Title: GATED CONVNETS FOR LETTER-BASED ASR

Abstract: In this paper we introduce a new speech recognition system, leveraging a simple letter-based ConvNet acoustic model. The acoustic model requires only audio transcription for training -no alignment annotations, nor any forced alignment step is needed. At inference, our decoder takes only a word list and a language model, and is fed with letter scores from the acoustic model -no phonetic word lexicon is needed. Key ingredients for the acoustic model are Gated Linear Units and high dropout. We show near state-of-the-art results in word error rate on the LibriSpeech corpus (Panayotov et al., 2015) with MFSC features, both on the CLEAN and OTHER configurations.

1. INTRODUCTION:

Top speech recognition systems are either complicated pipelines or using more data that is publicly available. We set out to show that it is possible to train a nearly state of the art speech recognition system for read speech, with a public dataset (LibriSpeech), on a GPU-equipped workstation. Thus, we present an end-to-end system for speech recognition, going from Mel-Frequency Spectral Coefficients (MFSCs) to the transcription in words. The acoustic model is trained using letters (graphemes) directly, which take out the need for an intermediate (human or automatic) phonetic transcription.

The classical pipeline to build state of the art systems for speech recognition consists in first training an HMM/GMM model to force align the units on which the final acoustic model operates (most often context-dependent phone states). This approach takes its roots in HMM/GMM training (Woodland & Young, 1993) . The improvements brought by deep neural networks (DNNs) (Mohamed et al., 2012; Hinton et al., 2012) and convolutional neural networks (CNNs) (Sercu et al., 2016; Soltau et al., 2014) for acoustic modeling only extend this training pipeline. The current state of the art on LibriSpeech belongs to this approach too (Panayotov et al., 2015; Peddinti et al., 2015b) , with an additional step of speaker adaptation (Saon et al., 2013; Peddinti et al., 2015a) . Recently, Senior et al. (2014) proposed GMM-free training, but the approach still requires to generate a forced alignment.

An approach that cut ties with the HMM/GMM pipeline (and with forced alignment) was to train with a recurrent neural network (RNN) (Graves et al., 2013) for phoneme transcription. There are now competitive end-to-end approaches of acoustic models toppled with RNNs layers as in (Hannun et al., 2014; Miao et al., 2015; Saon et al., 2015; Amodei et al., 2016) , trained with a sequence criterion (Graves et al., 2006) . However these models are computationally expensive, and thus often take a long time to train. On conversational speech (that is not the topic of this paper), the state of the art is still held by complex ConvNets+RNNs acoustic models, coupled to domain-adapted language models (Xiong et al., 2017; Saon et al., 2017) .

Compared to classical approaches that need phonetic annotation (often derived from a phonetic dictionary, rules, and generative training), we propose to train the model end-to-end, using graphemes directly. Compared to sequence criterion based approaches that train directly from speech signal to graphemes (Miao et al., 2015) , we propose an RNN-free architecture based on convolutional networks for the acoustic model, toppled with a simple sequence-level variant of CTC.

We reach the clean speech performance of (Peddinti et al., 2015b) , but without performing speaker adaptation. Our word-error-rate on clean speech is better than (Amodei et al., 2016) , while being worse on noisy speech, but they train on 11,900 hours while we only train on the 960h available in LibriSpeech's train set. The rest of the paper is structured as follows: the next section presents the convolutional networks used for acoustic modeling, along with the automatic segmentation criterion and decoding approaches. The last section shows experimental results on LibriSpeech. 

2. ARCHITECTURE:

Our acoustic model (see an overview in Figure 1 ) is a Convolutional Neural Network (ConvNet) (LeCun & Bengio, 1995) , with Gated Linear Units (GLUs) (Dauphin et al., 2017) . The model is fed with 40 MFSCs features, and is trained with a variant of the Connectionist Temporal Classification (CTC) criterion (Graves et al., 2006) , which does not have blank labels but embarks a simple duration model through letter transitions scores (Collobert et al., 2016) . During training, we use dropout on the neural network outputs. At inference, the acoustic model is coupled with a decoder which performs a beam search, constrained with a count-based language model. We detail each of these components in the following.

