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def activation_memory(
a, # attention heads
b, # micro batch size
h, # hidden dimension size
h_ff, # feedforward dimension size (often h_ff = 4h)
L, # number of layers
s, # sequence length
mixed=True,
recomputation="none"
):
# https://arxiv.org/pdf/2205.05198
if mixed:
bytes_per_value = 2
else:
bytes_per_value = 4
one_layer_attention = s * b * h * (bytes_per_value * 5 + 1) + ((2 * bytes_per_value + 1) * a * s * s * b) # eq (2)
one_layer_feedforward_mlp = (s * b * h * bytes_per_value + (s * b * h_ff * bytes_per_value) # inputs of 1st/2nd linear layers
+ s * b * h_ff * bytes_per_value # inputs of activation function (not really necessary for Relu though)
+ s * b * h) # dropout
one_layer_feedforward_swiglu = (s * b * h * bytes_per_value + (s * b * h_ff * bytes_per_value) # inputs of input/output linear layers
+ s * b * h_ff * bytes_per_value * 3 # inputs of activation function
+ s * b * h) # dropout (note that dropout is lower-precision - boolean)
if recomputation == "none":
one_layer = one_layer_attention # eq (2)
elif recomputation =="selective":
one_layer = s * b * h * 34 # eq (6)
elif recomputation =="full":
one_layer = s * b * h * 2
else:
raise ValueError()
input_dropout = 0 # s * b * h # section 4.3
total = L * one_layer + input_dropout
return total
def param_grads_opt(
h, # hidden dimension size
L, # number of layers
s, # sequence length
v, # vocab size
k=8, # parameters for optimizer (Adam: 8 = 4 bytes moments + 4 bytes variance)
mixed=True # mixed precision training
):
# https://michaelwornow.net/2024/01/18/counting-params-in-transformer
# note: this is without GQA or MQA
emb = h*(v+s)
one_layer = 12 * h**2 + 13*h
other = 2*h
n = emb + L * one_layer + other
# 3.1 https://arxiv.org/pdf/1910.02054
if mixed:
k += 4 # additional full precision weights
bytes_per_paramter = 2
else:
bytes_per_paramter = 4
return bytes_per_paramter*n, bytes_per_paramter*n, k*n
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