File size: 20,845 Bytes
59a9ccf
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
import torch
import torch.nn as nn
import torch.nn.functional as F
from opt_einsum import contract as einsum
import torch.utils.checkpoint as checkpoint
from util import cross_product_matrix
from util_module import *
from Attention_module import *
from SE3_network import SE3TransformerWrapper
from icecream import ic

# Components for three-track blocks
# 1. MSA -> MSA update (biased attention. bias from pair & structure)
# 2. Pair -> Pair update (biased attention. bias from structure)
# 3. MSA -> Pair update (extract coevolution signal)
# 4. Str -> Str update (node from MSA, edge from Pair)

# Update MSA with biased self-attention. bias from Pair & Str
class MSAPairStr2MSA(nn.Module):
    def __init__(self, d_msa=256, d_pair=128, n_head=8, d_state=16,
                 d_hidden=32, p_drop=0.15, use_global_attn=False):
        super(MSAPairStr2MSA, self).__init__()
        self.norm_pair = nn.LayerNorm(d_pair)
        self.proj_pair = nn.Linear(d_pair+36, d_pair)
        self.norm_state = nn.LayerNorm(d_state)
        self.proj_state = nn.Linear(d_state, d_msa)
        self.drop_row = Dropout(broadcast_dim=1, p_drop=p_drop)
        self.row_attn = MSARowAttentionWithBias(d_msa=d_msa, d_pair=d_pair,
                                                n_head=n_head, d_hidden=d_hidden) 
        if use_global_attn:
            self.col_attn = MSAColGlobalAttention(d_msa=d_msa, n_head=n_head, d_hidden=d_hidden) 
        else:
            self.col_attn = MSAColAttention(d_msa=d_msa, n_head=n_head, d_hidden=d_hidden) 
        self.ff = FeedForwardLayer(d_msa, 4, p_drop=p_drop)
        
        # Do proper initialization
        self.reset_parameter()

    def reset_parameter(self):
        # initialize weights to normal distrib
        self.proj_pair = init_lecun_normal(self.proj_pair)
        self.proj_state = init_lecun_normal(self.proj_state)

        # initialize bias to zeros
        nn.init.zeros_(self.proj_pair.bias)
        nn.init.zeros_(self.proj_state.bias)

    def forward(self, msa, pair, rbf_feat, state):
        '''
        Inputs:
            - msa: MSA feature (B, N, L, d_msa)
            - pair: Pair feature (B, L, L, d_pair)
            - rbf_feat: Ca-Ca distance feature calculated from xyz coordinates (B, L, L, 36)
            - xyz: xyz coordinates (B, L, n_atom, 3)
            - state: updated node features after SE(3)-Transformer layer (B, L, d_state)
        Output:
            - msa: Updated MSA feature (B, N, L, d_msa)
        '''
        B, N, L = msa.shape[:3]

        # prepare input bias feature by combining pair & coordinate info
        pair = self.norm_pair(pair)
        pair = torch.cat((pair, rbf_feat), dim=-1)
        pair = self.proj_pair(pair) # (B, L, L, d_pair)
        #
        # update query sequence feature (first sequence in the MSA) with feedbacks (state) from SE3
        state = self.norm_state(state)
        state = self.proj_state(state).reshape(B, 1, L, -1)

        msa = msa.index_add(1, torch.tensor([0,], device=state.device), state.type(torch.float32))
        #
        # Apply row/column attention to msa & transform 
        msa = msa + self.drop_row(self.row_attn(msa, pair))
        msa = msa + self.col_attn(msa)
        msa = msa + self.ff(msa)

        return msa

class PairStr2Pair(nn.Module):
    def __init__(self, d_pair=128, n_head=4, d_hidden=32, d_rbf=36, p_drop=0.15):
        super(PairStr2Pair, self).__init__()
        
        self.emb_rbf = nn.Linear(d_rbf, d_hidden)
        self.proj_rbf = nn.Linear(d_hidden, d_pair)

