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+# TOWARDS FASTER AND STABILIZED GAN TRAINING FOR HIGH-FIDELITY FEW-SHOT IMAGE SYNTHESIS
+
+Bingchen ${ \bf L i u ^ { 1 , 2 } }$ , Yizhe $\mathbf { Z } \mathbf { h } \mathbf { u } ^ { 2 }$ , Kunpeng $\mathbf { S o n g ^ { 1 , 2 } }$ , Ahmed Elgammal1,2
+
+1Playform - Artrendex Inc., USA   
+2Department of Computer Science, Rutgers University   
+{bingchen.liu,yizhe.zhu,kunpeng.song}@rutgers.edu   
+elgammal@artrendex.com
+
+# ABSTRACT
+
+Training Generative Adversarial Networks (GAN) on high-fidelity images usually requires large-scale GPU-clusters and a vast number of training images. In this paper, we study the few-shot image synthesis task for GAN with minimum computing cost. We propose a light-weight GAN structure that gains superior quality on $1 0 2 4 \times 1 0 2 4$ resolution. Notably, the model converges from scratch with just a few hours of training on a single RTX-2080 GPU, and has a consistent performance, even with less than 100 training samples. Two technique designs constitute our work, a skip-layer channel-wise excitation module and a self-supervised discriminator trained as a feature-encoder. With thirteen datasets covering a wide variety of image domains 1, we show our model’s superior performance compared to the state-of-the-art StyleGAN2, when data and computing budget are limited.
+
+# 1 INTRODUCTION
+
+The fascinating ability to synthesize images using the state-of-the-art (SOTA) Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) display a great potential of GANs for many intriguing real-life applications, such as image translation, photo editing, and artistic creation. However, expensive computing cost and the vast amount of required training data limit these SOTAs in real applications with only small image sets and low computing budgets.
+
+In real-life scenarios, the available samples to train a GAN can be minimal, such as the medical images of a rare disease, a particular celebrity’s portrait set, and a specific artist’s artworks. Transferlearning with a pre-trained model (Mo et al., 2020; Wang et al., 2020) is one solution for the lack of training images. Nevertheless, there is no guarantee to find a compatible pre-training dataset. Furthermore, if not, fine-tuning probably leads to even worse performance (Zhao et al., 2020).
+
+![](images/c37c9377cee1982078f16f7aeac8dc9e249edcaffd3edd4fe7ccab56d907150e.jpg)  
+Figure 1: Synthetic results on $1 0 2 4 ^ { 2 }$ resolution of our model, trained from scratch on single RTX 2080-Ti GPU, with only 1000 images. Left: 20 hours on Nature photos; Right: 10 hours on FFHQ.
+
+In a recent study, it was highlighted that in art creation applications, most artists prefers to train their models from scratch based on their own images to avoid biases from fine-tuned pre-trained model. Moreover, It was shown that in most cases artists want to train their models with datasets of less than
+
+100 images (Elgammal et al., 2020). Dynamic data-augmentation (Karras et al., 2020a; Zhao et al., 2020) smooths the gap and stabilizes GAN training with fewer images. However, the computing cost from the SOTA models such as StyleGAN2 (Karras et al., 2020b) and BigGAN (Brock et al., 2019) remain to be high, especially when trained with the image resolution on $1 0 2 4 \times 1 0 2 4$ .
+
+In this paper, our goal is to learn an unconditional GAN on high-resolution images, with low computational cost and few training samples. As summarized in Fig. 2, these training conditions expose the model to a high risk of overfitting and mode-collapse (Arjovsky & Bottou, 2017; Zhang & Khoreva, 2018). To train a GAN given the demanding training conditions, we need a generator $( G )$ that can learn fast, and a discriminator $( D )$ that can continuously provide useful signals to train $G$ . To address these challenges, we summarize our contribution as:
+
+• We design the Skip-Layer channel-wise Excitation (SLE) module, which leverages lowscale activations to revise the channel responses on high-scale feature-maps. SLE allows a more robust gradient flow throughout the model weights for faster training. It also leads to an automated learning of a style/content disentanglement like StyleGAN2. We propose a self-supervised discriminator $D$ trained as a feature-encoder with an extra decoder. We force $D$ to learn a more descriptive feature-map covering more regions from an input image, thus yielding more comprehensive signals to train $G$ . We test multiple selfsupervision strategies for $D$ , among which we show that auto-encoding works the best. • We build a computational-efficient GAN model based on the two proposed techniques, and show the model’s robustness on multiple high-fidelity datasets, as demonstrated in Fig. 1.
+
+# 2 RELATED WORKS
+
+Speed up the GAN training: Speeding up the training of GAN has been approached from various perspectives. Ngxande et al. propose to reduce the computing time with depth-wise convolutions. Zhong et al. adjust the GAN objective into a min-max-min problem for a shorter optimization path. Sinha et al. suggest to prepare each batch of training samples via a coreset selection, leverage the better data preparation for a faster convergence. However, these methods only bring a limited improvement in
+
+![](images/313531434cd1b23c89a559cfbb37e6abac9a1c7b9c963941b18d551e5aa6330a.jpg)  
+Figure 2: The causes and challenges for training GAN in our studied conditions.
+
+training speed. Moreover, the synthesis quality is not advanced within the shortened training time.
+
+Train GAN on high resolution: High-resolution training for GAN can be problematic. Firstly, the increased model parameters lead to a more rigid gradient flow to optimize $G$ . Secondly, the target distribution formed by the images on $1 0 2 4 \times 1 0 2 4$ resolution is super sparse, making GAN much harder to converge. Denton et al. (2015); Zhang et al. (2017); Huang et al. (2017); Wang et al. (2018); Karras et al. (2019); Karnewar & Wang (2020); Karras et al. (2020b); Liu et al. (2021) develop the multi-scale GAN structures to alleviate the gradient flow issue, where $G$ outputs images and receives feedback from several resolutions simultaneously. However, all these approaches further increase the computational cost, consuming even more GPU memory and training time.
+
+Stabilize the GAN training: Mode-collapse on $G$ is one of the big challenges when training GANs. And it becomes even more challenging given fewer training samples and a lower computational budget (a smaller batch-size). As $D$ is more likely to be overfitting on the datasets, thus unable to provide meaningful gradients to train $G$ (Gulrajani et al., 2017).
+
+Prior works tackle the overfitting issue by seeking a good regularization for $D$ , including different objectives (Arjovsky et al., 2017; Lim & Ye, 2017; Tran et al., 2017); regularizing the gradients (Gulrajani et al., 2017; Mescheder et al., 2018); normalizing the model weights (Miyato et al., 2018); and augmenting the training data (Karras et al., 2020a; Zhao et al., 2020). However, the effects of these methods degrade fast when the training batch-size is limited, since appropriate batch statistics can hardly be calculated for the regularization (normalization) over the training iterations.
+
+Meanwhile, self-supervision on $D$ has been shown to be an effective method to stabilize the GAN training as studied in Tran et al. (2019); Chen et al. (2019). However, the auxiliary self-supervision tasks in prior works have limited using scenario and image domain. Moreover, prior works only studied on low resolution images ( $3 2 ^ { 2 }$ to $1 2 8 ^ { 2 }$ ), and without a computing resource limitation.
+
+# 3 METHOD
+
+We adopt a minimalistic design for our model. In particular, we use a single conv-layer on each resolution in $G$ , and apply only three (input and output) channels for the conv-layers on the high resolutions $( \geq 5 1 2 \times 5 1 2 )$ in both $G$ and $D$ . Fig. 3 and Fig. 4 illustrate the model structure for our $G$ and $D$ , with descriptions of the component layers and forward flow. These structure designs make our GAN much smaller than SOTA models and substantially faster to train. Meanwhile, our model remains robust on small datasets due to its compact size with the two proposed techniques.
+
+![](images/77e9d791f8976014c759d5c16143c8185e618fe9385c486e187b8086d323338f.jpg)  
+Figure 3: The structure of the skip-layer excitation module and the Generator. Yellow boxes represent feature-maps (we show the spatial size and omit the channel number), blue box and blue arrows represent the same up-sampling structure, red box contains the SLE module as illustrated on the left.
+
+# 3.1 SKIP-LAYER CHANNEL-WISE EXCITATION
+
+For synthesizing higher resolution images, the generator $G$ inevitably needs to become deeper, with more conv-layers, in concert with the up-sampling needs. A deeper model with more convolution layers leads to a longer training time of GAN, due to the increased number of model parameters and a weaker gradient flow through $G$ (Zhang et al., 2017; Karras et al., 2018; Karnewar & Wang, 2020). To better train a deep model, He et al. design the Residual structure (ResBlock), which uses a skip-layer connection to strengthen the gradient signals between layers. However, while ResBlock has been widely used in GAN literature (Wang et al., 2018; Karras et al., 2020b), it also increases the computation cost.
+
+We reformulate the skip-connection idea with two unique designs into the Skip-Layer Excitation module (SLE). First, ResBlock implements skip-connection as an element-wise addition between the activations from different conv-layers. It requires the spatial dimensions of the activations to be the same. Instead of addition, we apply channel-wise multiplications between the activations, eliminating the heavy computation of convolution (since one side of the activations now has a spatial dimension of $1 ^ { 2 }$ ). Second, in prior GAN works, skip-connections are only used within the same resolution. In contrast, we perform skip-connection between resolutions with a much longer range (e.g., $8 ^ { 2 }$ and $1 2 8 ^ { 2 }$ , $1 6 ^ { 2 }$ and $2 5 6 ^ { 2 }$ ), since an equal spatial-dimension is no longer required. The two designs make SLE inherits the advantages of ResBlock with a shortcut gradient flow, meanwhile without an extra computation burden.
+
+Formally, we define the Skip-Layer Excitation module as:
+
+$$
+\mathbf { y } = \mathcal { F } ( \mathbf { x } _ { l o w } , \{ \mathbf { W } _ { i } \} ) \cdot \mathbf { x } _ { h i g h }
+$$
+
+Here $\mathbf { x }$ and $\mathbf { y }$ are the input and output feature-maps of the SLE module, the function $\mathcal { F }$ contains the operations on $\mathbf { x } _ { l o w }$ , and $\mathbf { W } _ { i }$ indicates the module weights to be learned. The left panel in Fig. 3 shows an SLE module in practice, where $\mathbf { x } _ { l o w }$ and ${ \bf x } _ { h i g h }$ are the feature-maps at $8 \times 8$ and $1 2 8 \times 1 2 8$ resolution respectively. An adaptive average-pooling layer in $\mathcal { F }$ first down-samples $\mathbf { x } _ { l o w }$ into $4 \times 4$ along the spatial-dimensions, then a conv-layer further down-samples it into $1 \times 1$ . A LeakyReLU is used to model the non-linearity, and another conv-layer projects $\mathbf { x } _ { l o w }$ to have the same channel size as ${ \bf x } _ { h i g h }$ . Finally, after a gating operation via a Sigmoid function, the output from $\mathcal { F }$ multiplies ${ \bf x } _ { h i g h }$ along the channel dimension, yielding y with the same shape as ${ \bf x } _ { h i g h }$ .
+
+SLE partially resembles the Squeeze-and-Excitation module (SE) proposed by Hu et al.. However, SE operates within one feature-map as a self-gating module. In comparison, SLE performs between feature-maps that are far away from each other. While SLE brings the benefit of channel-wise feature re-calibration just like SE, it also strengthens the whole model’s gradient flow like ResBlock. The channel-wise multiplication in SLE also coincides with Instance Normalization (Ulyanov et al., 2016; Huang & Belongie, 2017), which is widely used in style-transfer. Similarly, we show that SLE enables $G$ to automatically disentangle the content and style attributes, just like StyleGAN (Karras et al., 2019). As SLE performs on high-resolution feature-maps, altering these feature-maps is shown to be more likely to change the style attributes of the generated image (Karras et al., 2019; Liu et al., 2021). By replacing $\mathrm { x } _ { l o w }$ in SLE from another synthesized sample, our $G$ can generate an image with the content unchanged, but in the same style of the new replacing image.
+
+# 3.2 SELF-SUPERVISED DISCRIMINATOR
+
+Our approach to provide a strong regularization for $D$ is surprisingly simple. We treat $D$ as an encoder and train it with small decoders. Such auto-encoding training forces $D$ to extract image features that the decoders can give good reconstructions. The decoders are optimized together with $D$ on a simple reconstruction loss, which is only trained on real samples:
+
+$$
+\mathcal { L } _ { r e c o n s } = \mathbb { E } _ { { \mathbf { f } } \sim D _ { e n c o d e } ( x ) , x \sim I _ { r e a l } } [ | | \mathcal { G } ( { \mathbf { f } } ) - \mathcal { T } ( x ) | | ] ,
+$$
+
+where f is the intermediate feature-maps from $D$ , the function $\mathcal { G }$ contains the processing on $\mathbf { f }$ and the decoder, and the function $\tau$ represents the processing on sample $x$ from real images $I _ { r e a l }$ .
+
+![](images/9a306a457d02094cd3f62aa4073b58f603ba66c103909121121ac6ad9df1aca9.jpg)  
+Figure 4: The structure and the forward flow of the Discriminator. Blue box and arrows represent the same residual down-sampling structure, green boxes mean the same decoder structure.
+
+Our self-supervised $D$ is illustrated in Fig. 4, where we employ two decoders for the feature-maps on two scales: $\mathbf { f } _ { 1 }$ on $1 6 ^ { 2 }$ and $\mathbf { f } _ { 2 }$ on $8 ^ { 2 }$ . The decoders only have four conv-layers to produce images at $1 2 8 \times 1 2 8$ resolution, causing little extra computations (much less than other regularization methods). We randomly crop $\mathbf { f } _ { 1 }$ with $\frac { 1 } { 8 }$ of its height and width, then crop the real image on the same portion to get $I _ { p a r t }$ . We resize the real image to get $I$ . The decoders produce $I _ { p a r t } ^ { \prime }$ from the cropped $\mathbf { f } _ { 1 }$ , and $I ^ { \prime }$ from $\mathbf { f } _ { 2 }$ . Finally, $D$ and the decoders are trained together to minimize the loss in eq. 2, by matching $I _ { p a r t } ^ { \prime }$ to $I _ { p a r t }$ and $I ^ { \prime }$ to $I$ .
+
+Such reconstructive training makes sure that $D$ extracts a more comprehensive representation from the inputs, covering both the overall compositions (from $\mathbf { f } _ { 2 }$ ) and detailed textures (from $\mathbf { f } _ { 1 }$ ). Note that the processing in $\mathcal { G }$ and $\tau$ are not limited to cropping; more operations remain to be explored for better performance. The auto-encoding approach we employ is a typical method for self-supervised learning, which has been well recognized to improve the model robustness and generalization ability (He et al., 2020; Hendrycks et al., 2019; Jing & Tian, 2020; Goyal et al., 2019). In the context of GAN, we find that a regularized $D$ via self-supervision training strategies significantly improves the synthesis quality on $G$ , among which auto-encoding brings the most performance boost.
+
+Although our self-supervision strategy for $D$ comes in the form of an auto-encoder (AE), this approach is fundamentally different from works trying to combine GAN and AE (Larsen et al., 2016;
+
+Guo et al., 2019; Zhao et al., 2016; Berthelot et al., 2017). The latter works mostly train $G$ as a decoder on a learned latent space from $D$ , or treat the adversarial training with $D$ as an supplementary loss besides AE’s training. In contrast, our model is a pure GAN with a much simpler training schema. The auto-encoding training is only for regularizing $D$ , where $G$ is not involved.
+
+In sum, we employ the hinge version of the adversarial loss (Lim & Ye (2017); Tran et al. (2017)) to iteratively train our $\mathrm { D }$ and G. We find the different GAN losses make little performance difference, while hinge loss computes the fastest:
+
+$$
+\begin{array} { r l } & { \mathcal { L } _ { D } = - \mathbb { E } _ { x \sim I _ { r { e a l } } } [ m i n ( 0 , - 1 + D ( x ) ) ] - \mathbb { E } _ { \hat { x } \sim G ( z ) } [ m i n ( 0 , - 1 - D ( \hat { x } ) ] + \mathcal { L } _ { r e c o n s } } \\ & { \mathcal { L } _ { G } = - \mathbb { E } _ { z \sim N } [ D ( G ( z ) ) ] , } \end{array}
+$$
+
+# 4 EXPERIMENT
+
+Datasets: We conduct experiments on multiple datasets with a wide range of content categories. On $2 5 6 \times 2 5 6$ resolution, we test on Animal-Face Dog and Cat (Si & Zhu, 2011), 100-Shot-Obama, Panda, and Grumpy-cat (Zhao et al., 2020). On $1 0 2 4 \times 1 0 2 4$ resolution, we test on Flickr-FaceHQ (FFHQ) (Karras et al., 2019), Oxford-flowers (Nilsback & Zisserman, 2006), art paintings from WikiArt (wikiart.org), photographs on natural landscape from Unsplash (unsplash.com), Pokemon (pokemon.com), anime face, skull, and shell. These datasets are designed to cover images with different characteristics: photo realistic, graphic-illustration, and art-like images.
+
+Metrics: We use two metrics to measure the models’ synthesis performance: 1) Frechet Inception ´ Distance (FID) (Heusel et al., 2017) measures the overall semantic realism of the synthesized images. For datasets with less than 1000 images (most only have 100 images), we let $G$ generate 5000 images and compute FID between the synthesized images and the whole training set. 2) Learned perceptual similarity (LPIPS) (Zhang et al., 2018) provides a perceptual distance between two images. We use LPIPS to report the reconstruction quality when we perform latent space back-tracking on $G$ given real images, and measure the auto-encoding performance. We find it unnecessary to involve other metrics, as FID is unlikely to be inconsistent with the others, given the notable performance gap between our model and the compared ones. For all the testings, we train the models 5 times with random seeds, and report the highest scores. The relative error is less than five percent on average.
+
+Compared Models: We compare our model with: 1) the state-of-the-art (SOTA) unconditional model, StyleGAN2, 2) a baseline model ablated from our proposed one. Note that we adopt StyleGAN2 with recent studies from (Karras et al., 2020a; Zhao et al., 2020), including the model configuration and differentiable data-augmentation, for the best training on few-sample datasets. Since StyleGAN2 requires much more computing-cost (cc) to train, we derive an extra baseline model. In sum, we compare our model with StyleGAN2 on the absolute image synthesis quality regardless of cc, and use the baseline model for the reference within a comparable cc range.
+
+The baseline model is the strongest performer that we integrated from various GAN techniques based on DCGAN (Radford et al., 2015): 1) spectral-normalization (Miyato et al., 2018), 2) exponentialmoving-average (Yazıcı et al., 2018) optimization on $G$ , 3) differentiable-augmentation, 4) GLU (Dauphin et al., 2017) instead of ReLU in $G$ . We build our model upon the baseline with the two proposed techniques: the skip-layer excitation module and the self-supervised discriminator.
+
+Table 1: Computational cost comparison of the models.   
+
+<table><tr><td></td><td></td><td>StyleGAN2@0.25</td><td>StyleGAN2@0.5</td><td>StyleGAN2</td><td>Baseline</td><td>Ours</td></tr><tr><td rowspan="2">Resolution: 2562 Batch-size: 8</td><td>Training time (hour/10k iter) Training vram (GB)</td><td>1</td><td>1.8</td><td>3.8</td><td>0.7</td><td>1</td></tr><tr><td>Model parameters (million)</td><td>7 27.557</td><td>16 45.029</td><td>18 108.843</td><td>5</td><td>6.5 47.363</td></tr><tr><td rowspan="2">Resolution: 10242</td><td>Training time (hour/10k iter)</td><td></td><td></td><td></td><td>44.359</td><td></td></tr><tr><td>Training vram (GB)</td><td>3.6</td><td>5</td><td>7</td><td>1.3</td><td>1.7</td></tr><tr><td rowspan="2">Batch-size: 8</td><td>Model parameters (million)</td><td>12</td><td>23</td><td>36</td><td>9</td><td>10</td></tr><tr><td></td><td>27.591</td><td>45.15</td><td>109.229</td><td>44.377</td><td>47.413</td></tr></table>
+
+Table. 1 presents the normalized cc figures of the models on Nvidia’s RTX 2080-Ti GPU, implemented using PyTorch (Paszke et al., 2017). Importantly, the slimed StyleGAN2 with $\frac { 1 } { 4 }$ parameters cannot converge on the tested datasets at $1 0 2 4 ^ { 2 }$ resolution. We compare to the StyleGAN2 with $\frac { 1 } { 2 }$ parameters (if not specifically mentioned) in the following experiments.
+
+# 4.1 IMAGE SYNTHESIS PERFORMANCE
+
+Few-shot generation: Collecting large-scale image datasets are expensive, or even impossible, for a certain character, a genre, or a topic. On those few-shot datasets, a data-efficient model becomes especially valuable for the image generation task. In Table. 2 and Table. 3, we show that our model not only achieves superior performance on the few-shot datasets, but also much more computationalefficient than the compared methods. We save the checkpoints every 10k iterations during training and report the best FID from the checkpoints (happens at least after 15 hours of training for StyleGAN2 on all datasets). Among the 12 datasets, our model performs the best on 10 of them.
+
+Please note that, due to the VRAM requirement for StyleGAN2 when trained on $1 0 2 4 ^ { 2 }$ resolution, we have to train the models in Table. 3 on a RTX TITAN GPU. In practice, 2080-TI and TITAN share a similar performance, and our model runs the same time on both GPUs.
+
+Table 2: FID comparison at $2 5 6 ^ { 2 }$ resolution on few-sample datasets.   
+
+<table><tr><td colspan="4">Animal Face- Dog</td><td>Animal Face - Cat</td><td>Obama</td><td>Panda</td><td>Grumpy-cat</td></tr><tr><td colspan="3">Image number</td><td>389</td><td>160</td><td>100</td><td>100</td><td>100</td></tr><tr><td rowspan="5">Training time on one RTX 2080-Ti</td><td rowspan="5">20 hour</td><td>StyleGAN2</td><td>58.85</td><td>42.44</td><td>46.87</td><td>12.06</td><td>27.08</td></tr><tr><td>StyleGAN2 finetune</td><td>61.03</td><td>46.07</td><td>35.75</td><td>14.5</td><td>29.34</td></tr><tr><td>Baseline 5 hour</td><td>108.19</td><td>150.3</td><td>62.74</td><td>15.4</td><td>42.13</td></tr><tr><td>Baseline+Skip</td><td>94.21</td><td>72.97</td><td>52.50</td><td>14.39</td><td>38.17</td></tr><tr><td>Baseline+decode Ours (B+Skip+decode)</td><td>56.25 50.66</td><td>36.74 35.11</td><td>44.34 41.05</td><td>10.12 10.03</td><td>29.38 26.65</td></tr></table>
+
+Training from scratch vs. fine-tuning: Fine-tuning from a pre-trained GAN (Mo et al., 2020; Noguchi & Harada, 2019; Wang et al., 2020) has been the go-to method for the image generation task on datasets with few samples. However, its performance highly depends on the semantic consistency between the new dataset and the available pre-trained model. According to Zhao et al., fine-tuning performs worse than training from scratch in most cases, when the content from the new dataset strays away from the original one. We confirm the limitation of current fine-tuning methods from Table. 2 and Table. 3, where we fine-tune StyleGAN2 trained on FFHQ use the Freeze-D method from Mo et al.. Among all the tested datasets, only Obama and Skull favor the fine-tuning method, making sense since the two sets share the most similar contents to FFHQ.
+
+Module ablation study: We experiment with the two proposed modules in Table. 2, where both SLE (skip) and decoding-on- $. D$ (decode) can separately boost the model performance. It shows that the two modules are orthogonal to each other in improving the model performance, and the self-supervised $D$ makes the biggest contribution. Importantly, the baseline model and StyleGAN2 diverge fast after the listed training time. In contrast, our model is less likely to mode collapse among the tested datasets. Unlike the baseline model which usually model-collapse after trained for 10 hours, our model maintains a good synthesis quality and won’t collapse even after trained for 20 hours. We argue that it is the decoding regularization on $D$ that prevents the model from divergence.
+
+Table 3: FID comparison at $1 0 2 4 ^ { 2 }$ resolution on few-sample datasets.   
+
+<table><tr><td></td><td></td><td></td><td>Art Paintings</td><td>FFHQ</td><td>Flower</td><td>Pokemon</td><td>Anime Face</td><td>Skull</td><td>Shell</td></tr><tr><td colspan="3">Image number</td><td>1000</td><td>1000</td><td>1000</td><td>800</td><td>120</td><td>100</td><td>60</td></tr><tr><td rowspan="2">Training time on one RTX TITAN</td><td>24 hour</td><td>StyleGAN2 StyleGAN2 finetune</td><td>74.56 N/A</td><td>25.66 N/A</td><td>45.23 36.72</td><td>190.23 60.12</td><td>152.73 61.23</td><td>127.98 107.68</td><td>241.37</td></tr><tr><td>8 hour</td><td>Baseline Ours</td><td>62.27 45.08</td><td>38.35 24.45</td><td>42.25</td><td>67.86</td><td>101.23</td><td>186.45</td><td>220.45 202.32</td></tr></table>
+
+Table 4: FID comparison at $1 0 2 4 ^ { 2 }$ resolution on datasets with more images.   
+
+<table><tr><td rowspan="2">Model</td><td>Dataset</td><td colspan="3">Art Paintings</td><td colspan="3">FFHQ</td><td colspan="3">Nature Photograph</td></tr><tr><td>Image number</td><td>2k 5k</td><td>10k</td><td>2k</td><td>5k</td><td>10k</td><td>70k</td><td>2k</td><td>5k</td><td>10k</td></tr><tr><td colspan="2">StyleGAN2</td><td>70.02</td><td>48.36</td><td>41.23</td><td>18.38</td><td>10.45</td><td>7.86</td><td>4.4</td><td>67.12</td><td>41.47 39.05</td></tr><tr><td colspan="2">Baseline</td><td>60.02</td><td>51.23</td><td>49.38</td><td>36.45</td><td>27.86</td><td>25.12</td><td>17.62 71.47</td><td>66.05</td><td>62.28</td></tr><tr><td colspan="2">Ours</td><td>44.57</td><td>43.27</td><td>42.53</td><td>19.01</td><td>17.93</td><td>16.45</td><td>12.38 52.47</td><td>45.07</td><td>43.65</td></tr></table>
+
+Table 5: LPIPS of back-tracking with $G$   
+
+<table><tr><td></td><td>Cat</td><td>Dog</td><td>FFHQ</td><td>Art</td></tr><tr><td>Resolution</td><td colspan="2">256</td><td colspan="2">1024</td></tr><tr><td>Baseline @ 20k iter</td><td>2.113</td><td>2.073</td><td>2.589</td><td>2.916</td></tr><tr><td>Baseline @ 40k iter</td><td>2.513</td><td>2.171</td><td>2.583</td><td>2.812</td></tr><tr><td>Ours @ 40k iter</td><td>1.821</td><td>1.918</td><td>2.425</td><td>2.624</td></tr><tr><td>Ours @ 80k iter</td><td>1.897</td><td>1.986</td><td>2.342</td><td>2.601</td></tr></table>
+
+![](images/40e031b55ed0a6c6e2c80f2d7f05dbf26a14fdda2891f0c61671d35dead85d5f.jpg)  
+Figure 6: Latent space back-tracking and interpolation.
+
+Table 6: FID of self-supervisions for $D$   
+
+<table><tr><td></td><td>Art paintings</td><td>Nature photos</td></tr><tr><td>a. contrastive loss</td><td>47.14</td><td>57.04</td></tr><tr><td>b. predict aspect ratio</td><td>49.21</td><td>59.22</td></tr><tr><td>c.auto-encoding</td><td>42.53</td><td>43.65</td></tr><tr><td>d.a+b</td><td>46.02</td><td>54.23</td></tr><tr><td>e.a+b+c</td><td>44.21</td><td>47.65</td></tr></table>
+
+Training with more images: For more thorough evaluation, we also test our model on datasets with more sufficient training samples, as shown in Table. 4. We train the full StyleGAN2 for around five days on the Art and Photograph dataset with a batch-size of 16 on two TITAN RTX GPUs, and use the latest official figures on FFHQ from Zhao et al.. Instead, we train our model for only 24 hours, with a batch-size of 8 on a single 2080-Ti GPU. Specifically, for FFHQ with all 70000 images, we train our model with a larger batch-size of 32, to reflect an optimal performance of our model.
+
+In this test, we follow the common practice of computing FID by generating $5 0 \mathrm { k }$ images and use the whole training set as the reference distribution. Note that StyleGAN2 has more than double the parameters compared to our model, and trained with a much larger batch-size on FFHQ. These factors contribute to its better performances when given enough training samples and computing power. Meanwhile, our model keeps up well with StyleGAN2 across all testings with a considerably lower computing budget, showing a compelling performance even on larger-scale datasets, and a consistent performance boost over the baseline model.
+
+Qualitative results: The advantage of our model becomes more clear from the qualitative comparisons in Fig. 5. Given the same batch-size and training time, StyleGAN2 either converges slower or suffers from mode collapse. In contrast, our model consistently generates satisfactory images. Note that the best results from our model on Flower, Shell, and Pokemon only take three hours’ training, and for the rest three datasets, the best performance is achieved at training for eight hours. For StyleGAN2 on “shell”, “anime face”, and “Pokemon”, the images shown in Fig. 5 are already from the best epoch, which they match the scores in Table. 2 and Table. 3. For the rest of the datasets, the quality increase from StyleGAN2 is also limited given more training time.
+
+# 4.2 MORE ANALYSIS AND APPLICATIONS
+
+Testing mode collapse with back-tracking: From a well trained GAN, one can take a real image and invert it back to a vector in the latent space of $G$ , thus editing the image’s content by altering the back-tracked vector. Despite the various back-tracking methods (Zhu et al., 2016; Lipton & Tripathi, 2017; Zhu et al., 2020; Abdal et al., 2019), a well generalized $G$ is arguably as important for the good inversions. To this end, we show that our model, although trained on limited image samples, still gets a desirable performance on real image back-tracking.
+
+In Table 5, we split the images from each dataset with a training/testing ratio of 9:1, and train $G$ on the training set. We compute a reconstruction error between all the images from the testing set and their inversions from $G$ , after the same update of 1000 iterations on the latent vectors (to prevent the vectors from being far off the normal distribution). The baseline model’s performance is getting worse with more training iterations, which reflects mode-collapse on $G$ . In contrast, our model gives better reconstructions with consistent performance over more training iterations. Fig. 6 presents the back-tracked examples (left-most and right-most samples in the middle panel) given the real images.
+
+![](images/1b089ab672f80d73a3e1097e0c357e7475d1d83e616607b8144ca506fa52e69d.jpg)  
+Figure 5: Qualitative comparison between our model and StyleGAN2 on $1 0 2 4 ^ { 2 }$ resolution datasets. The left-most panel shows the training images, and the right two panels show the uncurated samples from StyleGAN2 and our model. Both models are trained from scratch for 10 hours with a batch-size of 8. The samples are generated from the checkpoint with the lowest FID.
+
+The smooth interpolations from the back-tracked latent vectors also suggest little mode-collapse of our $G$ (Radford et al., 2015; Zhao et al., 2020; Robb et al., 2020).
+
+In addition, we show qualitative comparisons in appendix D, where our model maintains a good generation while StyleGAN2 and baseline are model-collapsed.
+
+The self-supervision methods and generalization ability on $D$ : Apart from the auto-encoding training for $D$ , we show that $D$ with other common self-supervising strategies also boost GAN’s performance in our training settings. We test five self-supervision settings, as shown in Table 6, which all brings a substantial performance boost compared to the baseline model. Specifically, setting-a refers to contrastive learning which we treat each real image as a unique class and let $D$ classify them. For setting- $\mathbf { \sigma } . \mathbf { b }$ , we train $D$ to predict the real image’s original aspect-ratio since they are reshaped to square when fed to $D$ . Setting-c is the method we employ in our model, which trains $D$ as an encoder with a decoder to reconstruct real images. To better validate the benefit of self-supervision on $D$ , all the testings are conducted on full training sets with 10000 images, with a batch-size of 8 to be consistent with Table 4. We also tried training with a larger batch-size of 16, which the results are consistent to the batch-size of 8.
+
+![](images/2da992c184746b333c41d52b16369f17b9f833b9e36850835fc27919e5604135.jpg)  
+Figure 7: Style-mixing results from our model trained for only 5 hours on single GPU.
+
+Interestingly, according to Table 6, while setting-c performs the best, combining it with the rest two settings lead to a clear performance downgrade. The similar behavior can be found on some other self-supervision settings, e.g. when follow Chen et al. (2019) with a ”rotation-predicting” task on art-paintings and FFHQ datasets, we observe a performance downgrade even compared to the baseline model. We hypothesis the reason being that the auto-encoding forces $D$ to pay attention to more areas of the input image, thus extracts a more comprehensive feature-map to describe the input image (for a good reconstruction). In contrast, a classification task does not guarantee $D$ to cover the whole image. Instead, the task drives $D$ to only focus on small regions because the model can find class cues from small regions of the images. Focusing on limited regions (i.e., react to limited image patterns) is a typical overfitting behavior, which is also widely happening for $D$ in vanilla GANs. More discussion can be found in appendix B.
+
+Style mixing like StyleGAN. With the channel-wise excitation module, our model gets the same functionality as StyleGAN: it learns to disentangle the images’ high-level semantic attributes (style and content) in an unsupervised way, from $G$ ’s conv-layers at different scales. The style-mixing results are displayed in Fig. 7, where the top three datasets are $2 5 6 \times 2 5 6$ resolution, and the bottom three are $1 0 2 4 \times 1 0 2 4$ resolution. While StyleGAN2 suffers from converging on the bottom high-resolution datasets, our model successfully learns the style representations along the channel dimension on the “excited” layers (i.e., for feature-maps on $2 5 6 \times 2 5 6$ , $5 1 2 \times 5 1 2$ resolution). Please refer to appendix A and C for more information on SLE and style-mixing.
+
+# 5 CONCLUSION
+
+We introduce two techniques that stabilize the GAN training with an improved synthesis quality, given sub-hundred high-fidelity images and a limited computing resource. On thirteen datasets with a diverse content variation, we show that a skip-layer channel-wise excitation mechanism (SLE) and a self-supervised regularization on the discriminator significantly boost the synthesis performance of GAN. Both proposed techniques require minor changes to a vanilla GAN, enhancing GAN’s practicality with a desirable plug-and-play property. We hope this work can benefit downstream tasks of GAN and provide new study perspectives for future research.
+
+# REFERENCES
+
+Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE international conference on computer vision, pp. 4432–4441, 2019.
+
+Martin Arjovsky and Leon Bottou. Towards principled methods for training generative adversarial ´ networks. In International Conference on Learning Representations, 2017.
+
+Martin Arjovsky, Soumith Chintala, and Leon Bottou. Wasserstein generative adversarial networks. ´ In International conference on machine learning, pp. 214–223. PMLR, 2017.
+
+David Berthelot, Thomas Schumm, and Luke Metz. Began: Boundary equilibrium generative adversarial networks. arXiv preprint arXiv:1703.10717, 2017.
+
+Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale GAN training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2019.
+
+Ting Chen, Xiaohua Zhai, Marvin Ritter, Mario Lucic, and Neil Houlsby. Self-supervised gans via auxiliary rotation loss. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 12154–12163, 2019.
+
+Yann N Dauphin, Angela Fan, Michael Auli, and David Grangier. Language modeling with gated convolutional networks. In International conference on machine learning, pp. 933–941, 2017.
+
+Emily L Denton, Soumith Chintala, Rob Fergus, et al. Deep generative image models using a laplacian pyramid of adversarial networks. In Advances in neural information processing systems, pp. 1486–1494, 2015.
+
+Ahmed Elgammal, Marian Mazzone, et al. Artists, artificial intelligence and machine-based creativity in playform. Artnodes, (26):1–8, 2020.
+
+Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pp. 2672–2680, 2014.
+
+Priya Goyal, Dhruv Mahajan, Abhinav Gupta, and Ishan Misra. Scaling and benchmarking selfsupervised visual representation learning. In Proceedings of the IEEE International Conference on Computer Vision, pp. 6391–6400, 2019.
+
+Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. In Advances in neural information processing systems, pp. 5767–5777, 2017.
+
+Yong Guo, Qi Chen, Jian Chen, Qingyao Wu, Qinfeng Shi, and Mingkui Tan. Auto-embedding generative adversarial networks for high resolution image synthesis. IEEE Transactions on Multimedia, 21(11):2726–2737, 2019.
+
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016.
+
+Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9729–9738, 2020.
+
+Dan Hendrycks, Mantas Mazeika, Saurav Kadavath, and Dawn Song. Using self-supervised learning can improve model robustness and uncertainty. In Advances in Neural Information Processing Systems, pp. 15663–15674, 2019.
+
+Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In Advances in neural information processing systems, pp. 6626–6637, 2017.
+
+Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 7132–7141, 2018.
+
+Xun Huang and Serge Belongie. Arbitrary style transfer in real-time with adaptive instance normalization. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1501– 1510, 2017.
+
+Xun Huang, Yixuan Li, Omid Poursaeed, John Hopcroft, and Serge Belongie. Stacked generative adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 5077–5086, 2017.
+
+Longlong Jing and Yingli Tian. Self-supervised visual feature learning with deep neural networks: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020.
+
+Animesh Karnewar and Oliver Wang. Msg-gan: Multi-scale gradients for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 7799–7808, 2020.
+
+Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of GANs for improved quality, stability, and variation. In International Conference on Learning Representations, 2018.
+
+Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4401–4410, 2019.
+
+Tero Karras, Miika Aittala, Janne Hellsten, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Training generative adversarial networks with limited data. arXiv preprint arXiv:2006.06676, 2020a.
+
+Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8110–8119, 2020b.
+
+Anders Boesen Lindbo Larsen, Søren Kaae Sønderby, Hugo Larochelle, and Ole Winther. Autoencoding beyond pixels using a learned similarity metric. In International conference on machine learning, pp. 1558–1566. PMLR, 2016.
+
+Jae Hyun Lim and Jong Chul Ye. Geometric gan. arXiv preprint arXiv:1705.02894, 2017.
+
+Zachary C. Lipton and Subarna Tripathi. Precise recovery of latent vectors from generative adversarial networks. ICLR workshop, 2017.
+
+Bingchen Liu, Kunpeng Song, Yizhe Zhu, Gerard de Melo, and Ahmed Elgammal. Time: Text and image mutual-translation adversarial networks. In Thirty-Fifth AAAI Conference on Artificial Intelligence, 2021.
+
+Lars Mescheder, Andreas Geiger, and Sebastian Nowozin. Which training methods for gans do actually converge? In International conference on machine learning, pp. 3481–3490. PMLR, 2018.
+
+Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. Spectral normalization for generative adversarial networks. In International Conference on Learning Representations, 2018.
+
+Sangwoo Mo, Minsu Cho, and Jinwoo Shin. Freeze discriminator: A simple baseline for fine-tuning gans. arXiv preprint arXiv:2002.10964, 2020.
+
+Mkhuseli Ngxande, Jules-Raymond Tapamo, and Michael Burke. Depthwisegans: Fast training generative adversarial networks for realistic image synthesis. In 2019 Southern African Universities Power Engineering Conference/Robotics and Mechatronics/Pattern Recognition Association of South Africa (SAUPEC/RobMech/PRASA), pp. 111–116. IEEE, 2019.
+
+Maria-Elena Nilsback and Andrew Zisserman. A visual vocabulary for flower classification. In IEEE Conference on Computer Vision and Pattern Recognition, volume 2, pp. 1447–1454, 2006.
+
+Atsuhiro Noguchi and Tatsuya Harada. Image generation from small datasets via batch statistics adaptation. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2750– 2758, 2019.
+
+Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017.
+
+Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434, 2015.
+
+Esther Robb, Wen-Sheng Chu, Abhishek Kumar, and Jia-Bin Huang. Few-shot adaptation of generative adversarial networks. arXiv preprint arXiv:2010.11943, 2020.
+
+Zhangzhang Si and Song-Chun Zhu. Learning hybrid image templates (hit) by information projection. IEEE Transactions on pattern analysis and machine intelligence, 34(7):1354–1367, 2011.
+
+Samarth Sinha, Han Zhang, Anirudh Goyal, Yoshua Bengio, Hugo Larochelle, and Augustus Odena. Small-gan: Speeding up gan training using core-sets. arXiv preprint arXiv:1910.13540, 2019.
+
+Dustin Tran, Rajesh Ranganath, and David M Blei. Deep and hierarchical implicit models. arXiv preprint arXiv:1702.08896, 7(3):13, 2017.
+
+Ngoc-Trung Tran, Viet-Hung Tran, Bao-Ngoc Nguyen, Linxiao Yang, and Ngai-Man Man Cheung. Self-supervised gan: Analysis and improvement with multi-class minimax game. Advances in Neural Information Processing Systems, 32:13253–13264, 2019.
+
+Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky. Instance normalization: The missing ingredient for fast stylization. arXiv preprint arXiv:1607.08022, 2016.
+
+Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Highresolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 8798–8807, 2018.
+
+Yaxing Wang, Abel Gonzalez-Garcia, David Berga, Luis Herranz, Fahad Shahbaz Khan, and Joost van de Weijer. Minegan: effective knowledge transfer from gans to target domains with few images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9332–9341, 2020.
+
+Yasin Yazıcı, Chuan-Sheng Foo, Stefan Winkler, Kim-Hui Yap, Georgios Piliouras, and Vijay Chandrasekhar. The unusual effectiveness of averaging in gan training. arXiv preprint arXiv:1806.04498, 2018.
+
+Dan Zhang and Anna Khoreva. Pa-gan: Improving gan training by progressive augmentation. 2018.
+
+Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. In Proceedings of the IEEE international conference on computer vision, pp. 5907–5915, 2017.
+
+Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 586–595, 2018.
+
+Junbo Zhao, Michael Mathieu, and Yann LeCun. Energy-based generative adversarial network. arXiv preprint arXiv:1609.03126, 2016.
+
+Shengyu Zhao, Zhijian Liu, Ji Lin, Jun-Yan Zhu, and Song Han. Differentiable augmentation for data-efficient gan training. arXiv preprint arXiv:2006.10738, 2020.
+
+Jiachen Zhong, Xuanqing Liu, and Cho-Jui Hsieh. Improving the speed and quality of gan by adversarial training. arXiv preprint arXiv:2008.03364, 2020.
+
+Jiapeng Zhu, Yujun Shen, Deli Zhao, and Bolei Zhou. In-domain gan inversion for real image editing. arXiv preprint arXiv:2004.00049, 2020.
+
+Jun-Yan Zhu, Philipp Krahenb ¨ uhl, Eli Shechtman, and Alexei A Efros. Generative visual manipu- ¨ lation on the natural image manifold. In European conference on computer vision, pp. 597–613. Springer, 2016.

