Recurrent neural network language modeling toolkit 源码走读(七)
- RNNLM - Recurrent Neural Network Language Modeling Toolkit(点此阅读)
- Recurrent neural network based language model(点此阅读)
- EXTENSIONS OF RECURRENT NEURAL NETWORK LANGUAGE MODEL(点此阅读)
- Strategies for Training Large Scale Neural Network Language Models(点此阅读)
- STATISTICAL LANGUAGE MODELS BASED ON NEURAL NETWORKS(点此阅读)
- A guide to recurrent neural networks and backpropagation(点此阅读)
- A Neural Probabilistic Language Model(点此阅读)
- Learning Long-Term Dependencies with Gradient Descent is Difficult(点此阅读)
- Can Artificial Neural Networks Learn Language Models?(点此阅读)
//反传误差,更新网络权值 void CRnnLM::learnNet(int last_word, int word) { //word表示要预测的词,last_word表示当前输入层所在的词 int a, b, c, t, step; real beta2, beta3; //alpha表示学习率,初始值为0.1, beta初始值为0.0000001; beta2=beta*alpha; //这里注释不懂,希望明白的朋友讲下~ beta3=beta2*1; //beta3 can be possibly larger than beta2, as that is useful on small datasets (if the final model is to be interpolated wich backoff model) - todo in the future if (word==-1) return; //compute error vectors,计算输出层的(只含word所在类别的所有词)误差向量 for (c=0; c<class_cn[vocab[word].class_index]; c++) { a=class_words[vocab[word].class_index][c]; neu2[a].er=(0-neu2[a].ac); } neu2[word].er=(1-neu2[word].ac); //word part //flush error for (a=0; a<layer1_size; a++) neu1[a].er=0; for (a=0; a<layerc_size; a++) neuc[a].er=0; //计算输出层的class部分的误差向量 for (a=vocab_size; a<layer2_size; a++) { neu2[a].er=(0-neu2[a].ac); } neu2[vocab[word].class_index+vocab_size].er=(1-neu2[vocab[word].class_index+vocab_size].ac); //class part //计算特征所在syn_d中的下标,和上面一样,针对ME中word部分 if (direct_size>0) { //learn direct connections between words if (word!=-1) { unsigned long long hash[MAX_NGRAM_ORDER]; for (a=0; a<direct_order; a++) hash[a]=0; for (a=0; a<direct_order; a++) { b=0; if (a>0) if (history[a-1]==-1) break; hash[a]=PRIMES[0]*PRIMES[1]*(unsigned long long)(vocab[word].class_index+1); for (b=1; b<=a; b++) hash[a]+=PRIMES[(a*PRIMES[b]+b)%PRIMES_SIZE]*(unsigned long long)(history[b-1]+1); hash[a]=(hash[a]%(direct_size/2))+(direct_size)/2; } //更新ME中的权值部分,这部分是正对word的 for (c=0; c<class_cn[vocab[word].class_index]; c++) { a=class_words[vocab[word].class_index][c]; //这里的更新公式很容易推导,利用梯度上升,和RNN是一样的 //详见我的这篇文章,另外这里不同的是权值是放在一维数组里面的,所以程序写法有点不同 for (b=0; b<direct_order; b++) if (hash[b]) { syn_d[hash[b]]+=alpha*neu2[a].er - syn_d[hash[b]]*beta3; hash[b]++; hash[b]=hash[b]%direct_size; } else break; } } } //计算n元模型特征,这是对class计算的 //learn direct connections to classes if (direct_size>0) { //learn direct connections between words and classes unsigned long long hash[MAX_NGRAM_ORDER]; for (a=0; a<direct_order; a++) hash[a]=0; for (a=0; a<direct_order; a++) { b=0; if (a>0) if (history[a-1]==-1) break; hash[a]=PRIMES[0]*PRIMES[1]; for (b=1; b<=a; b++) hash[a]+=PRIMES[(a*PRIMES[b]+b)%PRIMES_SIZE]*(unsigned long long)(history[b-1]+1); hash[a]=hash[a]%(direct_size/2); } //和上面一样,更新ME中权值部分,这是对class的 for (a=vocab_size; a<layer2_size; a++) { for (b=0; b<direct_order; b++) if (hash[b]) { syn_d[hash[b]]+=alpha*neu2[a].er - syn_d[hash[b]]*beta3; hash[b]++; } else break; } } // //含压缩层的情况,更新sync, syn1 if (layerc_size>0) { //将输出层的误差传递到压缩层,即计算部分V × eo^T(符号含义表示见图) matrixXvector(neuc, neu2, sync, layerc_size, class_words[vocab[word].class_index][0], class_words[vocab[word].class_index][0]+class_cn[vocab[word].class_index], 0, layerc_size, 1); //这里把一维的权值转换为二维的权值矩阵好理解一些 //注意这里的t相当于定位到了参数矩阵的行,下面的下标a相当于列 t=class_words[vocab[word].class_index][0]*layerc_size; for (c=0; c<class_cn[vocab[word].class_index]; c++) { b=class_words[vocab[word].class_index][c]; //这里的更新公式见我写的另一篇文章的rnn推导 //并且每训练10次才L2正规化一次 if ((counter%10)==0) //regularization is done every 10. step for (a=0; a<layerc_size; a++) sync[a+t].weight+=alpha*neu2[b].er*neuc[a].ac - sync[a+t].weight*beta2; else for (a=0; a<layerc_size; a++) sync[a+t].weight+=alpha*neu2[b].er*neuc[a].ac; //参数矩阵下移动一行 t+=layerc_size; } //将输出层的误差传递到压缩层,即计算部分V × eo^T(符号含义表示见图) //这里计算输出层中class部分到压缩层 matrixXvector(neuc, neu2, sync, layerc_size, vocab_size, layer2_size, 0, layerc_size, 1); //propagates errors 2->c for classes //这里同样相当于定位的权值矩阵中的行,下面的a表示列 c=vocab_size*layerc_size; //更新和上面公式是一样的,不同的是更新的权值数组中不同的部分 for (b=vocab_size; b<layer2_size; b++) { if ((counter%10)==0) { for (a=0; a<layerc_size; a++) sync[a+c].weight+=alpha*neu2[b].er*neuc[a].ac - sync[a+c].weight*beta2; //weight c->2 update } else { for (a=0; a<layerc_size; a++) sync[a+c].weight+=alpha*neu2[b].er*neuc[a].ac; //weight c->2 update } //下一行 c+=layerc_size; } //这里是误差向量,即论文中的e hj (t) for (a=0; a<layerc_size; a++) neuc[a].er=neuc[a].er*neuc[a].ac*(1-neuc[a].ac); //error derivation at compression layer //// //下面都是同理,将误差再往下传,计算syn1(二维) × ec^T, ec表示压缩层的误差向量 matrixXvector(neu1, neuc, syn1, layer1_size, 0, layerc_size, 0, layer1_size, 1); //propagates errors c->1 //更新syn1,相应的见公式 for (b=0; b<layerc_size; b++) { for (a=0; a<layer1_size; a++) syn1[a+b*layer1_size].weight+=alpha*neuc[b].er*neu1[a].ac; //weight 1->c update } } else //无压缩层的情况,更新syn1 { //下面的情况和上面类似,只是少了一个压缩层 matrixXvector(neu1, neu2, syn1, layer1_size, class_words[vocab[word].class_index][0], class_words[vocab[word].class_index][0]+class_cn[vocab[word].class_index], 0, layer1_size, 1); t=class_words[vocab[word].class_index][0]*layer1_size; for (c=0; c<class_cn[vocab[word].class_index]; c++) { b=class_words[vocab[word].class_index][c]; if ((counter%10)==0) //regularization is done every 