        self.drop_row = Dropout(broadcast_dim=1, p_drop=p_drop)
        self.drop_col = Dropout(broadcast_dim=2, p_drop=p_drop)

        self.row_attn = BiasedAxialAttention(d_pair, d_pair, n_head, d_hidden, p_drop=p_drop, is_row=True)
        self.col_attn = BiasedAxialAttention(d_pair, d_pair, n_head, d_hidden, p_drop=p_drop, is_row=False)

        self.ff = FeedForwardLayer(d_pair, 2)
        
        self.reset_parameter()
    
    def reset_parameter(self):
        nn.init.kaiming_normal_(self.emb_rbf.weight, nonlinearity='relu')
        nn.init.zeros_(self.emb_rbf.bias)
        
        self.proj_rbf = init_lecun_normal(self.proj_rbf)
        nn.init.zeros_(self.proj_rbf.bias)

    def forward(self, pair, rbf_feat):
        B, L = pair.shape[:2]

        rbf_feat = self.proj_rbf(F.relu_(self.emb_rbf(rbf_feat)))

        pair = pair + self.drop_row(self.row_attn(pair, rbf_feat))
        pair = pair + self.drop_col(self.col_attn(pair, rbf_feat))
        pair = pair + self.ff(pair)
        return pair

class MSA2Pair(nn.Module):
    def __init__(self, d_msa=256, d_pair=128, d_hidden=32, p_drop=0.15):
        super(MSA2Pair, self).__init__()
        self.norm = nn.LayerNorm(d_msa)
        self.proj_left = nn.Linear(d_msa, d_hidden)
        self.proj_right = nn.Linear(d_msa, d_hidden)
        self.proj_out = nn.Linear(d_hidden*d_hidden, d_pair)
        
        self.reset_parameter()

    def reset_parameter(self):
        # normal initialization
        self.proj_left = init_lecun_normal(self.proj_left)
        self.proj_right = init_lecun_normal(self.proj_right)
        nn.init.zeros_(self.proj_left.bias)
        nn.init.zeros_(self.proj_right.bias)

        # zero initialize output
        nn.init.zeros_(self.proj_out.weight)
        nn.init.zeros_(self.proj_out.bias)

    def forward(self, msa, pair):
        B, N, L = msa.shape[:3]
        msa = self.norm(msa)
        left = self.proj_left(msa)
        right = self.proj_right(msa)
        right = right / float(N)
        out = einsum('bsli,bsmj->blmij', left, right).reshape(B, L, L, -1)
        out = self.proj_out(out)
       
        pair = pair + out
        
        return pair

class SCPred(nn.Module):
    def __init__(self, d_msa=256, d_state=32, d_hidden=128, p_drop=0.15):
        super(SCPred, self).__init__()
        self.norm_s0 = nn.LayerNorm(d_msa)
        self.norm_si = nn.LayerNorm(d_state)
        self.linear_s0 = nn.Linear(d_msa, d_hidden)
        self.linear_si = nn.Linear(d_state, d_hidden)

        # ResNet layers
        self.linear_1 = nn.Linear(d_hidden, d_hidden)
        self.linear_2 = nn.Linear(d_hidden, d_hidden)
        self.linear_3 = nn.Linear(d_hidden, d_hidden)
        self.linear_4 = nn.Linear(d_hidden, d_hidden)

        # Final outputs
        self.linear_out = nn.Linear(d_hidden, 20)

        self.reset_parameter()

    def reset_parameter(self):
        # normal initialization
        self.linear_s0 = init_lecun_normal(self.linear_s0)
        self.linear_si = init_lecun_normal(self.linear_si)
        self.linear_out = init_lecun_normal(self.linear_out)
        nn.init.zeros_(self.linear_s0.bias)
        nn.init.zeros_(self.linear_si.bias)
        nn.init.zeros_(self.linear_out.bias)
        
