就像查询一样。
k_layer0 = model ["layers.0.attention.wk.weight"]
k_layer0 = k_layer0.view (n_kv_heads, k_layer0.shape [0] //n_kv_heads, dim)k_layer0.shape
torch.Size ([8, 128, 4096])
k_layer0_head0 = k_layer0 [0]k_layer0_head0.shape
k_per_token = torch.matmul (token_embeddings, k_layer0_head0.T)k_per_token.shape
k_per_token_split_into_pairs = k_per_token.float ().view (k_per_token.shape [0], -1, 2)k_per_token_split_into_pairs.shape
k_per_token_as_complex_numbers = torch.view_as_complex (k_per_token_split_into_pairs)k_per_token_as_complex_numbers.shape
k_per_token_split_into_pairs_rotated = torch.view_as_real (k_per_token_as_complex_numbers * freqs_cis)k_per_token_split_into_pairs_rotated.shape
k_per_token_rotated = k_per_token_split_into_pairs_rotated.view (k_per_token.shape)k_per_token_rotated.shape
每个 token 查询和键的旋转值如下，每个查询和键现在的形状都是 [17x128]。
接下来一步是将查询和键矩阵相乘。注意力得分矩阵 (qk_per_token) 的形状为 [17x17]，其中 17 是提示中 token 的数量。
qk_per_token = torch.matmul (q_per_token_rotated, k_per_token_rotated.T)/(head_dim)**0.5
qk_per_token.shape
在 llama3 的训练过程中，未来 token 的 qk 分数被掩蔽。这是因为在训练期间，只学习使用过去的 token 来预测未来的 token。因此在推理过程中，将未来的 token 标记为零。
def display_qk_heatmap (qk_per_token): _, ax = plt.subplots () im = ax.imshow (qk_per_token.to (float).detach (), cmap='viridis') ax.set_xticks (range (len (prompt_split_as_tokens))) ax.set_yticks (range (len (prompt_split_as_tokens))) ax.set_xticklabels (prompt_split_as_tokens) ax.set_yticklabels (prompt_split_as_tokens) ax.figure.colorbar (im, ax=ax)
display_qk_heatmap (qk_per_token)
mask = torch.full ((len (tokens), len (tokens)), float ("-inf"), device=tokens.device) mask = torch.triu (mask, diagonal=1) mask
tensor ([[0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf, -inf],
[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf, -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -inf], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
qk_per_token_after_masking = qk_per_token + maskdisplay_qk_heatmap (qk_per_token_after_masking)
qk_per_token_after_masking_after_softmax = torch.nn.functional.softmax (qk_per_token_after_masking, dim=1).to (torch.bfloat16) display_qk_heatmap (qk_per_token_after_masking_after_softmax)
值（几乎在注意力结束时）
这些分数 (0-1) 被用于确定每个 token 使用了多少值矩阵。
v_layer0 = model ["layers.0.attention.wv.weight"] v_layer0 = v_layer0.view (n_kv_heads, v_layer0.shape [0] //n_kv_heads, dim) v_layer0.shape
torch.Size ([8, 128, 4096])
v_layer0_head0 = v_layer0 [0] v_layer0_head0.shape
现在使用值权重来获取每个 token 的注意力值，其大小为 [17x128]，其中 17 为提示中的 token 数，128 为每个 token 的值向量维数。v_per_token = torch.matmul (token_embeddings, v_layer0_head0.T)v_per_token.shape
与每个 token 的值相乘后得到的注意力向量的形状为 [17*128]。
qkv_attention = torch.matmul (qk_per_token_after_masking_after_softmax, v_per_token) qkv_attention.shape
接下来运行一个循环并执行与上面单元完全相同的数学运算，不过第一层中的每个头除外。qkv_attention_store = []for head in range (n_heads): q_layer0_head = q_layer0 [head] k_layer0_head = k_layer0 [head//4] # key weights are shared across 4 heads
v_layer0_head = v_layer0 [head//4] # value weights are shared across 4 headsq_per_token = torch.matmul (token_embeddings, q_layer0_head.T) k_per_token = torch.matmul (token_embeddings, k_layer0_head.T) v_per_token = torch.matmul (token_embeddings, v_layer0_head.T)