10. step for (a=0; a<layer1_size; a++) syn1[a+t].weight+=alpha*neu2[b].er*neu1[a].ac - syn1[a+t].weight*beta2; else for (a=0; a<layer1_size; a++) syn1[a+t].weight+=alpha*neu2[b].er*neu1[a].ac; t+=layer1_size; } // matrixXvector(neu1, neu2, syn1, layer1_size, vocab_size, layer2_size, 0, layer1_size, 1); //propagates errors 2->1 for classes c=vocab_size*layer1_size; for (b=vocab_size; b<layer2_size; b++) { if ((counter%10)==0) { //regularization is done every 10. step for (a=0; a<layer1_size; a++) syn1[a+c].weight+=alpha*neu2[b].er*neu1[a].ac - syn1[a+c].weight*beta2; //weight 1->2 update } else { for (a=0; a<layer1_size; a++) syn1[a+c].weight+=alpha*neu2[b].er*neu1[a].ac; //weight 1->2 update } c+=layer1_size; } } // //到这里,上面部分把到隐层的部分更新完毕 /////////////// //这里就是最常规的RNN,即t时刻往前只展开了s(t-1) if (bptt<=1) { //bptt==1 -> normal BP //计算隐层的误差,即eh(t) for (a=0; a<layer1_size; a++) neu1[a].er=neu1[a].er*neu1[a].ac*(1-neu1[a].ac); //error derivation at layer 1 //这部分更新隐层到word部分的权值 //注意由于word部分是1-of-V编码 //所以这里更新的循环式上有点不同,并且下面的更新都是每10次训练更新才进行一次L2正规化 a=last_word; if (a!=-1) { if ((counter%10)==0) for (b=0; b<layer1_size; b++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac - syn0[a+b*layer0_size].weight*beta2; else //我们可以把这里的权值看做一个矩阵 //b表示行,a表示列,非L2正规化的完整更新式如下: /*for (b=0; b<layer1_size; b++) { for (k=0; k<vocab_size; k++) { syn0[k+b*layer0_size].weight+=alpha*neu1[b].er*neu0[k].ac; } }*/ //但由于neu0[k]==1只有当k==a时,所以为了加快循环计算的速度,更新就变为如下了 //下面的代码是类似的道理,其实这里的neu0[a].ac可以直接省略掉,因为本身值为1 for (b=0; b<layer1_size; b++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac; } //这部分更新隐层到s(t-1)的权值 if ((counter%10)==0) { for (b=0; b<layer1_size; b++) for (a=layer0_size-layer1_size; a<layer0_size; a++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac - syn0[a+b*layer0_size].weight*beta2; } else { for (b=0; b<layer1_size; b++) for (a=layer0_size-layer1_size; a<layer0_size; a++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac; } }
下面是更新BPTT的部分, 还是先把BPTT算法部分的数据结构图上来,这样更方便对照:
else //BPTT { //BPTT部分权值就不在用syn0了,而是用bptt_syn0 //神经元部分的存储用bptt_hidden //将隐层的神经元信息复制到bptt_hidden,这里对neu1做备份 for (b=0; b<layer1_size; b++) bptt_hidden[b].ac=neu1[b].ac; for (b=0; b<layer1_size; b++) bptt_hidden[b].er=neu1[b].er; //bptt_block第一个条件是控制BPTT的,因为不能每训练一个word都用BPTT来深度更新参数 //这样每进行一次训练计算量太大,过于耗时 //word==0表示当前一个句子结束 //或者当independent开关不为0时,下一个词是句子的结束,则进行BPTT if (((counter%bptt_block)==0) || (independent && (word==0))) { //step表示 for (step=0; step<bptt+bptt_block-2; step++) { //计算隐层的误差向量,即eh(t) for (a=0; a<layer1_size; a++) neu1[a].er=neu1[a].er*neu1[a].ac*(1-neu1[a].ac); //error derivation at layer 1 //更新的是输入层中vocab_size那部分权值 //bptt_history下标从0开始依次存放的是wt, wt-1, wt-2... //比如当step == 0时,相当于正在进行普通的BPTT,这时bptt_history[step]表示当前输入word的在vocab中的索引 a=bptt_history[step]; if (a!