llama3 implemented from scratch
in this file, i implemented llama3 from scratch, one tensor and matrix multiplication at a time.
also, im going to load tensors directly from the model file that meta provided for llama3, you need to download the weights before running this file. here is the offical link to download the weights: https://llama.meta.com/llama-downloads/
tokenizer
im not going to implement a bpe tokenizer (but andrej karpathy has a really clean implementation)
link to his implementation: https://github.com/karpathy/minbpe
from pathlib import Path import tiktoken from tiktoken . load import load_tiktoken_bpe import torch import json import matplotlib . pyplot as plt tokenizer_path = "Meta-Llama-3-8B/tokenizer.model" special_tokens = [ "<|begin_of_text|>" , "<|end_of_text|>" , "<|reserved_special_token_0|>" , "<|reserved_special_token_1|>" , "<|reserved_special_token_2|>" , "<|reserved_special_token_3|>" , "<|start_header_id|>" , "<|end_header_id|>" , "<|reserved_special_token_4|>" , "<|eot_id|>" , # end of turn ] + [ f"<|reserved_special_token_ { 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
\p{L}\p{N}]?\p{L}+|\p{N}{1,3}| ?[^\s\p{L}\p{N}]+[\r
]*|\s*[\r
]+|\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!" ))
'hello world!'
reading the model file
normally, reading this depends on how the model classes are written and the variable names inside them.
but since we are implementing llama3 from scratch we will read the file one tensor at a time.
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}
we use this config to infer details about the model like
the model has 32 transformer layers each multi-head attention block has 32 heads the vocab size and so on
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" ])
converting text to tokens
here we use tiktoken (i think an openai library) as the tokenizer
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] ['<|begin_of_text|>', 'the', ' answer', ' to', ' the', ' ultimate', ' question', ' of', ' life', ',', ' the', ' universe', ',', ' and', ' everything', ' is', ' ']
converting tokens to their embedding
IM SORRY but this is the only part of the codebase where i use an inbuilt neural network module
anyway, so our [17x1] tokens are now [17x4096], i.e. 17 embeddings (one for each token) of length 4096
note: keep track of the shapes, it makes it much easier to understand everything
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
torch.Size([17, 4096])
we then normalize the embedding using rms normalization
please, note after this step the shapes dont change, the values are just normalized
things to keep in mind, we need a norm_eps (from config) because we dont want to accidently set rms to 0 and divide by 0
here is the formula:
# 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
building the first first layer of the transformer
normalization
you will see me accessing layer.0 from the model dict (this is the first layer)
anyway, so after normalizing our shapes are still [17x4096] same as embedding but normalized
token_embeddings = rms_norm ( token_embeddings_unnormalized , model [ "layers.0.attention_norm.weight" ]) token_embeddings . shape
torch.Size([17, 4096])
attention implemented from scratch
let's load the attention heads of the first layer of the transformer
> when we load the query, key, value and output vectors from the model we notice the shapes to be [4096x4096], [1024x4096], [1024x4096], [4096x4096]
> at first glance this is weird because ideally we want each q,k,v and o for each head individually
> the authors of the code bundled them togeather because its easy it helps parallize attention head multiplication.
> im going to unwrap everything...
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])
unwrapping query
in the next section we will unwrap the queries from multiple attention heads, the resulting shape is [32x128x4096]
here, 32 is the number of attention heads in llama3, 128 is the size of the query vector and 4096 is the size of the token embedding
q_layer0 = model [ "layers.0.attention.wq.weight" ] head_dim = q_layer0 . shape [ 0 ] // n_heads q_layer0 = q_layer0 . view ( n_heads , head_dim , dim ) q_layer0 . shape
torch.Size([32, 128, 4096])
im going to implement the first head of the first layer
here i access the query weight matrix first head of the first layer, the size of this query weight matrix is [128x4096]
q_layer0_head0 = q_layer0 [ 0 ] q_layer0_head0 . shape
torch.Size([128, 4096])
we now multiply the query weights with the token embedding, to recive a query for the token
here you can see the resulting shape is [17x128], this is because we have 17 tokens and for each token there is a 128 length query.
q_per_token = torch . matmul ( token_embeddings , q_layer0_head0 . T ) q_per_token . shape
torch.Size([17, 128])
positioning encoding
we are now at a stage where we have a query vector for each token in our prompt, but if you think about it -- the indivitually query vector has no idea about the position in the prompt.
query: "the answer to the ultimate question of life, the universe, and everything is "
in our prompt we have used "the" three times, we need the query vectors of all 3 "the" tokens to have different query vectors (each of size [1x128]) based on their positions in the query. we perform these rotations using RoPE (rotory positional embedding).
RoPE
watch this video (this is what i watched) to understand the math. https://www.youtube.com/watch?v=o29P0Kpobz0&t=530s
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
torch.Size([17, 64, 2])
in the above step, we split the query vectors into pairs, we apply a rotational angle shift to each pair!
we now have a vector of size [17x64x2], this is the 128 length queries split into 64 pairs for each token in the prompt! each of those 64 pairs will be rotated by m*(theta) where m is the position of the token for which we are rotating the query!
