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import numpy as np
def multiplication_in_int64(array):
return np.cumprod(np.array(array, dtype=np.int64))[-1]
def matrix_operation(shapeA, shapeB):
assert(shapeA[-1] == shapeB[0])
op = np.cumprod(np.array(shapeA[:-1], np.float64))
return multiplication_in_int64([2, op[-1], shapeA[-1], shapeB[-1]])
def word_embedding_operation(model_config, inference_config):
#Given:
#\begin{itemize}
# \item Matrix \( X \) of size \( B \times s \) (representing the batch size and sequence length respectively).
# \item Embedding matrix \( W_e \) of size \( n_{vocab} \times d_{model} \).
#\end{itemize}
#The resultant matrix after the multiplication will be of size \( B \times s \times d_{model} \).
#For each element in this resultant matrix, the number of FLOPs required is \( 2 \times n_{vocab} \). This is because for a single element in the output matrix, we have \( 2N \) FLOPs (with \( N \) being the common dimension), leading to the matrix multiplication FLOP count as:
#\begin{equation}
#2 \times B \times s \times n_{vocab} \times d_{model}
#\end{equation}
A = [inference_config['batchsize'], inference_config['input_seq_length'], model_config['vocab_size']]
B = [model_config['vocab_size'], model_config['hidden_size']]
return matrix_operation(A, B)
def positional_embedding_operation(model_config, inference_config):
return multiplication_in_int64([inference_config['batchsize'], inference_config['input_seq_length'], model_config['hidden_size']])
### Below three are the same
def attention_K_operation(model_config, inference_config, seq_length):
A = [inference_config['batchsize'], seq_length, model_config['hidden_size']]
B = [model_config['hidden_size'], model_config['hidden_size_per_head']]
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * matrix_operation(A, B)
def attention_Q_operation(model_config, inference_config, seq_length):
A = [inference_config['batchsize'], seq_length, model_config['hidden_size']]
B = [model_config['hidden_size'], model_config['hidden_size_per_head']]
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * matrix_operation(A, B)
def attention_V_operation(model_config, inference_config, seq_length):
A = [inference_config['batchsize'], seq_length, model_config['hidden_size']]
B = [model_config['hidden_size'], model_config['hidden_size_per_head']]
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * matrix_operation(A, B)
##
def attention_QK_operation(model_config, inference_config, seq_length_Q, seq_length_K):
A = [inference_config['batchsize'], seq_length_Q, model_config['hidden_size_per_head']]
B = [model_config['hidden_size_per_head'], seq_length_K]
return model_config['num_hidden_layers'] * model_config['num_attention_heads']* matrix_operation(A, B)
def attention_softmax_operation(model_config, inference_config,seq_length):
# Ref: Ouyang, A. (2023). Understanding the Performance of Transformer Inference (Doctoral dissertation, Massachusetts Institute of Technology).
# 3 is a modeled value
softmax_operation = (3*inference_config['batchsize']*seq_length*seq_length)
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * softmax_operation
def attention_multV_operation(model_config, inference_config, seq_length_Q, seq_length_V):
A = [inference_config['batchsize'], seq_length_Q, seq_length_V]
B = [seq_length_V, model_config['hidden_size_per_head']]
return model_config['num_hidden_layers'] * model_config['num_attention_heads']* matrix_operation(A, B)
def attention_out_operation(model_config, inference_config, seq_length):
A = [inference_config['batchsize'], seq_length, model_config['hidden_size']]
B = [model_config['hidden_size'], model_config['hidden_size']]
return model_config['num_hidden_layers'] * matrix_operation(A, B)
def layernorm_operation(model_config, inference_config, seq_length):
# Ref: Ouyang, A. (2023). Understanding the Performance of Transformer Inference (Doctoral dissertation, Massachusetts Institute of Technology).
