How is the number of BERT model parameters calculated?

[aslicedbread]

I‘m a bit confused about the 110M parameters. How is it calculated?

[superdu12138]

通常情况 transformer 模型有很多参数需要训练。譬如 BERT BASE 模型: L=12, H=768, A=12, 需要训练的模型参数总数是 12 * 768 * 12 = 110M

https://zhuanlan.zhihu.com/p/51413773

[superdu12138]

我对110M参数感到有点困惑。它是如何计算的？

通常情况变压器模型有很多参数需要训练。譬如BERT BASE模型：L = 12，H = 768，A = 12，需要训练的模型参数总数是12 * 768 * 12 = 110M

https://zhuanlan.zhihu.com/p/51413773

[careyee]

12 * 768 * 12 = 110M ？

[laohur]

here is one layer Transformer

#  parameters: 10152448	10152448
weight name: encoder.src_word_emb.weight	size:	[5395, 512]	count:	2762240
weight name: encoder.position_enc.weight	size:	[33, 512]	count:	16896
weight name: encoder.layer_stack.0.slf_attn.w_qs.weight	size:	[512, 512]	count:	262144
weight name: encoder.layer_stack.0.slf_attn.w_qs.bias	size:	[512]	count:	512
weight name: encoder.layer_stack.0.slf_attn.w_ks.weight	size:	[512, 512]	count:	262144
weight name: encoder.layer_stack.0.slf_attn.w_ks.bias	size:	[512]	count:	512
weight name: encoder.layer_stack.0.slf_attn.w_vs.weight	size:	[512, 512]	count:	262144
weight name: encoder.layer_stack.0.slf_attn.w_vs.bias	size:	[512]	count:	512
weight name: encoder.layer_stack.0.slf_attn.layer_norm.weight	size:	[512]	count:	512
weight name: encoder.layer_stack.0.slf_attn.layer_norm.bias	size:	[512]	count:	512
weight name: encoder.layer_stack.0.slf_attn.fc.weight	size:	[512, 512]	count:	262144
weight name: encoder.layer_stack.0.slf_attn.fc.bias	size:	[512]	count:	512
weight name: encoder.layer_stack.0.pos_ffn.w_1.weight	size:	[2048, 512, 1]	count:	1048576
weight name: encoder.layer_stack.0.pos_ffn.w_1.bias	size:	[2048]	count:	2048
weight name: encoder.layer_stack.0.pos_ffn.w_2.weight	size:	[512, 2048, 1]	count:	1048576
weight name: encoder.layer_stack.0.pos_ffn.w_2.bias	size:	[512]	count:	512
weight name: encoder.layer_stack.0.pos_ffn.layer_norm.weight	size:	[512]	count:	512
weight name: encoder.layer_stack.0.pos_ffn.layer_norm.bias	size:	[512]	count:	512
weight name: decoder.tgt_word_emb.weight	size:	[5395, 512]	count:	2762240
weight name: decoder.position_enc.weight	size:	[33, 512]	count:	16896
weight name: decoder.layer_stack.0.slf_attn.w_qs.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.slf_attn.w_qs.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.slf_attn.w_ks.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.slf_attn.w_ks.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.slf_attn.w_vs.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.slf_attn.w_vs.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.slf_attn.layer_norm.weight	size:	[512]	count:	512
weight name: decoder.layer_stack.0.slf_attn.layer_norm.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.slf_attn.fc.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.slf_attn.fc.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.enc_attn.w_qs.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.enc_attn.w_qs.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.enc_attn.w_ks.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.enc_attn.w_ks.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.enc_attn.w_vs.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.enc_attn.w_vs.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.enc_attn.layer_norm.weight	size:	[512]	count:	512
weight name: decoder.layer_stack.0.enc_attn.layer_norm.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.enc_attn.fc.weight	size:	[512, 512]	count:	262144
weight name: decoder.layer_stack.0.enc_attn.fc.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.pos_ffn.w_1.weight	size:	[2048, 512, 1]	count:	1048576
weight name: decoder.layer_stack.0.pos_ffn.w_1.bias	size:	[2048]	count:	2048
weight name: decoder.layer_stack.0.pos_ffn.w_2.weight	size:	[512, 2048, 1]	count:	1048576
weight name: decoder.layer_stack.0.pos_ffn.w_2.bias	size:	[512]	count:	512
weight name: decoder.layer_stack.0.pos_ffn.layer_norm.weight	size:	[512]	count:	512
weight name: decoder.layer_stack.0.pos_ffn.layer_norm.bias	size:	[512]	count:	512
weight name: tgt_word_prj.weight	size:	[5395, 512]	count:	2762240

-- vocab size=5395 seq len=33, embedding=512, you cand replace it with BERT

[liuqiangict]