using dot product of complex numbers to rotate a vector
zero_to_one_split_into_64_parts = torch . tensor ( range ( 64 )) / 64 zero_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_cis value = 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 ()
now that we have a complex number (the angle change vector) for every token's query element
we can convert our queries (the one we split into pairs) as complex numbers and then dot product to rotate the query based on the position
honeslty this is beautiful to think about :)
q_per_token_as_complex_numbers = torch . view_as_complex ( q_per_token_split_into_pairs ) q_per_token_as_complex_numbers . shape
torch.Size([17, 64])
q_per_token_as_complex_numbers_rotated = q_per_token_as_complex_numbers * freqs_cis q_per_token_as_complex_numbers_rotated . shape
torch.Size([17, 64])
after rotated vector is obtained
we can get back our the queries as pairs by viewing the complex numbers as real numbers again
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
torch.Size([17, 64, 2])
the rotated pairs are now merged, we now have a new query vector (rotated query vector) that is of the shape [17x128] where 17 is the number of tokens and the 128 is the dim of the query vector
q_per_token_rotated = q_per_token_split_into_pairs_rotated . view ( q_per_token . shape ) q_per_token_rotated . shape
torch.Size([17, 128])
keys (almost the same as queries)
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
torch.Size([128, 4096])
k_per_token = torch . matmul ( token_embeddings , k_layer0_head0 . T ) k_per_token . shape
torch.Size([17, 128])
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
torch.Size([17, 64, 2])
k_per_token_as_complex_numbers = torch . view_as_complex ( k_per_token_split_into_pairs ) k_per_token_as_complex_numbers . shape
torch.Size([17, 64])
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
torch.Size([17, 64, 2])
k_per_token_rotated = k_per_token_split_into_pairs_rotated . view ( k_per_token . shape ) k_per_token_rotated . shape
torch.Size([17, 128])
at this stage now have both the rotated values of queries and keys, for each token.
in the next step we will multiply the queries and key matrices
doing this will give us a score mapping each token with one another
this score describes how well each token's query relates to the each tokens's key. THIS IS SELF ATTENTION :)
the shape of the attention score matrix (qk_per_token) is [17x17] where 17 is the number of tokens in the prompt
qk_per_token = torch . matmul ( q_per_token_rotated , k_per_token_rotated . T ) / ( head_dim ) ** 0.5 qk_per_token . shape
torch.Size([17, 17])
we now have to mask query key scores
during the training process of llama3, the future token qk scores are masked.
why? because during training we only learn to predict tokens using past tokens.
as a result, during inference we set the future tokens to zero.
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 + mask display_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 )
values (almost the end of attention)
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])
the first layer, first head value weight matrix is given below
v_layer0_head0 = v_layer0 [ 0 ] v_layer0_head0 . shape
torch.Size([128, 4096])
value vectors
v_per_token = torch . matmul ( token_embeddings , v_layer0_head0 . T ) v_per_token . shape
torch.Size([17, 128])
attention
qkv_attention = torch . matmul ( qk_per_token_after_masking_after_softmax , v_per_token ) qkv_attention . shape
torch.Size([17, 128])
multi head attention
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 heads q_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 ) ** 0.5 mask = 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 + 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 = torch . matmul ( qk_per_token_after_masking_after_softmax , v_per_token ) qkv_attention_store . append ( qkv_attention ) len ( qkv_attention_store )
32
stacked_qkv_attention = torch . cat ( qkv_attention_store , dim = - 1 ) stacked_qkv_attention . shape
torch.Size([17, 4096])
weight matrix, one of the final steps
w_layer0 = model [ "layers.0.attention.wo.weight" ] w_layer0 . shape
torch.Size([4096, 4096])
this is a simple linear layer, so we just matmul
embedding_delta = torch . matmul ( stacked_qkv_attention , w_layer0 . T ) embedding_delta . shape
torch.Size([17, 4096])
embedding_after_edit = token_embeddings_unnormalized + embedding_delta embedding_after_edit . shape
torch.Size([17, 4096])
we normalize and then run a feed forward neural network through the embedding delta
embedding_after_edit_normalized = rms_norm ( embedding_after_edit , model [ "layers.0.ffn_norm.weight" ]) embedding_after_edit_normalized . shape
torch.Size([17, 4096])
loading the ff weights and implementing the feed forward network
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
torch.Size([17, 4096])
WE FINALLY HAVE NEW EDITED EMBEDDINGS FOR EACH TOKEN AFTER THE FIRST LAYER
just 31 more layers to go before we are done (one for loop away)
you can imagine this edited embedding as having information about all queries asked on the first layer
now each layer will encode more and more complex queries on the quesions asked, until we have an embedding that knows everything about the next token that we need.
layer_0_embedding = embedding_after_edit + output_after_feedforward layer_0_embedding . shape
torch.Size([17, 4096])
god, everything all at once
have fun reading :)
final_embedding = token_embeddings_unnormalized for 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
we now have the final embedding, the best guess the model could make about the next token
the shape of the embedding is the same as regular token embeddings [17x4096] where 17 is the number of tokens and 4096 is the embedding dim
final_embedding = rms_norm ( final_embedding , model [ "norm.weight" ]) final_embedding . shape
torch.Size([17, 4096])
finally, lets decode the embedding into the token value
model [ "output.weight" ]. shape
torch.Size([128256, 4096])
we use the embedding of the last token to predict the next value
hopefully in our case, 42 :) note: 42 is the answer to "the answer to the ultimate question of life, the universe, and everything is ", according to the book "hitchhiker's guide to the galaxy", most mordern llms would answer with 42 here, which should validate our entire code! wish me luck :)
logits = torch . matmul ( final_embedding [ - 1 ], model [ "output.weight" ]. T ) logits . shape
torch.Size([128256])
the model predicted token number 2983 as the next token, is this the token number for 42?
IM HYPING YOU UP, this is the last cell of code, hopefully you had fun :)
next_token = torch . argmax ( logits , dim = - 1 ) next_token
tensor(2983)
lets fucking go
tokenizer . decode ([ next_token . item ()])
'42'
thank you, i love you :)
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