# 5 is a modeled value
layernorm_operation = (5*inference_config['batchsize']*seq_length*model_config['hidden_size'])
return model_config['num_hidden_layers'] * model_config['layernorm_operation'] * layernorm_operation
def mlp1_operation(model_config, inference_config, seq_length):
A = [inference_config['batchsize'], seq_length, model_config['hidden_size']]
B = [model_config['hidden_size'], model_config['intermediate_size']]
return model_config['num_hidden_layers'] * matrix_operation(A, B)
def mlp2_operation(model_config, inference_config, seq_length):
A = [inference_config['batchsize'], seq_length, model_config['intermediate_size']]
B = [model_config['intermediate_size'], model_config['hidden_size']]
return model_config['num_hidden_layers'] * matrix_operation(A, B)
def prefilling_operation(model_config, inference_config):
prefilling_operation_count = {}
prefilling_operation_count['word_embedding'] = word_embedding_operation(model_config, inference_config)
prefilling_operation_count['positional_embedding'] = positional_embedding_operation(model_config, inference_config)
prefilling_operation_count['attention_Q'] = attention_Q_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['attention_K'] = attention_K_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['attention_V'] = attention_V_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['attention_QK'] = attention_QK_operation(model_config, inference_config, inference_config['input_seq_length'], inference_config['input_seq_length'])
prefilling_operation_count['attention_softmax'] = attention_softmax_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['attention_multV'] = attention_multV_operation(model_config, inference_config, inference_config['input_seq_length'], inference_config['input_seq_length'])
prefilling_operation_count['attention_out'] = attention_out_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['layernorm'] =layernorm_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['mlp1'] = mlp1_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['mlp2'] = mlp2_operation(model_config, inference_config, inference_config['input_seq_length'])
prefilling_operation_count['embeddings'] = prefilling_operation_count['word_embedding'] + prefilling_operation_count['positional_embedding']
prefilling_operation_count['attention'] = sum([v for k,v in prefilling_operation_count.items() if 'attention' in k])
prefilling_operation_count['mlp'] = prefilling_operation_count['mlp1'] + prefilling_operation_count['mlp2']
prefilling_operation_count['total'] = (prefilling_operation_count['embeddings'] + prefilling_operation_count['attention'] + prefilling_operation_count['mlp'] + prefilling_operation_count['layernorm'])
return prefilling_operation_count
def generation_operation(model_config, inference_config):
generation_operation_count = {}
generation_operation_count['word_embedding'] = 0
generation_operation_count['positional_embedding'] = 0
generation_operation_count['attention_K'] = 0
generation_operation_count['attention_V'] = 0
generation_operation_count['attention_Q'] = 0
generation_operation_count['attention_QK'] = 0
generation_operation_count['attention_softmax'] = 0
generation_operation_count['attention_multV'] = 0
generation_operation_count['attention_out'] = 0
generation_operation_count['mlp1'] = 0
generation_operation_count['mlp2'] = 0
generation_operation_count['layernorm'] = 0
for t in range(inference_config['output_seq_length']):
if inference_config['KV_cache']:
generation_operation_count['attention_K'] += attention_K_operation(model_config, inference_config, 1)
generation_operation_count['attention_V'] += attention_V_operation(model_config, inference_config, 1)
generation_operation_count['attention_Q'] += attention_Q_operation(model_config, inference_config, 1)
generation_operation_count['attention_QK'] += attention_QK_operation(model_config, inference_config, seq_length_Q=1, seq_length_K=(t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_softmax'] += attention_softmax_operation(model_config, inference_config, 1)
generation_operation_count['attention_multV'] += attention_multV_operation(model_config, inference_config, seq_length_Q=1, seq_length_V=(t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_out'] += attention_out_operation(model_config, inference_config, 1)
generation_operation_count['mlp1'] += mlp1_operation(model_config, inference_config, 1)
generation_operation_count['mlp2'] += mlp2_operation(model_config, inference_config, 1)
else:
generation_operation_count['attention_K'] += attention_K_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_V'] += attention_V_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_Q'] += attention_Q_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_QK'] += attention_QK_operation(model_config, inference_config, seq_length_Q=(t+1)+inference_config['input_seq_length'], seq_length_K=(t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_softmax'] += attention_softmax_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_multV'] += attention_multV_operation(model_config, inference_config, seq_length_Q=(t+1)+inference_config['input_seq_length'], seq_length_V=(t+1)+inference_config['input_seq_length'])
generation_operation_count['attention_out'] += attention_out_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['mlp1'] += mlp1_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['mlp2'] += mlp2_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['layernorm'] += layernorm_operation(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