q_per_token_split_into_pairs = q_per_token.float ().view (q_per_token.shape [0], -1, 2) q_per_token_as_complex_numbers = torch.view_as_complex (q_per_token_split_into_pairs) q_per_token_split_into_pairs_rotated = torch.view_as_real (q_per_token_as_complex_numbers * freqs_cis [:len (tokens)]) q_per_token_rotated = q_per_token_split_into_pairs_rotated.view (q_per_token.shape)
k_per_token_split_into_pairs = k_per_token.float ().view (k_per_token.shape [0], -1, 2) k_per_token_as_complex_numbers = torch.view_as_complex (k_per_token_split_into_pairs) k_per_token_split_into_pairs_rotated = torch.view_as_real (k_per_token_as_complex_numbers * freqs_cis [:len (tokens)]) k_per_token_rotated = k_per_token_split_into_pairs_rotated.view (k_per_token.shape)
qk_per_token = torch.matmul (q_per_token_rotated, k_per_token_rotated.T)/(128)**0.5mask = torch.full ((len (tokens), len (tokens)), float ("-inf"), device=tokens.device) mask = torch.triu (mask, diagonal=1) qk_per_token_after_masking = qk_per_token + maskqk_per_token_after_masking_after_softmax = torch.nn.functional.softmax (qk_per_token_after_masking, dim=1).to (torch.bfloat16) qkv_attention = torch.matmul (qk_per_token_after_masking_after_softmax, v_per_token) qkv_attention = torch.matmul (qk_per_token_after_masking_after_softmax, v_per_token) qkv_attention_store.append (qkv_attention)len (qkv_attention_store)
现在第一层上的所有 32 个头都有了 qkv_attention 矩阵，并在快结束的时候将所有注意力分数合并为一个大小为 [17x4096] 的大矩阵。stacked_qkv_attention = torch.cat (qkv_attention_store, dim=-1) stacked_qkv_attention.shape
第 0 层注意力要做的最后一件事是，对以下的权重矩阵进行乘法操作。
w_layer0 = model ["layers.0.attention.wo.weight"] w_layer0.shape
torch.Size ([4096, 4096])
这是一个简单的线性层，所以只做矩阵乘法（matmul）。
embedding_delta = torch.matmul (stacked_qkv_attention, w_layer0.T) embedding_delta.shape
现在，注意力之后的嵌入值有了变化，并应该被添加到原始 token 嵌入中。
embedding_after_edit = token_embeddings_unnormalized + embedding_deltaembedding_after_edit.shape
归一化并在嵌入 delta 过程中运行一个前馈神经网络。
embedding_after_edit_normalized = rms_norm (embedding_after_edit, model ["layers.0.ffn_norm.weight"]) embedding_after_edit_normalized.shape
llama3 使用 SwiGLU前馈网络，该网络架构非常擅长在模型需要时添加非线性。当前，在 LLMs 中使用这一前馈网络是非常标准的做法。
w1 = model ["layers.0.feed_forward.w1.weight"] w2 = model ["layers.0.feed_forward.w2.weight"] w3 = model ["layers.0.feed_forward.w3.weight"] output_after_feedforward = torch.matmul (torch.functional.F.silu (torch.matmul (embedding_after_edit_normalized, w1.T)) * torch.matmul (embedding_after_edit_normalized, w3.T), w2.T) output_after_feedforward.shape
现在终于在第一层之后为每个 token 提供了新的编辑后的嵌入，并且在完成之前只剩下 31 层需要处理（one for loop away）。你可以想象这个编辑后的嵌入拥有在第一层上所有查询的信息。现在每一层将在所问问题上编码越来越复杂的查询，直到得到的嵌入了解所需的下一个 token 的一切。
layer_0_embedding = embedding_after_edit+output_after_feedforwardlayer_0_embedding.shape
final_embedding = token_embeddings_unnormalizedfor layer in range (n_layers): qkv_attention_store = [] layer_embedding_norm = rms_norm (final_embedding, model [f"layers.{layer}.attention_norm.weight"]) q_layer = model [f"layers.{layer}.attention.wq.weight"] q_layer = q_layer.view (n_heads, q_layer.shape [0] //n_heads, dim) k_layer = model [f"layers.{layer}.attention.wk.weight"] k_layer = k_layer.view (n_kv_heads, k_layer.shape [0] //n_kv_heads, dim) v_layer = model [f"layers.{layer}.attention.wv.weight"] v_layer = v_layer.view (n_kv_heads, v_layer.shape [0] //n_kv_heads, dim) w_layer
