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### **4. Experiments**
In this section we evaluate our methods with pixel-wise
depth regression and semantic segmentation. An analysis
of these results is given in the following section. To show
the robustness of our learned loss attenuation – a side-effect
of modeling uncertainty – we present results on an array o... | {
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as aleatoric uncertainty using our developments presented
in §3.
**4.1. Semantic Segmentation**
To demonstrate our method for semantic segmentation, we
use two datasets, CamVid (Brostow et al., 2009) and NYU
v2 (Silberman et al., 2012).
Firstly, CamVid is a road scene understanding dataset with
367 training image... | {
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both uncertainties improves performance even further. This
shows that for this application it is more important to model
aleatoric uncertainty, suggesting that epistemic uncertainty
can be mostly explained away in this large data setting.
Secondly, NYUv2 (Silberman et al., 2012) is a challenging indoor segmentation d... | {
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"Header 3": "**4. Experiments**",
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![](/content/images/1703.0... | {
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"Header 2": "**What Uncertainties Do We Need in Bayesian Deep Learning** **for Computer Vision?**",
"Header 3": "**4. Experiments**",
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|---|---|---|---|---|---|---|
*Table 4.* Comparison to previous approaches on depth regression
dataset NYUv2 Depth. Modeling the combination of uncertainties improves accuracy.
hand, these qualitative results show that epistemic uncertainty captures difficulties due to lack of data. For example,
we observe larger u... | {
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"Header 3": "**4. Experiments**",
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### **5. Analysis: What Do Aleatoric and** **Epistemic Uncertainties Capture?**
In §4 we showed that modeling aleatoric and epistemic uncertainties improves prediction performance, with the combination performing even better. In this section we wish
to study the effectiveness of modeling aleatoric and epistemic uncer... | {
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-----
**What Uncertainties Do We Need in Ba** **y** **esian Dee** **p** **Learnin** **g** **for Com** **p** **uter Vision?**
|Train dataset|Test dataset|RMS|Aleatoric variance|Epistemic variance|
|---|---|---|---|---|
|Make3D / 4 Make3D / 2 Make3D|Make3D Make3D Make3D|5.76 4.62 3.87|0.506 0.521 0.485|7.73 4.38 2.78... | {
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relatively constant and cannot be explained away with more
data. Testing the models with a different test set (bottom
two lines) shows that epistemic uncertainty increases con
siderably on those test points which lie far from the training
sets.
These results reinforce the case that epistemic uncertainty
can be ex... | {
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"Header 3": "**5. Analysis: What Do Aleatoric and** **Epistemic Uncertainties Capture?**",
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### **6. Conclusions**
We presented a novel Bayesian deep learning framework
to learn a mapping to aleatoric uncertainty from the input
data, which is composed on top of epistemic uncertainty
models. We derived our framework for both regression and
classification applications. We showed that it is important
to model ... | {
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"categories": [
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"Header 3": "**6. Conclusions**",
"Header 4": null
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### **References**
Abadi, Mart´ın, Barham, Paul, Chen, Jianmin, Chen,
Zhifeng, Davis, Andy, Dean, Jeffrey, Devin, Matthieu,
Ghemawat, Sanjay, Irving, Geoffrey, Isard, Michael,
et al. Tensorflow: A system for large-scale machine
learning. In *Proceedings of the 12th USENIX Sympo-*
*sium on Operating Systems Design and... | {
"id": "1703.04977",
"title": "What Uncertainties Do We Need in Bayesian Deep Learning for Computer\n Vision?",
"categories": [
"cs.CV"
]
} | {
"Header 1": null,
"Header 2": "**What Uncertainties Do We Need in Bayesian Deep Learning** **for Computer Vision?**",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
Graves, Alex. Practical variational inference for neural networks. In *Advances in Neural Information Processing*
*Systems*, pp. 2348–2356, 2011.
Guynn, Jessica. Google photos labeled black people ’gorillas’. *USA Today*, 2015.
He, Kaiming, Zhang, Xiangyu, Ren, Shaoqing, and Sun,
Jian. Deep residual learning for im... | {
"id": "1703.04977",
"title": "What Uncertainties Do We Need in Bayesian Deep Learning for Computer\n Vision?",
"categories": [
"cs.CV"
]
} | {
"Header 1": null,
"Header 2": "**What Uncertainties Do We Need in Bayesian Deep Learning** **for Computer Vision?**",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
*sion and Pattern Recognition*, pp. 3168–3175, 2016.
Ladicky, Lubor, Shi, Jianbo, and Pollefeys, Marc. Pulling
things out of perspective. In *Proceedings of the IEEE*
*Conference on Computer Vision and Pattern Recogni-*
*tion*, pp. 89–96, 2014.
Laina, Iro, Rupprecht, Christian, Belagiannis, Vasileios,
Tombari, Fede... | {
"id": "1703.04977",
"title": "What Uncertainties Do We Need in Bayesian Deep Learning for Computer\n Vision?",
"categories": [
"cs.CV"
]
} | {
"Header 1": null,
"Header 2": "**What Uncertainties Do We Need in Bayesian Deep Learning** **for Computer Vision?**",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
*telligence*, 2016.
