LSTM TIME AND FREQUENCY RECURRENCE FOR AUTOMATIC SPEECH RECOGNITION

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1 LSTM TIME AND FREQUENCY RECURRENCE FOR AUTOMATIC SPEECH RECOGNITION Jinyu Li, Abderahman Mohamed, Geoffrey Zweig, and Yifan Gong Microsoft Corporation, One Microsoft Way, Redmond, WA { jinyi, asamir, gzweig, ygong}@microsoft.com ABSTRACT Long short-term memory (LSTM) recurrent neura networks (RNNs) have recenty shown significant performance improvements over deep feed-forward neura networks (DNNs). A key aspect of these modes is the use of time recurrence, combined with a gating architecture that ameiorates the vanishing gradient probem. Inspired by human spectrogram reading, in this paper we propose an extension to LSTMs that performs the recurrence in frequency as we as in time. This mode first scans the frequency bands to generate a summary of the spectra information, and then uses the output ayer activations as the input to a traditiona time LSTM (T-LSTM). Evauated on a Microsoft short message dictation task, the proposed mode obtained a 3.6% reative word error rate reduction over the T- LSTM. Index Terms LSTM, RNN, time and frequency 1. INTRODUCTION Recenty, significant progress has been made in automatic speech recognition (ASR) thanks to the appication of deep neura networks (DNNs) [1][2][3][4][5][6]. Unike in the 1990s, today s DNN systems often contain tens of miions of parameters and are more powerfu than their counterparts two decades ago [7][8] in modeing speech signas. DNNs, however, ony consider information in a fixed-ength siding window of frames and thus cannot expoit ong-range correations in the signa. Recurrent neura networks (RNNs), on the other hand, can encode sequence history in their interna state, and thus have the potentia to predict phonemes based on a the speech features observed up to the current frame. Unfortunatey, simpe RNNs, depending on the argest eigenvaue of the state-update matrix, may have gradients which either increase or decrease exponentiay over time. Thus, the basic RNN is difficut to train, and in practice can ony mode short-range effects. Long short-term memory (LSTM) RNNs [9][10] were deveoped to overcome these probems. LSTM-RNNs use input, output and forget gates to achieve a network that can maintain state and propagate gradients in a stabe fashion over ong spans of time. These networks have been shown to outperform DNNs on a variety of ASR tasks [11][12][13] [14][15][16]. A previousy proposed LSTMs use a recurrence aong the time axis to mode the tempora patterns of speech signas, and we ca them T-LSTMs in this paper. The main contribution of this paper is the proposa of a two-eve network where the first eve performs recurrence aong the frequency axis, and the second performs time recurrence. We term this the frequency-time LSTM or F-T-LSTM. Our mode is inspired by the way peope read spectrograms. Note that in common practice, og-fiter-bank features are often used as the input to the neura-networkbased acoustic mode [19][20]. In standard systems, the ogfiter-bank features are independent of one-another, i.e. switching the positions of two fiter-banks won t affect the performance of the DNN or LSTM. However, this is not the case when a human reads a spectrogram: a human reies on both patterns that evove on time, and frequency, to predict phonemes. Switching the positions of two fiter-banks wi destroy the frequency-wise patterns. Our mode addresses this phenomenon by expicity modeing the frequency-wise evoution of spectra patterns. Evauated on a Microsoft interna short message dictation task, the proposed F-T- LSTM obtained 3.6% reative word error rate (WER) reduction from the T-LSTM. The rest of the paper is organized as foows. In Section 2, we briefy introduce LSTMs and then we present the proposed mode which combines frequency LSTM and time LSTM in Section 3. We differentiate the proposed method from the convoutiona LSTM DNN (CLDNN) [16] and muti-dimensiona RNN [17][18] in Section 4. Experimenta evauation of the agorithm is provided in Section 5. We summarize our study and draw concusions in Section THE LSTM-RNN An RNN is fundamentay different from the feed-forward DNN in that the RNN does not operate on a fixed window of frames; instead, it maintains a hidden state vector, which is recursivey updated after seeing each time frame. The interna state encodes the history a the way from the beginning of an utterance up to the ast input, and can thus potentiay mode much onger span effects than a fixed-window DNN. In other words, an RNN is a dynamic system and is more genera than the DNN which performs a static input-output transformation. The incusion of interna states enabes RNNs to represent and earn ong-range sequentia dependencies.

