STEP 12 / 18

손실 함수: 너무 확신하지 않게

원본: 정규화 → 레이블 스무딩 · 손실 계산

정답 토큰에 확률 1을 주는 one-hot 대신, 정답에 0.9, 나머지에 0.1을 나눠 준 분포를 목표로 학습한다. 논문은 이를 label smoothing($\epsilon_{ls}=0.1$)이라고 부른다. 모델이 지나치게 확신하지 않게 되어 perplexity는 조금 나빠지지만 정확도와 BLEU는 좋아진다.

LabelSmoothing: 목표 분포 true_dist를 만든 뒤 모델의 로그 확률과의 KL divergence를 손실로 쓴다. - 모든 칸을 smoothing / (size - 2)로 채운다. 2를 빼는 이유는 정답 칸과 패딩 칸을 제외하기 때문이다. - 정답 칸(scatter_)에 confidence = 1 - smoothing을 넣는다. - 패딩 열은 0으로 만들고, 정답 자체가 패딩인 행(문장 뒤 채움)은 통째로 0으로 만들어 손실에서 뺀다.

SimpleLossCompute: generator를 거쳐 손실을 계산하고 토큰 수로 나눈다. 두 값을 돌려준다. 하나는 기록용 합계(sloss.data * norm)이고, 하나는 backward()를 부를 텐서(sloss)다.

실행 결과에서 볼 것

원본의 example_label_smoothing: 정답 칸 0.6, 나머지 0.133씩, 패딩이 정답인 3번째 행은 전부 0이다.
원본의 penalization_visualization: 정답 확률을 계속 키우면 손실이 내려가다가 다시 올라간다. 지나친 확신에 벌점을 준다는 뜻이다.

코드 변화

+43 −0 · 파일 전체 356줄

이전 단계의 transformer.py와 비교했다. 초록 줄이 새로 생긴 줄, 빨간 줄이 사라진 줄이다.

GitHub에서 보기 ↗

실행 결과

실행한 코드 demo.py 보기

1	import altair as alt
2	import pandas as pd
3	import torch
4
5	from show import show
6	from transformer import LabelSmoothing
7
8
9	# 원본 노트북의 example_label_smoothing
10	def example_label_smoothing():
11	crit = LabelSmoothing(5, 0, 0.4)
12	predict = torch.FloatTensor(
13	[
14	[0, 0.2, 0.7, 0.1, 0],
15	[0, 0.2, 0.7, 0.1, 0],
16	[0, 0.2, 0.7, 0.1, 0],
17	[0, 0.2, 0.7, 0.1, 0],
18	[0, 0.2, 0.7, 0.1, 0],
19	]
20	)
21	crit(x=predict.log(), target=torch.LongTensor([2, 1, 0, 3, 3]))
22	print("정답 [2, 1, 0, 3, 3]에 대한 목표 분포 (smoothing=0.4, 0번 = 패딩)")
23	print(crit.true_dist.round(decimals=3))
24	print("→ 정답 칸 0.6, 나머지 0.4를 패딩 아닌 칸 3개에 0.133씩. 정답이 패딩인 3번째 행은 통째로 0")
25	print()
26	LS_data = pd.concat(
27	[
28	pd.DataFrame(
29	{
30	"target distribution": crit.true_dist[x, y].flatten(),
31	"columns": y,
32	"rows": x,
33	}
34	)
35	for y in range(5)
36	for x in range(5)
37	]
38	)
39
40	return (
41	alt.Chart(LS_data)
42	.mark_rect(color="Blue", opacity=1)
43	.properties(height=200, width=200)
44	.encode(
45	alt.X("columns:O", title=None),
46	alt.Y("rows:O", title=None),
47	alt.Color(
48	"target distribution:Q", scale=alt.Scale(scheme="viridis")
49	),
50	)
51	.interactive()
52	)
53
54
55	show(example_label_smoothing(), "label_smoothing")
56
57
58	# 원본 노트북의 penalization_visualization
59	def loss(x, crit):
60	d = x + 3 * 1
61	predict = torch.FloatTensor([[0, x / d, 1 / d, 1 / d, 1 / d]])
62	return crit(predict.log(), torch.LongTensor([1])).data
63
64
65	def penalization_visualization():
66	crit = LabelSmoothing(5, 0, 0.1)
67	loss_data = pd.DataFrame(
68	{
69	"Loss": [loss(x, crit) for x in range(1, 100)],
70	"Steps": list(range(99)),
71	}
72	).astype("float")
73
74	return (
75	alt.Chart(loss_data)
76	.mark_line()
77	.properties(width=350)
78	.encode(
79	x="Steps",
80	y="Loss",
81	)
82	.interactive()
83	)
84
85
86	print("정답 확률을 점점 키울 때 손실 — 너무 확신하면 오히려 손실이 다시 오른다")
87	show(penalization_visualization(), "penalization")