=-1) for (b=0; b<layer1_size; b++) { //由于输入层word部分是1-of-V编码,所以neu0[a].ac==1 所以这里后面没有乘以它 //在step == 0时,bptt_syn0相当于原来的syn0 bptt_syn0[a+b*layer0_size].weight+=alpha*neu1[b].er; } //为从隐层往状态层传误差做准备 for (a=layer0_size-layer1_size; a<layer0_size; a++) neu0[a].er=0; //从隐层传递误差到状态层 matrixXvector(neu0, neu1, syn0, layer0_size, 0, layer1_size, layer0_size-layer1_size, layer0_size, 1); //propagates errors 1->0 //更新隐层到状态层的权值 //之所以先计算误差的传递就是因为更新完权值会发生改变 for (b=0; b<layer1_size; b++) for (a=layer0_size-layer1_size; a<layer0_size; a++) { //neu0[a].er += neu1[b].er * syn0[a+b*layer0_size].weight; bptt_syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac; } //todo这里我理解是把论文中的s(t-1)复制到s(t),准备下一次循环 for (a=0; a<layer1_size; a++) { //propagate error from time T-n to T-n-1 //后面为什么会加bptt_hidden呢 neu1[a].er=neu0[a+layer0_size-layer1_size].er + bptt_hidden[(step+1)*layer1_size+a].er; } //历史中的s(t-2)复制到s(t-1) if (step<bptt+bptt_block-3) for (a=0; a<layer1_size; a++) { neu1[a].ac=bptt_hidden[(step+1)*layer1_size+a].ac; neu0[a+layer0_size-layer1_size].ac=bptt_hidden[(step+2)*layer1_size+a].ac; }
到这里,无奈再把代码打断一下,把上面两个关键循环按照step的增加走一下,并假设当前时刻为t,展开一下上面的循环:
step = 0: 第一个for循环完成: neu1.er = neu0.er + btpp_hidden.er -> s(t) = s(t-1) + s(t-1) 第二个for循环完成: neu1.ac = bptt_hidden.ac -> s(t) = s(t-1) neu0.ac = bptt_hidden.ac -> s(t-1) = s(t-2) step = 1: 第一个for循环完成: neu1.er = neu0.er + btpp_hidden.er -> s(t-1) = s(t-2) + s(t-2) 第二个for循环完成: neu1.ac = bptt_hidden.ac -> s(t-1) = s(t-2) neu0.ac = bptt_hidden.ac -> s(t-2) = s(t-3)
通过上面列出的步骤,大概能知道原理,其中neu0,和bptt_hidden所对应的s(t-1)有不同,前者的er值隐层传下来的 后者的er值是在t-1时刻,压缩层传下来的,感觉直接让neu0.er覆盖neu1.er即可,这里不太明白为什么要将两者加起来希望明白的朋友告知一下哈,我的一个想法是bptt_hidden对应的误差是从输出传到隐层的,neu0的er是输出传到输入层的两者加起来更利于整个网络的优化,其二由于在循环网络中,误差梯度向量会随着网络深度增加而消失,加上bptt_hidden或许可以某种程度上预防这种情况的发生,也不知道是压根就没理解清楚上面的循环而瞎想还是其他什么问题,总之欢迎懂的朋友告知~
} //清空历史信息中的er值 for (a=0; a<(bptt+bptt_block)*layer1_size; a++) { bptt_hidden[a].er=0; } //这里恢复neu1,因为neu1反复在循环中使用 for (b=0; b<layer1_size; b++) neu1[b].ac=bptt_hidden[b].ac; //restore hidden layer after bptt //将BPTT后的权值改变作用到syn0上 for (b=0; b<layer1_size; b++) { //copy temporary syn0 //bptt完毕,将bptt_syn0的权值复制到syn0中来,这是复制状态层部分 if ((counter%10)==0) { for (a=layer0_size-layer1_size; a<layer0_size; a++) { syn0[a+b*layer0_size].weight+=bptt_syn0[a+b*layer0_size].weight - syn0[a+b*layer0_size].weight*beta2; bptt_syn0[a+b*layer0_size].weight=0; } } else { for (a=layer0_size-layer1_size; a<layer0_size; a++) { syn0[a+b*layer0_size].weight+=bptt_syn0[a+b*layer0_size].weight; bptt_syn0[a+b*layer0_size].weight=0; } } //bptt完毕,将bptt_syn0的权值复制到syn0中来,这是word部分 if ((counter%10)==0) { for (step=0; step<bptt+bptt_block-2; step++) if (bptt_history[step]!