parse/train/1Fqg133qRaI/1Fqg133qRaI_content_list.json

@@ -0,0 +1,1541 @@
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+    {
+        "type": "text",
+        "text": "TOWARDS FASTER AND STABILIZED GAN TRAINING FOR HIGH-FIDELITY FEW-SHOT IMAGE SYNTHESIS ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            98,
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+            146
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Bingchen ${ \\bf L i u ^ { 1 , 2 } }$ , Yizhe $\\mathbf { Z } \\mathbf { h } \\mathbf { u } ^ { 2 }$ , Kunpeng $\\mathbf { S o n g ^ { 1 , 2 } }$ , Ahmed Elgammal1,2 ",
+        "bbox": [
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+            169,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1Playform - Artrendex Inc., USA   \n2Department of Computer Science, Rutgers University   \n{bingchen.liu,yizhe.zhu,kunpeng.song}@rutgers.edu   \nelgammal@artrendex.com ",
+        "bbox": [
+            183,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+            292
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Training Generative Adversarial Networks (GAN) on high-fidelity images usually requires large-scale GPU-clusters and a vast number of training images. In this paper, we study the few-shot image synthesis task for GAN with minimum computing cost. We propose a light-weight GAN structure that gains superior quality on $1 0 2 4 \\times 1 0 2 4$ resolution. Notably, the model converges from scratch with just a few hours of training on a single RTX-2080 GPU, and has a consistent performance, even with less than 100 training samples. Two technique designs constitute our work, a skip-layer channel-wise excitation module and a self-supervised discriminator trained as a feature-encoder. With thirteen datasets covering a wide variety of image domains 1, we show our model’s superior performance compared to the state-of-the-art StyleGAN2, when data and computing budget are limited. ",
+        "bbox": [
+            233,
+            309,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
+            178,
+            489,
+            336,
+            505
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "The fascinating ability to synthesize images using the state-of-the-art (SOTA) Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) display a great potential of GANs for many intriguing real-life applications, such as image translation, photo editing, and artistic creation. However, expensive computing cost and the vast amount of required training data limit these SOTAs in real applications with only small image sets and low computing budgets. ",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In real-life scenarios, the available samples to train a GAN can be minimal, such as the medical images of a rare disease, a particular celebrity’s portrait set, and a specific artist’s artworks. Transferlearning with a pre-trained model (Mo et al., 2020; Wang et al., 2020) is one solution for the lack of training images. Nevertheless, there is no guarantee to find a compatible pre-training dataset. Furthermore, if not, fine-tuning probably leads to even worse performance (Zhao et al., 2020). ",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/c37c9377cee1982078f16f7aeac8dc9e249edcaffd3edd4fe7ccab56d907150e.jpg",
+        "image_caption": [
+            "Figure 1: Synthetic results on $1 0 2 4 ^ { 2 }$ resolution of our model, trained from scratch on single RTX 2080-Ti GPU, with only 1000 images. Left: 20 hours on Nature photos; Right: 10 hours on FFHQ. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            210,
+            683,
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+            794
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "In a recent study, it was highlighted that in art creation applications, most artists prefers to train their models from scratch based on their own images to avoid biases from fine-tuned pre-trained model. Moreover, It was shown that in most cases artists want to train their models with datasets of less than ",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "100 images (Elgammal et al., 2020). Dynamic data-augmentation (Karras et al., 2020a; Zhao et al., 2020) smooths the gap and stabilizes GAN training with fewer images. However, the computing cost from the SOTA models such as StyleGAN2 (Karras et al., 2020b) and BigGAN (Brock et al., 2019) remain to be high, especially when trained with the image resolution on $1 0 2 4 \\times 1 0 2 4$ . ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, our goal is to learn an unconditional GAN on high-resolution images, with low computational cost and few training samples. As summarized in Fig. 2, these training conditions expose the model to a high risk of overfitting and mode-collapse (Arjovsky & Bottou, 2017; Zhang & Khoreva, 2018). To train a GAN given the demanding training conditions, we need a generator $( G )$ that can learn fast, and a discriminator $( D )$ that can continuously provide useful signals to train $G$ . To address these challenges, we summarize our contribution as: ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "• We design the Skip-Layer channel-wise Excitation (SLE) module, which leverages lowscale activations to revise the channel responses on high-scale feature-maps. SLE allows a more robust gradient flow throughout the model weights for faster training. It also leads to an automated learning of a style/content disentanglement like StyleGAN2. We propose a self-supervised discriminator $D$ trained as a feature-encoder with an extra decoder. We force $D$ to learn a more descriptive feature-map covering more regions from an input image, thus yielding more comprehensive signals to train $G$ . We test multiple selfsupervision strategies for $D$ , among which we show that auto-encoding works the best. • We build a computational-efficient GAN model based on the two proposed techniques, and show the model’s robustness on multiple high-fidelity datasets, as demonstrated in Fig. 1. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2 RELATED WORKS ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Speed up the GAN training: Speeding up the training of GAN has been approached from various perspectives. Ngxande et al. propose to reduce the computing time with depth-wise convolutions. Zhong et al. adjust the GAN objective into a min-max-min problem for a shorter optimization path. Sinha et al. suggest to prepare each batch of training samples via a coreset selection, leverage the better data preparation for a faster convergence. However, these methods only bring a limited improvement in ",
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+    {
+        "type": "image",
+        "img_path": "images/313531434cd1b23c89a559cfbb37e6abac9a1c7b9c963941b18d551e5aa6330a.jpg",
+        "image_caption": [
+            "Figure 2: The causes and challenges for training GAN in our studied conditions. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "training speed. Moreover, the synthesis quality is not advanced within the shortened training time. ",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Train GAN on high resolution: High-resolution training for GAN can be problematic. Firstly, the increased model parameters lead to a more rigid gradient flow to optimize $G$ . Secondly, the target distribution formed by the images on $1 0 2 4 \\times 1 0 2 4$ resolution is super sparse, making GAN much harder to converge. Denton et al. (2015); Zhang et al. (2017); Huang et al. (2017); Wang et al. (2018); Karras et al. (2019); Karnewar & Wang (2020); Karras et al. (2020b); Liu et al. (2021) develop the multi-scale GAN structures to alleviate the gradient flow issue, where $G$ outputs images and receives feedback from several resolutions simultaneously. However, all these approaches further increase the computational cost, consuming even more GPU memory and training time. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Stabilize the GAN training: Mode-collapse on $G$ is one of the big challenges when training GANs. And it becomes even more challenging given fewer training samples and a lower computational budget (a smaller batch-size). As $D$ is more likely to be overfitting on the datasets, thus unable to provide meaningful gradients to train $G$ (Gulrajani et al., 2017). ",
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+    {
+        "type": "text",
+        "text": "Prior works tackle the overfitting issue by seeking a good regularization for $D$ , including different objectives (Arjovsky et al., 2017; Lim & Ye, 2017; Tran et al., 2017); regularizing the gradients (Gulrajani et al., 2017; Mescheder et al., 2018); normalizing the model weights (Miyato et al., 2018); and augmenting the training data (Karras et al., 2020a; Zhao et al., 2020). However, the effects of these methods degrade fast when the training batch-size is limited, since appropriate batch statistics can hardly be calculated for the regularization (normalization) over the training iterations. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Meanwhile, self-supervision on $D$ has been shown to be an effective method to stabilize the GAN training as studied in Tran et al. (2019); Chen et al. (2019). However, the auxiliary self-supervision tasks in prior works have limited using scenario and image domain. Moreover, prior works only studied on low resolution images ( $3 2 ^ { 2 }$ to $1 2 8 ^ { 2 }$ ), and without a computing resource limitation. ",
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+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "We adopt a minimalistic design for our model. In particular, we use a single conv-layer on each resolution in $G$ , and apply only three (input and output) channels for the conv-layers on the high resolutions $( \\geq 5 1 2 \\times 5 1 2 )$ in both $G$ and $D$ . Fig. 3 and Fig. 4 illustrate the model structure for our $G$ and $D$ , with descriptions of the component layers and forward flow. These structure designs make our GAN much smaller than SOTA models and substantially faster to train. Meanwhile, our model remains robust on small datasets due to its compact size with the two proposed techniques. ",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/77e9d791f8976014c759d5c16143c8185e618fe9385c486e187b8086d323338f.jpg",
+        "image_caption": [
+            "Figure 3: The structure of the skip-layer excitation module and the Generator. Yellow boxes represent feature-maps (we show the spatial size and omit the channel number), blue box and blue arrows represent the same up-sampling structure, red box contains the SLE module as illustrated on the left. "
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "3.1 SKIP-LAYER CHANNEL-WISE EXCITATION ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "For synthesizing higher resolution images, the generator $G$ inevitably needs to become deeper, with more conv-layers, in concert with the up-sampling needs. A deeper model with more convolution layers leads to a longer training time of GAN, due to the increased number of model parameters and a weaker gradient flow through $G$ (Zhang et al., 2017; Karras et al., 2018; Karnewar & Wang, 2020). To better train a deep model, He et al. design the Residual structure (ResBlock), which uses a skip-layer connection to strengthen the gradient signals between layers. However, while ResBlock has been widely used in GAN literature (Wang et al., 2018; Karras et al., 2020b), it also increases the computation cost. ",
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+    {
+        "type": "text",
+        "text": "We reformulate the skip-connection idea with two unique designs into the Skip-Layer Excitation module (SLE). First, ResBlock implements skip-connection as an element-wise addition between the activations from different conv-layers. It requires the spatial dimensions of the activations to be the same. Instead of addition, we apply channel-wise multiplications between the activations, eliminating the heavy computation of convolution (since one side of the activations now has a spatial dimension of $1 ^ { 2 }$ ). Second, in prior GAN works, skip-connections are only used within the same resolution. In contrast, we perform skip-connection between resolutions with a much longer range (e.g., $8 ^ { 2 }$ and $1 2 8 ^ { 2 }$ , $1 6 ^ { 2 }$ and $2 5 6 ^ { 2 }$ ), since an equal spatial-dimension is no longer required. The two designs make SLE inherits the advantages of ResBlock with a shortcut gradient flow, meanwhile without an extra computation burden. ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Formally, we define the Skip-Layer Excitation module as: ",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d9c79eb564e07c1b444daf7a02df7206eaaaa09fe5f7c937679b8cbb1385fe6e.jpg",
+        "text": "$$\n\\mathbf { y } = \\mathcal { F } ( \\mathbf { x } _ { l o w } , \\{ \\mathbf { W } _ { i } \\} ) \\cdot \\mathbf { x } _ { h i g h }\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Here $\\mathbf { x }$ and $\\mathbf { y }$ are the input and output feature-maps of the SLE module, the function $\\mathcal { F }$ contains the operations on $\\mathbf { x } _ { l o w }$ , and $\\mathbf { W } _ { i }$ indicates the module weights to be learned. The left panel in Fig. 3 shows an SLE module in practice, where $\\mathbf { x } _ { l o w }$ and ${ \\bf x } _ { h i g h }$ are the feature-maps at $8 \\times 8$ and $1 2 8 \\times 1 2 8$ resolution respectively. An adaptive average-pooling layer in $\\mathcal { F }$ first down-samples $\\mathbf { x } _ { l o w }$ into $4 \\times 4$ along the spatial-dimensions, then a conv-layer further down-samples it into $1 \\times 1$ . A LeakyReLU is used to model the non-linearity, and another conv-layer projects $\\mathbf { x } _ { l o w }$ to have the same channel size as ${ \\bf x } _ { h i g h }$ . Finally, after a gating operation via a Sigmoid function, the output from $\\mathcal { F }$ multiplies ${ \\bf x } _ { h i g h }$ along the channel dimension, yielding y with the same shape as ${ \\bf x } _ { h i g h }$ . ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "SLE partially resembles the Squeeze-and-Excitation module (SE) proposed by Hu et al.. However, SE operates within one feature-map as a self-gating module. In comparison, SLE performs between feature-maps that are far away from each other. While SLE brings the benefit of channel-wise feature re-calibration just like SE, it also strengthens the whole model’s gradient flow like ResBlock. The channel-wise multiplication in SLE also coincides with Instance Normalization (Ulyanov et al., 2016; Huang & Belongie, 2017), which is widely used in style-transfer. Similarly, we show that SLE enables $G$ to automatically disentangle the content and style attributes, just like StyleGAN (Karras et al., 2019). As SLE performs on high-resolution feature-maps, altering these feature-maps is shown to be more likely to change the style attributes of the generated image (Karras et al., 2019; Liu et al., 2021). By replacing $\\mathrm { x } _ { l o w }$ in SLE from another synthesized sample, our $G$ can generate an image with the content unchanged, but in the same style of the new replacing image. ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "3.2 SELF-SUPERVISED DISCRIMINATOR ",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "Our approach to provide a strong regularization for $D$ is surprisingly simple. We treat $D$ as an encoder and train it with small decoders. Such auto-encoding training forces $D$ to extract image features that the decoders can give good reconstructions. The decoders are optimized together with $D$ on a simple reconstruction loss, which is only trained on real samples: ",
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+    },
+    {
+        "type": "equation",
+        "img_path": "images/a7fa1ed3572f31934eba88f24c02b5712afb2ce782dc92d33521792b0e8dcbee.jpg",
+        "text": "$$\n\\mathcal { L } _ { r e c o n s } = \\mathbb { E } _ { { \\mathbf { f } } \\sim D _ { e n c o d e } ( x ) , x \\sim I _ { r e a l } } [ | | \\mathcal { G } ( { \\mathbf { f } } ) - \\mathcal { T } ( x ) | | ] ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where f is the intermediate feature-maps from $D$ , the function $\\mathcal { G }$ contains the processing on $\\mathbf { f }$ and the decoder, and the function $\\tau$ represents the processing on sample $x$ from real images $I _ { r e a l }$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/9a306a457d02094cd3f62aa4073b58f603ba66c103909121121ac6ad9df1aca9.jpg",
+        "image_caption": [
+            "Figure 4: The structure and the forward flow of the Discriminator. Blue box and arrows represent the same residual down-sampling structure, green boxes mean the same decoder structure. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            210,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Our self-supervised $D$ is illustrated in Fig. 4, where we employ two decoders for the feature-maps on two scales: $\\mathbf { f } _ { 1 }$ on $1 6 ^ { 2 }$ and $\\mathbf { f } _ { 2 }$ on $8 ^ { 2 }$ . The decoders only have four conv-layers to produce images at $1 2 8 \\times 1 2 8$ resolution, causing little extra computations (much less than other regularization methods). We randomly crop $\\mathbf { f } _ { 1 }$ with $\\frac { 1 } { 8 }$ of its height and width, then crop the real image on the same portion to get $I _ { p a r t }$ . We resize the real image to get $I$ . The decoders produce $I _ { p a r t } ^ { \\prime }$ from the cropped $\\mathbf { f } _ { 1 }$ , and $I ^ { \\prime }$ from $\\mathbf { f } _ { 2 }$ . Finally, $D$ and the decoders are trained together to minimize the loss in eq. 2, by matching $I _ { p a r t } ^ { \\prime }$ to $I _ { p a r t }$ and $I ^ { \\prime }$ to $I$ . ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Such reconstructive training makes sure that $D$ extracts a more comprehensive representation from the inputs, covering both the overall compositions (from $\\mathbf { f } _ { 2 }$ ) and detailed textures (from $\\mathbf { f } _ { 1 }$ ). Note that the processing in $\\mathcal { G }$ and $\\tau$ are not limited to cropping; more operations remain to be explored for better performance. The auto-encoding approach we employ is a typical method for self-supervised learning, which has been well recognized to improve the model robustness and generalization ability (He et al., 2020; Hendrycks et al., 2019; Jing & Tian, 2020; Goyal et al., 2019). In the context of GAN, we find that a regularized $D$ via self-supervision training strategies significantly improves the synthesis quality on $G$ , among which auto-encoding brings the most performance boost. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Although our self-supervision strategy for $D$ comes in the form of an auto-encoder (AE), this approach is fundamentally different from works trying to combine GAN and AE (Larsen et al., 2016; ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Guo et al., 2019; Zhao et al., 2016; Berthelot et al., 2017). The latter works mostly train $G$ as a decoder on a learned latent space from $D$ , or treat the adversarial training with $D$ as an supplementary loss besides AE’s training. In contrast, our model is a pure GAN with a much simpler training schema. The auto-encoding training is only for regularizing $D$ , where $G$ is not involved. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In sum, we employ the hinge version of the adversarial loss (Lim & Ye (2017); Tran et al. (2017)) to iteratively train our $\\mathrm { D }$ and G. We find the different GAN losses make little performance difference, while hinge loss computes the fastest: ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/0cdaec004160dce663bfda58e082f303350b6f79ecc4ee5dc68ed1b30bb31cc5.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\mathcal { L } _ { D } = - \\mathbb { E } _ { x \\sim I _ { r { e a l } } } [ m i n ( 0 , - 1 + D ( x ) ) ] - \\mathbb { E } _ { \\hat { x } \\sim G ( z ) } [ m i n ( 0 , - 1 - D ( \\hat { x } ) ] + \\mathcal { L } _ { r e c o n s } } \\\\ & { \\mathcal { L } _ { G } = - \\mathbb { E } _ { z \\sim N } [ D ( G ( z ) ) ] , } \\end{array}\n$$",
+        "text_format": "latex",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "4 EXPERIMENT ",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Datasets: We conduct experiments on multiple datasets with a wide range of content categories. On $2 5 6 \\times 2 5 6$ resolution, we test on Animal-Face Dog and Cat (Si & Zhu, 2011), 100-Shot-Obama, Panda, and Grumpy-cat (Zhao et al., 2020). On $1 0 2 4 \\times 1 0 2 4$ resolution, we test on Flickr-FaceHQ (FFHQ) (Karras et al., 2019), Oxford-flowers (Nilsback & Zisserman, 2006), art paintings from WikiArt (wikiart.org), photographs on natural landscape from Unsplash (unsplash.com), Pokemon (pokemon.com), anime face, skull, and shell. These datasets are designed to cover images with different characteristics: photo realistic, graphic-illustration, and art-like images. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Metrics: We use two metrics to measure the models’ synthesis performance: 1) Frechet Inception ´ Distance (FID) (Heusel et al., 2017) measures the overall semantic realism of the synthesized images. For datasets with less than 1000 images (most only have 100 images), we let $G$ generate 5000 images and compute FID between the synthesized images and the whole training set. 2) Learned perceptual similarity (LPIPS) (Zhang et al., 2018) provides a perceptual distance between two images. We use LPIPS to report the reconstruction quality when we perform latent space back-tracking on $G$ given real images, and measure the auto-encoding performance. We find it unnecessary to involve other metrics, as FID is unlikely to be inconsistent with the others, given the notable performance gap between our model and the compared ones. For all the testings, we train the models 5 times with random seeds, and report the highest scores. The relative error is less than five percent on average. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Compared Models: We compare our model with: 1) the state-of-the-art (SOTA) unconditional model, StyleGAN2, 2) a baseline model ablated from our proposed one. Note that we adopt StyleGAN2 with recent studies from (Karras et al., 2020a; Zhao et al., 2020), including the model configuration and differentiable data-augmentation, for the best training on few-sample datasets. Since StyleGAN2 requires much more computing-cost (cc) to train, we derive an extra baseline model. In sum, we compare our model with StyleGAN2 on the absolute image synthesis quality regardless of cc, and use the baseline model for the reference within a comparable cc range. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The baseline model is the strongest performer that we integrated from various GAN techniques based on DCGAN (Radford et al., 2015): 1) spectral-normalization (Miyato et al., 2018), 2) exponentialmoving-average (Yazıcı et al., 2018) optimization on $G$ , 3) differentiable-augmentation, 4) GLU (Dauphin et al., 2017) instead of ReLU in $G$ . We build our model upon the baseline with the two proposed techniques: the skip-layer excitation module and the self-supervised discriminator. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/1f4efb8d3334e411be43f2e7cd358faf2c1f379c1346cb2f0d460a8d48ba6f17.jpg",
+        "table_caption": [
+            "Table 1: Computational cost comparison of the models. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>StyleGAN2@0.25</td><td>StyleGAN2@0.5</td><td>StyleGAN2</td><td>Baseline</td><td>Ours</td></tr><tr><td rowspan=\"2\">Resolution: 2562 Batch-size: 8</td><td>Training time (hour/10k iter) Training vram (GB)</td><td>1</td><td>1.8</td><td>3.8</td><td>0.7</td><td>1</td></tr><tr><td>Model parameters (million)</td><td>7 27.557</td><td>16 45.029</td><td>18 108.843</td><td>5</td><td>6.5 47.363</td></tr><tr><td rowspan=\"2\">Resolution: 10242</td><td>Training time (hour/10k iter)</td><td></td><td></td><td></td><td>44.359</td><td></td></tr><tr><td>Training vram (GB)</td><td>3.6</td><td>5</td><td>7</td><td>1.3</td><td>1.7</td></tr><tr><td rowspan=\"2\">Batch-size: 8</td><td>Model parameters (million)</td><td>12</td><td>23</td><td>36</td><td>9</td><td>10</td></tr><tr><td></td><td>27.591</td><td>45.15</td><td>109.229</td><td>44.377</td><td>47.413</td></tr></table>",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table. 1 presents the normalized cc figures of the models on Nvidia’s RTX 2080-Ti GPU, implemented using PyTorch (Paszke et al., 2017). Importantly, the slimed StyleGAN2 with $\\frac { 1 } { 4 }$ parameters cannot converge on the tested datasets at $1 0 2 4 ^ { 2 }$ resolution. We compare to the StyleGAN2 with $\\frac { 1 } { 2 }$ parameters (if not specifically mentioned) in the following experiments. ",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1 IMAGE SYNTHESIS PERFORMANCE ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Few-shot generation: Collecting large-scale image datasets are expensive, or even impossible, for a certain character, a genre, or a topic. On those few-shot datasets, a data-efficient model becomes especially valuable for the image generation task. In Table. 2 and Table. 3, we show that our model not only achieves superior performance on the few-shot datasets, but also much more computationalefficient than the compared methods. We save the checkpoints every 10k iterations during training and report the best FID from the checkpoints (happens at least after 15 hours of training for StyleGAN2 on all datasets). Among the 12 datasets, our model performs the best on 10 of them. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Please note that, due to the VRAM requirement for StyleGAN2 when trained on $1 0 2 4 ^ { 2 }$ resolution, we have to train the models in Table. 3 on a RTX TITAN GPU. In practice, 2080-TI and TITAN share a similar performance, and our model runs the same time on both GPUs. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/d1ce73964e63035d02350b6e1d311fc9c5cc6aaf050bc351a12b847561ec349c.jpg",
+        "table_caption": [
+            "Table 2: FID comparison at $2 5 6 ^ { 2 }$ resolution on few-sample datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"4\">Animal Face- Dog</td><td>Animal Face - Cat</td><td>Obama</td><td>Panda</td><td>Grumpy-cat</td></tr><tr><td colspan=\"3\">Image number</td><td>389</td><td>160</td><td>100</td><td>100</td><td>100</td></tr><tr><td rowspan=\"5\">Training time on one RTX 2080-Ti</td><td rowspan=\"5\">20 hour</td><td>StyleGAN2</td><td>58.85</td><td>42.44</td><td>46.87</td><td>12.06</td><td>27.08</td></tr><tr><td>StyleGAN2 finetune</td><td>61.03</td><td>46.07</td><td>35.75</td><td>14.5</td><td>29.34</td></tr><tr><td>Baseline 5 hour</td><td>108.19</td><td>150.3</td><td>62.74</td><td>15.4</td><td>42.13</td></tr><tr><td>Baseline+Skip</td><td>94.21</td><td>72.97</td><td>52.50</td><td>14.39</td><td>38.17</td></tr><tr><td>Baseline+decode Ours (B+Skip+decode)</td><td>56.25 50.66</td><td>36.74 35.11</td><td>44.34 41.05</td><td>10.12 10.03</td><td>29.38 26.65</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Training from scratch vs. fine-tuning: Fine-tuning from a pre-trained GAN (Mo et al., 2020; Noguchi & Harada, 2019; Wang et al., 2020) has been the go-to method for the image generation task on datasets with few samples. However, its performance highly depends on the semantic consistency between the new dataset and the available pre-trained model. According to Zhao et al., fine-tuning performs worse than training from scratch in most cases, when the content from the new dataset strays away from the original one. We confirm the limitation of current fine-tuning methods from Table. 2 and Table. 3, where we fine-tune StyleGAN2 trained on FFHQ use the Freeze-D method from Mo et al.. Among all the tested datasets, only Obama and Skull favor the fine-tuning method, making sense since the two sets share the most similar contents to FFHQ. ",
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+    },
+    {
+        "type": "text",
+        "text": "Module ablation study: We experiment with the two proposed modules in Table. 2, where both SLE (skip) and decoding-on- $. D$ (decode) can separately boost the model performance. It shows that the two modules are orthogonal to each other in improving the model performance, and the self-supervised $D$ makes the biggest contribution. Importantly, the baseline model and StyleGAN2 diverge fast after the listed training time. In contrast, our model is less likely to mode collapse among the tested datasets. Unlike the baseline model which usually model-collapse after trained for 10 hours, our model maintains a good synthesis quality and won’t collapse even after trained for 20 hours. We argue that it is the decoding regularization on $D$ that prevents the model from divergence. ",
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+    {
+        "type": "table",
+        "img_path": "images/95a9a1c7aa2c305703e8a420a823e6a7526911ddf1b3442642e8c7e235e93ee9.jpg",
+        "table_caption": [
+            "Table 3: FID comparison at $1 0 2 4 ^ { 2 }$ resolution on few-sample datasets. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td></td><td>Art Paintings</td><td>FFHQ</td><td>Flower</td><td>Pokemon</td><td>Anime Face</td><td>Skull</td><td>Shell</td></tr><tr><td colspan=\"3\">Image number</td><td>1000</td><td>1000</td><td>1000</td><td>800</td><td>120</td><td>100</td><td>60</td></tr><tr><td rowspan=\"2\">Training time on one RTX TITAN</td><td>24 hour</td><td>StyleGAN2 StyleGAN2 finetune</td><td>74.56 N/A</td><td>25.66 N/A</td><td>45.23 36.72</td><td>190.23 60.12</td><td>152.73 61.23</td><td>127.98 107.68</td><td>241.37</td></tr><tr><td>8 hour</td><td>Baseline Ours</td><td>62.27 45.08</td><td>38.35 24.45</td><td>42.25</td><td>67.86</td><td>101.23</td><td>186.45</td><td>220.45 202.32</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/2c061e97690d06f7f35601a46b80e6e8eaa43f40c6855dda2141a49ab03996ab.jpg",
+        "table_caption": [
+            "Table 4: FID comparison at $1 0 2 4 ^ { 2 }$ resolution on datasets with more images. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td>Dataset</td><td colspan=\"3\">Art Paintings</td><td colspan=\"3\">FFHQ</td><td colspan=\"3\">Nature Photograph</td></tr><tr><td>Image number</td><td>2k 5k</td><td>10k</td><td>2k</td><td>5k</td><td>10k</td><td>70k</td><td>2k</td><td>5k</td><td>10k</td></tr><tr><td colspan=\"2\">StyleGAN2</td><td>70.02</td><td>48.36</td><td>41.23</td><td>18.38</td><td>10.45</td><td>7.86</td><td>4.4</td><td>67.12</td><td>41.47 39.05</td></tr><tr><td colspan=\"2\">Baseline</td><td>60.02</td><td>51.23</td><td>49.38</td><td>36.45</td><td>27.86</td><td>25.12</td><td>17.62 71.47</td><td>66.05</td><td>62.28</td></tr><tr><td colspan=\"2\">Ours</td><td>44.57</td><td>43.27</td><td>42.53</td><td>19.01</td><td>17.93</td><td>16.45</td><td>12.38 52.47</td><td>45.07</td><td>43.65</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e9b66b10f6acd7c0348aa845238107c97571493087ae17bae8f6ea22b251201c.jpg",
+        "table_caption": [
+            "Table 5: LPIPS of back-tracking with $G$ "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Cat</td><td>Dog</td><td>FFHQ</td><td>Art</td></tr><tr><td>Resolution</td><td colspan=\"2\">256</td><td colspan=\"2\">1024</td></tr><tr><td>Baseline @ 20k iter</td><td>2.113</td><td>2.073</td><td>2.589</td><td>2.916</td></tr><tr><td>Baseline @ 40k iter</td><td>2.513</td><td>2.171</td><td>2.583</td><td>2.812</td></tr><tr><td>Ours @ 40k iter</td><td>1.821</td><td>1.918</td><td>2.425</td><td>2.624</td></tr><tr><td>Ours @ 80k iter</td><td>1.897</td><td>1.986</td><td>2.342</td><td>2.601</td></tr></table>",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/40e031b55ed0a6c6e2c80f2d7f05dbf26a14fdda2891f0c61671d35dead85d5f.jpg",
+        "image_caption": [
+            "Figure 6: Latent space back-tracking and interpolation. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/0498847b141c6f275366b0767aa1f64c58577802c511f13906ab75cd2e0b5460.jpg",
+        "table_caption": [
+            "Table 6: FID of self-supervisions for $D$ "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Art paintings</td><td>Nature photos</td></tr><tr><td>a. contrastive loss</td><td>47.14</td><td>57.04</td></tr><tr><td>b. predict aspect ratio</td><td>49.21</td><td>59.22</td></tr><tr><td>c.auto-encoding</td><td>42.53</td><td>43.65</td></tr><tr><td>d.a+b</td><td>46.02</td><td>54.23</td></tr><tr><td>e.a+b+c</td><td>44.21</td><td>47.65</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Training with more images: For more thorough evaluation, we also test our model on datasets with more sufficient training samples, as shown in Table. 4. We train the full StyleGAN2 for around five days on the Art and Photograph dataset with a batch-size of 16 on two TITAN RTX GPUs, and use the latest official figures on FFHQ from Zhao et al.. Instead, we train our model for only 24 hours, with a batch-size of 8 on a single 2080-Ti GPU. Specifically, for FFHQ with all 70000 images, we train our model with a larger batch-size of 32, to reflect an optimal performance of our model. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this test, we follow the common practice of computing FID by generating $5 0 \\mathrm { k }$ images and use the whole training set as the reference distribution. Note that StyleGAN2 has more than double the parameters compared to our model, and trained with a much larger batch-size on FFHQ. These factors contribute to its better performances when given enough training samples and computing power. Meanwhile, our model keeps up well with StyleGAN2 across all testings with a considerably lower computing budget, showing a compelling performance even on larger-scale datasets, and a consistent performance boost over the baseline model. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Qualitative results: The advantage of our model becomes more clear from the qualitative comparisons in Fig. 5. Given the same batch-size and training time, StyleGAN2 either converges slower or suffers from mode collapse. In contrast, our model consistently generates satisfactory images. Note that the best results from our model on Flower, Shell, and Pokemon only take three hours’ training, and for the rest three datasets, the best performance is achieved at training for eight hours. For StyleGAN2 on “shell”, “anime face”, and “Pokemon”, the images shown in Fig. 5 are already from the best epoch, which they match the scores in Table. 2 and Table. 3. For the rest of the datasets, the quality increase from StyleGAN2 is also limited given more training time. ",
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+    {
+        "type": "text",
+        "text": "4.2 MORE ANALYSIS AND APPLICATIONS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Testing mode collapse with back-tracking: From a well trained GAN, one can take a real image and invert it back to a vector in the latent space of $G$ , thus editing the image’s content by altering the back-tracked vector. Despite the various back-tracking methods (Zhu et al., 2016; Lipton & Tripathi, 2017; Zhu et al., 2020; Abdal et al., 2019), a well generalized $G$ is arguably as important for the good inversions. To this end, we show that our model, although trained on limited image samples, still gets a desirable performance on real image back-tracking. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In Table 5, we split the images from each dataset with a training/testing ratio of 9:1, and train $G$ on the training set. We compute a reconstruction error between all the images from the testing set and their inversions from $G$ , after the same update of 1000 iterations on the latent vectors (to prevent the vectors from being far off the normal distribution). The baseline model’s performance is getting worse with more training iterations, which reflects mode-collapse on $G$ . In contrast, our model gives better reconstructions with consistent performance over more training iterations. Fig. 6 presents the back-tracked examples (left-most and right-most samples in the middle panel) given the real images. ",
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+    {
+        "type": "image",
+        "img_path": "images/1b089ab672f80d73a3e1097e0c357e7475d1d83e616607b8144ca506fa52e69d.jpg",
+        "image_caption": [
+            "Figure 5: Qualitative comparison between our model and StyleGAN2 on $1 0 2 4 ^ { 2 }$ resolution datasets. The left-most panel shows the training images, and the right two panels show the uncurated samples from StyleGAN2 and our model. Both models are trained from scratch for 10 hours with a batch-size of 8. The samples are generated from the checkpoint with the lowest FID. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The smooth interpolations from the back-tracked latent vectors also suggest little mode-collapse of our $G$ (Radford et al., 2015; Zhao et al., 2020; Robb et al., 2020). ",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In addition, we show qualitative comparisons in appendix D, where our model maintains a good generation while StyleGAN2 and baseline are model-collapsed. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The self-supervision methods and generalization ability on $D$ : Apart from the auto-encoding training for $D$ , we show that $D$ with other common self-supervising strategies also boost GAN’s performance in our training settings. We test five self-supervision settings, as shown in Table 6, which all brings a substantial performance boost compared to the baseline model. Specifically, setting-a refers to contrastive learning which we treat each real image as a unique class and let $D$ classify them. For setting- $\\mathbf { \\sigma } . \\mathbf { b }$ , we train $D$ to predict the real image’s original aspect-ratio since they are reshaped to square when fed to $D$ . Setting-c is the method we employ in our model, which trains $D$ as an encoder with a decoder to reconstruct real images. To better validate the benefit of self-supervision on $D$ , all the testings are conducted on full training sets with 10000 images, with a batch-size of 8 to be consistent with Table 4. We also tried training with a larger batch-size of 16, which the results are consistent to the batch-size of 8. ",
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/2da992c184746b333c41d52b16369f17b9f833b9e36850835fc27919e5604135.jpg",
+        "image_caption": [
+            "Figure 7: Style-mixing results from our model trained for only 5 hours on single GPU. "
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Interestingly, according to Table 6, while setting-c performs the best, combining it with the rest two settings lead to a clear performance downgrade. The similar behavior can be found on some other self-supervision settings, e.g. when follow Chen et al. (2019) with a ”rotation-predicting” task on art-paintings and FFHQ datasets, we observe a performance downgrade even compared to the baseline model. We hypothesis the reason being that the auto-encoding forces $D$ to pay attention to more areas of the input image, thus extracts a more comprehensive feature-map to describe the input image (for a good reconstruction). In contrast, a classification task does not guarantee $D$ to cover the whole image. Instead, the task drives $D$ to only focus on small regions because the model can find class cues from small regions of the images. Focusing on limited regions (i.e., react to limited image patterns) is a typical overfitting behavior, which is also widely happening for $D$ in vanilla GANs. More discussion can be found in appendix B. ",
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "Style mixing like StyleGAN. With the channel-wise excitation module, our model gets the same functionality as StyleGAN: it learns to disentangle the images’ high-level semantic attributes (style and content) in an unsupervised way, from $G$ ’s conv-layers at different scales. The style-mixing results are displayed in Fig. 7, where the top three datasets are $2 5 6 \\times 2 5 6$ resolution, and the bottom three are $1 0 2 4 \\times 1 0 2 4$ resolution. While StyleGAN2 suffers from converging on the bottom high-resolution datasets, our model successfully learns the style representations along the channel dimension on the “excited” layers (i.e., for feature-maps on $2 5 6 \\times 2 5 6$ , $5 1 2 \\times 5 1 2$ resolution). Please refer to appendix A and C for more information on SLE and style-mixing. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "5 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We introduce two techniques that stabilize the GAN training with an improved synthesis quality, given sub-hundred high-fidelity images and a limited computing resource. On thirteen datasets with a diverse content variation, we show that a skip-layer channel-wise excitation mechanism (SLE) and a self-supervised regularization on the discriminator significantly boost the synthesis performance of GAN. Both proposed techniques require minor changes to a vanilla GAN, enhancing GAN’s practicality with a desirable plug-and-play property. We hope this work can benefit downstream tasks of GAN and provide new study perspectives for future research. ",
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            102,
+            287,
+            117
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Rameen Abdal, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE international conference on computer vision, pp. 4432–4441, 2019. ",
+        "bbox": [
+            174,
+            126,
+            823,
+            169
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Martin Arjovsky and Leon Bottou. Towards principled methods for training generative adversarial ´ networks. In International Conference on Learning Representations, 2017. ",
+        "bbox": [
+            171,
+            178,
+            823,
+            208
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Martin Arjovsky, Soumith Chintala, and Leon Bottou. Wasserstein generative adversarial networks. ´ In International conference on machine learning, pp. 214–223. PMLR, 2017. ",
+        "bbox": [
+            171,
+            217,
+            823,
+            246
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "David Berthelot, Thomas Schumm, and Luke Metz. Began: Boundary equilibrium generative adversarial networks. arXiv preprint arXiv:1703.10717, 2017. ",
+        "bbox": [
+            171,
+            255,
+            823,
+            285
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale GAN training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2019. ",
+        "bbox": [
+            173,
+            294,
+            823,
+            323
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ting Chen, Xiaohua Zhai, Marvin Ritter, Mario Lucic, and Neil Houlsby. Self-supervised gans via auxiliary rotation loss. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 12154–12163, 2019. ",
+        "bbox": [
+            176,
+            332,
+            825,
+            376
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yann N Dauphin, Angela Fan, Michael Auli, and David Grangier. Language modeling with gated convolutional networks. In International conference on machine learning, pp. 933–941, 2017. ",
+        "bbox": [
+            173,
+            383,
+            821,
+            414
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Emily L Denton, Soumith Chintala, Rob Fergus, et al. Deep generative image models using a laplacian pyramid of adversarial networks. In Advances in neural information processing systems, pp. 1486–1494, 2015. ",
+        "bbox": [
+            171,
+            422,
+            823,
+            465
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ahmed Elgammal, Marian Mazzone, et al. Artists, artificial intelligence and machine-based creativity in playform. Artnodes, (26):1–8, 2020. ",
+        "bbox": [
+            173,
+            476,
+            823,
+            505
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. In Advances in neural information processing systems, pp. 2672–2680, 2014. ",
+        "bbox": [
+            173,
+            513,
+            823,
+            558
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Priya Goyal, Dhruv Mahajan, Abhinav Gupta, and Ishan Misra. Scaling and benchmarking selfsupervised visual representation learning. In Proceedings of the IEEE International Conference on Computer Vision, pp. 6391–6400, 2019. ",
+        "bbox": [
+            174,
+            566,
+            825,
+            609
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. In Advances in neural information processing systems, pp. 5767–5777, 2017. ",
+        "bbox": [
+            173,
+            618,
+            825,
+            661
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yong Guo, Qi Chen, Jian Chen, Qingyao Wu, Qinfeng Shi, and Mingkui Tan. Auto-embedding generative adversarial networks for high resolution image synthesis. IEEE Transactions on Multimedia, 21(11):2726–2737, 2019. ",
+        "bbox": [
+            174,
+            671,
+            825,
+            714
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770–778, 2016. ",
+        "bbox": [
+            173,
+            723,
+            825,
+            767
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9729–9738, 2020. ",
+        "bbox": [
+            173,
+            776,
+            823,
+            820
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Dan Hendrycks, Mantas Mazeika, Saurav Kadavath, and Dawn Song. Using self-supervised learning can improve model robustness and uncertainty. In Advances in Neural Information Processing Systems, pp. 15663–15674, 2019. ",
+        "bbox": [
+            176,
+            828,
+            823,
+            871
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. In Advances in neural information processing systems, pp. 6626–6637, 2017. ",
+        "bbox": [
+            174,
+            882,
+            825,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jie Hu, Li Shen, and Gang Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 7132–7141, 2018. ",
+        "bbox": [
+            169,
+            103,
+            825,
+            133
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Xun Huang and Serge Belongie. Arbitrary style transfer in real-time with adaptive instance normalization. In Proceedings of the IEEE International Conference on Computer Vision, pp. 1501– 1510, 2017. ",
+        "bbox": [
+            173,
+            141,
+            821,
+            183
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Xun Huang, Yixuan Li, Omid Poursaeed, John Hopcroft, and Serge Belongie. Stacked generative adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 5077–5086, 2017. ",
+        "bbox": [
+            174,
+            191,
+            823,
+            236
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Longlong Jing and Yingli Tian. Self-supervised visual feature learning with deep neural networks: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020. ",
+        "bbox": [
+            176,
+            243,
+            821,
+            273
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Animesh Karnewar and Oliver Wang. Msg-gan: Multi-scale gradients for generative adversarial networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 7799–7808, 2020. ",
+        "bbox": [
+            174,
+            281,
+            825,
+            324
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tero Karras, Timo Aila, Samuli Laine, and Jaakko Lehtinen. Progressive growing of GANs for improved quality, stability, and variation. In International Conference on Learning Representations, 2018. ",
+        "bbox": [
+            174,
+            333,
+            825,
+            376
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4401–4410, 2019. ",
+        "bbox": [
+            174,
+            383,
+            825,
+            428
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tero Karras, Miika Aittala, Janne Hellsten, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Training generative adversarial networks with limited data. arXiv preprint arXiv:2006.06676, 2020a. ",
+        "bbox": [
+            173,
+            435,
+            823,
+            465
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Tero Karras, Samuli Laine, Miika Aittala, Janne Hellsten, Jaakko Lehtinen, and Timo Aila. Analyzing and improving the image quality of stylegan. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8110–8119, 2020b. ",
+        "bbox": [
+            173,
+            473,
+            825,
+            516
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Anders Boesen Lindbo Larsen, Søren Kaae Sønderby, Hugo Larochelle, and Ole Winther. Autoencoding beyond pixels using a learned similarity metric. In International conference on machine learning, pp. 1558–1566. PMLR, 2016. ",
+        "bbox": [
+            174,
+            525,
+            825,
+            568
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jae Hyun Lim and Jong Chul Ye. Geometric gan. arXiv preprint arXiv:1705.02894, 2017. ",
+        "bbox": [
+            166,
+            575,
+            764,
+            592
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Zachary C. Lipton and Subarna Tripathi. Precise recovery of latent vectors from generative adversarial networks. ICLR workshop, 2017. ",
+        "bbox": [
+            171,
+            599,
+            825,
+            630
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Bingchen Liu, Kunpeng Song, Yizhe Zhu, Gerard de Melo, and Ahmed Elgammal. Time: Text and image mutual-translation adversarial networks. In Thirty-Fifth AAAI Conference on Artificial Intelligence, 2021. ",
+        "bbox": [
+            173,
+            637,
+            825,
+            680
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Lars Mescheder, Andreas Geiger, and Sebastian Nowozin. Which training methods for gans do actually converge? In International conference on machine learning, pp. 3481–3490. PMLR, 2018. ",
+        "bbox": [
+            171,
+            689,
+            825,
+            732
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Takeru Miyato, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. Spectral normalization for generative adversarial networks. In International Conference on Learning Representations, 2018. ",
+        "bbox": [
+            174,
+            739,
+            825,
+            784
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sangwoo Mo, Minsu Cho, and Jinwoo Shin. Freeze discriminator: A simple baseline for fine-tuning gans. arXiv preprint arXiv:2002.10964, 2020. ",
+        "bbox": [
+            169,
+            791,
+            825,
+            821
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mkhuseli Ngxande, Jules-Raymond Tapamo, and Michael Burke. Depthwisegans: Fast training generative adversarial networks for realistic image synthesis. In 2019 Southern African Universities Power Engineering Conference/Robotics and Mechatronics/Pattern Recognition Association of South Africa (SAUPEC/RobMech/PRASA), pp. 111–116. IEEE, 2019. ",
+        "bbox": [
+            173,
+            829,
+            825,
+            887
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Maria-Elena Nilsback and Andrew Zisserman. A visual vocabulary for flower classification. In IEEE Conference on Computer Vision and Pattern Recognition, volume 2, pp. 1447–1454, 2006. ",
+        "bbox": [
+            173,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Atsuhiro Noguchi and Tatsuya Harada. Image generation from small datasets via batch statistics adaptation. In Proceedings of the IEEE International Conference on Computer Vision, pp. 2750– 2758, 2019. ",
+        "bbox": [
+            173,
+            103,
+            823,
+            146
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017. ",
+        "bbox": [
+            173,
+            154,
+            823,
+            196
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Alec Radford, Luke Metz, and Soumith Chintala. Unsupervised representation learning with deep convolutional generative adversarial networks. arXiv preprint arXiv:1511.06434, 2015. ",
+        "bbox": [
+            173,
+            205,
+            823,
+            234
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Esther Robb, Wen-Sheng Chu, Abhishek Kumar, and Jia-Bin Huang. Few-shot adaptation of generative adversarial networks. arXiv preprint arXiv:2010.11943, 2020. ",
+        "bbox": [
+            173,
+            242,
+            823,
+            271
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Zhangzhang Si and Song-Chun Zhu. Learning hybrid image templates (hit) by information projection. IEEE Transactions on pattern analysis and machine intelligence, 34(7):1354–1367, 2011. ",
+        "bbox": [
+            173,
+            279,
+            823,
+            309
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Samarth Sinha, Han Zhang, Anirudh Goyal, Yoshua Bengio, Hugo Larochelle, and Augustus Odena. Small-gan: Speeding up gan training using core-sets. arXiv preprint arXiv:1910.13540, 2019. ",
+        "bbox": [
+            173,
+            315,
+            821,
+            345
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dustin Tran, Rajesh Ranganath, and David M Blei. Deep and hierarchical implicit models. arXiv preprint arXiv:1702.08896, 7(3):13, 2017. ",
+        "bbox": [
+            171,
+            353,
+            823,
+            382
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ngoc-Trung Tran, Viet-Hung Tran, Bao-Ngoc Nguyen, Linxiao Yang, and Ngai-Man Man Cheung. Self-supervised gan: Analysis and improvement with multi-class minimax game. Advances in Neural Information Processing Systems, 32:13253–13264, 2019. ",
+        "bbox": [
+            174,
+            390,
+            823,
+            434
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky. Instance normalization: The missing ingredient for fast stylization. arXiv preprint arXiv:1607.08022, 2016. ",
+        "bbox": [
+            171,
+            440,
+            823,
+            470
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Ting-Chun Wang, Ming-Yu Liu, Jun-Yan Zhu, Andrew Tao, Jan Kautz, and Bryan Catanzaro. Highresolution image synthesis and semantic manipulation with conditional gans. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 8798–8807, 2018. ",
+        "bbox": [
+            176,
+            478,
+            825,
+            522
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yaxing Wang, Abel Gonzalez-Garcia, David Berga, Luis Herranz, Fahad Shahbaz Khan, and Joost van de Weijer. Minegan: effective knowledge transfer from gans to target domains with few images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9332–9341, 2020. ",
+        "bbox": [
+            174,
+            529,
+            826,
+            585
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Yasin Yazıcı, Chuan-Sheng Foo, Stefan Winkler, Kim-Hui Yap, Georgios Piliouras, and Vijay Chandrasekhar. The unusual effectiveness of averaging in gan training. arXiv preprint arXiv:1806.04498, 2018. ",
+        "bbox": [
+            174,
+            594,
+            825,
+            637
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Dan Zhang and Anna Khoreva. Pa-gan: Improving gan training by progressive augmentation. 2018. ",
+        "bbox": [
+            169,
+            645,
+            821,
+            661
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Han Zhang, Tao Xu, Hongsheng Li, Shaoting Zhang, Xiaogang Wang, Xiaolei Huang, and Dimitris N Metaxas. Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. In Proceedings of the IEEE international conference on computer vision, pp. 5907–5915, 2017. ",
+        "bbox": [
+            174,
+            667,
+            825,
+            724
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 586–595, 2018. ",
+        "bbox": [
+            173,
+            733,
+            825,
+            776
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Junbo Zhao, Michael Mathieu, and Yann LeCun. Energy-based generative adversarial network. arXiv preprint arXiv:1609.03126, 2016. ",
+        "bbox": [
+            174,
+            784,
+            823,
+            813
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Shengyu Zhao, Zhijian Liu, Ji Lin, Jun-Yan Zhu, and Song Han. Differentiable augmentation for data-efficient gan training. arXiv preprint arXiv:2006.10738, 2020. ",
+        "bbox": [
+            173,
+            820,
+            823,
+            851
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Jiachen Zhong, Xuanqing Liu, and Cho-Jui Hsieh. Improving the speed and quality of gan by adversarial training. arXiv preprint arXiv:2008.03364, 2020. ",
+        "bbox": [
+            173,
+            858,
+            821,
+            887
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Jiapeng Zhu, Yujun Shen, Deli Zhao, and Bolei Zhou. In-domain gan inversion for real image editing. arXiv preprint arXiv:2004.00049, 2020. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Jun-Yan Zhu, Philipp Krahenb ¨ uhl, Eli Shechtman, and Alexei A Efros. Generative visual manipu- ¨ lation on the natural image manifold. In European conference on computer vision, pp. 597–613. Springer, 2016. ",
+        "bbox": [
+            173,
+            103,
+            825,
+            146
+        ],
+        "page_idx": 12
+    }
+]

parse/train/HJOQ7MgAW/HJOQ7MgAW.md

@@ -0,0 +1,226 @@
+# LONG SHORT-TERM MEMORY AS A DYNAMICALLYCOMPUTED ELEMENT-WISE WEIGHTED SUM
+
+Anonymous authors Paper under double-blind review
+
+# ABSTRACT
+
+Long short-term memory networks (LSTMs) were introduced to combat vanishing gradients in simple recurrent neural networks (S-RNNs) by augmenting them with additive recurrent connections controlled by gates. We present an alternate view to explain the success of LSTMs: the gates themselves are powerful recurrent models that provide more representational power than previously appreciated. We do this by showing that the LSTM’s gates can be decoupled from the embedded S-RNN, producing a restricted class of RNNs where the main recurrence computes an element-wise weighted sum of context-independent functions of the inputs. Experiments on a range of challenging NLP problems demonstrate that the simplified gate-based models work substantially better than S-RNNs, and often just as well as the original LSTMs, strongly suggesting that the gates are doing much more in practice than just alleviating vanishing gradients.
