Building High-level Features
Using Large Scale Unsupervised Learning - Google
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Building High-level Features Using Large Scale Unsupervised Learning Quoc V. Le quocle@cs.stanford.edu Marc’Aurelio Ranzato ranzato@google.com Rajat Monga rajatmonga@google.com Matthieu Devin mdevin@google.com Kai Chen kaichen@google.com Greg S. Corrado gcorrado@google.com Jeff Dean jeff@google.com Andrew Y. Ng ang@cs.stanford.edu Abstract We consider the problem of building highlevel, class-specific feature detectors from only unlabeled data. For example, is it possible to learn a face detector using only unlabeled images? To answer this, we train a 9- layered locally connected sparse autoencoder with pooling and local contrast normalization on a large dataset of images (the model has 1 billion connections, the dataset has 10 million 200x200 pixel images downloaded from the Internet). We train this network using model parallelism and asynchronous SGD on a cluster with 1,000 machines (16,000 cores) for three days. Contrary to what appears to be a widely-held intuition, our experimental results reveal that it is possible to train a face detector without having to label images as containing a face or not. Control experiments show that this feature detector is robust not only to translation but also to scaling and out-of-plane rotation. We also find that the same network is sensitive to other high-level concepts such as cat faces and human bodies. Starting with these learned features, we trained our network to obtain 15.8% accuracy in recognizing 22,000 object categories from ImageNet, a leap of 70% relative improvement over the previous state-of-the-art. Appearing in Proceedings of the 29 th International Conference on Machine Learning, Edinburgh, Scotland, UK, 2012. Copyright 2012 by the author(s)/owner(s). 1. Introduction The focus of this work is to build high-level, classspecific feature detectors from unlabeled images. For instance, we would like to understand if it is possible to build a face detector from only unlabeled images. This approach is inspired by the neuroscientific conjecture that there exist highly class-specific neurons in the human brain, generally and informally known as “grandmother neurons.” The extent of class-specificity of neurons in the brain is an area of active investigation, but current experimental evidence suggests the possibility that some neurons in the temporal cortex are highly selective for object categories such as faces or hands (Desimone et al., 1984), and perhaps even specific people (Quiroga et al., 2005). Contemporary computer vision methodology typically emphasizes the role of labeled data to obtain these class-specific feature detectors. For example, to build a face detector, one needs a large collection of images labeled as containing faces, often with a bounding box around the face. The need for large labeled sets poses a significant challenge for problems where labeled data are rare. Although approaches that make use of inexpensive unlabeled data are often preferred, they have not been shown to work well for building high-level features. This work investigates the feasibility of building highlevel features from only unlabeled data. A positive answer to this question will give rise to two significant results. Practically, this provides an inexpensive way to develop features from unlabeled data. But perhaps more importantly, it answers an intriguing question as to whether the specificity of the “grandmother neuron” could possibly be learned from unlabeled data. Informally, this would suggest that it is at least in principle possible that a baby learns to group faces into one classBuilding high-level features using large-scale unsupervised learning because it has seen many of them and not because it is guided by supervision or rewards. Unsupervised feature learning and deep learning have emerged as methodologies in machine learning for building features from unlabeled data. Using unlabeled data in the wild to learn features is the key idea behind the self-taught learning framework (Raina et al., 2007). Successful feature learning algorithms and their applications can be found in recent literature using a variety of approaches such as RBMs (Hinton et al., 2006), autoencoders (Hinton & Salakhutdinov, 2006; Bengio et al., 2007), sparse coding (Lee et al., 2007) and K-means (Coates et al., 2011). So far, most of these algorithms have only succeeded in learning lowlevel features such as “edge” or “blob” detectors. Going beyond such simple features and capturing complex invariances is the topic of this work. Recent studies observe that it is quite time intensive to train deep learning algorithms to yield state of the art results (Ciresan et al., 2010). We conjecture that the long training time is partially responsible for the lack of high-level features reported in the literature. For instance, researchers typically reduce the sizes of datasets and models in order to train networks in a practical amount of time, and these reductions undermine the learning of high-level features. We address this problem by scaling up the core components involved in training deep networks: the dataset, the model, and the computational resources. First, we use a large dataset generated by sampling random frames from random YouTube videos.1 Our input data are 200x200 images, much larger than typical 32x32 images used in deep learning and unsupervised feature learning (Krizhevsky, 2009; Ciresan et al., 2010; Le et al., 2010; Coates et al., 2011). Our model, a deep autoencoder with pooling and local contrast normalization, is scaled to these large images by using a large computer cluster. To support parallelism on this cluster, we use the idea of local receptive fields, e.g., (Raina et al., 2009; Le et al., 2010; 2011b). This idea reduces communication costs between machines and thus allows model parallelism (parameters are distributed across machines). Asynchronous SGD is employed to support data parallelism. The model was trained in a distributed fashion on a cluster with 1,000 machines (16,000 cores) for three days. Experimental results using classification and visualization confirm that it is indeed possible to build highlevel features from unlabeled data. In particular, using a hold-out test set consisting of faces and distractors, we discover a feature that is highly selective for faces. 1This is different from the work of (Lee et al., 2009) who trained their model on images from one class. This result is also validated by visualization via numerical optimization. Control experiments show that the learned detector is not only invariant to translation but also to out-of-plane rotation and scaling. Similar experiments reveal the network also learns the concepts of cat faces and human bodies. The learned representations are also discriminative. Using the learned features, we obtain significant leaps in object recognition with ImageNet. For instance, on ImageNet with 22,000 categories, we achieved 15.8% accuracy, a relative improvement of 70% over the stateof-the-art. Note that, random guess achieves less than 0.005% accuracy for this dataset. 2. Training set construction Our training dataset is constructed by sampling frames from 10 million YouTube videos. To avoid duplicates, each video contributes only one image to the dataset. Each example is a color image with 200x200 pixels. A subset of training images is shown in Appendix A. To check the proportion of faces in the dataset, we run an OpenCV face detector on 60x60 randomly-sampled patches from the dataset (http://opencv.willowgarage.com/wiki/). This experiment shows that patches, being detected as faces by the OpenCV face detector, account for less than 3% of the 100,000 sampled patches 3. Algorithm In this section, we describe the algorithm that we use to learn features from the unlabeled training set. 3.1. Previous work Our work is inspired by recent successful algorithms in unsupervised feature learning and deep learning (Hinton et al., 2006; Bengio et al., 2007; Ranzato et al., 2007; Lee et al., 2007). It is strongly influenced by the work of (Olshausen & Field, 1996) on sparse coding. According to their study, sparse coding can be trained on unlabeled natural images to yield receptive fields akin to V1 simple cells (Hubel & Wiesel, 1959). One shortcoming of early approaches such as sparse coding (Olshausen & Field, 1996) is that their architectures are shallow and typically capture low-level concepts (e.g., edge “Gabor” filters) and simple invariances. Addressing this issue is a focus of recent work in deep learning (Hinton et al., 2006; Bengio et al., 2007; Bengio & LeCun, 2007; Lee et al., 2008; 2009) which build hierarchies of feature representations. In particular, Lee et al (2008) show that stacked sparse RBMs can model certain simple functions of the V2 area ofBuilding high-level features using large-scale unsupervised learning the cortex. They also demonstrate that convolutional DBNs (Lee et al., 2009), trained on aligned images of faces, can learn a face detector. This result is interesting, but unfortunately requires a certain degree of supervision during dataset construction: their training images (i.e., Caltech 101 images) are aligned, homogeneous and belong to one selected category. Figure 1. The architecture and parameters in one layer of our network. The overall network replicates this structure three times. For simplicity, the images are in 1D. 3.2. Architecture Our algorithm is built upon these ideas and can be viewed as a sparse deep autoencoder with three important ingredients: local receptive fields, pooling and local contrast normalization. First, to scale the autoencoder to large images, we use a simple idea known as local receptive fields (LeCun et al., 1998; Raina et al., 2009; Lee et al., 2009; Le et al., 2010). This biologically inspired idea proposes that each feature in the autoencoder can connect only to a small region of the lower layer. Next, to achieve invariance to local deformations, we employ local L2 pooling (Hyv¨arinen et al., 2009; Gregor & LeCun, 2010; Le et al., 2010) and local contrast normalization (Jarrett et al., 2009). L2 pooling, in particular, allows the learning of invariant features (Hyv¨arinen et al., 2009; Le et al., 2010). Our deep autoencoder is constructed by replicating three times the same stage composed of local filtering, local pooling and local contrast normalization. The output of one stage is the input to the next one and the overall model can be interpreted as a nine-layered network (see Figure 1). The first and second sublayers are often known as filtering (or simple) and pooling (or complex) respectively. The third sublayer performs local subtractive and divisive normalization and it is inspired by biological and computational models (Pinto et al., 2008; Lyu & Simoncelli, 2008; Jarrett et al., 2009).2 As mentioned above, central to our approach is the use of local connectivity between neurons. In our experiments, the first sublayer has receptive fields of 18x18 pixels and the second sub-layer pools over 5x5 overlapping neighborhoods of features (i.e., pooling size). The neurons in the first sublayer connect to pixels in all input channels (or maps) whereas the neurons in the second sublayer connect to pixels of only one channel (or map).3 While the first sublayer outputs linear filter responses, the pooling layer outputs the square root of the sum of the squares of its inputs, and therefore, it is known as L2 pooling. Our style of stacking a series of uniform modules, switching between selectivity and tolerance layers, is reminiscent of Neocognition and HMAX (Fukushima & Miyake, 1982; LeCun et al., 1998; Riesenhuber & Poggio, 1999). It has also been argued to be an architecture employed by the brain (DiCarlo et al., 2012). Although we use local receptive fields, they are not convolutional: the parameters are not shared across different locations in the image. This is a stark difference between our approach and previous work (LeCun et al., 1998; Jarrett et al., 2009; Lee et al., 2009). In addition to being more biologically plausible, unshared weights allow the learning of more invariances other than translational invariances (Le et al., 2010). In terms of scale, our network is perhaps one of the largest known networks to date. It has 1 billion trainable parameters, which is more than an order of magnitude larger than other large networks reported in literature, e.g., (Ciresan et al., 2010; Sermanet & LeCun, 2011) with around 10 million parameters. It is worth noting that our network is still tiny compared to the human visual cortex, which is 106 times larger in terms of the number of neurons and synapses (Pakkenberg et al., 2003). 3.3. Learning and Optimization Learning: During learning, the parameters of the second sublayers (H) are fixed to uniform weights, 2The subtractive normalization removes the weighted average of neighboring neurons from the current neuron gi,j,k = hi,j,k − P iuv Guvhi,j+u,i+v The divisive normalization computes yi,j,k = gi,j,k/ max{c,( P iuv Guvg 2 i,j+u,i+v) 0.5 }, where c is set to be a small number, 0.01, to prevent numerical errors. G is a Gaussian weighting window. (Jarrett et al., 2009) 3For more details regarding connectivity patterns and parameter sensitivity, see Appendix B and E.Building high-level features using large-scale unsupervised learning whereas the encoding weights W1 and decoding weights W2 of the first sublayers are adjusted using the following optimization problem minimize W1,W2 Xm i=1 W2WT 1 x (i) − x (i) 2 2 + λ Xk j=1 q ǫ + Hj (WT 1 x(i)) 2 . (1) Here, λ is a tradeoff parameter between sparsity and reconstruction; m, k are the number of examples and pooling units in a layer respectively; Hj is the vector of weights of the j-th pooling unit. In our experiments, we set λ = 0.1. This optimization problem is also known as reconstruction Topographic Independent Component Analysis (Hyv¨arinen et al., 2009; Le et al., 2011a).4 The first term in the objective ensures the representations encode important information about the data, i.e., they can reconstruct input data; whereas the second term encourages pooling features to group similar features together to achieve invariances. Optimization: All parameters in our model were trained jointly with the objective being the sum of the objectives of the three layers. To train the model, we implemented model parallelism by distributing the local weights W1, W2 and H to different machines. A single instance of the model partitions the neurons and weights out across 169 machines (where each machine had 16 CPU cores). A set of machines that collectively make up a single copy of the model is referred to as a “model replica.” We have built a software framework called DistBelief that manages all the necessary communication between the different machines within a model replica, so that users of the framework merely need to write the desired upwards and downwards computation functions for the neurons in the model, and don’t have to deal with the low-level communication of data across machines. We further scaled up the training by implementing asynchronous SGD using multiple replicas of the core model. For the experiments described here, we divided the training into 5 portions and ran a copy of the model on each of these portions. The models communicate updates through a set of centralized “parameter servers,” which keep the current state of all parameters for the model in a set of partitioned servers (we used 256 parameter server partitions for training the model described in this paper). In the simplest 4 In (Bengio et al., 2007; Le et al., 2011a), the encoding weights and the decoding weights are tied: W1 = W2. However, for better parallelism and better features, our implementation does not enforce tied weights. implementation, before processing each mini-batch a model replica asks the centralized parameter servers for an updated copy of its model parameters. It then processes a mini-batch to compute a parameter gradient, and sends the parameter gradients to the appropriate parameter servers, which then apply each gradient to the current value of the model parameter. We can reduce the communication overhead by having each model replica request updated parameters every P steps and by sending updated gradient values to the parameter servers every G steps (where G might not be equal to P). Our DistBelief software framework automatically manages the transfer of parameters and gradients between the model partitions and the parameter servers, freeing implementors of the layer functions from having to deal with these issues. Asynchronous SGD is more robust to failure and slowness than standard (synchronous) SGD. Specifically, for synchronous SGD, if one of the machines is slow, the entire training process is delayed; whereas for asynchronous SGD, if one machine is slow, only one copy of SGD is delayed while the rest of the optimization can still proceed. In our training, at every step of SGD, the gradient is computed on a minibatch of 100 examples. We trained the network on a cluster with 1,000 machines for three days. See Appendix B, C, and D for more details regarding our implementation of the optimization. 