정답 [2, 1, 0, 3, 3]에 대한 목표 분포 (smoothing=0.4, 0번 = 패딩)
tensor([[0.0000, 0.1330, 0.6000, 0.1330, 0.1330],
        [0.0000, 0.6000, 0.1330, 0.1330, 0.1330],
        [0.0000, 0.0000, 0.0000, 0.0000, 0.0000],
        [0.0000, 0.1330, 0.1330, 0.6000, 0.1330],
        [0.0000, 0.1330, 0.1330, 0.6000, 0.1330]])
→ 정답 칸 0.6, 나머지 0.4를 패딩 아닌 칸 3개에 0.133씩. 정답이 패딩인 3번째 행은 통째로 0

차트 불러오는 중…

정답 확률을 점점 키울 때 손실 — 너무 확신하면 오히려 손실이 다시 오른다

차트 불러오는 중…


1	1		import copy
2	2		import math
3	3
4	4		import torch
5	5		import torch.nn as nn
6	6		from torch.nn.functional import log_softmax
7	7
8	8
9	9		def attention(query, key, value, mask=None, dropout=None):
10	10		"Compute 'Scaled Dot Product Attention'"
11	11		d_k = query.size(-1)
12	12		scores = torch.matmul(query, key.transpose(-2, -1)) / math.sqrt(d_k)
13	13		if mask is not None:
14	14		scores = scores.masked_fill(mask == 0, -1e9)
15	15		p_attn = scores.softmax(dim=-1)
16	16		if dropout is not None:
17	17		p_attn = dropout(p_attn)
18	18		return torch.matmul(p_attn, value), p_attn
19	19
20	20
21	21		def subsequent_mask(size):
22	22		"Mask out subsequent positions."
23	23		attn_shape = (1, size, size)
24	24		subsequent_mask = torch.triu(torch.ones(attn_shape), diagonal=1).type(
25	25		torch.uint8
26	26		)
27	27		return subsequent_mask == 0
28	28
29	29
30	30		def clones(module, N):
31	31		"Produce N identical layers."
32	32		return nn.ModuleList([copy.deepcopy(module) for _ in range(N)])
33	33
34	34
35	35		class MultiHeadedAttention(nn.Module):
36	36		def __init__(self, h, d_model, dropout=0.1):
37	37		"Take in model size and number of heads."
38	38		super(MultiHeadedAttention, self).__init__()
39	39		assert d_model % h == 0
40	40		# We assume d_v always equals d_k
41	41		self.d_k = d_model // h
42	42		self.h = h
43	43		self.linears = clones(nn.Linear(d_model, d_model), 4)
44	44		self.attn = None
45	45		self.dropout = nn.Dropout(p=dropout)
46	46
47	47		def forward(self, query, key, value, mask=None):
48	48		"Implements Figure 2"
49	49		if mask is not None:
50	50		# Same mask applied to all h heads.
51	51		mask = mask.unsqueeze(1)
52	52		nbatches = query.size(0)
53	53
54	54		# 1) Do all the linear projections in batch from d_model => h x d_k
55	55		query, key, value = [
56	56		lin(x).view(nbatches, -1, self.h, self.d_k).transpose(1, 2)
57	57		for lin, x in zip(self.linears, (query, key, value))
58	58		]
59	59
60	60		# 2) Apply attention on all the projected vectors in batch.
61	61		x, self.attn = attention(
62	62		query, key, value, mask=mask, dropout=self.dropout
63	63		)
64	64
65	65		# 3) "Concat" using a view and apply a final linear.
66	66		x = (
67	67		x.transpose(1, 2)
68	68		.contiguous()
69	69		.view(nbatches, -1, self.h * self.d_k)
70	70		)
71	71		del query
72	72		del key
73	73		del value
74	74		return self.linears[-1](x)
75	75
76	76
77	77		class PositionwiseFeedForward(nn.Module):
78	78		"Implements FFN equation."
79	79
80	80		def __init__(self, d_model, d_ff, dropout=0.1):
81	81		super(PositionwiseFeedForward, self).__init__()
82	82		self.w_1 = nn.Linear(d_model, d_ff)
83	83		self.w_2 = nn.Linear(d_ff, d_model)
84	84		self.dropout = nn.Dropout(dropout)
85	85
86	86		def forward(self, x):
87	87		return self.w_2(self.dropout(self.w_1(x).relu()))
88	88
89	89