+
+# 1 INTRODUCTION
+
+Long short-term memory networks (LSTM) (Hochreiter & Schmidhuber, 1997) have become the de-facto recurrent neural network (RNN) for learning representations of sequences in many research areas, including natural language processing (NLP). Like simple recurrent neural networks (SRNNs) (Elman, 1990), LSTMs are able to learn non-linear functions of arbitrary-length input sequences. However, they also introduce an additional memory cell to mitigate the vanishing gradient problem (Hochreiter, 1991; Bengio et al., 1994). This memory is controlled by a mechanism of gates, whose additive connections allow long-distance dependencies to be learned more easily during backpropagation. While this view is mathematically accurate, in this paper we argue that it does not provide a complete picture of why LSTMs work in practice.
+
+We present an alternate view to explain the success of LSTMs: the gates themselves are powerful recurrent models that provide more representational power than previously appreciated. To demonstrate this, we first show that LSTMs can be seen as a combination of two recurrent models: (1) an S-RNN, and (2) an element-wise weighted sum of the S-RNN’s outputs over time, which is implicitly computed by the gates. We hypothesize that, for many practical NLP problems, the weighted sum serves as the main modeling component. The S-RNN, while theoretically expressive, is in practice only a minor contributor that clouds the mathematical clarity of the model. By replacing the S-RNN with a context-independent function of the input, we arrive at a much more restricted class of RNNs, where the main recurrence is via the element-wise weighted sums that the gates are computing.
+
+We test our hypothesis on NLP problems, where LSTMs are wildly popular at least in part due to their ability to model crucial language phenomena such as word order (Adi et al., 2017), syntactic structure (Linzen et al., 2016), and even long-range semantic dependencies (He et al., 2017). We consider four challenging tasks: language modeling, question answering, dependency parsing, and machine translation. Experiments show that while removing the gates from an LSTM can severely hurt performance, replacing the S-RNN with a simple linear transformation of the input results in minimal or no loss in model performance. We further show that in many cases, LSTMs can be further simplified by removing the output gate, arriving at an even more transparent architecture, where the output is a context-independent function of the weighted sum. Together, these results suggest that the gates’ ability to compute an element-wise weighted sum, rather than the non-linear transition dynamics of S-RNNs, are the driving force behind LSTM’s success.
+
+# 2 THE MEMORY CELL COMPUTES AN ELEMENT-WISE WEIGHTED SUM
+
+LSTMs are typically motivated as an augmentation of simple RNNs (S-RNNs), defined as follows:
+
+$$
+\pmb { h } _ { t } = \operatorname { t a n h } ( \pmb { W } _ { h h } \pmb { h } _ { t - 1 } + \pmb { W } _ { h x } \pmb { x } _ { t } + \pmb { b } _ { h } )
+$$
+
+S-RNNs suffer from the vanishing gradient problem (Hochreiter, 1991; Bengio et al., 1994) due to compounding multiplicative updates of the hidden state. By introducing a memory cell and an output layer that are controlled by a set of gates, LSTMs enable shortcuts through which gradients can flow easily when learning with backpropagation. This mechanism enables learning of long-distance dependencies while preserving the expressive power of recurrent non-linear transformations provided by S-RNNs.
+
+Rather than viewing the gates as simply an auxiliary mechanism to address a learning problem, we present an alternate view that emphasizes their modeling strengths. We argue that the LSTM should be interpreted as a hybrid of two distinct recurrent architectures: (1) the S-RNN which provides multiplicative connections across timesteps, and (2) the memory cell which provides additive connections across timesteps. On top of these recurrences, an output layer is included that simply squashes and filters the memory cell at each step.
+
+Throughout this paper, let $\{ \pmb { x } _ { 1 } , \ldots , \pmb { x } _ { n } \}$ be the sequence of input vectors, $\{ h _ { 1 } , \ldots , h _ { n } \}$ be the sequence of output vectors, and $\{ c _ { 1 } , \ldots , c _ { n } \}$ be the memory cell’s states. Then, given the basic LSTM definition below, we can formally identify three sub-components.
+
+$$
+\begin{array} { r l } & { \tilde { c } _ { t } = \mathrm { t a n h } ( W _ { c h } h _ { t - 1 } + W _ { c x } { \boldsymbol x } _ { t } + { \boldsymbol b } _ { c } ) } \\ & { ~ i _ { t } = \sigma ( W _ { i h } h _ { t - 1 } + W _ { i x } { \boldsymbol x } _ { t } + { \boldsymbol b } _ { i } ) } \\ & { f _ { t } = \sigma ( W _ { f h } h _ { t - 1 } + W _ { f x } { \boldsymbol x } _ { t } + { \boldsymbol b } _ { f } ) } \\ & { c _ { t } = i _ { t } \circ \tilde { c } _ { t } + f _ { t } \circ c _ { t - 1 } } \\ & { o _ { t } = \sigma ( W _ { o h } h _ { t - 1 } + W _ { o x } { \boldsymbol x } _ { t } + { \boldsymbol b } _ { o } ) } \\ & { h _ { t } = o _ { t } \circ \mathrm { t a n h } ( c _ { t } ) } \end{array}
+$$
+
+Content Layer (Equation 2) We refer to $\widetilde { c } _ { t }$ as the content layer, which is the output of an S-RNN. eEvaluating the need for the multiplicative recurrent connections in this content layer is the focus of this work. The content layer is passed to the memory cell, which decides which parts of it to store.
+
+Memory Cell (Equations 3-5) The memory cell $c _ { t }$ is controlled by two gates. The input gate $\mathbf { \delta } _ { i _ { t } }$ controls what part of the content $( \widetilde { c } _ { t } )$ is written to the memory, while the forget gate $f _ { t }$ controls what epart of the memory is deleted by filtering the previous state of the memory $( c _ { t - 1 } )$ . Writing to the memory is done by adding the filtered content $( i _ { t } \circ \widetilde { c } _ { t } )$ to the retained memory $( f _ { t } \circ c _ { t - 1 } )$ .
+
+Output Layer (Equations 6-7) The output layer $h _ { t }$ passes the memory cell through a tanh activation function and uses an output gate $\mathbf { } _ { o _ { t } }$ to read selectively from the squashed memory cell.
+
+Our goal is to study how much each of these components contribute to the empirical performance of LSTMs. In particular, it is worth considering the memory cell in more detail to reveal why it could serve as a standalone powerful model of long-distance context. It is possible to show that it implicitly computes an element-wise weighted sum of all the previous content layers by expanding the recurrence relation in equation (5):
+
+$$
+\begin{array} { l } { { \displaystyle c _ { t } = \dot { a } _ { t } \circ \widetilde c _ { t } + f _ { t } \circ c _ { t - 1 } } } \\ { { \displaystyle \quad = \sum _ { j = 0 } ^ { t } \left( \dot { a } _ { j } \circ \prod _ { k = j + 1 } ^ { t } f _ { k } \right) \circ \widetilde c _ { j } } } \\ { { \displaystyle \quad = \sum _ { j = 0 } ^ { t } w _ { j } ^ { t } \circ \widetilde c _ { j } } } \end{array}
+$$
+
+Each weight $\boldsymbol { w } _ { j } ^ { t }$ is a product of the input gate $i _ { j }$ (when its respective input $\widetilde { c } _ { j }$ was read) and every subsequent forget gate $f _ { k }$ e. An interesting property of these weights is that, like the gates, they are also soft element-wise binary filters.1
+
+This sum is similar to recent architectures that rely on self-attention to learn context-dependent word representations (Cheng et al., 2016; Parikh et al., 2016; Vaswani et al., 2017). There are two major differences from self-attention: (1) instead of computing a weighted sum for each attention head, a separate weighted sum is computed for every dimension of the memory cell, (2) the weighted sum is accumulated with a dynamic program, enabling a linear rather than quadratic complexity in comparison to self-attention.
+
+# 3 MEMORY CELLS ARE POWERFUL STANDALONE MODELS
+
+The restricted space of element-wise weighted sums allows for easier mathematical analysis, visualization, and perhaps even learnability. However, constrained function spaces are also less expressive, and a natural question is whether these models will work well for NLP problems that need highly contextualized word representations. We hypothesize that the memory cell (which computes weighted sums) can function as a standalone contextualizer. To test this hypothesis, we present several simplifications of the LSTM’s architecture (Section 3.1), and show on a variety of NLP benchmarks that there is a qualitative performance difference between models that contain a memory cell and those that do not (Section 3.2). We conclude that the content and output layers are relatively minor contributors, and that the space of element-wise weighted sums is sufficiently powerful to compete with fully parameterized LSTMs (Section 3.3).
+
+# 3.1 SIMPLIFIED MODELS
+
+The modeling power of LSTMs is commonly assumed to derive from the S-RNN in the content layer, with the rest of the model acting as a learning aid to bypass the vanishing gradient problem. We first isolate the S-RNN by ablating the gates (denoted as $L S T M - G A T E S$ for consistency).
+
+To test whether the memory cell has enough modeling power of its own, we take an LSTM and replace the S-RNN in the content layer from Equation 2 with a simple linear transformation, creating the LSTM – S-RNN model:
+
+$$
+\begin{array} { r l } & { \tilde { c } _ { t } = W _ { c x } { \boldsymbol x } _ { t } } \\ & { i _ { t } = \sigma ( W _ { i h } h _ { t - 1 } + W _ { i x } { \boldsymbol x } _ { t } + b _ { i } ) } \\ & { f _ { t } = \sigma ( W _ { f h } h _ { t - 1 } + W _ { f x } { \boldsymbol x } _ { t } + b _ { f } ) } \\ & { c _ { t } = i _ { t } \circ \tilde { c } _ { t } + f _ { t } \circ c _ { t - 1 } } \\ & { o _ { t } = \sigma ( W _ { o h } h _ { t - 1 } + W _ { o x } { \boldsymbol x } _ { t } + b _ { o } ) } \\ & { h _ { t } = o _ { t } \circ \operatorname { t a n h } ( c _ { t } ) } \end{array}
+$$
+
+We further simplify the LSTM by removing the output gate from Equation 7, leaving only the activation function in the output layer $( L S T M - S - R N N - O U T )$ :
+
+$$
+\begin{array} { r l } & { \tilde { c } _ { t } = W _ { c x } { \boldsymbol x } _ { t } } \\ & { i _ { t } = \sigma ( W _ { i h } h _ { t - 1 } + W _ { i x } { \boldsymbol x } _ { t } + b _ { i } ) } \\ & { f _ { t } = \sigma ( W _ { f h } h _ { t - 1 } + W _ { f x } { \boldsymbol x } _ { t } + b _ { f } ) } \\ & { c _ { t } = i _ { t } \circ \tilde { c } _ { t } + f _ { t } \circ c _ { t - 1 } } \\ & { h _ { t } = \operatorname { t a n h } ( c _ { t } ) } \end{array}
+$$
+
+After removing the S-RNN and the output gate from the LSTM, the entire ablated model can be written in a modular, compact form:
+
+$$
+\pmb { h } _ { t } = \mathrm { O U T P U T } \Big ( \sum _ { j = 0 } ^ { t } \pmb { w } _ { j } ^ { t } \circ \mathrm { C O N T E N T } ( \pmb { x } _ { j } ) \Big )
+$$
+
+where the content layer CONTENT $( \cdot )$ and the output layer OUTPUT $( \cdot )$ are both context-independent functions, making the entire model highly constrained and interpretable. The complexity of modeling contextual information is needed only for computing the weights $\boldsymbol { w } _ { j } ^ { t }$ . As we will see in Section 3.2, both of these ablations perform on par with LSTMs on language modeling, question answering, dependency parsing, and machine translation.
+
+There are many other models that can be expressed in the weighted-sum form (Equation 11). In this work, we focus on the closest variant of LSTM that satisfies this property; removing the S-RNN and the output gate is sufficient for the content and output functions to be context-independent. We leave more thorough investigations into the necessity of the remaining architecture as future work.
+
+# 3.2 EXPERIMENTS
+
+We compare model performance on four NLP tasks, with an experimental setup that is lenient towards LSTMs and harsh towards its simplifications. In each case, we use existing implementations and previously reported hyperparameter settings. Since these settings were tuned for LSTMs, any simplification that performs equally to (or better than) LSTMs under these LSTM-friendly settings provides strong evidence that the ablated component is not a contributing factor. For each task we also report the mean and standard deviation of 5 runs of the LSTM settings to demonstrate the typical variance observed due to training with different random initializations.2 The code and settings to replicate these experiments are publicly available.3
+
+# 3.2.1 LANGUAGE MODELING
+
+We evaluate on two language modeling datasets: the Penn Treebank (PTB) (Marcus et al., 1993), and Google’s billion-word benchmark (BWB) (Chelba et al., 2014). PTB contains approximately 1M tokens over a vocabulary of 10K words. We used the implementation of Zaremba et al. (2014) while replacing any invocation of LSTMs with simpler models. We tested two of their configurations: medium, which uses two layers of 650-dimension LSTMs, and large, which uses two layers of 1500-dimension LSTMs.
+
+BWB is about a thousand times larger than PTB, and uses a more diverse vocabulary of 800K words. Using the implementation of Józefowicz et al. (2016), we tested their LSTM-2048-512 configuration. Our experiments use exactly the same hyperparameters (dimensions, dropout, learning rates, etc) that were originally tuned for LSTMs (Józefowicz et al., 2016). Following their implementation, we project the hidden state at each time step down to 512 dimensions. Due to the enormous size of this dataset, we stopped training after 5 epochs.
+
+Table 1 shows overall model performance. In all three cases, replacing the LSTM’s content layer with a linear transformation results in small differences in perplexity. The most important result is that the small fluctuations in performance between the various gated architectures are minuscule in comparison to the enormous gap between the S-RNN $( L S T M - G A T E S )$ and the original LSTM. This striking difference strongly supports our hypothesis that the weighted sums computed by the gates – not the S-RNN – is the recurrent model that contributes mostly strongly to the final performance.
+
+# 3.2.2 QUESTION ANSWERING
+
+For question answering, we use two different QA systems on the Stanford question answering dataset (SQuAD) (Rajpurkar et al., 2016): the Bidirectional Attention Flow model (BiDAF) (Seo et al., 2016) and DrQA (Chen et al., 2017). BiDAF contains 3 LSTMs, which are referred to as the phrase layer, the modeling layer, and the span end encoder. Our experiments replace each of these LSTMs with their simplified counterparts. We directly use the implementation of BiDAF from AllenNLP (Gardner et al., 2017), and all experiments reuse the existing hyperparameters that were tuned for LSTMs. Likewise, we use an open-source implementation of $\mathrm { \dot { D r } Q A } ^ { 4 }$ and replace only the LSTMs, while leaving everything else intact.
+
+Table 2 shows that all the gated models do comparably. Most importantly, ablating the S-RNN from the LSTM has a minor effect in comparison to the drop in performance when ablating the gates.
+
+# 3.2.3 DEPENDENCY PARSING
+
+For dependency parsing, we use the Deep Biaffine Dependency Parser (Dozat & Manning, 2016), which relies on stacked bidirectional LSTMs to learn context-sensitive word embeddings for determining arcs between a pair of words. We directly use their released implementation, which is evaluated on the Universal Dependencies English Web Treebank v1.3 (Silveira et al., 2014). In our experiments, we use the existing hyperparameters and only replace the LSTMs with the simplified architectures.
+
+Table 1: The performance of simplified LSTM architectures on language modeling benchmarks, measured by perplexity.   
+
+<table><tr><td>Configuration</td><td>Model</td><td>Perplexity</td></tr><tr><td rowspan="4">PTB</td><td>LSTM</td><td>83.9 ± 0.3</td></tr><tr><td>- GATES</td><td>140.9</td></tr><tr><td>- S-RNN</td><td>80.5</td></tr><tr><td>- S-RNN-OUT</td><td>81.6</td></tr><tr><td rowspan="4">PTB (Large Model)</td><td>LSTM</td><td>78.8± 0.2</td></tr><tr><td>- GATES</td><td>126.1</td></tr><tr><td>- S-RNN</td><td>76.0</td></tr><tr><td>- S-RNN -OUT</td><td>78.5</td></tr><tr><td rowspan="4">BWB</td><td>LSTM (J6zefowicz et al., 2016)</td><td>47.5</td></tr><tr><td>- GATES</td><td>82.2</td></tr><tr><td>- S-RNN</td><td>45.4</td></tr><tr><td>- S-RNN-OUT</td><td>47.9</td></tr></table>
+
+Table 2: The performance of simplified LSTM architectures on the question answering benchmark, SQuAD, measured by exact match (EM) and span overlap (F1).   
+
+<table><tr><td>System</td><td>Model</td><td>EM</td><td>F1</td></tr><tr><td rowspan="5">BiDAF</td><td>LSTM</td><td>67.9 ± 0.3</td><td>77.5 ± 0.2</td></tr><tr><td>- GATES</td><td>62.9</td><td>73.3</td></tr><tr><td>- S-RNN</td><td>68.4</td><td>78.2</td></tr><tr><td>- S-RNN-OUT</td><td>67.4</td><td>77.2</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan="4">DrQA</td><td>LSTM</td><td>68.8 ± 0.2</td><td>78.2 ± 0.2</td></tr><tr><td>- GATES</td><td>56.4</td><td>66.5</td></tr><tr><td>- S-RNN</td><td>67.7</td><td>77.0</td></tr><tr><td>- S-RNN -OUT</td><td>67.0</td><td>76.2</td></tr></table>
+
+Table 3: The performance of simplified LSTM architectures on the universal dependencies parsing benchmark, measured by unlabeled attachment score (UAS) and labeled attachment score (LAS).   
+
+<table><tr><td>Model</td><td>UAS</td><td>LAS</td></tr><tr><td>LSTM</td><td>90.60 ± 0.21</td><td>88.05 ± 0.33</td></tr><tr><td>- GATES</td><td>87.75</td><td>84.61</td></tr><tr><td>- S-RNN</td><td>90.77</td><td>88.49</td></tr><tr><td>- S-RNN-OUT</td><td>90.70</td><td>88.31</td></tr></table>
+
+We observe the same pattern in the ablations for dependency parsing. The differences in performance between the gated models fall within the differences between multiple experiments with LSTMs. Consistent with ablation results from other tasks, removing the gating mechanisms causes a 3-4 point drop in performance.
+
+# 3.2.4 MACHINE TRANSLATION
+
+For machine translation, we used OpenNMT (Klein et al., 2017) to train English to German translation models on the multi-modal benchmarks from WMT 2016 (used in OpenNMT’s readme file). We use OpenNMT’s default model and hyperparameters, replacing the stacked bidirectional LSTM of its
+
+<table><tr><td>Model</td><td>BLEU</td></tr><tr><td>LSTM</td><td>35.95</td></tr><tr><td>- GATES</td><td>12.22</td></tr><tr><td>- S-RNN</td><td>36.66</td></tr><tr><td>- S-RNN-OUT</td><td>36.39</td></tr></table>
+
+Table 4: The performance of simplified LSTM architectures on the WMT 2016 multi-modal English to German translation benchmark, measured by BLEU.
+
+encoder with the simplified architectures. Table 4 shows that while models containing memory cells perform more-or-less on par, removing the memory cell yields a substantial performance drop.
+
+# 3.3 DISCUSSION
+
+In the above experiments, we show three major ablations of the LSTM. In the S-RNN experiments $( L S T M - G A T E S )$ , we ablate the memory cell and the output layer. In the LSTM �� S-RNN and LSTM – $S – R M N - O U T$ experiments, we ablate the S-RNN. As consistent with previous literature, removing the memory cell degrades performance drastically. In contrast, removing the S-RNN makes little to no difference in the final performance, suggesting that the memory cell alone is largely responsible for the success of LSTMs in NLP. The results also confirm our hypothesis that weighted sums of context words is a powerful, yet more interpretable, model of contextual information.
+
+# 4 WEIGHT VISUALIZATION
+
+Given the empirical evidence that LSTMs are effectively learning weighted sums of the content layers, it is natural to investigate what weights the model learns in practice. Using the more mathematically transparent simplification of LSTMs, we can visualize the weights $\boldsymbol { w } _ { j } ^ { t }$ that are placed on every input $j$ at every timestep $t$ (see Equation 11).
+
+Unlike attention mechanisms, these weights are vectors rather than scalar values. Therefore, we can only provide a coarse-grained visualization of the weights by rendering their $L ^ { 2 }$ -norm, as shown in Table 5. In the visualization, each column indicates the word represented by the weighted sum, and each row indicates the word over which the weighted sum is computed. Dark horizontal streaks indicate the duration for which a word was remembered. Unsurprisingly, the weights on the diagonal are always the largest since it indicates the weight of the current word. More interesting task-specific patterns emerge when inspecting the off-diagonals that represent the weight on the context words.
+
+The first visualization uses the language model from BWB. Due to the language modeling setup, there are only non-zero weights on the current or previous words. We find that the common function words are quickly forgotten, while infrequent words that signal the topic are remembered over very long distances.
+
+The second visualization uses the dependency parser. In this setting, since the recurrent architectures are bidirectional, there are non-zero weights on all words in the sentence. The top-right triangle indicates weights from the forward direction, and the bottom-left triangle indicates from the backward direction. For syntax, we see a significantly different pattern. Function words that are useful for determining syntax are more likely to be remembered. Weights on head words are also likely to persist until the end of a constituent.
+
+This illustration provides only a glimpse into what the model is capturing, and perhaps future, more detailed visualizations that take the individual dimensions into account can provide further insight into what LSTMs are learning in practice.
+
+# 5 RELATED WORK
+
+Many variants of LSTMs (Hochreiter & Schmidhuber, 1997) have been previously explored. These typically consist of a different parameterization the gates, such as LSTMs with peephole connections (Gers & Schmidhuber, 2000), or a rewiring of the connections, such as GRUs (Cho et al., 2014).
+
+![](images/116dcdff4d795d2dbda889b8d0af463695037f8ed08b70dd44a413daf868c26c.jpg)  
+Table 5: Visualization of the weights on context words learned by the memory cell. Each column represents the current word $t$ , and each row represents a context word $j$ . The gating mechanism implicitly computes element-wise weighted sums over each column. The darkness of each square indicates the $L ^ { \dot { 2 } }$ -norm of the vector weights $\boldsymbol { w } _ { j } ^ { t }$ from Equation 11. Figures on the left show weights learned by a language model. Figures on the right show weights learned by a dependency parser.
+
+However, these modifications invariably maintain the recurrent content layer. Even more systematic explorations of LSTM variants (Józefowicz et al., 2015; Greff et al., 2016; Zoph & Le, 2017) do not question the importance of the embedded S-RNN. This is the first study to provide apples-to-apples comparisons between LSTMs and LSTMs without the recurrent content layer.
+
+Several other recent works have also reported promising results with recurrent models that are vastly simpler than LSTMs, such as quasi-recurrent neural networks (Bradbury et al., 2016), strongly-typed recurrent neural networks (Balduzzi & Ghifary, 2016), kernel neural networks (Lei et al., 2017), and simple recurrent units (Lei & Zhang, 2017), making it increasingly apparent that LSTMs are over-parameterized. While these works indicate an obvious trend, their focus is not to provide insight into what exactly LSTMs are learning. In our carefully controlled ablation studies, we propose and evaluate the minimal changes required to test our hypothesis that LSTMs are powerful because they dynamically compute element-wise weighted sums of content layers.
+
+As mentioned in Section 2, this weighted-sum view of LSTMs is highly related to neural attention (Bahdanau et al., 2015), which assigns a normalized scalar weight to each element as a function of its compatibility with an external element. The ability to inspect attention weights has driven the use of more interpretable neural models. Self-attention (Cheng et al., 2016; Parikh et al., 2016) extends this notion by computing intra-sequence attention. Vaswani et al. (2017) further showed that state-of-the-art machine translation can be achieved using only self-attention and without LSTMs. Recently, Arora et al. (2017) proposed a theory-driven approach to assign scalar weights to elements in a bag of words. The success of self-attention corroborates our findings that weighted sums are indeed a more effective method of learning context-sensitive representations than previously appreciated.
+
+# 6 CONCLUSION
+
+We presented an alternate view of LSTMs: they are a hybrid of S-RNNs and a gated model that dynamically computes weighted sums of the S-RNN outputs. Our experiments investigated whether the S-RNN is a necessary component of LSTMs. In other words, are the gates alone as powerful of a model as an LSTM? Results across four major NLP tasks (language modeling, question answering, dependency parsing, and machine translation) indicate that LSTMs suffer little to no performance loss when removing the S-RNN, but removing the gates can degrade performance substantially. This provides evidence that the gating mechanism is doing the heavy lifting in modeling context, and that element-wise weighted sums of context-independent functions of the inputs are often as effective as fully-parameterized LSTMs.
+
+This work sheds light on the inner workings of the relatively opaque LSTM. By removing the S-RNN and the output gate, we also show that the resulting model is a far more mathematically transparent variant of LSTMs. This transparency enables a visualization of how the context affects the output of the model at every timestep, much like in attention-based models. We hope that this new outlook on LSTMs will foster better and more efficient models of contextualization.
+
+# REFERENCES
+
+Yossi Adi, Einat Kermany, Yonatan Belinkov, Ofer Lavi, and Yoav Goldberg. Fine-grained analysis of sentence embeddings using auxiliary prediction tasks. In ICLR, 2017.
+
+Sanjeev Arora, Yingyu Liang, and Tengyu Ma. A simple but tough-to-beat baseline for sentence embeddings. In ICLR, 2017.
+
+Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. In ICLR, 2015.
+
+David Balduzzi and Muhammad Ghifary. Strongly-typed recurrent neural networks. In Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19-24, 2016, pp. 1292–1300, 2016. URL http://jmlr.org/proceedings/ papers/v48/balduzzi16.html.
+
+Yoshua Bengio, Patrice Y. Simard, and Paolo Frasconi. Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5(2):157–166, 1994.
+
+James Bradbury, Stephen Merity, Caiming Xiong, and Richard Socher. Quasi-recurrent neural networks. CoRR, abs/1611.01576, 2016.
+
+Ciprian Chelba, Tomas Mikolov, Mike Schuster, Qi Ge, Thorsten Brants, and Phillipp Koehn. One billion word benchmark for measuring progress in statistical language modeling. In INTERSPEECH, 2014.
+
+Danqi Chen, Adam Fisch, Jason Weston, and Antoine Bordes. Reading Wikipedia to answer open-domain questions. In Association for Computational Linguistics (ACL), 2017.
+
+Jianpeng Cheng, Li Dong, and Mirella Lapata. Long short-term memory-networks for machine reading. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pp. 551–561, Austin, Texas, November 2016. Association for Computational Linguistics. URL https://aclweb.org/anthology/D16-1053.
+
+Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder–decoder for statistical machine translation. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 1724–1734, Doha, Qatar, October 2014. Association for Computational Linguistics. URL http://www.aclweb.org/anthology/D14-1179.
+
+Timothy Dozat and Christopher D. Manning. Deep biaffine attention for neural dependency parsing. CoRR, abs/1611.01734, 2016.
+
+Jeffrey L. Elman. Finding structure in time. Cognitive Science, 14:179–211, 1990.
+
+Matt Gardner, Joel Grus, Mark Neumann, Oyvind Tafjord, Pradeep Dasigi, Nelson Liu, Matthew Peters, Michael Schmitz, and Luke Zettlemoyer. Allennlp: A deep semantic natural language processing platform, 2017. URL http://allennlp.org/papers/AllenNLP_white_ paper.pdf.
+
+Felix A. Gers and Jürgen Schmidhuber. Recurrent nets that time and count. In IJCNN, 2000.
+
+Klaus Greff, Rupesh K Srivastava, Jan Koutník, Bas R Steunebrink, and Jürgen Schmidhuber. Lstm: A search space odyssey. IEEE Transactions on Neural Networks and Learning Systems, 2016.
+
+Luheng He, Kenton Lee, Mike Lewis, and Luke Zettlemoyer. Deep semantic role labeling: What works and what’s next. In Proceedings of the Annual Meeting of the Association for Computational Linguistics, 2017.
+
+Sepp Hochreiter. Untersuchungen zu dynamischen neuronalen netzen. Diploma, Technische Universität München, 91, 1991.
+
+Sepp Hochreiter and Jürgen Schmidhuber. Long Short-term Memory. Neural computation, 9(8): 1735–1780, 1997.
+
+Rafal Józefowicz, Wojciech Zaremba, and Ilya Sutskever. An empirical exploration of recurrent network architectures. In ICML, 2015.
+
+Rafal Józefowicz, Oriol Vinyals, Mike Schuster, Noam Shazeer, and Yonghui Wu. Exploring the limits of language modeling. arXiv preprint arXiv:1602.02410, 2016.
+
+Guillaume Klein, Yoon Kim, Yuntian Deng, Jean Senellart, and Alexander M. Rush. Opennmt: Opensource toolkit for neural machine translation. In Proc. ACL, 2017. doi: 10.18653/v1/P17-4012. URL https://doi.org/10.18653/v1/P17-4012.
+
+Tao Lei and Yu Zhang. Training rnns as fast as cnns. arXiv preprint arXiv:1709.02755, 2017.
+
+Tao Lei, Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Deriving neural architectures from sequence and graph kernels. In ICML, 2017.
+
+Tal Linzen, Emmanuel Dupoux, and Yoav Goldberg. Assessing the ability of lstms to learn syntaxsensitive dependencies. TACL, 4:521–535, 2016.
+
+Mitchell P. Marcus, Beatrice Santorini, and Mary Ann Marcinkiewicz. Building a large annotated corpus of english: The penn treebank. Computational Linguistics, 19:313–330, 1993.
+
+Ankur Parikh, Oscar Täckström, Dipanjan Das, and Jakob Uszkoreit. A decomposable attention model for natural language inference. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pp. 2249–2255, Austin, Texas, November 2016. Association for Computational Linguistics. URL https://aclweb.org/anthology/D16-1244.
+
+Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: 100, $0 0 0 +$ questions for machine comprehension of text. In EMNLP, 2016.
+
+Min Joon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. CoRR, abs/1611.01603, 2016.
+
+Natalia Silveira, Timothy Dozat, Marie-Catherine de Marneffe, Samuel Bowman, Miriam Connor, John Bauer, and Christopher D. Manning. A gold standard dependency corpus for English. In Proceedings of the Ninth International Conference on Language Resources and Evaluation (LREC-2014), 2014.
+
+Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017.
+
+Wojciech Zaremba, Ilya Sutskever, and Oriol Vinyals. Recurrent neural network regularization. arXiv preprint arXiv:1409.2329, 2014.
+
+Barret Zoph and Quoc V Le. Neural architecture search with reinforcement learning. In ICLR, 2017.