Silberman, Nathan, Hoiem, Derek, Kohli, Pushmeet, and
Fergus, Rob. Indoor segmentation and support inference
from rgbd images. In *European Conference on Com-*
*puter Vision*, pp. 746–760. Springer, 2012.
Yu, Fisher and Koltun, Vladlen. Multi-scale context
aggregation by dilated convolutions. *a... | {
"id": "1703.04977",
"title": "What Uncertainties Do We Need in Bayesian Deep Learning for Computer\n Vision?",
"categories": [
"cs.CV"
]
} | {
"Header 1": null,
"Header 2": "**What Uncertainties Do We Need in Bayesian Deep Learning** **for Computer Vision?**",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
Under review as a conference p a p er at ICLR 2017 | {
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## N EURAL A RCHITECTURE S EARCH WITH R EINFORCEMENT L EARNING
**Barret Zoph, Quoc V. Le** *[∗]*
Google Brain
*{* barretzoph,qvl *}* @google.com | {
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#### A BSTRACT
Neural networks are powerful and flexible models that work well for many difficult learning tasks in image, speech and natural language understanding. Despite
their success, neural networks are still hard to design. In this paper, we use a recurrent network to generate the model descriptions of neural ... | {
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#### 1 I NTRODUCTION
The last few years have seen much success of deep neural networks in many challenging applications, such as speech recognition (Hinton et al., 2012), image recognition (LeCun et al., 1998;
Krizhevsky et al., 2012) and machine translation (Sutskever et al., 2014; Bahdanau et al., 2015; Wu
et al., ... | {
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current best model. On language modeling with Penn Treebank, Neural Architecture Search can
design a novel recurrent cell that is also better than previous RNN and LSTM architectures. The cell
that our model found achieves a test set perplexity of 62.4 on the Penn Treebank dataset, which is
3.6 perplexity better than t... | {
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#### 2 R ELATED W ORK
Hyperparameter optimization is an important research topic in machine learning, and is widely used
in practice (Bergstra et al., 2011; Bergstra & Bengio, 2012; Snoek et al., 2012; 2015). Despite their
success, these methods are still limited in that they only search models from a fixed-length sp... | {
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Also related to our work is the idea of learning to learn or meta-learning (Thrun & Pratt, 2012), a
general framework of using information learned in one task to improve a future task. More closely
related is the idea of using a neural network to learn the gradient descent updates for another network (Andrychowicz et a... | {
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#### 3 M ETHODS
In the following section, we will first describe a simple method of using a recurrent network to
generate convolutional architectures. We will show how the recurrent network can be trained with
a policy gradient method to maximize the expected accuracy of the sampled architectures. We will
present sev... | {
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3.2 T RAINING WITH REINFORCE
The list of tokens that the controller predicts can be viewed as a list of actions *a* 1: *T* to design an
architecture for a child network. At convergence, this child network will achieve an accuracy *R* on
a held-out dataset. We can use this accuracy *R* as the reward signal and use rei... | {
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asynchronous parameter updates in order to speed up the learning process of the controller (Dean
et al., 2012). We use a parameter-server scheme where we have a parameter server of *S* shards, that
store the shared parameters for *K* controller replicas. Each controller replica samples *m* different
child architectures... | {
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where *h* *j* represents the hiddenstate of the controller at anchor point for the *j* -th layer, where *j*
ranges from 0 to *N −* 1. We then sample from these sigmoids to decide what previous layers to be
4
-----
Under review as a conference p a p er at ICLR 2017
used as inputs to the current layer. The matric... | {
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In this section, we will modify the above method to generate recurrent cells. At every time step *t*,
the controller needs to find a functional form for *h* *t* that takes *x* *t* and *h* *t−* 1 as inputs. The simplest
way is to have *h* *t* = tanh( *W* 1 *∗x* *t* + *W* 2 *∗h* *t−* 1 ), which is the formulation of a ba... | {
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Right: the computation graph of the recurrent cell constructed from example predictions of the
controller.
tion method and an activation function for each tree index. After that it needs to predict the last 2
blocks that specify how to connect *c* *t* and *c* *t−* 1 to temporary variables inside the tree. Specificall... | {
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#### 4 E XPERIMENTS AND R ESULTS
We apply our method to an image classification task with CIFAR-10 and a language modeling task
with Penn Treebank, two of the most benchmarked datasets in deep learning. On CIFAR-10, our
goal is to find a good convolutional architecture whereas on Penn Treebank our goal is to find a g... | {
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800 GPUs concurrently at any time.