=-1) { syn0[bptt_history[step]+b*layer0_size].weight+=bptt_syn0[bptt_history[step]+b*layer0_size].weight - syn0[bptt_history[step]+b*layer0_size].weight*beta2; bptt_syn0[bptt_history[step]+b*layer0_size].weight=0; } } else { //因为输入的word层是1-of-V编码,并不是全部的权值改变 //这样写可以加快计算速度,避免不必要的循环检索 for (step=0; step<bptt+bptt_block-2; step++) if (bptt_history[step]!=-1) { syn0[bptt_history[step]+b*layer0_size].weight+=bptt_syn0[bptt_history[step]+b*layer0_size].weight; bptt_syn0[bptt_history[step]+b*layer0_size].weight=0; } } } } } } //将隐层神经元的ac值复制到输出层后layer1_size那部分 void CRnnLM::copyHiddenLayerToInput() { int a; for (a=0; a<layer1_size; a++) { neu0[a+layer0_size-layer1_size].ac=neu1[a].ac; } }
最后仍然和前面一样,把整个函数完整的注释版贴在下面:
//反传误差,更新网络权值 void CRnnLM::learnNet(int last_word, int word) { //word表示要预测的词,last_word表示当前输入层所在的词 int a, b, c, t, step; real beta2, beta3; //alpha表示学习率,初始值为0.1, beta初始值为0.0000001; beta2=beta*alpha; //这里注释不懂,希望明白的朋友讲下~ beta3=beta2*1; //beta3 can be possibly larger than beta2, as that is useful on small datasets (if the final model is to be interpolated wich backoff model) - todo in the future if (word==-1) return; //compute error vectors,计算输出层的(只含word所在类别的所有词)误差向量 for (c=0; c<class_cn[vocab[word].class_index]; c++) { a=class_words[vocab[word].class_index][c]; neu2[a].er=(0-neu2[a].ac); } neu2[word].er=(1-neu2[word].ac); //word part //flush error for (a=0; a<layer1_size; a++) neu1[a].er=0; for (a=0; a<layerc_size; a++) neuc[a].er=0; //计算输出层的class部分的误差向量 for (a=vocab_size; a<layer2_size; a++) { neu2[a].er=(0-neu2[a].ac); } neu2[vocab[word].class_index+vocab_size].er=(1-neu2[vocab[word].class_index+vocab_size].ac); //class part //计算特征所在syn_d中的下标,和上面一样,针对ME中word部分 if (direct_size>0) { //learn direct connections between words if (word!=-1) { unsigned long long hash[MAX_NGRAM_ORDER]; for (a=0; a<direct_order; a++) hash[a]=0; for (a=0; a<direct_order; a++) { b=0; if (a>0) if (history[a-1]==-1) break; hash[a]=PRIMES[0]*PRIMES[1]*(unsigned long long)(vocab[word].class_index+1); for (b=1; b<=a; b++) hash[a]+=PRIMES[(a*PRIMES[b]+b)%PRIMES_SIZE]*(unsigned long long)(history[b-1]+1); hash[a]=(hash[a]%(direct_size/2))+(direct_size)/2; } //更新ME中的权值部分,这部分是正对word的 for (c=0; c<class_cn[vocab[word].class_index]; c++) { a=class_words[vocab[word].class_index][c]; //这里的更新公式很容易推导,利用梯度上升,和RNN是一样的 //详见我的这篇文章,另外这里不同的是权值是放在一维数组里面的,所以程序写法有点不同 for (b=0; b<direct_order; b++) if (hash[b]) { syn_d[hash[b]]+=alpha*neu2[a].er - syn_d[hash[b]]*beta3; hash[b]++; hash[b]=hash[b]%direct_size; } else break; } } } //计算n元模型特征,这是对class计算的 //learn direct connections to classes if (direct_size>0) { //learn direct connections between