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+        "text": "Long short-term memory networks (LSTMs) were introduced to combat vanishing gradients in simple recurrent neural networks (S-RNNs) by augmenting them with additive recurrent connections controlled by gates. We present an alternate view to explain the success of LSTMs: the gates themselves are powerful recurrent models that provide more representational power than previously appreciated. We do this by showing that the LSTM’s gates can be decoupled from the embedded S-RNN, producing a restricted class of RNNs where the main recurrence computes an element-wise weighted sum of context-independent functions of the inputs. Experiments on a range of challenging NLP problems demonstrate that the simplified gate-based models work substantially better than S-RNNs, and often just as well as the original LSTMs, strongly suggesting that the gates are doing much more in practice than just alleviating vanishing gradients. ",
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+        "text": "1 INTRODUCTION ",
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+        "text": "Long short-term memory networks (LSTM) (Hochreiter & Schmidhuber, 1997) have become the de-facto recurrent neural network (RNN) for learning representations of sequences in many research areas, including natural language processing (NLP). Like simple recurrent neural networks (SRNNs) (Elman, 1990), LSTMs are able to learn non-linear functions of arbitrary-length input sequences. However, they also introduce an additional memory cell to mitigate the vanishing gradient problem (Hochreiter, 1991; Bengio et al., 1994). This memory is controlled by a mechanism of gates, whose additive connections allow long-distance dependencies to be learned more easily during backpropagation. While this view is mathematically accurate, in this paper we argue that it does not provide a complete picture of why LSTMs work in practice. ",
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Throughout this paper, let $\\{ \\pmb { x } _ { 1 } , \\ldots , \\pmb { x } _ { n } \\}$ be the sequence of input vectors, $\\{ h _ { 1 } , \\ldots , h _ { n } \\}$ be the sequence of output vectors, and $\\{ c _ { 1 } , \\ldots , c _ { n } \\}$ be the memory cell’s states. Then, given the basic LSTM definition below, we can formally identify three sub-components. ",
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+        "type": "equation",
+        "img_path": "images/5467701ad584dd6418040f42a4488889f4c0765436c752c6aad6980a684d330e.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\tilde { c } _ { t } = \\mathrm { t a n h } ( W _ { c h } h _ { t - 1 } + W _ { c x } { \\boldsymbol x } _ { t } + { \\boldsymbol b } _ { c } ) } \\\\ & { ~ i _ { t } = \\sigma ( W _ { i h } h _ { t - 1 } + W _ { i x } { \\boldsymbol x } _ { t } + { \\boldsymbol b } _ { i } ) } \\\\ & { f _ { t } = \\sigma ( W _ { f h } h _ { t - 1 } + W _ { f x } { \\boldsymbol x } _ { t } + { \\boldsymbol b } _ { f } ) } \\\\ & { c _ { t } = i _ { t } \\circ \\tilde { c } _ { t } + f _ { t } \\circ c _ { t - 1 } } \\\\ & { o _ { t } = \\sigma ( W _ { o h } h _ { t - 1 } + W _ { o x } { \\boldsymbol x } _ { t } + { \\boldsymbol b } _ { o } ) } \\\\ & { h _ { t } = o _ { t } \\circ \\mathrm { t a n h } ( c _ { t } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "type": "text",
+        "text": "Content Layer (Equation 2) We refer to $\\widetilde { c } _ { t }$ as the content layer, which is the output of an S-RNN. eEvaluating the need for the multiplicative recurrent connections in this content layer is the focus of this work. The content layer is passed to the memory cell, which decides which parts of it to store. ",
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+        "type": "text",
+        "text": "Memory Cell (Equations 3-5) The memory cell $c _ { t }$ is controlled by two gates. The input gate $\\mathbf { \\delta } _ { i _ { t } }$ controls what part of the content $( \\widetilde { c } _ { t } )$ is written to the memory, while the forget gate $f _ { t }$ controls what epart of the memory is deleted by filtering the previous state of the memory $( c _ { t - 1 } )$ . Writing to the memory is done by adding the filtered content $( i _ { t } \\circ \\widetilde { c } _ { t } )$ to the retained memory $( f _ { t } \\circ c _ { t - 1 } )$ . ",
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+    {
+        "type": "text",
+        "text": "Output Layer (Equations 6-7) The output layer $h _ { t }$ passes the memory cell through a tanh activation function and uses an output gate $\\mathbf { } _ { o _ { t } }$ to read selectively from the squashed memory cell. ",
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+        "type": "text",
+        "text": "Our goal is to study how much each of these components contribute to the empirical performance of LSTMs. In particular, it is worth considering the memory cell in more detail to reveal why it could serve as a standalone powerful model of long-distance context. It is possible to show that it implicitly computes an element-wise weighted sum of all the previous content layers by expanding the recurrence relation in equation (5): ",
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+        "type": "equation",
+        "img_path": "images/171eae8314fed08e1db7bb9670fac2bf29d1e1ae5456febe476e5bccec770de4.jpg",
+        "text": "$$\n\\begin{array} { l } { { \\displaystyle c _ { t } = \\dot { a } _ { t } \\circ \\widetilde c _ { t } + f _ { t } \\circ c _ { t - 1 } } } \\\\ { { \\displaystyle \\quad = \\sum _ { j = 0 } ^ { t } \\left( \\dot { a } _ { j } \\circ \\prod _ { k = j + 1 } ^ { t } f _ { k } \\right) \\circ \\widetilde c _ { j } } } \\\\ { { \\displaystyle \\quad = \\sum _ { j = 0 } ^ { t } w _ { j } ^ { t } \\circ \\widetilde c _ { j } } } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Each weight $\\boldsymbol { w } _ { j } ^ { t }$ is a product of the input gate $i _ { j }$ (when its respective input $\\widetilde { c } _ { j }$ was read) and every subsequent forget gate $f _ { k }$ e. An interesting property of these weights is that, like the gates, they are also soft element-wise binary filters.1 ",
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+        "type": "text",
+        "text": "This sum is similar to recent architectures that rely on self-attention to learn context-dependent word representations (Cheng et al., 2016; Parikh et al., 2016; Vaswani et al., 2017). There are two major differences from self-attention: (1) instead of computing a weighted sum for each attention head, a separate weighted sum is computed for every dimension of the memory cell, (2) the weighted sum is accumulated with a dynamic program, enabling a linear rather than quadratic complexity in comparison to self-attention. ",
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+    },
+    {
+        "type": "text",
+        "text": "3 MEMORY CELLS ARE POWERFUL STANDALONE MODELS",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "The restricted space of element-wise weighted sums allows for easier mathematical analysis, visualization, and perhaps even learnability. However, constrained function spaces are also less expressive, and a natural question is whether these models will work well for NLP problems that need highly contextualized word representations. We hypothesize that the memory cell (which computes weighted sums) can function as a standalone contextualizer. To test this hypothesis, we present several simplifications of the LSTM’s architecture (Section 3.1), and show on a variety of NLP benchmarks that there is a qualitative performance difference between models that contain a memory cell and those that do not (Section 3.2). We conclude that the content and output layers are relatively minor contributors, and that the space of element-wise weighted sums is sufficiently powerful to compete with fully parameterized LSTMs (Section 3.3). ",
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+    {
+        "type": "text",
+        "text": "3.1 SIMPLIFIED MODELS ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The modeling power of LSTMs is commonly assumed to derive from the S-RNN in the content layer, with the rest of the model acting as a learning aid to bypass the vanishing gradient problem. We first isolate the S-RNN by ablating the gates (denoted as $L S T M - G A T E S$ for consistency). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To test whether the memory cell has enough modeling power of its own, we take an LSTM and replace the S-RNN in the content layer from Equation 2 with a simple linear transformation, creating the LSTM – S-RNN model: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/5a2c9bdaf6f3deb0591636a5b3c0c95ac2f8434c6de5b70e2342972adeb86649.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\tilde { c } _ { t } = W _ { c x } { \\boldsymbol x } _ { t } } \\\\ & { i _ { t } = \\sigma ( W _ { i h } h _ { t - 1 } + W _ { i x } { \\boldsymbol x } _ { t } + b _ { i } ) } \\\\ & { f _ { t } = \\sigma ( W _ { f h } h _ { t - 1 } + W _ { f x } { \\boldsymbol x } _ { t } + b _ { f } ) } \\\\ & { c _ { t } = i _ { t } \\circ \\tilde { c } _ { t } + f _ { t } \\circ c _ { t - 1 } } \\\\ & { o _ { t } = \\sigma ( W _ { o h } h _ { t - 1 } + W _ { o x } { \\boldsymbol x } _ { t } + b _ { o } ) } \\\\ & { h _ { t } = o _ { t } \\circ \\operatorname { t a n h } ( c _ { t } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We further simplify the LSTM by removing the output gate from Equation 7, leaving only the activation function in the output layer $( L S T M - S - R N N - O U T )$ : ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/6617fd930e6a6f0e313c5dc8995a605fd9f7bdfb21e05098bcab3f6c06d604e9.jpg",
+        "text": "$$\n\\begin{array} { r l } & { \\tilde { c } _ { t } = W _ { c x } { \\boldsymbol x } _ { t } } \\\\ & { i _ { t } = \\sigma ( W _ { i h } h _ { t - 1 } + W _ { i x } { \\boldsymbol x } _ { t } + b _ { i } ) } \\\\ & { f _ { t } = \\sigma ( W _ { f h } h _ { t - 1 } + W _ { f x } { \\boldsymbol x } _ { t } + b _ { f } ) } \\\\ & { c _ { t } = i _ { t } \\circ \\tilde { c } _ { t } + f _ { t } \\circ c _ { t - 1 } } \\\\ & { h _ { t } = \\operatorname { t a n h } ( c _ { t } ) } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "After removing the S-RNN and the output gate from the LSTM, the entire ablated model can be written in a modular, compact form: ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "img_path": "images/d567c87e2b80f73ffa895b046f3ca811fa7ea512282059d7d9d35e7d67842dc9.jpg",
+        "text": "$$\n\\pmb { h } _ { t } = \\mathrm { O U T P U T } \\Big ( \\sum _ { j = 0 } ^ { t } \\pmb { w } _ { j } ^ { t } \\circ \\mathrm { C O N T E N T } ( \\pmb { x } _ { j } ) \\Big )\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where the content layer CONTENT $( \\cdot )$ and the output layer OUTPUT $( \\cdot )$ are both context-independent functions, making the entire model highly constrained and interpretable. The complexity of modeling contextual information is needed only for computing the weights $\\boldsymbol { w } _ { j } ^ { t }$ . As we will see in Section 3.2, both of these ablations perform on par with LSTMs on language modeling, question answering, dependency parsing, and machine translation. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "There are many other models that can be expressed in the weighted-sum form (Equation 11). In this work, we focus on the closest variant of LSTM that satisfies this property; removing the S-RNN and the output gate is sufficient for the content and output functions to be context-independent. We leave more thorough investigations into the necessity of the remaining architecture as future work. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2 EXPERIMENTS ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We compare model performance on four NLP tasks, with an experimental setup that is lenient towards LSTMs and harsh towards its simplifications. In each case, we use existing implementations and previously reported hyperparameter settings. Since these settings were tuned for LSTMs, any simplification that performs equally to (or better than) LSTMs under these LSTM-friendly settings provides strong evidence that the ablated component is not a contributing factor. For each task we also report the mean and standard deviation of 5 runs of the LSTM settings to demonstrate the typical variance observed due to training with different random initializations.2 The code and settings to replicate these experiments are publicly available.3 ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.1 LANGUAGE MODELING ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We evaluate on two language modeling datasets: the Penn Treebank (PTB) (Marcus et al., 1993), and Google’s billion-word benchmark (BWB) (Chelba et al., 2014). PTB contains approximately 1M tokens over a vocabulary of 10K words. We used the implementation of Zaremba et al. (2014) while replacing any invocation of LSTMs with simpler models. We tested two of their configurations: medium, which uses two layers of 650-dimension LSTMs, and large, which uses two layers of 1500-dimension LSTMs. ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "BWB is about a thousand times larger than PTB, and uses a more diverse vocabulary of 800K words. Using the implementation of Józefowicz et al. (2016), we tested their LSTM-2048-512 configuration. Our experiments use exactly the same hyperparameters (dimensions, dropout, learning rates, etc) that were originally tuned for LSTMs (Józefowicz et al., 2016). Following their implementation, we project the hidden state at each time step down to 512 dimensions. Due to the enormous size of this dataset, we stopped training after 5 epochs. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 1 shows overall model performance. In all three cases, replacing the LSTM’s content layer with a linear transformation results in small differences in perplexity. The most important result is that the small fluctuations in performance between the various gated architectures are minuscule in comparison to the enormous gap between the S-RNN $( L S T M - G A T E S )$ and the original LSTM. This striking difference strongly supports our hypothesis that the weighted sums computed by the gates – not the S-RNN – is the recurrent model that contributes mostly strongly to the final performance. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.2 QUESTION ANSWERING ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For question answering, we use two different QA systems on the Stanford question answering dataset (SQuAD) (Rajpurkar et al., 2016): the Bidirectional Attention Flow model (BiDAF) (Seo et al., 2016) and DrQA (Chen et al., 2017). BiDAF contains 3 LSTMs, which are referred to as the phrase layer, the modeling layer, and the span end encoder. Our experiments replace each of these LSTMs with their simplified counterparts. We directly use the implementation of BiDAF from AllenNLP (Gardner et al., 2017), and all experiments reuse the existing hyperparameters that were tuned for LSTMs. Likewise, we use an open-source implementation of $\\mathrm { \\dot { D r } Q A } ^ { 4 }$ and replace only the LSTMs, while leaving everything else intact. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Table 2 shows that all the gated models do comparably. Most importantly, ablating the S-RNN from the LSTM has a minor effect in comparison to the drop in performance when ablating the gates. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.3 DEPENDENCY PARSING ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            820,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For dependency parsing, we use the Deep Biaffine Dependency Parser (Dozat & Manning, 2016), which relies on stacked bidirectional LSTMs to learn context-sensitive word embeddings for determining arcs between a pair of words. We directly use their released implementation, which is evaluated on the Universal Dependencies English Web Treebank v1.3 (Silveira et al., 2014). In our experiments, we use the existing hyperparameters and only replace the LSTMs with the simplified architectures. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/63d9237a0d4c313ae0332db25309abbaa02d4f2603820898c4bf7b76e46c8a18.jpg",
+        "table_caption": [
+            "Table 1: The performance of simplified LSTM architectures on language modeling benchmarks, measured by perplexity. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Configuration</td><td>Model</td><td>Perplexity</td></tr><tr><td rowspan=\"4\">PTB</td><td>LSTM</td><td>83.9 ± 0.3</td></tr><tr><td>- GATES</td><td>140.9</td></tr><tr><td>- S-RNN</td><td>80.5</td></tr><tr><td>- S-RNN-OUT</td><td>81.6</td></tr><tr><td rowspan=\"4\">PTB (Large Model)</td><td>LSTM</td><td>78.8± 0.2</td></tr><tr><td>- GATES</td><td>126.1</td></tr><tr><td>- S-RNN</td><td>76.0</td></tr><tr><td>- S-RNN -OUT</td><td>78.5</td></tr><tr><td rowspan=\"4\">BWB</td><td>LSTM (J6zefowicz et al., 2016)</td><td>47.5</td></tr><tr><td>- GATES</td><td>82.2</td></tr><tr><td>- S-RNN</td><td>45.4</td></tr><tr><td>- S-RNN-OUT</td><td>47.9</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/194b9011fae87b1997c7733bb818feb5a4aac1e118b1109b42ea99f5ad8bb89f.jpg",
+        "table_caption": [
+            "Table 2: The performance of simplified LSTM architectures on the question answering benchmark, SQuAD, measured by exact match (EM) and span overlap (F1). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>System</td><td>Model</td><td>EM</td><td>F1</td></tr><tr><td rowspan=\"5\">BiDAF</td><td>LSTM</td><td>67.9 ± 0.3</td><td>77.5 ± 0.2</td></tr><tr><td>- GATES</td><td>62.9</td><td>73.3</td></tr><tr><td>- S-RNN</td><td>68.4</td><td>78.2</td></tr><tr><td>- S-RNN-OUT</td><td>67.4</td><td>77.2</td></tr><tr><td></td><td></td><td></td></tr><tr><td rowspan=\"4\">DrQA</td><td>LSTM</td><td>68.8 ± 0.2</td><td>78.2 ± 0.2</td></tr><tr><td>- GATES</td><td>56.4</td><td>66.5</td></tr><tr><td>- S-RNN</td><td>67.7</td><td>77.0</td></tr><tr><td>- S-RNN -OUT</td><td>67.0</td><td>76.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/3129b60252f421282f6f1391d76bb306baaab02caefbfc2a2d89d11276f1df54.jpg",
+        "table_caption": [
+            "Table 3: The performance of simplified LSTM architectures on the universal dependencies parsing benchmark, measured by unlabeled attachment score (UAS) and labeled attachment score (LAS). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>UAS</td><td>LAS</td></tr><tr><td>LSTM</td><td>90.60 ± 0.21</td><td>88.05 ± 0.33</td></tr><tr><td>- GATES</td><td>87.75</td><td>84.61</td></tr><tr><td>- S-RNN</td><td>90.77</td><td>88.49</td></tr><tr><td>- S-RNN-OUT</td><td>90.70</td><td>88.31</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We observe the same pattern in the ablations for dependency parsing. The differences in performance between the gated models fall within the differences between multiple experiments with LSTMs. Consistent with ablation results from other tasks, removing the gating mechanisms causes a 3-4 point drop in performance. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.2.4 MACHINE TRANSLATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            856,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For machine translation, we used OpenNMT (Klein et al., 2017) to train English to German translation models on the multi-modal benchmarks from WMT 2016 (used in OpenNMT’s readme file). We use OpenNMT’s default model and hyperparameters, replacing the stacked bidirectional LSTM of its ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/2d9a927a1b20326552303a2bb9eee06dc2d283f11d4d99988b82f925ad6eec3d.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Model</td><td>BLEU</td></tr><tr><td>LSTM</td><td>35.95</td></tr><tr><td>- GATES</td><td>12.22</td></tr><tr><td>- S-RNN</td><td>36.66</td></tr><tr><td>- S-RNN-OUT</td><td>36.39</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 4: The performance of simplified LSTM architectures on the WMT 2016 multi-modal English to German translation benchmark, measured by BLEU. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "encoder with the simplified architectures. Table 4 shows that while models containing memory cells perform more-or-less on par, removing the memory cell yields a substantial performance drop. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "3.3 DISCUSSION ",
+        "text_level": 1,
+        "bbox": [
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+            292,
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+            308
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the above experiments, we show three major ablations of the LSTM. In the S-RNN experiments $( L S T M - G A T E S )$ , we ablate the memory cell and the output layer. In the LSTM – S-RNN and LSTM – $S – R M N - O U T$ experiments, we ablate the S-RNN. As consistent with previous literature, removing the memory cell degrades performance drastically. In contrast, removing the S-RNN makes little to no difference in the final performance, suggesting that the memory cell alone is largely responsible for the success of LSTMs in NLP. The results also confirm our hypothesis that weighted sums of context words is a powerful, yet more interpretable, model of contextual information. ",
+        "bbox": [
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+            319,
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+            416
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4 WEIGHT VISUALIZATION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            436,
+            415,
+            452
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Given the empirical evidence that LSTMs are effectively learning weighted sums of the content layers, it is natural to investigate what weights the model learns in practice. Using the more mathematically transparent simplification of LSTMs, we can visualize the weights $\\boldsymbol { w } _ { j } ^ { t }$ that are placed on every input $j$ at every timestep $t$ (see Equation 11). ",
+        "bbox": [
+            174,
+            467,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Unlike attention mechanisms, these weights are vectors rather than scalar values. Therefore, we can only provide a coarse-grained visualization of the weights by rendering their $L ^ { 2 }$ -norm, as shown in Table 5. In the visualization, each column indicates the word represented by the weighted sum, and each row indicates the word over which the weighted sum is computed. Dark horizontal streaks indicate the duration for which a word was remembered. Unsurprisingly, the weights on the diagonal are always the largest since it indicates the weight of the current word. More interesting task-specific patterns emerge when inspecting the off-diagonals that represent the weight on the context words. ",
+        "bbox": [
+            174,
+            530,
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+            628
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The first visualization uses the language model from BWB. Due to the language modeling setup, there are only non-zero weights on the current or previous words. We find that the common function words are quickly forgotten, while infrequent words that signal the topic are remembered over very long distances. ",
+        "bbox": [
+            174,
+            635,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The second visualization uses the dependency parser. In this setting, since the recurrent architectures are bidirectional, there are non-zero weights on all words in the sentence. The top-right triangle indicates weights from the forward direction, and the bottom-left triangle indicates from the backward direction. For syntax, we see a significantly different pattern. Function words that are useful for determining syntax are more likely to be remembered. Weights on head words are also likely to persist until the end of a constituent. ",
+        "bbox": [
+            174,
+            696,
+            825,
+            781
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "This illustration provides only a glimpse into what the model is capturing, and perhaps future, more detailed visualizations that take the individual dimensions into account can provide further insight into what LSTMs are learning in practice. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            851,
+            344,
+            867
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Many variants of LSTMs (Hochreiter & Schmidhuber, 1997) have been previously explored. These typically consist of a different parameterization the gates, such as LSTMs with peephole connections (Gers & Schmidhuber, 2000), or a rewiring of the connections, such as GRUs (Cho et al., 2014). ",
+        "bbox": [
+            176,
+            881,
+            825,
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/116dcdff4d795d2dbda889b8d0af463695037f8ed08b70dd44a413daf868c26c.jpg",
+        "image_caption": [
+            "Table 5: Visualization of the weights on context words learned by the memory cell. Each column represents the current word $t$ , and each row represents a context word $j$ . The gating mechanism implicitly computes element-wise weighted sums over each column. The darkness of each square indicates the $L ^ { \\dot { 2 } }$ -norm of the vector weights $\\boldsymbol { w } _ { j } ^ { t }$ from Equation 11. Figures on the left show weights learned by a language model. Figures on the right show weights learned by a dependency parser. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            186,
+            103,
+            797,
+            829
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "However, these modifications invariably maintain the recurrent content layer. Even more systematic explorations of LSTM variants (Józefowicz et al., 2015; Greff et al., 2016; Zoph & Le, 2017) do not question the importance of the embedded S-RNN. This is the first study to provide apples-to-apples comparisons between LSTMs and LSTMs without the recurrent content layer. ",
+        "bbox": [
+            174,
+            103,
+            823,
+            159
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Several other recent works have also reported promising results with recurrent models that are vastly simpler than LSTMs, such as quasi-recurrent neural networks (Bradbury et al., 2016), strongly-typed recurrent neural networks (Balduzzi & Ghifary, 2016), kernel neural networks (Lei et al., 2017), and simple recurrent units (Lei & Zhang, 2017), making it increasingly apparent that LSTMs are over-parameterized. While these works indicate an obvious trend, their focus is not to provide insight into what exactly LSTMs are learning. In our carefully controlled ablation studies, we propose and evaluate the minimal changes required to test our hypothesis that LSTMs are powerful because they dynamically compute element-wise weighted sums of content layers. ",
+        "bbox": [
+            174,
+            166,
+            825,
+            279
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "As mentioned in Section 2, this weighted-sum view of LSTMs is highly related to neural attention (Bahdanau et al., 2015), which assigns a normalized scalar weight to each element as a function of its compatibility with an external element. The ability to inspect attention weights has driven the use of more interpretable neural models. Self-attention (Cheng et al., 2016; Parikh et al., 2016) extends this notion by computing intra-sequence attention. Vaswani et al. (2017) further showed that state-of-the-art machine translation can be achieved using only self-attention and without LSTMs. Recently, Arora et al. (2017) proposed a theory-driven approach to assign scalar weights to elements in a bag of words. The success of self-attention corroborates our findings that weighted sums are indeed a more effective method of learning context-sensitive representations than previously appreciated. ",
+        "bbox": [
+            174,
+            285,
+            825,
+            410
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            431,
+            318,
+            446
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We presented an alternate view of LSTMs: they are a hybrid of S-RNNs and a gated model that dynamically computes weighted sums of the S-RNN outputs. Our experiments investigated whether the S-RNN is a necessary component of LSTMs. In other words, are the gates alone as powerful of a model as an LSTM? Results across four major NLP tasks (language modeling, question answering, dependency parsing, and machine translation) indicate that LSTMs suffer little to no performance loss when removing the S-RNN, but removing the gates can degrade performance substantially. This provides evidence that the gating mechanism is doing the heavy lifting in modeling context, and that element-wise weighted sums of context-independent functions of the inputs are often as effective as fully-parameterized LSTMs. ",
+        "bbox": [
+            174,
+            463,
+            825,
+            588
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This work sheds light on the inner workings of the relatively opaque LSTM. By removing the S-RNN and the output gate, we also show that the resulting model is a far more mathematically transparent variant of LSTMs. This transparency enables a visualization of how the context affects the output of the model at every timestep, much like in attention-based models. We hope that this new outlook on LSTMs will foster better and more efficient models of contextualization. ",
+        "bbox": [
+            174,
+            595,
+            825,
+            665
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            688,
+            285,
+            702
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Yossi Adi, Einat Kermany, Yonatan Belinkov, Ofer Lavi, and Yoav Goldberg. Fine-grained analysis of sentence embeddings using auxiliary prediction tasks. In ICLR, 2017. ",
+        "bbox": [
+            174,
+            710,
+            823,
+            739
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Sanjeev Arora, Yingyu Liang, and Tengyu Ma. A simple but tough-to-beat baseline for sentence embeddings. In ICLR, 2017. ",
+        "bbox": [
+            173,
+            750,
+            821,
+            779
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. In ICLR, 2015. ",
+        "bbox": [
+            171,
+            789,
+            825,
+            818
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "David Balduzzi and Muhammad Ghifary. Strongly-typed recurrent neural networks. In Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19-24, 2016, pp. 1292–1300, 2016. URL http://jmlr.org/proceedings/ papers/v48/balduzzi16.html. ",
+        "bbox": [
+            173,
+            828,
+            826,
+            885
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Yoshua Bengio, Patrice Y. Simard, and Paolo Frasconi. Learning long-term dependencies with gradient descent is difficult. IEEE Transactions on Neural Networks, 5(2):157–166, 1994. ",
+        "bbox": [
+            174,
+            895,
+            821,
+            922
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "James Bradbury, Stephen Merity, Caiming Xiong, and Richard Socher. Quasi-recurrent neural networks. CoRR, abs/1611.01576, 2016. ",
+        "bbox": [
+            169,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Ciprian Chelba, Tomas Mikolov, Mike Schuster, Qi Ge, Thorsten Brants, and Phillipp Koehn. One billion word benchmark for measuring progress in statistical language modeling. In INTERSPEECH, 2014. ",
+        "bbox": [
+            174,
+            141,
+            823,
+            184
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Danqi Chen, Adam Fisch, Jason Weston, and Antoine Bordes. Reading Wikipedia to answer open-domain questions. In Association for Computational Linguistics (ACL), 2017. ",
+        "bbox": [
+            171,
+            194,
+            823,
+            223
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jianpeng Cheng, Li Dong, and Mirella Lapata. Long short-term memory-networks for machine reading. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pp. 551–561, Austin, Texas, November 2016. Association for Computational Linguistics. URL https://aclweb.org/anthology/D16-1053. ",
+        "bbox": [
+            173,
+            233,
+            826,
+            290
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kyunghyun Cho, Bart van Merrienboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. Learning phrase representations using rnn encoder–decoder for statistical machine translation. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pp. 1724–1734, Doha, Qatar, October 2014. Association for Computational Linguistics. URL http://www.aclweb.org/anthology/D14-1179. ",
+        "bbox": [
+            174,
+            299,
+            825,
+            369
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Timothy Dozat and Christopher D. Manning. Deep biaffine attention for neural dependency parsing. CoRR, abs/1611.01734, 2016. ",
+        "bbox": [
+            169,
+            378,
+            823,
+            409
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Jeffrey L. Elman. Finding structure in time. Cognitive Science, 14:179–211, 1990. ",
+        "bbox": [
+            173,
+            417,
+            714,
+            433
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Matt Gardner, Joel Grus, Mark Neumann, Oyvind Tafjord, Pradeep Dasigi, Nelson Liu, Matthew Peters, Michael Schmitz, and Luke Zettlemoyer. Allennlp: A deep semantic natural language processing platform, 2017. URL http://allennlp.org/papers/AllenNLP_white_ paper.pdf. ",
+        "bbox": [
+            173,
+            443,
+            826,
+            500
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Felix A. Gers and Jürgen Schmidhuber. Recurrent nets that time and count. In IJCNN, 2000. ",
+        "bbox": [
+            171,
+            508,
+            781,
+            525
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Klaus Greff, Rupesh K Srivastava, Jan Koutník, Bas R Steunebrink, and Jürgen Schmidhuber. Lstm: A search space odyssey. IEEE Transactions on Neural Networks and Learning Systems, 2016. ",
+        "bbox": [
+            176,
+            534,
+            826,
+            563
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Luheng He, Kenton Lee, Mike Lewis, and Luke Zettlemoyer. Deep semantic role labeling: What works and what’s next. In Proceedings of the Annual Meeting of the Association for Computational Linguistics, 2017. ",
+        "bbox": [
+            173,
+            571,
+            826,
+            614
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Sepp Hochreiter. Untersuchungen zu dynamischen neuronalen netzen. Diploma, Technische Universität München, 91, 1991. ",
+        "bbox": [
+            173,
+            625,
+            825,
+            654
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Sepp Hochreiter and Jürgen Schmidhuber. Long Short-term Memory. Neural computation, 9(8): 1735–1780, 1997. ",
+        "bbox": [
+            173,
+            662,
+            825,
+            693
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Rafal Józefowicz, Wojciech Zaremba, and Ilya Sutskever. An empirical exploration of recurrent network architectures. In ICML, 2015. ",
+        "bbox": [
+            173,
+            702,
+            825,
+            731
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Rafal Józefowicz, Oriol Vinyals, Mike Schuster, Noam Shazeer, and Yonghui Wu. Exploring the limits of language modeling. arXiv preprint arXiv:1602.02410, 2016. ",
+        "bbox": [
+            171,
+            739,
+            825,
+            770
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Guillaume Klein, Yoon Kim, Yuntian Deng, Jean Senellart, and Alexander M. Rush. Opennmt: Opensource toolkit for neural machine translation. In Proc. ACL, 2017. doi: 10.18653/v1/P17-4012. URL https://doi.org/10.18653/v1/P17-4012. ",
+        "bbox": [
+            178,
+            779,
+            826,
+            821
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tao Lei and Yu Zhang. Training rnns as fast as cnns. arXiv preprint arXiv:1709.02755, 2017. ",
+        "bbox": [
+            171,
+            832,
+            787,
+            848
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tao Lei, Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Deriving neural architectures from sequence and graph kernels. In ICML, 2017. ",
+        "bbox": [
+            174,
+            856,
+            820,
+            886
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Tal Linzen, Emmanuel Dupoux, and Yoav Goldberg. Assessing the ability of lstms to learn syntaxsensitive dependencies. TACL, 4:521–535, 2016. ",
+        "bbox": [
+            176,
+            895,
+            823,
+            924
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Mitchell P. Marcus, Beatrice Santorini, and Mary Ann Marcinkiewicz. Building a large annotated corpus of english: The penn treebank. Computational Linguistics, 19:313–330, 1993. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ankur Parikh, Oscar Täckström, Dipanjan Das, and Jakob Uszkoreit. A decomposable attention model for natural language inference. In Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pp. 2249–2255, Austin, Texas, November 2016. Association for Computational Linguistics. URL https://aclweb.org/anthology/D16-1244. ",
+        "bbox": [
+            174,
+            141,
+            823,
+            196
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: 100, $0 0 0 +$ questions for machine comprehension of text. In EMNLP, 2016. ",
+        "bbox": [
+            169,
+            207,
+            823,
+            236
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Min Joon Seo, Aniruddha Kembhavi, Ali Farhadi, and Hannaneh Hajishirzi. Bidirectional attention flow for machine comprehension. CoRR, abs/1611.01603, 2016. ",
+        "bbox": [
+            171,
+            243,
+            825,
+            272
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Natalia Silveira, Timothy Dozat, Marie-Catherine de Marneffe, Samuel Bowman, Miriam Connor, John Bauer, and Christopher D. Manning. A gold standard dependency corpus for English. In Proceedings of the Ninth International Conference on Language Resources and Evaluation (LREC-2014), 2014. ",
+        "bbox": [
+            173,
+            281,
+            826,
+            338
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. arXiv preprint arXiv:1706.03762, 2017. ",
+        "bbox": [
+            171,
+            347,
+            823,
+            376
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Wojciech Zaremba, Ilya Sutskever, and Oriol Vinyals. Recurrent neural network regularization. arXiv preprint arXiv:1409.2329, 2014. ",
+        "bbox": [
+            174,
+            385,
+            823,
+            414
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Barret Zoph and Quoc V Le. Neural architecture search with reinforcement learning. In ICLR, 2017. ",
+        "bbox": [
+            171,
+            422,
+            823,
+            438
+        ],
+        "page_idx": 9
+    }
+]

parse/train/ZzwDy_wiWv/ZzwDy_wiWv.md

@@ -0,0 +1,346 @@
+# KNOWLEDGE DISTILLATION VIA SOFTMAX REGRESSION REPRESENTATION LEARNING
+
+Jing Yang   
+University of Nottingham   
+Nottingham, UK   
+jing.yang2@nottingham.ac.uk   
+Brais Marinez   
+Samsung AI Center   
+Cambridge, UK   
+brais.mart@gmail.com   
+Adrian Bulat   
+Samsung AI Center   
+Cambridge, UK   
+adrian@adrianbulat.com,   
+Georgios Tzimiropoulos   
+Samsung AI Center   
+Cambridge, UK   
+Queen Mary University of London   
+London, UK   
+g.tzimiropoulos@qmul.ac.uk
+
+# ABSTRACT
+
+This paper addresses the problem of model compression via knowledge distillation. We advocate for a method that optimizes the output feature of the penultimate layer of the student network and hence is directly related to representation learning. To this end, we firstly propose a direct feature matching approach which focuses on optimizing the student’s penultimate layer only. Secondly and more importantly, because feature matching does not take into account the classification problem at hand, we propose a second approach that decouples representation learning and classification and utilizes the teacher’s pre-trained classifier to train the student’s penultimate layer feature. In particular, for the same input image, we wish the teacher’s and student’s feature to produce the same output when passed through the teacher’s classifier, which is achieved with a simple $L _ { 2 }$ loss. Our method is extremely simple to implement and straightforward to train and is shown to consistently outperform previous state-of-the-art methods over a large set of experimental settings including different (a) network architectures, (b) teacher-student capacities, (c) datasets, and (d) domains. The code is available at https://github.com/jingyang2017/KD_SRRL.
+
+# 1 INTRODUCTION
+
+Recently, there has been a great amount of research effort to make Convolutional Neural Networks (CNNs) lightweight so that they can be deployed in devices with limited resources. To this end, several approaches for model compression have been proposed, including network pruning (Han et al., 2016; Lebedev & Lempitsky, 2016), network quantization (Rastegari et al., 2016; Wu et al., 2016), knowledge transfer/distillation (Hinton et al., 2015; Zagoruyko & Komodakis, 2017), and neural architecture search (Zoph & Le, 2017; Liu et al., 2018). Knowledge distillation (Bucilua et al., ˇ 2006; Hinton et al., 2015) aims to transfer knowledge from one network (the so-called “teacher”) to another (the so-called “student”). Typically, the teacher is a high-capacity model capable of achieving high accuracy, while the student is a compact model with much fewer parameters, thus also requiring much less computation. The goal of knowledge distillation is to use the teacher to improve the training of the student and push its accuracy closer to that of the teacher.
+
+The rationale behind knowledge distillation can be explained from an optimization perspective: there is evidence that high capacity models (i.e. the teacher) can find good local minima due to over-parameterization (Du & Lee, 2018; Soltanolkotabi et al., 2018). In knowledge distillation, such models are used to facilitate the optimization of lower capacity models (i.e. the student) during training. For example, in the seminal work of (Hinton et al., 2015), the softmax outputs of the teacher provide extra supervisory signals of inter-class similarities which facilitate the training of the student. In other influential works, intermediate representations extracted from the teacher such as feature tensors (Romero et al., 2015) or attention maps (Zagoruyko & Komodakis, 2017) have been used to define auxiliary loss functions used in the optimization of the student.
+
+![](images/60b4a02c23326bdf1e9c5923ad7cf0931787c8865d068a3bcf6e90a28a55ffc3.jpg)  
+Figure 1: Our method performs knowledge distillation by minimizing the discrepancy between the penultimate feature representations $h _ { T }$ and $h _ { S }$ of the teacher and the student, respectively. To this end, we propose to use two losses: (a) the Feature Matching loss $L _ { F M }$ , and (b) the so-called Softmax Regression loss $L _ { S R }$ . In contrary to $L _ { F M }$ , our main contribution, $L _ { S R }$ , is designed to take into account the classification task at hand. To this end, $L _ { S R }$ imposes that for the same input image, the teacher’s and student’s feature produce the same output when passed through the teacher’s pre-trained and frozen classifier. Note that, for simplicity, the function for making the feature dimensionality of $h _ { T }$ and $h _ { S }$ the same is not shown.
+
+Training a network whose output feature representation is rich and powerful has been shown crucial for achieving high accuracy for the subsequent classification task in recent works in both unsupervised and supervised learning, see for example (Chen et al., 2020; He et al., 2020) and (Kang et al., 2020). Hence, in this paper, we are advocating for representation learning-based knowledge distillation by optimizing the student’s penultimate layer output feature. If we are able to do this effectively, we expect (and show experimentally) to end up with a student network which can generalize better than one trained with logit matching as in the KD paper of (Hinton et al., 2015).
+
+Main contributions: To accomplish the aforementioned goal we propose two loss functions: The first loss function, akin to (Romero et al., 2015; Zagoruyko & Komodakis, 2017), is based on direct feature matching but focuses on optimizing the student’s penultimate layer feature only. Because direct feature matching might be difficult due to the lower representation capacity of the student and, more importantly, is detached from the classification task at hand, we also propose a second loss function: we propose to decouple representation learning and classification and utilize the teacher’s pre-trained classifier to train the student’s penultimate layer feature. In particular, for the same input image, we wish the teacher’s and student’s feature to produce the same output when passed through the teacher’s classifier, which is achieved with a simple $L _ { 2 }$ loss (see Fig. 1). This softmax regression projection is used to retain from the student’s feature the information that is relevant to classification, but since the projection matrix is pre-trained (learned during the teacher’s training phase) this does not compromise the representational power of the student’s feature.
+
+Main results: Our method has two advantages: (1) It is simple and straightforward to implement. (2) It consistently outperforms state-of-the-art methods over a large set of experimental settings including different (a) network architectures (WideResNets, ResNets, MobileNets), (b) teacherstudent capacities, (c) datasets (CIFAR-10/100, ImageNet), and (d) domains (real-to-binary).
+
+# 2 RELATED WORK
+
+Knowledge transfer: In the work of (Hinton et al., 2015), knowledge is defined as the teacher’s outputs after the final softmax layer. The softmax outputs carry richer information than one-hot labels because they provide extra supervision signals in terms of the inter-class similarities learned by the teacher. In a similar fashion to (Hinton et al., 2015), intermediate representations extracted from the teacher such as feature tensors (Romero et al., 2015) or attention maps (Zagoruyko & Komodakis, 2017) have been used to define loss functions used to facilitate the optimization of the student. Trying to match the whole feature tensor, as in FitNets (Romero et al., 2015), is hard and, in certain circumstances, such an approach may adversely affect the performance and convergence of the student. To relax the assumption of FitNet, Attention Transfer (AT) was proposed in (Zagoruyko & Komodakis, 2017) where knowledge takes the form of attention maps which are summaries of the energies of the feature tensors over the channel dimension. An extension of (Zagoruyko & Komodakis, 2017) using Maximum Mean Discrepancy of the network activations as a loss term for distillation was proposed in (Huang & Wang, 2017). Cho & Hariharan (2019) showed that very accurate networks are “too good” to be good teachers and proposed to mitigate this with early stopping of the teacher’s training. Recently, the work of (Heo et al., 2019a) studied the location within the network at which feature distillation should be applied and proposed margin ReLU and a specifically designed distance function that transfers only the useful (positive) information from the teacher to the student. More recently, Li et al. (Li et al., 2020a) proposed to supervise the blockwise architecture search by the architecture knowledge distilled from a teacher model. Another NAS based method was proposed in (Guan et al., 2020), in which a student-to-teacher loss is used to find the aggregation weights that match the learning ability of the student. Passalis et al. (2020) claimed that traditional KD ignores information plasticity during the training process, and proposed to model the information flow through the various layers of the teacher.
+
+Feature relationship transfer: Another line of knowledge distillation methods focus on exploring transferring the relationship between features, rather than the actual features themselves. In (Yim et al., 2017), feature correlations are captured by computing the Gram matrix of features across layers for both teacher and student and then applying an $L _ { 2 }$ loss on pairs of teacher-student Gram matrices. The limitation of this work is the high computational cost, which is addressed to some extent in (Lee et al., 2018) by compressing the feature maps by singular value decomposition. Park et al. (2019) proposed a relational knowledge distillation method which computes distance-wise and angle-wise relations of each embedded feature vector. This idea is further explored in (Peng et al., 2019) and (Liu et al., 2019). In (Peng et al., 2019), Taylor series expansion is proposed to better capture the correlation between multiple instances. In (Liu et al., 2019), the instance feature and relationships are considered as vertexes and edges respectively in a graph and instance relationship graph is proposed to model the feature space transformation across layers. Inspired by the observation that semantically similar inputs should have similar activation patterns, (Tung & Mori, 2019) proposed a similarity-preserving knowledge distillation method which guides the student to mimic the teacher with respect to generating similar or dissimilar activations. More recently, (Jain et al., 2020) proposed to matching the student output with the teacher’s by distilling the knowledge through a quantized visual words space. Li et al. (2020b) proposed the local correlation exploration framework to represent the relationships of local regions in the feature space which contains more details and discriminative patterns.
+
+Finally, a similar connection between distillation and representation learning was very recently made in (Tian et al., 2020) which uses contrastive learning for knowledge distillation. We note that our loss is not related to the one used in (Tian et al., 2020), is simpler, and as shown in Section 5, outperforms it for all of our experiments, often by a significant margin.
+
+# 3 METHOD
+
+We denote by $T$ and $S$ the teacher and student networks respectively. We split these networks into two parts: (i) A convolutional feature extractor $f _ { N e t } , N e t = \{ T , S \}$ , the output of which at the $i$ -th layer is a feature tensor $F _ { N e t } ^ { i } \in \mathbb { R } ^ { C _ { N e t } ^ { i } \times H ^ { i } \times W ^ { i } }$ , where $C _ { N e t } ^ { i }$ is the output feature dimensionality, and $H ^ { i } , W ^ { i }$ the output spatial dimensions. We also denote by $\begin{array} { r } { h _ { N e t } = \sum _ { h = 1 } ^ { { H } ^ { L } } \sum _ { w = 1 } ^ { { W } ^ { L } } F _ { N e t } ^ { L } \in \mathbb { R } ^ { C _ { N e t } ^ { L } } } \end{array}$ the last layer feature representation learned by $f _ { N e t }$ . (ii) A projection matrix $W _ { N e t } \in \mathbb { R } ^ { C _ { N e t } ^ { L } \times K }$ which projects the feature representation $h _ { N e t }$ into $K$ class logits $z _ { N e t } ^ { i } , i = 1 , \dots , K$ , followed by the softmax function $\begin{array} { r } { s ( z _ { N e t } ^ { i } ) = \frac { \exp ( z _ { N e t } ^ { i } / \tau ) } { \sum _ { j } \exp ( z _ { N e t } ^ { j } / \tau ) } } \end{array}$ with temperature $\tau$ $\mathit { \Pi } _ { \tau } = 1$ for Cross Entropy loss) which put together form a softmax regression classifier into $K$ classes.
+
+Knowledge Distillation (KD) (Hinton et al., 2015) trains the student with the following loss:
+
+$$
+L _ { K D } = - \sum _ { k = 1 } ^ { K } s ( z _ { T } ^ { k } ) \log s ( z _ { S } ^ { k } ) ,
+$$
+
+so that the discrepancy between the teacher’s and student’s classifiers is directly minimized.
+
+FitNets (Romero et al., 2015) match intermediate feature representations. For the $i$ -th layer, the following loss is defined:
+
+$$
+L _ { F i t } = \left\| F _ { T } ^ { i } - r ( F _ { S } ^ { i } ) \right\| ^ { 2 } ,
+$$
+
+where $r ( . )$ is a function for matching the feature tensor dimensions.
+
+In our work, we propose to minimize the discrepancy between the representations $h _ { T }$ and $h _ { S }$ . To accomplish this goal, we propose to use two losses. The first one is an $L _ { 2 }$ feature matching loss:
+
+$$
+L _ { F M } = \left\| h _ { T } - h _ { S } \right\| ^ { 2 } ,
+$$
+
+where for notational simplicity we dropped the dependency on $r ( . )$ . Hence, $L _ { F M }$ loss is a simplified FitNet loss which focuses only on the final representation learned. The intuition for this is that this feature is directly connected to the classifier and hence imposing the student’s feature to be similar to that of the teacher could have more impact on classification accuracy. Moreover, it might be questionable why one should optimize for other intermediate representations as in (Romero et al., 2015) especially when the student is a network of lower representational capacity. In Section 4: Where should the losses be applied?, we confirm that $L _ { F M }$ alone has a positive impact but feature matching in other layers is not helpful.
+
+We found $L _ { F M }$ to be effective but only to limited extent. One disadvantage of $L _ { F M }$ and, in general, of all feature matching losses e.g. (Romero et al., 2015; Zagoruyko & Komodakis, 2017), is that it treats each channel dimension in the feature space independently, and ignores the inter-channel dependencies of the feature representations $h _ { S }$ and $h _ { T }$ for the final classification. This is in contrast to the original logit matching loss proposed by Hinton et al. in (Hinton et al., 2015) which directly targets classification accuracy. To alleviate the aforementioned problem, in this work, we propose a second loss for optimizing $h _ { S }$ which is directly linked with classification accuracy. To this end, we will use the teacher’s pre-trained Softmax Regression (SR) classifier.
+
+Let us denote by $p$ the output of the teacher network when fed with some input image $x$ . Let us also feed the same image through the student network to obtain feature $h _ { S } ( x )$ . Finally let us pass $h _ { S } ( x )$ through the teacher’s SR classifier to obtain output $q$ . See also Fig. 1. Our loss is defined as:
+
+$$
+L _ { S R } = - p \log q .
+$$
+
+At this point, we make the following two observations: (1) If $p = q$ (and since the teacher’s classifier is frozen), then this implies that $\bar { h _ { S } } ( x ) = h _ { T } ( x )$ which shows that indeed Eq. (4) optimizes the student’s feature representation $h _ { S }$ ( $h _ { T }$ is also frozen). (2) The loss of Eq.(4) can be written as:
+
+$$
+\begin{array} { r } { L _ { S R } = - s ( W _ { T } ^ { \prime } h _ { T } ) \log s ( W _ { T } ^ { \prime } h _ { S } ) . } \end{array}
+$$
+
+Now let us now write KD loss in a similar way:
+
+$$
+\begin{array} { r } { L _ { K D } = - s ( W _ { T } ^ { \prime } h _ { T } ) \log s ( W _ { s } ^ { \prime } h _ { S } ) . } \end{array}
+$$
+
+By comparing Eq. (5) with Eq. (6), we see that the only difference in our method is that the frozen, pre-trained teacher’s classifier is used for both teacher and the student. On the contrary, in KD, $W _ { S }$ is also optimized. This gives more degrees of freedom to the optimization algorithm, in particular, to adjust the weights of both the student’s feature extractor $f _ { S }$ and the student’s classifier $W _ { S }$ in order to minimize the loss. This has an impact on the learning of the student’s feature representation $h _ { S }$ which, in turn, hinders the generalization capability of the student on the test set. We confirm this hypothesis with the experiment of Section 4: Transferability of representations.
+
+Finally, we note that we found that, in practice, an $L _ { 2 }$ loss between the logits:
+
+$$
+L _ { K D } = \left\| \boldsymbol { W _ { T } ^ { \prime } } \boldsymbol { h _ { T } } - \boldsymbol { W _ { T } ^ { \prime } } \boldsymbol { h _ { S } } \right\| ^ { 2 } = \left\| \boldsymbol { h _ { T } } - \boldsymbol { h _ { S } } \right\| _ { W _ { T } } ^ { 2 } ,
+$$
+
+works slightly better than the cross-entropy loss. The comparison between different types of losses for $L _ { S R }$ is given in the appendix.
+
+Table 1: Effect of proposed losses ( ${ \cal L } _ { F M }$ and $L _ { S R }$ ) and position of distillation on the test set of CIFAR-100.   
+
+<table><tr><td>Method</td><td>Layer</td><td>Top-1 (%)</td><td>Top-5 (%)</td></tr><tr><td colspan="2">Student (WRN-16-4)</td><td>76.97</td><td>93.89</td></tr><tr><td colspan="2">Teacher (WRN-40-4) LFM</td><td>79.50 78.05</td><td>94.57 94.45</td></tr><tr><td>LSR</td><td>conv4 conv4</td><td>79.10</td><td>94.99</td></tr><tr><td>LFM+LSR</td><td>conv4</td><td>79.58</td><td>95.21</td></tr><tr><td>LFM+LsR</td><td>conv2</td><td>77.03</td><td>93.94</td></tr><tr><td>LFM+LsR</td><td>conv3</td><td>77.34</td><td>94.22</td></tr><tr><td></td><td>conv2+3+4</td><td></td><td></td></tr><tr><td>LFM+LsR</td><td></td><td>79.43</td><td>94.80</td></tr></table>
+
+Overall, in our method, we train the student network using three losses:
+
+$$
+{ \cal L } = { \cal L } _ { C E } + \alpha { \cal L } _ { F M } + \beta { \cal L } _ { S R } ,
+$$
+
+where $\alpha$ and $\beta$ are the weights used to scale the losses. The teacher network is pretrained and fixed during training the student. $L _ { C E }$ is the standard loss based on ground truth labels for the task in hand (e.g. cross-entropy loss for image classification). Note that this results in a very simple algorithm for training the student, summarized in Algorithm 1.
+
+# Algorithm 1 Knowledge distillation via Softmax Regression Representation Learning
+
+Input: Teacher network $T$ , Student network $S$ , input image x, ground truth label $y$ , weights $\alpha$ , $\beta$ . 1. Input $\mathbf { x }$ to $S$ to obtain feature $h _ { S }$ and class prediction $\hat { y }$ . Calculate cross entropy loss $\boldsymbol { L _ { C E } } = \mathcal { H } ( \boldsymbol { \hat { y } } , \boldsymbol { y } )$ ; 2. Input $\mathbf { x }$ to $T$ to obtain feature $h _ { T }$ . Calculate distillation losses from Eqs. (3) and (7); 3. Update $S$ by optimizing Eq. (8)
+
+Output: the updated $S$
+
+# 4 ABLATION STUDIES
+
+We conducted a set of ablation studies on CIFAR-100 (see Section 5.1) using a Wide ResNet (WRN) for both teacher (WRN-40-4) and student (WRN-16-4) (for network definitions, see Section 5).
+
+Are both $L _ { F M }$ and $L _ { S R }$ useful? To answer this question, we ran 3 experiments: using $L _ { F M }$ alone, $L _ { S R }$ alone, and combining them together ${ \cal L } _ { F M } + { \cal L } _ { S R }$ . The results of Table 1 (first 3 rows) clearly show that all proposed variants offer significant gains: when using $L _ { F M }$ and $L _ { S R }$ alone, $\sim 1 \%$ and $\sim 2 \%$ improvements in Top-1 accuracy were obtained. Moreover, when combining them together, an additional $\sim 0 . 4 \%$ improvement was gained. Importantly, the results show that $L _ { S R }$ is significantly more effective than $L _ { F M }$ . We further note at this point that we found that $L _ { F M }$ offers diminishing gains on ImageNet experiments.
+
+Where should the losses be applied? The proposed losses can be applied at other layers of the networks too. This is straightforward for $L _ { F M }$ . We can also extend $L _ { S R }$ to more layers, by transferring the mean feature of the student at each layer to the corresponding layer of the teacher using an AdaIN layer (Huang & Belongie, 2017). On one hand, applying the losses early in the network could ensure that the subsequent layers receive “better” features. On the other hand, features produced by early layers are not specialised to a particular class. Thus, applying the distillation losses towards the end of the network, where the activations encode discriminative, task-related features should lead to potentially stronger models. The results from Table 1 (last 3 rows) confirm our hypothesis: Applying the loss at multiple points in the network actually rather hurts accuracy.
+
+Teacher-student similarity: The overall aim of knowledge distillation is to make the student mimic the teacher’s output, so that the student is able to obtain similar performance to that of the teacher. Therefore, to see how well the student mimics the teacher, we measured the similarity between the teacher’s and student’s outputs using (a) the KL divergence between the teacher’s and student’s outputs, and (b) the cross-entropy loss between the student’s predictions and the ground truth labels.
+
+Table 2: KL divergence between teacher and student, and cross-entropy between student and ground truth on the test set of CIFAR-100. Teacher’s top-1 accuracy is $7 9 . 5 0 \%$ .   
+
+<table><tr><td>Method</td><td>KL div.with teacher</td><td>Cross-entropy with label</td><td>Top-1 (%)</td></tr><tr><td rowspan="3">Student KD AT</td><td>0.5964</td><td>0.9383</td><td>76.97</td></tr><tr><td>0.5818</td><td>0.9492</td><td>78.35</td></tr><tr><td>0.5406</td><td>0.9049</td><td>78.06</td></tr><tr><td rowspan="3">LFM LsR LFM+LSR</td><td>0.5701</td><td>0.8980</td><td>78.05</td></tr><tr><td>0.4828</td><td>0.8418</td><td>79.10</td></tr><tr><td>0.4597</td><td>0.8247</td><td>79.58</td></tr></table>
+
+Table 3: $L _ { 2 }$ Distance $\left\| h _ { T } - h _ { S } \right\| ^ { 2 }$ , and NMI calculated on the test set of CIFAR-100.   
+
+<table><tr><td>Method</td><td>Student</td><td>LFM</td><td>LsR</td><td>LFM+LSR</td></tr><tr><td>L2Distance</td><td>1.48</td><td>1.33</td><td>1.07</td><td>1.01</td></tr><tr><td>NMI (%).</td><td>77.20</td><td>78.31</td><td>79.35</td><td>79.85</td></tr><tr><td>Top-1(%).</td><td>76.97</td><td>78.05</td><td>79.10</td><td>79.58</td></tr></table>
+
+From Table 2, it can be observed that KD (Hinton et al., 2015) reduces the KL divergence with the teacher’s output offering $\sim 1 . 5 \%$ accuracy gain. AT (Zagoruyko & Komodakis, 2017) also decreases the KL divergence with the teacher’s output offering a smaller accuracy gain of $\sim 1 . 0 \%$ . Moreover, both proposed losses $L _ { F M }$ and $L _ { S R }$ and their combination ${ \cal L } _ { F M } + { \cal L } _ { S R }$ show considerably high similarity compared to the KD and AT. This similarity is one of the main reasons for the improved student’s accuracy offered by our method.
+
+![](images/e4ea2cd3fa645b65227bf0f46523a5ce32bfcc1dfad328554cc6553958df6451.jpg)  
+Figure 2: Visualization of $h _ { S }$ and $h _ { T }$ on the test set of CIFAR-100. Better viewed in color.
+
+Representations distance: Table 3 shows the $L _ { 2 }$ distance between the teacher and student representations $h _ { T }$ and $h _ { S }$ . The results, presented in Table 3, clearly show that both $L _ { F M }$ and $L _ { S R }$ narrow the distance, with their combination being the closest to the teacher.