        # right before relu activation: He initializer (kaiming normal)
        nn.init.kaiming_normal_(self.linear_1.weight, nonlinearity='relu')
        nn.init.zeros_(self.linear_1.bias)
        nn.init.kaiming_normal_(self.linear_3.weight, nonlinearity='relu')
        nn.init.zeros_(self.linear_3.bias)

        # right before residual connection: zero initialize
        nn.init.zeros_(self.linear_2.weight)
        nn.init.zeros_(self.linear_2.bias)
        nn.init.zeros_(self.linear_4.weight)
        nn.init.zeros_(self.linear_4.bias)
    
    def forward(self, seq, state):
        '''
        Predict side-chain torsion angles along with backbone torsions
        Inputs:
            - seq: hidden embeddings corresponding to query sequence (B, L, d_msa)
            - state: state feature (output l0 feature) from previous SE3 layer (B, L, d_state)
        Outputs:
            - si: predicted torsion angles (phi, psi, omega, chi1~4 with cos/sin, Cb bend, Cb twist, CG) (B, L, 10, 2)
        '''
        B, L = seq.shape[:2]
        seq = self.norm_s0(seq)
        state = self.norm_si(state)
        si = self.linear_s0(seq) + self.linear_si(state)

        si = si + self.linear_2(F.relu_(self.linear_1(F.relu_(si))))
        si = si + self.linear_4(F.relu_(self.linear_3(F.relu_(si))))

        si = self.linear_out(F.relu_(si))
        return si.view(B, L, 10, 2)


class Str2Str(nn.Module):
    def __init__(self, d_msa=256, d_pair=128, d_state=16, 
            SE3_param={'l0_in_features':32, 'l0_out_features':16, 'num_edge_features':32}, p_drop=0.1):
        super(Str2Str, self).__init__()
        
        # initial node & pair feature process
        self.norm_msa = nn.LayerNorm(d_msa)
        self.norm_pair = nn.LayerNorm(d_pair)
        self.norm_state = nn.LayerNorm(d_state)
    
        self.embed_x = nn.Linear(d_msa+d_state, SE3_param['l0_in_features'])
        self.embed_e1 = nn.Linear(d_pair, SE3_param['num_edge_features'])
        self.embed_e2 = nn.Linear(SE3_param['num_edge_features']+36+1, SE3_param['num_edge_features'])
        
        self.norm_node = nn.LayerNorm(SE3_param['l0_in_features'])
        self.norm_edge1 = nn.LayerNorm(SE3_param['num_edge_features'])
        self.norm_edge2 = nn.LayerNorm(SE3_param['num_edge_features'])
        
        self.se3 = SE3TransformerWrapper(**SE3_param)
        self.sc_predictor = SCPred(d_msa=d_msa, d_state=SE3_param['l0_out_features'],
                                   p_drop=p_drop)
        
        self.reset_parameter()

    def reset_parameter(self):
        # initialize weights to normal distribution
        self.embed_x = init_lecun_normal(self.embed_x)
        self.embed_e1 = init_lecun_normal(self.embed_e1)
        self.embed_e2 = init_lecun_normal(self.embed_e2)

        # initialize bias to zeros
        nn.init.zeros_(self.embed_x.bias)
        nn.init.zeros_(self.embed_e1.bias)
        nn.init.zeros_(self.embed_e2.bias)
    
    @torch.cuda.amp.autocast(enabled=False)
    def forward(self, msa, pair, R_in, T_in, xyz, state, idx, top_k=64, eps=1e-5):
        B, N, L = msa.shape[:3]
        
        state = state.type(torch.float32)
        mas = msa.type(torch.float32)
        pair = pair.type(torch.float32)
        R_in = R_in.type(torch.float32)
        T_in = T_in.type(torch.float32)
        xyz = xyz.type(torch.float32)
        