words and classes unsigned long long hash[MAX_NGRAM_ORDER]; for (a=0; a<direct_order; a++) hash[a]=0; for (a=0; a<direct_order; a++) { b=0; if (a>0) if (history[a-1]==-1) break; hash[a]=PRIMES[0]*PRIMES[1]; for (b=1; b<=a; b++) hash[a]+=PRIMES[(a*PRIMES[b]+b)%PRIMES_SIZE]*(unsigned long long)(history[b-1]+1); hash[a]=hash[a]%(direct_size/2); } //和上面一样,更新ME中权值部分,这是对class的 for (a=vocab_size; a<layer2_size; a++) { for (b=0; b<direct_order; b++) if (hash[b]) { syn_d[hash[b]]+=alpha*neu2[a].er - syn_d[hash[b]]*beta3; hash[b]++; } else break; } } // //含压缩层的情况,更新sync, syn1 if (layerc_size>0) { //将输出层的误差传递到压缩层,即计算部分V × eo^T(符号含义表示见图) matrixXvector(neuc, neu2, sync, layerc_size, class_words[vocab[word].class_index][0], class_words[vocab[word].class_index][0]+class_cn[vocab[word].class_index], 0, layerc_size, 1); //这里把一维的权值转换为二维的权值矩阵好理解一些 //注意这里的t相当于定位到了参数矩阵的行,下面的下标a相当于列 t=class_words[vocab[word].class_index][0]*layerc_size; for (c=0; c<class_cn[vocab[word].class_index]; c++) { b=class_words[vocab[word].class_index][c]; //这里的更新公式见我写的另一篇文章的rnn推导 //并且每训练10次才L2正规化一次 if ((counter%10)==0) //regularization is done every 10. step for (a=0; a<layerc_size; a++) sync[a+t].weight+=alpha*neu2[b].er*neuc[a].ac - sync[a+t].weight*beta2; else for (a=0; a<layerc_size; a++) sync[a+t].weight+=alpha*neu2[b].er*neuc[a].ac; //参数矩阵下移动一行 t+=layerc_size; } //将输出层的误差传递到压缩层,即计算部分V × eo^T(符号含义表示见图) //这里计算输出层中class部分到压缩层 matrixXvector(neuc, neu2, sync, layerc_size, vocab_size, layer2_size, 0, layerc_size, 1); //propagates errors 2->c for classes //这里同样相当于定位的权值矩阵中的行,下面的a表示列 c=vocab_size*layerc_size; //更新和上面公式是一样的,不同的是更新的权值数组中不同的部分 for (b=vocab_size; b<layer2_size; b++) { if ((counter%10)==0) { for (a=0; a<layerc_size; a++) sync[a+c].weight+=alpha*neu2[b].er*neuc[a].ac - sync[a+c].weight*beta2; //weight c->2 update } else { for (a=0; a<layerc_size; a++) sync[a+c].weight+=alpha*neu2[b].er*neuc[a].ac; //weight c->2 update } //下一行 c+=layerc_size; } //这里是误差向量,即论文中的e hj (t) for (a=0; a<layerc_size; a++) neuc[a].er=neuc[a].er*neuc[a].ac*(1-neuc[a].ac); //error derivation at compression layer //// //下面都是同理,将误差再往下传,计算syn1(二维) × ec^T, ec表示压缩层的误差向量 matrixXvector(neu1, neuc, syn1, layer1_size, 0, layerc_size, 0, layer1_size, 1); //propagates errors c->1 //更新syn1,相应的见公式 for (b=0; b<layerc_size; b++) { for (a=0; a<layer1_size; a++) syn1[a+b*layer1_size].weight+=alpha*neuc[b].er*neu1[a].ac; //weight 1->c update } } else //无压缩层的情况,更新syn1 { //下面的情况和上面类似,只是少了一个压缩层 matrixXvector(neu1, neu2, syn1, layer1_size, class_words[vocab[word].class_index][0], class_words[vocab[word].class_index][0]+class_cn[vocab[word].class_index], 0, layer1_size, 1); t=class_words[vocab[word].class_index][0]*layer1_size; for (c=0; c<class_cn[vocab[word].class_index]; c++) { b=class_words[vocab[word].class_index][c]; if ((counter%10)==0) //regularization is done every 10. step for (a=0; a<layer1_size; a++) syn1[a+t].weight+=alpha*neu2[b].er*neu1[a].ac - syn1[a+t].weight*beta2; else for (a=0; a<layer1_size; a++) syn1[a+t].weight+=alpha*neu2[b].er*neu1[a].ac; t+=layer1_size; } // matrixXvector(neu1, neu2, syn1, layer1_size, vocab_size, layer2_size, 0, layer1_size, 1); //propagates errors 2->1 for classes c=vocab_size*layer1_size; for (b=vocab_size; b<layer2_size; b++) { if ((counter%10)==0) { //regularization is done every 10. step for (a=0; a<layer1_size; a++) syn1[a+c].weight+=alpha*neu2[b].er*neu1[a].ac - syn1[a+c].weight*beta2; //weight 1->2 update } else { for (a=0; a<layer1_size; a++) syn1[a+c].weight+=alpha*neu2[b].er*neu1[a].ac; //weight 1->2 update } c+=layer1_size; } } // //到这里,上面部分把到隐层的部分更新完毕 /////////////// //这里就是最常规的RNN,即t时刻往前只展开了s(t-1) if (bptt<=1) { //bptt==1 -> normal BP //计算隐层的误差,即eh(t) for (a=0; a<layer1_size; a++) neu1[a].er=neu1[a].er*neu1[a].ac*(1-neu1[a].ac); //error derivation at layer 1 //这部分更新隐层到word部分的权值 //注意由于word部分是1-of-V编码 //所以这里更新的循环式上有点不同,并且下面的更新都是每10次训练更新才进行一次L2正规化 a=last_word; if (a!=-1) { if ((counter%10)==0) for (b=0; b<layer1_size; b++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac - syn0[a+b*layer0_size].weight*beta2; else //我们可以把这里的权值看做一个矩阵 //b表示行,a表示列,非L2正规化的完整更新式如下: /*for (b=0; b<layer1_size; b++) { for (k=0; k<vocab_size; k++) { syn0[k+b*layer0_size].weight+=alpha*neu1[b].er*neu0[k].ac; } }*/ //但由于neu0[k]==1只有当k==a时,所以为了加快循环计算的速度,更新就变为如下了 //下面的代码是类似的道理,其实这里的neu0[a].ac可以直接省略掉,因为本身值为1 for (b=0; b<layer1_size; b++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac; } //这部分更新隐层到s(t-1)的权值 if ((counter%10)==0) { for (b=0; b<layer1_size; b++) for (a=layer0_size-layer1_size; a<layer0_size; a++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac - syn0[a+b*layer0_size].weight*beta2; } else { for (b=0; b<layer1_size; b++) for (a=layer0_size-layer1_size; a<layer0_size; a++) syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac; } } else //BPTT { //BPTT部分权值就不在用syn0了,而是用bptt_syn0 //神经元部分的存储用bptt_hidden //将隐层的神经元信息复制到bptt_hidden,这里对neu1做备份 for (b=0; b<layer1_size; b++) bptt_hidden[b].ac=neu1[b].ac; for (b=0; b<layer1_size; b++) bptt_hidden[b].er=neu1[b].er; //bptt_block第一个条件是控制BPTT的,因为不能每训练一个word都用BPTT来深度更新参数 //这样每进行一次训练计算量太大,过于耗时 //word==0表示当前一个句子结束 //或者当independent开关不为0时,下一个词是句子的结束,则进行BPTT if (((counter%bptt_block)==0) || (independent && (word==0))) { //step表示 for (step=0; step<bptt+bptt_block-2; step++) { //计算隐层的误差向量,即eh(t) for (a=0; a<layer1_size; a++) neu1[a].er=neu1[a].er*neu1[a].ac*(1-neu1[a].ac); //error derivation at layer 1 //更新的是输入层中vocab_size那部分权值 //bptt_history下标从0开始依次存放的是wt, wt-1, wt-2... //比如当step == 0时,相当于正在进行普通的BPTT,这时bptt_history[step]表示当前输入word的在vocab中的索引 a=bptt_history[step]; if (a!