Learning Noise-Invariant Representations for Robust Speech Recognition

Introduction

Over the past several years, a series of papers have developed end-to-end deep learning systems for automatic speech recognition (ASR), advancing the state of the art on a variety of benchmarks . Typically, these models consist of either Recurrent Neural Networks (RNNs) with Sequence-to-Sequence (Seq2Seq) architectures and attention mechanisms , RNN transducers , transformer networks , convolutional neural networks paired with transformer networks , or RNNs trained with CTC loss . Often, these models act on spectral features, e.g., Mel-Frequency Cepstral Coefficients (MFCC) .

While these systems achieve impressive accuracy when trained and evaluated on clean data, they suffer a well-documented sensitivity to changing noise levels and various noise types . Perhaps this vulnerability should not be surprising, given the significant impact that background noise can have on MFCC features .

One simple strategy to combat the vulnerability of deep nets to background noise is a technique known generally as data augmentation, and as multi-condition training in the speech recognition community. Here, we augment the original data by applying transformations to which we want our models to be invariant and assigning these perturbed data points the same label as the unperturbed originals. While the computer vision literature has long focused on perturbations like random crops, rotations, translations, and Gaussian noise , data augmentation papers in the ASR literature commonly sample snippets of additive background noise from datasets such as MUSAN , which contains environmental noise (dial tones, thunder, footsteps, animal noises, etc), music (baroque, classical, romantic, jazz, bluegrass, hip-hop, etc.), and speech. ASR models trained with such augmented data have demonstrated lower grapheme error rates on noisy data .

In this paper, we draw inspiration from the human ability to recognize not only that a clean clip and its noisy counterpart belong to the same category but that they are produced from the same exact recording. Thus, we propose models that map both clean inputs and their noisy counterparts onto the same point in representation space, introducing this inductive bias via regularization terms, penalizing differences between the hidden representations produced from real and noisy data. Throughout training, for each clean example, we synthesize one noisy counterpart, using a custom data augmentation pipeline that first selects a random noise snippet and volume level, adding the two raw waveforms and then generating the corresponding MFCC features on the fly. At each iteration, we apply the original cross-entropy loss on the predictions for both clean and perturbed inputs and also penalize the difference in hidden activations encouraging corresponding activations as quantified by both cosine distance and $L_{2}$ distance.

Our experiments address the Librispeech dataset , building on a Seq2Seq baseline with cross-entropy loss. To keep the empirical study clean, we do not use a language model. We run all experiments both on the standard dev and test sets and also under a variety of out-of-domain noise conditions. First, we show that while data augmentation improves generalization error on both the original task and under out-of-domain noise, the models still suffer significant degradation in performance. Next, we show that Invariant-Representation Learners (IRLs) improve significantly over generic data augmentation models, both on the clean and other (the more challenging dataset with higher word error rate) subsets of the LibriSpeech test set. Comparisons against an adversarial approach proposed by and the logit pairing approach due to demonstrate the significant advantage of IRL. We then demonstrate that on a variety of simulated out-of-domain noise conditions, the IRL models are considerably more robust than all baselines. Finally, we perform ablation experiments, showing that our models trained with the IRL algorithm outperform well-known regularization tactics like weight decay applied on the same representations.

A number of proposed models address the goal of noise-robust speech recognition: proposes a method called noise-aware training that introduces information about the environment as additional inputs to DNN-based acoustic models. proposes augmenting training examples with additive noise sampled from the DEMAND noise database training examples. seeks noise-invariant representations in DNN-HMM architectures through an adversarial learning setup. shows the training on multi-modal data leads to noise robust models. demonstrates that modeling speech as a linear combination of exemplars results in noise-robust ASR models. proposes deep recurrent autoencoders to denoise input features. presents an overview of methods for noise-robust ASR, including recursive cepstral mean and variance normalization , joint adaptive training , and speaker adaptive training . To our knowledge, no prior work in speech recognition employs our simple approach of penalizing distance between the hidden representations corresponding to clean and noisy signals.

In the most similar paper, claimed that with adversarially trained DNN-HMM systems, the best performance gain is achieved when a small number of noise types are available for training. When using $6$ noise classes (airport, babble, car, restaurant, street, and train), found that there was no significant difference between the adversarial and baseline models. In contrast, our models show a CER improvement over baseline of 3.1% absolute on test-clean and 6.5% absolute on test-other using hundreds of noise classes.

Noise-Invariant Representations

To begin, we formally describe our loss function for enforcing noise-invariant representations on the outputs of a given layer. Because our first proposed model focuses noise-invariance in the encoding layer, we dub models using such loss functions IRL-E. In other experiments, we apply a cumulative penalty, additionally requiring noise-invariant representations at all subsequent layers, naming this model IRL-C. We begin by describing IRL-E. Subsequently, extension to IRL-C will be straightforward.