4. Experiments on Faces In this section, we describe our analysis of the learned representations in recognizing faces (“the face detector”) and present control experiments to understand invariance properties of the face detector. Results for other concepts are presented in the next section. 4.1. Test set The test set consists of 37,000 images sampled from two datasets: Labeled Faces In the Wild dataset (Huang et al., 2007) and ImageNet dataset (Deng et al., 2009). There are 13,026 faces sampled from non-aligned Labeled Faces in The Wild.5 The rest are distractor objects randomly sampled from ImageNet. These images are resized to fit the visible areas of the top neurons. Some example images are shown in Appendix A. 4.2. Experimental protocols After training, we used this test set to measure the performance of each neuron in classifying faces against distractors. For each neuron, we found its maximum 5http://vis-www.cs.umass.edu/lfw/lfw.tgzBuilding high-level features using large-scale unsupervised learning and minimum activation values, then picked 20 equally spaced thresholds in between. The reported accuracy is the best classification accuracy among 20 thresholds. 4.3. Recognition Surprisingly, the best neuron in the network performs very well in recognizing faces, despite the fact that no supervisory signals were given during training. The best neuron in the network achieves 81.7% accuracy in detecting faces. There are 13,026 faces in the test set, so guessing all negative only achieves 64.8%. The best neuron in a one-layered network only achieves 71% accuracy while best linear filter, selected among 100,000 filters sampled randomly from the training set, only achieves 74%. To understand their contribution, we removed the local contrast normalization sublayers and trained the network again. Results show that the accuracy of best neuron drops to 78.5%. This agrees with previous study showing the importance of local contrast normalization (Jarrett et al., 2009). We visualize histograms of activation values for face images and random images in Figure 2. It can be seen, even with exclusively unlabeled data, the neuron learns to differentiate between faces and random distractors. Specifically, when we give a face as an input image, the neuron tends to output value larger than the threshold, 0. In contrast, if we give a random image as an input image, the neuron tends to output value less than 0. Figure 2. Histograms of faces (red) vs. no faces (blue). The test set is subsampled such that the ratio between faces and no faces is one. 4.4. Visualization In this section, we will present two visualization techniques to verify if the optimal stimulus of the neuron is indeed a face. The first method is visualizing the most responsive stimuli in the test set. Since the test set is large, this method can reliably detect near optimal stimuli of the tested neuron. The second approach is to perform numerical optimization to find the optimal stimulus (Berkes & Wiskott, 2005; Erhan et al., 2009; Le et al., 2010). In particular, we find the normbounded input x which maximizes the output f of the tested neuron, by solving: x ∗ = arg min x f(x; W, H), subject to ||x||2 = 1. Here, f(x; W, H) is the output of the tested neuron given learned parameters W, H and input x. In our experiments, this constraint optimization problem is solved by projected gradient descent with line search. These visualization methods have complementary strengths and weaknesses. For instance, visualizing the most responsive stimuli may suffer from fitting to noise. On the other hand, the numerical optimization approach can be susceptible to local minima. Results, shown in Figure 3, confirm that the tested neuron indeed learns the concept of faces. Figure 3. Top: Top 48 stimuli of the best neuron from the test set. Bottom: The optimal stimulus according to numerical constraint optimization. 4.5. Invariance properties We would like to assess the robustness of the face detector against common object transformations, e.g., translation, scaling and out-of-plane rotation. First, we chose a set of 10 face images and perform distortions to them, e.g., scaling and translating. For outof-plane rotation, we used 10 images of faces rotating in 3D (“out-of-plane”) as the test set. To check the robustness of the neuron, we plot its averaged response over the small test set with respect to changes in scale, 3D rotation (Figure 4), and translation (Figure 5).6 6Scaled, translated faces are generated by standard cubic interpolation. For 3D rotated faces, we used 10 se-Building high-level features using large-scale unsupervised learning Figure 4. Scale (left) and out-of-plane (3D) rotation (right) invariance properties of the best feature. Figure 5. Translational invariance properties of the best feature. x-axis is in pixels The results show that the neuron is robust against complex and difficult-to-hard-wire invariances such as out-of-plane rotation and scaling. Control experiments on dataset without faces: As reported above, the best neuron achieves 81.7% accuracy in classifying faces against random distractors. What if we remove all images that have faces from the training set? We performed the control experiment by running a face detector in OpenCV and removing those training images that contain at least one face. The recognition accuracy of the best neuron dropped to 72.5% which is as low as simple linear filters reported in section 4.3. 5. Cat and human body detectors Having achieved a face-sensitive neuron, we would like to understand if the network is also able to detect other high-level concepts. For instance, cats and body parts are quite common in YouTube. Did the network also learn these concepts? To answer this question and quantify selectivity properties of the network with respect to these concepts, we constructed two datasets, one for classifying human bodies against random backgrounds and one for classifying cat faces against other random distractors. For the ease of interpretation, these datasets have a positive-to-negative ratio identical to the face dataset. The cat face images are collected from the dataset dequences of rotated faces from The Sheffield Face Database – http://www.sheffield.ac.uk/eee/research/iel/research/face. See Appendix F for a sample sequence. Figure 6. Visualization of the cat face neuron (left) and human body neuron (right). scribed in (Zhang et al., 2008). In this dataset, there are 10,000 positive images and 18,409 negative images (so that the positive-to-negative ratio is similar to the case of faces). The negative images are chosen randomly from the ImageNet dataset. Negative and positive examples in our human body dataset are subsampled at random from a benchmark dataset (Keller et al., 2009). In the original dataset, each example is a pair of stereo black-and-white images. But for simplicity, we keep only the left images. In total, like in the case of human faces, we have 13,026 positive and 23,974 negative examples. We then followed the same experimental protocols as before. The results, shown in Figure 6, confirm that the network learns not only the concept of faces but also the concepts of cat faces and human bodies. Our high-level detectors also outperform standard baselines in terms of recognition rates, achieving 74.8% and 76.7% on cat and human body respectively. In comparison, best linear filters (sampled from the training set) only achieve 67.2% and 68.1% respectively. In Table 1, we summarize all previous numerical results comparing the best neurons against other baselines such as linear filters and random guesses. To understand the effects of training, we also measure the performance of best neurons in the same network at random initialization. We also compare our method against several other algorithms such as deep autoencoders (Hinton & Salakhutdinov, 2006; Bengio et al., 2007) and K-means (Coates et al., 2011). Results of these baselines are reported in the bottom of Table 1. 6. Object recognition with ImageNet We applied the feature learning method to the task of recognizing objects in the ImageNet dataset (Deng et al., 2009). We started from a network that already learned features from YouTube and ImageNet images using the techniques described in this paper. We then added one-versus-all logistic classifiers on top of the highest layer of this network. This method of initializing a network by unsupervisedBuilding high-level features using large-scale unsupervised learning Table 1. Summary of numerical comparisons between our algorithm against other baselines. Top: Our algorithm vs. simple baselines. Here, the first three columns are results for methods that do not require training: random guess, random weights (of the network at initialization, without any training) and best linear filters selected from 100,000 examples sampled from the training set. The last three columns are results for methods that have training: the best neuron in the first layer, the best neuron in the highest layer after training, the best neuron in the network when the contrast normalization layers are removed. Bottom: Our algorithm vs. autoencoders and K-means. Concept Random Same architecture Best Best first Best Best neuron without guess with random weights linear filter layer neuron neuron contrast normalization Faces 64.8% 67.0% 74.0% 71.0% 81.7% 78.5% Human bodies 64.8% 66.5% 68.1% 67.2% 76.8% 71.8% Cats 64.8% 66.0% 67.8% 67.1% 74.6% 69.3% Concept Our Deep autoencoders Deep autoencoders K-means on network 3 layers 6 layers 40x40 images Faces 81.7% 72.3% 70.9% 72.5% Human bodies 76.7% 71.2% 69.8% 69.3% Cats 74.8% 67.5% 68.3% 68.5% Table 2. Summary of classification accuracies for our method and other state-of-the-art baselines on ImageNet. Dataset version 2009 (∼9M images, ∼10K categories) 2011 (∼14M images, ∼22K categories) State-of-the-art 16.7% (Sanchez & Perronnin, 2011) 9.3% (Weston et al., 2011) Our method 16.1% (without unsupervised pretraining) 13.6% (without unsupervised pretraining) 19.2% (with unsupervised pretraining) 15.8% (with unsupervised pretraining) learning is also known as “unsupervised pretraining.” During supervised learning with labeled ImageNet images, the parameters of lower layers and the logistic classifiers were both adjusted. This was done by first adjusting the logistic classifiers and then adjusting the entire network (also known as “fine-tuning”). As a control experiment, we also train a network starting with all random weights (i.e., without unsupervised pretraining: all parameters are initialized randomly and only adjusted by ImageNet labeled data). We followed the experimental protocols specified by (Deng et al., 2010; Sanchez & Perronnin, 2011), in which, the datasets are randomly split into two halves for training and validation. We report the performance on the validation set and compare against state-of-theart baselines in Table 2. Note that the splits are not identical to previous work but validation set performances vary slightly across different splits. The results show that our method, starting from scratch (i.e., raw pixels), bests many state-of-the-art hand-engineered features. On ImageNet with 10K categories, our method yielded a 15% relative improvement over previous best published result. On ImageNet with 22K categories, it achieved a 70% relative improvement over the highest other result of which we are aware (including unpublished results known to the authors of (Weston et al., 2011)). Note, random guess achieves less than 0.005% accuracy for this dataset. 7. Conclusion In this work, we simulated high-level class-specific neurons using unlabeled data. We achieved this by combining ideas from recently developed algorithms to learn invariances from unlabeled data. Our implementation scales to a cluster with thousands of machines thanks to model parallelism and asynchronous SGD. Our work shows that it is possible to train neurons to be selective for high-level concepts using entirely unlabeled data. In our experiments, we obtained neurons that function as detectors for faces, human bodies, and cat faces by training on random frames of YouTube videos. These neurons naturally capture complex invariances such as out-of-plane and scale invariances. The learned representations also work well for discriminative tasks. Starting from these representations, we obtain 15.8% accuracy for object recognition on ImageNet with 20,000 categories, a significant leap of 70% relative improvement over the state-of-the-art. 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In CVPR, 2007. Riesenhuber, M. and Poggio, T. Hierarchical models of object recognition in cortex. Nature Neuroscience, 1999. Sanchez, J. and Perronnin, F. High-dimensional signature compression for large-scale image-classification. In CVPR, 2011. Sermanet, P. and LeCun, Y. Traffic sign recognition with multiscale convolutional neural networks. In IJCNN, 2011. Weston, J., Bengio, S., and Usunier, N. Wsabie: Scaling up to large vocabulary image annotation. In IJCAI, 2011. Zhang, W., Sun, J., and Tang, X. Cat head detection - how to effectively exploit shape and texture features. In ECCV, 2008.Building high-level features using large-scale unsupervised learning A. Training and test images A subset of training images is shown in Figure 7. As can be seen, the positions, scales, orientations of faces in the dataset are diverse. A subset of test images for Figure 7. Thirty randomly-selected training images (shown before the whitening step). identifying the face neuron is shown in Figure 8. Figure 8. Some example test set images (shown before the whitening step). B. Models Central to our approach in this paper is the use of locally-connected networks. In these networks, neurons only connect to a local region of the layer below. In Figure 9, we show the connectivity patterns of the neural network architecture described in the paper. The actual images in the experiments are 2D, but for simplicity, our images in the visualization are in 1D. Figure 9. Diagram of the network we used with more detailed connectivity patterns. Color arrows mean that weights only connect to only one map. Dark arrows mean that weights connect to all maps. Pooling neurons only connect to one map whereas simple neurons and LCN neurons connect to all maps. C. Model Parallelism We use model parallelism to distribute the storage of parameters and gradient computations to different machines. In Figure 10, we show how the weights are divided and stored in different “partitions,” or more simply, machines (see also (Krizhevsky, 2009)). D. Further multicore parallelism Machines in our cluster have many cores which allow further parallelism. Hence, we split these cores to perform different tasks. In our implementation, the cores are divided into three groups: reading data, sending (or writing) data, and performing arithmetic computations. At every time instance, these groups work in parallel to load data, compute numerical results and send to network or write data to disks. E. Parameter sensitivity The hyper-parameters of the network are chosen to fit computational constraints and optimize the training time of our algorithm. These parameters can be changed at the expense of longer training time or more computational resources. For instance, one could increase the size of the receptive fields at an expense of using more memory, more computation, and more net-Building high-level features using large-scale unsupervised learning Figure 10. Model parallelism with the network architecture in use. Here, it can be seen that the weights are divided according to the locality of the image and stored on different machines. Concretely, the weights that connect to the left side of the image are stored in machine 1 (“partition 1”). The weights that connect to the central part of the image are stored in machine 2 (“partition 2”). The weights that connect to the right side of the image are stored in machine 3 (“partition 3”). work bandwidth per machine; or one could increase the number of maps at an expense of using more machines and memories. These hyper-parameters also could affect the performance of the features. We performed control experiments to understand the effects of the two hyperparameters: the size of the receptive fields and the number of maps. By varying each of these parameters and observing the test set accuracies, we can gain an understanding of how much they affect the performance on the face recognition task. Results, shown in Figure 11, confirm that the results are only slightly sensitive to changes in these control parameters. 