+
+Normalized Mutual Information (NMI): Moreover, we calculated the NMI (Manning et al., 2008) which is a balanced metric that can be used to determine the quality of feature clustering. The results, presented in Table 3, show that ${ \cal L } _ { F M } + { \cal L } _ { S R }$ has the highest NMI score, meaning that the features are better clustered. Qualitative results are shown in Figure 2, which visualizes the features $h _ { S }$ and $h _ { T }$ . It can be observed that ${ \cal L } _ { F M } + { \cal L } _ { S R }$ is able to learn more discriminative features, which also correlates with quantitative accuracy gains.
+
+Transferability of representations: Following (Tian et al., 2020), this section aims to compare the representational power of the learned student’s representation $h _ { S }$ . To this end, we trained the student on CIFAR100, and then used it as a frozen feature extractor on top of which we train a linear classifier for 2 datasets: STL10 Coates et al. (2011) and CIFAR100. We compare the transfer ability of KD, CRD, $L _ { F M }$ , $L _ { S R }$ , and ${ \cal L } _ { F M } + { \cal L } _ { S R }$ . The superiority of the proposed losses over KD on STL is evident. Importantly, $L _ { S R }$ largely outperforms KD which confirms our analysis of Eqs. (5) and (6). The best results on STL are obtained by CRD. However, on CIFAR100, which is the target distillation dataset our method outperforms CRD.
+
+# 5 COMPARISON WITH STATE-OF-THE-ART
+
+We thoroughly evaluated the effectiveness of our method across multiple (a) network architectures (ResNet (He et al., 2016), Wide ResNet (Zagoruyko & Komodakis, 2016), MobileNetV2 (Sandler et al., 2018), MobileNet (Howard et al., 2017)) with different teacher-student capacities, (b) datasets (CIFAR10/100, ImageNet), and (c) domains (real-valued and binary networks). The training details for all experiments are provided in the appendix. We denote with ResNet-N a Residual Network with N convolutional layers (He et al., 2016). We denote with WRN-D- $k$ a WRN architecture with $D$ layers and an expansion rate of $k$ (Zagoruyko & Komodakis, 2017).
+
+Table 4: Transferability of representations from CIFAR100 to STL-10 and CIFAR100 by freezing $f ^ { S }$ and training a linear classifier on top. Top 1 $( \% )$ accuracy is provided.   
+
+<table><tr><td>Student</td><td>Dataset</td><td>KD</td><td>CRD</td><td>LFM</td><td>LSR</td><td>LFM+LsR</td></tr><tr><td>WRN16-4</td><td>STL10</td><td>68.75</td><td>72.45</td><td>69.3</td><td>71.44</td><td>72.17</td></tr><tr><td>WRN16-4</td><td>CIFAR100</td><td>78.28</td><td>78.46</td><td>77.95</td><td>79.03</td><td>79.34</td></tr><tr><td>MobileNetV2</td><td>STL10</td><td>62.17</td><td>69.74</td><td>66.12</td><td>68.23</td><td>68.95</td></tr><tr><td>MobileNetV2</td><td>CIFAR100</td><td>69.17</td><td>70.68</td><td>70.66</td><td>71.00</td><td>71.63</td></tr></table>
+
+Table 5: Top-1 accuracy $( \% )$ of various knowledge distillation methods on CIFAR-10.   
+
+<table><tr><td>Student(Params)</td><td>Teacher(Params)</td><td>Student</td><td>KD AT</td><td>OFD</td><td>RKD</td><td>Ours</td><td>Teacher</td></tr><tr><td>WRN-16-1 (0.18M)</td><td>WRN-16-2 (0.69M)</td><td>91.04</td><td>92.57 92.15</td><td>92.28</td><td>92.51</td><td>92.95</td><td>93.98</td></tr><tr><td>WRN-16-2 (0.69M)</td><td>WRN-40-2 (2.2M)</td><td>93.98</td><td>94.46 94.39</td><td>94.30</td><td>94.41</td><td>94.66</td><td>95.07</td></tr><tr><td>ResNet-8 (0.08M)</td><td>ResNet-26 (0.37M)</td><td>87.78</td><td>88.75 88.15</td><td>87.49</td><td>88.50</td><td>89.02</td><td>93.58</td></tr><tr><td>ResNet-14 (0.17M)</td><td>ResNet-26 (0.37M)</td><td>91.59</td><td>92.57 92.11</td><td>92.51</td><td>92.36</td><td>92.70</td><td>93.58</td></tr><tr><td>ResNet-18 (0.7M)</td><td>ResNet-34 (1.4M)</td><td>93.35</td><td>93.74 93.52</td><td>93.80</td><td>92.95</td><td>93.92</td><td>94.11</td></tr><tr><td>WRN-16-1 (0.18M)</td><td>ResNet-26 (0.37M)</td><td>91.04</td><td>92.42 91.32</td><td>92.47</td><td>92.08</td><td>92.94</td><td>93.58</td></tr></table>
+
+For the above mentioned settings, we compare our method with KD (Hinton et al., 2015) and AT (Zagoruyko & Komodakis, 2017), and the more recent methods of OFD (Heo et al., 2019a), RKD (Park et al., 2019), CRD (Tian et al., 2020).
+
+Overview of results: From our experiments, we conclude that our approach offers consistent gains across all of the above scenarios, outperforming all methods considered for all settings. Notably, our method is particularly effective for the most difficult datasets (i.e. CIFAR-100 and ImageNet).
+
+# 5.1 CIFAR-10/100
+
+For CIFAR-10, Top-1 performance of our method is shown in Table 5. We tested three cases representing different network architectures for student and teacher networks: the first two experiments are with WRNs. The following three experiments are with ResNets. In the last experiment, teacher and student have different network architectures. Overall, our method achieves the best results for all cases, with KD (Hinton et al., 2015) closely following.
+
+For CIFAR-100 (Krizhevsky & Hinton, 2009), we experimented with several student-teacher network pairs using different structures. Experiments are grouped in three sets. The first shows performance for different teacher and student capacities using WRNs: poor student - good teacher (WRN-16-2; WRN-40-4), descent student - good teacher (WRN-10-10; WRN-16-10); good student - good teacher (WRN-16-4; WRN-40-4). In the second set, we show that these results hold when using a different architecture, ResNet in this case. The final set is designed to show performance when teacher and student have different architectures (MobileNetV2, ResNet and WRN).
+
+Top-1 performance of our method is shown in Table 11. We observe that for almost all configurations, our method achieves consistent and significant accuracy gains over prior work. Furthermore, it is hard to tell which is the second best method as the remaining methods have their own advantages for different configurations. For WRN experiments, OFD ranks second. For ResNet and mixed structure experiments, CRD ranks second. More comparisons with other methods and results obtained by combining our method with KD and AT are provided in the supplementary material. Further improvements could be obtained by combining our method with others but this requires a comprehensive investigation which goes beyond the scope of this paper.
+
+Table 6: Top-1 accuracy $( \% )$ of various knowledge distillation methods on CIFAR-100.   
+
+<table><tr><td>Student (Params)</td><td>Teacher (Params)</td><td>Student</td><td>KD</td><td>AT</td><td>OFD</td><td>RKD</td><td>CRD</td><td>Ours</td><td>Teacher</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>WRN-40-4 (8.97M)</td><td>72.70</td><td>74.52</td><td>74.33</td><td>75.57</td><td>74.23</td><td>75.27</td><td>75.96</td><td>79.50</td></tr><tr><td>WRN-16-4 (2.77M)</td><td>WRN-40-4 (8.97M)</td><td>76.97</td><td>78.35</td><td>78.06</td><td>79.29</td><td>78.38</td><td>78.83</td><td>79.58</td><td>79.50</td></tr><tr><td>WRN-10-10 (7.49M)</td><td>WRN-16-10 (17.2M)</td><td>76.27</td><td>78.20</td><td>76.44</td><td>78.72</td><td>77.84</td><td>78.35</td><td>79.17</td><td>79.77</td></tr><tr><td>ResNet-10 (0.34M)</td><td>ResNet-34(1.39M)</td><td>68.42</td><td>69.18</td><td>68.49</td><td>68.94</td><td>68.70</td><td>70.24</td><td>69.91</td><td>72.05</td></tr><tr><td>ResNet-18 (0.75M)</td><td>ResNet-50 (1.99M)</td><td>71.07</td><td>73.41</td><td>71.90</td><td>72.79</td><td>70.93</td><td>73.23</td><td>73.47</td><td>73.31</td></tr><tr><td>ResNet-10 (4.95M)</td><td>ResNet-34 (21.33M)</td><td>75.01</td><td>77.35</td><td>76.87</td><td>77.35</td><td>77.46</td><td>77.37</td><td>77.90</td><td>78.44</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>ResNet-34 (21.33M)</td><td>72.70</td><td>73.95</td><td>72.32</td><td>74.78</td><td>73.91</td><td>74.88</td><td>75.38</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>ResNet-34 (21.33M)</td><td>68.42</td><td>69.36</td><td>68.60</td><td>69.45</td><td>68.75</td><td>71.36</td><td>71.58</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>WRN-40-4 (8.97M)</td><td>68.42</td><td>69.15</td><td>68.95</td><td>70.08</td><td>68.19</td><td>71.46</td><td>71.82</td><td>79.50</td></tr></table>
+
+Table 7: Comparison with state-of-the-art on ImageNet.   
+
+<table><tr><td>Student (Params)</td><td>Teacher (Params)</td><td></td><td>Student</td><td>KD</td><td>AT</td><td>OFD</td><td>RKD</td><td>CRD</td><td>Ours</td><td>Teacher</td></tr><tr><td>ResNet18 (11.69M)</td><td>ResNet34 (21.80M)</td><td>Top-1 Top-5</td><td>70.04 89.48</td><td>70.68 90.16</td><td>70.59 89.73</td><td>71.08 90.07</td><td>71.34 90.37</td><td>71.17 90.13</td><td>71.73 90.60</td><td>73.31 91.42</td></tr><tr><td>MobileNet (4.23M)）]</td><td>ResNet50 (25.56M)</td><td>Top-1 Top-5</td><td>70.13 89.49</td><td>70.68 90.30</td><td>70.72 90.03</td><td>71.25 90.34</td><td>71.32 90.62</td><td>71.40 90.42</td><td>72.49 90.92</td><td>76.16 92.86</td></tr></table>
+
+# 5.2 IMAGENET-1K
+
+Our experiments include two pairs of networks which are popular settings for ImageNet (Russakovsky et al., 2015). The first is distillation from ResNet-34 to ResNet-18 and the second one is distillation from ResNet-50 to MobileNet (Howard et al., 2017). Note that, following (Tian et al., 2020) on ImageNet, for KD, we set the weight for the KL loss to 0.9, the weight for cross-entropy loss to 0.5 which helps to obtain better accuracy.
+
+Our results are presented in Table 7. Again, we observe that our method achieves significant improvements over all competing methods. Moreover, there is no method which is consistently second: for ResNet-34 to ResNet-18 experiment, RKD is the second best while for ResNet-50 to MobileNet, CRD is the second best. Notably, for the latter experiment, CRD reduces the gap between the teacher and the student by $1 . 2 7 \%$ , while our method narrows it by $2 . 3 6 \%$ . Overall, our results on ImageNet validate the scalability of our method, and show that, when applied to a large-scale dataset, we achieve an even more favourable performance compared against competing methods.
+
+Table 8: Real-to-binary distillation results on CIFAR-100: a real-valued teacher ResNet-34 is used to distill a binary student. Real-to-binary distillation results on ImageNet-1K: a real-valued ResNet-18 is used to distill a binary student. OFD result might be suboptimal.   
+
+<table><tr><td>Dataset</td><td>Method</td><td>Binary</td><td>KD</td><td>AT</td><td>OFD</td><td>RKD</td><td>CRD</td><td>Ours</td><td>Real</td></tr><tr><td>CIFAR-100</td><td>ResNet34</td><td>65.34</td><td>68.65</td><td>68.54</td><td>66.84</td><td>68.61</td><td>68.78</td><td>70.50</td><td>75.08</td></tr><tr><td>ImageNet-1K</td><td>ResNet18</td><td>56.70</td><td>57.39</td><td>58.45</td><td>55.74</td><td>58.84</td><td>58.25</td><td>59.57</td><td>70.20</td></tr></table>
+
+# 5.3 BINARY NETWORKS DISTILLATION
+
+Training highly accurate binary neural networks (i.e. the most extreme case of quantization) is a very challenging task (Rastegari et al., 2016; Bulat & Tzimiropoulos, 2019), and to this end, knowledge distillation appears to be a promising direction. In this section, we present results by applying distillation for the task of training binary student networks guided by real-valued teacher networks. The network architecture is kept the same for both the student and the teacher in this case: specifically we used a ResNet using the modifications described in (Bulat & Tzimiropoulos, 2019).
+
+Table 8 presents our results. Again, we observe that our method outperforms all methods considerably, showing that it can effectively transfer knowledge between different domains. Note that it was not clear to us where to place the distillation position for OFD, so although we included our result for this method, we emphasize that this result might be suboptimal.
+
+# 5.4 FACIAL LANDMARK DETECTION
+
+Given a face image, the task is to localise a set of facial landmarks in terms of their (x,y) coordinates. This is often solved by using a CNN to directly regress the (x,y) coordinates of the facial landmarks. In order to show the suitability of our method for this problem, we use the WFLW Wu et al. (2018) dataset, which is one of the hardest benchmarks for this task. Performance is measured in terms of Normalised Mean Error (lower is better), which is the standard metric for the problem. In our experiment, we use a ResNet50 as the teacher and a ResNet8 as the student. The results, shown in Table 9, confirm the superior performance of our method when compared to other state-of-the-art methods.
+
+Table 9: Facial landmark detection with ResNet50 as teacher and ResNet8 as student. KD is adapted by using an L2 loss instead of a KL loss to measure the discrepancy between the teach and student predictions.   
+
+<table><tr><td>Student(Params)</td><td>Teacher(Params)</td><td>1</td><td>Student</td><td>KD</td><td>RKD</td><td>PKT</td><td>LFM</td><td>AT</td><td>Ours</td><td>Teacher</td></tr><tr><td></td><td>ResNet8(7.25M) ResNet50(26.25M)</td><td>NME</td><td>7.43</td><td>7.32</td><td>6.94</td><td>7.09</td><td>7.14</td><td>6.96</td><td>6.81</td><td>6.38</td></tr></table>
+
+# 6 CONCLUSION
+
+We presented a method for knowledge distillation that optimizes the output feature of the penultimate layer of the student network and hence is directly related to representation learning. A key to our method is the newly proposed Softmax Regression Loss which was found necessary for effective representation learning. We showed that our method consistently outperforms other stateof-the-art distillation methods for a wide range of experimental settings including multiple network architectures (ResNet, Wide ResNet, MobileNet) with different teacher-student capacities, datasets (CIFAR10/100, ImageNet), and domains (real-valued and binary networks).
+
+# REFERENCES
+
+Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In CVPR, 2019.   
+Cristian Bucilua, Rich Caruana, and Alexandru Niculescu-Mizil. Model compression. In ˇ KDD, 2006.   
+Adrian Bulat and Georgios Tzimiropoulos. XNOR-Net $^ { + + }$ : Improved binary neural networks. In BMVC, 2019.   
+Ting Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. ICML, 2020.   
+Jang Hyun Cho and Bharath Hariharan. On the efficacy of knowledge distillation. In ICCV, 2019.   
+Adam Coates, Andrew Ng, and Honglak Lee. An analysis of single-layer networks in unsupervised feature learning. In International conference on artificial intelligence and statistics, 2011.   
+Simon S Du and Jason D Lee. On the power of over-parametrization in neural networks with quadratic activation. In ICML, 2018.   
+Yushuo Guan, Pengyu Zhao, Bingxuan Wang, Yuanxing Zhang, Cong Yao, Kaigui Bian, and Jian Tang. Differentiable feature aggregation search for knowledge distillation. In ECCV, 2020.   
+Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and Huffman coding. ICLR, 2016.   
+Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, 2016.
+
+Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In CVPR, 2020.
+
+Byeongho Heo, Jeesoo Kim, Sangdoo Yun, Hyojin Park, Nojun Kwak, and Jin Young Choi. A comprehensive overhaul of feature distillation. In ICCV, 2019a.
+
+Byeongho Heo, Minsik Lee, Sangdoo Yun, and Jin Young Choi. Knowledge transfer via distillation of activation boundaries formed by hidden neurons. In AAAI, 2019b.
+
+Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv:1503.02531, 2015.
+
+Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. MobileNets: Efficient convolutional neural networks for mobile vision applications. arXiv:1704.04861, 2017.
+
+Xun Huang and Serge Belongie. Arbitrary style transfer in real-time with adaptive instance normalization. In ICCV, 2017.
+
+Zehao Huang and Naiyan Wang. Like what you like: Knowledge distill via neuron selectivity transfer. arXiv:1707.01219, 2017.
+
+Himalaya Jain, Spyros Gidaris, Nikos Komodakis, Patrick Perez, and Matthieu Cord. QUEST: ´ Quantized embedding space for transferring knowledge. In ECCV, 2020.
+
+Bingyi Kang, Saining Xie, Marcus Rohrbach, Zhicheng Yan, Albert Gordo, Jiashi Feng, and Yannis Kalantidis. Decoupling representation and classifier for long-tailed recognition. In ICLR, 2020.
+
+Jangho Kim, SeongUk Park, and Nojun Kwak. Paraphrasing complex network: Network compression via factor transfer. In NeurIPS, 2018.
+
+Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. Technical report, 2009.
+
+Vadim Lebedev and Victor Lempitsky. Fast convnets using group-wise brain damage. In CVPR, 2016.
+
+Seung Hyun Lee, Dae Ha Kim, and Byung Cheol Song. Self-supervised knowledge distillation using singular value decomposition. In ECCV, 2018.
+
+Changlin Li, Jiefeng Peng, Liuchun Yuan, Guangrun Wang, Xiaodan Liang, Liang Lin, and Xiaojun Chang. Block-wisely supervised neural architecture search with knowledge distillation. In CVPR, 2020a.
+
+Xiaojie Li, Jianlong Wu, Hongyu Fang, Yue Liao, Fei Wang, and Chen Qian. Local correlation consistency for knowledge distillation. In ECCV, 2020b.
+
+Hanxiao Liu, Karen Simonyan, and Yiming Yang. DARTS: Differentiable architecture search. arXiv, 2018.
+
+Yufan Liu, Jiajiong Cao, Bing Li, Chunfeng Yuan, Weiming Hu, Yangxi Li, and Yunqiang Duan. Knowledge distillation via instance relationship graph. In CVPR, 2019.
+
+Christopher D Manning, Prabhakar Raghavan, and Hinrich Schutze. ¨ Introduction to information retrieval (chapter 16). Cambridge university press, 2008.
+
+Wonpyo Park, Dongju Kim, Yan Lu, and Minsu Cho. Relational knowledge distillation. In CVPR, 2019.
+
+Nikolaos Passalis, Maria Tzelepi, and Anastasios Tefas. Heterogeneous knowledge distillation using information flow modeling. In CVPR, 2020.
+
+Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017.
+
+Baoyun Peng, Xiao Jin, Jiaheng Liu, Shunfeng Zhou, Yichao Wu, Yu Liu, Dongsheng Li, and Zhaoning Zhang. Correlation congruence for knowledge distillation. In ICCV, 2019.
+
+Mohammad Rastegari, Vicente Ordonez, Joseph Redmon, and Ali Farhadi. XNOR-Net: ImageNet classification using binary convolutional neural networks. In ECCV, 2016.
+
+Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo Gatta, and Yoshua Bengio. Fitnets: Hints for thin deep nets. ICLR, 2015.
+
+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. ImageNet Large Scale Visual Recognition Challenge. IJCV, 2015.
+
+Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, and Liang-Chieh Chen. MobileNetV2: Inverted residuals and linear bottlenecks. In CVPR, 2018.
+
+Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. TIT, 2018.
+
+Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive representation distillation. In ICLR, 2020.
+
+Frederick Tung and Greg Mori. Similarity-preserving knowledge distillation. In ICCV, 2019.
+
+Jiaxiang Wu, Cong Leng, Yuhang Wang, Qinghao Hu, and Jian Cheng. Quantized convolutional neural networks for mobile devices. In CVPR, 2016.
+
+Wayne Wu, Chen Qian, Shuo Yang, Quan Wang, Yici Cai, and Qiang Zhou. Look at boundary: A boundary-aware face alignment algorithm. In CVPR, 2018.
+
+Junho Yim, Donggyu Joo, Jihoon Bae, and Junmo Kim. A gift from knowledge distillation: Fast optimization, network minimization and transfer learning. In CVPR, 2017.
+
+Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. In BMVC, 2016.
+
+Sergey Zagoruyko and Nikos Komodakis. Paying more attention to attention: Improving the perfor mance of convolutional neural networks via attention transfer. In ICLR, 2017.
+
+Barret Zoph and Quoc V Le. Neural architecture search with reinforcement learning. ICLR, 2017.
+
+# A APPENDIX
+
+# A.1 STUDY OF THE HYPER-PARAMETERS $\alpha$ AND $\beta$
+
+We only performed a very basic search to find the best hyper-parameters. First, we fix $\alpha$ and search for the best $\beta$ . Then, we used the best $\beta$ , and search for the best $\alpha$ . This is sub-optimal compared to a full grid search over $\alpha$ and $\beta$ . Furthermore, after some preliminary experimentation, we considered only for 2 values: 1 and 5. Notably, we found that for all teacher-student pairs but (T:WRN40 4, S:MV2) alpha $^ { = 1 }$ is the optimal value. Furthermore, on ImageNet, the optimal values were $\alpha = 1$ , $\beta = 1$ for all teacher-student pairs considered.
+
+# A.2 DATASETS AND TRAINING DETAILS
+
+CIFAR-10 CIFAR-10 is a popular image classification dataset consisting of 50,000 training and 10,000 testing images equally distributed across 10 classes. All images are of resolution $3 2 \times 3 2 \mathrm { p x }$ . Following (Zagoruyko & Komodakis, 2017), during training, we randomly cropped and horizontally flipped the images. The ResNet models were trained for 350 epochs using SGD. The initial learning rate was set to 0.1, and then it was reduced by a factor of 10 at epochs 150, 250 and 320. Similarly, the WRN models were trained for 200 epochs with a learning rate of 0.1 that was subsequently reduced by 5 at epochs 60, 120 and 160. In all experiments, we set the dropout rate to 0.
+
+For traditional KD (Hinton et al., 2015), we set $\alpha \ : = \ : 0 . 9$ and $T \ = \ 4$ . For AT (Zagoruyko & Komodakis, 2017), as in (Zagoruyko & Komodakis, 2017; Tung & Mori, 2019), we set the weight of distillation loss to 1000. We note that, in our experiments, the AT loss is added after each layer group for WRN and the last two groups for ResNet as in (Zagoruyko & Komodakis, 2017). Following OFD (Heo et al., 2019a), we set the weight of distillation loss to $1 0 ^ { - 3 }$ . For RKD (Park et al., 2019), we set $\beta _ { 1 } = 2 5$ for distance, and $\beta _ { 2 } = 5 0$ for angle, as described in (Park et al., 2019; Tian et al., 2020). We did not compare with CRD (Tian et al., 2020) on CIFAR-10 because, in our experiments, we found that their parameter setting (used in their paper for CIFAR-100 and ImageNet-1K) does not obtain good performance on CIFAR-10.
+
+CIFAR-100 For CIFAR-100 (Krizhevsky & Hinton, 2009), we used a standard data augmentation scheme (Zagoruyko & Komodakis, 2017) including padding 4 pixels prior to random cropping and horizontal flipping. We used SGD with weight decay 5e-4 and momentum 0.9. Batch size was set to 128. Learning rate was set to 0.1; then decayed by 0.1 at epochs 100, 150, until training reached 200 epochs (Heo et al., 2019a).
+
+ImageNet-1K Images are cropped to $2 2 4 \times 2 2 4$ pixels for both training and evaluation. We used SGD with Nesterov momentum 0.9, weight decay $1 e - 4$ , initial learning rate 0.2 which was then dropped by a factor of 10 every 30 epochs, training in total for 100 epochs (for CRD we trained with 10 more epochs as suggested by the authors). Batch size was set to 512. For simplicity and to enable a fair comparison, we used pretrained PyTorch models Paszke et al. (2017) as teacher networks Heo et al. (2019a); Tian et al. (2020). For binary experiments, we used Adam as the optimizer with initial learning 0.002 which was then reduced by a factor of 10 every 30 epochs, training in total for 100 epochs.
+
+# A.3 ADDITIONAL ABLATION STUDIES
+
+Different losses for $L _ { S R }$ : This part expands Section 4 of our paper by evaluating different losses for $L _ { S R }$ . The following loss functions are compared:
+
+1. L2 loss: $L _ { S R - L 2 } ( p , q ) = \left\| p - q \right\| ^ { 2 }$ . This is the loss used in Section 4 of our paper   
+2. Cross Entropy loss (CE) with label $y$ $: L _ { S R - C E } ( q , y ) = \mathcal { H } ( q , y )$ .   
+3. KL loss with temperature $\tau$ Hinton et al. (2015): $L _ { S R - K L } ( p , q ) = K L ( q / \tau , p / \tau ) .$
+
+The results, presented in Table 10, show that all loss functions offer significant improvement gains while $L _ { F M } + L _ { S R - L 2 }$ achieves the best accuracy. Therefore, in our paper, $L _ { S R - L 2 }$ is used in all cases.
+
+Table 10: Evaluation of different loss functions for $L _ { S R }$ in terms of Top-1 accuracy on CIFAR-100.   
+
+<table><tr><td>Method</td><td>Top-1(%)</td><td>Top-5(%)</td></tr><tr><td>Student: WRN-16-4</td><td>76.97</td><td>93.89</td></tr><tr><td>Teacher:WRN-40-4</td><td>79.50</td><td>94.57</td></tr><tr><td>LFM+LSR-L2</td><td>79.58</td><td>95.21</td></tr><tr><td>LFM+LSR-CE</td><td>78.80</td><td>95.13</td></tr><tr><td>LFM+LSR-KL</td><td>79.04</td><td>95.12</td></tr></table>
+
+Combining our method with KD and AT: Table 11 shows additional comparisons on CIFAR100 by combining our method with AT Zagoruyko & Komodakis (2017) and KD Hinton et al. (2015), respectively. The results show that a straightforward combination did not provide satisfactory results, however it could be possible that a more comprehensive investigation might prove to be beneficial.
+
+# A.4 ADDITIONAL COMPARISONS
+
+This section provides additional comparisons using the evaluation framework of CRD Tian et al. (2020). Comparisons include distillation between models with the same architecture (e.g. ResNet56 to ResNet20) and between different architectures (e.g. ResNet50 to MobileNetV2). In order to maximize the fairness of the comparison, we followed their experimental setting. Thus, we did not choose the training parameters, teacher-student architecture pairs or methods to compare against. The competing methods included are:
+
+Table 11: Top-1 accuracy $( \% )$ of combining our method with KD and AT on CIFAR-100.   
+
+<table><tr><td>Student (Params)</td><td>Teacher (Params)</td><td>Student</td><td>KD</td><td>AT</td><td>KD+Ours</td><td>AT+Ours</td><td>Ours</td><td>Teacher</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>WRN-40-4 (8.97M)</td><td>72.70</td><td>74.52</td><td>74.33</td><td>74.97</td><td>75.01</td><td>75.96</td><td>79.50</td></tr><tr><td>WRN-16-4 (2.77M)</td><td>WRN-40-4 (8.97M)</td><td>76.97</td><td>78.35</td><td>78.06</td><td>79.00</td><td>79.09</td><td>79.58</td><td>79.50</td></tr><tr><td>WRN-10-10 (7.49M)</td><td>WRN-16-10 (17.2M)</td><td>76.27</td><td>78.20</td><td>76.44</td><td>78.84</td><td>77.79</td><td>79.17</td><td>79.77</td></tr><tr><td>ResNet-10 (0.34M)</td><td>ResNet-34 (1.39M)</td><td>68.42</td><td>69.18</td><td>68.49</td><td>70.41</td><td>69.41</td><td>69.91</td><td>72.05</td></tr><tr><td>ResNet-18 (0.75M)</td><td>ResNet-50 (1.99M)</td><td>71.07</td><td>73.41</td><td>71.90</td><td>73.46</td><td>73.17</td><td>73.47</td><td>72.83</td></tr><tr><td>ResNet-10 (4.95M)</td><td>ResNet-34 (21.33M)</td><td>75.01</td><td>77.35</td><td>76.87</td><td>77.64</td><td>77.48</td><td>77.90</td><td>78.44</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>ResNet-34 (21.33M)</td><td>72.70</td><td>73.95</td><td>72.32</td><td>74.90</td><td>74.71</td><td>75.38</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>ResNet-34(21.33M)</td><td>68.42</td><td>69.36</td><td>68.60</td><td>71.08</td><td>70.70</td><td>71.58</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>WRN-40-4 (8.97M)</td><td>68.42</td><td>69.15</td><td>68.95</td><td>70.85</td><td>70.63</td><td>71.82</td><td>79.50</td></tr></table>
+
+• Classic: Knowledge Distillation (KD) Hinton et al. (2015), FitNet Romero et al. (2015), Attention Transfer (AT) Zagoruyko & Komodakis (2017).   
+Most recent: Similarity-Preserving KD (SP) (Tung & Mori, 2019), Correlation Congruence (CC) (Peng et al., 2019), Variational Information Distillation (VID) (Ahn et al., 2019), Relational Knowledge Distillation (RKD) (Park et al., 2019), Distillation of Activation Boundaries (AB) (Heo et al., 2019b), Factor Transfer (FT) (Kim et al., 2018), Flow of Solution (FSP) (Yim et al., 2017) and Contrastive Representation Distillation (CRD) (Tian et al., 2020).
+
+Table 12: Distillation experiment with the same architectures (Tian et al., 2020): Top-1 accuracy $( \% )$ on CIFAR-100. The student models were trained with a teacher of the same architecture. We report average over 3 runs as in (Tian et al., 2020).   
+
+<table><tr><td>Teacher Student</td><td>wrn-40-2 wrn-16-2 75.61 73.26</td><td>wrn-40-2 wrn-40-1 75.61 71.98</td><td>resnet56 resnet20 72.34 69.06</td><td>resnet110 resnet20 74.31 69.06</td><td>resnet110 resnet32 74.31 71.14</td><td>resnet32x4 resnet8x4 79.42 72.50</td><td>vgg13 vgg8 74.64 70.36</td></tr><tr><td>KD</td><td>74.92</td><td>73.54</td><td>70.66</td><td>70.67</td><td>73.08</td><td>73.33</td><td>72.98</td></tr><tr><td>FitNet</td><td>73.58</td><td>72.24</td><td>69.21</td><td>68.99</td><td>71.06</td><td>73.50</td><td>71.02</td></tr><tr><td>AT</td><td>74.08</td><td>72.77</td><td>70.55</td><td>70.22</td><td>72.31</td><td>73.44</td><td>71.43</td></tr><tr><td>SP</td><td>73.83</td><td>72.43</td><td>69.67</td><td>70.04</td><td>72.69</td><td>72.94</td><td>72.68</td></tr><tr><td>CC</td><td>73.56</td><td>72.21</td><td>69.63</td><td>69.48</td><td>71.48</td><td>72.97</td><td>70.71</td></tr><tr><td>VID</td><td>74.11</td><td>73.30</td><td>70.38</td><td>70.16</td><td>72.61</td><td>73.09</td><td>71.23</td></tr><tr><td>RKD</td><td>73.35</td><td>72.22</td><td>69.61</td><td>69.25</td><td>71.82</td><td>71.90</td><td>71.48</td></tr><tr><td>PKT</td><td>74.54</td><td>73.45</td><td>70.34</td><td>70.25</td><td>72.61</td><td>73.64</td><td>72.88</td></tr><tr><td>AB</td><td>72.50</td><td>72.38</td><td>69.47</td><td>69.53</td><td>70.98</td><td>73.17</td><td>70.94</td></tr><tr><td>FT</td><td>73.25</td><td>71.59</td><td>69.84</td><td>70.22</td><td>72.37</td><td>72.86</td><td>70.58</td></tr><tr><td>FSP</td><td>72.91</td><td>0.00</td><td>69.95</td><td>70.11</td><td>71.89</td><td>72.62</td><td>70.23</td></tr><tr><td>NST</td><td>73.68</td><td>72.24</td><td>69.60</td><td>69.53</td><td>71.96</td><td>73.30</td><td>71.53</td></tr><tr><td>CRD</td><td>75.48</td><td>74.14</td><td>71.16</td><td>71.46</td><td>73.48</td><td>75.51</td><td>73.94</td></tr><tr><td>Ours</td><td>75.96</td><td>74.75</td><td>71.44</td><td>71.51</td><td>73.80</td><td>75.92</td><td>74.40</td></tr></table>
+
+Table 13: Distillation experiment with different architectures (Tian et al., 2020): Top-1 accuracy $( \% )$ on CIFAR-100. The student models were trained with a teacher of different architecture. We report average over 3 runs as in (Tian et al., 2020).   