The IRL algorithm is simple: First, during training, for each example $\mathbf{x}$, we produce a noisy version by sampling from $\mathbf{x}^{\prime}\sim\nu(\mathbf{x})$, where $\nu$ is a stochastic function. In our experiments, this function takes a random snippet from a noise database, sets its amplitude by drawing from a normal distribution, and adds it to the original (in sample space), before converting to spectral features. We then incorporate a penalty term in our loss function to penalize the distance between the encodings of the original data point $\phi_{e}(\mathbf{x})$ and the noisy data point $\phi_{e}(\mathbf{x}^{\prime})$, where $\phi_{l}$ is representation at layer $l$. In our experiments, we choose $\phi_{e}$ to be the output of the encoder in our Seq2Seq model. We illustrate the learning setup graphically in Figure 1. In short, our loss function consists of three terms, one to maximize the probability assigned to the the clean example’s label, another to maximize the probability our model assigned to the noisy example’s (identical) label scaled by hyper-parameter $\alpha$, and a penalty term to induce noise-invariant representations $L_{d}$. In the following equations, we express the loss calculated on a single example $\mathbf{x}$ and its noisy counterpart $\mathbf{x}^{\prime}$, omitting sums over the dataset for brevity.

where $\theta$ denotes our model parameters. Because our experiments address multiclass classification, our primary loss $L_{c}$ is cross-entropy:

where C denotes the vocabulary size and $\hat{y}$ is our model’s softmax output. To induce similar representations for clean and noised data, we apply a penalty consisting of two terms, the first penalizes the $L_{2}$ distance between $\phi_{e}(\mathbf{x})$ and $\phi_{e}(\mathbf{x}^{\prime})$, the second penalizes their negative cosine distance.

We jointly penalize the $L_{2}$ and cosine distance for the following reason. It is possible to lower the $L_{2}$ distance between the two (clean and noisy) hidden representations simply by shrinking the scale of all encoded representations. Trivially, these could then be dilated again simply by setting large weights in the following layer. On the other hand, it is possible to assign high cosine similarity to the two vectors but for their magnitudes to vary significantly. By jointly penalizing $L_{2}$ and cosine distance, we require that both the clean and noisy representations point in the same direction and are close to each other in magnitude.

2 Applying IRL Cumulatively Across Layers (IRL-C)

It is possible for representations to be close (but not identical) in the encoder layer, but to subsequently be pushed apart in subsequent decoder layers. Thus, we introduce another model, IRL-C (C for cumulative), that additionally applies the IRL penalty on all subsequent decoder layers. By requiring noise-invariant representations in multiple layers, we ensure that each training example and its randomly-sampled noisy counterpart have similar representations throughout the network. Note that if the encodings of the clean and noisy examples are identical at the encoder layer, then all subsequent layers will also be identical and thus those penalties will go to . We can express this loss as a sum over successive representations $\phi_{l}$ of the clean $\phi_{l}(\mathbf{x})$ and noisy $\phi_{l}(\mathbf{x}^{\prime})$ data:

In our experiments, we find that IRL-C consistently gives a small improvement over results achieved with IRL-E.

3 Application to Recurrent Speech Models

As described to this point, our loss can be applied on any feedforward neural network with any noise process $\nu$. Applying our technique to recurrent neural networks requires just a few additional considerations. Primarily, we must decide how to deal with the sequence structure. Two natural choices are (i) to concatenate the representations for a given layer across time steps, and then to apply our penalty on the concatenated representations and (ii) to apply the penalty separately at each time step and then to sum (or equivalently, up to a scaling factor to average) over the time steps. These approaches are identical for the $L_{2}$ penalty but not for the cosine distance penalty, owing to the normalizing factor which may be different at each time step. In this work we take approach (i) concatenating the representations across time steps and then calculating the penalty.

All of our models are based off of the sequence-to-sequence due to . The input to the encoder is a sequence of spectral features, here MFCC, which are encoded by several consecutive layers of LSTM units. The encoder output states are then passed through an attention mechanism which computes the similarity between the decoder hidden states and the encoder output states. The output is a softmax over the vocabulary (here, characters) at each decoder time step.

In our experiments with IRL-E (penalty applied on a single layers), we use the output of the encoder to calculate the penalty. Note that there is one output per step in the input sequence and thus we are concatenating across the $T_{1}$ steps.

To calculate IRL-C, we also start with the encoder output concatenating across all $T_{1}$ sequence steps to calculate the IRL penalty. However, for all subsequent layers, we are acting upon layers in the decoder, and thus concatenating across the number of decoding sequence steps $T_{2}$ for calculating these terms in the IRL-C penalty.