12 14 16 18 20 60 65 70 75 80 85 receptive field size test set accuracy 6 7 8 9 10 60 65 70 75 80 85 number of maps test set accuracy Figure 11. Left: effects of receptive field sizes on the test set accuracy. Right: effects of number of maps on the test set accuracy. F. Example out-of-plane rotated face sequence In Figure 12, we show an example sequence of 3D (out-of-plane) rotated faces. Note that the faces are black and white but treated as a color picture in the test. More details are available at the webpage for The Sheffield Face Database dataset – http://www.sheffield.ac.uk/eee/research/ iel/research/face Figure 12. A sequence of 3D (out-of-plane) rotated face of one individual. The dataset consists of 10 sequences. G. Best linear filters In the paper, we performed control experiments to compare our features against “best linear filters.” This baseline works as follows. The first step is to sample 100,000 random patches (or filters) from the training set (each patch has the size of a test set image). Then for each patch, we compute its cosine distances between itself and the test set images. The cosine distances are treated as the feature values. Using these feature values, we then search among 20 thresholds to find the best accuracy of a patch in classifying faces against distractors. Each patch gives one accuracy for our test set. The reported accuracy is the best accuracy among 100,000 patches randomly-selected from the training set. H. Histograms on the entire test set Here, we also show the detailed histograms for the neurons on the entire test sets. The fact that the histograms are distinctive for positive and negative images suggests that the network has learned the concept detectors.Building high-level features using large-scale unsupervised learning Figure 13. Histograms of neuron’s activation values for the best face neuron on the test set. Red: the histogram for face images. Blue: the histogram for random distractors. Figure 14. Histograms for the best human body neuron on the test set. Red: the histogram for human body images. Blue: the histogram for random distractors. I. Most responsive stimuli for cats and human bodies In Figure 16, we show the most responsive stimuli for cat and human body neurons on the test sets. Note that, the top stimuli for the human body neuron are black and white images because the test set images are black and white (Keller et al., 2009). J. Implementation details for autoencoders and K-means In our implementation, deep autoencoders are also locally connected and use sigmoidal activation function. For K-means, we downsample images to 40x40 in order to lower computational costs. We also varied the parameters of autoencoders, K-means and chose them to maximize performances given resource constraints. In our experiments, we used 30,000 centroids for Kmeans. These models also employed parallelism in a similar fashion described in the paper. They also used 1,000 machines for three days. Figure 15. Histograms for the best cat neuron on the test set. Red: the histogram for cat images. Blue: the histogram for random distractors. Figure 16. Top: most responsive stimuli on the test set for the cat neuron. Bottom: Most responsive human body stimuli on the test set for the human body neuron. On-Demand Language Model Interpolation for Mobile Speech Input Brandon Ballinger1, Cyril Allauzen2, Alexander Gruenstein1, Johan Schalkwyk2 1Google, 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA 2Google, 76 Ninth Avenue, New York, NY 10011, USA brandonb@google.com, allauzen@google.com, alexgru@google.com, johans@google.com Abstract Google offers several speech features on the Android mobile operating system: search by voice, voice input to any text field, and an API for application developers. As a result, our speech recognition service must support a wide range of usage scenarios and speaking styles: relatively short search queries, addresses, business names, dictated SMS and e-mail messages, and a long tail of spoken input to any of the applications users may install. We present a method of on-demand language model interpolation in which contextual information about each utterance determines interpolation weights among a number of n-gram language models. On-demand interpolation results in an 11.2% relative reduction in WER compared to using a single language model to handle all traffic. Index Terms: language modeling, interpolation, mobile 1. Introduction Entering text on mobile devices is often slow and error-prone in comparison to typing on a full-sized keyboard. Google offers several features on Android aimed at making speech a viable alternative input method: search by voice, voice input into any text field, and a speech API for application developers. To search by voice, users simply tap a microphone icon on the desktop search box, or hold down the physical search button. They can speak any query, and are then shown the Google search results. To use the Voice Input feature, users tap the microphone key on the on-screen keyboard, and then speak to enter text virtually anywhere they would normally type. Users may dictate e-mail and SMS messages, fill in forms on web pages, or enter text into any application. Finally, the Android Speech API is a simple way for developers to integrate speech recognition capabilities into their own applications. While a large portion of usage of the speech recognition service is comprised of spoken queries and dictation of SMS messages, there is a long tail of usage from thousands of other applications. Due to this diversity, choosing an appropriate language model for each utterance (recorded audio) is challenging. Two viable options are to build a single language model to handle all traffic, or to train a language model appropriate to each major use case and then choose the “best” one for each utterance, depending on the context of that utterance. We develop and compare a third option in this paper, in which a development set of utterances from each context is used to optimize interpolation weights among a small number of component language models. Since there may be thousands of such “contexts”, the language models are interpolated ondemand, either during decoding or as a post-processing rescoring phase. On-demand interpolation is performed efficiently via the use of a “compact interpolated” finite state transducer (FST), in which transition weights are dynamically computed. Percent of utterances Voice input 49% Search by Voice 44% Speech API 7% Table 1: Breakdown of speech traffic on Android devices that support Voice Input, Search by Voice, and Speech API. 2. Related Work The technique of creating interpolated language models for different contexts has been used with success in a number of conversational interfaces [1, 2, 3] In this case, the pertinent context is the system’s “dialogue state”, and it’s typical to group transcribed utterances by dialogue state and build one language model per state. Typically, states with little data are merged, and the state-specific language models are interpolated, or otherwise merged. Language models corresponding to multiple states may also be interpolated, to share information across similar states. The technique we develop here differs in two key respects. First, we derive interpolation weights for thousands of recognition contexts, rather than a handful of dialogue states. This makes it impractical to create each interpolated language model offline and swap in the desired one at runtime. Our language models are large, and we only learn the recognition context for a particular utterance when the audio starts to arrive. Second, rather than relying on transcribed utterances from each recognition context to train state-specific language modes, we instead interpolate a small number of language models trained from large corpora. 3. Android Speech Usage Analysis The challenge of supporting a variety of use cases is illustrated by examining the usage of the speech features available on Android. Table 1 breaks down the portion of utterances from the Android platform associated with the three speech features: voice input, search by voice, and the speech API. We note that this distinction isn’t perfect, as some users might, for example, speak a search query into a text box in the browser using the voice input feature. In addition, a large majority of the speech API utterances come from built-in Google applications – Google Maps provides a popular voice-enabled search box, for example. Overall, we observe roughly an even split between searching and dictation. The voice input feature encourages a wide range of usage. Since its launch in January, 2010, users have dictated text into over 8,000 distinct text fields. Table 2 shows the 10 most popular text fields. SMS is extremely popular, with usage levels an order of magnitude greater than any other application. Moreover, among the top 10 fields, 4 of them come from either the built-in SMS application, or one of the many SMS applicaCopyright © 2010 ISCA 26-30 September 2010, Makuhari, Chiba, Japan INTERSPEECH 2010 1812Text Field Usage SMS - Compose 63.1% An SMS app from Market - Compose 4.9% Browser 4.8% Google Talk 4.5% Gmail - Compose 3.3% Android Market - Search 2.4% Email - Compose 1.8% SMS - To 1.3% Maps - Directions Endpoint 1.0% An SMS app from Market - Compose 1.0% Table 2: The 10 most popular voice input text fields and their percent usage. 0 10 20 30 40 50 60 70 80 90 100 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Number of fields, sorted by usage Cumulative percent of utterances Figure 1: Cumulative usage for the most popular 100 text fields, rank ordered by usage. tions available on the Android Market. Also popular are other dictation-style applications: Gmail, Email, and Google Talk. Android Market and Maps, both of which also appear in the top 10, represent different kinds of utterances – search queries. Finally, the Browser category here actually encompasses a wide range of fields – any text field on any web page. Figure 1 shows the cumulative usage per text field of the 100 most popular text fields, rank ordered by usage. Although the usage is certainly concentrated among a handful of applications, there remains a significant tail. While increasing accuracy for the tail may not have a huge effect on the overall accuracy of the system, it’s important for users to have a seamless experience using voice input: users will have a difficult time discerning that voice input may work better in some text fields than others. 4. Compact Interpolated FST In this setting, we have a relatively small set of language models that is fixed and known in advance. At recognition time, each utterance comes with a custom set of interpolation (or mixture) weights and we need to be able to efficiently compute ondemand the corresponding interpolated model. In a backoff language model, the conditional probability of w ∈ Σ given context h ∈ Σ∗ is recursively defined as P(w | h) = P(w | h) if hw ∈ S αhP(w | h ) otherwise, where P is the adjusted maximum likelihood probability (derived from the training corpus), S is the skeleton of the model, αh is the backoff weight for the context h and h is the longest common suffix of h. The order of the model is maxhw∈S |hw|. Such a language model can naturally be represented by a weighted automaton over the real semiring (R, +, ×, 0, 1) using failure transitions [4]: the set of states is Q = x y φ/.5 xa a/.5 ya a/.4 yb b/.4 yc c/.04 x y φ/.4 xb b/.6 ya a/.6 yb b/.2 yc c/.02 x y φ/(.5,.4) a/(.5,.24) xa xb b/(.2,.6) a/(.4,.6) ya yb b/(.4,.2) c/(.04,.02) yc (a) (b) (c) Figure 2: Outgoing transitions from state x in (a) G1, (b) G2 and (c) I. For λ = (.6, .4)T , PIλ (a | x) = .6 × .5 + .4 × .24. {h ∈ Σ∗ | ∃w ∈ Σ such that hw ∈ S}, for each state h, there is a failure transition from h to h labeled by φ and with weight αh, and for each hw ∈ S, there is a transition from h to the longest suffix of hw that belongs to Q, labeled by w and with weight P(w | h). Given a set G = {G1,...,Gm} of m backoff language models and a vector of mixture weights λ = (λ1,...λm) T , the linear interpolation of G by λ is defined as the language model Iλ assigning the conditional probability: PIλ (w | h) = m i=1 λiPGi (w | h). (1) Using (1) directly to perform on-demand interpolation would be inefficient because for a given pair (w, h) we might need to backoff several times in several of the models and this can become rather expensive when using the automata representation. Instead, we chose to reformulate the interpolated model as a backoff model: PIλ (w | h) = λT phw if hw ∈ S(G), f(λ, αh)PIλ (w | h ) otherwise, where phw = (PG1 (w|h),..., PGm(w|h))T , S(G) = ∪m i=1S(Gi) and αh = (αh(G1),...,αh(Gm))T . There exists a closed-form expression of f(λ, α) that ensure the proper normalization of the model. However, in practice we decided to approximate it by the dot product of λ and αh: f(λ, αh) = λT αh. The benefit of this formulation is that it perfectly fits our requirement. Since the set of models is known in advance we can precompute S(G) and all the relevant vectors (phw and αh) effectively building a generic interpolated model I as a model over Rm. Given a new utterance and a corresponding vector of mixture weights λ, we can obtain the relevant interpolated model Iλ by taking the dot product of each component vector of I with λ. Moreover, this approach also allows for an efficient representation of I as a weighted automaton over the semiring (Rm, +, ◦, 0, 1) (◦ denotes componentwise multiplication), the weight of each transition in the automaton being a vector in Rm. The set of states is Q = {h ∈ Σ∗ | ∃w ∈ Σ such that hw ∈ S(G)}. For each state h, there is a failure transition from h to h labeled by φ and with weight αh, and for each hw ∈ S(G), there is a transition from h to the longest suffix of hw that belongs to Q, labeled by w and with weight phw. Figure 2 illustrates this construction. Given a new utterance and a corresponding vector of mixture weights λ, this automaton can be converted on-demand into a weighted automaton over the real semiring by taking the dot product of λ and the weight vector of each visited transition. 