1. bert-base-uncased, 110M parameters

Bert-base-uncased	Key	Shape	Count
Embedding	embeddings.word_embeddings.weight	[30522, 768]	23,440,896	23,837,184
	embeddings.position_embeddings.weight	[512, 768]	393,216
	embeddings.token_type_embeddings.weight	[2, 768]	1,536
	embeddings.LayerNorm.weight	[768]	768
	embeddings.LayerNorm.bias	[768]	768
Transformer * 12	encoder.layer.0.attention.self.query.weight	[768, 768]	589,824	7,087,872  * 12 = 85,054,464
	encoder.layer.0.attention.self.query.bias	[768]	768
	encoder.layer.0.attention.self.key.weight	[768, 768]	589,824
	encoder.layer.0.attention.self.key.bias	[768]	768
	encoder.layer.0.attention.self.value.weight	[768, 768]	589,824
	encoder.layer.0.attention.self.value.bias	[768]	768
	encoder.layer.0.attention.output.dense.weight	[768, 768]	589,824
	encoder.layer.0.attention.output.dense.bias	[768]	768
	encoder.layer.0.attention.output.LayerNorm.weight	[768]	768
	encoder.layer.0.attention.output.LayerNorm.bias	[768]	768
	encoder.layer.0.intermediate.dense.weight	[3072, 768]	2,359,296
	encoder.layer.0.intermediate.dense.bias	[3072]	3072
	encoder.layer.0.output.dense.weight	[768, 3072]	2,359,296
	encoder.layer.0.output.dense.bias	[768]	768
	encoder.layer.0.output.LayerNorm.weight	[768]	768
	encoder.layer.0.output.LayerNorm.bias	[768]	768
Pooler	pooler.dense.weight	[768, 768]	589,824	590,592
	pooler.dense.bias	[768]	768
				109,482,240

2. bert-large-uncased, 340M parameters

Bert-large-uncased	Key	Shape	Count	Count All
Embedding	embeddings.word_embeddings.weight	[30522, 1024]	31,254,528	31,782,912
	embeddings.position_embeddings.weight	[512, 1024]	524,288
	embeddings.token_type_embeddings.weight	[2, 1024]	2,048
	embeddings.LayerNorm.weight	[1024]	1,024
	embeddings.LayerNorm.bias	[1024]	1,024
Transformer * 24	encoder.layer.0.attention.self.query.weight	[1024, 1024]	1,048,576	12,592,128 * 24 = 302,211,072
	encoder.layer.0.attention.self.query.bias	[1024]	1,024
	encoder.layer.0.attention.self.key.weight	[1024, 1024]	1,048,576
	encoder.layer.0.attention.self.key.bias	[1024]	1,024
	encoder.layer.0.attention.self.value.weight	[1024, 1024]	1,048,576
	encoder.layer.0.attention.self.value.bias	[1024]	1,024
	encoder.layer.0.attention.output.dense.weight	[1024, 1024]	1,048,576
	encoder.layer.0.attention.output.dense.bias	[1024]	1,024
	encoder.layer.0.attention.output.LayerNorm.weight	[1024]	1,024
	encoder.layer.0.attention.output.LayerNorm.bias	[1024]	1,024
	encoder.layer.0.intermediate.dense.weight	[4096, 1024]	4,194,304
	encoder.layer.0.intermediate.dense.bias	[4096]	4,096
	encoder.layer.0.output.dense.weight	[1024, 4096]	4,194,304
	encoder.layer.0.output.dense.bias	[1024]	1,024
	encoder.layer.0.output.LayerNorm.weight	[1024]	1,024
	encoder.layer.0.output.LayerNorm.bias	[1024]	1,024
Pooler	pooler.dense.weight	[1024, 1024]	1,048,576	1,049,600
	pooler.dense.bias	[1024]	1,024
				335,043,584

[hezq06]

So does the attention head number get included?

[oyvistee]

I think the attention head number is chosen such that H / A = 64 for all models, where H is the hidden size and A is the number of attention heads

[amineabdaoui]

Thanks @liuqiangict So the query, key and value weights are shared across all the attention heads of the same layer?

[careyee]

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[jong-won-lee]

Thanks @liuqiangict So the query, key and value weights are shared across all the attention heads of the same layer?

They are different. If they are shared, weight size can be reduced by the number of heads.

[careyee]

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[DongqiShen]

So does the attention head number get included?

Yes, It does. Actually, for each head, the attention layer project input (which is [768]) to a small size (which is [64]). There are 12 heads in attention layer. We can see that 64 * 12 = 768. The implementation in transformer do not have 12 head explicitly, otherwise, 12 head was put together which is one linear layer (768 * 768). For the code, actually, they are the same.