        #ic(msa.dtype)
        #ic(pair.dtype)
        #ic(R_in.dtype)
        #ic(T_in.dtype)
        #ic(xyz.dtype)
        #ic(state.dtype)
        #ic(idx.dtype)
        

        # process msa & pair features
        node = self.norm_msa(msa[:,0])
        pair = self.norm_pair(pair)
        state = self.norm_state(state)
        
        node = torch.cat((node, state), dim=-1)
        node = self.norm_node(self.embed_x(node))
        pair = self.norm_edge1(self.embed_e1(pair))
        
        neighbor = get_seqsep(idx)
        rbf_feat = rbf(torch.cdist(xyz[:,:,1], xyz[:,:,1]))
        pair = torch.cat((pair, rbf_feat, neighbor), dim=-1)
        pair = self.norm_edge2(self.embed_e2(pair))
        
        # define graph
        if top_k != 0:
            G, edge_feats = make_topk_graph(xyz[:,:,1,:], pair, idx, top_k=top_k)
        else:
            G, edge_feats = make_full_graph(xyz[:,:,1,:], pair, idx, top_k=top_k)
        l1_feats = xyz - xyz[:,:,1,:].unsqueeze(2)
        l1_feats = l1_feats.reshape(B*L, -1, 3)
        
        # apply SE(3) Transformer & update coordinates
        shift = self.se3(G, node.reshape(B*L, -1, 1), l1_feats, edge_feats)

        state = shift['0'].reshape(B, L, -1) # (B, L, C)
        
        offset = shift['1'].reshape(B, L, 2, 3)
        delTi = offset[:,:,0,:] / 10.0 # translation
        R = offset[:,:,1,:] / 100.0 # rotation
        
        Qnorm = torch.sqrt( 1 + torch.sum(R*R, dim=-1) )
        qA, qB, qC, qD = 1/Qnorm, R[:,:,0]/Qnorm, R[:,:,1]/Qnorm, R[:,:,2]/Qnorm

        delRi = torch.zeros((B,L,3,3), device=xyz.device)
        delRi[:,:,0,0] = qA*qA+qB*qB-qC*qC-qD*qD
        delRi[:,:,0,1] = 2*qB*qC - 2*qA*qD
        delRi[:,:,0,2] = 2*qB*qD + 2*qA*qC
        delRi[:,:,1,0] = 2*qB*qC + 2*qA*qD
        delRi[:,:,1,1] = qA*qA-qB*qB+qC*qC-qD*qD
        delRi[:,:,1,2] = 2*qC*qD - 2*qA*qB
        delRi[:,:,2,0] = 2*qB*qD - 2*qA*qC
        delRi[:,:,2,1] = 2*qC*qD + 2*qA*qB
        delRi[:,:,2,2] = qA*qA-qB*qB-qC*qC+qD*qD
        #
        ## convert vector to rotation matrix
        #R_angle = torch.norm(R, dim=-1, keepdim=True) # (B, L, 1)
        #cos_angle = torch.cos(R_angle).unsqueeze(2) # (B, L, 1, 1)
        #sin_angle = torch.sin(R_angle).unsqueeze(2) # (B, L, 1, 1)
        #R_vector = R / (R_angle+eps) # (B, L, 3)

        #delRi = cos_angle*torch.eye(3, device=R.device).reshape(1,1,3,3) \
        #      + sin_angle*cross_product_matrix(R_vector) \
        #      + (1.0-cos_angle)*einsum('bni,bnj->bnij', R_vector, R_vector)