1813 ReFr: An Open-Source Reranker Framework Daniel M. Bikel, Keith B. Hall Google Research, New York, NY {dbikel,kbhall}@google.com Abstract ReFr (http://refr.googlecode.com) is a software architecture for specifying, training and using reranking models, which take the n-best output of some existing system and produce new scores for each of the n hypotheses that potentially induce a different ranking, ideally yielding better results than the original system. The Reranker Framework has some special support for building discriminative language models, but can be applied to any reranking problem. The framework is designed with parallelism and scalability in mind, being able to run on any Hadoop cluster out of the box. While extremely efficient, ReFr is also quite flexible, allowing researchers to explore a wide variety of features and learning methods. ReFr has been used for building state-of-the-art discriminative LM’s for both speech recognition and machine translation systems. Index Terms: language modeling, discriminative language modeling, reranking, structured prediction 1. Introduction Creating effective software tools for research is a tricky business. The classic tension between flexibility and efficiency arises with greater urgency. We want researchers to be able to try out many different ideas easily, but we also want them to be able to have a quick code-test-evaluate cycle. ReFr grew out of the 2011 Johns Hopkins Summer Workshop, from the team using automatically generated confusions to synthesize training data for discriminative language models for speech and machine translation, led by Prof. Brian Roark of OHSU. That approach required tools that would scale up to training data sizes orders of magnitude larger than had previously been used to build discriminative language models, so we not only needed our training and inference to be inherently fast, but we needed to design tools with distributed computing in mind from the outset. This paper describes the tools we have developed to solve not only the immediate research problem of exploring confusions for discriminative language modeling, but also the more general problem of reranking approaches to speech and language processing, including structured prediction. We designed ReFr to have the following properites: • “library quality” code • industrial strength • academic flexibility • easy exploration of different types of features, different update methods (e.g., MIRA-style, direct loss minimization, loss-sensitive) and different learning methods (e.g., perceptron-style, log-linear, kernel methods) • modern, object-oriented design, complete with dynamic factories and dynamic composition for flexibility • parallelizable, especially for distributed-computing environments 2. Data Format for I/O There are two main choices when building discriminative reranking models for speech or machine translation: (a) rescore a lattice or hypergraph or (b) simply use a strict reranking approach applied to n-best lists. For ReFr, early on we decided to use (b) reranking n-best lists. The primary reasons were the flexibility this would allow us in designing features and tools. N-best lists readily allow for sentence-level features in a way that, say, lattices do not. Additionally, it is far easier to de- fine generic schemes of passing around n-best lists than it is for designing schemes to take speech lattices as well as machine translation hypergraphs or other, problem-specific data types. ReFr is meant to be flexible enough to allow for a variety of data sources. In order to avoid the need for overly complex data formats, we have chosen to adopt a formalism which allows one to augment the input format, allowing for flexible feature extraction and data manipulation/analysis. We opted to use a data format which mirrors the data-structures that are used internally for training. The Google protocol buffers[1] provide a programming-language independent specification framework to define data formats. The protocol buffers specification language is used by the protocol buffer tools to generate source-code for serializing and deserializing the data stored in the format. Code is generated to allow for native programming-language encapsulation of the data. For example, in C++ each item of data is stored in an object based on a object oriented data specification (a C++ class) allowing for access to the data.1 3. Core learning framework Consider Algorithm 1, which describes the training procedure for a generic online-learning algorithm. Each training example ei comprises a set of candidate hypotheses, each of which is projected via some function Φ into a feature space, R F . We typically think of Φ as being a suite of feature functions, one per dimension. The model itself is defined as a weight vector in this space, w. Decoding, or inference, is carried out simply by taking the dot product of the model and a test instance. More generally, any kernel function K may be used. The training procedure iterates over the training data T—each iteration is called an epoch—until the NEEDTOKEEPTRAINING() predicate returns false. Often, such a predicate is based on the average loss of the current model on some held-out development data D, which is the purpose of the EVALUATE(D) line in the TRAIN(T) procedure. 1For the 2011 Johns Hopkins Workshop, we were targeting multiple tasks (ASR and MT), and so our toolkit provides a means to convert from two types of text-based n-best formats, one the output of an ASR system, the other the output of an MT system. These conversion tools are not only useful in their own right, but serve as example implementations for any developer converting from their own, proprietary format to the Google Protocol Buffer format used by ReFr. Copyright © 2013 ISCA 25-29 August 2013, Lyon, France INTERSPEECH 2013: Show & Tell Contribution 756Algorithm 1 Training algorithm for online-learning reranking models. Let ei = {c1, . . . , ck} be a training example, where each cj is a candidate hypothesis. Similarly, let di = {c1, . . . , ck} be a held-out development data example, also consisting of k candidate hypotheses. Finally, let K be a kernel function. procedure TRAIN(T = {e1, . . . , en}, D = {d1, . . . , dm}) while NEEDTOKEEPTRAINING() do TRAINONEEPOCH(T) EVALUATE(D) end while end procedure procedure TRAINONEEPOCH(T) foreach training example ei do SCORECANDIDATES(ei) if NEEDTOUPDATE() then UPDATE() end if end for end procedure procedure SCORECANDIDATES(ei) foreach candidate hypothesis cj ∈ ei do cj .score ← K(wt, cj ) end for end procedure Model Candidate Scorer Update Predicate Updater … Figure 1: A pictorial view of how a Model wraps instances of other interfaces that specify the predicates and functions needed to carry out model training. For the basic perceptron, the model starts out at time step 0 as the zero vector; that is, wo = ~0. The update is wt+1 = wt + Rt [Φ (yoracle (ei)) − Φ (ˆy (ei))] , (1) where yoracle is a function that picks out the hypothesis towards which we want to bias our model, yˆ is a function that picks out the candidate hypothesis we want to bias our model against and Rt is a learning rate or step size. Most often, yoracle is defined to pick the hypothesis with the lowest loss relative to some goldstandard truth, and yˆ is defined to pick the candidate hypothesis that scores highest under the current model wt. Most of the variations of this basic learning method involve finding different ways of defining Rt, Φ, yoracle and yˆ, along with the various procedures and predicates shown in Algorithm 1. Therefore, we would like our Reranker Framework to make it easy for the researcher to define these various functions, as well as to specify which ones to use at run-time. ReFr defines a Model interface with virtual methods for all of the functions shown in Algorithm 1. To avoid the exponential blow-up of overriding different combinations of these methods, ReFr also employs dynamic composition. That is, we keep the idea of a Model interface, but additionally have each Model instance wrap a set of predicate/manipulator objects, each of which itself conforms to an interface. Figure 1 shows a pictorial representation of this scheme. As we discussed above, we employ dynamic composition to avoid defining a new subclass of Model every time we wish model file = "my model file"; // model output file model = PerceptronModel( name("my model"), score comparator(DirectLossScoreComparator())); exec feature extractor = ExecutiveFeatureExtractorImpl( feature extractors({NgramFeatureExtractor(n(2)), RankFeatureExtractor()}); training efe = exec feature extractor; dev efe = exec feature extractor; training files = {"training1.gz", "training2.gz"}; devtest files = {"dev1.gz", "dev2.gz"}; Figure 2: An example ReFr configuration file, read by its Interpreter class. to explore a new combination of learning method functions. To do this, ReFr includes a very lightweight and yet powerful interpreter for a language that allows for assignment statements for primitives, vectors of primitives, Factory-constructible objects and vectors of Factory-constructible objects. Figure 2 shows an example ReFr configuration file. The syntax is intentionally very similar to that of C++. This lightweight language provides a flexible mechanism by which to specify how feature extraction, training and inference shall occur. 4. Cluster-based distributed training As Algorithm 1 shows, the basic perceptron algorithm involves “online” updating, and thus it is possible to read in each training example from file each time it is needed, only keeping the model’s parameters persistently in memory. The Reranker Framework allows both the memory-intensive way of training as well as this “streaming mode” version of training, essential for distributed learning. The structured perceptron [2] and it’s variants have proven to be effective in supervised, discriminative language modeling work [3]. We have centered the development of our opensource discriminative learning toolkit around perceptron-style algorithms, which are, by definition, online learning algorithms. Identifying the optimal solution for a distributed online optimization algorithm is still an open research question. We borrow from our previous work on distributed perceptron training in [4, 5] and use the Iterative Parameter Mixtures algorithm for distributed computation. The Reranker Framework makes it easy to switch between single processor and distributed training, which uses the Hadoop implementation of MapReduce [6]. 5. Demo Plan Our demo will consist of a walk-through of all ReFr’s features, followed by a hands-on demonstration of how easy it is to implement a new class of features for the reranker based on the rank of each candidate hypothesis. We will also show how easy it is to integrate that new class of features into training and inference. We will then demonstrate the ease with which one can use the API and the interpreted configuration language to alter the training algorithm. Finally, we will demonstrate the simple way that a user can switch from single processor training to large-scale distributed training. 6. Acknowledgements The authors would like to thank Prof. Brian Roark of Oregon Health and Science University for leading a fantastic team at the 2011 Johns Hopkins Workshop, and we would also like to thank all of our teammates, especially Prof. Izhak Shafran of OHSU and Ph.D. candidate Maider Lehr, who are actively working with and helping us improve ReFr. 7577. References [1] Google, “Protocol buffers,” http://code.google.com/apis/protocolbuffers/. [2] M. Collins, “Discriminative training methods for hidden Markov models: Theory and experiments with perceptron algorithms,” in Proc. EMNLP, 2002, pp. 1–8. [3] B. Roark, M. Sarac¸lar, and M. Collins, “Discriminative n-gram language modeling,” Computer Speech and Language, vol. 21, no. 2, pp. 373 – 392, 2007. [Online]. Available: http: //www.sciencedirect.com/science/article/pii/S0885230806000271 [4] R. McDonald, K. Hall, and G. Mann, “Distributed training strategies for the structured perceptron,” in HLT-NAACL, 2010. [5] K. Hall, S. Gilpin, and G. Mann, “Mapreduce/bigtable for distributed optimization,” in NIPS Workshop on Leaning on Cores, Clusters, and Clouds, 2010. [6] J. Dean and S. Ghemawat, “Mapreduce: simplified data processing on large clusters,” CACM, vol. 51:1, 2008. 758 Accurate and Compact Large Vocabulary Speech Recognition on Mobile Devices Xin Lei1 Andrew Senior2 Alexander Gruenstein1 Jeffrey Sorensen2 1Google Inc., Mountain View, CA USA 2Google Inc., New York, NY USA {xinlei,andrewsenior,alexgru,sorenj}@google.com Abstract In this paper we describe the development of an accurate, smallfootprint, large vocabulary speech recognizer for mobile devices. To achieve the best recognition accuracy, state-of-the-art deep neural networks (DNNs) are adopted as acoustic models. A variety of speedup techniques for DNN score computation are used to enable real-time operation on mobile devices. To reduce the memory and disk usage, on-the-fly language model (LM) rescoring is performed with a compressed n-gram LM. We were able to build an accurate and compact system that runs well below real-time on a Nexus 4 Android phone. Index Terms: Deep neural networks, embedded speech recognition, SIMD, LM compression. 1. Introduction Smartphones and tablets are rapidly overtaking desktop and laptop computers as people’s primary computing device. They are heavily used to access the web, read and write messages, interact on social networks, etc. This popularity comes despite the fact that it is significantly more difficult to input text on these devices, predominantly by using an on-screen keyboard. Automatic speech recognition (ASR) is a natural, and increasingly popular, alternative to typing on mobile sevices. Google offers the ability to search by voice [1] on Android, iOS, and Chrome; Apple’s iOS devices come with Siri, a conversational assistant. On both Android and iOS devices, users can also speak to fill in any text field where they can type (see, e.g., [2]), a capability heavily used to dictate SMS messages and e-mail. A major limitation of these products is that speech recognition is performed on a server. Mobile network connections are often slow or intermittent, and sometimes non-existant. Therefore, in this study, we investigate techniques to build an accurate, small-footprint speech recognition system that can run in real-time on modern mobile devices. Previously, speech recognition on handheld computers and smartphones has been studied in the DARPA sponsored Transtac Program, where speech-to-speech translation systems were developed on the phone [3, 4, 5]. In the Transtac systems, Gaussian mixture models (GMMs) were used to as acoustic models. While the task was a small domain, with limited training data, the memory usage in the resulting systems was moderately high. In this paper, we focus on large vocabulary on-device dictation. We show that deep neural networks (DNNs) can provide large accuracy improvements over GMM acoustic models, with a significantly smaller footprint. We also demonstrate how memory usage can be significantly reduced by performing onthe-fly rescoring with a compressed language model during decoding. The rest of this paper is organized as follows. In Section 2, the embedded GMM acoustic model is described. Section 3 presents the training of embedded DNNs, and the techniques we employed to speed up DNN inference at runtime. Section 4 describes the compressed language models for on-the-fly rescoring. Section 5 shows the experimental results of recognition accuracy and speed on Nexus 4 platform. Finally, Section 6 concludes the paper and discusses future work. 2. GMM Acoustic Model Our embedded GMM acoustic model is trained on 4.2M utterances, or more than 3,000 hours of speech data containing randomly sampled anonymized voice search queries and other dictation requests on mobile devices. The acoustic features are 9 contiguous frames of 13-dimensional PLP features spliced and projected to 40 dimensions by linear discriminant analysis (LDA). Semi-tied covariances [6] are used to further diagonalize the LDA transformed features. Boosted-MMI [7] was used to train the model discriminatively. The GMM acoustic model contains 1.3k clustered acoustic states, with a total of 100k Gaussians. To reduce model size and speed up computation on embedded platforms, the floatingpoint GMM model is converted to a fixed-point representation, similar to that described in [8]. Each dimension of the Gaussian mean vector is quantized into 8 bits, and 16-bit for precision vector. The resulting fixed-point GMM model size is about 1/3 of the floating-point model, and there is no loss of accuracy due to this conversion in our empirical testing. 