generation_operation_count['embeddings'] = generation_operation_count['word_embedding'] + generation_operation_count['positional_embedding']
generation_operation_count['attention'] = sum([v for k,v in generation_operation_count.items() if 'attention' in k])
generation_operation_count['mlp'] = generation_operation_count['mlp1'] + generation_operation_count['mlp2']
generation_operation_count['total'] = (generation_operation_count['attention'] + generation_operation_count['mlp'] + generation_operation_count['layernorm'])
return generation_operation_count
def word_embedding_activation_memory(model_config, inference_config, seq_length):
return inference_config['batchsize'] * seq_length * (model_config['vocab_size'] + model_config['hidden_size'])
def positional_embedding_activation_memory(model_config, inference_config, seq_length):
return 2 * inference_config['batchsize'] * seq_length * model_config['hidden_size']
def attention_K_activation_memory(model_config, inference_config, seq_length):
per_head_per_layer = inference_config['batchsize'] * seq_length * (model_config['hidden_size'] + model_config['hidden_size_per_head'])
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * per_head_per_layer
def attention_V_activation_memory(model_config, inference_config, seq_length):
per_head_per_layer = inference_config['batchsize'] * seq_length * (model_config['hidden_size'] + model_config['hidden_size_per_head'])
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * per_head_per_layer
def attention_Q_activation_memory(model_config, inference_config, seq_length):
per_head_per_layer = inference_config['batchsize'] * seq_length * (model_config['hidden_size'] + model_config['hidden_size_per_head'])
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * per_head_per_layer
def attention_QK_activation_memory(model_config, inference_config, seq_length_Q, seq_length_K):
inputs_Q = inference_config['batchsize'] * seq_length_Q * model_config['hidden_size_per_head']
inputs_K = inference_config['batchsize'] * seq_length_K * model_config['hidden_size_per_head']
outputs = inference_config['batchsize'] * seq_length_Q * seq_length_K
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * (inputs_Q + inputs_K + outputs)
def attention_softmax_activation_memory(model_config, inference_config, seq_length):
per_head_per_layer = (2 * inference_config['batchsize'] * seq_length * seq_length)
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * per_head_per_layer
def attention_multV_activation_memory(model_config, inference_config, seq_length_Q, seq_length_V):
per_head_per_layer = inference_config['batchsize'] * seq_length_Q * seq_length_V + inference_config['batchsize'] * seq_length_Q * model_config['hidden_size_per_head'] + inference_config['batchsize'] * seq_length_V * model_config['hidden_size_per_head']
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * per_head_per_layer
def attention_out_activation_memory(model_config, inference_config, seq_length):
per_head_per_layer = 2 * inference_config['batchsize'] * seq_length * model_config['hidden_size']
return model_config['num_hidden_layers'] * model_config['num_attention_heads'] * per_head_per_layer
def layernorm_activation_memory(model_config, inference_config, seq_length):
per_layernorm_per_layer = 2 * inference_config['batchsize'] * seq_length * model_config['hidden_size']
return model_config['num_hidden_layers'] * model_config['layernorm_operation'] * per_layernorm_per_layer
def mlp1_activation_memory(model_config, inference_config, seq_length):
per_layer = inference_config['batchsize'] * seq_length * (model_config['hidden_size'] + model_config['intermediate_size'])
return model_config['num_hidden_layers'] * per_layer
def mlp2_activation_memory(model_config, inference_config, seq_length):
per_layer = inference_config['batchsize'] * seq_length * (model_config['intermediate_size'] + model_config['hidden_size'])
return model_config['num_hidden_layers'] * per_layer
def prefilling_activation_memory(model_config, inference_config):
activation_memory = {}
activation_memory['word_embedding'] = word_embedding_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['positional_embedding'] = positional_embedding_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['attention_Q'] = attention_Q_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['attention_K'] = attention_K_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['attention_V'] = attention_V_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['attention_QK'] = attention_QK_activation_memory(model_config, inference_config, inference_config['input_seq_length'], inference_config['input_seq_length'])
activation_memory['attention_softmax'] = attention_softmax_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['attention_multV'] = attention_multV_activation_memory(model_config, inference_config, inference_config['input_seq_length'], inference_config['input_seq_length'])
activation_memory['attention_out'] = attention_out_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['layernorm'] = layernorm_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['mlp1'] = mlp1_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['mlp2'] = mlp2_activation_memory(model_config, inference_config, inference_config['input_seq_length'])
activation_memory['embeddings'] = activation_memory['word_embedding'] + activation_memory['positional_embedding']
activation_memory['attention'] = (
activation_memory['attention_Q'] + activation_memory['attention_K'] +
activation_memory['attention_V'] + activation_memory['attention_QK'] +