2.1. MFSC FEATURES:

Our system relies on Mel-Frequency Spectral Coefficients (MFSCs), which are obtained by averaging spectrogram values with mel-scale filters. MFSCs are the step preceding the cosine transform required to compute Mel-Frequency Cepstrum Coefficients (MFCCs), often found in classical HMM/GMM speech systems (Woodland & Young, 1993) because of their dimensionality compression (13 coefficients are often enough to span speech frequencies). Compared to spectrogram coefficients, MFSCs have the advantage to be more robust to small time-warping deformations.

2.2. GATED CONVNETS FOR ACOUSTIC MODELING:

Our acoustic model is fed with the MFSC frames, and output letter scores for each input frame. At each time step, there is one score per letter in a given dictionary L. Words are separated by a special letter <sil>.

The acoustic model architecture is based on a 1D Gated Convolutional Neural Network (Gated ConvNet) (Dauphin et al., 2017) . Gated ConvNets stack 1D convolutions with Gated Linear Units. More formally, given an input sequence X ∈ R T ×d i with T frames of d-dimensional vectors, the i th layer of our network performs the following computation:

EQUATION

)

where * is the convolution operator, W i , V i ∈ R d i+1 ×d i ×k i and b, c ∈ R d i+1 are the learned parameters (with convolution kernel size k i ), σ(•) is the sigmoid function and ⊗ is the element-wise product between matrices.

Gated ConvNets have been shown to reduce the vanishing gradient problem, as they provide a linear path for the gradients while retaining non-linear capabilities, leading to state-of-the-art performance both for natural language modeling and machine translation tasks (Dauphin et al., 2017; Gehring et al., 2017) .

2.2.1. FEATURE NORMALIZATION AND ZERO-PADDING:

Each MFSC input sequence is normalized with mean 0 and variance 1. Given an input sequence X ∈ R T ×d , a convolution with kernel size k will output Tk + 1 frames, due to border effects. To compensate those border effects, we pad the MFSC features X 0 with zeroed frames. To take in account the whole network, the padding size is i (k i -1), divided in two equal parts at the beginning and the end of the sequence.

EQUATION

2.3. ACOUSTIC MODEL TRAINING:

Most large labeled speech databases provide only a text transcription for each audio file. In a classification framework (and given our acoustic model produces letter predictions), one would need the segmentation of each letter in the transcription to train properly the model. Manually labeling the segmentation of each letter would be tedious. Several solutions have been explored in the speech community to alleviate this issue:

1. HMM/GMM models use an iterative EM procedure: during the Estimation step, the best segmentation is inferred according to the current model, during the Maximization step the model is optimized using the current inferred segmentation. This approach is also often used to boostrap the training of neural network-based acoustic models.

2. In the context of hybrid HMM/NN systems, the MMI criterion (Bahl et al., 1986) maximizes the mutual information between the acoustic sequence and word sequences or the Minimum Bayes Risk (MBR) criterion (Gibson & Hain, 2006) . Recent state-of-the-art systems leverage the MMI criterion (Povey et al., 2016) .

3. Standalone neural network architectures have also been trained using the Connectionist Temporal Classification (CTC), which jointly infers the segmentation of the transcription while increase the overall score of the right transcription (Graves et al., 2006) . In (Amodei et al., 2016) it has been shown that letter-based acoustic models trained with CTC could compete with existing phone-based systems, assuming enough training data is provided.

In this paper, we chose a variant of the Connectionist Temporal Classification. CTC considers all possible sequence sub-word units (e.g. letters), which can lead to the correct transcription. It also allow a special "blank" state to be optionally inserted between each sub-word unit. The rational behind the blank state is two-folds: (i) modeling "garbage" frames which might occur between each letter and (ii) identifying the separation between two identical consecutive sub-word unit in a transcription. Figure 2a shows the CTC graph describing all the possible sequences of letters leading to the word "cat", over 6 frames. We denote G ctc (θ, T ) the CTC acceptance graph over T frames for a given transcription θ, and π = π 1 , . . . , π T ∈ G ctc (θ, T ) a path in this graph representing a (valid) sequence of letters for this transcription. CTC assumes that the network output probability scores, normalized at the frame level. At each time step t, each node of the graph is assigned with its corresponding log-probability letter i (that we denote f t i (X)) output by the acoustic model (given an acoustic sequence X). CTC minimizes the Forward score over the graph G ctc (θ, T ):

EQUATION

where the "logadd" operation (also called "log-sum-exp") is defined as logadd(a, b) = log(exp(a) + exp(b)). This overall score can be efficiently computed with the Forward algorithm.