Once the controller RNN samples an architecture, a child model is constructed and trained for 50
epochs. The reward used for updating the controller is the maximum validation accuracy of the last
5 epochs cubed. The validation set has 5,000 examples randomly sampled from the trainin... | {
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|Wide ResNet (Zagoruyko & Komodakis, 2016)|16 11.0M 28 36.5M|4.81 4.17|
|---|---|---|
|Wide ResNet (Zagoruyko & Komodakis, 2016)|16 11.0M 28 36.5M|4.81 4.17|
|---|---|---|
|ResNet (pre-activation) (He et al., 2016b)|164 1.7M 1001 10.2M|5.46 4.62|
|DenseNet (L = 40, k = 12) Huang et al. (2016a) DenseNet(L = 100, k = 1... | {
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the best human-invented architecture that achieves 3.74%. To limit the search space complexity we
have our model predict 13 layers where each layer prediction is a fully connected block of 3 layers.
Additionally, we change the number of filters our model can predict from [24, 36, 48, 64] to [6,
12, 24, 36]. Our result ... | {
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and *m* to 1, which means there are 400 networks being trained on 400 CPUs concurrently at any
time, 3) during asynchronous training we only do parameter updates to the parameter-server once
10 gradients from replicas have been accumulated.
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more than two times faster because the previous best network requires running a cell 10 times per
time step (Zilly et al., 2016).
|Model|Parameters Test Perplexity|
|---|---|
|Mikolov & Zweig (2012) - KN-5 Mikolov & Zweig (2012) - KN5 + cache Mikolov & Zweig (2012) - RNN Mikolov & Zweig (2012) - RNN-LDA Mikolov & Z... | {
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state-of-art methods are reported in Table 3. The results confirm that the cell does indeed generalize,
and is better than the LSTM cell.
|RNN Cell Type|Parameters Test Bits Per Character|
|---|---|
|Ha et al. (2016) - Layer Norm HyperLSTM Ha et al. (2016) - 2-Layer Norm HyperLSTM|4.92M 1.250 14.41M 1.219|
|---|---... | {
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#### 5 C ONCLUSION
In this paper we introduce Neural Architecture Search, an idea of using a recurrent neural network
to compose neural network architectures. By using recurrent network as the controller, our method
is flexible so that it can search variable-length architecture space. Our method has strong empirical
... | {
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#### R EFERENCES
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networks for question answering. In *NAACL*, 2016.
Marcin Andrychowicz, Misha Denil, Sergio Gomez, Matthew W Hoffman, David Pfau, Tom Schaul,
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"Header 3": null,
"Header 4": "R EFERENCES"
} | {
"chunk_type": "references"
} |
for acoustic modeling in speech recognition: The shared views of four research groups. *IEEE*
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"Header 3": null,
"Header 4": "R EFERENCES"
} | {
"chunk_type": "references"
} |
David G. Lowe. Object recognition from local scale-invariant features. In *CVPR*, 1999.
Stephen Merity, Caiming Xiong, James Bradbury, and Richard Socher. Pointer sentinel mixture
models. *arXiv preprint arXiv:1609.07843*, 2016.
Tomas Mikolov and Geoffrey Zweig. Context dependent recurrent neural network language m... | {
"id": "1611.01578",
"title": "Neural Architecture Search with Reinforcement Learning",
"categories": [
"cs.LG",
"cs.AI",
"cs.NE"
]
} | {
"Header 1": null,
"Header 2": "N EURAL A RCHITECTURE S EARCH WITH R EINFORCEMENT L EARNING",
"Header 3": null,
"Header 4": "R EFERENCES"
} | {
"chunk_type": "references"
} |
evolving large-scale neural networks. *Artificial Life*, 2009.
Phillip D. Summers. A methodology for LISP program construction from examples. *Journal of the*
*ACM*, 1977.
Ilya Sutskever, James Martens, George Dahl, and Geoffrey Hinton. On the importance of initialization and momentum in deep learning. In *ICML*, 2... | {
"id": "1611.01578",
"title": "Neural Architecture Search with Reinforcement Learning",
"categories": [
"cs.LG",
"cs.AI",
"cs.NE"
]
} | {
"Header 1": null,
"Header 2": "N EURAL A RCHITECTURE S EARCH WITH R EINFORCEMENT L EARNING",
"Header 3": null,
"Header 4": "R EFERENCES"
} | {
"chunk_type": "references"
} |
#### A A PPENDIX
Figure 7: Convolutional architecture discovered by our method, when the search space does not
have strides or pooling layers. FH is filter height, FW is filter width and N is number of filters.