3. DNNs for Embedded Recognition We have previously described the use of deep neural networks for probability estimation in our cloud-based mobile voice recognition system [9]. We have adopted this system for developing DNN models for embedded recognition, and summarize it here. The model is a standard feed-forward neural network with k hidden layers of nh nodes, each computing a nonlinear function of the weighted sum of the outputs of the previous layer. The input layer is the concatenation of ni consecutive frames of 40-dimensional log filterbank energies calculated on 25ms windows of speech every 10ms. The no softmax outputs estimate the posterior of each acoustic state. We have experimented with conventional logistic nonlinearities and rectified linear units that have recently shown superior performance in our large scale task [10], while also reducing computation. Copyright © 2013 ISCA 25-29 August 2013, Lyon, France INTERSPEECH 2013 662While our server-based model has 50M parameters (k = 4, nh = 2560, ni = 26 and no = 7969), to reduce the memory and computation requirement for the embedded model, we experimented with a variety of sizes and chose k = 6, nh = 512, ni = 16 and no = 2000, or 2.7M parameters. The input window is asymmetric; each additional frame of future context adds 10ms of latency to the system so we limit ourselves to 5 future frames, and choose around 10 frames of past context, trading off accuracy and computation. Our context dependency (CD) phone trees were initially constructed using a GMM training system that gave 14,247 states. By pruning this system using likelihood gain thresholds, we can choose an arbitrary number of CD states. We used an earlier large scale model with the full state inventory that achieved around 14% WER to align the training data, then map the 14k states to the desired smaller inventory. Thus we use a better model to label the training data to an accuracy that cannot be achieved with the embedded scale model. 3.1. Training Training uses conventional backpropagation of gradients from a cross entropy error criterion. We use minibatches of 200 frames with an exponentially decaying learning rate and a momentum of 0.9. We train our neural networks on a dedicated GPU based system. With all of the data available locally on this system, the neural network trainer can choose minibatches and calculate the backpropagation updates. 3.2. Decoding speedup Mobile CPUs are designed primarily for lower power usage and do not have as many or as powerful math units as CPUs used in server or desktop applications. This makes DNN inference, which is mathematically computationally expensive, a particular challenge. We exploit a number of techniques to speed up the DNN score computation on these platforms. As described in [11], we use a fixed-point representation of DNNs. All activations and intermediate layer weights are quantized into 8-bit signed char, and biases are encoded as 32-bit int. The input layer remains floating-point, to better accommodate the larger dynamic ranges of input features. There is no measured accuracy loss resulting from this conversion to fixed-point format. Single Instruction Multiple Data (SIMD) instructions are used to speed up the DNN computation. With our choice of smaller-sized fixed-point integer units, the SIMD acceleration is significantly more efficient, exploiting up to 8 way parallelism in each computation. We use a combination of inline assembly to speed up the most expensive matrix multiplication functions, and compiler intrinsics in the sigmoid and rectified linear calculations. Batched lazy computation [11] is also performed. To exploit the multiple cores present on modern smartphones, we compute the activations up to the last layer in a dedicated thread. The output posteriors of the last layer are computed only when needed by the decoder in a separate thread. Each thread computes results for a batch of frames at a time. The choice of batch size is a tradeoff between computation efficiency and recognition latency. Finally, frame skipping [12] is adopted to further reduce computation. Activations and posteriors are computed only every nb frames and used for nb consecutive frames. In experiments we find that for nb = 2, the accuracy loss is negligible; however for nb ≥ 3, the accuracy degrades quickly. 4. Language Model Compression We create n-gram language models appropriate for embedded recognition by first training a 1M word vocabulary and 18M n-gram Katz-smoothed 4-gram language model using Google’s large-scale LM training infrastructure [13]. The language model is trained using a very large corpus (on the order of 20 billion words) from a variety of sources, including search queries, web documents and transcribed speech logs. To reduce memory usage, we use two language models during decoding. First, a highly-pruned LM is used to build a small CLG transducer [14] that is traversed by the decoder. Second, we use a larger LM to perform on-the-fly lattice rescoring during search, similar to [15]. We have observed that a CLG transducer is generally two to three times larger than a standalone LM, so this rescoring technique significantly reduces the memory footprint. Both language models used in decoding are obtained by shrinking the 1M vocabulary and 18M n-gram LM. We aggressively reduce the vocabulary to the 50K highest unigram terms. We then apply relative entropy pruning [16] as implemented in the OpenGrm toolkit [17]. The resulting finite state model for rescoring LM has 1.4M n-grams, with just 280K states and 1.7M arcs. The LM for first pass decoding contains only unigrams and about 200 bigrams. We further reduce the memory footprint of the rescoring LM by storing it in an extremely memory-efficient manner, discussed below. 4.1. Succinct storage using LOUDS If you consider a backoff language model’s structure, the failure arcs from (n + 1)-gram contexts to n-gram contexts and, ultimately, to the unigram state form a tree. Trees can be stored using 2 bits per node using a level-order unary degree sequence (LOUDS), where we visit the nodes breadth-first writing 1s for the number of (n + 1)-gram contexts and then terminating with a 0 bit. We build a bit sequence similarly for the degree of outbound non-φ arcs. The LOUDS data structure provides first-child, last-child, and parent navigation, so we are able to store a language model without storing any next-state values. As a contiguous, indexfree data object, the language model can be easily memory mapped. The implementation of this model is part of the OpenFst library [18] and covered in detail in [19]. The precise storage requirements, measured in bits, are 4ns + na + (W + L)(ns + na) + W nf + c where ns is the number of states, nf the number of final states, na is the number of arcs, L is the number of bits per wordid, and W is the number of bits per probability value. This is approximately one third the storage required by OpenFst’s vector representation. For the models discussed here, we use 16 bits for both labels and weights. During run time, to support fast navigation in the language model, we build additional indexes of the LOUDS bit sequences to support the operations rankb(i) the number of b valued bits before index i, and its inverse selectb(r). We maintain a two level index that adds an additional 0.251(4ns + na) bits. Here it is important to make use of fast assembly operations such as find first set during decoding, which we do through compiler intrinsics. 6634.2. Symbol table compression The word symbol table for an LM is used to map words to unique identifiers. Symbol tabels are another example of a data structure that can be represented as a tree. In this case we relied upon the implementation contained in the MARISA library [20]. This produces a symbol table that fits in just one third the space of the concatenated strings of the vocabulary, yet provides a bidirectional mapping between integers and vocabulary strings. We are able to store our vocabulary in about 126K bytes, less than 3 bytes per entry in a memory mappable image. The MARISA library assigns the string to integer ids during compression, so we relabel all of the other components in our system to match this assignment. 5. Experimental Results To evaluate accuracy performance, we use a test set of 20,000 anonymized transcribed utterances from users speaking in order to fill in text fields on mobile devices. This biases the test set towards dictation, as opposed to voice search queries, because dictation is more useful than search when no network connection is available. To measure speed performance, we decode a subset of 100 utterances on an Android Nexus 4 (LG) phone. The Nexus 4 is equipped with a 1.5GHz quad-core Qualcomm Snapdragon S4 pro CPU, and 2GB of RAM. It runs the Android 4.2 operating system. To reduce start up loading time, all data files, including the acoustic model, the CLG transducer, the rescoring LM and the symbol tables are memory mapped on the device. We use a background thread to “prefetch” the memory mapped resources when decoding starts, which mitigates the slowdown in decoding for the first several utterances. 5.1. GMM acoustic model The GMM configuration achieves a word error rate (WER) of 20.7% on this task, with an average real-time (RT) factor of 0.63. To achieve this speed, the system uses integer arithmetic for likelihood calculation and decoding. The Mahalanobis distance computation is accelerated using fixed-point SIMD instructions. Gaussian selection is used to reduce the burden of likelihood computation, and further efficiencies come from computing likelihoods for batches of frames. 5.2. Accuracy with DNNs We compare the accuracy of DNNs with different configurations to the baseline GMM acoustic model in Table 1. A DNN with 1.48M parameters already outperforms the GMM in accuracy, with a disk size of only 17% of the GMM’s. By increasing the number of hidden layers from 4 to 6 and number of outputs from 1000 to 2000, we obtain a large improvement of 27.5% relative in WER compared to the GMM baseline. The disk size of this DNN is 26% of the size of the GMMs. For comparison, we also evaluate a server-sized DNN with an order of magnitude of more parameters, and it gives 12.3% WER. Note that all experiments in Table 1 use smaller LMs in decoding. In addition, with an un-pruned server LM, the server DNN achieves 9.9% WER while the server GMM achieves 13.5%. Therefore, compared to a full-size DNN server system, there is a 2.4% absolute loss due to smaller LMs, and 2.8% due to smaller DNN. Compared to the full-size GMM server system, the embedded DNN system is about 10% relatively worse in WER. The impact of frame skipping is evaluated with the DNN 6×512 model. As shown in Table 2, the accuracy performance quickly degrades when nb is larger than 2. Table 2: Accuracy results with frame skipping in a DNN system. nb 1 2 3 4 5 WER (%) 15.1 15.2 15.6 16.0 16.7 5.3. Speed benchmark For speed benchmark, we measure average RT factor as well as 90-percentile RT factor. As shown in Table 3, the baseline GMM system with SIMD optimization gives an average RT factor of 0.63. The fixed-point DNN gives 1.32×RT without SIMD optimization, and 0.75×RT with SIMD. Batched lazy computation improves average RT by 0.06 but degrades the 90- percentile RT performance, probably due to less efficient ondemand computation for difficult utterances. After frame skipping with nb = 2, the speed of DNN system is further improved slightly to 0.66×RT. Finally, the overhead of the compact LOUDS based LM is about 0.13×RT on average. Table 3: Averge real-time (RT) and 90-percentile RT factors of different system settings. Average RT RT(90) GMM 0.63 0.90 DNN (fixed-point) 1.32 1.43 + SIMD 0.75 0.87 + lazy batch 0.69 1.01 + frame skipping 0.66 0.97 + LOUDS 0.79 1.24 5.4. System Footprint Compared to the baseline GMM system, the new system with LM compression and DNN acoustic model achieves a much smaller footprint. The data files sizes are listed in Table 4. Note that conversion of the 34MB floating-point GMM model to a 14MB fixed-point GMM model itself provides a large reduction in size. The use of DNN reduces the size by 10MB, and the LM compression contributed to another 18MB reduction. Our final embedded DNN system size is reduced from 46MB to 17MB, while achieving a big WER reduction from 20.7% to 15.2%. 6. Conclusions In this paper, we have described a fast, accurate and smallfootprint speech recognition system for large vocabulary dictation on the device. DNNs are used as acoustic model, which provides a 27.5% relative WER improvement over the baseline GMM models. The use of DNNs also significantly reduces the memory usage. Various techniques are adopted to speed up the DNN inference at decoding time. In addition, a LOUDS based language model compression reduces the rescoring LM size by more than 60% relative. Overall, the size of the data files of the system is reduced from 46MB to 17MB. 664Table 1: Comparison of GMM and DNNs with different sizes. The input layer is denoted by number of filterbank energies × the context window size (left + current + right). The hidden layers are denoted by number of hidden layers × number of nodes per layer. The number of outputs is the number of HMM states in the model. Model WER (%) Input Layer Hidden Layers # Outputs # Parameters Size GMM 20.7 - - 1314 8.08M 14MB DNN 4×400 22.6 40×(8+1+4) 4×400 512 0.9M 1.5MB DNN 4×480 20.3 40×(10+1+5) 4×480 1000 1.5M 2.4MB DNN 6×512 15.1 40×(10+1+5) 6×512 2000 2.7M 3.7MB Server DNN 12.3 40×(20+1+5) 4×2560 7969 49.3M 50.8MB Table 4: Comparison of data file sizes (in MB) in baseline GMM system and DNN system with and without LOUDS LM compression. AM denotes acoustic model, CLG is the transducer for decoding, LM denotes the rescoring LM, and symbols denote the word symbol table. System AM CLG LM Symbols Total GMM 14 2.7 29 0.55 46 + LOUDS 14 2.7 10.7 0.13 27 DNN 3.7 2.8 29 0.55 36 + LOUDS 3.7 2.8 10.7 0.13 17 Future work includes speeding up rescoring using the LOUDS LM as well as further compression techniques. We also continue to investigate the accuracy performance with different sizes of LM for CLG and rescoring. 