90	90		class Embeddings(nn.Module):
91	91		def __init__(self, d_model, vocab):
92	92		super(Embeddings, self).__init__()
93	93		self.lut = nn.Embedding(vocab, d_model)
94	94		self.d_model = d_model
95	95
96	96		def forward(self, x):
97	97		return self.lut(x) * math.sqrt(self.d_model)
98	98
99	99
100	100		class PositionalEncoding(nn.Module):
101	101		"Implement the PE function."
102	102
103	103		def __init__(self, d_model, dropout, max_len=5000):
104	104		super(PositionalEncoding, self).__init__()
105	105		self.dropout = nn.Dropout(p=dropout)
106	106
107	107		# Compute the positional encodings once in log space.
108	108		pe = torch.zeros(max_len, d_model)
109	109		position = torch.arange(0, max_len).unsqueeze(1)
110	110		div_term = torch.exp(
111	111		torch.arange(0, d_model, 2) * -(math.log(10000.0) / d_model)
112	112		)
113	113		pe[:, 0::2] = torch.sin(position * div_term)
114	114		pe[:, 1::2] = torch.cos(position * div_term)
115	115		pe = pe.unsqueeze(0)
116	116		self.register_buffer("pe", pe)
117	117
118	118		def forward(self, x):
119	119		x = x + self.pe[:, : x.size(1)].requires_grad_(False)
120	120		return self.dropout(x)
121	121
122	122
123	123		class LayerNorm(nn.Module):
124	124		"Construct a layernorm module (See citation for details)."
125	125
126	126		def __init__(self, features, eps=1e-6):
127	127		super(LayerNorm, self).__init__()
128	128		self.a_2 = nn.Parameter(torch.ones(features))
129	129		self.b_2 = nn.Parameter(torch.zeros(features))
130	130		self.eps = eps
131	131
132	132		def forward(self, x):
133	133		mean = x.mean(-1, keepdim=True)
134	134		std = x.std(-1, keepdim=True)
135	135		return self.a_2 * (x - mean) / (std + self.eps) + self.b_2
136	136
137	137
138	138		class SublayerConnection(nn.Module):
139	139		"""
140	140		A residual connection followed by a layer norm.
141	141		Note for code simplicity the norm is first as opposed to last.
142	142		"""
143	143
144	144		def __init__(self, size, dropout):
145	145		super(SublayerConnection, self).__init__()
146	146		self.norm = LayerNorm(size)
147	147		self.dropout = nn.Dropout(dropout)
148	148
149	149		def forward(self, x, sublayer):
150	150		"Apply residual connection to any sublayer with the same size."
151	151		return x + self.dropout(sublayer(self.norm(x)))
152	152
153	153
154	154		class EncoderLayer(nn.Module):
155	155		"Encoder is made up of self-attn and feed forward (defined below)"
156	156
157	157		def __init__(self, size, self_attn, feed_forward, dropout):
158	158		super(EncoderLayer, self).__init__()
159	159		self.self_attn = self_attn
160	160		self.feed_forward = feed_forward
161	161		self.sublayer = clones(SublayerConnection(size, dropout), 2)
162	162		self.size = size
163	163
164	164		def forward(self, x, mask):
165	165		"Follow Figure 1 (left) for connections."
166	166		x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, mask))
167	167		return self.sublayer[1](x, self.feed_forward)
168	168
169	169
170	170		class Encoder(nn.Module):
171	171		"Core encoder is a stack of N layers"
172	172
173	173		def __init__(self, layer, N):
174	174		super(Encoder, self).__init__()
175	175		self.layers = clones(layer, N)
176	176		self.norm = LayerNorm(layer.size)
177	177
178	178		def forward(self, x, mask):