2 However, the simpe RNN suffers from the vanishing/expoding gradient probem [21] when the error signa is back-propagated through time. This probem is we handed in the LSTM-RNNs through the use of the foowing four components: Memory units: these store the tempora state of the network; Input gates: these moduate the input activations into the ces; Output gates: these moduate the output activations of the ces ; Forget gates: these adaptivey reset the ce s memory. Taken together as in Figure 1 beow, these four components are termed a LSTM ce. 3. FREQUENCY-TIME LSTM-RNN In this section, we propose a frequency-time LSTM (F-T- LSTM) which combines frequency LSTM with time LSTM as shown in Figure 2. We first use a frequency LSTM (F- LSTM) to scan the frequency bands so that frequencyevoving information is summarized by the output of the F- LSTM. The formuation of the F-LSTM is the same as that of the T-LSTM except that the index j now stands for frequency steps instead of time steps. Then we can take the outputs from a F-LSTM steps and use them as the input to T-LSTM to do time anaysis in the traditiona way. Time Anaysis Figure 1. Architecture of LSTM-RNNs with one recurrent ayer. Z 1 is a time-deay node. Figure 1 depicts the architecture of an LSTM-RNN with one recurrent ayer. In LSTM-RNNs, in addition to the past hidden-ayer output h t 1, the past memory activation c t 1 is aso an input to the LSTM ce. This mode can be described as: i j = σ(w xi x j + W hi h j 1 + W ci c j 1 + b i ), (1) f j = σ(w xf c j = f j. c j 1 o j = σ(w xo x j + W hf h j 1 + W cf + i j. tanh(w xc x j + W ho h j 1 + W co c j 1 + b f ), (2) x j + W hc h j 1 + b c ), (3) c j + b o ), (4) h j = o j. tanh(c j ), (5) where i j, o j, f j, and c j denote the activation vectors of input gate, output gate, forget gate, and memory ce at the -th ayer and time j, respectivey. h j is the output of the LSTM ces at ayer and time j. W terms denote different weight matrices. For exampe, W xi is the weight matrix from the ce input to the input gate at the -th ayer. b terms are the bias terms (e.g., b i is the bias of input gate at ayer ).. denotes eement wise mutipication. In [13], a LSTM with an additiona projection ayer prior to the output (termed ) was proposed to reduce the computationa compexity of LSTM. A projection ayer is appied to h j as r j = W hr h j And then h j 1 in Eqs (1)--(4) is repaced by r j 1. Frequency Time Frequency Anaysis Figure 2: A frequency- time LSTM-RNN which scans the frequency axis first for frequency anaysis and then scans the time axis for time anaysis. The detaied F-LSTM processing for each time step is described as foows. Divide tota N og-fiter-banks at current time into M overapped chunks and each chunk contains B ogfiter-banks. There are C og-fiter-banks overapped between adjacent chunks. Here we have the reationship M = N C. An extreme case is C=0 B C where there is no overapped og-fiter-bank. In such a case, M = N. B Use the M overapped chunks as the frequency steps of F-LSTM and generate the output of h m, m = 0 M 1.