+
+<table><tr><td>Teacher</td><td>vgg13 MobileNetV2 74.64</td><td>ResNet50 MobileNetV2 79.34</td><td>ResNet50 vgg8 79.34</td><td>resnet32x4 ShuffleNetV1 79.42</td><td>resnet32x4 ShuffleNetV2 79.42</td><td>wrn-40-2 ShuffleNetV1 75.61</td></tr><tr><td>Student</td><td>64.60</td><td>64.60 67.35</td><td>70.36 73.81</td><td>70.50 74.07</td><td>71.82 74.45</td><td>70.50 74.83</td></tr><tr><td>KD FitNet</td><td>67.37 64.14</td><td>63.16</td><td>70.69</td><td>73.59</td><td>73.54</td><td>73.73</td></tr><tr><td>AT</td><td>59.40</td><td>58.58</td><td>71.84</td><td>71.73</td><td>72.73</td><td>73.32</td></tr><tr><td>SP</td><td>66.30</td><td>68.08</td><td>73.34</td><td>73.48</td><td>74.56</td><td>74.52</td></tr><tr><td>CC</td><td>64.86</td><td>65.43</td><td>70.25</td><td>71.14</td><td>71.29</td><td>71.38</td></tr><tr><td>VID</td><td>65.56</td><td>67.57</td><td>70.30</td><td>73.38</td><td>73.40</td><td>73.61</td></tr><tr><td>RKD</td><td>64.52</td><td>64.43</td><td>71.50</td><td>72.28</td><td>73.21</td><td>72.21</td></tr><tr><td>PKT</td><td>67.13</td><td>66.52</td><td>73.01</td><td>74.10</td><td>74.69</td><td>73.89</td></tr><tr><td>AB</td><td>66.06</td><td>67.20</td><td>70.65</td><td>73.55</td><td>74.31</td><td>73.34</td></tr><tr><td>FT</td><td>61.78</td><td>60.99</td><td>70.29</td><td>71.75</td><td>72.50</td><td>72.03</td></tr><tr><td>NST</td><td>58.16</td><td>64.96</td><td>71.28</td><td>74.12</td><td>74.68</td><td>74.89</td></tr><tr><td>CRD</td><td>69.73</td><td>69.11</td><td>74.30</td><td>75.11</td><td>75.65</td><td>76.05</td></tr><tr><td>Ours</td><td>69.14</td><td>69.45</td><td>74.46</td><td>75.66</td><td>76.40</td><td>76.61</td></tr></table>

parse/train/ZzwDy_wiWv/ZzwDy_wiWv_content_list.json

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+    {
+        "type": "text",
+        "text": "KNOWLEDGE DISTILLATION VIA SOFTMAX REGRESSION REPRESENTATION LEARNING ",
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+        "type": "text",
+        "text": "Jing Yang   \nUniversity of Nottingham   \nNottingham, UK   \njing.yang2@nottingham.ac.uk   \nBrais Marinez   \nSamsung AI Center   \nCambridge, UK   \nbrais.mart@gmail.com   \nAdrian Bulat   \nSamsung AI Center   \nCambridge, UK   \nadrian@adrianbulat.com,   \nGeorgios Tzimiropoulos   \nSamsung AI Center   \nCambridge, UK   \nQueen Mary University of London   \nLondon, UK   \ng.tzimiropoulos@qmul.ac.uk ",
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+    {
+        "type": "text",
+        "text": "ABSTRACT ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "This paper addresses the problem of model compression via knowledge distillation. We advocate for a method that optimizes the output feature of the penultimate layer of the student network and hence is directly related to representation learning. To this end, we firstly propose a direct feature matching approach which focuses on optimizing the student’s penultimate layer only. Secondly and more importantly, because feature matching does not take into account the classification problem at hand, we propose a second approach that decouples representation learning and classification and utilizes the teacher’s pre-trained classifier to train the student’s penultimate layer feature. In particular, for the same input image, we wish the teacher’s and student’s feature to produce the same output when passed through the teacher’s classifier, which is achieved with a simple $L _ { 2 }$ loss. Our method is extremely simple to implement and straightforward to train and is shown to consistently outperform previous state-of-the-art methods over a large set of experimental settings including different (a) network architectures, (b) teacher-student capacities, (c) datasets, and (d) domains. The code is available at https://github.com/jingyang2017/KD_SRRL. ",
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+    {
+        "type": "text",
+        "text": "1 INTRODUCTION ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Recently, there has been a great amount of research effort to make Convolutional Neural Networks (CNNs) lightweight so that they can be deployed in devices with limited resources. To this end, several approaches for model compression have been proposed, including network pruning (Han et al., 2016; Lebedev & Lempitsky, 2016), network quantization (Rastegari et al., 2016; Wu et al., 2016), knowledge transfer/distillation (Hinton et al., 2015; Zagoruyko & Komodakis, 2017), and neural architecture search (Zoph & Le, 2017; Liu et al., 2018). Knowledge distillation (Bucilua et al., ˇ 2006; Hinton et al., 2015) aims to transfer knowledge from one network (the so-called “teacher”) to another (the so-called “student”). Typically, the teacher is a high-capacity model capable of achieving high accuracy, while the student is a compact model with much fewer parameters, thus also requiring much less computation. The goal of knowledge distillation is to use the teacher to improve the training of the student and push its accuracy closer to that of the teacher. ",
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+        "text": "The rationale behind knowledge distillation can be explained from an optimization perspective: there is evidence that high capacity models (i.e. the teacher) can find good local minima due to over-parameterization (Du & Lee, 2018; Soltanolkotabi et al., 2018). In knowledge distillation, such models are used to facilitate the optimization of lower capacity models (i.e. the student) during training. For example, in the seminal work of (Hinton et al., 2015), the softmax outputs of the teacher provide extra supervisory signals of inter-class similarities which facilitate the training of the student. In other influential works, intermediate representations extracted from the teacher such as feature tensors (Romero et al., 2015) or attention maps (Zagoruyko & Komodakis, 2017) have been used to define auxiliary loss functions used in the optimization of the student. ",
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+        "image_caption": [
+            "Figure 1: Our method performs knowledge distillation by minimizing the discrepancy between the penultimate feature representations $h _ { T }$ and $h _ { S }$ of the teacher and the student, respectively. To this end, we propose to use two losses: (a) the Feature Matching loss $L _ { F M }$ , and (b) the so-called Softmax Regression loss $L _ { S R }$ . In contrary to $L _ { F M }$ , our main contribution, $L _ { S R }$ , is designed to take into account the classification task at hand. To this end, $L _ { S R }$ imposes that for the same input image, the teacher’s and student’s feature produce the same output when passed through the teacher’s pre-trained and frozen classifier. Note that, for simplicity, the function for making the feature dimensionality of $h _ { T }$ and $h _ { S }$ the same is not shown. "
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+    {
+        "type": "text",
+        "text": "Training a network whose output feature representation is rich and powerful has been shown crucial for achieving high accuracy for the subsequent classification task in recent works in both unsupervised and supervised learning, see for example (Chen et al., 2020; He et al., 2020) and (Kang et al., 2020). Hence, in this paper, we are advocating for representation learning-based knowledge distillation by optimizing the student’s penultimate layer output feature. If we are able to do this effectively, we expect (and show experimentally) to end up with a student network which can generalize better than one trained with logit matching as in the KD paper of (Hinton et al., 2015). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Main contributions: To accomplish the aforementioned goal we propose two loss functions: The first loss function, akin to (Romero et al., 2015; Zagoruyko & Komodakis, 2017), is based on direct feature matching but focuses on optimizing the student’s penultimate layer feature only. Because direct feature matching might be difficult due to the lower representation capacity of the student and, more importantly, is detached from the classification task at hand, we also propose a second loss function: we propose to decouple representation learning and classification and utilize the teacher’s pre-trained classifier to train the student’s penultimate layer feature. In particular, for the same input image, we wish the teacher’s and student’s feature to produce the same output when passed through the teacher’s classifier, which is achieved with a simple $L _ { 2 }$ loss (see Fig. 1). This softmax regression projection is used to retain from the student’s feature the information that is relevant to classification, but since the projection matrix is pre-trained (learned during the teacher’s training phase) this does not compromise the representational power of the student’s feature. ",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Main results: Our method has two advantages: (1) It is simple and straightforward to implement. (2) It consistently outperforms state-of-the-art methods over a large set of experimental settings including different (a) network architectures (WideResNets, ResNets, MobileNets), (b) teacherstudent capacities, (c) datasets (CIFAR-10/100, ImageNet), and (d) domains (real-to-binary). ",
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+    {
+        "type": "text",
+        "text": "2 RELATED WORK ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Knowledge transfer: In the work of (Hinton et al., 2015), knowledge is defined as the teacher’s outputs after the final softmax layer. The softmax outputs carry richer information than one-hot labels because they provide extra supervision signals in terms of the inter-class similarities learned by the teacher. In a similar fashion to (Hinton et al., 2015), intermediate representations extracted from the teacher such as feature tensors (Romero et al., 2015) or attention maps (Zagoruyko & Komodakis, 2017) have been used to define loss functions used to facilitate the optimization of the student. Trying to match the whole feature tensor, as in FitNets (Romero et al., 2015), is hard and, in certain circumstances, such an approach may adversely affect the performance and convergence of the student. To relax the assumption of FitNet, Attention Transfer (AT) was proposed in (Zagoruyko & Komodakis, 2017) where knowledge takes the form of attention maps which are summaries of the energies of the feature tensors over the channel dimension. An extension of (Zagoruyko & Komodakis, 2017) using Maximum Mean Discrepancy of the network activations as a loss term for distillation was proposed in (Huang & Wang, 2017). Cho & Hariharan (2019) showed that very accurate networks are “too good” to be good teachers and proposed to mitigate this with early stopping of the teacher’s training. Recently, the work of (Heo et al., 2019a) studied the location within the network at which feature distillation should be applied and proposed margin ReLU and a specifically designed distance function that transfers only the useful (positive) information from the teacher to the student. More recently, Li et al. (Li et al., 2020a) proposed to supervise the blockwise architecture search by the architecture knowledge distilled from a teacher model. Another NAS based method was proposed in (Guan et al., 2020), in which a student-to-teacher loss is used to find the aggregation weights that match the learning ability of the student. Passalis et al. (2020) claimed that traditional KD ignores information plasticity during the training process, and proposed to model the information flow through the various layers of the teacher. ",
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+    {
+        "type": "text",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Feature relationship transfer: Another line of knowledge distillation methods focus on exploring transferring the relationship between features, rather than the actual features themselves. In (Yim et al., 2017), feature correlations are captured by computing the Gram matrix of features across layers for both teacher and student and then applying an $L _ { 2 }$ loss on pairs of teacher-student Gram matrices. The limitation of this work is the high computational cost, which is addressed to some extent in (Lee et al., 2018) by compressing the feature maps by singular value decomposition. Park et al. (2019) proposed a relational knowledge distillation method which computes distance-wise and angle-wise relations of each embedded feature vector. This idea is further explored in (Peng et al., 2019) and (Liu et al., 2019). In (Peng et al., 2019), Taylor series expansion is proposed to better capture the correlation between multiple instances. In (Liu et al., 2019), the instance feature and relationships are considered as vertexes and edges respectively in a graph and instance relationship graph is proposed to model the feature space transformation across layers. Inspired by the observation that semantically similar inputs should have similar activation patterns, (Tung & Mori, 2019) proposed a similarity-preserving knowledge distillation method which guides the student to mimic the teacher with respect to generating similar or dissimilar activations. More recently, (Jain et al., 2020) proposed to matching the student output with the teacher’s by distilling the knowledge through a quantized visual words space. Li et al. (2020b) proposed the local correlation exploration framework to represent the relationships of local regions in the feature space which contains more details and discriminative patterns. ",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Finally, a similar connection between distillation and representation learning was very recently made in (Tian et al., 2020) which uses contrastive learning for knowledge distillation. We note that our loss is not related to the one used in (Tian et al., 2020), is simpler, and as shown in Section 5, outperforms it for all of our experiments, often by a significant margin. ",
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+    },
+    {
+        "type": "text",
+        "text": "3 METHOD ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We denote by $T$ and $S$ the teacher and student networks respectively. We split these networks into two parts: (i) A convolutional feature extractor $f _ { N e t } , N e t = \\{ T , S \\}$ , the output of which at the $i$ -th layer is a feature tensor $F _ { N e t } ^ { i } \\in \\mathbb { R } ^ { C _ { N e t } ^ { i } \\times H ^ { i } \\times W ^ { i } }$ , where $C _ { N e t } ^ { i }$ is the output feature dimensionality, and $H ^ { i } , W ^ { i }$ the output spatial dimensions. We also denote by $\\begin{array} { r } { h _ { N e t } = \\sum _ { h = 1 } ^ { { H } ^ { L } } \\sum _ { w = 1 } ^ { { W } ^ { L } } F _ { N e t } ^ { L } \\in \\mathbb { R } ^ { C _ { N e t } ^ { L } } } \\end{array}$ the last layer feature representation learned by $f _ { N e t }$ . (ii) A projection matrix $W _ { N e t } \\in \\mathbb { R } ^ { C _ { N e t } ^ { L } \\times K }$ which projects the feature representation $h _ { N e t }$ into $K$ class logits $z _ { N e t } ^ { i } , i = 1 , \\dots , K$ , followed by the softmax function $\\begin{array} { r } { s ( z _ { N e t } ^ { i } ) = \\frac { \\exp ( z _ { N e t } ^ { i } / \\tau ) } { \\sum _ { j } \\exp ( z _ { N e t } ^ { j } / \\tau ) } } \\end{array}$ with temperature $\\tau$ $\\mathit { \\Pi } _ { \\tau } = 1$ for Cross Entropy loss) which put together form a softmax regression classifier into $K$ classes. ",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Knowledge Distillation (KD) (Hinton et al., 2015) trains the student with the following loss: ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "equation",
+        "img_path": "images/885f60af07cfb42db01ce6ecbe803233a1da74455bc9b3ce245c0dc8fc44a761.jpg",
+        "text": "$$\nL _ { K D } = - \\sum _ { k = 1 } ^ { K } s ( z _ { T } ^ { k } ) \\log s ( z _ { S } ^ { k } ) ,\n$$",
+        "text_format": "latex",
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "so that the discrepancy between the teacher’s and student’s classifiers is directly minimized. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "FitNets (Romero et al., 2015) match intermediate feature representations. For the $i$ -th layer, the following loss is defined: ",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "equation",
+        "img_path": "images/07f570ac1bd090b572a4ac64292241810499c1b7f14b4cc8216b8e90417cb760.jpg",
+        "text": "$$\nL _ { F i t } = \\left\\| F _ { T } ^ { i } - r ( F _ { S } ^ { i } ) \\right\\| ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where $r ( . )$ is a function for matching the feature tensor dimensions. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our work, we propose to minimize the discrepancy between the representations $h _ { T }$ and $h _ { S }$ . To accomplish this goal, we propose to use two losses. The first one is an $L _ { 2 }$ feature matching loss: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/dde36850b2bbd61d2af01b073b1e8cd8bb9b3693356302de3767a2b95b237b12.jpg",
+        "text": "$$\nL _ { F M } = \\left\\| h _ { T } - h _ { S } \\right\\| ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where for notational simplicity we dropped the dependency on $r ( . )$ . Hence, $L _ { F M }$ loss is a simplified FitNet loss which focuses only on the final representation learned. The intuition for this is that this feature is directly connected to the classifier and hence imposing the student’s feature to be similar to that of the teacher could have more impact on classification accuracy. Moreover, it might be questionable why one should optimize for other intermediate representations as in (Romero et al., 2015) especially when the student is a network of lower representational capacity. In Section 4: Where should the losses be applied?, we confirm that $L _ { F M }$ alone has a positive impact but feature matching in other layers is not helpful. ",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We found $L _ { F M }$ to be effective but only to limited extent. One disadvantage of $L _ { F M }$ and, in general, of all feature matching losses e.g. (Romero et al., 2015; Zagoruyko & Komodakis, 2017), is that it treats each channel dimension in the feature space independently, and ignores the inter-channel dependencies of the feature representations $h _ { S }$ and $h _ { T }$ for the final classification. This is in contrast to the original logit matching loss proposed by Hinton et al. in (Hinton et al., 2015) which directly targets classification accuracy. To alleviate the aforementioned problem, in this work, we propose a second loss for optimizing $h _ { S }$ which is directly linked with classification accuracy. To this end, we will use the teacher’s pre-trained Softmax Regression (SR) classifier. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Let us denote by $p$ the output of the teacher network when fed with some input image $x$ . Let us also feed the same image through the student network to obtain feature $h _ { S } ( x )$ . Finally let us pass $h _ { S } ( x )$ through the teacher’s SR classifier to obtain output $q$ . See also Fig. 1. Our loss is defined as: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/7347e09d1c5a0126ab5ac5d63f7edcc429acb5331e8335b85b5e2b802b1e39cd.jpg",
+        "text": "$$\nL _ { S R } = - p \\log q .\n$$",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "At this point, we make the following two observations: (1) If $p = q$ (and since the teacher’s classifier is frozen), then this implies that $\\bar { h _ { S } } ( x ) = h _ { T } ( x )$ which shows that indeed Eq. (4) optimizes the student’s feature representation $h _ { S }$ ( $h _ { T }$ is also frozen). (2) The loss of Eq.(4) can be written as: ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/e13ecc1ef95814038833da14ee0db93728cb9d6cd860366f85ebb5672a79ef3a.jpg",
+        "text": "$$\n\\begin{array} { r } { L _ { S R } = - s ( W _ { T } ^ { \\prime } h _ { T } ) \\log s ( W _ { T } ^ { \\prime } h _ { S } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Now let us now write KD loss in a similar way: ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "img_path": "images/4c5445e74dfd16dfabfb9b5f592751432ddb6e3bab6d4be8d8c01998af7488e8.jpg",
+        "text": "$$\n\\begin{array} { r } { L _ { K D } = - s ( W _ { T } ^ { \\prime } h _ { T } ) \\log s ( W _ { s } ^ { \\prime } h _ { S } ) . } \\end{array}\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By comparing Eq. (5) with Eq. (6), we see that the only difference in our method is that the frozen, pre-trained teacher’s classifier is used for both teacher and the student. On the contrary, in KD, $W _ { S }$ is also optimized. This gives more degrees of freedom to the optimization algorithm, in particular, to adjust the weights of both the student’s feature extractor $f _ { S }$ and the student’s classifier $W _ { S }$ in order to minimize the loss. This has an impact on the learning of the student’s feature representation $h _ { S }$ which, in turn, hinders the generalization capability of the student on the test set. We confirm this hypothesis with the experiment of Section 4: Transferability of representations. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Finally, we note that we found that, in practice, an $L _ { 2 }$ loss between the logits: ",
+        "bbox": [
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+    {
+        "type": "equation",
+        "img_path": "images/bccddf51c45a2b059355e9eb98733930b6e958568b1588f3bee66d70caef91a6.jpg",
+        "text": "$$\nL _ { K D } = \\left\\| \\boldsymbol { W _ { T } ^ { \\prime } } \\boldsymbol { h _ { T } } - \\boldsymbol { W _ { T } ^ { \\prime } } \\boldsymbol { h _ { S } } \\right\\| ^ { 2 } = \\left\\| \\boldsymbol { h _ { T } } - \\boldsymbol { h _ { S } } \\right\\| _ { W _ { T } } ^ { 2 } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "works slightly better than the cross-entropy loss. The comparison between different types of losses for $L _ { S R }$ is given in the appendix. ",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/a99681133514e9fe15a956063a4f10e10b8e2754bab8a56a75a213cadf12015f.jpg",
+        "table_caption": [
+            "Table 1: Effect of proposed losses ( ${ \\cal L } _ { F M }$ and $L _ { S R }$ ) and position of distillation on the test set of CIFAR-100. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Layer</td><td>Top-1 (%)</td><td>Top-5 (%)</td></tr><tr><td colspan=\"2\">Student (WRN-16-4)</td><td>76.97</td><td>93.89</td></tr><tr><td colspan=\"2\">Teacher (WRN-40-4) LFM</td><td>79.50 78.05</td><td>94.57 94.45</td></tr><tr><td>LSR</td><td>conv4 conv4</td><td>79.10</td><td>94.99</td></tr><tr><td>LFM+LSR</td><td>conv4</td><td>79.58</td><td>95.21</td></tr><tr><td>LFM+LsR</td><td>conv2</td><td>77.03</td><td>93.94</td></tr><tr><td>LFM+LsR</td><td>conv3</td><td>77.34</td><td>94.22</td></tr><tr><td></td><td>conv2+3+4</td><td></td><td></td></tr><tr><td>LFM+LsR</td><td></td><td>79.43</td><td>94.80</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Overall, in our method, we train the student network using three losses: ",
+        "bbox": [
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+            640,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "img_path": "images/2c4fc57121bedb6273d32a766f9e2cc5a0ddadffcfa08bee9a0c8cb2206e56cb.jpg",
+        "text": "$$\n{ \\cal L } = { \\cal L } _ { C E } + \\alpha { \\cal L } _ { F M } + \\beta { \\cal L } _ { S R } ,\n$$",
+        "text_format": "latex",
+        "bbox": [
+            398,
+            311,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where $\\alpha$ and $\\beta$ are the weights used to scale the losses. The teacher network is pretrained and fixed during training the student. $L _ { C E }$ is the standard loss based on ground truth labels for the task in hand (e.g. cross-entropy loss for image classification). Note that this results in a very simple algorithm for training the student, summarized in Algorithm 1. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Algorithm 1 Knowledge distillation via Softmax Regression Representation Learning ",
+        "text_level": 1,
+        "bbox": [
+            179,
+            404,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Input: Teacher network $T$ , Student network $S$ , input image x, ground truth label $y$ , weights $\\alpha$ , $\\beta$ . 1. Input $\\mathbf { x }$ to $S$ to obtain feature $h _ { S }$ and class prediction $\\hat { y }$ . Calculate cross entropy loss $\\boldsymbol { L _ { C E } } = \\mathcal { H } ( \\boldsymbol { \\hat { y } } , \\boldsymbol { y } )$ ; 2. Input $\\mathbf { x }$ to $T$ to obtain feature $h _ { T }$ . Calculate distillation losses from Eqs. (3) and (7); 3. Update $S$ by optimizing Eq. (8) ",
+        "bbox": [
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+            421,
+            825,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Output: the updated $S$ ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4 ABLATION STUDIES ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We conducted a set of ablation studies on CIFAR-100 (see Section 5.1) using a Wide ResNet (WRN) for both teacher (WRN-40-4) and student (WRN-16-4) (for network definitions, see Section 5). ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Are both $L _ { F M }$ and $L _ { S R }$ useful? To answer this question, we ran 3 experiments: using $L _ { F M }$ alone, $L _ { S R }$ alone, and combining them together ${ \\cal L } _ { F M } + { \\cal L } _ { S R }$ . The results of Table 1 (first 3 rows) clearly show that all proposed variants offer significant gains: when using $L _ { F M }$ and $L _ { S R }$ alone, $\\sim 1 \\%$ and $\\sim 2 \\%$ improvements in Top-1 accuracy were obtained. Moreover, when combining them together, an additional $\\sim 0 . 4 \\%$ improvement was gained. Importantly, the results show that $L _ { S R }$ is significantly more effective than $L _ { F M }$ . We further note at this point that we found that $L _ { F M }$ offers diminishing gains on ImageNet experiments. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Where should the losses be applied? The proposed losses can be applied at other layers of the networks too. This is straightforward for $L _ { F M }$ . We can also extend $L _ { S R }$ to more layers, by transferring the mean feature of the student at each layer to the corresponding layer of the teacher using an AdaIN layer (Huang & Belongie, 2017). On one hand, applying the losses early in the network could ensure that the subsequent layers receive “better” features. On the other hand, features produced by early layers are not specialised to a particular class. Thus, applying the distillation losses towards the end of the network, where the activations encode discriminative, task-related features should lead to potentially stronger models. The results from Table 1 (last 3 rows) confirm our hypothesis: Applying the loss at multiple points in the network actually rather hurts accuracy. ",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Teacher-student similarity: The overall aim of knowledge distillation is to make the student mimic the teacher’s output, so that the student is able to obtain similar performance to that of the teacher. Therefore, to see how well the student mimics the teacher, we measured the similarity between the teacher’s and student’s outputs using (a) the KL divergence between the teacher’s and student’s outputs, and (b) the cross-entropy loss between the student’s predictions and the ground truth labels. ",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/a05297133e0e330092f5d2e6bb153060312b537d2625343ec5cb893f5d78f2bb.jpg",
+        "table_caption": [
+            "Table 2: KL divergence between teacher and student, and cross-entropy between student and ground truth on the test set of CIFAR-100. Teacher’s top-1 accuracy is $7 9 . 5 0 \\%$ . "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>KL div.with teacher</td><td>Cross-entropy with label</td><td>Top-1 (%)</td></tr><tr><td rowspan=\"3\">Student KD AT</td><td>0.5964</td><td>0.9383</td><td>76.97</td></tr><tr><td>0.5818</td><td>0.9492</td><td>78.35</td></tr><tr><td>0.5406</td><td>0.9049</td><td>78.06</td></tr><tr><td rowspan=\"3\">LFM LsR LFM+LSR</td><td>0.5701</td><td>0.8980</td><td>78.05</td></tr><tr><td>0.4828</td><td>0.8418</td><td>79.10</td></tr><tr><td>0.4597</td><td>0.8247</td><td>79.58</td></tr></table>",
+        "bbox": [
+            236,
+            140,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/3d5f5482ee8da4c56b9fd3af67f6deb1db54c63833bbc6a9c75006bc93183347.jpg",
+        "table_caption": [
+            "Table 3: $L _ { 2 }$ Distance $\\left\\| h _ { T } - h _ { S } \\right\\| ^ { 2 }$ , and NMI calculated on the test set of CIFAR-100. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Student</td><td>LFM</td><td>LsR</td><td>LFM+LSR</td></tr><tr><td>L2Distance</td><td>1.48</td><td>1.33</td><td>1.07</td><td>1.01</td></tr><tr><td>NMI (%).</td><td>77.20</td><td>78.31</td><td>79.35</td><td>79.85</td></tr><tr><td>Top-1(%).</td><td>76.97</td><td>78.05</td><td>79.10</td><td>79.58</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "From Table 2, it can be observed that KD (Hinton et al., 2015) reduces the KL divergence with the teacher’s output offering $\\sim 1 . 5 \\%$ accuracy gain. AT (Zagoruyko & Komodakis, 2017) also decreases the KL divergence with the teacher’s output offering a smaller accuracy gain of $\\sim 1 . 0 \\%$ . Moreover, both proposed losses $L _ { F M }$ and $L _ { S R }$ and their combination ${ \\cal L } _ { F M } + { \\cal L } _ { S R }$ show considerably high similarity compared to the KD and AT. This similarity is one of the main reasons for the improved student’s accuracy offered by our method. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/e4ea2cd3fa645b65227bf0f46523a5ce32bfcc1dfad328554cc6553958df6451.jpg",
+        "image_caption": [
+            "Figure 2: Visualization of $h _ { S }$ and $h _ { T }$ on the test set of CIFAR-100. Better viewed in color. "
+        ],
+        "image_footnote": [],
+        "bbox": [
+            184,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Representations distance: Table 3 shows the $L _ { 2 }$ distance between the teacher and student representations $h _ { T }$ and $h _ { S }$ . The results, presented in Table 3, clearly show that both $L _ { F M }$ and $L _ { S R }$ narrow the distance, with their combination being the closest to the teacher. ",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Normalized Mutual Information (NMI): Moreover, we calculated the NMI (Manning et al., 2008) which is a balanced metric that can be used to determine the quality of feature clustering. The results, presented in Table 3, show that ${ \\cal L } _ { F M } + { \\cal L } _ { S R }$ has the highest NMI score, meaning that the features are better clustered. Qualitative results are shown in Figure 2, which visualizes the features $h _ { S }$ and $h _ { T }$ . It can be observed that ${ \\cal L } _ { F M } + { \\cal L } _ { S R }$ is able to learn more discriminative features, which also correlates with quantitative accuracy gains. ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Transferability of representations: Following (Tian et al., 2020), this section aims to compare the representational power of the learned student’s representation $h _ { S }$ . To this end, we trained the student on CIFAR100, and then used it as a frozen feature extractor on top of which we train a linear classifier for 2 datasets: STL10 Coates et al. (2011) and CIFAR100. We compare the transfer ability of KD, CRD, $L _ { F M }$ , $L _ { S R }$ , and ${ \\cal L } _ { F M } + { \\cal L } _ { S R }$ . The superiority of the proposed losses over KD on STL is evident. Importantly, $L _ { S R }$ largely outperforms KD which confirms our analysis of Eqs. (5) and (6). The best results on STL are obtained by CRD. However, on CIFAR100, which is the target distillation dataset our method outperforms CRD. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5 COMPARISON WITH STATE-OF-THE-ART ",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We thoroughly evaluated the effectiveness of our method across multiple (a) network architectures (ResNet (He et al., 2016), Wide ResNet (Zagoruyko & Komodakis, 2016), MobileNetV2 (Sandler et al., 2018), MobileNet (Howard et al., 2017)) with different teacher-student capacities, (b) datasets (CIFAR10/100, ImageNet), and (c) domains (real-valued and binary networks). The training details for all experiments are provided in the appendix. We denote with ResNet-N a Residual Network with N convolutional layers (He et al., 2016). We denote with WRN-D- $k$ a WRN architecture with $D$ layers and an expansion rate of $k$ (Zagoruyko & Komodakis, 2017). ",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/cb4ccc8c509356ccd86e99e73eeeb617d0cdfb617526279d3b1ce345eb308eb5.jpg",
+        "table_caption": [
+            "Table 4: Transferability of representations from CIFAR100 to STL-10 and CIFAR100 by freezing $f ^ { S }$ and training a linear classifier on top. Top 1 $( \\% )$ accuracy is provided. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Student</td><td>Dataset</td><td>KD</td><td>CRD</td><td>LFM</td><td>LSR</td><td>LFM+LsR</td></tr><tr><td>WRN16-4</td><td>STL10</td><td>68.75</td><td>72.45</td><td>69.3</td><td>71.44</td><td>72.17</td></tr><tr><td>WRN16-4</td><td>CIFAR100</td><td>78.28</td><td>78.46</td><td>77.95</td><td>79.03</td><td>79.34</td></tr><tr><td>MobileNetV2</td><td>STL10</td><td>62.17</td><td>69.74</td><td>66.12</td><td>68.23</td><td>68.95</td></tr><tr><td>MobileNetV2</td><td>CIFAR100</td><td>69.17</td><td>70.68</td><td>70.66</td><td>71.00</td><td>71.63</td></tr></table>",
+        "bbox": [
+            233,
+            145,
+            763,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/27c93ecb61e8341d2ed7d30decbd6946aa59fc07539e102e4d6ae4256aff14e7.jpg",
+        "table_caption": [
+            "Table 5: Top-1 accuracy $( \\% )$ of various knowledge distillation methods on CIFAR-10. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Student(Params)</td><td>Teacher(Params)</td><td>Student</td><td>KD AT</td><td>OFD</td><td>RKD</td><td>Ours</td><td>Teacher</td></tr><tr><td>WRN-16-1 (0.18M)</td><td>WRN-16-2 (0.69M)</td><td>91.04</td><td>92.57 92.15</td><td>92.28</td><td>92.51</td><td>92.95</td><td>93.98</td></tr><tr><td>WRN-16-2 (0.69M)</td><td>WRN-40-2 (2.2M)</td><td>93.98</td><td>94.46 94.39</td><td>94.30</td><td>94.41</td><td>94.66</td><td>95.07</td></tr><tr><td>ResNet-8 (0.08M)</td><td>ResNet-26 (0.37M)</td><td>87.78</td><td>88.75 88.15</td><td>87.49</td><td>88.50</td><td>89.02</td><td>93.58</td></tr><tr><td>ResNet-14 (0.17M)</td><td>ResNet-26 (0.37M)</td><td>91.59</td><td>92.57 92.11</td><td>92.51</td><td>92.36</td><td>92.70</td><td>93.58</td></tr><tr><td>ResNet-18 (0.7M)</td><td>ResNet-34 (1.4M)</td><td>93.35</td><td>93.74 93.52</td><td>93.80</td><td>92.95</td><td>93.92</td><td>94.11</td></tr><tr><td>WRN-16-1 (0.18M)</td><td>ResNet-26 (0.37M)</td><td>91.04</td><td>92.42 91.32</td><td>92.47</td><td>92.08</td><td>92.94</td><td>93.58</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "For the above mentioned settings, we compare our method with KD (Hinton et al., 2015) and AT (Zagoruyko & Komodakis, 2017), and the more recent methods of OFD (Heo et al., 2019a), RKD (Park et al., 2019), CRD (Tian et al., 2020). ",
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+    },
+    {
+        "type": "text",
+        "text": "Overview of results: From our experiments, we conclude that our approach offers consistent gains across all of the above scenarios, outperforming all methods considered for all settings. Notably, our method is particularly effective for the most difficult datasets (i.e. CIFAR-100 and ImageNet). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1 CIFAR-10/100 ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For CIFAR-10, Top-1 performance of our method is shown in Table 5. We tested three cases representing different network architectures for student and teacher networks: the first two experiments are with WRNs. The following three experiments are with ResNets. In the last experiment, teacher and student have different network architectures. Overall, our method achieves the best results for all cases, with KD (Hinton et al., 2015) closely following. ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "For CIFAR-100 (Krizhevsky & Hinton, 2009), we experimented with several student-teacher network pairs using different structures. Experiments are grouped in three sets. The first shows performance for different teacher and student capacities using WRNs: poor student - good teacher (WRN-16-2; WRN-40-4), descent student - good teacher (WRN-10-10; WRN-16-10); good student - good teacher (WRN-16-4; WRN-40-4). In the second set, we show that these results hold when using a different architecture, ResNet in this case. The final set is designed to show performance when teacher and student have different architectures (MobileNetV2, ResNet and WRN). ",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Top-1 performance of our method is shown in Table 11. We observe that for almost all configurations, our method achieves consistent and significant accuracy gains over prior work. Furthermore, it is hard to tell which is the second best method as the remaining methods have their own advantages for different configurations. For WRN experiments, OFD ranks second. For ResNet and mixed structure experiments, CRD ranks second. More comparisons with other methods and results obtained by combining our method with KD and AT are provided in the supplementary material. Further improvements could be obtained by combining our method with others but this requires a comprehensive investigation which goes beyond the scope of this paper. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8f34d51311cc656bd07ef493504b4d1f0586aac090713ab8d59a8e60a7d03c0e.jpg",
+        "table_caption": [
+            "Table 6: Top-1 accuracy $( \\% )$ of various knowledge distillation methods on CIFAR-100. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Student (Params)</td><td>Teacher (Params)</td><td>Student</td><td>KD</td><td>AT</td><td>OFD</td><td>RKD</td><td>CRD</td><td>Ours</td><td>Teacher</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>WRN-40-4 (8.97M)</td><td>72.70</td><td>74.52</td><td>74.33</td><td>75.57</td><td>74.23</td><td>75.27</td><td>75.96</td><td>79.50</td></tr><tr><td>WRN-16-4 (2.77M)</td><td>WRN-40-4 (8.97M)</td><td>76.97</td><td>78.35</td><td>78.06</td><td>79.29</td><td>78.38</td><td>78.83</td><td>79.58</td><td>79.50</td></tr><tr><td>WRN-10-10 (7.49M)</td><td>WRN-16-10 (17.2M)</td><td>76.27</td><td>78.20</td><td>76.44</td><td>78.72</td><td>77.84</td><td>78.35</td><td>79.17</td><td>79.77</td></tr><tr><td>ResNet-10 (0.34M)</td><td>ResNet-34(1.39M)</td><td>68.42</td><td>69.18</td><td>68.49</td><td>68.94</td><td>68.70</td><td>70.24</td><td>69.91</td><td>72.05</td></tr><tr><td>ResNet-18 (0.75M)</td><td>ResNet-50 (1.99M)</td><td>71.07</td><td>73.41</td><td>71.90</td><td>72.79</td><td>70.93</td><td>73.23</td><td>73.47</td><td>73.31</td></tr><tr><td>ResNet-10 (4.95M)</td><td>ResNet-34 (21.33M)</td><td>75.01</td><td>77.35</td><td>76.87</td><td>77.35</td><td>77.46</td><td>77.37</td><td>77.90</td><td>78.44</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>ResNet-34 (21.33M)</td><td>72.70</td><td>73.95</td><td>72.32</td><td>74.78</td><td>73.91</td><td>74.88</td><td>75.38</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>ResNet-34 (21.33M)</td><td>68.42</td><td>69.36</td><td>68.60</td><td>69.45</td><td>68.75</td><td>71.36</td><td>71.58</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>WRN-40-4 (8.97M)</td><td>68.42</td><td>69.15</td><td>68.95</td><td>70.08</td><td>68.19</td><td>71.46</td><td>71.82</td><td>79.50</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/e31f32fd993feef0b0908cff7f7a68d7559e2375274b9dbc61450dfd0a50b1e1.jpg",
+        "table_caption": [
+            "Table 7: Comparison with state-of-the-art on ImageNet. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Student (Params)</td><td>Teacher (Params)</td><td></td><td>Student</td><td>KD</td><td>AT</td><td>OFD</td><td>RKD</td><td>CRD</td><td>Ours</td><td>Teacher</td></tr><tr><td>ResNet18 (11.69M)</td><td>ResNet34 (21.80M)</td><td>Top-1 Top-5</td><td>70.04 89.48</td><td>70.68 90.16</td><td>70.59 89.73</td><td>71.08 90.07</td><td>71.34 90.37</td><td>71.17 90.13</td><td>71.73 90.60</td><td>73.31 91.42</td></tr><tr><td>MobileNet (4.23M)）]</td><td>ResNet50 (25.56M)</td><td>Top-1 Top-5</td><td>70.13 89.49</td><td>70.68 90.30</td><td>70.72 90.03</td><td>71.25 90.34</td><td>71.32 90.62</td><td>71.40 90.42</td><td>72.49 90.92</td><td>76.16 92.86</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "5.2 IMAGENET-1K ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Our experiments include two pairs of networks which are popular settings for ImageNet (Russakovsky et al., 2015). The first is distillation from ResNet-34 to ResNet-18 and the second one is distillation from ResNet-50 to MobileNet (Howard et al., 2017). Note that, following (Tian et al., 2020) on ImageNet, for KD, we set the weight for the KL loss to 0.9, the weight for cross-entropy loss to 0.5 which helps to obtain better accuracy. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Our results are presented in Table 7. Again, we observe that our method achieves significant improvements over all competing methods. Moreover, there is no method which is consistently second: for ResNet-34 to ResNet-18 experiment, RKD is the second best while for ResNet-50 to MobileNet, CRD is the second best. Notably, for the latter experiment, CRD reduces the gap between the teacher and the student by $1 . 2 7 \\%$ , while our method narrows it by $2 . 3 6 \\%$ . Overall, our results on ImageNet validate the scalability of our method, and show that, when applied to a large-scale dataset, we achieve an even more favourable performance compared against competing methods. ",
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+    {
+        "type": "table",
+        "img_path": "images/37b9ebe0a0b329ea2f1ca6810026440925ea3ea1b7118978cf003157cca90265.jpg",
+        "table_caption": [
+            "Table 8: Real-to-binary distillation results on CIFAR-100: a real-valued teacher ResNet-34 is used to distill a binary student. Real-to-binary distillation results on ImageNet-1K: a real-valued ResNet-18 is used to distill a binary student. OFD result might be suboptimal. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Method</td><td>Binary</td><td>KD</td><td>AT</td><td>OFD</td><td>RKD</td><td>CRD</td><td>Ours</td><td>Real</td></tr><tr><td>CIFAR-100</td><td>ResNet34</td><td>65.34</td><td>68.65</td><td>68.54</td><td>66.84</td><td>68.61</td><td>68.78</td><td>70.50</td><td>75.08</td></tr><tr><td>ImageNet-1K</td><td>ResNet18</td><td>56.70</td><td>57.39</td><td>58.45</td><td>55.74</td><td>58.84</td><td>58.25</td><td>59.57</td><td>70.20</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3 BINARY NETWORKS DISTILLATION ",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Training highly accurate binary neural networks (i.e. the most extreme case of quantization) is a very challenging task (Rastegari et al., 2016; Bulat & Tzimiropoulos, 2019), and to this end, knowledge distillation appears to be a promising direction. In this section, we present results by applying distillation for the task of training binary student networks guided by real-valued teacher networks. The network architecture is kept the same for both the student and the teacher in this case: specifically we used a ResNet using the modifications described in (Bulat & Tzimiropoulos, 2019). ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 8 presents our results. Again, we observe that our method outperforms all methods considerably, showing that it can effectively transfer knowledge between different domains. Note that it was not clear to us where to place the distillation position for OFD, so although we included our result for this method, we emphasize that this result might be suboptimal. ",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4 FACIAL LANDMARK DETECTION ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            104,
+            436,
+            117
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Given a face image, the task is to localise a set of facial landmarks in terms of their (x,y) coordinates. This is often solved by using a CNN to directly regress the (x,y) coordinates of the facial landmarks. In order to show the suitability of our method for this problem, we use the WFLW Wu et al. (2018) dataset, which is one of the hardest benchmarks for this task. Performance is measured in terms of Normalised Mean Error (lower is better), which is the standard metric for the problem. In our experiment, we use a ResNet50 as the teacher and a ResNet8 as the student. The results, shown in Table 9, confirm the superior performance of our method when compared to other state-of-the-art methods. ",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/1848b213c4ac61b4e5775f5337e2255144278f0caab66df83d003814e362e911.jpg",
+        "table_caption": [
+            "Table 9: Facial landmark detection with ResNet50 as teacher and ResNet8 as student. KD is adapted by using an L2 loss instead of a KL loss to measure the discrepancy between the teach and student predictions. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Student(Params)</td><td>Teacher(Params)</td><td>1</td><td>Student</td><td>KD</td><td>RKD</td><td>PKT</td><td>LFM</td><td>AT</td><td>Ours</td><td>Teacher</td></tr><tr><td></td><td>ResNet8(7.25M) ResNet50(26.25M)</td><td>NME</td><td>7.43</td><td>7.32</td><td>6.94</td><td>7.09</td><td>7.14</td><td>6.96</td><td>6.81</td><td>6.38</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "6 CONCLUSION ",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "We presented a method for knowledge distillation that optimizes the output feature of the penultimate layer of the student network and hence is directly related to representation learning. A key to our method is the newly proposed Softmax Regression Loss which was found necessary for effective representation learning. We showed that our method consistently outperforms other stateof-the-art distillation methods for a wide range of experimental settings including multiple network architectures (ResNet, Wide ResNet, MobileNet) with different teacher-student capacities, datasets (CIFAR10/100, ImageNet), and domains (real-valued and binary networks). ",
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+    {
+        "type": "text",
+        "text": "REFERENCES ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            540,
+            285,
+            555
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Sungsoo Ahn, Shell Xu Hu, Andreas Damianou, Neil D Lawrence, and Zhenwen Dai. Variational information distillation for knowledge transfer. In CVPR, 2019.   \nCristian Bucilua, Rich Caruana, and Alexandru Niculescu-Mizil. Model compression. In ˇ KDD, 2006.   \nAdrian Bulat and Georgios Tzimiropoulos. XNOR-Net $^ { + + }$ : Improved binary neural networks. In BMVC, 2019.   \nTing Chen, Simon Kornblith, Mohammad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. ICML, 2020.   \nJang Hyun Cho and Bharath Hariharan. On the efficacy of knowledge distillation. In ICCV, 2019.   \nAdam Coates, Andrew Ng, and Honglak Lee. An analysis of single-layer networks in unsupervised feature learning. In International conference on artificial intelligence and statistics, 2011.   \nSimon S Du and Jason D Lee. On the power of over-parametrization in neural networks with quadratic activation. In ICML, 2018.   \nYushuo Guan, Pengyu Zhao, Bingxuan Wang, Yuanxing Zhang, Cong Yao, Kaigui Bian, and Jian Tang. Differentiable feature aggregation search for knowledge distillation. In ECCV, 2020.   \nSong Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and Huffman coding. ICLR, 2016.   \nKaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In CVPR, 2016. ",
+        "bbox": [
+            171,
+            563,
+            826,
+            926
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "text",
+        "text": "Kaiming He, Haoqi Fan, Yuxin Wu, Saining Xie, and Ross Girshick. Momentum contrast for unsupervised visual representation learning. In CVPR, 2020. ",
+        "bbox": [
+            171,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Byeongho Heo, Jeesoo Kim, Sangdoo Yun, Hyojin Park, Nojun Kwak, and Jin Young Choi. A comprehensive overhaul of feature distillation. In ICCV, 2019a. ",
+        "bbox": [
+            174,
+            140,
+            823,
+            170
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Byeongho Heo, Minsik Lee, Sangdoo Yun, and Jin Young Choi. Knowledge transfer via distillation of activation boundaries formed by hidden neurons. In AAAI, 2019b. ",
+        "bbox": [
+            173,
+            178,
+            823,
+            208
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Geoffrey Hinton, Oriol Vinyals, and Jeff Dean. Distilling the knowledge in a neural network. arXiv:1503.02531, 2015. ",
+        "bbox": [
+            174,
+            215,
+            821,
+            244
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam. MobileNets: Efficient convolutional neural networks for mobile vision applications. arXiv:1704.04861, 2017. ",
+        "bbox": [
+            176,
+            252,
+            823,
+            296
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Xun Huang and Serge Belongie. Arbitrary style transfer in real-time with adaptive instance normalization. In ICCV, 2017. ",
+        "bbox": [
+            173,
+            304,
+            823,
+            333
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Zehao Huang and Naiyan Wang. Like what you like: Knowledge distill via neuron selectivity transfer. arXiv:1707.01219, 2017. ",
+        "bbox": [
+            171,
+            342,
+            823,
+            371
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Himalaya Jain, Spyros Gidaris, Nikos Komodakis, Patrick Perez, and Matthieu Cord. QUEST: ´ Quantized embedding space for transferring knowledge. In ECCV, 2020. ",
+        "bbox": [
+            173,
+            378,
+            821,
+            410
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Bingyi Kang, Saining Xie, Marcus Rohrbach, Zhicheng Yan, Albert Gordo, Jiashi Feng, and Yannis Kalantidis. Decoupling representation and classifier for long-tailed recognition. In ICLR, 2020. ",
+        "bbox": [
+            173,
+            416,
+            823,
+            446
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Jangho Kim, SeongUk Park, and Nojun Kwak. Paraphrasing complex network: Network compression via factor transfer. In NeurIPS, 2018. ",
+        "bbox": [
+            173,
+            454,
+            823,
+            484
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Alex Krizhevsky and Geoffrey Hinton. Learning multiple layers of features from tiny images. Technical report, 2009. ",
+        "bbox": [
+            173,
+            492,
+            823,
+            521
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Vadim Lebedev and Victor Lempitsky. Fast convnets using group-wise brain damage. In CVPR, 2016. ",
+        "bbox": [
+            174,
+            529,
+            823,
+            559
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Seung Hyun Lee, Dae Ha Kim, and Byung Cheol Song. Self-supervised knowledge distillation using singular value decomposition. In ECCV, 2018. ",
+        "bbox": [
+            173,
+            566,
+            823,
+            597
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Changlin Li, Jiefeng Peng, Liuchun Yuan, Guangrun Wang, Xiaodan Liang, Liang Lin, and Xiaojun Chang. Block-wisely supervised neural architecture search with knowledge distillation. In CVPR, 2020a. ",
+        "bbox": [
+            176,
+            604,
+            823,
+            647
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Xiaojie Li, Jianlong Wu, Hongyu Fang, Yue Liao, Fei Wang, and Chen Qian. Local correlation consistency for knowledge distillation. In ECCV, 2020b. ",
+        "bbox": [
+            171,
+            655,
+            823,
+            685
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Hanxiao Liu, Karen Simonyan, and Yiming Yang. DARTS: Differentiable architecture search. arXiv, 2018. ",
+        "bbox": [
+            173,
+            693,
+            821,
+            723
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Yufan Liu, Jiajiong Cao, Bing Li, Chunfeng Yuan, Weiming Hu, Yangxi Li, and Yunqiang Duan. Knowledge distillation via instance relationship graph. In CVPR, 2019. ",
+        "bbox": [
+            174,
+            731,
+            821,
+            761
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Christopher D Manning, Prabhakar Raghavan, and Hinrich Schutze. ¨ Introduction to information retrieval (chapter 16). Cambridge university press, 2008. ",
+        "bbox": [
+            174,
+            768,
+            821,
+            797
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Wonpyo Park, Dongju Kim, Yan Lu, and Minsu Cho. Relational knowledge distillation. In CVPR, 2019. ",
+        "bbox": [
+            173,
+            805,
+            823,
+            835
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Nikolaos Passalis, Maria Tzelepi, and Anastasios Tefas. Heterogeneous knowledge distillation using information flow modeling. In CVPR, 2020. ",
+        "bbox": [
+            173,
+            843,
+            825,
+            873
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. Automatic differentiation in pytorch. 2017. ",
+        "bbox": [
+            176,
+            881,
+            825,
+            924
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Baoyun Peng, Xiao Jin, Jiaheng Liu, Shunfeng Zhou, Yichao Wu, Yu Liu, Dongsheng Li, and Zhaoning Zhang. Correlation congruence for knowledge distillation. In ICCV, 2019. ",
+        "bbox": [
+            173,
+            103,
+            823,
+            132
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mohammad Rastegari, Vicente Ordonez, Joseph Redmon, and Ali Farhadi. XNOR-Net: ImageNet classification using binary convolutional neural networks. In ECCV, 2016. ",
+        "bbox": [
+            173,
+            142,
+            823,
+            171
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Adriana Romero, Nicolas Ballas, Samira Ebrahimi Kahou, Antoine Chassang, Carlo Gatta, and Yoshua Bengio. Fitnets: Hints for thin deep nets. ICLR, 2015. ",
+        "bbox": [
+            173,
+            181,
+            823,
+            210