        Ri = einsum('bnij,bnjk->bnik', delRi, R_in)
        Ti = delTi + T_in #einsum('bnij,bnj->bni', delRi, T_in) + delTi
            
        alpha = self.sc_predictor(msa[:,0], state)
        return Ri, Ti, state, alpha

class IterBlock(nn.Module):
    def __init__(self, d_msa=256, d_pair=128,
                 n_head_msa=8, n_head_pair=4,
                 use_global_attn=False,
                 d_hidden=32, d_hidden_msa=None, p_drop=0.15,
                 SE3_param={'l0_in_features':32, 'l0_out_features':16, 'num_edge_features':32}):
        super(IterBlock, self).__init__()
        if d_hidden_msa == None:
            d_hidden_msa = d_hidden

        self.msa2msa = MSAPairStr2MSA(d_msa=d_msa, d_pair=d_pair,
                                      n_head=n_head_msa,
                                      d_state=SE3_param['l0_out_features'],
                                      use_global_attn=use_global_attn,
                                      d_hidden=d_hidden_msa, p_drop=p_drop)
        self.msa2pair = MSA2Pair(d_msa=d_msa, d_pair=d_pair,
                                 d_hidden=d_hidden//2, p_drop=p_drop)
                                 #d_hidden=d_hidden, p_drop=p_drop)
        self.pair2pair = PairStr2Pair(d_pair=d_pair, n_head=n_head_pair, 
                                      d_hidden=d_hidden, p_drop=p_drop)
        self.str2str = Str2Str(d_msa=d_msa, d_pair=d_pair,
                               d_state=SE3_param['l0_out_features'],
                               SE3_param=SE3_param,
                               p_drop=p_drop)

    def forward(self, msa, pair, R_in, T_in, xyz, state, idx, use_checkpoint=False):
        rbf_feat = rbf(torch.cdist(xyz[:,:,1,:], xyz[:,:,1,:]))
        if use_checkpoint:
            msa = checkpoint.checkpoint(create_custom_forward(self.msa2msa), msa, pair, rbf_feat, state)
            pair = checkpoint.checkpoint(create_custom_forward(self.msa2pair), msa, pair)
            pair = checkpoint.checkpoint(create_custom_forward(self.pair2pair), pair, rbf_feat)
            R, T, state, alpha = checkpoint.checkpoint(create_custom_forward(self.str2str, top_k=0), msa, pair, R_in, T_in, xyz, state, idx)
        else:
            msa = self.msa2msa(msa, pair, rbf_feat, state)
            pair = self.msa2pair(msa, pair)
            pair = self.pair2pair(pair, rbf_feat)
            R, T, state, alpha = self.str2str(msa, pair, R_in, T_in, xyz, state, idx, top_k=0) 
        
        return msa, pair, R, T, state, alpha

class IterativeSimulator(nn.Module):
    def __init__(self, n_extra_block=4, n_main_block=12, n_ref_block=4,
                 d_msa=256, d_msa_full=64, d_pair=128, d_hidden=32,
                 n_head_msa=8, n_head_pair=4,
                 SE3_param_full={'l0_in_features':32, 'l0_out_features':16, 'num_edge_features':32},
                 SE3_param_topk={'l0_in_features':32, 'l0_out_features':16, 'num_edge_features':32},
                 p_drop=0.15):
        super(IterativeSimulator, self).__init__()
        self.n_extra_block = n_extra_block
        self.n_main_block = n_main_block
        self.n_ref_block = n_ref_block
        
        self.proj_state = nn.Linear(SE3_param_topk['l0_out_features'], SE3_param_full['l0_out_features'])
        # Update with extra sequences
        if n_extra_block > 0:
            self.extra_block = nn.ModuleList([IterBlock(d_msa=d_msa_full, d_pair=d_pair,
                                                        n_head_msa=n_head_msa,
                                                        n_head_pair=n_head_pair,
                                                        d_hidden_msa=8,
                                                        d_hidden=d_hidden,
                                                        p_drop=p_drop,
                                                        use_global_attn=True,
                                                        SE3_param=SE3_param_full)
                                                        for i in range(n_extra_block)])