2.3.1. THE ASG CRITERION:

Blank labels introduce complexity when decoding letters into words. Indeed, with blank labels "ø", a word gets many entries in the sub-word unit transcription dictionary (e.g. the word "cat" can be represented as "c a t", "c ø a t", "c ø a t", "c ø a ø t", etc... -instead of only "c a t"). We replace the blank label by special letters modeling repetitions of preceding letters. For example "caterpillar" can be written as "caterpil1ar", where "1" is a label to represent one repetition of the previous letter.

Removing blank labels from the CTC acceptance graph G ctc (θ, T ) (shown in Figure 2a ) leads to a simpler graph that we denote G asg (θ, T ) (shown in Figure 2b ). Unfortunately, in practice we observed that most models do not train with this simplification of CTC. Adding unormalized transition scores g i,j (•) on each edge of the graph, when moving from label i to label j fix the issue. We observed in practice that normalized transitions led to similar issue that not having transitions. Considering unnormalized transition scores implies implementing a sequence-level normalization, to avoid the model to diverge (represented by the graph G asg (θ, T ), as shown in Figure 2c ). This leads to the following criterion, dubbed ASG for "Auto SeGmentation":

ASG(θ, T ) = -logadd π∈Gasg(θ,T ) T t=1 (f t πt (X)+g πt-1,πt (X))+ logadd π∈G f ull (θ,T ) T t=1 (f t πt (X)+g πt-1,πt (X)) .

(3) The left-hand part in Equation (3) promotes the score of sequences letters leading to the right transcription (as in Equation (2) for CTC), and the right-hand part demotes the score of all sequences of letters (as does the frame-level normalization -that is the softmax on the acoustic model -for CTC). As for CTC, these two parts can be efficiently computed with the Forward algorithm. When removing transitions in Equation (3), the sequence-level normalization becomes equivalent to the frame-level normalization and the ASG criterion is mathematically equivalent to CTC with no blank labels.

2.3.2. OTHER TRAINING CONSIDERATIONS:

We apply dropout at the output to all layers of the acoustic model. Dropout retains each output with a probability p, by applying a multiplication with a Bernoulli random variable taking value 1/p with probability p and 0 otherwise (Srivastava et al., 2014) .

Following the original implementation of Gated ConvNets (Dauphin et al., 2017), we found that using both weight normalization (Salimans & Kingma, 2016) and gradient clipping (Pascanu et al., 2013) were speeding up training convergence. The clipping we implemented performs:

EQUATION

)

where C is either the CTC or ASG criterion, and is some hyper-parameters which controls the maximum amplitude of the gradients. 

2.4. BEAM-SEARCH DECODER:

We wrote our own one-pass decoder, which performs a simple beam-search with beam threholding, histogram pruning and language model smearing Steinbiss et al. (1994) . We kept the decoder as simple as possible (under 1000 lines of C code). We did not implement any sort of model adaptation before decoding, nor any word graph rescoring. Our decoder relies on KenLM Heafield et al. (2013) for the language modeling part. It also accepts unnormalized acoustic scores (transitions and emissions from the acoustic model) as input. The decoder attempts to maximize the following:

EQUATION

)

where P lm (θ) is the probability of the language model given a transcription θ, α, β, and γ are three hyper-parameters which control the weight of the language model, the word insertion penalty, and the silence insertion penalty, respectively.

The beam of the decoder tracks paths with highest scores according to Equation ( 5), by bookkeeping pair of (language model, lexicon) states, as it goes through time. The language model state corresponds the (n -1)-gram history of the n-gram language model, while the lexicon state is the sub-word unit position in the current word hypothesis. To maintain diversity in the beam, paths with identical (language model, lexicon) states are merged. Note that traditional decoders combine the scores of the merge paths with a max(•) operation (as in a Viterbi beam-search) -which would correspond to a max(•) operation in Equation ( 5) instead of logadd(•). We consider instead the logadd(•) operation, as it takes in account the contribution of all the paths leading to the same transcription, in the same way we do during training (see Equation ( 3)). In Section 3.1, we show that this leads to better accuracy in practice.