14
--... | {
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"title": "Neural Architecture Search with Reinforcement Learning",
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} | {
"Header 1": null,
"Header 2": "N EURAL A RCHITECTURE S EARCH WITH R EINFORCEMENT L EARNING",
"Header 3": null,
"Header 4": "A A PPENDIX"
} | {
"chunk_type": "body"
} |
## **Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**
### Priya Goyal Piotr Doll´ar Ross Girshick Pieter Noordhuis Lukasz Wesolowski Aapo Kyrola Andrew Tulloch Yangqing Jia Kaiming He Facebook | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "Priya Goyal Piotr Doll´ar Ross Girshick Pieter Noordhuis Lukasz Wesolowski Aapo Kyrola Andrew Tulloch Yangqing Jia Kaiming He Facebook",
"Header 4": null
} | {
"chunk_type": "title"
} |
### **Abstract**
*Deep learning thrives with large neural networks and*
*large datasets.* *However, larger networks and larger*
*datasets result in longer training times that impede re-*
*search and development progress. Distributed synchronous*
*SGD offers a potential solution to this problem by dividing*
*SGD minib... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**Abstract**",
"Header 4": null
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### **1. Introduction**
Scale matters. We are in an unprecedented era in AI
research history in which the increasing data and model
scale is rapidly improving accuracy in computer vision
[22, 40, 33, 34, 35, 16], speech [17, 39], and natural language processing [7, 37]. Take the profound impact in computer vision a... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**1. Introduction**",
"Header 4": null
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to larger minibatches (see Figure 1). In particular, we
show that *with a large minibatch size of 8192, using 256*
*GPUs, we can train ResNet-50 in 1 hour while maintain-*
1
-----
*ing the same level of accuracy as the 256 minibatch base-*
*line* . While distributed synchronous SGD is now commonplace, no existing... | {
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"Header 3": "**1. Introduction**",
"Header 4": null
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Our strategy applies regardless of framework, but
achieving efficient linear scaling requires nontrivial communication algorithms. We use the recently open-sourced
*Caffe2* [1] deep learning framework and *Big Basin* GPU
servers [24], which operates efficiently using standard Ethernet networking (as opposed to speciali... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**1. Introduction**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **2. Large Minibatch SGD**
We start by reviewing the formulation of Stochastic Gradient Descent (SGD), which will be the foundation of our
discussions in the following sections. We consider supervised learning by minimizing a loss *L* ( *w* ) of the form:
1
*L* ( *w* ) = *|X|* *x* � *∈X* *l* ( *x, w* ) *.* (1) ... | {
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"Header 3": "**2. Large Minibatch SGD**",
"Header 4": null
} | {
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#### **2.1. Learning Rates for Large Minibatches**
Our goal is to use large minibatches in place of small
minibatches while *maintaining training and generalization*
*accuracy* . This is of particular interest in distributed learning, because it can allow us to scale to multiple workers [2] using simple data parallel... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**2. Large Minibatch SGD**",
"Header 4": "**2.1. Learning Rates for Large Minibatches**"
} | {
"chunk_type": "body"
} |
assume *∇l* ( *x, w* *t* ) *≈∇l* ( *x, w* *t* + *j* ) for *j < k*, then setting
ˆ
*η* = *kn* would yield ˆ *w* *t* + *k* *≈* *w* *t* + *k*, and the updates from
small and large minibatch SGD would be similar. Note that
even under this strong assumption, we emphasize that the
two updates can be similar *only* if we se... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**2. Large Minibatch SGD**",
"Header 4": "**2.1. Learning Rates for Large Minibatches**"
} | {
"chunk_type": "body"
} |
#### **2.2. Warmup**
As we discussed, for large minibatches ( *e.g* ., 8k) the linear scaling rule breaks down when the network is changing
rapidly, which commonly occurs in early stages of training. We find that this issue can be alleviated by a properly
designed *warmup* [16], namely, a strategy of using less aggre... | {
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"Header 1": null,
"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**2. Large Minibatch SGD**",
"Header 4": "**2.2. Warmup**"
} | {
"chunk_type": "body"
} |
#### **2.3. Batch Normalization with Large Minibatches**
Batch Normalization (BN) [19] computes statistics along
the minibatch dimension: this breaks the independence of
each sample’s loss, and changes in minibatch size change
the underlying definition of the loss function being optimized. In the following we will sh... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**2. Large Minibatch SGD**",
"Header 4": "**2.3. Batch Normalization with Large Minibatches**"
} | {
"chunk_type": "body"
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*j<k*
*w* ˆ *t* +1 = *w* *t* *−* *η* ˆ *k* [1] � *∇L* ( *B* *j* *, w* *t* ) *.* (7)
*j<k*
Following similar logic as in §2.1, we set ˆ *η* = *kη* and *we*
*keep the per-worker sample size n constant when we change*
*the number of workers k* .