7. Acknowledgements The authors would like to thank our former colleague Patrick Nguyen for implementing the portable neural network runtime engine used in this study. Thanks also to Vincent Vanhoucke and Johan Schalkwyk for helpful discussions and support during this work. [9] N. Jaitly, P. Nguyen, A. W. Senior, and V. Vanhoucke, “Application of pretrained deep neural networks to large vocabulary speech recognition,” in Proc. Interspeech, 2012. [10] M. D. Zeiler et al., “On rectified linear units for speech processing,” in Proc. ICASSP, 2013. [11] V. Vanhoucke, A. Senior, and M. Z. Mao, “Improving the speed of neural networks on CPUs,” in Proc. Deep Learning and Unsupervised Feature Learning NIPS Workshop, 2011. [12] V. Vanhoucke, M. Devin, and G. Heigold, “Multiframe deep neural networks for acoustic modeling,” in Proc. ICASSP, 2013. [13] T. Brants, A. C. Popat, P. Xu, F. J. Och, and J. Dean, “Large language models in machine translation,” in EMNLP, 2007, pp. 858–867. [14] M. Mohri, F. Pereira, and M. Riley, “Speech recognition with weighted finite-state transducers,” Handbook of Speech Processing, pp. 559–582, 2008. [15] T. Hori and A. Nakamura, “Generalized fast on-the-fly composition algorithm for WFST-based speech recognition,” in Proc. Interspeech, 2005. [16] A. Stolcke, “Entropy-based pruning of backoff language models,” in DARPA Broadcast News Transcription and Understanding Workshop, 1998, pp. 8–11. [17] B. Roark, R. Sproat, C. Allauzen, M. Riley, J. Sorensen, and T. Tai, “The OpenGrm open-source finite-state grammar software libraries,” in Proceedings of the ACL 2012 System Demonstrations. 2012, ACL ’12, pp. 61–66, Association for Computational Linguistics. 8. References [1] J. Schalkwyk, D. Beeferman, F. Beaufays, B. Byrne, C. Chelba, M. Cohen, M. Kamvar, and B. Strope, “Google search by voice: A case study,” in Advances in Speech Recognition: Mobile Environments, Call Centers and Clinics, pp. 61–90. Springer, 2010. [2] B. Ballinger, C. Allauzen, A. Gruenstein, and J. Schalkwyk, “Ondemand language model interpolation for mobile speech input,” in Proc. Interspeech, 2010. [3] J. Zheng et al., “Implementing SRI’s Pashto speech-to-speech translation system on a smart phone,” in SLT, 2010. [4] J. Xue, X. Cui, G. Daggett, E. Marcheret, and B. Zhou, “Towards high performance LVCSR in speech-to-speech translation system on smart phones,” in Proc. Interspeech, 2012. [5] R. Prasad et al., “BBN Transtalk: Robust multilingual two-way speech-to-speech translation for mobile platforms,” Computer Speech and Language, vol. 27, pp. 475–491, February 2013. [6] M. J. F. Gales, “Semi-tied covariance matrices for hidden Markov models,” IEEE Trans. Speech and Audio Processing, vol. 7, pp. 272–281, 1999. [7] D. Povey, D. Kanevsky, B. Kingsbury, B. Ramabhadran, G. Saon, and K. Visweswariah, “Boosted MMI for model and feature-space discriminative training,” in Proc. ICASSP, 2008. [8] E. Bocchieri, “Fixed-point arithmetic,” Automatic Speech Recognition on Mobile Devices and over Communication Networks, pp. 255–275, 2008. [18] C. Allauzen, M. Riley, J. Schalkwyk, W. Skut, and M. Mohri, “OpenFst: A general and efficient weighted finite-state transducer library,” in Proceedings of the Ninth International Conference on Implementation and Application of Automata, (CIAA 2007). 2007, vol. 4783 of Lecture Notes in Computer Science, pp. 11– 23, Springer, http://www.openfst.org. [19] J. Sorensen and C. Allauzen, “Unary data structures for language models,” in Proc. Interspeech, 2011. [20] S. Yata, “Prefix/Patricia trie dictionary compression by nesting prefix/Patricia tries (japanese),” in Proceedings of 17th Annual Meeting of the Association for Natural Language, Toyohashi, Japan, 2011, NLP2011, https://code.google.com/p/marisa-trie/. 665 Backoff Inspired Features for Maximum Entropy Language Models Fadi Biadsy, Keith Hall, Pedro Moreno and Brian Roark Google, Inc. {biadsy,kbhall,pedro,roark}@google.com Abstract Maximum Entropy (MaxEnt) language models [1, 2] are linear models that are typically regularized via well-known L1 or L2 terms in the likelihood objective, hence avoiding the need for the kinds of backoff or mixture weights used in smoothed ngram language models using Katz backoff [3] and similar techniques. Even though backoff cost is not required to regularize the model, we investigate the use of backoff features in MaxEnt models, as well as some backoff-inspired variants. These features are shown to improve model quality substantially, as shown in perplexity and word-error rate reductions, even in very large scale training scenarios of tens or hundreds of billions of words and hundreds of millions of features. Index Terms: maximum entropy modeling, language modeling, n-gram models, linear models 1. Introduction A central problem in language modeling is how to combine information from various model components, e.g., mixing models trained with differing Markov orders for smoothing or on distinct corpora for adaptation. Smoothing (regularization) for n-gram language models is typically presented as a mechanism whereby higher-order models are combined with lower-order models so as to achieve both the specificity of the higher-order model and the more robust generality of the lower-order model. Most commonly, this combination is effected via an interpolation or backoff mechanism, in which each prefix (history) of an n-gram has a parameter which dictates how much cost is associated with making use of lower-order n-gram estimates, often called the “backoff cost”. This becomes a parameter estimation problem in its own right, either through discounting or mixing parameters; and these are often estimated via extensive parameter tying, heuristics based on count histograms, or both. Log linear models provide an alternative to n-gram backoff or interpolated models for combining evidence from multiple, overlapping sources of evidence, with very different regularization methods. Instead of defining a specific model structure with backoff costs and/or mixing parameters, these models combine features from many sources into a single linear feature vector, and score a word by taking the dot product of the feature vector with a learned parameter vector. Learning can be via locally normalized likelihood objective functions, as in Maximum Entropy (MaxEnt) models [1, 2, 4] or global “whole sentence” objectives [5, 6, 7]. For locally normalized MaxEnt models, which estimate a conditional distribution over a vocabulary given the prefix history (just as the backoff smoothed n-gram models do), the brute-force local normalization over the vocabulary obviates the need for complex backoff schemes to avoid zero probabilities. One can simply toss in n-gram features of all the orders, and learn their relative contribution. Recall, however, that the standard backoff n-gram models do not only contain parameters associated with n-grams; they also contain parameters associated with the backoff weights for each prefix history. For every proper prefix of an n-gram in the model, there will be an associated backoff weight, which penalizes to a greater or lesser extent words that have been previously unseen following that prefix history. For some histories we should have a relatively high expectation of seeing something new, either because the history itself is rare (hence we do not have enough observations yet to be strongly predictive) or it simply predicts relatively open classes of possible words, e.g., “the”, which can precede many possible words, including many that were presumably unobserved following “the” in the training corpus. Other prefixes may be highly predictive so that the expectation of seeing something previously unobserved is relatively low, e.g., “Barack”. Granted, MaxEnt language models (LMs) do not need this information about prefix histories to estimate regularized probabilities. Chen and Rosenfeld [4] survey various smoothing and regularization methods for MaxEnt language models, including reducing the number of features (as L1 regularization does), optimizing to match expected frequencies to discounted counts, or optimizing to modified objectives, such as L2 regularization. In none of these methods are there parameters in the model associated with the sort of “otherwise” semantics of conventional n-gram backoffs. Because such features are not required for smoothing, they are not part of the typical feature set used in log linear language modeling, yet our results demonstrate that they should be. The ultimate usefulness of such features likely depends on the amount of training data available, and we have thus applied highly optimized MaxEnt training to very large data sets. In large scale n-gram modeling, it has been shown that the specific details of the smoothing algorithm is typically less important than the scale. So-called “stupid backoff” [8] is an efficient, scalable estimation method that, despite lack of normalization guarantees, is shown to be extremely effective in very large data set scenarios. While this has been taken to demonstrate that the specifics of smoothing is unimportant as the data gets large, those parameters are still important components of the modeling approach, even if their usefulness is robust to variation in parameter value. We demonstrate that features patterned after backoff weights, and several related generalizations of these features, can in fact make a large difference to a MaxEnt language model, even if the amount of training data is very large. In the next section, we present background for language modeling and cover related work. We then present our MaxEnt training approach, and the new features. Finally, we present experimental results on a range of large scale speech tasks. 2. Background and Related Work Let wi be the word at position i in the string, and let w i−1 i−k = wi−k . . . wi−1 be the prefix history of the string prior to wi, and P a probability estimate assigned to seen n-grams by the specific smoothing method. Then the standard backoff language model formulation is as follows: P(wi | w i−1 i−k ) = ( P(wi | w i−1 i−k ) if c(wi i−k ) > 0 α(w i−1 i−k ) P(wi | w i−1 i−k+1) otherwise This recursive smoothing formulation has two kinds of paramCopyright © 2014 ISCA 14-18 September 2014, Singapore INTERSPEECH 2014 2645eters: n-gram probabilities P(wi | w i−1 i−k ) and backoff weights α(w i−1 i−k ), which are parameters associated with the prefix history w i−1 i−k . MaxEnt models are log linear models score that alternatives by taking the exponential of the dot product between a feature vector and a parameter vector and normalizing. Let Φ(wi−k . . . wi) be a d-dimensional feature vector, θ a ddimensional parameter vector, and V a vocabulary. Then P(wi | w i−1 i−k ) = exp(Φ(wi−k . . . wi) · θ) Z(wi−k . . . wi−1, θ) where Z is a partition function (normalization constant): Z(wi−k, . . . , wi−1, θ) = X v∈V exp(Φ(wi−k, . . . , wi−1v) · θ) Training with a likelihood objective function is a convex optimization problem, with well-studied efficient estimation techniques, such as stochastic gradient descent. Regularization techniques are also well-studied, and include L1 and L2 regularization, or their combination, which are modifications of the likelihood objective to either keep parameter values as close to zero as possible (L2) or reduce the number of features with nonzero parameter weights by pushing many parameters to zero (L1). We employ a distributed approximation to L1, see Section 3.1. The most expensive part of this optimization is the calculation of the partition function, since it requires summing over the entire vocabulary, which can be very large. Efficient methods to enable training with very large corpora and large vocabularies have been investigated over the past decades, from methods to exploit structural overlap between features [9, 10] to methods for decomposing the multi-class language modeling problem into many binary language modeling problems (one versus the rest) and sampling less data to effectively learn the models [11]. For this paper, we employed many optimizations to enable training with very large vocabularies (several hundred thousand words) and very large training sets (>100B words). 3. Methods 3.1. Maximum Entropy training Many features have been used in MaxEnt language models, including standard n-grams and trigger words [1], topic-based features [12] and morphological and sub-word based features [13, 14]. Feature engineering is a major consideration in this sort of modeling, and in Section 3.2 we detail our newly designed feature templates. Before we do so, we present the training methods that allow us to scale up to a very large vocabulary and many training instances. In this work, we wish to scale up MaxEnt language model training to learn from the same amount of data used for standard backoff n-gram language models. We achieve this by exploiting recent work on gradient-based distributed optimization; specifically, distributed stochastic gradient descent (SGD) [15, 16, 17, 18, 19]. We differ slightly from previous work in multiple aspects: (1) we apply a final L1 regularization setp at the end of each reducer using statistics collected from the mappers; (2) We estimate the gradient using a mini-batch of 16 samples where the mini-batch is processed in parallel via multi-threading; (3) We do not perform any binarization or subsampling as in [20]; (4) Unlike [21], we do not peform any clustering of our vocabulary. Algorithm 1 presents our variant of the iterative parameter mixtures (IPM) algorithm based on sampling. This presents a merging of concepts from the original IPM algorithm described in [16] and the distributed sample-based algorithm in [18] as well as the lazy L1 SGD computation from [22]. Algorithm 1 Sample-based Iterative Parameter Mixtures Require: n is the number of samples per worker per epoch Require: Break S into K partitions 1: S ← {D 1 , . . . , Dj , . . . , DK} 2: t ← 0 3: Θt ← 0 4: repeat 5: t ← t + 1 6: {θ 1 1, . . . , θK L } ← IPMMAP(D 1 , . . . , DK, Θt−1, n) 7: Θ 0 t ← IPMREDUCE(θ 1 1, . . . , θj l , . . . , θK L ) 8: Θt ← APPLYL1(Θ0 t) 9: until converged 10: function IPMMAP(D, Θ, n) 11: . IPMMAP processes training data in parallel 12: Θ0 ← Θ 13: for i = 1 . . . n do . n examples from D 14: Sample di from D 15: Θ 0 i ← ApplyLazyL1(ActiveF eatures(di, Θi−1)) 16: Θi ← Θ 0 i − α∇Fdi (Θ0 i) 17: α ← U pdateAlpha(α, i) 18: end for 19: return Θn 20: end function 21: function IPMREDUCE(θ 1 l , . . . , θj l , . . . , θK l ) 22: . IPMREDUCE processes model parameters in parallel 23: θl ← 1 K P j θ j l 24: return θl 25: end function While this is a general paradigm for distributed optimization, we show the MapReduce [23] implementation in Algorithm 1. We begin the process by partitioning the training data S into multiple units D j , processing each of these units with the IPMMAP function on separate processing nodes. On each of these nodes, IPMMAP samples a subset of D j which we call di. This can be a single example or a mini-batch of examples. We perform the Lazy L1 regularization update to the model, compute the gradient of the regularized loss associated with the mini-batch (which can be also be done in parallel), update the local copy of the model parameters Θ, and update the learningrate α. Each node samples n examples from its data partition. Finally, IPMREDUCE collects the local model parameters from each IPMMAP and averages them in parallel. Parallelization here can be done over subsets of the parameter indices (each IPMREDUCE node averages a subset of the parameter space). We refer to each full MapReduce pass as an epoch of training. Starting with the second epoch, the IPMMAP nodes are initialized with the previous epoch’s merged, regularized model. In a general shared distributed framework, which is used at Google, some machines may be slower than others (due to hardware or overload), machines may fail, or jobs may be preempted. When using a large number of machines this is inevitable. To avoid starting the training process over in these cases, and make all others wait for for the lagging machines, we enforce a timeout on our trainers. In other words, all mappers have to finish within a certain amount of time. Therefore, the reducer will merge all models when they either finished processing their samples or timed-out. 3.2. Backoff inspired features MaxEnt language models commonly have n-gram features, which we denote here as a function of the string, the position, 2646and the order as follows: NGram(w1 . . . wn, i, k) =Voir également :