179	179		"Pass the input (and mask) through each layer in turn."
180	180		for layer in self.layers:
181	181		x = layer(x, mask)
182	182		return self.norm(x)
183	183
184	184
185	185		class DecoderLayer(nn.Module):
186	186		"Decoder is made of self-attn, src-attn, and feed forward (defined below)"
187	187
188	188		def __init__(self, size, self_attn, src_attn, feed_forward, dropout):
189	189		super(DecoderLayer, self).__init__()
190	190		self.size = size
191	191		self.self_attn = self_attn
192	192		self.src_attn = src_attn
193	193		self.feed_forward = feed_forward
194	194		self.sublayer = clones(SublayerConnection(size, dropout), 3)
195	195
196	196		def forward(self, x, memory, src_mask, tgt_mask):
197	197		"Follow Figure 1 (right) for connections."
198	198		m = memory
199	199		x = self.sublayer[0](x, lambda x: self.self_attn(x, x, x, tgt_mask))
200	200		x = self.sublayer[1](x, lambda x: self.src_attn(x, m, m, src_mask))
201	201		return self.sublayer[2](x, self.feed_forward)
202	202
203	203
204	204		class Decoder(nn.Module):
205	205		"Generic N layer decoder with masking."
206	206
207	207		def __init__(self, layer, N):
208	208		super(Decoder, self).__init__()
209	209		self.layers = clones(layer, N)
210	210		self.norm = LayerNorm(layer.size)
211	211
212	212		def forward(self, x, memory, src_mask, tgt_mask):
213	213		for layer in self.layers:
214	214		x = layer(x, memory, src_mask, tgt_mask)
215	215		return self.norm(x)
216	216
217	217
218	218		class EncoderDecoder(nn.Module):
219	219		"""
220	220		A standard Encoder-Decoder architecture. Base for this and many
221	221		other models.
222	222		"""
223	223
224	224		def __init__(self, encoder, decoder, src_embed, tgt_embed, generator):
225	225		super(EncoderDecoder, self).__init__()
226	226		self.encoder = encoder
227	227		self.decoder = decoder
228	228		self.src_embed = src_embed
229	229		self.tgt_embed = tgt_embed
230	230		self.generator = generator
231	231
232	232		def forward(self, src, tgt, src_mask, tgt_mask):
233	233		"Take in and process masked src and target sequences."
234	234		return self.decode(self.encode(src, src_mask), src_mask, tgt, tgt_mask)
235	235
236	236		def encode(self, src, src_mask):
237	237		return self.encoder(self.src_embed(src), src_mask)
238	238
239	239		def decode(self, memory, src_mask, tgt, tgt_mask):
240	240		return self.decoder(self.tgt_embed(tgt), memory, src_mask, tgt_mask)
241	241
242	242
243	243		class Generator(nn.Module):
244	244		"Define standard linear + softmax generation step."
245	245
246	246		def __init__(self, d_model, vocab):
247	247		super(Generator, self).__init__()
248	248		self.proj = nn.Linear(d_model, vocab)
249	249
250	250		def forward(self, x):
251	251		return log_softmax(self.proj(x), dim=-1)
252	252
253	253
254	254		def make_model(
255	255		src_vocab, tgt_vocab, N=6, d_model=512, d_ff=2048, h=8, dropout=0.1
256	256		):
257	257		"Helper: Construct a model from hyperparameters."
258	258		c = copy.deepcopy
259	259		attn = MultiHeadedAttention(h, d_model)
260	260		ff = PositionwiseFeedForward(d_model, d_ff, dropout)
261	261		position = PositionalEncoding(d_model, dropout)
262	262		model = EncoderDecoder(
263	263		Encoder(EncoderLayer(d_model, c(attn), c(ff), dropout), N),
264	264		Decoder(DecoderLayer(d_model, c(attn), c(attn), c(ff), dropout), N),