In this work, we use *n* = 32 which has performed well
for a wide range... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**2. Large Minibatch SGD**",
"Header 4": "**2.3. Batch Normalization with Large Minibatches**"
} | {
"chunk_type": "body"
} |
### **3. Subtleties and Pitfalls of Distributed SGD**
In practice a distributed implementation has many subtleties. Many common implementation errors change the
definitions of hyper-parameters, leading to models that train
but whose error may be higher than expected, and such issues can be difficult to discover. Whil... | {
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"Header 3": "**3. Subtleties and Pitfalls of Distributed SGD**",
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For a fixed *η*, the two are equivalent. However, we note that
while *u* only depends on the gradients and is independent
of *η*, *v* is entangled with *η* . When *η* changes, to maintain
equivalence with the reference variant in (9), the update for
*v* should be: *v* *t* +1 = *m* *[η]* *[t]* *η* [+] *t* [1] *[v]* *[t]... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**3. Subtleties and Pitfalls of Distributed SGD**",
"Header 4": null
} | {
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training set during each SGD epoch, which can give better
results [3, 13]. To provide fair comparisons with baselines
that use shuffling ( *e.g* ., [16]), we ensure the samples in one
epoch done by *k* workers are from a single consistent random shuffling of the training set. To achieve this, for each
epoch we use a ra... | {
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"Header 3": "**3. Subtleties and Pitfalls of Distributed SGD**",
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} | {
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### **4. Communication**
In order to scale beyond the 8 GPUs in a single Big Basin
server [24], gradient aggregation has to span across servers
on a network. To allow for near perfect linear scaling, the
aggregation must be performed *in parallel* with backprop.
This is possible because there is no data dependency be... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**4. Communication**",
"Header 4": null
} | {
"chunk_type": "body"
} |
#### **4.1. Gradient Aggregation**
For every gradient, aggregation is done using an *allre-*
*duce* operation (similar to the MPI collective operation
*MPI Allreduce* [11]). Before allreduce starts every GPU has
its locally computed gradients and after allreduce completes
every GPU has the sum of all *k* gradients. A... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**4. Communication**",
"Header 4": "**4.1. Gradient Aggregation**"
} | {
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( *i.e* ., for small buffer sizes and/or large server counts). In
practice, we found the halving/doubling algorithm to perform much better than the ring algorithm for buffer sizes
up to a million elements (and even higher on large server
counts). On 32 servers (256 GPUs), using halving/doubling
led to a speedup of 3 *×... | {
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} | {
"Header 1": null,
"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**4. Communication**",
"Header 4": "**4.1. Gradient Aggregation**"
} | {
"chunk_type": "body"
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#### **4.2. Software**
The allreduce algorithms described are implemented in
*Gloo* [4], a library for collective communication. It supports
4 [https://github.com/facebookincubator/gloo](https://github.com/facebookincubator/gloo)
5
-----
multiple communication contexts, which means no additional synchronizati... | {
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} | {
"Header 1": null,
"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**4. Communication**",
"Header 4": "**4.2. Software**"
} | {
"chunk_type": "body"
} |
#### **4.3. Hardware**
We used Facebook’s Big Basin [24] GPU servers for
our experiments. Each server contains 8 NVIDIA Tesla
P100 GPUs that are interconnected with NVIDIA NVLink.
For local storage, each server has 3.2TB of NVMe SSDs.
For network connectivity, the servers have a Mellanox
ConnectX-4 50Gbit Ethernet ... | {
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"Header 1": null,
"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**4. Communication**",
"Header 4": "**4.3. Hardware**"
} | {
"chunk_type": "body"
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### **5. Main Results and Analysis**
Our main result is that we can train ResNet-50 [16] on
ImageNet [32] using 256 workers in one hour, while matching the accuracy of small minibatch training. Applying the
linear scaling rule along with a warmup strategy allows us to
seamlessly scale between small and large minibatc... | {
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"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**5. Main Results and Analysis**",
"Header 4": null
} | {
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#### **5.1. Experimental Settings**
The 1000-way ImageNet classification task [32] serves
as our main experimental benchmark. Models are trained
on the *[∼]* 1.28 million training images and evaluated by top1 error on the 50,000 validation images.
We use the ResNet-50 [16] variant from [12], noting that
the stride-2 ... | {
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which we found to ease optimization at the start of training.
This initialization improves all models but is particularly
helpful for large minibatch training as we will show.
6
-----
We use scale and aspect ratio data augmentation [35] as
in [12]. The network input image is a 224 *×* 224 pixel random crop from a... | {
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"Header 3": "**5. Main Results and Analysis**",
"Header 4": "**5.1. Experimental Settings**"
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#### **5.2. Optimization or Generalization Issues?**
We establish our main results on large minibatch training by exploring optimization and generalization behaviors.
We will demonstrate that with a proper warmup strategy,
large minibatch SGD can both match the *training curves* of
small minibatch SGD and also match ... | {
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close: 23.60% *±* 0.12 *vs* . 23.74% *±* 0.09, respectively.
**Training error.** Training curves are shown in Figure 2.
With no warmup (2a), the training curve for large minibatch
of *kn* = 8k is inferior to training with a small minibatch of
*kn* = 256 across all epochs. A constant warmup strategy
(2b) actually degr... | {
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using the running average (see also caption in Figure 4).