=-1) for (b=0; b<layer1_size; b++) { //由于输入层word部分是1-of-V编码,所以neu0[a].ac==1 所以这里后面没有乘以它 //在step == 0时,bptt_syn0相当于原来的syn0 bptt_syn0[a+b*layer0_size].weight+=alpha*neu1[b].er; } //为从隐层往状态层传误差做准备 for (a=layer0_size-layer1_size; a<layer0_size; a++) neu0[a].er=0; //从隐层传递误差到状态层 matrixXvector(neu0, neu1, syn0, layer0_size, 0, layer1_size, layer0_size-layer1_size, layer0_size, 1); //propagates errors 1->0 //更新隐层到状态层的权值 //之所以先计算误差的传递就是因为更新完权值会发生改变 for (b=0; b<layer1_size; b++) for (a=layer0_size-layer1_size; a<layer0_size; a++) { //neu0[a].er += neu1[b].er * syn0[a+b*layer0_size].weight; bptt_syn0[a+b*layer0_size].weight+=alpha*neu1[b].er*neu0[a].ac; } //todo这里我理解是把论文中的s(t-1)复制到s(t),准备下一次循环 for (a=0; a<layer1_size; a++) { //propagate error from time T-n to T-n-1 //后面为什么会加bptt_hidden呢 neu1[a].er=neu0[a+layer0_size-layer1_size].er + bptt_hidden[(step+1)*layer1_size+a].er; } //历史中的s(t-2)复制到s(t-1) if (step<bptt+bptt_block-3) for (a=0; a<layer1_size; a++) { neu1[a].ac=bptt_hidden[(step+1)*layer1_size+a].ac; neu0[a+layer0_size-layer1_size].ac=bptt_hidden[(step+2)*layer1_size+a].ac; } } //清空历史信息中的er值 for (a=0; a<(bptt+bptt_block)*layer1_size; a++) { bptt_hidden[a].er=0; } //这里恢复neu1,因为neu1反复在循环中使用 for (b=0; b<layer1_size; b++) neu1[b].ac=bptt_hidden[b].ac; //restore hidden layer after bptt //将BPTT后的权值改变作用到syn0上 for (b=0; b<layer1_size; b++) { //copy temporary syn0 //bptt完毕,将bptt_syn0的权值复制到syn0中来,这是复制状态层部分 if ((counter%10)==0) { for (a=layer0_size-layer1_size; a<layer0_size; a++) { syn0[a+b*layer0_size].weight+=bptt_syn0[a+b*layer0_size].weight - syn0[a+b*layer0_size].weight*beta2; bptt_syn0[a+b*layer0_size].weight=0; } } else { for (a=layer0_size-layer1_size; a<layer0_size; a++) { syn0[a+b*layer0_size].weight+=bptt_syn0[a+b*layer0_size].weight; bptt_syn0[a+b*layer0_size].weight=0; } } //bptt完毕,将bptt_syn0的权值复制到syn0中来,这是word部分 if ((counter%10)==0) { for (step=0; step<bptt+bptt_block-2; step++) if (bptt_history[step]!=-1) { syn0[bptt_history[step]+b*layer0_size].weight+=bptt_syn0[bptt_history[step]+b*layer0_size].weight - syn0[bptt_history[step]+b*layer0_size].weight*beta2; bptt_syn0[bptt_history[step]+b*layer0_size].weight=0; } } else { //因为输入的word层是1-of-V编码,并不是全部的权值改变 //这样写可以加快计算速度,避免不必要的循环检索 for (step=0; step<bptt+bptt_block-2; step++) if (bptt_history[step]!=-1) { syn0[bptt_history[step]+b*layer0_size].weight+=bptt_syn0[bptt_history[step]+b*layer0_size].weight; bptt_syn0[bptt_history[step]+b*layer0_size].weight=0; } } } } } }
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