3 Merge h m, m = 0 M 1. into a super-vector h which can be considered as a trajectory of frequency patterns at current time. Then use h as the input to a T-LSTM with mutipe ayers. Figure 3 shows an exampe setup of the F-LSTM used in our experiments. The input at each frame consists of a 40 dimensiona vector of og-fiter-bank vaues at the current time t. We divide the 40 og-fiter-bank channes into 33 overapped chunks with each chunk containing 8 og-fiterbanks. This resuts in 7 og-fiter-banks of overap between adjacent chunks (C=7). Therefore, the first F-LSTM ce takes eight inputs: the og-fiter-banks from 0 to 7, and the second F-LSTM ce takes the og-fiter-banks from 1 to 8, and so on. The m-th F-LSTM ce generates outputs h m, which wi be passed into the m+1-th F-LSTM ce. Finay, h m, m = 0 M 1 (M=33 in this exampe) wi be concatenated as the input to a T-LSTM. 4. RELATION TO PRIOR WORK In this section, we first discuss the difference between our proposed F-T-LSTM and the convoutiona LSTM DNN (CLDNN) [16] which combines CNNs, LSTMs, and DNNs together. The CLDNN first uses a CNN [22][23] to reduce the spectra variation, and then the output of the CNN ayer is fed into a muti-ayer LSTM to earn the tempora patterns. Finay, the output of the ast LSTM ayer is fed into severa fuy connected DNN ayers for the purpose of cassification. The key difference between the proposed F-T-LSTM and the CLDNN is that the F-T-LSTM uses frequency recurrence with the F-LSTM, whereas the CLDNN uses a siding convoutiona window for pattern detection with the CNN. Whie the siding window achieves some invariance through shifting, it is not the same as a fuy recurrent network. The two approaches both aim to achieve invariance to input distortions, but the pattern detectors in the CNN maintain a constant dimensionaity, whie the F-LSTM can perform a genera frequency warping. The proposed F-T-LSTM performs 1-D recurrence over the frequency axis and then performs 1-D recurrence over the time axis. This is different from the concept of mutidimensiona processing which has been proved very successfu in the handwriting recognition tasks [17][18] and outperformed the traditiona handwriting systems that use CNNs [22][23] as the feature extractor. To summarize, the T-F-LSTM works on mutidimensiona space separatey with simpicity whie the mutidimensiona RNN [17][18] works jointy on mutidimensiona space with more powerfu modeing. 5. EXPERIMENTS AND DISCISSIONS In this section, we use a Windows Phone short message dictation task to evauate the proposed method. The training data consists of 60 hours of transcribed US-Engish audio. The test set consists of 3 hours of data from the same Windows Phone task. The audio data is 16k HZ samped, recorded in mobie environments using Windows phones. The vocabuary has around 130k words and the LM has around 6.6M ngrams (up to trigram). A experiments were conducted using the computationa network tookit (CNTK) [24], which aows us to buid and evauate various network structures efficienty without deriving and impementing compicated training agorithms. A the modes were trained to minimize the frame-eve cross-entropy criterion. Figure 3: An exampe setup of F-LSTM. The input to the baseine CD-DNN-HMM system consists of 40-dimensiona og-fiter-bank features. We augment these feature vectors with 5 frames of context on either side (5-1-5). The DNN has 5 hidden ayers, each with 2048 sigmoid units. Both the baseine and LSTM systems use 1812 tied-triphone states or senones. The baseine T- is modeed after that in [13]. It has four T- ayers: each has 1024 hidden units and the