265	265		nn.Sequential(Embeddings(d_model, src_vocab), c(position)),
266	266		nn.Sequential(Embeddings(d_model, tgt_vocab), c(position)),
267	267		Generator(d_model, tgt_vocab),
268	268		)
269	269
270	270		# This was important from their code.
271	271		# Initialize parameters with Glorot / fan_avg.
272	272		for p in model.parameters():
273	273		if p.dim() > 1:
274	274		nn.init.xavier_uniform_(p)
275	275		return model
276	276
277	277
278	278		def greedy_decode(model, src, src_mask, max_len, start_symbol):
279	279		memory = model.encode(src, src_mask)
280	280		ys = torch.zeros(1, 1).fill_(start_symbol).type_as(src.data)
281	281		for i in range(max_len - 1):
282	282		out = model.decode(
283	283		memory, src_mask, ys, subsequent_mask(ys.size(1)).type_as(src.data)
284	284		)
285	285		prob = model.generator(out[:, -1])
286	286		_, next_word = torch.max(prob, dim=1)
287	287		next_word = next_word.data[0]
288	288		ys = torch.cat(
289	289		[ys, torch.zeros(1, 1).type_as(src.data).fill_(next_word)], dim=1
290	290		)
291	291		return ys
292	292
293	293
294	294		class Batch:
295	295		"""Object for holding a batch of data with mask during training."""
296	296
297	297		def __init__(self, src, tgt=None, pad=2): # 2 = <blank>
298	298		self.src = src
299	299		self.src_mask = (src != pad).unsqueeze(-2)
300	300		if tgt is not None:
301	301		self.tgt = tgt[:, :-1]
302	302		self.tgt_y = tgt[:, 1:]
303	303		self.tgt_mask = self.make_std_mask(self.tgt, pad)
304	304		self.ntokens = (self.tgt_y != pad).data.sum()
305	305
306	306		@staticmethod
307	307		def make_std_mask(tgt, pad):
308	308		"Create a mask to hide padding and future words."
309	309		tgt_mask = (tgt != pad).unsqueeze(-2)
310	310		tgt_mask = tgt_mask & subsequent_mask(tgt.size(-1)).type_as(
311	311		tgt_mask.data
312	312		)
313	313		return tgt_mask
	314	+
	315	+
	316	+	class LabelSmoothing(nn.Module):
	317	+	"Implement label smoothing."
	318	+
	319	+	def __init__(self, size, padding_idx, smoothing=0.0):
	320	+	super(LabelSmoothing, self).__init__()
	321	+	self.criterion = nn.KLDivLoss(reduction="sum")
	322	+	self.padding_idx = padding_idx
	323	+	self.confidence = 1.0 - smoothing
	324	+	self.smoothing = smoothing
	325	+	self.size = size
	326	+	self.true_dist = None
	327	+
	328	+	def forward(self, x, target):
	329	+	assert x.size(1) == self.size
	330	+	true_dist = x.data.clone()
	331	+	true_dist.fill_(self.smoothing / (self.size - 2))
	332	+	true_dist.scatter_(1, target.data.unsqueeze(1), self.confidence)
	333	+	true_dist[:, self.padding_idx] = 0
	334	+	mask = torch.nonzero(target.data == self.padding_idx)
	335	+	if mask.dim() > 0:
	336	+	true_dist.index_fill_(0, mask.squeeze(), 0.0)
	337	+	self.true_dist = true_dist
	338	+	return self.criterion(x, true_dist.clone().detach())
	339	+
	340	+
	341	+	class SimpleLossCompute:
	342	+	"A simple loss compute and train function."
	343	+
	344	+	def __init__(self, generator, criterion):
	345	+	self.generator = generator
	346	+	self.criterion = criterion
	347	+
	348	+	def __call__(self, x, y, norm):
	349	+	x = self.generator(x)
	350	+	sloss = (
	351	+	self.criterion(
	352	+	x.contiguous().view(-1, x.size(-1)), y.contiguous().view(-1)
	353	+	)
	354	+	/ norm
	355	+	)
	356	+	return sloss.data * norm, sloss