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. ImageNet Large Scale Visual Recognition Challenge. IJCV, 2015. ",
+        "bbox": [
+            176,
+            219,
+            823,
+            263
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mark Sandler, Andrew Howard, Menglong Zhu, Andrey Zhmoginov, and Liang-Chieh Chen. MobileNetV2: Inverted residuals and linear bottlenecks. In CVPR, 2018. ",
+        "bbox": [
+            174,
+            273,
+            823,
+            303
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Mahdi Soltanolkotabi, Adel Javanmard, and Jason D Lee. Theoretical insights into the optimization landscape of over-parameterized shallow neural networks. TIT, 2018. ",
+        "bbox": [
+            174,
+            313,
+            823,
+            342
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Yonglong Tian, Dilip Krishnan, and Phillip Isola. Contrastive representation distillation. In ICLR, 2020. ",
+        "bbox": [
+            174,
+            351,
+            825,
+            381
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Frederick Tung and Greg Mori. Similarity-preserving knowledge distillation. In ICCV, 2019. ",
+        "bbox": [
+            173,
+            390,
+            787,
+            406
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Jiaxiang Wu, Cong Leng, Yuhang Wang, Qinghao Hu, and Jian Cheng. Quantized convolutional neural networks for mobile devices. In CVPR, 2016. ",
+        "bbox": [
+            173,
+            415,
+            823,
+            445
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Wayne Wu, Chen Qian, Shuo Yang, Quan Wang, Yici Cai, and Qiang Zhou. Look at boundary: A boundary-aware face alignment algorithm. In CVPR, 2018. ",
+        "bbox": [
+            173,
+            454,
+            823,
+            484
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Junho Yim, Donggyu Joo, Jihoon Bae, and Junmo Kim. A gift from knowledge distillation: Fast optimization, network minimization and transfer learning. In CVPR, 2017. ",
+        "bbox": [
+            173,
+            494,
+            825,
+            522
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sergey Zagoruyko and Nikos Komodakis. Wide residual networks. In BMVC, 2016. ",
+        "bbox": [
+            176,
+            534,
+            727,
+            547
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Sergey Zagoruyko and Nikos Komodakis. Paying more attention to attention: Improving the perfor mance of convolutional neural networks via attention transfer. In ICLR, 2017. ",
+        "bbox": [
+            174,
+            558,
+            818,
+            587
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "Barret Zoph and Quoc V Le. Neural architecture search with reinforcement learning. ICLR, 2017. ",
+        "bbox": [
+            173,
+            597,
+            816,
+            612
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A APPENDIX ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            640,
+            297,
+            656
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.1 STUDY OF THE HYPER-PARAMETERS $\\alpha$ AND $\\beta$ ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            672,
+            534,
+            686
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "We only performed a very basic search to find the best hyper-parameters. First, we fix $\\alpha$ and search for the best $\\beta$ . Then, we used the best $\\beta$ , and search for the best $\\alpha$ . This is sub-optimal compared to a full grid search over $\\alpha$ and $\\beta$ . Furthermore, after some preliminary experimentation, we considered only for 2 values: 1 and 5. Notably, we found that for all teacher-student pairs but (T:WRN40 4, S:MV2) alpha $^ { = 1 }$ is the optimal value. Furthermore, on ImageNet, the optimal values were $\\alpha = 1$ , $\\beta = 1$ for all teacher-student pairs considered. ",
+        "bbox": [
+            174,
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+            782
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "A.2 DATASETS AND TRAINING DETAILS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            800,
+            460,
+            814
+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "CIFAR-10 CIFAR-10 is a popular image classification dataset consisting of 50,000 training and 10,000 testing images equally distributed across 10 classes. All images are of resolution $3 2 \\times 3 2 \\mathrm { p x }$ . Following (Zagoruyko & Komodakis, 2017), during training, we randomly cropped and horizontally flipped the images. The ResNet models were trained for 350 epochs using SGD. The initial learning rate was set to 0.1, and then it was reduced by a factor of 10 at epochs 150, 250 and 320. Similarly, the WRN models were trained for 200 epochs with a learning rate of 0.1 that was subsequently reduced by 5 at epochs 60, 120 and 160. In all experiments, we set the dropout rate to 0. ",
+        "bbox": [
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+        ],
+        "page_idx": 10
+    },
+    {
+        "type": "text",
+        "text": "For traditional KD (Hinton et al., 2015), we set $\\alpha \\ : = \\ : 0 . 9$ and $T \\ = \\ 4$ . For AT (Zagoruyko & Komodakis, 2017), as in (Zagoruyko & Komodakis, 2017; Tung & Mori, 2019), we set the weight of distillation loss to 1000. We note that, in our experiments, the AT loss is added after each layer group for WRN and the last two groups for ResNet as in (Zagoruyko & Komodakis, 2017). Following OFD (Heo et al., 2019a), we set the weight of distillation loss to $1 0 ^ { - 3 }$ . For RKD (Park et al., 2019), we set $\\beta _ { 1 } = 2 5$ for distance, and $\\beta _ { 2 } = 5 0$ for angle, as described in (Park et al., 2019; Tian et al., 2020). We did not compare with CRD (Tian et al., 2020) on CIFAR-10 because, in our experiments, we found that their parameter setting (used in their paper for CIFAR-100 and ImageNet-1K) does not obtain good performance on CIFAR-10. ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "CIFAR-100 For CIFAR-100 (Krizhevsky & Hinton, 2009), we used a standard data augmentation scheme (Zagoruyko & Komodakis, 2017) including padding 4 pixels prior to random cropping and horizontal flipping. We used SGD with weight decay 5e-4 and momentum 0.9. Batch size was set to 128. Learning rate was set to 0.1; then decayed by 0.1 at epochs 100, 150, until training reached 200 epochs (Heo et al., 2019a). ",
+        "bbox": [
+            174,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "ImageNet-1K Images are cropped to $2 2 4 \\times 2 2 4$ pixels for both training and evaluation. We used SGD with Nesterov momentum 0.9, weight decay $1 e - 4$ , initial learning rate 0.2 which was then dropped by a factor of 10 every 30 epochs, training in total for 100 epochs (for CRD we trained with 10 more epochs as suggested by the authors). Batch size was set to 512. For simplicity and to enable a fair comparison, we used pretrained PyTorch models Paszke et al. (2017) as teacher networks Heo et al. (2019a); Tian et al. (2020). For binary experiments, we used Adam as the optimizer with initial learning 0.002 which was then reduced by a factor of 10 every 30 epochs, training in total for 100 epochs. ",
+        "bbox": [
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.3 ADDITIONAL ABLATION STUDIES ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            443,
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+            455
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Different losses for $L _ { S R }$ : This part expands Section 4 of our paper by evaluating different losses for $L _ { S R }$ . The following loss functions are compared: ",
+        "bbox": [
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+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "1. L2 loss: $L _ { S R - L 2 } ( p , q ) = \\left\\| p - q \\right\\| ^ { 2 }$ . This is the loss used in Section 4 of our paper   \n2. Cross Entropy loss (CE) with label $y$ $: L _ { S R - C E } ( q , y ) = \\mathcal { H } ( q , y )$ .   \n3. KL loss with temperature $\\tau$ Hinton et al. (2015): $L _ { S R - K L } ( p , q ) = K L ( q / \\tau , p / \\tau ) .$ ",
+        "bbox": [
+            210,
+            508,
+            774,
+            566
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "The results, presented in Table 10, show that all loss functions offer significant improvement gains while $L _ { F M } + L _ { S R - L 2 }$ achieves the best accuracy. Therefore, in our paper, $L _ { S R - L 2 }$ is used in all cases. ",
+        "bbox": [
+            176,
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+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/7cffba765bc7c2c5afadb404a9bc6dcb699ad003e932eb4308928b6cecbcb293.jpg",
+        "table_caption": [
+            "Table 10: Evaluation of different loss functions for $L _ { S R }$ in terms of Top-1 accuracy on CIFAR-100. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Top-1(%)</td><td>Top-5(%)</td></tr><tr><td>Student: WRN-16-4</td><td>76.97</td><td>93.89</td></tr><tr><td>Teacher:WRN-40-4</td><td>79.50</td><td>94.57</td></tr><tr><td>LFM+LSR-L2</td><td>79.58</td><td>95.21</td></tr><tr><td>LFM+LSR-CE</td><td>78.80</td><td>95.13</td></tr><tr><td>LFM+LSR-KL</td><td>79.04</td><td>95.12</td></tr></table>",
+        "bbox": [
+            338,
+            662,
+            660,
+            750
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "Combining our method with KD and AT: Table 11 shows additional comparisons on CIFAR100 by combining our method with AT Zagoruyko & Komodakis (2017) and KD Hinton et al. (2015), respectively. The results show that a straightforward combination did not provide satisfactory results, however it could be possible that a more comprehensive investigation might prove to be beneficial. ",
+        "bbox": [
+            173,
+            773,
+            826,
+            830
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "A.4 ADDITIONAL COMPARISONS ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            848,
+            413,
+            862
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "text",
+        "text": "This section provides additional comparisons using the evaluation framework of CRD Tian et al. (2020). Comparisons include distillation between models with the same architecture (e.g. ResNet56 to ResNet20) and between different architectures (e.g. ResNet50 to MobileNetV2). In order to maximize the fairness of the comparison, we followed their experimental setting. Thus, we did not choose the training parameters, teacher-student architecture pairs or methods to compare against. The competing methods included are: ",
+        "bbox": [
+            174,
+            882,
+            825,
+            924
+        ],
+        "page_idx": 11
+    },
+    {
+        "type": "table",
+        "img_path": "images/cdad6ac77fb17e288b18d36d436dd280325d90645c6ff6f1830b2eaf96e11091.jpg",
+        "table_caption": [
+            "Table 11: Top-1 accuracy $( \\% )$ of combining our method with KD and AT on CIFAR-100. "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Student (Params)</td><td>Teacher (Params)</td><td>Student</td><td>KD</td><td>AT</td><td>KD+Ours</td><td>AT+Ours</td><td>Ours</td><td>Teacher</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>WRN-40-4 (8.97M)</td><td>72.70</td><td>74.52</td><td>74.33</td><td>74.97</td><td>75.01</td><td>75.96</td><td>79.50</td></tr><tr><td>WRN-16-4 (2.77M)</td><td>WRN-40-4 (8.97M)</td><td>76.97</td><td>78.35</td><td>78.06</td><td>79.00</td><td>79.09</td><td>79.58</td><td>79.50</td></tr><tr><td>WRN-10-10 (7.49M)</td><td>WRN-16-10 (17.2M)</td><td>76.27</td><td>78.20</td><td>76.44</td><td>78.84</td><td>77.79</td><td>79.17</td><td>79.77</td></tr><tr><td>ResNet-10 (0.34M)</td><td>ResNet-34 (1.39M)</td><td>68.42</td><td>69.18</td><td>68.49</td><td>70.41</td><td>69.41</td><td>69.91</td><td>72.05</td></tr><tr><td>ResNet-18 (0.75M)</td><td>ResNet-50 (1.99M)</td><td>71.07</td><td>73.41</td><td>71.90</td><td>73.46</td><td>73.17</td><td>73.47</td><td>72.83</td></tr><tr><td>ResNet-10 (4.95M)</td><td>ResNet-34 (21.33M)</td><td>75.01</td><td>77.35</td><td>76.87</td><td>77.64</td><td>77.48</td><td>77.90</td><td>78.44</td></tr><tr><td>WRN-16-2 (0.70M)</td><td>ResNet-34 (21.33M)</td><td>72.70</td><td>73.95</td><td>72.32</td><td>74.90</td><td>74.71</td><td>75.38</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>ResNet-34(21.33M)</td><td>68.42</td><td>69.36</td><td>68.60</td><td>71.08</td><td>70.70</td><td>71.58</td><td>78.44</td></tr><tr><td>MobileNetV2 (2.37M)</td><td>WRN-40-4 (8.97M)</td><td>68.42</td><td>69.15</td><td>68.95</td><td>70.85</td><td>70.63</td><td>71.82</td><td>79.50</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "text",
+        "text": "• Classic: Knowledge Distillation (KD) Hinton et al. (2015), FitNet Romero et al. (2015), Attention Transfer (AT) Zagoruyko & Komodakis (2017).   \nMost recent: Similarity-Preserving KD (SP) (Tung & Mori, 2019), Correlation Congruence (CC) (Peng et al., 2019), Variational Information Distillation (VID) (Ahn et al., 2019), Relational Knowledge Distillation (RKD) (Park et al., 2019), Distillation of Activation Boundaries (AB) (Heo et al., 2019b), Factor Transfer (FT) (Kim et al., 2018), Flow of Solution (FSP) (Yim et al., 2017) and Contrastive Representation Distillation (CRD) (Tian et al., 2020). ",
+        "bbox": [
+            212,
+            330,
+            825,
+            448
+        ],
+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/23fb2d4769208be4e657a3ccc11e031ca1265609802401321b1f9202dc426f92.jpg",
+        "table_caption": [
+            "Table 12: Distillation experiment with the same architectures (Tian et al., 2020): Top-1 accuracy $( \\% )$ on CIFAR-100. The student models were trained with a teacher of the same architecture. We report average over 3 runs as in (Tian et al., 2020). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Teacher Student</td><td>wrn-40-2 wrn-16-2 75.61 73.26</td><td>wrn-40-2 wrn-40-1 75.61 71.98</td><td>resnet56 resnet20 72.34 69.06</td><td>resnet110 resnet20 74.31 69.06</td><td>resnet110 resnet32 74.31 71.14</td><td>resnet32x4 resnet8x4 79.42 72.50</td><td>vgg13 vgg8 74.64 70.36</td></tr><tr><td>KD</td><td>74.92</td><td>73.54</td><td>70.66</td><td>70.67</td><td>73.08</td><td>73.33</td><td>72.98</td></tr><tr><td>FitNet</td><td>73.58</td><td>72.24</td><td>69.21</td><td>68.99</td><td>71.06</td><td>73.50</td><td>71.02</td></tr><tr><td>AT</td><td>74.08</td><td>72.77</td><td>70.55</td><td>70.22</td><td>72.31</td><td>73.44</td><td>71.43</td></tr><tr><td>SP</td><td>73.83</td><td>72.43</td><td>69.67</td><td>70.04</td><td>72.69</td><td>72.94</td><td>72.68</td></tr><tr><td>CC</td><td>73.56</td><td>72.21</td><td>69.63</td><td>69.48</td><td>71.48</td><td>72.97</td><td>70.71</td></tr><tr><td>VID</td><td>74.11</td><td>73.30</td><td>70.38</td><td>70.16</td><td>72.61</td><td>73.09</td><td>71.23</td></tr><tr><td>RKD</td><td>73.35</td><td>72.22</td><td>69.61</td><td>69.25</td><td>71.82</td><td>71.90</td><td>71.48</td></tr><tr><td>PKT</td><td>74.54</td><td>73.45</td><td>70.34</td><td>70.25</td><td>72.61</td><td>73.64</td><td>72.88</td></tr><tr><td>AB</td><td>72.50</td><td>72.38</td><td>69.47</td><td>69.53</td><td>70.98</td><td>73.17</td><td>70.94</td></tr><tr><td>FT</td><td>73.25</td><td>71.59</td><td>69.84</td><td>70.22</td><td>72.37</td><td>72.86</td><td>70.58</td></tr><tr><td>FSP</td><td>72.91</td><td>0.00</td><td>69.95</td><td>70.11</td><td>71.89</td><td>72.62</td><td>70.23</td></tr><tr><td>NST</td><td>73.68</td><td>72.24</td><td>69.60</td><td>69.53</td><td>71.96</td><td>73.30</td><td>71.53</td></tr><tr><td>CRD</td><td>75.48</td><td>74.14</td><td>71.16</td><td>71.46</td><td>73.48</td><td>75.51</td><td>73.94</td></tr><tr><td>Ours</td><td>75.96</td><td>74.75</td><td>71.44</td><td>71.51</td><td>73.80</td><td>75.92</td><td>74.40</td></tr></table>",
+        "bbox": [
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+        "page_idx": 12
+    },
+    {
+        "type": "table",
+        "img_path": "images/359f3c0c341c89702acb0387051f6ca2fe82a5c2dd2a9ebae8f53d2354a36e77.jpg",
+        "table_caption": [
+            "Table 13: Distillation experiment with different architectures (Tian et al., 2020): Top-1 accuracy $( \\% )$ on CIFAR-100. The student models were trained with a teacher of different architecture. We report average over 3 runs as in (Tian et al., 2020). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Teacher</td><td>vgg13 MobileNetV2 74.64</td><td>ResNet50 MobileNetV2 79.34</td><td>ResNet50 vgg8 79.34</td><td>resnet32x4 ShuffleNetV1 79.42</td><td>resnet32x4 ShuffleNetV2 79.42</td><td>wrn-40-2 ShuffleNetV1 75.61</td></tr><tr><td>Student</td><td>64.60</td><td>64.60 67.35</td><td>70.36 73.81</td><td>70.50 74.07</td><td>71.82 74.45</td><td>70.50 74.83</td></tr><tr><td>KD FitNet</td><td>67.37 64.14</td><td>63.16</td><td>70.69</td><td>73.59</td><td>73.54</td><td>73.73</td></tr><tr><td>AT</td><td>59.40</td><td>58.58</td><td>71.84</td><td>71.73</td><td>72.73</td><td>73.32</td></tr><tr><td>SP</td><td>66.30</td><td>68.08</td><td>73.34</td><td>73.48</td><td>74.56</td><td>74.52</td></tr><tr><td>CC</td><td>64.86</td><td>65.43</td><td>70.25</td><td>71.14</td><td>71.29</td><td>71.38</td></tr><tr><td>VID</td><td>65.56</td><td>67.57</td><td>70.30</td><td>73.38</td><td>73.40</td><td>73.61</td></tr><tr><td>RKD</td><td>64.52</td><td>64.43</td><td>71.50</td><td>72.28</td><td>73.21</td><td>72.21</td></tr><tr><td>PKT</td><td>67.13</td><td>66.52</td><td>73.01</td><td>74.10</td><td>74.69</td><td>73.89</td></tr><tr><td>AB</td><td>66.06</td><td>67.20</td><td>70.65</td><td>73.55</td><td>74.31</td><td>73.34</td></tr><tr><td>FT</td><td>61.78</td><td>60.99</td><td>70.29</td><td>71.75</td><td>72.50</td><td>72.03</td></tr><tr><td>NST</td><td>58.16</td><td>64.96</td><td>71.28</td><td>74.12</td><td>74.68</td><td>74.89</td></tr><tr><td>CRD</td><td>69.73</td><td>69.11</td><td>74.30</td><td>75.11</td><td>75.65</td><td>76.05</td></tr><tr><td>Ours</td><td>69.14</td><td>69.45</td><td>74.46</td><td>75.66</td><td>76.40</td><td>76.61</td></tr></table>",
+        "bbox": [
+            173,
+            414,
+            880,
+            660
+        ],
+        "page_idx": 13
+    }
+]

parse/train/rkgAGAVKPr/rkgAGAVKPr.md

@@ -0,0 +1,427 @@
+# META-DATASET: A DATASET OF DATASETS FORLEARNING TO LEARN FROM FEW EXAMPLES
+
+Eleni Triantafillou∗†, Tyler $\mathbf { Z } \mathbf { h } \mathbf { u } ^ { \dagger }$ , Vincent Dumoulin†, Pascal Lamblin†, Utku Evci†,   
+Kelvin $\mathbf { X } \mathbf { u } ^ { \mathrm { { f } \dagger } }$ , Ross Goroshin†, Carles Gelada†, Kevin Swersky†,   
+Pierre-Antoine Manzagol† & Hugo Larochelle†   
+∗University of Toronto and Vector Institute, †Google AI, ‡University of California, Berkeley   
+Correspondence to: eleni@cs.toronto.edu
+
+# ABSTRACT
+
+Few-shot classification refers to learning a classifier for new classes given only a few examples. While a plethora of models have emerged to tackle it, we find the procedure and datasets that are used to assess their progress lacking. To address this limitation, we propose META-DATASET: a new benchmark for training and evaluating models that is large-scale, consists of diverse datasets, and presents more realistic tasks. We experiment with popular baselines and meta-learners on META-DATASET, along with a competitive method that we propose. We analyze performance as a function of various characteristics of test tasks and examine the models’ ability to leverage diverse training sources for improving their generalization. We also propose a new set of baselines for quantifying the benefit of meta-learning in META-DATASET. Our extensive experimentation has uncovered important research challenges and we hope to inspire work in these directions.
+
+# 1 INTRODUCTION
+
+Few-shot learning refers to learning new concepts from few examples, an ability that humans naturally possess, but machines still lack. Improving on this aspect would lead to more efficient algorithms that can flexibly expand their knowledge without requiring large labeled datasets. We focus on few-shot classification: classifying unseen examples into one of $N$ new ‘test’ classes, given only a few reference examples of each. Recent progress in this direction has been made by considering a meta-problem: though we are not interested in learning about any training class in particular, we can exploit the training classes for the purpose of learning to learn new classes from few examples, thus acquiring a learning procedure that can be directly applied to new few-shot learning problems too.
+
+This intuition has inspired numerous models of increasing complexity (see Related Work for some examples). However, we believe that the commonly-used setup for measuring success in this direction is lacking. Specifically, two datasets have emerged as de facto benchmarks for few-shot learning: Omniglot (Lake et al., 2015), and mini-ImageNet (Vinyals et al., 2016), and we believe that both of them are approaching their limit in terms of allowing one to discriminate between the merits of different approaches. Omniglot is a dataset of 1623 handwritten characters from 50 different alphabets and contains 20 examples per class (character). Most recent methods obtain very high accuracy on Omniglot, rendering the comparisons between them mostly uninformative. mini-ImageNet is formed out of 100 ImageNet (Russakovsky et al., 2015) classes (64/16/20 for train/validation/test) and contains 600 examples per class. Albeit harder than Omniglot, it has the same property that most recent methods trained on it present similar accuracy when controlling for model capacity. We advocate that a more challenging and realistic benchmark is required for further progress in this area.
+
+More specifically, current benchmarks: 1) Consider homogeneous learning tasks. In contrast, real-life learning experiences are heterogeneous: they vary in terms of the number of classes and examples per class, and are unbalanced. 2) Measure only within-dataset generalization. However, we are eventually after models that can generalize to entirely new distributions (e.g., datasets). 3) Ignore the relationships between classes when forming episodes. Specifically, the coarse-grained classification of dogs and chairs may present different difficulties than the fine-grained classification of dog breeds, and current benchmarks do not establish a distinction between the two.
+
+META-DATASET aims to improve upon previous benchmarks in the above directions: it is significantly larger-scale and is comprised of multiple datasets of diverse data distributions; its task creation is informed by class structure for ImageNet and Omniglot; it introduces realistic class imbalance; and it varies the number of classes in each task and the size of the training set, thus testing the robustness of models across the spectrum from very-low-shot learning onwards.
+
+The main contributions of this work are: 1) A more realistic, large-scale and diverse environment for training and testing few-shot learners. 2) Experimental evaluation of popular models, and a new set of baselines combining inference algorithms of meta-learners with non-episodic training. 3) Analyses of whether different models benefit from more data, heterogeneous training sources, pre-trained weights, and meta-training. 4) A novel meta-learner that performs strongly on META-DATASET.
+
+# 2 FEW-SHOT CLASSIFICATION: TASK FORMULATION AND APPROACHES
+
+Task Formulation The end-goal of few-shot classification is to produce a model which, given a new learning episode with $N$ classes and a few labeled examples ( $k _ { c }$ per class, $c \in { 1 , \ldots , N } )$ , is able to generalize to unseen examples for that episode. In other words, the model learns from a training (support) set $\mathcal { S } = \{ ( \mathbf { x } _ { 1 } , y _ { 1 } ) , ( \mathbf { x } _ { 2 } , y _ { 2 } ) , \dots , ( \mathbf { x } _ { K } , y _ { K } ) \}$ (with $\textstyle K = \sum _ { c } k _ { c } )$ and is evaluated on a held-out test (query) set $\mathcal { Q } = \{ ( \mathbf { x } _ { 1 } ^ { * } , y _ { 1 } ^ { * } ) , ( \mathbf { x } _ { 2 } ^ { * } , y _ { 2 } ^ { * } ) , . . . , ( \mathbf { x } _ { T } ^ { * } , y _ { T } ^ { * } ) \}$ . Each example $\left( \mathbf { x } , y \right)$ is formed of an input vector $\mathbf { x } \in \mathbb { R } ^ { D }$ and a class label $y \in \{ 1 , \ldots , N \}$ . Episodes with balanced training sets (i.e., $k _ { c } = k$ , $\forall c )$ are usually described as ‘ $N$ -way, $k$ -shot’ episodes. Evaluation episodes are constructed by sampling their $N$ classes from a larger set $\mathcal { C } _ { t e s t }$ of classes and sampling the desired number of examples per class.
+
+A disjoint set $\mathcal { C } _ { t r a i n }$ of classes is available to train the model; note that this notion of training is distinct from the training that occurs within a few-shot learning episode. Few-shot learning does not prescribe a specific procedure for exploiting $\mathcal { C } _ { t r a i n }$ , but a common approach matches the conditions in which the model is trained and evaluated (Vinyals et al., 2016). In other words, training often (but not always) proceeds in an episodic fashion. Some authors use training and testing to refer to what happens within any given episode, and meta-training and meta-testing to refer to using $\mathcal { C } _ { t r a i n }$ to turn the model into a learner capable of fast adaptation and $\mathcal { C } _ { t e s t }$ for evaluating its success to learn using few shots, respectively. This nomenclature highlights the meta-learning perspective alluded to earlier, but to avoid confusion we will adopt another common nomenclature and refer to the training and test sets of an episode as the support and query sets and to the process of learning from $\mathcal { C } _ { t r a i n }$ simply as training. We use the term ‘meta-learner’ to describe a model that is trained episodically, i.e., learns to learn across multiple tasks that are sampled from the training set $\mathcal { C } _ { t r a i n }$ .
+
+Non-episodic Approaches to Few-shot Classification A natural non-episodic approach simply trains a classifier over all of the training classes $\mathcal { C } _ { t r a i n }$ at once, which can be parameterized by a neural network with a linear layer on top with one output unit per class. After training, this neural network is used as an embedding function $g$ that maps images into a meaningful representation space. The hope of using this model for few-shot learning is that this representation space is useful even for examples of classes that were not included in training. It would then remain to define an algorithm for performing few-shot classification on top of these representations of the images of a task. We consider two choices for this algorithm, yielding the $^ { \bullet } k$ -NN’ and ‘Finetune’ variants of this baseline.
+
+Given a test episode, the $^ { \bullet } k$ -NN’ baseline classifies each query example as the class that its ‘closest’ support example belongs to. Closeness is measured by either Euclidean or cosine distance in the learned embedding space; a choice that we treat as a hyperparameter. On the other hand, the ‘Finetune’ baseline uses the support set of the given test episode to train a new ‘output layer’ on top of the embeddings $g$ , and optionally finetune those embedding too (another hyperparameter), for the purpose of classifying between the $N$ new classes of the associated task.
+
+A variant of the ‘Finetune’ baseline has recently become popular: Baseline+ $^ { - + }$ (Chen et al., 2019), originally inspired by Gidaris & Komodakis (2018); Qi et al. (2018). It uses a ‘cosine classifier’ as the final layer $\ell ^ { 2 }$ -normalizing embeddings and weights before taking the dot product), both during the non-episodic training phase, and for evaluation on test episodes. We incorporate this idea in our codebase by adding a hyperparameter that optionally enables using a cosine classifier for the $\cdot _ { k }$ -NN’ (training only) and ‘Finetune’ (both phases) baselines.
+
+Meta-Learners for Few-shot Classification In the episodic setting, models are trained end-to-end for the purpose of learning to build classifiers from a few examples. We choose to experiment with Matching Networks (Vinyals et al., 2016), Relation Networks (Sung et al., 2018), Prototypical Networks (Snell et al., 2017) and Model Agnostic Meta-Learning (MAML, Finn et al., 2017) since they cover a diverse set of approaches to few-shot learning. We also introduce a novel meta-learner which is inspired by the last two models.
+
+In each training episode, episodic models compute for each query example ${ \mathbf { x } } ^ { * } \in \mathcal { Q }$ , the distribution for its label $p ( y ^ { * } | \mathbf { x } ^ { * } , \mathcal { S } )$ conditioned on the support set $s$ and allow to train this differentiablyparameterized conditional distribution end-to-end via gradient descent. The different models are distinguished by the manner in which this conditioning on the support set is realized. In all cases, the performance on the query set drives the update of the meta-learner’s weights, which include (and sometimes consist only of) the embedding weights. We briefly describe each method below.
+
+Prototypical Networks Prototypical Networks construct a prototype for each class and then classify each query example as the class whose prototype is ‘nearest’ to it under Euclidean distance. More concretely, the probability that a query example $\mathbf { x } ^ { * }$ belongs to class $k$ is defined as:
+
+$$
+p ( y ^ { * } = k | \mathbf { x } ^ { * } , \mathcal { S } ) = \frac { \exp ( - | | g ( \mathbf { x } ^ { * } ) - \mathbf { c } _ { k } | | _ { 2 } ^ { 2 } ) } { \sum _ { k ^ { \prime } \in \{ 1 , \dots , N \} } \exp ( - | | g ( \mathbf { x } ^ { * } ) - \mathbf { c } _ { k ^ { \prime } } | | _ { 2 } ^ { 2 } ) }
+$$
+
+where $\mathbf { c } _ { k }$ is the ‘prototype’ for class $k$ : the average of the embeddings of class $k$ ’s support examples.
+
+Matching Networks Matching Networks (in their simplest form) label each query example as a (cosine) distance-weighted linear combination of the support labels:
+
+$$
+p ( y ^ { \ast } = k | \mathbf { x } ^ { \ast } , S ) = \sum _ { i = 1 } ^ { | S | } \alpha ( \mathbf { x } ^ { \ast } , \mathbf { x } _ { i } ) \mathbf { 1 } _ { y _ { i } = k } ,
+$$
+
+where $\mathbf { 1 } _ { A }$ is the indicator function and $\alpha ( \mathbf { x } ^ { * } , \mathbf { x } _ { i } )$ is the cosine similarity between $g ( \mathbf { x } ^ { * } )$ and $g ( \mathbf { x } _ { i } )$ softmax-normalized over all support examples $\mathbf { x } _ { i }$ , where $1 \leq i \leq | S |$ .
+
+Relation Networks Relation Networks are comprised of an embedding function $g$ as usual, and a ‘relation module’ parameterized by some additional neural network layers. They first embed each support and query using $g$ and create a prototype $p _ { c }$ for each class $c$ by averaging its support embeddings. Each prototype $p _ { c }$ is concatenated with each embedded query and fed through the relation module which outputs a number in [0, 1] representing the predicted probability that that query belongs to class $c$ . The query loss is then defined as the mean square error of that prediction compared to the (binary) ground truth. Both $g$ and the relation module are trained to minimize this loss.
+
+MAML MAML uses a linear layer parametrized by $\mathbf { W }$ and $\mathbf { b }$ on top of the embedding function $g ( \cdot ; \theta )$ and classifies a query example as
+
+$$
+p ( y ^ { * } | \mathbf { x } ^ { * } , S ) = \mathrm { s o f t m a x } ( \mathbf { b } ^ { \prime } + \mathbf { W } ^ { \prime } g ( \mathbf { x } ^ { * } ; \theta ^ { \prime } ) ) ,
+$$
+
+where the output layer parameters $\mathbf { W } ^ { \prime }$ and $\mathbf { b } ^ { \prime }$ and the embedding function parameters $\theta ^ { \prime }$ are obtained by performing a small number of within-episode training steps on the support set $S$ , starting from initial parameter values $( \mathbf { b } , \mathbf { W } , \theta )$ . The model is trained by backpropagating the query set loss through the within-episode gradient descent procedure and into $( \mathbf { b } , \mathbf { W } , \theta )$ . This normally requires computing second-order gradients, which can be expensive to obtain (both in terms of time and memory). For this reason, an approximation is often used whereby gradients of the within-episode descent steps are ignored. This variant is referred to as first-order MAML (fo-MAML) and was used in our experiments. We did attempt to use the full-order version, but found it to be impractically expensive (e.g., it caused frequent out-of-memory problems).
+
+Moreover, since in our setting the number of ways varies between episodes, b, W are set to zero and are not trained (i.e., $\mathbf { b } ^ { \prime }$ , $\mathbf { W } ^ { \prime }$ are the result of within-episode gradient descent initialized at 0), leaving only $\theta$ to be trained. In other words, MAML focuses on learning the within-episode initialization $\theta$ of the embedding network so that it can be rapidly adapted for a new task.
+
+Introducing Proto-MAML We introduce a novel meta-learner that combines the complementary strengths of Prototypical Networks and MAML: the former’s simple inductive bias that is evidently effective for very-few-shot learning, and the latter’s flexible adaptation mechanism.
+
+As explained by Snell et al. (2017), Prototypical Networks can be re-interpreted as a linear classifier applied to a learned representation $g ( \mathbf { x } )$ . The use of a squared Euclidean distance means that output logits are expressed as
+
+$$
+- \| g ( \mathbf { x } ^ { * } ) - \mathbf { c } _ { k } \| ^ { 2 } = - g ( \mathbf { x } ^ { * } ) ^ { T } g ( \mathbf { x } ^ { * } ) + 2 \mathbf { c } _ { k } ^ { T } g ( \mathbf { x } ^ { * } ) - \mathbf { c } _ { k } ^ { T } \mathbf { c } _ { k } = 2 \mathbf { c } _ { k } ^ { T } g ( \mathbf { x } ^ { * } ) - \| \mathbf { c } _ { k } \| ^ { 2 } + c o n s t a n t
+$$
+
+where constant is a class-independent scalar which can be ignored, as it leaves output probabilities unchanged. The $k$ -th unit of the equivalent linear layer therefore has weights $\mathbf { W } _ { k , \cdot } = 2 \mathbf { c } _ { k }$ and biases $b _ { k } = - | | \mathbf { c } _ { k } | | ^ { 2 }$ , which are both differentiable with respect to $\theta$ as they are a function of $g ( \cdot ; \theta )$ .
+
+We refer to (fo-)Proto-MAML as the (fo-)MAML model where the task-specific linear layer of each episode is initialized from the Prototypical Network-equivalent weights and bias defined above and subsequently optimized as usual on the given support set. When computing the update for $\theta$ , we allow gradients to flow through the Prototypical Network-equivalent linear layer initialization. We show that this simple modification significantly helps the optimization of this model and outperforms vanilla fo-MAML by a large margin on META-DATASET.
+
+# 3 META-DATASET: A NEW FEW-SHOT CLASSIFICATION BENCHMARK
+
+META-DATASET aims to offer an environment for measuring progress in realistic few-shot classification tasks. Our approach is twofold: 1) changing the data and 2) changing the formulation of the task (i.e., how episodes are generated). The following sections describe these modifications in detail. The code is open source and publicly available1.
+
+# 3.1 META-DATASET’S DATA
+
+META-DATASET’s data is much larger in size than any previous benchmark, and is comprised of multiple existing datasets. This invites research into how diverse sources of data can be exploited by a meta-learner, and allows us to evaluate a more challenging generalization problem, to new datasets altogether. Specifically, META-DATASET leverages data from the following 10 datasets: ILSVRC-2012 (ImageNet, Russakovsky et al., 2015), Omniglot (Lake et al., 2015), Aircraft (Maji et al., 2013), CUB-200-2011 (Birds, Wah et al., 2011), Describable Textures (Cimpoi et al., 2014), Quick Draw (Jongejan et al., 2016), Fungi (Schroeder & Cui, 2018), VGG Flower (Nilsback & Zisserman, 2008), Traffic Signs (Houben et al., 2013) and MSCOCO (Lin et al., 2014). These datasets were chosen because they are free and easy to obtain, span a variety of visual concepts (natural and human-made) and vary in how fine-grained the class definition is. More information about each of these datasets is provided in the Appendix.
+
+To ensure that episodes correspond to realistic classification problems, each episode generated in META-DATASET uses classes from a single dataset. Moreover, two of these datasets, Traffic Signs and MSCOCO, are fully reserved for evaluation, meaning that no classes from them participate in the training set. The remaining ones contribute some classes to each of the training, validation and test splits of classes, roughly with $70 \%$ / $15 \%$ / $15 \%$ proportions. Two of these datasets, ImageNet and Omniglot, possess a class hierarchy that we exploit in META-DATASET. For each dataset, the composition of splits is available online2.
+
+ImageNet ImageNet is comprised of 82,115 ‘synsets’, i.e., concepts of the WordNet ontology, and it provides ‘is-a’ relationships for its synsets, thus defining a DAG over them. META-DATASET uses the 1K synsets that were chosen for the ILSVRC 2012 classification challenge and defines a new class split for it and a novel procedure for sampling classes from it for episode creation, both informed by its class hierarchy.
+
+Specifically, we construct a sub-graph of the overall DAG whose leaves are the 1K classes of ILSVRC2012. We then ‘cut’ this sub-graph into three pieces, for the training, validation, and test splits, such that there is no overlap between the leaves of any of these pieces. For this, we selected the synsets ‘carnivore’ and ‘device’ as the roots of the validation and test sub-graphs, respectively. The leaves that are reachable from ‘carnivore’ and ‘device’ form the sets of the validation and test classes, respectively. All of the remaining leaves constitute the training classes. This method of splitting ensures that the training classes are semantically different from the test classes. We end up with 712 training, 158 validation and 130 test classes, roughly adhering to the standard $7 0 / 1 5 / 1 5 ( \% )$ splits.
+
+Omniglot This dataset is one of the established benchmarks for few-shot classification as mentioned earlier. However, contrary to the common setup that flattens and ignores its two-level hierarchy of alphabets and characters, we allow it to influence the episode class selection in META-DATASET, yielding finer-grained tasks. We also use the original splits proposed in Lake et al. (2015): (all characters of) the ‘background’ and ‘evaluation’ alphabets are used for training and testing, respectively. However, we reserve the 5 smallest alphabets from the ‘background’ set for validation.
+
+# 3.2 EPISODE SAMPLING
+
+In this section we outline META-DATASET’s algorithm for sampling episodes, featuring hierarchicallyaware procedures for sampling classes of ImageNet and Omniglot, and an algorithm that yields realistically imbalanced episodes of variable shots and ways. The steps for sampling an episode for a given split are: Step 0) uniformly sample a dataset $\mathcal { D }$ , Step 1) sample a set of classes $\mathcal { C }$ from the classes of $\mathcal { D }$ assigned to the requested split, and Step 2) sample support and query examples from $\mathcal { C }$ .
+
+Step 1: Sampling the episode’s class set This procedure differs depending on which dataset is chosen. For datasets without a known class organization, we sample the ‘way’ uniformly from the range [5, MAX-CLASSES], where MAX-CLASSES is either 50 or as many as there are available. Then we sample ‘way’ many classes uniformly at random from the requested class split of the given dataset. ImageNet and Omniglot use class-structure-aware procedures outlined below.
+
+ImageNet class sampling We adopt a hierarchy-aware sampling procedure: First, we sample an internal (non-leaf) node uniformly from the DAG of the given split. The chosen set of classes is then the set of leaves spanned by that node (or a random subset of it, if more than 50). We prevent nodes that are too close to the root to be selected as the internal node, as explained in more detail in the Appendix. This procedure enables the creation of tasks of varying degrees of fine-grainedness: the larger the height of the internal node, the more coarse-grained the resulting episode.
+
+Omniglot class sampling We sample classes from Omniglot by first sampling an alphabet uniformly at random from the chosen split of alphabets (train, validation or test). Then, the ‘way’ of the episode is sampled uniformly at random using the same restrictions as for the rest of the datasets, but taking care not to sample a larger number than the number of characters that belong to the chosen alphabet. Finally, the prescribed number of characters of that alphabet are randomly sampled. This ensures that each episode presents a within-alphabet fine-grained classification.
+
+Step 2: Sampling the episode’s examples Having already selected a set of classes, the choice of the examples from them that will populate an episode can be broken down into three steps. We provide a high-level description here and elaborate in the Appendix with the accompanying formulas.
+
+Step 2a: Compute the query set size The query set is class-balanced, reflecting the fact that we care equally to perform well on all classes of an episode. The number of query images per class is set to a number such that all chosen classes have enough images to contribute that number and still remain with roughly half on their images to possibly add to the support set (in a later step). This number is capped to 10 images per class.
+
+Step 2b: Compute the support set size We allow each chosen class to contribute to the support set at most 100 of its remaining examples (i.e., excluding the ones added to the query set). We multiply this remaining number by a scalar sampled uniformly from the interval $( 0 , 1 ]$ to enable the potential generation of ‘few-shot’ episodes even when multiple images are available, as we are also interested in studying that end of the spectrum. We do enforce, however, that each chosen class has a budget for at least one image in the support set, and we cap the total support set size to 500 examples.
+
+Step 2c: Compute the shot of each class We now discuss how to distribute the total support set size chosen above across the participating classes. The un-normalized proportion of the support set that will be occupied by a given chosen class is a noisy version of the total number of images of that class in the dataset. This design choice is made in the hopes of obtaining realistic class ratios, under the hypothesis that the dataset class statistics are a reasonable approximation of the real-world statistics of appearances of the corresponding classes. We ensure that each class has at least one image in the support set and distribute the rest according to the above rule.
+
+After these steps, we complete the episode creation process by choosing the prescribed number of examples of each chosen class uniformly at random to populate the support and query sets.
+
+# 4 RELATED WORK
+
+In this work we evaluate four meta-learners on META-DATASET that we believe capture a good diversity of well-established models. Evaluating other few-shot classifiers on META-DATASET is beyond the scope of this paper, but we discuss some additional related models below.
+
+Similarly to MAML, some train a meta-learner for quick adaptation to new tasks (Ravi & Larochelle, 2017; Munkhdalai & Yu, 2017; Rusu et al., 2019; Yoon et al., 2018). Others relate to Prototypical Networks by learning a representation on which differentiable training can be performed on some form of classifier (Bertinetto et al., 2019; Gidaris & Komodakis, 2018; Oreshkin et al., 2018). Others relate to Matching Networks in that they perform comparisons between pairs of support and query examples, using either a graph neural network (Satorras & Estrach, 2018) or an attention mechanism (Mishra et al., 2018). Finally, some make use of memory-augmented recurrent networks (Santoro et al., 2016), some learn to perform data augmentation (Hariharan & Girshick, 2017; Wang et al., 2018) in a low-shot learning setting, and some learn to predict the parameters of a large-shot classifier from the parameters learned in a few-shot setting (Wang & Hebert, 2016; Wang et al., 2017). Of relevance to Proto-MAML is MAML $^ { + + }$ (Antoniou et al., 2019), which consists of a collection of adjustments to MAML, such as multiple meta-trained inner loop learning rates and derivative-order annealing. Proto-MAML instead modifies the output weight initialization scheme and could be combined with those adjustments.
+
+Finally, META-DATASET relates to other recent image classification benchmarks. The CVPR 2017 Visual Domain Decathlon Challenge trains a model on 10 different datasets, many of which are included in our benchmark, and measures its ability to generalize to held-out examples for those same datasets but does not measure generalization to new classes (or datasets). Hariharan & Girshick (2017) propose a benchmark where a model is given abundant data from certain base ImageNet classes and is tested on few-shot learning novel ImageNet classes in a way that doesn’t compromise its knowledge of the base classes. Wang et al. (2018) build upon that benchmark and propose a new evaluation protocol for it. Chen et al. (2019) investigate fine-grained few-shot classification using the CUB dataset (Wah et al., 2011, also featured in our benchmark) and crossdomain transfer between mini-ImageNet and CUB. Larger-scale few-shot classification benchmarks were also proposed using CIFAR-100 (Krizhevsky et al., 2009; Bertinetto et al., 2019; Oreshkin et al., 2018), tiered-ImageNet (Ren et al., 2018), and ImageNet-21k (Dhillon et al., 2019). Compared to these, META-DATASET contains the largest set of diverse datasets in the context of few-shot learning and is additionally accompanied by an algorithm for creating learning scenarios from that data that we advocate are more realistic than the previous ones.
+
+# 5 EXPERIMENTS
+
+Training procedure META-DATASET does not prescribe a procedure for learning from the training data. In these experiments, keeping with the spirit of matching training and testing conditions, we trained the meta-learners via training episodes sampled using the same algorithm as we used for META-DATASET’s evaluation episodes, described above. The choice of the dataset from which to sample the next episode was random uniform. The non-episodic baselines are trained to solve the large classification problem that results from ‘concatenating’ the training classes of all datasets.
+
+Validation Another design choice was to perform validation on (the validation split of) ImageNet only, ignoring the validation sets of the other datasets. The rationale behind this choice is that the performance on ImageNet has been known to be a good proxy for the performance on different datasets. We used this validation performance to select our hyperparameters, including backbone architectures, image resolutions and model-specific ones. We describe these further in the Appendix.
+
+Table 1: Few-shot classification results on META-DATASET using models trained on ILSVRC-2012 only (top) and trained on all datasets (bottom).   
+
+<table><tr><td rowspan=1 colspan=1>Test Source</td><td rowspan=1 colspan=1>k-NN</td><td rowspan=1 colspan=1>Finetune</td><td rowspan=1 colspan=1>MatchingNet</td><td rowspan=1 colspan=1>ProtoNet</td><td rowspan=1 colspan=1>fo-MAML</td><td rowspan=1 colspan=1>RelationNet</td><td rowspan=1 colspan=1>fo-Proto-MAML</td></tr><tr><td rowspan=1 colspan=1>ILSVRC</td><td rowspan=1 colspan=1>41.03</td><td rowspan=1 colspan=1>45.78</td><td rowspan=1 colspan=1>45.00</td><td rowspan=1 colspan=1>50.50</td><td rowspan=1 colspan=1>45.51</td><td rowspan=1 colspan=1>34.69</td><td rowspan=1 colspan=1>49.53</td></tr><tr><td rowspan=1 colspan=1>Omniglot</td><td rowspan=1 colspan=1>37.07</td><td rowspan=1 colspan=1>60.85</td><td rowspan=1 colspan=1>52.27</td><td rowspan=1 colspan=1>59.98</td><td rowspan=1 colspan=1>55.55</td><td rowspan=1 colspan=1>45.35</td><td rowspan=1 colspan=1>63.37</td></tr><tr><td rowspan=1 colspan=1>Aircraft</td><td rowspan=1 colspan=1>46.81</td><td rowspan=1 colspan=1>68.69</td><td rowspan=1 colspan=1>48.97</td><td rowspan=1 colspan=1>53.10</td><td rowspan=1 colspan=1>56.24</td><td rowspan=1 colspan=1>40.73</td><td rowspan=1 colspan=1>55.95</td></tr><tr><td rowspan=1 colspan=1>Birds</td><td rowspan=1 colspan=1>50.13</td><td rowspan=1 colspan=1>57.31</td><td rowspan=1 colspan=1>62.21</td><td rowspan=1 colspan=1>68.79</td><td rowspan=1 colspan=1>63.61</td><td rowspan=1 colspan=1>49.51</td><td rowspan=1 colspan=1>68.66</td></tr><tr><td rowspan=1 colspan=1>Textures</td><td rowspan=1 colspan=1>66.36</td><td rowspan=1 colspan=1>69.05</td><td rowspan=1 colspan=1>64.15</td><td rowspan=1 colspan=1>66.56</td><td rowspan=1 colspan=1>68.04</td><td rowspan=1 colspan=1>52.97</td><td rowspan=1 colspan=1>66.49</td></tr><tr><td rowspan=1 colspan=1>Quick Draw</td><td rowspan=1 colspan=1>32.06</td><td rowspan=1 colspan=1>42.60</td><td rowspan=1 colspan=1>42.87</td><td rowspan=1 colspan=1>48.96</td><td rowspan=1 colspan=1>43.96</td><td rowspan=1 colspan=1>43.30</td><td rowspan=1 colspan=1>51.52</td></tr><tr><td rowspan=1 colspan=1>Fungi</td><td rowspan=1 colspan=1>36.16</td><td rowspan=1 colspan=1>38.20</td><td rowspan=1 colspan=1>33.97</td><td rowspan=1 colspan=1>39.71</td><td rowspan=1 colspan=1>32.10</td><td rowspan=1 colspan=1>30.55</td><td rowspan=1 colspan=1>39.96</td></tr><tr><td rowspan=1 colspan=1>VGGFlower</td><td rowspan=1 colspan=1>83.10</td><td rowspan=1 colspan=1>85.51</td><td rowspan=1 colspan=1>80.13</td><td rowspan=1 colspan=1>85.27</td><td rowspan=1 colspan=1>81.74</td><td rowspan=1 colspan=1>68.76</td><td rowspan=1 colspan=1>87.15</td></tr><tr><td rowspan=1 colspan=1>Traffic Signs</td><td rowspan=1 colspan=1>44.59</td><td rowspan=1 colspan=1>66.79</td><td rowspan=1 colspan=1>47.80</td><td rowspan=1 colspan=1>47.12</td><td rowspan=1 colspan=1>50.93</td><td rowspan=1 colspan=1>33.67</td><td rowspan=1 colspan=1>48.83</td></tr><tr><td rowspan=1 colspan=1>MSCOCO</td><td rowspan=1 colspan=1>30.38</td><td rowspan=1 colspan=1>34.86</td><td rowspan=1 colspan=1>34.99</td><td rowspan=1 colspan=1>41.00</td><td rowspan=1 colspan=1>35.30</td><td rowspan=1 colspan=1>29.15</td><td rowspan=1 colspan=1>43.74</td></tr><tr><td rowspan=1 colspan=1>Avg.rank</td><td rowspan=1 colspan=1>5.7</td><td rowspan=1 colspan=1>2.9</td><td rowspan=1 colspan=1>4.65</td><td rowspan=1 colspan=1>2.65</td><td rowspan=1 colspan=1>3.7</td><td rowspan=1 colspan=1>6.55</td><td rowspan=1 colspan=1>1.85</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1>Test Source</td><td rowspan=1 colspan=1>k-NN</td><td rowspan=1 colspan=1>Finetune</td><td rowspan=1 colspan=1>MatchingNet</td><td rowspan=1 colspan=1>ProtoNet</td><td rowspan=1 colspan=1>fo-MAML</td><td rowspan=1 colspan=1>RelationNet</td><td rowspan=1 colspan=1>fo-Proto-MAML</td></tr><tr><td rowspan=1 colspan=1>ILSVRC</td><td rowspan=1 colspan=1>38.55</td><td rowspan=1 colspan=1>43.08</td><td rowspan=1 colspan=1>36.08</td><td rowspan=1 colspan=1>44.50</td><td rowspan=1 colspan=1>37.83</td><td rowspan=1 colspan=1>30.89</td><td rowspan=1 colspan=1>46.52</td></tr><tr><td rowspan=1 colspan=1>Omniglot</td><td rowspan=1 colspan=1>74.60</td><td rowspan=1 colspan=1>71.11</td><td rowspan=1 colspan=1>78.25</td><td rowspan=1 colspan=1>79.56</td><td rowspan=1 colspan=1>83.92</td><td rowspan=1 colspan=1>86.57</td><td rowspan=1 colspan=1>82.69</td></tr><tr><td rowspan=1 colspan=1>Aircraft</td><td rowspan=1 colspan=1>64.98</td><td rowspan=1 colspan=1>72.03</td><td rowspan=1 colspan=1>69.17</td><td rowspan=1 colspan=1>71.14</td><td rowspan=1 colspan=1>76.41</td><td rowspan=1 colspan=1>69.71</td><td rowspan=1 colspan=1>75.23</td></tr><tr><td rowspan=1 colspan=1>Birds</td><td rowspan=1 colspan=1>66.35</td><td rowspan=1 colspan=1>59.82</td><td rowspan=1 colspan=1>56.40</td><td rowspan=1 colspan=1>67.01</td><td rowspan=1 colspan=1>62.43</td><td rowspan=1 colspan=1>54.14</td><td rowspan=1 colspan=1>69.88</td></tr><tr><td rowspan=1 colspan=1>Textures</td><td rowspan=1 colspan=1>63.58</td><td rowspan=1 colspan=1>69.14</td><td rowspan=1 colspan=1>61.80</td><td rowspan=1 colspan=1>65.18</td><td rowspan=1 colspan=1>64.16</td><td rowspan=1 colspan=1>56.56</td><td rowspan=1 colspan=1>68.25</td></tr><tr><td rowspan=1 colspan=1>Quick Draw</td><td rowspan=1 colspan=1>44.88</td><td rowspan=1 colspan=1>47.05</td><td rowspan=1 colspan=1>60.81</td><td rowspan=1 colspan=1>64.88</td><td rowspan=1 colspan=1>59.73</td><td rowspan=1 colspan=1>61.75</td><td rowspan=1 colspan=1>66.84</td></tr><tr><td rowspan=1 colspan=1>Fungi</td><td rowspan=1 colspan=1>37.12</td><td rowspan=1 colspan=1>38.16</td><td rowspan=1 colspan=1>33.70</td><td rowspan=1 colspan=1>40.26</td><td rowspan=1 colspan=1>33.54</td><td rowspan=1 colspan=1>32.56</td><td rowspan=1 colspan=1>41.99</td></tr><tr><td rowspan=1 colspan=1>VGGFlower</td><td rowspan=1 colspan=1>83.47</td><td rowspan=1 colspan=1>85.28</td><td rowspan=1 colspan=1>81.90</td><td rowspan=1 colspan=1>86.85</td><td rowspan=1 colspan=1>79.94</td><td rowspan=1 colspan=1>76.08</td><td rowspan=1 colspan=1>88.72</td></tr><tr><td rowspan=1 colspan=1>Traffic Signs</td><td rowspan=1 colspan=1>40.11</td><td rowspan=1 colspan=1>66.74</td><td rowspan=1 colspan=1>55.57</td><td rowspan=1 colspan=1>46.48</td><td rowspan=1 colspan=1>42.91</td><td rowspan=1 colspan=1>37.48</td><td rowspan=1 colspan=1>52.42</td></tr><tr><td rowspan=1 colspan=1>MSCOCO</td><td rowspan=1 colspan=1>29.55</td><td rowspan=1 colspan=1>35.17</td><td rowspan=1 colspan=1>28.79</td><td rowspan=1 colspan=1>39.87</td><td rowspan=1 colspan=1>29.37</td><td rowspan=1 colspan=1>27.41</td><td rowspan=1 colspan=1>41.74</td></tr><tr><td rowspan=1 colspan=1>Avg.rank</td><td rowspan=1 colspan=1>5.05</td><td rowspan=1 colspan=1>3.6</td><td rowspan=1 colspan=1>4.95</td><td rowspan=1 colspan=1>2.85</td><td rowspan=1 colspan=1>4.25</td><td rowspan=1 colspan=1>5.8</td><td rowspan=1 colspan=1>1.5</td></tr></table>
+
+Pre-training We gave each meta-learner the opportunity to initialize its embedding function from the embedding weights to which the $k$ -NN Baseline model trained on ImageNet converged to. We treated the choice of starting from scratch or starting from this initialization as a hyperparameter. For a fair comparison with the baselines, we allowed the non-episodic models to start from this initialization too. This is especially important for the baselines in the case of training on all datasets since it offers the opportunity to start from ImageNet-pretrained weights.