        # Update with seed sequences
        if n_main_block > 0:
            self.main_block = nn.ModuleList([IterBlock(d_msa=d_msa, d_pair=d_pair,
                                                       n_head_msa=n_head_msa,
                                                       n_head_pair=n_head_pair,
                                                       d_hidden=d_hidden,
                                                       p_drop=p_drop,
                                                       use_global_attn=False,
                                                       SE3_param=SE3_param_full)
                                                       for i in range(n_main_block)])

        self.proj_state2 = nn.Linear(SE3_param_full['l0_out_features'], SE3_param_topk['l0_out_features'])
        # Final SE(3) refinement
        if n_ref_block > 0:
            self.str_refiner = Str2Str(d_msa=d_msa, d_pair=d_pair,
                                       d_state=SE3_param_topk['l0_out_features'],
                                       SE3_param=SE3_param_topk,
                                       p_drop=p_drop)
    
        self.reset_parameter()
    def reset_parameter(self):
        self.proj_state = init_lecun_normal(self.proj_state)
        nn.init.zeros_(self.proj_state.bias)
        self.proj_state2 = init_lecun_normal(self.proj_state2)
        nn.init.zeros_(self.proj_state2.bias)

    def forward(self, seq, msa, msa_full, pair, xyz_in, state, idx, use_checkpoint=False):
        # input:
        #   seq: query sequence (B, L)
        #   msa: seed MSA embeddings (B, N, L, d_msa)
        #   msa_full: extra MSA embeddings (B, N, L, d_msa_full)
        #   pair: initial residue pair embeddings (B, L, L, d_pair)
        #   xyz_in: initial BB coordinates (B, L, n_atom, 3)
        #   state: initial state features containing mixture of query seq, sidechain, accuracy info (B, L, d_state)
        #   idx: residue index

        B, L = pair.shape[:2]

        R_in = torch.eye(3, device=xyz_in.device).reshape(1,1,3,3).expand(B, L, -1, -1)
        T_in = xyz_in[:,:,1].clone()
        xyz_in = xyz_in - T_in.unsqueeze(-2)
        
        state = self.proj_state(state)

        R_s = list()
        T_s = list()
        alpha_s = list()
        for i_m in range(self.n_extra_block):
            R_in = R_in.detach() # detach rotation (for stability)
            T_in = T_in.detach()
            # Get current BB structure
            xyz = einsum('bnij,bnaj->bnai', R_in, xyz_in) + T_in.unsqueeze(-2)

            msa_full, pair, R_in, T_in, state, alpha = self.extra_block[i_m](msa_full, pair,
                                                                             R_in, T_in, xyz, state, idx,
                                                                             use_checkpoint=use_checkpoint)
            R_s.append(R_in)
            T_s.append(T_in)
            alpha_s.append(alpha)

        for i_m in range(self.n_main_block):
            R_in = R_in.detach()
            T_in = T_in.detach()
            # Get current BB structure
            xyz = einsum('bnij,bnaj->bnai', R_in, xyz_in) + T_in.unsqueeze(-2)
            
            msa, pair, R_in, T_in, state, alpha = self.main_block[i_m](msa, pair,
                                                                R_in, T_in, xyz, state, idx,
                                                                use_checkpoint=use_checkpoint)
            R_s.append(R_in)
            T_s.append(T_in)
            alpha_s.append(alpha)
       
        state = self.proj_state2(state)
        for i_m in range(self.n_ref_block):
            R_in = R_in.detach()
            T_in = T_in.detach()
            xyz = einsum('bnij,bnaj->bnai', R_in, xyz_in) + T_in.unsqueeze(-2)
            R_in, T_in, state, alpha = self.str_refiner(msa, pair, R_in, T_in, xyz, state, idx, top_k=64)
            R_s.append(R_in)
            T_s.append(T_in)
            alpha_s.append(alpha)

        R_s = torch.stack(R_s, dim=0)
        T_s = torch.stack(T_s, dim=0)
        alpha_s = torch.stack(alpha_s, dim=0)

        return msa, pair, R_s, T_s, alpha_s, state