4 output size of each T-LSTM ayer is reduced to 512 using a inear projection ayer. There is no frame stacking, and the output HMM state abe is deayed by 5 frames as in [13]. When training T-, the backpropagation through time (BPTT) [25] step is 20. We buit the F-T-LSTM with a singe F-LSTM that scans the og-fiter-banks and three T- ayers. The number of parameters of the F-T-LSTM is between the numbers of parameters of the three- and four- ayer s. To generate the input to the F-LSTM, we use the exampe setup in Section 3 by dividing the 40 og-fiter-bank channes into 33 overapped chunks with each chunk containing 8 og-fiterbanks. The F-LSTM has 24 memory ces. In Tabe 1, we compare the WERs of a DNN, T-LSTM, and F-T-LSTM. The T-LSTM is ceary better than the DNN due to its tempora modeing power. With both the frequency and tempora modeing, the F-T-LSTM is better than the 4- ayer T-LSTM, with 3.6% reative WER reduction. Tabe 1: WER comparison of DNN, T-LSTM, and F-T- LSTM Mode WER (%) DNN ayer T ayer T F-LSTM (24 ces)+3-ayer T We investigate the impact of different ce numbers in the F-LSTM in Tabe 2. When the number of ces is very sma, e.g., 8, the power of F-LSTM is very imited with ony a sight improvement over the T-LSTM. However, when the number of ces becomes 24, the F-LSTM shows its advantage because the memory ces are powerfu enough to store the frequency patterns. When we increase the number of ces to 48, there is no further improvement. Tabe 2: Impact of ce numbers in F-LSTM Mode WER (%) F-LSTM (8 ces)+3-ayer T F-LSTM (24 ces)+3-ayer T F-LSTM (48 ces)+3-ayer T In a the aforementioned experiments, we have not stacked mutipe frames of og-fiter-banks as the input to F-T-LSTM. This decision is made based on our previous experience with T-LSTMs, where we found that stacking mutipe frame inputs doesn t have any benefit, and [13] aso doesn t have the frame stacking. In Tabe 3, we compare the setup with and without mutipe-frame stacking. Stacking N frames means that every chunk now has 8*N og-fiter-banks. When stacking 11 frames, we predict the center frame s abe. As shown in Tabe 3, it doesn t provide any benefit to WER by stacking 11 frames as the input to F-LSTM. Tabe 3: Comparison of F-T-LSTM with and without stacking frame inputs Mode Number of Input Frames WER (%) F-LSTM (24 ces) ayer T- F-LSTM (24 ces) ayer T- F-LSTM (48 ces) ayer T- F-LSTM (48 ces)+3- ayer T CONCLUSIONS AND FUTURE WORK In this paper, we have presented a FT--LSTM architecture that scans both the time and frequency axis to mode the evoving patterns of the spectrogram. The F-T-LSTM first uses an F-LSTM to performs a frequency recurrence that summarizes frequency-wise patterns. This is then fed into a T-LSTM. The proposed F-T-LSTM obtained a 3.6% reative WER reduction from the traditiona T-LSTM on a short message dictation task. We have shown that as ong as the number of memory ces in the F-LSTM is reasonabe, the F- T-LSTM can achieve good performance. We aso evauated the impact of stacking mutipe frames as the input to F- LSTM, and found that it is best to simpy present the frames one at a time Severa research issues wi be addressed in the future to further increase the effectiveness of the agorithm presented in this paper. First, we wi compare the performance of F-T- LSTMs with CLDNNs to better understand their reative advantages. Second, we want to expore architectura variants of the F-T-LSTM. For exampe, we wi examine whether frequency overapping of the input to F-LSTM is necessary. Third, we wi move the input of F-LSTM from og-fiterbanks directy to og-spectrum. There are studies showing that directy working of og-spectrum can be beneficia to DNN [26]. By appying the F-LSTM directy on ogspectrum, we can naturay remove the hand-crafted fiterbanks, and automaticay earn the frequency patterns that benefit the recognizer. Fourth, in [27] it is shown that CNNs can consistenty provide advantages over DNNs in mismatched training-test conditions. It is interesting to see whether the frequency recurrence brought by the F-LSTM can be more hepfu in the mismatched conditions. Last and most importanty, we wi advance our study by proposing a mutidimensiona LSTM with a simpified structure which performs recurrence over the time and frequency axes jointy [28]. We term it the time-frequency LSTM (TF-LSTM). We wi compare TF-LSTM and F-T-LSTM in [28] by using a much arger ASR task. It wi be shown that F-T-LSTM is sti effective on that arger ASR task.

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