Datasets

We evaluate all models on the LibriSpeech dataset. This dataset consists of roughly $1000$ hours of audio split into training, dev and test partitions. The dataset was carefully designed to ensure that no speaker (person) appears in multiple partitions. Within both the dev and the test partitions, the data is further subdivided into “clean” and “other” subsets based on the speakers. The “clean” portion contains those speakers for which a baseline model had the lowest CER, and the “other” portion contains those speakers for whom the error rate was high. Following common practice in the literature on these datasets, we evaluate all models on the dev-clean, dev-other, test-clean, and test-other splits separately.

The MUSAN Noise Dataset

For our additive noise, we draw upon samples from the MUSAN noise dataset . MUSAN was released under a flexible Creative Commons license and consists of approximately $109$ hours of noise sampled at $16$kHz. The dataset contains music from several genres, namely baroque, classical, romantic jazz, bluegrass, and hip-hop, among others, speech from twelve languages, and a wide assortment of technical and non-technical noises. To generate noisy audio, we first add MUSAN noise to the training data point at a signal-to-noise ratio drawn from a Gaussian with a mean of $12$dB and a variance of $8$dB. This aligns roughly with the scale of noise employed in other papers using multi-condition training .

Experiments

Before presenting our main results, we briefly describe the model architectures, training details, and the various baselines that we compare against. We also present details on our pipeline for synthesizing noisy speech and explain the experimental setup for evaluating on out-of-domain noise.

To facilitate reliable comparisons between our methods and various baseline training schemes, we conduct all experiments using identical architectures and tuning schemes. Because we conduct a large number of experiments and because of the computational expense of unrolling of long speech sequences, we struck a balance between performance and speed when choosing the basic architecture. The encoder for our base model consists of $4$ layers: $2$ encoder BLSTM layers with $320$ hidden units each, followed by $2$ encoder LSTM layers with $320$ hidden units each. Our decoder accesses the encoded representations using dot product attention, and contains $4$ decoder LSTM layers, with $320$ hidden units each. Notably, our first encoder layer halves the sequence length by concatenating adjacent inputs along the temporal axis. Each model across all of our comparisons has the exact same number of trainable parameters. To keep things simple, we do not use an external language model. Instead we decode predictions from all models via beam search with width $10$.

To ensure fair comparisons, we perform hyper-parameter searches separately for each model and account for variability due to initialization by training each model 5 times and keeping the best run as determined on the dev-other partition. Specifically, we tune the weights on our losses by trying each of the scale values ($0.001$, $0.01$, $0.1$, $1$, $10$, and $100$). We found that an $\alpha$ of $1$ (the weight on the cross-entropy loss of the noised data), a $\gamma$ of $0.01$ (the weight on the L2 distance loss), and a $\lambda$ of $0.01$ (the weight on the cosine distance loss) worked well.

2 Training Details

We train all models with the Adam optimizer with an initial learning rate of $0.001$. We employ a learning rate schedule similar to NewBob that decreases by a factor of $2$ if there is an increase in validation perplexity epoch-over-epoch. We employ a stopping criterion that ends training if validation perplexity does not decrease for three epochs in a row. We limit each models to a maximum of $40$ epochs, although our networks generally converge within $20$ epochs.

The primary loss function for each model is cross-entropy loss and our primary evaluation metric to evaluate all models is the character error rate. As described above, the additional loss terms for our IRL models are L2 loss and cosine distance between representations of clean and noisy audio.

3 Baselines

Our baseline models include a model trained on the standard training data, a model trained with noise-augmented data, a model trained with noise augmented data and weight decay, and a data augmented model supervised with L2 loss to push activations of the encodings to . These ablation tests provide evidence that our IRL algorithm isn’t simply penalizing the norm of the encodings.

Baseline: Our base model trains the baseline sequence-to-sequence model on the original $960$ hours of Librispeech training data.

Data Augmentation: Our data augmentation model trains the sequence-to-sequence model on both the examples from the 960 hour Librispeech training corpus and the randomly generated noisy counterparts.

Adversarial: The adversarial model consists of an adversarial noise discriminator trained on top of the encoder outputs. The discriminator consists of $2$ layers of $256$ ReLu units and a single unit sigmoid output. We train the discriminator to classify whether the representation originates from clean or noised inputs. The encoder meanwhile is trained both to minimize the classification loss and to fool the discriminator, in a scheme similar to the reverse gradient technique in the domain-adversarial approach due to and applied to speech by .

Logit Pairing: Our final baseline consists of the logit pairing model due to which applies L2 loss and cosine distance loss on the final decoder layer logits, enforcing noise-invariant representations but only on the output layer.