= model [f"layers.{layer}.attention.wo.weight"] for head in range (n_heads): q_layer_head = q_layer [head] k_layer_head = k_layer [head//4] v_layer_head = v_layer [head//4] q_per_token = torch.matmul (layer_embedding_norm, q_layer_head.T) k_per_token = torch.matmul (layer_embedding_norm, k_layer_head.T) v_per_token = torch.matmul (layer_embedding_norm, v_layer_head.T) q_per_token_split_into_pairs = q_per_token.float ().view (q_per_token.shape [0], -1, 2) q_per_token_as_complex_numbers = torch.view_as_complex (q_per_token_split_into_pairs) q_per_token_split_into_pairs_rotated = torch.view_as_real (q_per_token_as_complex_numbers * freqs_cis) q_per_token_rotated = q_per_token_split_into_pairs_rotated.view (q_per_token.shape) k_per_token_split_into_pairs = k_per_token.float ().view (k_per_token.shape [0], -1, 2) k_per_token_as_complex_numbers = torch.view_as_complex (k_per_token_split_into_pairs) k_per_token_split_into_pairs_rotated = torch.view_as_real (k_per_token_as_complex_numbers * freqs_cis) k_per_token_rotated = k_per_token_split_into_pairs_rotated.view (k_per_token.shape) qk_per_token = torch.matmul (q_per_token_rotated, k_per_token_rotated.T)/(128)**0.5 mask = torch.full ((len (token_embeddings_unnormalized), len (token_embeddings_unnormalized)), float ("-inf")) mask = torch.triu (mask, diagonal=1) qk_per_token_after_masking = qk_per_token + mask qk_per_token_after_masking_after_softmax = torch.nn.functional.softmax (qk_per_token_after_masking, dim=1).to (torch.bfloat16) qkv_attention = torch.matmul (qk_per_token_after_masking_after_softmax, v_per_token) qkv_attention_store.append (qkv_attention)
stacked_qkv_attention = torch.cat (qkv_attention_store, dim=-1) w_layer = model [f"layers.{layer}.attention.wo.weight"] embedding_delta = torch.matmul (stacked_qkv_attention, w_layer.T) embedding_after_edit = final_embedding + embedding_delta embedding_after_edit_normalized = rms_norm (embedding_after_edit, model [f"layers.{layer}.ffn_norm.weight"]) w1 = model [f"layers.{layer}.feed_forward.w1.weight"] w2 = model [f"layers.{layer}.feed_forward.w2.weight"] w3 = model [f"layers.{layer}.feed_forward.w3.weight"] output_after_feedforward = torch.matmul (torch.functional.F.silu (torch.matmul (embedding_after_edit_normalized, w1.T)) * torch.matmul (embedding_after_edit_normalized, w3.T), w2.T) final_embedding = embedding_after_edit+output_after_feedforward
现在有了最终的嵌入，即该模型对下一个 token 的最佳猜测。该嵌入的形状与常见的 token 嵌入 [17x4096] 相同，其中 17 为 token 数，4096 为嵌入维数。
final_embedding = rms_norm (final_embedding, model ["norm.weight"]) final_embedding.shape
使用该输入解码器将最终的嵌入转换为一个 token。
model ["output.weight"].shape
torch.Size ([128256, 4096])
使用最后 token 的嵌入来预测下一个值。在示例中，42 是「生命、宇宙和万物终极问题的答案是什么」的答案，根据《银河系漫游指南》一书，大多数现代 LLMs 都会回答 42，应该验证了整个代码。
logits = torch.matmul (final_embedding [-1], model ["output.weight"].T) logits.shape
模型预测 token 数 2983 为下一个 token，这是 42 的 token 数吗？以下是最后的代码单元。
next_token = torch.argmax (logits, dim=-1) next_token
tokenizer.decode ([next_token.item ()])