7
-----
|kn=256,|Col2|Col3|Col4|Col5|
|---|---|---|---|---|
|||= 0.1,|23.60%|0.12|
|kn= 8k,||= 3.2,|24.84%|0.37|
||||||
||||||
||||||
||||||
||||||
||||||
||||||
|100 kn=256, = 0.1, 23.60% 90 kn= 8k, = 3.2, 24.84% 80 % 70 error 60 training 50 40 30 20 0 ... | {
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"Header 4": "**5.2. Optimization or Generalization Issues?**"
} | {
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} |
||||||||||||||||||||||
||||||||||||||||||||||
||||||||||||||||||||||
||||||||||||||||||||||
||||||||||||||||||||||
||||||||||||||||||||||
|20 0 20 40 60 100|||||80 0||20 40 60 8|||0 0||20 40 60 80|||||||||
||||||||||||||||||||||
|kn=256, = 0.1, 23.60% 90 kn=16k, = 6.4, 24.79% 80 % 70 error 60 training 50 40 30 20 0 20 ... | {
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"Header 4": "**5.2. Optimization or Generalization Issues?**"
} | {
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#### **5.3. Analysis Experiments**
**Minibatch size** ***vs*** **. error.** Figure 1 (page 1) shows top1 validation error for models trained with minibatch sizes
ranging from of 64 to 65536 (64k). For all models we used
the linear scaling rule and set the reference learning rate
*kn*
as *η* = 0 *.* 1 *·* 256 [. For... | {
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0 20 40 60 80
epochs
Figure 5. **Training curves for small minibatches with different**
**learning rates** *η* **.** As expected, changing *η* results in curves that *do*
*not match* . This is in contrast to changing batch-size (and linearly
scaling *η* ), which results in curves that *do match*, *e.g* . see Figure... | {
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improved optimization and initialization methods will help
push the boundary of large minibatch training.
**ResNet-101.** Results for ResNet-101 [16] are shown in Table 2c. Training ResNet-101 with a batch-size of *kn* = 8k
9
-----
*kn* *η* to p -1 error (%)
256 0 *.* 05 23.92 *±* 0.10
256 0 *.* 10 23.60 *±... | {
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the speed-accuracy tradeoff of ResNet-101 is preferred.
**ImageNet-5k.** Observing the sharp increase in validation
error between minibatch sizes of 8k and 16k on ImageNet1k (Figure 1), a natural question is if the position of this
‘elbow’ in the error curve is a function of dataset infor
mation content. To investiga... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": null,
"Header 2": "**Accurate, Large Minibatch SGD:** **Training ImageNet in 1 Hour**",
"Header 3": "**5. Main Results and Analysis**",
"Header 4": "**5.3. Analysis Experiments**"
} | {
"chunk_type": "body"
} |
# GPUs *kn* *η ·* 1000 iterations box AP (%) mask AP (%)
1 2 2.5 1,280,000 35.7 33.6
2 4 5.0 640,000 35.7 33.7
4 8 10.0 320,000 35.7 33.5
8 16 20.0 160,000 35.6 33.6
(b) **Linear learning rate scaling applied to Mask R-CNN.** Using the single ResNet-50 model from [16] (thus no std is reported), we train Mask
... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs *kn* *η ·* 1000 iterations box AP (%) mask AP (%)",
"Header 2": null,
"Header 3": null,
"Header 4": null
} | {
"chunk_type": "body"
} |
#### **5.4. Generalization to Detection and Segmentation**
A low error rate on ImageNet is not typically an end
goal. Instead, the utility of ImageNet training lies in learn
10
-----
0.3
0.28
0.26
0.24
0.22
16
8
4
2
1
32k
16k
256 512 1k 2k... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs *kn* *η ·* 1000 iterations box AP (%) mask AP (%)",
"Header 2": null,
"Header 3": null,
"Header 4": "**5.4. Generalization to Detection and Segmentation**"
} | {
"chunk_type": "body"
} |
To test how large minibatch *pre-training* effects Mask RCNN, we take ResNet-50 models trained on ImageNet-1k
with 256 to 16k minibatches and use them to initialize Mask
R-CNN training. For each minibatch size we pre-train 5
models and then train Mask R-CNN using all 5 models on
COCO (35 models total). We report the ... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs *kn* *η ·* 1000 iterations box AP (%) mask AP (%)",
"Header 2": null,
"Header 3": null,
"Header 4": "**5.4. Generalization to Detection and Segmentation**"
} | {
"chunk_type": "body"
} |
# GPUs
Figure 8. **Distributed synchronous SGD throughput.** The small
overhead when moving from a single server with 8 GPUs to multiserver distributed training (Figure 7, blue curve) results in linear
throughput scaling that is marginally below ideal scaling ( *[∼]* 90%
efficiency). Most of the allreduce communicati... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs",
"Header 2": null,
"Header 3": null,
"Header 4": null
} | {
"chunk_type": "body"
} |
#### **5.5. Run Time**
Figure 7 shows two visualizations of the run time characteristics of our system. The blue curve is the time per
iteration as minibatch size varies from 256 to 11264 (11k).