3. EXPERIMENTS:

We benchmarked our system on LibriSpeech, a large speech database freely available for download (Panayotov et al., 2015) . We kept the original 16 kHz sampling rate. We considered the two available setups in LibriSpeech: CLEAN data and OTHER. We picked all the available data (about 960h of audio files) for training, and the available development sets (both for CLEAN, and OTHER) for tuning all the hyper-parameters of our system. Test sets were used only for the final evaluations.

The letter vocabulary L contains 30 graphemes: the standard English alphabet plus the apostrophe, silence (<SIL>), and two special "repetition" graphemes which encode the duplication (once or twice) of the previous letter (see Section 2.3.1). Decoding is achieved with our own decoder (see Section 2.4), with the standard 4-gram language model provided with LibriSpeech1 , which contains 200, 000 words. In the following, we either report letter-error-rates (LERs) or word-error-rates (WERs).

MFSC features are computed with 40 coefficients, a 25 ms sliding window and 10 ms stride.

We implemented everything using TORCH72 . The ASG criterion as well as the decoder were implemented in C (and then interfaced into TORCH). We tuned our acoustic model architectures by grid search, validating on the dev sets. We consider here two architectures, with low and high amount of dropout (see the parameter p in Section 2.3.2). Table 1 reports the details of our architectures. The amount of dropout, number of hidden units, as well as the convolution kernel width are increased linearly with the depth of the neural network. Note that as we use Gated Linear Units (see Section 2.2), each layer is duplicated as stated in Equation (1).

Convolutions are followed by a fully connected layer, before the final layer which outputs 30 scores (one for each letter in the dictionary). This leads to about 130M and 208M of trainable parameters for the LOW DROPOUT and HIGH DROPOUT architectures, respectively.

Figure 3 shows the LER and WER on the LibriSpeech development sets, for the first 40 training epochs of our LOW DROPOUT architecture. LER and WER appear surpringly well correlated, both on the "clean" and "other" version of the dataset.

In Table 2 , we report WERs on the LibriSpeech development sets, both for our LOW DROPOUT and HIGH DROPOUT architectures. Increasing dropout regularize the acoustic model in a way which impacts significantly generalization, the effect being stronger on noisy speech. We also report the WER for the decoder ran with the max(•) operation (instead of logadd(•) for other results) used to aggregate paths in the beam with identical (language model, lexicon) states. It appears advantageous (as there is no complexity increase in the decoder) to use the logadd(•) aggregation.

3.2. COMPARISON WITH OTHER SYSTEMS:

In Table 3 , we compare our system with several of the best systems on LibriSpeech reported in the literature. We highlighted the acoustic model architectures, as well as the type of underlying sub-word unit. Note that phone-based acoustic models output in general senomes; senomes are carefully selected through a complicated procedure involving a phonetic-context-based decision tree built from another GMM/HMM system. Phone-based system also require an additional word lexicon which translates words into a sequence of phones. Most systems also perform speaker adaptation; iVectors compute a speaker embedding capturing both speaker and environment information (Xue (Waibel, 1989) . We also report extra information (besides word transcriptions) which might be used by each system, including speaker adaptation, or any other domain-specific data. Woodland, 1996) .

DEEP SPEECH 2 (Amodei et al., 2016) is the system which is the most related to ours. In contrast to other systems which combine a Hidden Markov Model (HMM) with a ConvNet, DEEP SPEECH 2 is a standalone neural network. In contrast to our system, DEEP SPEECH 2 embarks a more complicated acoustic model composed of a ConvNet and a Recurrent Neural Network (RNN), while our system is a simple ConvNet. Both Deep Speech 2 and our system rely on letters for acoustic modeling, alleviating the need of a phone-based word lexicon. DEEP SPEECH 2 relies on a lot of speech data (combined with a very large 5-gram language model) to make the letter-base approach competitive , while we limited ourselves to the available data in the LibriSpeech benchmark.