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Rues-Zone-Artisanale..> 30-May-2013 18:36 602KRues de France : Adresse ALEZ ALEZ AL LENN ALEZ AR GOSKER ALEZ GLAZ ALEZ GOZ KERGWENN ALEZ HIR ALEZ IZELA ALEZ IZELLA ALEZ KERBILIEZ ALEZ UHELA ABBE FRANZ STOCK ABER WRAC H ACHILLE BEL AJONCS ALAIN BOUCHART ALAIN COLAS ALBATROS ALEXANDRE DUMAS ALEXANDRE VERCHIN ALIZEES AMPERE ANATOLE FRANCE ANATOLE BRAZ ANDRE JARLAND ANEMONES ANGELA DUVAL ANGELE VANNIER ANNECY ANNE MESMEUR ANTOINE WATTEAU TRINITE ARCHIMEDE AR C HURE AR FAOU AR FOENNEG AR GALL ARGOAT ARMAND CHARPENTIER ARMAND ROBIN ARTHUR BORDERIE AUBEPINES AUGUSTE DUPOUY AUGUSTIN FRESNEL BECQUEREL BEG MENEZ BEL ABRI BELLEVUE BENIGUET BENJAMIN CONSTANT BERGERONNETTES BERLIOZ BERNACHES BERTRAND D ARGENTRE BOIS D AMOUR PINS NEUF QUENVEL ROCHE BONEZE BOULOUARN BRISE BRUYERES CALMETTE GUERIN CAMELIAS CAMILLE COROT CANAPE CAPITAINE JEANNAULT PEZENNEC CARN YAN CERISIERS CHAMONIX CHARDONNERETS GOFFIC PEGUY ROLLAND CHARMILLES CHARMILLES LANDE LOTHAN CHATAIGNERS CHATAIGNIERS CHAUMIERE FER CHENES 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KERARIS KERBELLEC KERBEOCH KERBERON IZELLA KERBRIGENT KERCOLIN KERDANET KERDANET COSQUER KERDERO KEREQUEL KERFEUNTEUN KERGANOU KERGOZ KERGRIMEN KERGUESTEN KERHOS KERHUEL KERIEQUEL KERIOUANT KERIVOAL KERIVOALEN KERLANO KERLEIGUER KERLIFRIN KERMARIG KERMOJEAN KERNEC KERNEOST KERNILIS KERNIOU KERNISY KERNON KEROHAN KERORGANT KEROUANT KEROUES KEROUZACH KERRICHARD KERRIEN KERSALE KERSEAL KERSYVET KERUSTER KERVARGON KERVELLIC KERVENNOS KERVEUR KERVIHAN KERYANNO KERZERVAN KILOURIN KORRIGANS KRINNOC CARRIERE CROIX LAFFLOSQUE LANNIDY TREVIDY LANNOU LANTIGEN LARENVOIE LAVOIR LAVOIR SAINTE CHRISTINE LAVOIRS LEN GOZ LESQUIDIC IZELLA LESQUIDIC NEVEZ LESQUIDIC TRAON LEURGADORET LEZOUZARD LILAS LINGOZ LINIOUS LISTRY VRAZ LOCAL AMAND LOUIS GUENNEC LOZ MANOIR TREGUER MAT PILOTE MEIL PRY MEJOU KERANDOUIN MELAZE COSQUER MENDIANTS MENEC MENEZ MENEZ BRAS NEVEZ MENEZ BRAZ MENEZ BRUG MENEZ GURET MENEZ KERGUESTEN MENEZ KER GUYOCH MENEZ LAE MENEZ PLENN MENEZ ROUZ MENHIR MESLAN MESSOUDALC H MEZALE MEZALE COSQUER MEZOU VOURCH MINEZ GOUYEN MOGUEROU MOINEAUX MOINES BLANCS MOLENE MOUETTES HENANT KERANGOC TRESIGNEAU MUR NOGUELLOU NOISETIERS NOISETIERS KEREZ OUESSANT PACIFIQUE PARC AR CASTEL PARC BRIS PARC C HOESSANT PARC MARCHE PARC MINE PARK DOUAR BERGE PARK MINN PARK ROZ SERUZIER PEINTRES PEMPOUL PEN PEN AN ENEZ PEN AR C HOAT MOUSTERLIN PEN AR C HRA PEN AR HOAT PEN AR PARC PEN AR PAVE PEN AR STER PENFOENNEC PENFRAT PENHOAT SALAUN PENN AR VUR PENQUER PERCHE FONTAINE SUISSE PHARE TRAIN PEUPLIERS PIGEONNIER PINS PLAGE PLAGE GRISE POINTE POINTE PRIMEL POINTE GLUGEAU ALIBEN AR BLEIZ AR CHLAN PONTI PONTUAL VIAN PORS AR VILIN VRAS PORS CAVE PORSMELLEC PORZ OLIER POUL POUL ALEN POULALLANICK POUL AR COQUET POUL AR GOQUET POUL FANG POULGIGOU POULL CALLAC POULLOGODEN PRAIRIE PRAT CUIC PRAT HIR PRES PRESBYTERE PUITS QUISTILLIC REA RELIQUES RELUYEN RESTAURANT KEROUDOT RESTIC VIAN RIVIERE ROC AR C HAD ROCHES ROCH YAN ROSCAROC ROSCOLER ROUDOUIC ROZ AR GRILLET ROZBEG ROZ DANIELOU ROZ GLAZ RUBIERN RUISSEAU SAINTE CHRISTINE RUMORVAN RUN AN ILIZ RUN AR C HAD RUN AR HAD RUN AR LOUARN RUN LAND RUZ CONAN GONVEL ARGENTON GUENOLE JULIEN PHILIBERT SALAMANDRES SAN DIVY BOURG SERINGAS SKEIZ SOURCE SQUIVIT STADE STANG KORRIQUET STANG ROHAN STER CHLAON TAHLI TERRASSE THEVEN CARN TI BRAS TI LIPIG TI NEVEZ KERLAGATHU TORREYEUN TOUL BLEIS TOUL PESKET TOURTERELLES TRAON BIAN TRAON BIHAN LAMBEZELLEC TRAON KER ILLIEN SERPIL TREAS TREBERRE TREOMPAN TRESSENI TREVARGUEN IZELLA TROBORN TROIS CHENES TROLAN TRONEOLY TROVERN TY KELES TY NOD TY RUZ TY STER TY TAD COZ VALANEC VANDREE VARQUES VERDIERS VERN GLAZ VERT VIEUX CAPTAGE VIEUX FOURS VILLEMET VILLENEUVE VINIOU Y RHEUN AR CHEM QUENEACH CHENES CHENES KERANDRO CHERON CHEROU CHEVREL CHEZ MME GILLES C 153 HENT CHRA BOHAST CHRIST CINQ 4 VENTS ABER AJONCS AJONCS D OR ALLAIN ALOUETTES ANCIENS ARGOAT AR VERN VRICK AR VODENIC AR VODENIG AR VODENNIC AR VODENNIG ARZELLIS AUBEPINES AULNE BARADOZIC BEAUSEJOUR BEL AIR BELENOU BELLEVUE BELVEDERE BIS BOULEAUX BOULVAS BRUYERES BUTTE CAMELIAS CAVENTOU CHALONIC D EAU CLAIR LOGIS COADIC COMMERCIALE COSQUER VIAN CREAC AL LEO CREACH AR LEO CREACH MICKAEL CRINOU CROAS AR BEUZ CROAS AR GARREC CROAS HIR CROIX MISSIONS CROIX ROUGE D ANTIN BELLEVUE KER ANNA KER ELO KERGUELEN KERMENGUY KERSAUX KROAS SALIOU PAIX RUCHE TERRE NOIRE L ODET PORS MOELAN AJONCS D OR ANCIENS BRUYERES CHARDONS BLEUS FLEURS GENETS HORTENSIAS MARRONNIERS PINS RAMIERS ROSIERS TY BOURHIS DUTERQUE DOURIC CHANOINE CHAPALAIN CROIZIOU GUESCLIN MENEZ BIROU PICHERI 18 ALEZ AR GOSKER PICHERI 19 ALEZ AR GOSKER EGLANTIERS EGLANTIERS NIZON ERNEST RENAN AIRIAU FAO FONTAINE FONTAINES FONTAINE FREDLAND FRELAND FRIEDLAND GARO GARVAN GARZABIC GENETS GENETS D OR GLYCINES GOLLEN GORREKEAR GRATZ GUENAN GUENANS GUENON GUEVEN GUILLY GWEL KAER HENT COZ HIRONDELLES HLM KERHALLON VIHAN HORTENSIAS ILES IRLANDE IZELLA JARDINS ASSOLANT JAURES JEANNE D ARC JONQUILLES JULES DUTERQUE JULIA KER ABARDAEZ KERADENNEC KERALGUY PORSMILIN KER ANNA KERARZANT KERAVEL KERAZAN KERBINIOU KERBLEUNIOU KERBRUG KER COADIC KERDOUSSAL KEREAN KERELLEAU KER ELLEZ KERENTRECH KER EOL KERESPERN KEREVER KERFEUNTEN KERFEUNTEUN KERGALL KERGANAVAL KERGAUTHIER KERGAUTIER KERGOFF KERGUEN KERHEUN KERHORNOU KERIBIN KERIEQUEL KERIFAOUEN KERILIS KERINCUFF KERIVARCH KER IZELLA KERJACOB KERJEAN KERLAOUEN KERLEVEN HUELLA KERLOCH KERLOQUIC KERMARIA KERMILIAU KERMILLAU KERMILLEAU KERMILLIAU KERMOOR KERNAOGUER KERNEVEZ KEROHOU KEROZA KERRENTRECH KERRIOU KERROZA KERSABILIC KERSIOUL KERVAO KERVENNEC KERVEUR KERVILAR KERVIZIGOU KERVOAZEC KERYEQUEL LAENNEC LANNIEN LANN ROHOU LANORGANT LAURIERS LESSARD LILAS LOCH POAS MADELEINE MAHE MATHIEU DONNARD MATHIEU DONNART MEIL COAT BIHAN MENEZ BIHAN MENEZ GOUERON MENEZ HOM MESANGES MESMEUR MIMOSAS MONTGOLFIER MOULIN VENT NEVEZ KERBRAT NOTRE DAME ODET ORATOIRE PARC AN DOSSEN PARC EN DOSSEN PARK AR ROZ PARK BRAS PARK FEUNTEUN PARMENTIER PAU PENAMPRAT PEN AR DORGUEN PEN KERNEVEZ PENMEUR PENN KERNEVEZ PESMARCH PHARES PICHERI 15 ALEZ AR GOSKER BENOIT PINS POL AURELIEN POMMIERS PONANT AR MANACH GUEN ILIS PER PORS NEVEZ PRAJOU GUEN PRAJOUS GUEN PRAT HIR PRAT KERGOE PRAT PER PRAT TUDAL PRATUDAL PRIMEVERES QUATRE VENTS QUEFFELEC QUILLIEN QUILLIMADEC RADIOPHARE RAMIERS REUN AR MOAL RHUNEMEZ ROSCO ROSIERS ROUALLOU ROUALOU ROUELLOU ROZ ROZ AVEL ROZENGALL ROZ VOEN RUMERIOU SABLES BLANCS SAINTE BARBE LAURENT MARC MAUDET AURELIEN POL AURELIEN POL D AURELIEN ROCH STANISLAS SAULES SOLEIL LEVANT STADE STANG LOUVARD STANG VIAN STANG VIHAN STANKOU SUFFREN TACHEN FOIRE TACH GLAZ TAL AR VORC H TARROS THEODORE BOTREL TOUL AR HOAT TREGONETER TREGOR TREMENTIN TREMINTIN TROENES TY BODEL TY FEUNTEUN TY GLAS TY GLAZ TY GUEN TY GWEN TY JEROME TY LANN TY VOUGERET USINE HERBOT VELNEVEZ VILIN AVEL VILLENEUVE YANN D ARGENT YEUN PARGAMOU CLAIRE FONTAINE CLARTE CLASTRINEC CLECH BURTUL CLECH MOEN ILE MOLENE ILE QUEFFEN ILES ILE ILE S COMBOUT ILE TRISTAN ILE VIERGE ILIS COZ 19 MARS 1962 ABBADIE ABBE FLEURY ABER BENOIT ACACIAS ADOLPHE BEAUFRERE AJONCS AJONCS D OR AJONCS KEROU ALAIN SAGE ALAVOINE ALBERT CAMUS ALEXANDER GRAHAM BELL BEAU VIGNY NOBEL AL LANN VERTE ALOUETTES ALPHONSE DAUDET ALSACE AMBROISE PARE AMEDEO MODIGLIANI AMIRAL RONARC H ANATOLE BRAS ANATOLE BRAZ AN AVEL C HOUZI AN AVEL VIZ ANCIENNE ROUTE QUILLOUARN AN DIOU GER ANDRE CHENIER ANDRE SUAREZ AN DREZEC ANEMONES ANEMONES MAISON ANJELA DUVAL ANNE BRETAGNE ANSE ANTOINE WATEAU ANTOINE WATTEAU AR C HOAT PIN AR FOENNEC AR FOENNOG AR FORHEN AR GOAREM NEVEZ AR GOAREM VIHAN ARGOAT AR GORRE AR MEAN ARMEN ARMOOR ARMOR ARMORIQUE AR ROZ BRAS AR ROZ BRAZ AR ROZIG AR STERENN AR STIVELL AR VEL AR WAREMM VANAL ATLANTIQUE AUBEPINES AUGUSTE BERGOT AUGUSTE BRIZEUX AUGUSTE RENOIR AUGUSTIN MORVAN AVEL AR MOOR AVEL DRO AVEL VOR AYMER BAIE BALANEC BANINE BAR AL LAN BAR AL LANN BAUDELAIRE BEAUMARCHAIS BEAUSEJOUR BEG AL LANN BEG AN ENEZ BEG AN ISTR BEG AR C HASTEL BEG AR GROAS BEG AR ROZ BEG AVEL BEG LAND BEG LAND RIEC BEG NENEZ BEL AIR BELLEVUE BELLE VUE BELVEDERE BERNARDINE GARREC BERNARD PALISSY BERVILLE BETHEREL BIRDIE BLAISE CENDRARS BLAISE PASCAL BLANQUI BLERIOT BODROC H BOGEY BOILEAU BOISSIERE BONEZE BORIS VIAN BOUILLEN BOUTONS D OR BOUVREUILS BRANLY BREIZ IZEL BRENNANVEC BREZEHEN BRIZEUX BROUAN BRUYERES BUTOU BUTTE CALMETTE CALMETTE GUERIN CAMELIAS CAMILLE COROT CAPUCINES CARBONT CARREC ZU CASSARD CASTEL DOUR CAVE CENDRES CERISIERS CHAISES CHALUTIERS CHAMAILLARD CHAMP LIN CHAPELLE CHARCOT COTTET GOFFIC GOUNOD BASTARD GOFFIC PEGUY VOISIN CHARLIE PARKER CHATAIGNERAIE CHATAIGNIERS CHATEAUBRIAND D EAU CHAUMIERE DAMES CHEMINOTS CHENES CHEVREUILS CHRYSALIDES IMPASSE E D F CLAUDE BERNARD CLAUDE GUEN CLAUDE MONET CLEMENT MAROT CLIZIT CLOS CLOS NEVEZ COAT EOZEN COAT PIN COLBERT COLIBRIS COLLINE COMMANDANT CHARCOT COMMANDANT MOGUEROUX COMMANDANT NOEL COMPAS COQUELICOTS CORAN CORBEAU CORDELIERE CORDIER CORMORANS CORNGAD CORNICHE COSQUER COST AR STER COSTE BRIX COTEAU KERANGLIEN COURBET COURLIS COZ CASTEL COZ DOUAR COZ MANER CRAPAUD CREACH CREAC H CREAC AVEL CREAC GUEN CREACH COAT CROAS AR BLEON CROAS AR VILLAR CROAS KERLOCH CROAS VILAR CROISEUR LEYGUES CROISEUR GLOIRE CROISEUR MONTCALM CROIX ROUGE CRUGUEL CYPRES DAHUT DANIEL BERNARD D ARVOR BENIGUET CANAPE COAT HALEG COAT KERHUEL COAT MENGUY COAT MEZ CORNOUAILLE D ECOSSE CROAS AR GAC CROAS AR VOSSEN GALICE GUERNESEY JERSEY KERANDRAON KERAUDY KERBERVET KERBIRIOU KERDANIEL KERDIDREN KEREDERN KERFOS KERFRES KERGONAN KERGONIAM KERGRENN KERGROAS KERGROES KERGUIDAN KERGUS KERHELENE KERHUN KERIEZOU KERIVARCH KERLEGUER KERLEREC KERLIES KERLIGRISTIC KERLOSQUET KERMAHOTOU KERMARRON KERMEUR KERONTEC KEROURVOIS KERSCOFF KERSENE KERSINAL KERSQUINE KERUCHEN KERVEZINGAR HUELLA KERVIGNOUNEN KERVILER KERZOURAT BARRIERE L ABER CARAVELLE CHAPELLE EDF CROIX ROUGE DUNDEE FEE MORGANE FEE VIVIANE FELOUQUE FONDERIE FONTAINE FONTAINE AU LAIT FORET FORGE FREGATE GALICE GALIOTE GOELETTE LANDE MAISON BLANCHE MAISON ROUGE MINOTERIE MISAINE MONTAGNE MOTTE LANDOUARDON NEF L ANSE PRAIRIE ROCHE ROCHE BEAUBOIS RUCHE SOURCE TOUR TROMENIE VIERGE NOIRE VILLENEUVE L AVOCETTE VOIE ROMAINE L L L ELORN LEN GOZ LESTONAN VIAN L ILE L ODET DELORISSE LUDUGRIS L USINE MENEZ KEREM MENEZ KERGUESTEN MENEZ KERIVOAS MENEZ KERVEADY MENEZ RHUN DENIS PAPIN PENANGUER PEN AR CREACH PEN AR PEN AR STANG PEN AR VALY PEN AR VIR PICARDIE PONTANE NEVEZ PORS AR PAGN DEPORTES POULGALLEC QUELARNOU RUCROISIC 4 VENTS ABEILLES ACACIAS GUENOLE AJONCS ALIZES ALOUETTES ANEMONES BEGONIAS BRUYERES BUTINEUSES CAMELIAS CAPUCINES CARMES CERISIERS CHARDONNERETS CHATAIGNIERS CHENES COLIBRIS COLVERTS CORMORANS COURLIS CYPRES CYTISES DARDANELLES DENTELLIERES DUNES ECUREUILS FAUVETTES FILETS BLEUS FLANDRES FULMARS FUSILLES GENETS GIRONDINS GLAIEULS GLENAN GLENANS GLYCINES GUILLEMOTS HIBISCUS HIRONDELLES HORTENSIAS HUITRIERS HULOTTES DESIRE LUCAS JACINTHES JUSTICES KORRIGANS LAURIERS LILAS MESANGES MIMOSAS MOUETTES NAVIGATEURS OISEAUX ORMES PETRELS PETUNIAS PEUPLIERS PIGEONS PINS POMMIERS PRES PRIMEVERES PROFESSEURS CURIE SQUIVIDAN RENONCULES RESERVOIRS ROCHES ROMAINS ROSES SANTOLINES SAULES SERINGAS SORBIERS TADORNES TAMARIS TANNERIES TOURTERELLES TRITONS TROENES VANNEAUX DETENTE TOUL AN DREZ TREBEHORET VERDUN DEYROLLE DIBEN VIAN DIDIER DAURAT DIEUDONNE COSTES D IRLANDE DIXMUDE D IZAC CALMETTE PALAUX DOLMEN DOMAINE MICHEL NOBLETZ DOSSEN DRENEC DREZIC 18 JUIN 1940 BEREVEN BERGOT D AMOUR BOULOGNE BRICK BRIGANTIN CALVAIRE CAPITAINE COOK CARBONT CELTIC CERISIER ROSE D EAU CLOS DUVAL CONTE COTRE DUCOUEDIC COUEDIC DUCRETET CRUGUEL MORVAN ROUX VOURCH DRAKKAR DRENEC FLIMIOU FROMVEUR GOLVEZ GRAAL KERVEN DUGUAY TROUIN GUESCLIN HEROS DUKE ELLINGTON LARGE LAVOIR LAYOU LOCH MEJOU LEZANNOU MERLE BLANC MINEZ MITAN MOGUER MONITOR KERLOBRETD DUNES NEVET DUNOIS PAYS GALLES PELICAN PERCEVAL POMMIER BLANC PONTIGOU PORS GWIR PUITS REUNIAT REVEL RIVAGE ROALIS ROHOU ROI ARTHUR ROZ RUMEN SOLEIL LEVANT STAND STANG VERGER VIBEN VIEUX ECOLE FILLES ECOLES ECURIEES ECURIES EDMOND CERIA EDMOND ROSTAND EDOUARD CORBIERE EDOUARD LALO EMBRUNS EMERAUDE EMILE BERNARD EMILE ERNAULT EMILE MASSON EMILE SOUVESTRE EMILE ZOLA EN BAS EN BAS LESTREVET EN BAS VILLA KERJANYVIERE EOLE EPERVIERS ERABLES ERIC TABARLY ERMITAGE ERNEST RENAN ESTIENNE D ORVES E TAL ARMOR ETANG EUGENE BELEGUIC EUGENE BERTHOU EUGENE GONIDEC FALC HUN FAUVETTES FERNAND GUEY FEUNTEUN AR ROZEN FEUNTEUN BOL FEUNTEUNIC AR LEZ FEUNTEUNIGOU FEUNTEUN VENELLE FEUNTEUN VERO FIGUIERS FLEURS FLEURUS FONTAINE FOUGERES FOYER 1 ER CUEFF DUAULT LALAISSE VILLON FRANKLIN ROOSEVELT FREDERIC GUYADER FREDERIC MISTRAL FREGATE DECOUVERTE FREGATE LAPLACE FRENES FROMVEUR GABRIEL SIGNE GABRIEL LIPPMANN GAGARINE GALETS GAMBETTA GARENNE GAUGUIN GENETS GENETTES GEORGE SAND BIZET BRASSENS BAIL GERARD NERVAL GIROFLEES GLAIEULS GLENAN GLINEC GLYCINES GOAREM HUEL GOAREM IZELLA GOAREM PERZEL GOARIVEN GOLF GORLANIC GORREQUEAR GOUELET AR LEN GOUEROU GOULET GOULITQUER GOURANOU GRADLON TERRE VENELLE LARGE GREEN GRILLONS GUEL GUELEDIGOU CALVEZ JAN GUIP GUSTAVE FLAUBERT GUSTAVE LOISEAU GUYNEMER GWALARN GWAREMM AR GWELTOC GWEZ KIGNEZ HARAS HAUTS GUERN HAUTS TERENEZ HELENE BOUCHER HENRI BECQUEREL HENRI CARIO HENRI DRONIOU HENRI LAUTREDOU HENT AR VEIL HENT BIAN HENT GLAZ HERVE PORTZMOGUER HIRONDELLES HONORE DAUMIER HORTENSIAS HUEL POULDU ILDUT ILE D YOC K ILE NOIRE ILES IROISE JACINTHES JACQUES BREL JACQUES CARTIER JACQUES DAGUERRE JACQUES GIOCONDI JAOUA JARDINS BARRE BART BOSCO CABIOCH CLOAREC TARTU GIONO JACQUES ROUSSEAU JAURES JULIEN LEMORDANT MERMOZ JEANNE D ARC OBERLE RACINE RICHEPIN JEMMAPES JOACHIM BELLAY JOLAIS JONQUILLES JOS PARKER JULES GOFF JULES MASSENET JULES JULES VERNE KARECK HIR KASTEL KASTELL DOUN KERADEN KERALLE KERAMBAIL KERAMBARBER KERAMBRAS KERAMERRIEN KERANDEN KERANDOUIN KERANDRAON KERANDREON KERITY KERANGUEN KERANGUYON VIHAN KERANGWEN KERANNA KERANROCH KERANROUX KERARMOIGN KERAUDREN KERAVEEC KERAVEL KERAVEN VRAS KERBELEYEN KERBRAT KERBRIANT KERCO KERCONAN BIHAN KERDIES KERDREVOR KEREOL KER EOL KER EOL TREZ HIR KEREON KEREVEN KERFRAM KERFREQUANT KERGARADEC KERGLEDIG KERGLOS KERGOALABRE 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MENEZ QUENEACH MENEZ QUENECADARE MENEZ QUILLIEN MENEZ RENGLEO MENEZ REUN MENEZ RHEUN MENEZ RIOU MENEZ RIOU BIHAN MENEZ RIOU BRAS MENEZ ROCH CRENN MENEZ ROCH MEUR MENEZ ROCHTOURMENT MENEZ ROHOU MENEZ ROSPOAS MENEZ ROST MENEZ ROTULEN MENEZ ROUE MONTAGNE ROI MENEZ ROUS MENEZ ROUX MENEZ ROUZ MENEZ ROZ BIHAN MENEZ ROZ COZ MENEZ ROZ YAN MENEZ RUGUEL MENEZ RUIEN MENEZ MENEZ SALUDEN MENEZ SIZUN MENEZ STANG MENEZ STEUD MENEZ TREBREVAN MENEZ TREVIGODOU MENEZ TROMILLOU MENEZ TROPIC MENEZ TY AR GALL MENEZ TY COZ MENEZ VEIL AVEL MENEZVEN SEACH MENEZ VERIENEC MENEZ VERIENNEC MENEZ VIAN MENEZ VRAS MENEZ VRIZED MENEZ VUR MENEZ YANN MENEZ YEUN MENFAOUTET MENFILOUS MENFRANCAN MENGAOULOU MEN GLAZ MENGLAZOU MENGLEUFF MENGLEUX MENGLEUZ MENGLEUZ AR MENGUEN MENGUY MENHARS MENHIR MENHIR KERVIGOT MENIC MENLAOUER MENMEUR MENN BREACH MENNIC AN TRI PERSON MENOC MENOIGNON MENPEVAL MENSAVET MENTAFFRET MENTAVA MENTOUL MENUCH MEN ZAO MEOT MEOUET MEOUET VIAN MEOUET VRAS MEOUT MEOUT VRAS MERDI MERDIEZ MERDY MERDY BIAN MERDY BURUNOU MERDY VIHAN MERICLEN MERIENEN MEROS MERRIEN MERROS HUELLA MERROS IZELLA MERROURY MESALORET MESANGE 130 GORREQUER MESANGROAS MESARC HANT MES AR C HOZ TY MES AR CREACH MESARGAS MESARGROAS MESARGROAS TY NEVEZ MESARPONT MESAVEN BRAS MESBALANEC MESBER MESBER STREJOU MESBIAN MESBRIAND MESCALET MESCAM MESCAM HUELLA MESCARADEC MESCLEGUER MESCLEO MESCOAT MESCODEN MESCODEN ELOI MESCODENT MESCOLLE MESCOSQUER MESCOUECHOU MESCOUEL MESCOUES MESCOUEZ MESCOUEZEL MESCOUEZEL VRAZ MESCOUIN MESCOZENEC MESCRAN MESCRENEC MESCUFURUST MESCULAN MESCURUNEC MESCURUNEC PENZE MESDALAE MESDON MESDOUN MESDOUN BRAS MESDOUN VIAN MESDOUREC MESDREZOC MESFALL MESGALL MESGLOAGUEN MESGOUECHOU MESGOUEZ MESGOUEZ BIAN MESGOUIN MESGRALL MESGUEN MESGUEN LILIA MESHIR MESHUEL MESIVEN MESLANN MESLE MESLEDANNOU MESLEIN MESLIA MESMANIC MESMAY MESMEAN MESMEILLAN MESMELLEC MESMENEZ MESMENIOU MESMERC HOU MESMERCHOU MESMEULEUGAN MESMEUR MESMEUR HUELLA MESMEUR IZELLA MESMILLOUR MESNARS MESNAVALAN MESNEAN MESNESCOP MESNOD 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MINE MINE BRENELIO MINE DERO MINE