Notably this curve is relatively flat and the time per iteration increases only 12% while scaling the minibatch size by
44 ... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs",
"Header 2": null,
"Header 3": null,
"Header 4": "**5.5. Run Time**"
} | {
"chunk_type": "body"
} |
### **References**
[1] J. Bagga, H. Morsy, and Z. Yao. Opening
designs for 6-pack and Wedge 100. [https:](https://code.facebook.com/posts/203733993317833/opening-designs-for-6-pack-and-wedge-100)
[//code.facebook.com/posts/203733993317833/](https://code.facebook.com/posts/203733993317833/opening-designs-for-6-pack-... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs",
"Header 2": null,
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
[13] M. G¨urb¨uzbalaban, A. Ozdaglar, and P. Parrilo. Why
random reshuffling beats stochastic gradient descent.
*arXiv:1510.08560*, 2015.
[14] K. He, G. Gkioxari, P. Doll´ar, and R. Girshick. Mask RCNN. *arXiv:1703.06870*, 2017.
[15] K. He, X. Zhang, S. Ren, and J. Sun. Delving deep into
rectifiers: Surpassing huma... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs",
"Header 2": null,
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
[27] J. Long, E. Shelhamer, and T. Darrell. Fully convolutional
networks for semantic segmentation. In *CVPR*, 2015.
[28] Y. Nesterov. *Introductory lectures on convex optimization: A*
*basic course* . Springer, 2004.
[29] R. Rabenseifner. Optimization of collective reduction operations. In *ICCS* . Springer, 2004.... | {
"id": "1706.02677",
"title": "Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour",
"categories": [
"cs.CV",
"cs.DC",
"cs.LG"
]
} | {
"Header 1": "GPUs",
"Header 2": null,
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
## **Character-level Convolutional Networks for Text** Classification [∗]
**Xiang Zhang** **Junbo Zhao** **Yann LeCun**
Courant Institute of Mathematical Sciences, New York University
719 Broadway, 12th Floor, New York, NY 10003
*{* xiang, junbo.zhao, yann *}* @cs.nyu.edu | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": null,
"Header 4": null
} | {
"chunk_type": "title"
} |
### **Abstract**
This article offers an empirical exploration on the use of character-level convolutional networks (ConvNets) for text classification. We constructed several largescale datasets to show that character-level convolutional networks could achieve
state-of-the-art or competitive results. Comparisons are o... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
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} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**Abstract**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **1 Introduction**
Text classification is a classic topic for natural language processing, in which one needs to assign
predefined categories to free-text documents. The range of text classification research goes from
designing the best features to choosing the best possible machine learning classifiers. To date,... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**1 Introduction**",
"Header 4": null
} | {
"chunk_type": "body"
} |
This article is the first to apply ConvNets only on characters. We show that when trained on largescale datasets, deep ConvNets do not require the knowledge of words, in addition to the conclusion
*∗* An early version of this work entitled “Text Understanding from Scratch” was posted in Feb 2015 as
arXiv:1502.01710. ... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**1 Introduction**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **2 Character-level Convolutional Networks**
In this section, we introduce the design of character-level ConvNets for text classification. The design is modular, where the gradients are obtained by back-propagation [27] to perform optimization.
**2.1** **Key Modules**
The main component is the temporal convol... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**2 Character-level Convolutional Networks**",
"Header 4": null
} | {
"chunk_type": "body"
} |
0 *.* 9 and initial step size 0 *.* 01 which is halved every 3 epoches for 10 times. Each epoch takes a fixed
number of random training samples uniformly sampled across classes. This number will later be
detailed for each dataset sparately. The implementation is done using Torch 7 [4].
**2.2** **Character quantizatio... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**2 Character-level Convolutional Networks**",
"Header 4": null
} | {
"chunk_type": "body"
} |
#### ...
Conv. and Pool. layers Fully-connected
Convolutions Max-pooling
Figure 1: Illustration of our model
The input have number of features equal to 70 due to our character quantization method, and the
input feature length is 1014. It seems that 1014 characters could already capture most of the texts of
inte... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**2 Character-level Convolutional Networks**",
"Header 4": "..."
} | {
"chunk_type": "body"
} |
reasonable to augment the data using signal transformations as done in image or speech recognition,
because the exact order of characters may form rigorous syntactic and semantic meaning. Therefore,
3
-----
the best way to do data augmentation would have been using human rephrases of sentences, but this
is unreal... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**2 Character-level Convolutional Networks**",
"Header 4": "..."
} | {
"chunk_type": "body"
} |
### **3 Comparison Models**
To offer fair comparisons to competitive models, we conducted a series of experiments with both traditional and deep learning methods. We tried our best to choose models that can provide comparable
and competitive results, and the results are reported faithfully without any model selection... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**3 Comparison Models**",
"Header 4": null
} | {
"chunk_type": "body"
} |
text classification, one of the differences is the choice of using pretrained or end-to-end learned word
representations. We offer comparisons with both using the pretrained word2vec [23] embedding [16]
and using lookup tables [5]. The embedding size is 300 in both cases, in the same way as our bagof-means model. To en... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**3 Comparison Models**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **4 Large-scale Datasets and Results**
Previous research on ConvNets in different areas has shown that they usually work well with largescale datasets, especially when the model takes in low-level raw features like characters in our
case. However, most open datasets for text classification are quite small, and la... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
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and content.