In Table 4 , we report a comparison in WER performance for all systems introduced in Table 3 . Our system is very competitive with existing approaches. DEEP SPEECH 2 -which is also a letter-based system -is outperformed on clean data, even though our system has been trained with an order of magnitude less data. We report also the WER with no decoder, that is taking the raw output of the neural network, with no alterations. The Gated ConvNet appears very good at modeling true words.

Using a single GPU (no batching), our HIGH DROPOUT Gated ConvNet goes over the CLEAN (5.4h) and OTHER (5.1h) test sets in 4min26s and 4min43s, respectively. The decoder runs over the CLEAN and OTHER sets in 3min56s and 30min5s, using only one CPU thread -which (considering the decoder alone) corresponds to a .01 and 0.1 Real Time Factor (RTF), respectively.

4. CONCLUSION:

We have introduced a simple end-to-end automatic speech recognition system, which combines a large (208M parameters) but efficient ConvNet acoustic model, an easy sequence criterion which can infer the segmentation, and a simple beam-search decoder. The decoding results are competitive on the LibriSpeech corpus (4.8% WER dev-clean). Our approach breaks free from HMM/GMM pre-training and forced alignment, as well as not being as computationally intensive as RNN-based approaches (Amodei et al., 2016) . We based all our work on a publicly available (free) dataset, all of which should make it easier to reproduce. Further work should include leveraging speaker identity, training from the raw waveform, data augmentation, training with more data, better language models.

:

http://www.openslr.org/11.

http://www.torch.ch.

Figures and Tables:

Figure1: Overview of our acoustic model, which computes MFSC features which are fed to a Gated ConvNet. The ConvNet output one score for each letter in the dictionary, and for each MFSC frame. At inference time, theses scores are fed to a decoder (see Section 2.4) to form the most likely sequence of words. At training time, the scores are fed to the ASG criterion (see Figure2) which promotes sequences of letters leading to the transcrition sequence (here "c a t").

Figure 2: (a) The CTC graph which represents all the acceptable sequences of letters for the transcription "cat" over 6 frames. (b) The same graph used by ASG, where blank labels have been discarded. (c) The fully connected graph describing all possible sequences of letter; this graph is used for normalization purposes in ASG. Un-normalized transitions scores are possible on edges of these graphs. At each time step, nodes are assigned a conditional un-normalized score, output by the Gated ConvNet acoustic model.

Figure 3: LibriSpeech Letter Error Rate (LER) and Word Error Rate (WER) for the first training epochs of our LOW DROPOUT architecture. (a) is on dev-clean, (b) on dev-other.

Architectures details. "#conv." is the number of convolutional layers. Dropout amplitude, "#hu" (number of output hidden units) and "kw" (convolution kernel width) are provided for the first and last layer (all are linearly increased with layer depth). The size of the final layer is also provided.

Table content: <table><tr><td>Architecture</td><td colspan="2">#conv. dropout</td><td>dropout</td><td>#hu</td><td>#hu</td><td>kw</td><td>kw</td><td>#hu</td></tr><tr><td/><td/><td colspan="7">first layer last layer first layer last layer first layer last layer full connect</td></tr><tr><td>Low Dropout</td><td>17</td><td>0.25</td><td>0.25</td><td>200</td><td>750</td><td>13</td><td>27</td><td>1500</td></tr><tr><td>High Dropout</td><td>19</td><td>0.20</td><td>0.60</td><td>200</td><td>1000</td><td>13</td><td>29</td><td>2000</td></tr></table>

Comparison in LER and WER of variants of our model on LibriSpeech. When not specified, decoding is performed with the logadd(•) operation to aggregate similar hypothesis (see Section 2.4).

Table content: <table><tr><td>dev-clean</td><td>dev-other</td></tr></table>

Comparison of different ASR systems. We report the type of acoustic model used for various systems, as well as the type of sub-word unit. HMM stands for Hidden Markov Model, CNN for ConvNet; when not specified, CNNs are 1D (also called Time-Delay Neural Networks -TDNN -in the literature). pNorm is a particular non-linearity

Table content: <table/>

Comparison in WER of our model with other systems on LibriSpeech.