GLAZ MINE GROAS NE MINE GUERVEUR MINE PORS AR MANER MINE RULAN MINE DAVID MINE MINE SEACH MINE TREOUZAL MINE YEUN MINEZ MINEZ BRENELIO MINEZ GWE FAO MINEZ KERGUEN MINEZ KERSCLIPPON MINEZ MEUR MINEZ POAN MINEZ MINEZ TREOUZAL MINGAM MINGAN HUELLA TRAON HIR MINGANT MINIHY MINIOC MINIOU MINIOU BRAS MINIOU ROUZ MINODIC MINOU MIN PEN AR ROZ MINTERNOC MINUELLO MINVEN MINVEN KEREST MIRINIT MI ROUTE MISECLUN MISELCUN MISSIOUARN MLINN NEVEZ MOABREN MOC GOUEZ KERABUS MOELLIEN MOENNEC MOGERAN IZELLA MOGUEL BRAS MOGUER MOGUERAN MOGUERAN CREAC AN AVEL MOGUERAN HUELLA MOGUERAN IZELLA MOGUERANT MOGUERGREAN MOGUER HALVEZ MOGUERIC MOGUERIEC MOGUERIEC AR MANER MOGUERIEC CHANEL MOGUERIEC KERAVAL MOGUERIEC POUL AR STREAT MOGUERIEC POULMORVAN MOGUERIGOU MOGUEROU MOITIE MOLETTE MONCOUAR MON DESIR MONDRAGON MONGARDI MONGARIOU MONIVEN MONIVEN IZELLA MON REPOS KERBREZILLIC MONTAGNE MONT NEVET MONTORET MONTORET VIHAN MONTOURGARD MONTSERRAT MORBIC MORBOULLOU MORDUC MORGANT MORGAT 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BRONOLO CABORNES CASTELLIEN CASTELLIN CHEF CHOUENNER COAT CAER COAT CANTON COATSQUIRIOU DOULVEN FONTEYOU GLUJEAU GOASMOAL GUENGAT GUERVENNEC GUINIGOU KERANGOC KERANROCH KERBIRIOU KERDU KEREFFREN KERFRES KERGAERIC KERGONAN KERGONVAN KERGUELEN KERHUON KERLEVENE KERLOAS KERLOSTREC KERMARGUIN KERMEUR KERMORVAN KERNAULT KERNEVEZ KERNONGAL KEROLVEN KEROUALLON KERROCH KERSTRAD KERVELLA KERVERNIOU KERVOUSTER L ABBE BOISSIERE BOULAIE CHAUSSEE HAIE MER LESTREVET MOTHE MOTTE DELANGUIONAS LANHOULOU LANNIDY LANNIEC PALUE ROCHE TOUR LAUNAY VILLENEUVE LESCUZ LESVOYEN LEZAFF LEZERAZIEN L HERMITAGE LIVINOT LOSSULIEN LOSTEVIR D ENEZ D EN HAUT PENLANN PENQUELEN AR MARC HAT PORSMOGUER QUINQUIS QUISTINIC ROGNAN ROUDOUMEUR ROZVEUR ALOUARN CLOUD MOULIN PRES TREMADUR TRESSEOL TREVIEN TROAGUILLY TROANEZ TROYON TY VARLEN DEUFFIC DONAN DONANT DOURGUEN DREZEC BUIS BEG AEL DUC CAM CANAL CHANTRE CHAT CRANN CRECQ DUC FAOU FOLGOET GUERN HILGUY HILGUY TY CHASS JET JUCH LAY LAZ PENHOAT PLESSIX MOULIN PRE PRIEURE QUINQUIS ROI ROY ROZ ROZOS RUFFA SEQUER STALE STANG TEMPLE VARCH ENFER ETANG FOLGOET FONTAINE BLANCHE FOURDEN GARDES GARDEZ GARO GAUCHE GILLETTA GOASSELEN GOEL GOFF GOUENNOU GOUEZ GOUZIOU PALUD GUILER HAIE HASCOET HAUT HAUT HELOU HENRY HENVEZ HILBARS HILVERN JET JEUNE JOANET JOANNET KASTELL BOC H KERALLE KERAMBELLEC KERANFLEC H KERANGOC KERANGOMAR KERANY KERBEOC H KERBERN KERBIZIEN KERDREIN KERDUNIC KERELLEC KERELLOU KERENIEL KEREON KEREUZEN KERFEUTEUNIOU KERGAER KERGANAPE KERGARAOC KERGARAOC NORD KERGOAT KERGOFF KERGONADEACH KERGONIOU KERGONVAN KERGOULOUARN KERGUESTEN KERGUNUS KERGUS KERHALS KERHAO PENHARN KERHAS KERHINE KERIAR KERIBER KERIBERT KERINGARD KERIVARCH KERLEAU KERLEO KERLIGONAN KERLOCH KERNABAT KERNAVENO KERNO KEROCUN KEROMNES KEROUE KERRIEGARS KERROT KERROUANT KERSABIEC KERSANDY KERSCOULET KERSTRAD KERSTRAT KERVAO KERVASTAL KERVEN KERVIZIN KERZUOT KOZ KASTEL L ABBE LABBE LANNIEC LANNOGAT LANNOUEDIC LANORGARD LANSOLOT LANVERN LAUNAY LESCOAT LESCOP LESPOUL LIDIEN MANACH MARANT MARCHE MAREGUEZ MER MEUR MOALHIC MOELLIEN MOGUEL MOGUEROU MOTTE NARCH NEUF NEUF QUILLIEN NEUF MATHIEU NEZET NOHENNEC PAPIER PARLAVANT PELL PEN AR GUER PENARUN PEN AR VERN PEN ENEZ PENFROUT PENGUERN PENHOAT PENLAN PENMARC H PENNAYEUN PERAN PLOMB PLUFERN POAS PONCHOU MOULIN PONTALENNEC CARADEC COUALCH CROACH GARVAN HERE LEY MORVAN OURS QUEAU RHEUN PORS MILIN VALLY PORSMOGUER PORS MORO POUL BLEIS POULFANC PRE PROVOST PRY QUELENNEC QUENIC BEUZEC QUENICTUEC QUESTEL QUIDAN QUILLIEN QUILLIOU QUINIOU QUISTILLIC RABAT RAGOT RICHET RIVE RIVOALEN ROCHE ROGUAN RONVARCH ROSQUIJEAN ROSQUIJEAU ROSSIOU ROSTIC ROUAL ROUDOU GLAZ ROUDOUGOALEN ROUDOUS ROUX ROY ROZOS CLOUD CLOUE ELOI MOULIN NORGARD OUARNEAU SINAN SOUL SQUIRRIOU STANG STANG ZU SUGUENSOU MOULINS VERTS TALARN PENFELD TANNE TARIEC TERRE TOULGOAT TRAON TRAOUNEVEZEC TREANNA TREAS TREDIEC TREGALET TREGONGUEN TREGUIER TREOURON TREUSCOAT TREVAN TREVILIS TROGOFF TROMELIN TY MEN TY VARLEN VERGRAON VERN VERT VEYER VIEUX MOUSTANGUERN MOUSTARGOLL MOUST AR GUERN MOUSTER MOUSTERLANN MOUSTERLIN 13 METAIRIE MOUSTERLIN 17 GARN GLAZ MOUSTERLIN 19 LEN C HANKED MOUSTERLIN 27 KARN STER MOUSTERLIN 4 HENT KROAS KERNEING MOUSTERLIN 9 METAIRIE MOUSTERLIN HENT CLEUT ROUZ MOUSTERLIN KARN MENEZ KERBADER MOUSTEROU MOUSTOIR MOUSTOIR MENEC MOUSTOIR CADO MOUSTOIR VIHAN MOUSTOULGOAT MOUSTREN MOUSTRENN MUNUGUIC MUNUT MUR MUR HUELLA MURIOU MUR MESGOUEZ MUR NEUF NAMOUHIC NANCH NANCLIC NANGELOU NAONT NAOT HIR NAOUGOAD NAOUNT NAOUT NARC GWEN NARGOAT NARRET NARTOUS NATELLIOU NATOR NAVALENNOU NAVALHARS NAVALIC NAVAN NAVANT NAVARO KERASCOET NEC HOAT NEDER NEHELEN NEILLOU NEISCAOUEN NEIS VRAN NEIZ VRAN NELEHEN NELLACH NELOHAN NEMBLACH NENCHES NENEZ NENEZ NEVEZ NENEZ TREFLADUS NENGOAT NENVEZ NEOLENNOU NEONEC NERGOAT NERGOZ NERIZELEC NERODINE NESLARCH HUELLA NESLARCH IZELLA NESTAVEL BIAN NESTAVEL BRAS NESTOU NEUVE NEUZIOU NEVARS NEVARS BIHAN NEVARS HUELLA NEVARS IZELLA NEVEIC NEVEIT NEVEN NEVEZ CREACH NEZ AR C HANT NEZARD NEZERDY NEZERS NEZERT NIADEC QUILLOUARN NIGOLOU NILIZIC NILVIT NIOU NIOU HUELLA NIOU IZELLA NIQUELVEZ NIVEN NIVER NIVERN NIVERNIC NIVERROT NIVIEZ NIVINEN NIVIRIT BRAS NIZERDY NIZON CROISSANT ANDRE NIZON KERAMBEUX NIZON KERANGALL NIZON KERANGOFF NIZON KERCAUDAN KERGORNET NIZON KERFUR NIZON KERGANET NIZON KERGAZUEL NIZON KERGOADIC NIZON KERGOADIC VRAS NIZON KERHUIL NIZON KERLARET NIZON KERLARRET NIZON KERMANN NIZON KERMOAL NIZON KERNONEN NIZON LANDEDEO NIZON LUZUEN NIZON ANDRE NIZON TREMALO NIZON VILLENEUVE NODET NODEVEN NOGUELLOU NOHENNEC NOISERAIE NONAOU NONEN NONNAT HUELLA NONNAT IZELLA NONNOT NORMANDIE NORMANDY NORVENNIC NORVEZ NOTERIC NOTERIOU NOUARNEC NOUSTE POULFANC NOUVELLE COTE NOYELLOU NUOC ODE AR GLOUET ODEBLEIS ODE BLEIZ ODEGALET ODEGAR ODE LOUC H ODEVEN ODEVEUR ODE VEUR ODE VRAZ ORATOIRE OREE OROBANCHES OUENNEC PAGOTAIE PALAE PALAIS PALUD PALUD AN HIR PALUD BIAN PALUD BRAS PALUD CREMUNY PALUD CRUGOU PALUD CRUMUNI PALUD DOURDUFF PALUDEN PALUDEN BEL ABRI PALUD GORREBEUZEC PALUD GOURINET PALUD GRONDVAL PALUD KEREMMA PALUD KERGUELLEC PALUD KERGURUN PALUD KERISTENVET PALUD KERISTEVET PALUD PELLAN PALUD PENLAN PALUD TREBANEC PALUD TREBANNEC PALUE PALUE KERGUELLEC PALUE KERSUGAL PANT PAOTR TREOURE PAOU PAPEREZ PAPETERIE MAUDIT KERISOLE PAPIOLET PARADEN PARADEN TY POAS PARADIS PARALUCHEN PAR AR VEROURI PARC AN AGNIEL PARC AN ALE PARC AN AOD BRAZ KERLIOU PARC AN AOT PARC AN AUTROU PARC AN AVEL QUELVEZ PARC AN BROC PARC AN DOSSEN PARC AN HIVER PARC AN ILLIS PARC AN IVERN PARC AN NOAN PARC AN OACH PARC AN OGUEN PARC AN PICARD PARC AN TRAON PARC AN ZANT PARC AR BARENNOU PARC AR BARNOU PARC AR BARRES PARC AR BASTARD PARC AR BELLEC PARC AR BEYER MENEZ NOAS PARC AR BOURG PARC AR BREACH PARC AR BREUR PARC AR BROC PARC AR CHAEL PARC AR CHAPEL PARC AR C HOAT PARC AR CHOAT PARC AR FAVEN PARC AR FEUNTEUN PARC AR GLOAN PARC AR GO PARC AR GROAS PARC AR HAD PARC AR HEZEC PARC AR HOAT PARC AR JOL PARC AR LAND PARC AR LANDE PARC AR LANN PARC AR MEIN GUEN PARC AR MENEZ PARC AR MENGUEN PARC AR MENHIR PARC AR MILINER PARC AR PARQUER PARC AR PONTIC PARC AR PORS PARC AR PORS KERNEAVAL PARC AR PRAT PARC AR RHEUN TREGONDERN PARC AR ROUE PARC AR STANG PARC AR TRAON LEZABANNEC PARC AR VALIS PARC AR VALLY PARC AR VEIL PARC AR VEROURI PARC AR VUR PARC AR YAR PARC AU DUC PARC VEROURI PARC BALAN PARC BANALOU PARC BEAUSEJOUR PARC BIHAN PARC BLEUD PARC BRAS PARC COAT PARC COLIN PARC COSQUER PARC COZ PARC CREIS PARC D ARVOR PARC DAVID PARC EXPOSITIONS LANGOLVAS PARC FANQUIC PARC FEUNTEUN PARC FOEN PARC FOENNEC PARC FRIC PARC FROST PARCFUR PARC GALLO PARC GUEOT KERNAVENO PARC GWEN PARC HAUT PARC HIR PARC HOAT BEO PARC HUELLA PARC HUELTREC PARC ILIS PARC IZELLA PARC JAFFRE PARC KERHAPPS PARC KERINGARD PARC KERISTIN PARC KERIZIT PARC KEROHAN PARC KERVEGUEN PARCKIGOU PARC KROAS PARC LAER PARC LAGADEC PARC MAIS BLANCHE M LANINON PARC LAND PARC LANGOLEN PARC LANN PARC LANN ROHOU PARC LEC PARC LEONNEC PARC LEUR PARC LEVENEZ PARC LOCH GUEN PARC MARC PARC MARCHE PARC MARCHE COAT BEUZ PARC MARCHE SEACH PARC MARVAIL PARC MAURICE PARC MEIL TRESSEOL PARC MELINER PARC MENEZ PARC MENEZ KERSABY PARC MESNIGOALEN PARC MINE PARC MINOR KERDAENES PARC MOROS BIHAN PARC MORVAN PARC NEVEZ PARCOAM PARC OLLIVIER PARCOSQUER PARCOU PARCOU BIHAN PARCOU BRAS PARCOU BRAZ PARCOU BRIS PARCOU GORREKEAR PARCOU JACQ PARCOU LAND PARCOU LEUHAN PARCOU MENEZ PARCOU MENGLAZ PARCOU PENHOAT SALAUN PARCOU ROYAL PARCOU SEGAL PARCOUYARD PARC PALUD TY PALUD PARC PELL KEREVEN PARC POST PARC QUESTEN PARC QUISTINIC PARC ROCH PARC ROUTE PENMARCH PARC RULAN PARC SCOUDOU PARC SEVEAN PARC STANG PARC STER PARC STER CAP COZ PARC TAL AN ILIS BOURG PARC THOMAS PARC TOUL AR BLEIS PARC TREHERN KERLEAN PARC TRI HORN PARC TY LAI PARC VEIL PARC VENARCH PARC VEROURY PARC VIAN PARC YANN PARC YDER PARC ZALE PARGAMOU PARIAL PARICHARD PARIOU PARK LEUR PARK AL LEUR PARK AN AVEL PARK AN DOUR PARK AN DREZEG PARK AN HIVER PARK AN TIEZ PARK AR BELEG PARK AR BELEG LANVISCAR PARK AR C HIVIGER PARK AR C HOAT PARK AR GOZHKER PARK AR GROAZ PARK AR GWIADER PARK AR LEUR PARK AR MENHIR PARK AR ROZ KERHARO PARK AR RUN BOURG PARK AR STANKOU PARK AR STREAT BOURG PARK AVALOU PARK BALAN PARK BRAS PARK BRAZ PARK CLOS PARK L ISLE PARK FORN PARK GOUEL Y 28 HENT KERBORC H PARK GUEN KERSTRAT PARK HENT GLAZ PARK HUELLA PARK HUELLA KERMARIA PARKING INTERMARCHE KERCHAPALAIN PARK KERCO PARK KERGREAC H PARK KREIS AR VOURC H PARK KREIZ PARK LAE PARK LANIG PERES PARK LEUR PARK LEURIOU PARK MARGOD PARK MENN MEUR PARK MERVENT PARK MEUR PARK MONTOUARC H PARK N ALLE PARK NEVEZ PARKOU PARK PEN DUICK PARK ROUZIG PARK VRAS PARLUCHEN PARLU HEN PAROU KERMAVIOU PARVIS BLAISE PASCAL PASSAGE PASSAGE AUGUSTE BRIZEUX PASSAGE BOBBY SANDS PASSAGE PASSAGE CORENTIN CELTON PASSAGE CORNOUAILLES PASSAGE KERGUELEN PASSAGE LEVEE PASSAGE POSTE PASSAGE L ARMEN PASSAGE FEUX FOLLETS PASSAGE FRENES PASSAGE LAVANDIERES PASSAGE LUTINS PASSAGE ONDINES PASSAGE SIRENES PASSAGE DOMREMY PASSAGE DOURIC COZ PASSAGE FOUR PASSAGE HENAN PASSAGE BART PASSAGE KERGUELEN PASSAGE LUCIEN PICARD PASSAGE PRAD AR ZANT PASSAGE HERLE PASSAGE SIRENES PASSAGE SURCOUF PASTOURON PAVILLON 2 COSQUER PAVILLON ALBERT LARHER PAVILLON LOCH PAYAOU PAYS FRUIT PEDEL PELEUZ PELHET PELLAE PELLAIN PELLAN PELLAN BIHAN PELLAND PELLAVON PELLAY PELLEM PELLEN PELLEOC PEMBRAT PEMP HENT PEMPHENT PEMPIC PEMPOUL PEMPRAT PEN PENAHARS PEN HOAT PENAHOAT PENALAN PEN ALAN PEN LAN PEN LAND PENALAND MEROS PENALEIN PENALEN PEN LEN PEN AL LAN PENALLAN PEN ALLAN GARO PEN AL LAN KERIZUR PEN AL LANN PEN AL LAN VIAN PENALLEN PEN ALLEN 2 HENT MENEZ BRIS PENALLEURGUER PEN ALLEUR GUER PENALLEURGUEUR PENAMENEZ PENAMPRAT PEN AN PEN AN DAIL PEN AN DALLAR PENANDAOUENT PEN AN DELCH PEN AN DOUR PENANDOUR PENANDREFF PENANDREFF BIAN PENANEAC H PEN ANEACH PENANEACH TREANNA PENANECH PEN AN ERO PENANGUER PEN AN HEDER PEN AN ILIS KERVILLIC PEN AN NATIL PEN AN NEACH PEN AN NEAC H PEN AN NEC H PEN AN PRAT PENANREST PENANROS PENANROS PHILIBERT PENANROUS PENANROZ PEN AN ROZ BODIVIT PEN AN ROZ KERGOFF PENANRUN PEN AN TEVEN PEN AN THEVEN PEN AN TRAON PENANTRAON PENANVERN PEN AN VERN PENANVEUR PENANVOAS PEN AR PEN RAS PEN AR BAREZ PEN AR BARREZ PEN AR BED PEN AR BEZ PEN AR C HA PEN AR C HARS PEN AR C HASTEL PEN AR C HEAR PEN AR CHLEUZ PEN AR C HLOZ PEN AR C HLUN PEN AR C HOAS PEN AR C HOAT PEN AR CHOAT PENARC HOAT PEN AR C HOAT AR GARS PEN AR C HOAT AR GORE PEN AR C HOAT BIAN PEN AR CHRA PEN AR C HRA PEN AR C HRANN PEN AR CHRASSEN PEN AR C HREAC H PEN AR CLHEUS PEN AR COAT PEN AR CRASSEN PEN AR CREACH PEN AR CREAC H PENARCREACH PEN AR CREAC HENT KERGONOEN PEN AR CREAC LAMBER PEN AR CREAC VRAS PENARCREACH COATAUDON PEN AR CREARC H PEN AR CREC H PEN AR CROAS PEN AR CROISSANT KERSCO PEN AREUN PENAREUN PEN REUN PEN AR FAVOT PEN AR FEUNTEUN PEN AR FOREST PEN AR GARRONT PEN AR GOARIMIC PEN AR GORRET PEN AR GOUER PEN AR GROAS PEN AR GROAS FREDE PEN AR GROAS MAILLE PEN AR GUEAR PENARGUEAR PEN AR GUEL PEN AR GUEN PEN AR GUER PENARGUER PEN AR HADEN PEN AR HARDEN PEN AR HARS PEN AR HELF PEN AR HEUN PEN AR HISTILLY PEN AR HLEUZ PEN AR HOAD PEN AR HOAS PEN AR HOAT PEN AR HOAT BIAN PEN AR HOAT SALIOU PEN AR HOAZ PEN AR HOEL PENARLAN PEN AR LAND PEN AR LEN PEN AR LENN PEN AR LEORZOU PENARLIORZOU PEN AR LIORZOU PEN AR MEAS PEN AR MENEZ PENARMENEZ PEN AR MENEZ BESCOND PENAROS PENAROZ PENAROZ BOHAST PENAROZ KERANGUEVEN PENAROZ LEZOUALC H PEN AR PALUD PEN AR PAVE PEN AR PORS PEN AR POUL PEN AR POUL TREMET PEN AR POUNT PEN AR PRAD PEN AR PRAJOU PEN AR PRAT PENARPRAT PEN AR PUNS PEN AR QUINQUIS PEN AR RAZ PEN AR REUN PEN AR RHUN PEN AR ROCH PEN AR ROS PEN AR ROUDOUS PEN AR ROUZ PEN AR ROZ PENARROZ PEN AR ROZ VRAS PEN AR RUGEL PEN AR RUGUEL PEN AR RUN PEN AR STANG PENARSTANG PEN AR STEIR PEN AR STER PEN AR STREAT PEN AR STREJOU PEN AR STREJOU MICHEL PENARSUIL PENARUGUEL PEN AR VALANEC PEN AR VALLY PEN AR VALY PENARVALY PEN AR VERN PENARVERN PEN AR VEUR PEN AR VILARS PEN AR VOAS PEN AR VOAZ PEN AR VOEZ PEN AR VOGAR PEN AR VOUEZ PEN AR VOUILLEN PEN AR VUR PEN AR YEUN PEN AR YUN PEN AVEL PENAVERN PEN VERN PENAVERN TURLUER PEN VOAS PEN VOUEZ PENBANAL PENBANAL NEVEZ PEN BATZ PENBIS PEN BLEIS KERVEVENN PEN BODENNEC PENBRAN PENBROES PEN BUELLE PEN CARN NIVERROT PENCHAOU PENC HER PEN CHOAT CRUTIUS PENCLEU PENCLEUZ PENCLUZIOU PEN COAT CESSOU PENCOATLOCH PENCRAN PENCREACH PENCREAC H PENDANVAT PENDON PENDOULIC PENDOULLIC PENDREAU PENDREFF 23 HENT PENNKER BLOAZ PENDREFF PENDREFF CREIS PENDREFF IZELLA PENDREFF VIAN PENDREIGN PENDREO PENDRUC GWAREMM DISKARN PENDRUC KERLAERON PEN DRUC LOCH PENDRUC POULDOHAN PENEMPRAT PEN ENEZ PEN EN NEARC H PENESQUEN BRAS PENESQUEN VIAN PENETTY PENFAO PENFAO HUELLA PENFELD PENFELD BRAS PEN FEREL PENFEUNTEUN PEN FEUNTEUN PENFEUNTEUNIOU PENFEUNTEUN VIAN PENFEUNTEUN VIHAN PENFEUNTEUN VRAS PENFO PENFOENNEC PENFOENNEC HUELLA PENFOENNEC IZELLA PENFOND PENFOND BIHAN PENFOND VRAS PENFONT PENFOUL PEN FOUL PENFRAD AN TRAON PENFRAD AN TREC H PENFRAJOU PENFRAP PENFRAT PENFRAT COZ PENFRAT HUELLA PENFRAT NEVEZ PENFRAT VIAN PENFRAT VRAS PENFROUT PENGOAZIOU PENGOAZIOUT PENGORBEL PENGOURVEN PENGOYEN PENGOYEN VIAN PENGOYEN VIHAN PENGUEL PENGUEREC PENGUERN PENGUILLI VIAN PENGUILLI VRAS PENGUILLY PENGUILY PENHARN PENHARO PENHAROS PENHARS PENHAST PENHAUBAN PEN HAVRE PENHEP PENHER PENHER HUEL PENHER IZEL PENHERO PENHIEL PEN HIR PENHLEUNIOU PENHOAD PEN HOAD PENHOADEN PENHOADEN IZELLA PENHOADIC PENHOAT PEN HOAT PENHOAT BIHAN PENHOAT BRAS PENHOAT BROEZ PENHOAT CADOL PENHOATHUON PENHOAT JONCOUR PENHOAT LANN PENHOAT MAUGUEN PENHOAT MOUSTOIR PENHOAT NEVEZ PENHOAT POSTEC PENHOAT PUNZ PENHOAT ROSMADEC PENHOAT ROUSSICA PENHOAT THOMAS PENHOAT TY NAOU PENHOAT VIAN PENHOAT VIHAN PENHOET PENHORS PENHORS 3 HENT AN AOD PENHORS AN TRAON PENHORS KERSCAO PENHORS KERVET PENHUEL PEN HUELLA GUER PENHUIL PENHUIL BIAN PENHUIL BRAS PENINGUIN PENISQUIN PENISTIN PENITY PENITY RAOUL PENITY LAURENT PENJAMET PEN KARVAN PEN KEAR PENKEAR PENKER PENKER BIAN PENKER BLOAS VIAN PENKER BOURGEL PENKER BRAZ PENKER CHOLL PENKER DRENNEC PENKER KERAUTRET PENKER KERBAUL PENKER KERDAENES PENKER KERLEC PENKER KERYENNEC PENKERLEN PEN KERLEO PENKER LIJOUR PENKER LOIS PENKER LONCHEG PENKERNAVELLOU PENKER NEVEZ PEN KER ELOI PENKER TRAON PENLAN PENLAND HUELLA PENLAN IZELLA PENLANN PEN LANN KAREK KREIS BEG AR LAND PENLAN VIAN PENLAN VIHAN PENLAN VRAZ PEN LEN VIAN PENLOCH TREVIGNON PENLOUCH PEN LOURCH PEN MAO PENMARCH PENMARC H PEN MEN PENMENEZ PEN MENEZ PEN MENEZ KAOUSENN PEN MEO PENMERGUES PENMESHIR PENMEZ PENMEZEN PENN PENNAGOUER PENNAGUER PENNAHEO PENNAHOAT PENNAJEUN PENNALAN PENNALAND PENNALAND CLAIR PENNALE PENNALEN PENNALLAN PENN AL LANN PENN AN DREFF PENN AN DREFF BIAN PENN AN DREFF STANC PENNANEACH PENNANEAC H PENNANEACH CUZEOL PENNANEACH ROSEGAT PENNANEACH SAO EOL PENNANEACH SAVEOL PENNANEACH TANGUY PENNANEARC H PENNANEC H PENNANGOAT PENNANGUER PENNANGUER LOCHRIST PENNANHAYE PENN AN NEAC H PENNANPRAT PENNANROS PENNANROZ PENNANRUN PENNANTERIEN PENNANVERN PENNANVOAS PENN AN VOAZ PENNAPRAT PENNAPRAT LORETTE PENNAPRAT NEVET PENNAPRAT NEVEZ PENN AR PENNARA PENN AR BARREZ PENNARC HOAD PENN AR C HOAT PENN AR 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