2 [http://www.di.unipi.it/˜gulli/AG_corpus_of_news_articles.html](http://www.di.unipi.it/~gulli/AG_corpus_of_news_articles.html)
5
-----
Table 4: Testing errors of all the models. Numbers are in percentage. “Lg” stands for “large” and
“Sm” stands for “small”. “w2v” is an abbreviation for “word2vec”... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
} |
**Yelp reviews** . The Yelp reviews dataset is obtained from the Yelp Dataset Challenge in 2015. This
dataset contains 1,569,264 samples that have review texts. Two classification tasks are constructed
from this dataset – one predicting full number of stars the user has given, and the other predicting a polarity label ... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
} |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
||90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%|||||||||||||||||||||||||
|||90.00% 80.00% 70.00% 60.00% 50.00% 40.00% 30.00% 20.00% 10.00% 0.00%||||||||||60.00% 40.00% 20.00% 0.00% -20.00% -4... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
} |
|20.00% 20.00% 20.00% 10.00% 10.00% 10.00% 0.00% -100 .. 00 00% % 0.00% -10.00% -10.00% -20.00% -20.00% -20.00% -30.00% -40.00% -30.00% -30.00% -50.00% -40.00% -40.00% -60.00% -50.00% (d) word2vec ConvNet (e) Lookup table ConvNet (f) Full alphabet ConvNet AG News DBPedia Yelp P. Yelp F. Yahoo A. Amazon F. Amazon P. Fig... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
} |
that ConvNets may have better applicability to real-world scenarios. However, further analysis is needed to validate the hypothesis that ConvNets are truly good at identifying exotic character combinations such as misspellings and emoticons, as our experiments alone do not show any explicit evidence. Choice of alphabet... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
} |
|||20.00% 10.00% 0.00% -10.00% -20.00% -30.00% -40.00%||||||||||20.00% 10.00% 0.00% -10.00% -20.00% -30.00% -40.00% -50.00% -60.00%||||||20.00% 10.00% 0.00% -10.00% -20.00% -30.00% -40.00% -50.00%||||||||
|||||||||||||||||||||||||||
|||||||||||||||||||||||||||
|||||||||||||||||||||||||||
|||||||||||||||||||||||||||
|||... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**4 Large-scale Datasets and Results**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **6 Conclusion and Outlook**
This article offers an empirical study on character-level convolutional networks for text classification. We compared with a large number of traditional and deep learning models using several largescale datasets. On one hand, analysis shows that character-level ConvNet is an effective... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**6 Conclusion and Outlook**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **Acknowledgement**
We gratefully acknowledge the support of NVIDIA Corporation with the donation of 2 Tesla K40
GPUs used for this research. We gratefully acknowledge the support of Amazon.com Inc for an
AWS in Education Research grant used for this research. | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**Acknowledgement**",
"Header 4": null
} | {
"chunk_type": "body"
} |
### **References**
[1] L. Bottou, F. Fogelman Souli´e, P. Blanchet, and J. Lienard. Experiments with time delay networks and
dynamic time warping for speaker independent isolated digit recognition. In *Proceedings of EuroSpeech*
*89*, volume 2, pages 537–540, Paris, France, 1989.
[2] Y.-L. Boureau, F. Bach, Y. LeCu... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
1997.
[12] T. Joachims. Text categorization with suport vector machines: Learning with many relevant features. In
*Proceedings of the 10th European Conference on Machine Learning*, pages 137–142. Springer-Verlag,
1998.
[13] R. Johnson and T. Zhang. Effective use of word order for text categorization with convolutio... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
review text. In *Proceedings of the 7th ACM Conference on Recommender Systems*, RecSys ’13, pages
165–172, New York, NY, USA, 2013. ACM.
[23] T. Mikolov, I. Sutskever, K. Chen, G. S. Corrado, and J. Dean. Distributed representations of words and
phrases and their compositionality. In C. Burges, L. Bottou, M. Welling,... | {
"id": "1509.01626",
"title": "Character-level Convolutional Networks for Text Classification",
"categories": [
"cs.LG",
"cs.CL"
]
} | {
"Header 1": null,
"Header 2": "**Character-level Convolutional Networks for Text** Classification [∗]",
"Header 3": "**References**",
"Header 4": null
} | {
"chunk_type": "references"
} |
## **Recurrent Models of Visual Attention**
**Volodymyr Mnih** **Nicolas Heess** **Alex Graves** **Koray Kavukcuoglu**
Google DeepMind
*{* vmnih,heess,gravesa,korayk *}* @ google.com | {
"id": "1406.6247",
"title": "Recurrent Models of Visual Attention",
"categories": [
"cs.LG",
"cs.CV",
"stat.ML"
]
} | {
"Header 1": null,
"Header 2": "**Recurrent Models of Visual Attention**",
"Header 3": null,
"Header 4": null
} | {
"chunk_type": "title"
} |
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