Table content: <table><tr><td/><td colspan="2">test-clean test-other</td></tr><tr><td>(Panayotov et al., 2015)</td><td>5.5</td><td>14.0</td></tr><tr><td>(Amodei et al., 2016)</td><td>5.3</td><td>13.3</td></tr><tr><td>(Peddinti et al., 2015b)</td><td>4.8</td><td>-</td></tr><tr><td>(Povey et al., 2016)</td><td>4.3</td><td>-</td></tr><tr><td>(Ko et al., 2015)</td><td>-</td><td>12.5</td></tr><tr><td>this paper</td><td>4.8</td><td>14.5</td></tr><tr><td>this paper (no decoder)</td><td>6.7</td><td>20.8</td></tr><tr><td colspan="3">et al., 2014), while fMMLR is a two-pass decoder technique which computes a speaker transform in</td></tr><tr><td>the first pass (Gales &amp;</td><td/><td/></tr></table>

Peer review (iclr2018):
 The paper is interesting, but needs more work, and should provide clear and fair comparisons. Per se, the model is incrementally new, but it is not clear what the strengths are, and the presentations needs to be done more carefully. In detail: - please fix several typos throughout the manuscript, and have a native speaker (and preferably an ASR expert) proofread the paper Introduction - please define HMM/GMM model (and other abbreviations that will be introduced later), it cannot be assumed that the reader is familiar with all of them ("ASG" is used before it is defined, ...) - The standard units that most ASR systems use can be called "senones", and they are context dependent sub-phonetic units (see http://ssli.ee.washington.edu/~mhwang/), not phonetic states. Also the units that generate the alignment and the units that are trained on an alignment can be different (I can use a system with 10000 states to write alignments for a system with 3000 states) - this needs to be corrected. - When introducing CNNs, please also cite Waibel and TDNNs - they are *the same* as 1-d CNNs, and predate them. They have been extended to 2-d later on (Spatio-temporal TDNNs) - The most influential deep learning paper here might be Seide, Li, Yu Interspeech 2011 on CD-DNN-HMMs, rather than overview articles - Many papers get rid of the HMM pipeline, I would add https://arxiv.org/abs/1408.2873, which predates Deep Speech - What is a "sequence-level variant of CTC"? CTC is a sequence training criterion - The reason that Deep Speech 2 is better on noisy test sets is not only the fact they trained on more data, but they also trained on "noisy" (matched) data - how is this an end-to-end approach if you are using an n-gram language model for decoding? Architecture - MFSC are log Filterbanks ... - 1D CNNs would be TDNNs - Figure 2: can you plot the various transition types (normalized, un-normalized, ...) in the plots? not sure if it would help, but it might - Maybe provide a reference for HMM/GMM and EM (forward backward training) - MMI was also widely used in HMM/GMM systems, not just NN systems - the "blank" states do *not* model "garbage" frames, if one wants to interpret them, they might be said to model "non-stationary" frames between CTC "peaks", but these are different from silence, garbage, noise, ... - what is the relationship of the presented ASG criterion to MMI? the form of equation (3) looks like an MMI criterion to me? Experiments - Many of the previous comments still hold, please proofread - you say there is no "complexity" incrase when using "logadd" - how do you measure this? number of operations? is there an implementation of "logadd" that is (absolutely) as fast as "add"? - There is discussion as to what i-vectors model (speaker or environment information) - I would leave out this discussion entirely here, it is enough to mention that other systems use adaptation, and maybe re-run an unadapted baselien for comparsion - There are techniques for incremental adaptation and a constrained MLLR (feature adaptation) approaches that are very eficient, if one wnats to get into this - it may also be interesting to discuss the role of the language model to see which factors influence system performance - some of the other papers might use data augmentation, which would increase noise robustness (did not check, but this might explain some of the results in table 4) - I am confused by the references in the caption of Table 3 - surely the Waibel reference is meant to be for TDNNs (and should appear earlier in the paper), while p-norm came later (Povey used it first for ASR, I think) and is related to Maxout - can you also compare the training times? Conculsion - can you show how your approach is not so computationally expensive as RNN based approaches? either in terms of FLOPS or measured times