4 Synthesizing Noise

We train all models on the LibriSpeech corpus, generating noisy data by adding randomly selected noise tracks from the MUSAN dataset with a signal to noise ratio drawn from a Gaussian distribution ($12$dB mean, $8$dB standard deviation) and temporal shift drawn from a uniform distribution (with a range of to $1000$ms). For the data augmentation model, this result resembles the typical data augmentation (multi-condition training) procedure.

5 Out-of-Domain Noise

Next, we evaluate each of our models on a variety of noise conditions that were not seen at training time. In particular, we consider the following out-of-domain noise conditions: (i) augmenting the test-clean split with overlapping out-of-domain speech from the WSJ-0 dataset to simulate multi-speaker environments, (ii) applying additive noise with various SNRdb to simulate varying noise levels, (iii) modulating the volume of the clean signal to simulate different levels of speaker loudness, (iv) convolving the original wave file with room impulse responses to simulate the effect of room reverberation on speech, and (v) re-sampling to $8$kHz to simulate telephoney data. For each setting, we measure CER on the out-of-domain noise-augmented test-clean data.

Results

Our IRL-C model achieves the best CER on both test-clean and test-other 3.3% and 11%, respectively (Table 1). This compares baseline scores of $6.5\%$ and $18.1\%$, respectively. We note that by comparison, conventional data augmentation is only marginally effective. Among the baselines that we consider, logit pairing performs best (5.1% and 14.8%) although the improvements are not comparable to either IRL model.

We found that weight decay slowed down network convergence and did not outperform pure data augmented training. However, showed that weight decay is most effective with separate $\lambda_{rec}$ and $\lambda_{nonrec}$ hyper-parameters for determining the strength of regularization for the recurrent and non-recurrent weight matrices. We have not tried this in our experiments. Additionally, we discovered that applying multi-condition training while naively lowering the activations of hidden representations leads to nearly identical performance (on both the original and out-of-domain noise perturbed test data) and convergence trajectory as the base model trained on noise augmented data. These results support our hypothesis that models trained with the IRL algorithm do not trivially decrease the magnitude of intermediate representations.

Our final experiments test the effects of various out-of-domain noise on our models. The results are shown in Table 2. We found that our models trained with the IRL procedure had stronger results (and significantly less degradation) across all tasks compared to the baseline and the purely data augmented models. When applying various room reverberation on speech, we found that the IRL-C model had a character error rate of $13.8\%$ compared to $21.0\%$ on the data augmented model and $24.1\%$ on the baseline model. Our IRL-C model shows $14.1\%$ character error rate on out-of-domain overlapping speech compared to $91.5\%$ for the baseline and $32.0\%$ on the data augmented model. We found that decreasing the signal-to-noise ratio also effected the baseline models more than the models trained on the IRL algorithm: our IRL-C model received a character error rate of $5.7\%$ compared to $10.8\%$ for baseline and $27.8\%$ for the purely data augmented model. We found that modifying the volume of the speaker did not effect the accuracy of any of the networks. Finally, we found that our models trained with the IRL algorithm performed better for re-sampled telephoney data, achieving a character error rate of $6.4\%$ for IRL-C compared to $14.2\%$ for baseline and $12.2\%$ for the purely data augmented model.

We also executed some empirical analysis to determine the effect of the various approaches on the distances between noisy examples and their clean counterparts in representation space. In general, our IRL models have the lowest L2 and cosine distances between noisy representations and the clean counterparts. In Figure 2, you can see that although the IRL-E and IRL-C model models have similarly close representations at the encoder layer, neither reaches distance. Then for IRL-E over the subsequent layers, the clean and noisy representations diverge again, while for IRL-C they remain close throughout.

Conclusions

In this paper, we demonstrated that enforcing noise-invariant representations by penalizing differences between pairs of clean and noisy data can increase model accuracy on the ASR task, produce models that are robust to out-of-domain noise, and improve convergence speed. The performance gains achieved by IRL come without any impact to inference throughput. We note that our core ideas here can be applied broadly to deep networks for any supervised task. While the speech setting is particularly interesting to us, our methods are equally applicable to other machine learning fields, notably computer vision. One natural extension might be to experiment with various other loss functions such as triplet losses, requiring that noisy data be both close to its clean counterpart and further away from different clean data. Additionally, our approach might be well-suited to conferring greater robustness to adversarial examples. The comparative improvements over requiring invariant hidden representations vs. invariant logits here raises the possibility that we might be able to realize similar gains over logit pairing in the adversarial setting.

Acknowledgements

The authors would like to thank Jeremy Cohen, Mukul Kumar, Karishma Malkan, Julian Salazar, Alex Smola, and Jerry Zhang for helpful discussions and suggestions.

References