activation_memory['attention_softmax'] + activation_memory['attention_multV'] +
activation_memory['attention_out']
)
activation_memory['mlp'] = activation_memory['mlp1'] + activation_memory['mlp2']
activation_memory['total'] = (
activation_memory['embeddings'] + activation_memory['attention'] +
activation_memory['mlp'] + activation_memory['layernorm']
)
activation_memory['embeddings'] = activation_memory['word_embedding'] + activation_memory['positional_embedding']
activation_memory['attention'] = sum([v for k,v in activation_memory.items() if 'attention' in k])
activation_memory['mlp'] = activation_memory['mlp1'] + activation_memory['mlp2']
activation_memory['total'] = (activation_memory['attention'] + activation_memory['mlp'] + activation_memory['layernorm'])
return activation_memory
def generation_activation_memory(model_config, inference_config):
activation_memory = {}
activation_memory['word_embedding'] = 0
activation_memory['positional_embedding'] = 0
activation_memory['attention_K'] = 0
activation_memory['attention_V'] = 0
activation_memory['attention_Q'] = 0
activation_memory['attention_QK'] = 0
activation_memory['attention_softmax'] = 0
activation_memory['attention_multV'] = 0
activation_memory['attention_out'] = 0
activation_memory['mlp1'] = 0
activation_memory['mlp2'] = 0
activation_memory['layernorm'] = 0
for t in range(inference_config['output_seq_length']):
if inference_config['KV_cache']:
activation_memory['attention_K'] += attention_K_activation_memory(model_config, inference_config, 1)
activation_memory['attention_V'] += attention_V_activation_memory(model_config, inference_config, 1)
activation_memory['attention_Q'] += attention_Q_activation_memory(model_config, inference_config, 1)
activation_memory['attention_QK'] += attention_QK_activation_memory(model_config, inference_config, seq_length_Q=1, seq_length_K=(t+1)+inference_config['input_seq_length'])
activation_memory['attention_softmax'] += attention_softmax_activation_memory(model_config, inference_config, 1)
activation_memory['attention_multV'] += attention_multV_activation_memory(model_config, inference_config, seq_length_Q=1, seq_length_V=(t+1)+inference_config['input_seq_length'])
activation_memory['attention_out'] += attention_out_activation_memory(model_config, inference_config, 1)
activation_memory['mlp1'] += mlp1_activation_memory(model_config, inference_config, 1)
activation_memory['mlp2'] += mlp2_activation_memory(model_config, inference_config, 1)
else:
activation_memory['attention_K'] += attention_K_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['attention_V'] += attention_V_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['attention_Q'] += attention_Q_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['attention_QK'] += attention_QK_activation_memory(model_config, inference_config, seq_length_Q=(t+1)+inference_config['input_seq_length'], seq_length_K=(t+1)+inference_config['input_seq_length'])
activation_memory['attention_softmax'] += attention_softmax_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['attention_multV'] += attention_multV_activation_memory(model_config, inference_config, seq_length_Q=(t+1)+inference_config['input_seq_length'], seq_length_V=(t+1)+inference_config['input_seq_length'])
activation_memory['attention_out'] += attention_out_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['mlp1'] += mlp1_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['mlp2'] += mlp2_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['layernorm'] += layernorm_activation_memory(model_config, inference_config, (t+1)+inference_config['input_seq_length'])
activation_memory['embeddings'] = activation_memory['word_embedding'] + activation_memory['positional_embedding']
activation_memory['attention'] = (
activation_memory['attention_K'] + activation_memory['attention_V'] +
activation_memory['attention_Q'] + activation_memory['attention_QK'] +
activation_memory['attention_softmax'] + activation_memory['attention_multV'] +
activation_memory['attention_out']
)
activation_memory['mlp'] = activation_memory['mlp1'] + activation_memory['mlp2']
activation_memory['total'] = (
activation_memory['embeddings'] + activation_memory['attention'] +
activation_memory['mlp'] + activation_memory['layernorm']
)
return activation_memory
def calc_prefilling_throughput(model_config, inference_config, inference_info):
inference_info['prefilling_throughput'] = inference_config['input_seq_length']*inference_config['batchsize'] / max([inference_info['inference_prefilling_time'], inference_info['prefilling_memory_latency']])
inference_info['prefilling_bound_type'] = "memory" if inference_info['inference_prefilling_time'] < inference_info['prefilling_memory_latency'] else "arithmetic"
def calc_generation_throughput(model_config, inference_config, inference_info):
inference_info['generation_throughput'] = inference_config['input_seq_length']*inference_config['batchsize'] / max([inference_info['inference_generation_time'], inference_info['generation_memory_latency']])
inference_info['generation_bound_type'] = "memory" if inference_info['inference_generation_time'] < inference_info['generation_memory_latency'] else "arithmetic"
total_time = max([inference_info['inference_prefilling_time'], inference_info['prefilling_memory_latency']]) + max([inference_info['inference_generation_time'], inference_info['generation_memory_latency']])
inference_info['client_generation_throughput'] = inference_config['output_seq_length']*inference_config['batchsize'] / total_time |