+
+Main results Table 1 displays the accuracy of each model on the test set of each dataset, after they were trained on ImageNet-only or all datasets. Traffic Signs and MSCOCO are not used for training in either case, as they are reserved for evaluation. We propose to use the average (over the datasets) rank of each method as our metric for comparison, where smaller is better. A method receives rank 1 if it has the highest accuracy, rank 2 if it has the second highest, and so on. If two models share the best accuracy, they both get rank 1.5, and so on. We find that fo-Proto-MAML is the top-performer according to this metric, Prototypical Networks also perform strongly, and the Finetune Baseline notably presents a worthy opponent3. We include more detailed versions of these tables displaying confidence intervals and per-dataset ranks in the Appendix.
+
+Effect of training on all datasets instead of ImageNet only It’s interesting to examine whether training on (the training splits of) all datasets leads to improved generalizaton compared to training on (the training split of) ImageNet only. Specifically, while we might expect that training on more data helps improve generalization, it is an empirical question whether that still holds for heterogeneous data. We can examine this by comparing the performance of each model between the top and bottom sets of results of Table 1, corresponding to the two training sources (ImageNet only and all datasets, respectively). For convenience, Figure 1 visualizes this difference in a barplot. Notably, for Omniglot, Quick Draw and Aircraft we observe a substantial increase across the board from training on all sources. This is reasonable for datasets whose images are significantly different from ImageNet’s: we indeed expect to gain a large benefit from training on some images from (the training classes of) these datasets. Interestingly though, on the remainder of the test sources, we don’t observe a gain from all-dataset training. This result invites research into methods for exploiting heterogeneous data for generalization to unseen classes of diverse sources. Our experiments show that learning ‘naively’ across the training datasets (e.g., by picking the next dataset to use uniformly at random) does not automatically lead to that desired benefit in most cases.
+
+![](images/92522071ee7e709f051c1e59a78e5cc1c66c12a817f4b0df012e5155ad136062.jpg)  
+Figure 1: The performance difference on test datasets, when training on all datasets instead of ILSVRC only. A positive value indicates an improvement from all-dataset training.
+
+![](images/8502a9bb7a88872ae77c44cba52fa3e522accd74133ac8e8614e995521eb8bc1.jpg)  
+Figure 2: The effect of different ways and shots on test performance (w/ $9 5 \%$ confidence intervals) when training on ImageNet.
+
+Ways and shots analysis We further study the accuracy as a function of ‘ways’ (Figure 2a) and the class precision as a function of ‘shots’ (Figure 2b). As expected, we found that the difficulty increases as the way increases, and performance degrades. More examples per class, on the other hand, indeed make it easier to correctly classify that class. Interestingly, though, not all models benefit at the same rate from more data: Prototypical Networks and fo-Proto-MAML outshine other models in very-low-shot settings but saturate faster, whereas the Finetune baseline, Matching Networks, and fo-MAML improve at a higher rate when the shot increases. We draw the same conclusions when performing this analysis on all datasets, and include those plots in the Appendix. As discussed in the Appendix, we recommend including this analysis when reporting results on Meta-Dataset, aside from the main table. The rationale is that we’re not only interested in performing well on average, but also in performing well under different specifications of test tasks.
+
+Effect of pre-training In Figures 3a and 3b, we quantify how beneficial it is to initialize the embedding network of meta-learners using the weights of the $k$ -NN baseline pre-trained on ImageNet, as opposed to starting their episodic training from scratch. We find this procedure to often be beneficial, both for ImageNet-only training and for training on all datasets. It seems that this ImageNet-influenced initialization drives the meta-learner towards a solution which yields increased performance on natural image test datasets, especially ILSVRC, Birds, Fungi, Flowers and MSCOCO.
+
+![](images/ba5386aac14d8aea40ef1d75c98ecda25b5f73373bbdbe912f52032db0f03019.jpg)  
+Figure 3: The effects of pre-training and meta-training (w/ $9 5 \%$ confidence intervals). (ImageNet) or (All datasets) is the training source.
+
+Perhaps unsusprisingly, though, it underperforms on significantly different datasets such as Omniglot and Quick Draw. These findings show that, aside from the choice of the training data source(s) (e.g., ImageNet only or all datasets, as discussed above), the choice of the initialization scheme can also influence to an important degree the final solution and consequently the aptness of applying the resulting meta-learner to different data sources at test time. Finally, an interesting observation is that MAML seems to benefit the most from the pre-trained initialization, which may speak to the difficulty of optimization associated with that model.
+
+Effect of meta-training We propose to disentangle the inference algorithm of each meta-learner from the fact that it is meta-learned, to assess the benefit of meta-learning on META-DATASET. To this end, we propose a new set of baselines: ‘Prototypical Networks Inference’, ‘Matching Networks Inference’, and ‘fo-Proto-MAML Inference’, that are trained non-episodically but evaluated episodically (for validation and testing) using the inference algorithm of the respective meta-learner. This is possible for these meta-learners as they don’t have any additional parameters aside from the embedding function that explicitly need to be learned episodically (as opposed to the relation module of Relation Networks, for example). We compare each Inference-only method to its corresponding meta-learner in Figures 3c and 3d. We find that these baselines are strong: when training on ImageNet only, we can usually observe a small benefit from meta-learning the embedding weights but this benefit often disappears when training on all datasets, in which case meta-learning sometimes actually hurts. We find this result very interesting and we believe it emphasizes the need for research on how to meta-learn across multiple diverse sources, an important challenge that META-DATASET puts forth.
+
+Fine-grainedness analysis We use ILVRC-2012 to investigate the hypothesis that finer-grained tasks are harder than coarse-grained ones. Our findings suggest that while the test sub-graph is not rich enough to exhibit any trend, the performance on the train sub-graph does seem to agree with this hypothesis. We include the experimental setup and results for this analysis in the Appendix.
+
+# 6 CONCLUSION
+
+We have introduced a new large-scale, diverse, and realistic environment for few-shot classification. We believe that our exploration of various models on META-DATASET has uncovered interesting directions for future work pertaining to meta-learning across heterogeneous data: it remains unclear what is the best strategy for creating training episodes, the most appropriate validation creation and the most appropriate initialization. Current models don’t always improve when trained on multiple sources and meta-learning is not always beneficial across datasets. Current models are also not robust to the amount of data in test episodes, each excelling in a different part of the spectrum. We believe that addressing these shortcomings consitutes an important research goal moving forward.
+
+# AUTHOR CONTRIBUTIONS
+
+Eleni, Hugo, and Kevin came up with the benchmark idea and requirements. Eleni developed the core of the project, and worked on the experiment design and management with Tyler and Kevin, as well as experiment analysis. Carles, Ross, Kelvin, Pascal, Vincent, and Tyler helped extend the benchmark by adding datasets. Eleni, Vincent, and Utku contributed the Prototypical Networks, Matching Networks, and Relation Networks implementations, respectively. Tyler implemented baselines, MAML (with Kevin) and Proto-MAML models, and updated the backbones to support them. Writing was mostly led by Eleni, with contributions by Hugo, Vincent, and Kevin and help from Tyler and Pascal for visualizations. Pascal and Pierre-Antoine worked on code organization, efficiency, and open-sourcing, Pascal and Vincent optimized the efficiency of the data input pipeline. Pierre-Antoine supervised the code development process and reviewed most of the changes, Hugo and Kevin supervised the overall direction of the research.
+
+# ACKNOWLEDGMENTS
+
+We would like to thank Chelsea Finn for fruitful discussions and advice on tuning fo-MAML and ensuring the correctness of implementation, as well as Zack Nado and Dan Moldovan for the initial dataset code that was adapted, and Cristina Vasconcelos for spotting an issue in the ranking of models. Finally, we’d like to thank John Bronskill for suggesting that we experiment with a larger inner-loop learning rate for MAML which indeed significantly improved our fo-MAML results on META-DATASET.
+
+# REFERENCES
+
+Antreas Antoniou, Harrison Edwards, and Amos Storkey. How to train your MAML. In Proceedings of the International Conference on Learning Representations, 2019.
+
+Luca Bertinetto, Joao F. Henriques, Philip Torr, and Andrea Vedaldi. Meta-learning with differentiable closed-form solvers. In Proceedings of the International Conference on Learning Representations, 2019.
+
+Wei-Yu Chen, Yen-Cheng Liu, Zsolt Kira, Yu-Chiang Frank Wang, and Jia-Bin Huang. A closer look at few-shot classification. In Proceedings of the International Conference on Learning Representations, 2019.
+
+M. Cimpoi, S. Maji, I. Kokkinos, S. Mohamed, and A. Vedaldi. Describing textures in the wild. In IEEE Conference on Computer Vision and Pattern Recognition, 2014.
+
+Guneet S. Dhillon, Pratik Chaudhari, Avinash Ravichandran, and Stefano Soatto. A baseline for few-shot image classification. arXiv, abs/1909.02729, 2019.
+
+Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks. In Proceedings of the International Conference of Machine Learning, 2017.
+
+Spyros Gidaris and Nikos Komodakis. Dynamic few-shot visual learning without forgetting. In IEEE Conference on Computer Vision and Pattern Recognition, 2018.
+
+Bharath Hariharan and Ross Girshick. Low-shot visual recognition by shrinking and hallucinating features. In Proceedings of the IEEE International Conference on Computer Vision, pp. 3018–3027, 2017.
+
+Sebastian Houben, Johannes Stallkamp, Jan Salmen, Marc Schlipsing, and Christian Igel. Detection of traffic signs in real-world images: The German Traffic Sign Detection Benchmark. In International Joint Conference on Neural Networks, 2013.
+
+Jonas Jongejan, Henry Rowley, Takashi Kawashima, Jongmin Kim, and Nick Fox-Gieg. The Quick, Draw! – A.I. experiment. quickdraw.withgoogle.com, 2016.
+
+Alex Krizhevsky et al. Learning multiple layers of features from tiny images. Technical report, University of Toronto, 2009.
+
+Brenden M Lake, Ruslan Salakhutdinov, and Joshua B Tenenbaum. Human-level concept learning through probabilistic program induction. Science, 350(6266):1332–1338, 2015.
+
+Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C Lawrence Zitnick. Microsoft COCO: Common objects in context. In European Conference on Computer Vision, pp. 740–755, 2014.
+
+Subhransu Maji, Esa Rahtu, Juho Kannala, Matthew Blaschko, and Andrea Vedaldi. Fine-grained visual classification of aircraft. arXiv, abs/1306.5151, 2013.
+
+Nikhil Mishra, Mostafa Rohaninejad, Xi Chen, and Pieter Abbeel. A simple neural attentive metalearner. In Proceedings of the International Conference on Learning Representations, 2018.
+
+Tsendsuren Munkhdalai and Hong Yu. Meta networks. In Proceedings of the International Conference on Machine Learning, pp. 2554–2563, 2017.
+
+M-E. Nilsback and A. Zisserman. Automated flower classification over a large number of classes. In Proceedings of the Indian Conference on Computer Vision, Graphics and Image Processing, 2008.
+
+Boris N. Oreshkin, Pau Rodriguez, and Alexandre Lacoste. TADAM: Task dependent adaptive metric for improved few-shot learning. In Advances in Neural Information Processing Systems, pp. 719–729, 2018.
+
+Hang Qi, Matthew Brown, and David G Lowe. Low-shot learning with imprinted weights. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 5822–5830, 2018.
+
+Sachin Ravi and Hugo Larochelle. Optimization as a model for few-shot learning. In Proceedings of the International Conference on Learning Representations, 2017.
+
+Mengye Ren, Eleni Triantafillou, Sachin Ravi, Jake Snell, Kevin Swersky, Joshua B Tenenbaum, Hugo Larochelle, and Richard S Zemel. Meta-learning for semi-supervised few-shot classification. In Proceedings of the International Conference on Learning Representations, 2018.
+
+Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C Berg, and Li Fei-Fei. Imagenet large scale visual recognition challenge. International Journal of Computer Vision, 115(3):211–252, 2015.
+
+Andrei A. Rusu, Dushyant Rao, Jakub Sygnowski, Oriol Vinyals, Razvan Pascanu, Simon Osindero, and Raia Hadsell. Meta-learning with latent embedding optimization. In Proceedings of the International Conference on Learning Representations, 2019.
+
+Tim Salimans and Durk P Kingma. Weight normalization: A simple reparameterization to accelerate training of deep neural networks. In Advances in Neural Information Processing Systems, pp. 901–909, 2016.
+
+Adam Santoro, Sergey Bartunov, Matthew Botvinick, Daan Wierstra, and Timothy Lillicrap. Metalearning with memory-augmented neural networks. In Proceedings of the International Conference on Machine Learning, pp. 1842–1850, 2016.
+
+Victor Garcia Satorras and Joan Bruna Estrach. Few-shot learning with graph neural networks. In Proceedings of the International Conference on Learning Representations, 2018.
+
+Brigit Schroeder and Yin Cui. FGVCx fungi classification challenge 2018. github.com/ visipedia/fgvcx_fungi_comp, 2018.
+
+Jake Snell, Kevin Swersky, and Richard Zemel. Prototypical networks for few-shot learning. In Advances in Neural Information Processing Systems, pp. 4077–4087, 2017.
+
+Flood Sung, Yongxin Yang, Li Zhang, Tao Xiang, Philip HS Torr, and Timothy M Hospedales. Learning to compare: Relation network for few-shot learning. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1199–1208, 2018.
+
+Oriol Vinyals, Charles Blundell, Tim Lillicrap, and Daan Wierstra. Matching networks for one shot learning. In Advances in Neural Information Processing Systems, pp. 3630–3638, 2016.
+
+C. Wah, S. Branson, P. Welinder, P. Perona, and S. Belongie. The Caltech-UCSD Birds-200-2011 Dataset. Technical Report CNS-TR-2011-001, California Institute of Technology, 2011.
+
+Yu-Xiong Wang and Martial Hebert. Learning to learn: Model regression networks for easy small sample learning. In European Conference on Computer Vision, pp. 616–634. Springer, 2016.
+
+Yu-Xiong Wang, Deva Ramanan, and Martial Hebert. Learning to model the tail. In Advances in Neural Information Processing Systems, pp. 7029–7039, 2017.
+
+Yu-Xiong Wang, Ross Girshick, Martial Hebert, and Bharath Hariharan. Low-shot learning from imaginary data. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 7278–7286, 2018.
+
+Jaesik Yoon, Taesup Kim, Ousmane Dia, Sungwoong Kim, Yoshua Bengio, and Sungjin Ahn. Bayesian model-agnostic meta-learning. In Advances in Neural Information Processing Systems, 2018.
+
+# APPENDIX
+
+.1 RECOMMENDATION FOR REPORTING RESULTS ON META-DATASET
+
+We recommend that future work on META-DATASET reports two sets of results:
+
+1. The main tables storing the average (over 600 test episodes) accuracy of each method on each dataset, after it has been trained on ImageNet only and on All datasets, where the evaluation metric is the average rank. This corresponds to Table 1 in our case (or the more complete version in Table 2 in the Appendix).   
+2. The plots that measure robustness in variations of shots and ways. In our case these are Figures 2b and 2a in the main text for ImageNet-only training, and Figures 5b and 5a in the Appendix for the case of training on all datasets.
+
+We propose to use both of these aspects to evaluate performance on META-DATASET: it is not only desirable to perform well on average, but also to perform well under different specifications of test tasks, as it is not realistic in general to assume that we will know in advance what setup (number of ways and shots) will be encountered at test time. Our final source code will include scripts for generating these plots and for automatically computing ranks given a table to help standardize the procedure for reporting results.
+
+# .2 DETAILS OF META-DATASET’S SAMPLING ALGORITHM
+
+We now provide a complete description of certain steps that were explained on a higher level in the main paper.
+
+STEP 1: SAMPLING THE EPISODE’S CLASS SET
+
+ImageNet class sampling The procedure we use for sampling classes for an ImageNet episode is the following. First, we sample a node uniformly at random from the set of ‘eligible’ nodes of the DAG structure corresponding to the specified split (train, validation or test). An internal node is ‘eligible’ for this selection if it spans at least 5 leaves, but no more than 392 leaves. The number 392 was chosen because it is the smallest number so that, collectively, all eligible internal nodes span all leaves in the DAG. Once an eligible node is selected, some of the leaves that it spans will constitute the classes of the episode. Specifically, if the number of those leaves is no greater than 50, we use all of them. Otherwise, we randomly choose 50 of them.
+
+This procedure enables the creation of tasks of varying degrees of fine-grainedness. For instance, if the sampled internal node has a small height, the leaf classes that it spans will represent semanticallyrelated concepts, thus posing a fine-grained classification task. As the height of the sampled node increases, we ‘zoom out’ to consider a broader scope from which we sample classes and the resulting episodes are more coarse-grained.
+
+STEP 2: SAMPLING THE EPISODE’S EXAMPLES
+
+a) Computing the query set size The query set is class-balanced, reflecting the fact that we care equally to perform well on all classes of an episode. The number of query images per class is computed as:
+
+$$
+q = \operatorname* { m i n } \left\{ 1 0 , \left( \operatorname* { m i n } _ { c \in \mathcal { C } } \lfloor 0 . 5 * \lvert I m ( c ) \rvert \rfloor \right) \right\}
+$$
+
+where $\mathcal { C }$ is the set of selected classes and $I m ( c )$ denotes the set of images belonging to class $c$ . The min over classes ensures that each class has at least $q$ images to add to the query set, thus allowing it to be class-balanced. The 0.5 multiplier ensures that enough images of each class will be available to add to the support set, and the minimum with 10 prevents the query set from being too large.
+
+b) Computing the support set size We compute the total support set size as:
+
+$$
+| S | = \operatorname* { m i n } \left\{ 5 0 0 , \sum _ { c \in \mathcal { C } } \left[ \beta \operatorname* { m i n } \{ 1 0 0 , | I m ( c ) | - q \} \right] \right\}
+$$
+
+where $\beta$ is a scalar sampled uniformly from interval $( 0 , 1 ]$ . Intuitively, each class on average contributes either all its remaining examples (after placing $q$ of them in the query set) if there are less than 100 or 100 otherwise, to avoid having too large support sets. The multiplication with $\beta$ enables the potential generation of smaller support sets even when multiple images are available, since we are also interested in examining the very-low-shot end of the spectrum. The ‘ceiling’ operation ensures that each selected class will have at least one image in the support set. Finally, we cap the total support set size to 500.
+
+c) Computing the shot of each class We are now ready to compute the ‘shot’ of each class. Specifically, the proportion of the support set that will be devoted to class $c$ is computed as:
+
+$$
+R _ { c } = \frac { \exp ( \alpha _ { c } ) | I m ( c ) | } { \displaystyle \sum _ { c ^ { \prime } \in \mathcal { C } } \exp ( \alpha _ { c } ^ { \prime } ) | I m ( c ^ { \prime } ) | }
+$$
+
+where $\alpha _ { c }$ is sampled uniformly from the interval $[ \log ( 0 . 5 ) , \log ( 2 ) )$ . Intuitively, the un-normalized proportion of the support set that will be occupied by class $c$ is a noisy version of the total number of images of that class in the dataset $I m ( c )$ . This design choice is made in the hopes of obtaining realistic class ratios, under the hypothesis that the dataset class statistics are a reasonable approximation of the real-world statistics of appearances of the corresponding classes. The shot of a class $c$ is then set to:
+
+$$
+k _ { c } = \operatorname* { m i n } \left\{ \lfloor { R _ { c } * ( | S | - | \mathcal { C } | ) } \rfloor + 1 , | I m ( c ) | - q \right\}
+$$
+
+which ensures that at least one example is selected for each class, with additional examples selected proportionally to $R _ { c }$ , if enough are available.
+
+# .3 DATASETS
+
+META-DATASET is formed of data originating from 10 different image datasets. A complete list of the datasets we use is the following.
+
+![](images/bcfa517399940eb13bdc4646d2d0f2e579808ba760f23fd7316cd9c5151284db.jpg)  
+Figure 4: Training examples taken from the various datasets forming META-DATASET.
+
+ILSVRC-2012 (ImageNet, Russakovsky et al., 2015) A dataset of natural images from 1000 categories (Figure 4a). We removed some images that were duplicates of images in another dataset in META-DATASET (43 images that were also part of Birds) or other standard datasets of interest (92 from Caltech-101 and 286 from Caltech-256). The complete list of duplicates is part of the source code release.
+
+Omniglot (Lake et al., 2015) A dataset of images of 1623 handwritten characters from 50 different alphabets, with 20 examples per class (Figure 4b). While recently Vinyals et al. (2016) proposed a new split for this dataset, we instead make use of the original intended split Lake et al. (2015) which is more challenging since the split is on the level of alphabets (30 training alphabets and 20 evaluation alphabets), not characters from those alphabets, therefore posing a more challenging generalization problem. Out of the 30 training alphabets, we hold out the 5 smallest ones (i.e., with the least number of character classes) to form our validation set, and use the remaining 25 for training.
+
+Aircraft (Maji et al., 2013) A dataset of images of aircrafts spanning 102 model variants, with 100 images per class (Figure 4c). The images are cropped according to the providing bounding boxes, in order not to include other aircrafts, or the copyright text at the bottom of images.
+
+CUB-200-2011 (Birds, Wah et al., 2011) A dataset for fine-grained classification of 200 different bird species (Figure 4d). We did not use the provided bounding boxes to crop the images, instead the full images are used, which provides a harder challenge.
+
+Describable Textures (DTD, Cimpoi et al., 2014) A texture database, consisting of 5640 images, organized according to a list of 47 terms (categories) inspired from human perception (Figure 4e).
+
+Quick Draw (Jongejan et al., 2016) A dataset of 50 million black-and-white drawings across 345 categories, contributed by players of the game Quick, Draw! (Figure 4f).
+
+Fungi (Schroeder & Cui, 2018) A large dataset of approximately 100K images of nearly 1,500 wild mushrooms species (Figure 4g).
+
+VGG Flower (Nilsback & Zisserman, 2008) A dataset of natural images of 102 flower categories. The flowers chosen to be ones commonly occurring in the United Kingdom. Each class consists of between 40 and 258 images (Figure 4h).
+
+Traffic Signs (Houben et al., 2013) A dataset of 50,000 images of German road signs in 43 classes (Figure 4i).
+
+MSCOCO Lin et al. (2014) A dataset of images collected from Flickr with 1.5 million object instances belonging to 80 classes labelled and localized using bounding boxes. We choose the train2017 split and create images crops from original images using each object instance’s groundtruth bounding box (Figure 4j).
+
+# .4 HYPERPARAMETERS
+
+We used three architectures: a commonly-used four-layer convolutional network, an 18-layer residual network and a wide residual network. While some of the baseline models performed best with the latter, we noticed that the meta-learners preferred the resnet-18 backbone and rarely the four-layerconvnet. For Relation Networks only, we also allow the option to use another architecture, aside from the aforementioned three, inspired by the four-layer-convnet used in the Relation Networks paper (Sung et al., 2018). The main difference is that they used the usual max-pooling operation only in the first two layers, omitting it in the last two, yielding activations of larger spatial dimensions. In our case, we found that these increased spatial dimensions did not fit in memory, so as a compromise we used max-pooling on the first 3 out of the 4 layer of the convnet.
+
+For fo-MAML and fo-Proto-MAML, we tuned the inner-loop learning rate, the number of inner loop steps, and the number of additional such steps to be performed in evaluation (i.e., validation or test) episodes.
+
+For the baselines, we tuned whether the cosine classifier of Baseline $^ { + + }$ will be used, as opposed to a standard forward pass through a linear classification layer. Also, since Chen et al. (2019) added weight normalization (Salimans & Kingma, 2016) to their implementation of the cosine classifier layer, we also implemented this and created a hyperparameter choice for whether or not it is enabled. This hyperparameter is independent from the one that decides if the cosine classifier is used. Both are applicable to the $k$ -NN Basline (for its all-way training classification task) and to the Finetune Baseline (both for its all-way training classification and for its within-episode classification at validation and test times). For the Finetune Baseline, we tuned a binary hyperparameter deciding if gradient descent or ADAM is used for the within-task optimization. We also tuned the decision of whether all embedding layers are finetuned or, alternatively, the embedding is held fixed and only the final classifier on top of it is optimized. Finally, we tuned the number of finetuning steps that will be carried out.
+
+We also tried two different image resolutions: the commonly-used $8 4 \mathrm { x } 8 4$ and $1 2 6 \mathrm { x } 1 2 6$ . Finally, we tuned the learning rate schedule and weight decay and we used ADAM to train all of our models. All other details, dataset splits and the complete set of best hyperparameters discovered for each model are included in the source code.
+
+# .5 COMPLETE MAIN RESULTS AND RANK COMPUTATION
+
+Rank computation We rank models by decreasing order of accuracy and handle ties by assigning tied models the average of their ranks. A tie between two models occurs when a $9 5 \%$ confidence interval statistical test on the difference between their mean accuracies is inconclusive in rejecting the null hypothesis that this difference is 0. Our recommendation is that this test is ran to determine if ties occur. As mentioned earlier, our source code will include this computation.
+
+Complete main tables For completeness, Table 2 presents a more detailed version of Table 1 that also displays confidence intervals and per-dataset ranks computed using the above procedure.
+
+# .6 ANALYSIS OF PERFORMANCE ACROSS SHOTS AND WAYS
+
+For completeness, in Figure 5 we show the results of the analysis of the robustness to different ways and shots for the variants of the models that were trained on all datasets. We observe the same trends as discussed in our Experiments section for the variants of the models that were trained on ImageNet.
+
+![](images/86355f17a73987d65551854e2c353a810d782f473b27fa85b69536f908a52e75.jpg)  
+Figure 5: Analysis of performance as a function of the episode’s way, shots for models whose training source is (the training data of) all datasets. The bands display $9 5 \%$ confidence intervals.
+
+# .7 EFFECT OF TRAINING ON ALL DATASETS OVER TRAINING ON ILSVRC-2012 ONLY
+
+For more clearly observing whether training on all datasets leads to improved generalization over training on ImageNet only, Figure 6 shows side-to-side the performance of each model trained on ILSVRC only vs. all datasets. The difference between the performance of the all-dataset trained models versus the ImageNet-only trained ones is also visualized in Figure 1 in the main paper.
+
+As discussed in the main paper, we notice that we do not always observe a clear generalization advantage in training from a wider collection of image datasets. While some of the datasets that were added to the meta-training phase did see an improvement across all models, in particular for Omniglot and Quick Draw, this was not true across the board. In fact, in certain cases the performance is slightly worse. We believe that more successfully leveraging diverse sources of data is an interesting open research problem.
+
+<table><tr><td rowspan=12 colspan=2>P1II-1IINPreriieaerTIAW-AN（%) eoeepgate(h) roeghtat :prrataPP0I1LIE1NuileleTrieegNN-JJnos ssse</td><td rowspan=1 colspan=1>P1II-1IIN</td><td rowspan=1 colspan=1>171) 75533555</td><td rowspan=1 colspan=1>33 33333535</td><td rowspan=1 colspan=1>355 555055.75</td><td rowspan=1 colspan=1>(1.1) 96.:0999.99</td><td rowspan=1 colspan=1>14)08006599</td><td rowspan=1 colspan=1>31 1511-1111</td><td rowspan=1 colspan=1>31) 451-15.61</td><td rowspan=1 colspan=1>（1) 69051518</td><td rowspan=1 colspan=1>27370533355</td><td rowspan=1 colspan=1>11 15121111</td><td rowspan=1 colspan=1>18%</td><td rowspan=12 colspan=2>&#x27;sjarerep l tt larern saaert (g)</td><td rowspan=12 colspan=2>PPPI-010INPerreleryae) （y） sorapgrte （y) rrerhee pogiaTIVW-0J1N010IduleieTrmeueNN-Jrsnne see</td><td rowspan=1 colspan=1>PPPI-010IN</td><td rowspan=1 colspan=1>13 1:535155</td><td rowspan=1 colspan=1>（77) /6:0099:57</td><td rowspan=1 colspan=1>17) 713-15.55</td><td rowspan=1 colspan=1>(1) 70:1干88:69</td><td rowspan=1 colspan=1>155) 5351555</td><td rowspan=1 colspan=1>(1)46:0048.99</td><td rowspan=1 colspan=1>(1/1111</td><td rowspan=1 colspan=1>(1) /9:0-7788</td></tr><tr><td rowspan=2 colspan=1>Preriieaer</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>12)1531555</td><td rowspan=2 colspan=1>(1.1) 155511:55</td><td rowspan=2 colspan=1>37) 6906771</td><td rowspan=2 colspan=1>32:11.3351155</td><td rowspan=2 colspan=1>32)55153730</td><td rowspan=2 colspan=1>(2) 080591&#x27;89</td><td rowspan=2 colspan=1>3） 5335731</td><td rowspan=2 colspan=1>279) 111571:65</td><td rowspan=2 colspan=1>555</td><td></td><td rowspan=2 colspan=1>Perreler</td><td rowspan=2 colspan=1>30） 135537.30</td><td rowspan=2 colspan=1>(1) 6/0711.98</td><td rowspan=2 colspan=1>(77)33555:65</td><td rowspan=2 colspan=1>34) 574/55.41</td><td rowspan=2 colspan=1>33) 355355551</td><td rowspan=2 colspan=1>（.1) 571511.55</td><td rowspan=2 colspan=1>39) 35335555</td><td rowspan=2 colspan=1>(L) 9/0干80&#x27;9,</td><td rowspan=2 colspan=1>33） 17.5335.31</td><td rowspan=2 colspan=1>2) 7:0-11-71</td><td rowspan=2 colspan=1>58</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td></td></tr><tr><td rowspan=2 colspan=1>TIAW-AN</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>32.4) 71:3355.55</td><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>() 18:0055:58</td><td rowspan=2 colspan=1>35 57535331</td><td rowspan=2 colspan=1>35531333321</td><td rowspan=2 colspan=1>23</td><td></td><td rowspan=2 colspan=1>TIVW-0J</td><td rowspan=2 colspan=1>3.11311311:11</td><td rowspan=2 colspan=1>370)7753575</td><td rowspan=2 colspan=1>11) 67.011.94</td><td rowspan=2 colspan=1>14) 83:131124</td><td rowspan=2 colspan=1>31:113:355555</td><td rowspan=2 colspan=1>35 315511.51</td><td rowspan=2 colspan=1>39)33331115</td><td rowspan=2 colspan=1>(9) 18:005666</td><td rowspan=2 colspan=1>2) 113337:55</td><td rowspan=2 colspan=1>（9) 801153:65</td><td rowspan=2 colspan=1>5</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td></td></tr><tr><td rowspan=2 colspan=1>PP0I1LIE</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>35.) 71111115</td><td rowspan=2 colspan=1>42) 111-1511</td><td rowspan=2 colspan=1>() 111-11.14</td><td rowspan=2 colspan=1>97</td><td></td><td rowspan=2 colspan=1>1N010Id</td><td rowspan=2 colspan=1>(275555155</td><td rowspan=2 colspan=1>111)1515155</td><td rowspan=2 colspan=1>111) .75.5555.55</td><td rowspan=2 colspan=1>(72) 77-1215:19</td><td rowspan=2 colspan=1>35555555555</td><td rowspan=2 colspan=1>(7) 680-8859</td><td rowspan=2 colspan=1>40115:3:7535</td><td rowspan=2 colspan=1>(8) 151515.97</td><td rowspan=2 colspan=1>44) 41:1-1144</td><td rowspan=2 colspan=1>37) 70.3758.30</td><td rowspan=2 colspan=1>2</td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>(7) 80.1-96.84</td><td rowspan=1 colspan=1></td><td></td></tr><tr><td rowspan=1 colspan=1>1Nuilele</td><td rowspan=1 colspan=1>（4)111-11.14</td><td rowspan=1 colspan=1>32) 31335155</td><td rowspan=1 colspan=1>11)77.0056.85</td><td rowspan=1 colspan=1>(75 7555555</td><td rowspan=1 colspan=1>（9)15051555</td><td rowspan=1 colspan=1>444) 10.1-1.55</td><td rowspan=1 colspan=1>35301-57.00</td><td rowspan=1 colspan=1>(9) 15071108</td><td rowspan=1 colspan=1>222)451-1145</td><td rowspan=1 colspan=1>32)10:1-66.50</td><td rowspan=1 colspan=1>49.4</td><td></td><td rowspan=1 colspan=1>uleie</td><td rowspan=1 colspan=1>9) 001-80.90</td><td rowspan=1 colspan=1>171) 111511135</td><td rowspan=1 colspan=1>(59) 960F11.69</td><td rowspan=1 colspan=1>39) 00:1-1594</td><td rowspan=1 colspan=1>(9) 4/:0F08:19</td><td rowspan=1 colspan=1>（6155.3353:35</td><td rowspan=1 colspan=1>33) 55.5311.15</td><td rowspan=1 colspan=1>(1) 7/0517:17</td><td rowspan=1 colspan=1>35 83115171</td><td rowspan=1 colspan=1>（6) 96:0561:85</td><td rowspan=1 colspan=1>5</td></tr><tr><td rowspan=2 colspan=1>Trieeg</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>35 71333155</td><td rowspan=2 colspan=1>(7.0) 07:0015.99</td><td rowspan=2 colspan=1>424)151-175</td><td rowspan=2 colspan=1>33 55:3355.33</td><td rowspan=2 colspan=1>355 85555575</td><td rowspan=2 colspan=1>(1) 11357/.99</td><td rowspan=2 colspan=1>35) 360578.51</td><td rowspan=2 colspan=1>29</td><td></td><td rowspan=2 colspan=1>Trmeue</td><td rowspan=2 colspan=1>21) 001-7.55</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>（9) 951-15.14</td><td rowspan=1 colspan=1>3.5) 55.531581</td><td rowspan=2 colspan=1>33 555353555</td><td rowspan=2 colspan=1>1) 17:331599</td><td rowspan=2 colspan=1>338011175</td><td rowspan=2 colspan=1>3</td></tr><tr><td rowspan=1 colspan=1>4)011-1114</td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1>（9) 951-15.14</td><td rowspan=1 colspan=1></td></tr><tr><td rowspan=1 colspan=1></td><td rowspan=1 colspan=1></td><td rowspan=2 colspan=1>(9) 68:0-18.94AEiett</td><td rowspan=2 colspan=1>55) 05535535PPg</td><td rowspan=2 colspan=1>4)15357399Janees</td><td rowspan=2 colspan=1>33) 80.3570.71mrra rinn</td><td rowspan=2 colspan=1>34) 77:1-75.99un</td><td rowspan=2 colspan=1>34) 8900358JAEDte</td><td rowspan=2 colspan=1>(9)71177155susis orgerg</td><td rowspan=2 colspan=1>39) 3553335HPCCCO</td><td rowspan=2 colspan=1>57YeI B</td><td></td><td rowspan=2 colspan=1>3555555551ITSSSC</td><td rowspan=2 colspan=1>(9) 80.1707.541o8ru0</td><td rowspan=2 colspan=1>(L) 78:0-86:69Arrtett</td><td rowspan=2 colspan=1>3.5 5.5555.55sppg</td><td rowspan=2 colspan=1>35) 55353759saanixes</td><td rowspan=2 colspan=1>() 11-88t4mrrarainn</td><td rowspan=2 colspan=1>37.5 .75.535531un</td><td rowspan=2 colspan=1>37)57005438JAEEelee</td><td rowspan=2 colspan=1>(9) 01IF1104susis ogger</td><td rowspan=2 colspan=1>35) 96557555HPCCCO</td><td rowspan=2 colspan=1>5Va</td></tr><tr><td rowspan=1 colspan=1>JTSSSI</td><td rowspan=1 colspan=1>1o8iu0i</td><td></td></tr></table>
+
+![](images/b4ac5f916f0eca3c5119bc8ff64b93af7b29dbf7066aeba2ca018ffd13c715d8.jpg)  
+Figure 6: Accuracy on the test datasets, when training on ILSVRC only or All datasets (same results as shown in the main tables). The bars display $9 5 \%$ confidence intervals.
+
+# .8 EFFECT OF PRE-TRAINING VERSUS TRAINING FROM SCRATCH
+
+For each meta-learner, we selected the best model (based on validation on ImageNet’s validation split) out of the ones that used the pre-trained initialization, and the best out of the ones that trained from scratch. We then ran the evaluation of each on (the test split of) all datasets in order to quantify how beneficial this pre-trained initialization is. We performed this experiment twice: for the models that are trained on ImageNet only and for the models that are trained on (the training splits of) all datasets.
+
+The results of this investigation were reported in the main paper in Figure 3a and Figure 3b, for ImageNet-only training and all dataset training, respectively. We show the same results in Figure 7, printed larger to facilitate viewing of error bars. For easier comparison, we also plot the difference in performance of the models that were pre-trained over the ones that weren’t, in Figures 8a and 8b. These figures make it easier to spot that while using the pre-trained solution usually helps for datasets that are visually not too different from ImageNet, it may hurt for datasets that are significantly different from it, such as Omniglot, Quickdraw (and surprisingly Aircraft). Note that these three datasets are the same three that we found benefit from training on All datasets instead of ImageNet-only. It appears that using the pre-trained solution biases the final solution to specialize on ImageNet-like datasets.
+
+# .9 EFFECT OF META-LEARNING VERSUS INFERENCE-ONLY
+
+Figure 9 shows the same plots as in Figures 3c and 3d but printed larger to facilitate viewing of error bars. Furthermore, as we have done for visualizing the observed gain of pre-training, we also present in Figures 10a and 10b the gain observed from meta-learning as opposed to training the corresponding inference-only baseline, as explained in the Experiments section of the main paper. This visulization makes it clear that while meta-training usually helps on ImageNet (or doesn’t hurt too much), it sometimes hurts when it is performed on all datasets, emphasizing the need for further research into best practices of meta-learning across heterogeneous sources.
+
+# .10 FINEGRAINEDNESS ANALYSIS
+
+We investigate the hypothesis that finer-grained tasks are more challenging than coarse-grained ones by creating binary ImageNet episodes with the two classes chosen uniformly at random from the DAG’s set of leaves. We then define the degree of coarse-grainedness of a task as the height of the lowest common ancestor of the two chosen leaves, where the height is defined as the length of the longest path from the lowest common ancestor to one of the selected leaves. Larger heights then correspond to coarser-grained tasks. We present these results in Figure 11. We do not detect a significant trend when performing this analysis on the test DAG. The results on the training DAG, though, do seem to indicate that our hypothesis holds to some extent. We conjecture that this may be due to the richer structure of the training DAG, but we encourage further investigation.
+
+![](images/467f9dd61a51262716d208b551892393cfcb11a8fab1f29d8c508b2e055e1273.jpg)  
+Figure 7: Comparing pre-training to starting from scratch. Same plots as Figure 3a and Figure 3b, only larger.
+
+![](images/a2fb06cadc55568beb6dc90936d57e237f8c817c405e0c90edc7d80adcc62281.jpg)  
+(a) The gain from pre-training (ImageNet).
+
+![](images/1478f08128ee6bf5d2f4fa5a39b7afb4869fb4254634787960dded740198c977.jpg)  
+(b) The gain from pre-training (All datasets).   
+Figure 8: The performance difference of initializing the embedding weights from a pre-trained solution, before episodically training on ImageNet or all datasets, over using a random initialization of those weights. The pre-trained weights that we consider are the ones that the $k$ -NN baseline converged to when it was trained on ImageNet. Positive values indicate that this pre-training was beneficial.
+
+![](images/e47d72231ade3a6adbdf4fc8aeccbeebd9dfd58bddc8130fbec26581d311c4ba.jpg)  
+Figure 9: Comparing the meta-trained variant of meta-learners against their inference-only counterpart. Same plots as Figure 3c and Figure 3d, only larger.
+
+![](images/024ea9c8957a699f5f6132eb88ae063684a4bc642be107bf3b6859919119f779.jpg)  
+Figure 10: The performance difference of meta-learning over the corresponding inference-only baseline of each meta-learner. Positive values indicate that meta-learning was beneficial.
+
+![](images/5fa6cea99fd76e21538db833d56e3203086f0db2ba75b4ed6469d5379e721448.jpg)  
+(a) Fine-grainedness Analysis (on ImageNet’s test (b) Fine-grainedness Analysis (on ImageNet’s train graph) graph graph)   
+Figure 11: Analysis of performance as a function of the degree of fine-grainedness. Larger heights correspond to coarser-grained tasks. The bands display $9 5 \%$ confidence intervals.
+
+Table 3: Improvement of fo-MAML when using a larger inner learning rate $\alpha$   
+(a) Models trained on ILSVRC-2012 only.   
+
+<table><tr><td rowspan="2">Test Source</td><td colspan="2">Method: Accuracy (%) ± confidence (%)</td></tr><tr><td>fo-MAML α = 0.01 (old)</td><td>fo-MAML α≈ 0.1</td></tr><tr><td>ILSVRC</td><td>36.09±1.01</td><td>45.51±1.11</td></tr><tr><td>Omniglot</td><td>38.67±1.39</td><td>55.55±1.54</td></tr><tr><td>Aircraft</td><td>34.50±0.90</td><td>56.24±1.11</td></tr><tr><td>Birds</td><td>49.10±1.18</td><td>63.61±1.06</td></tr><tr><td>Textures</td><td>56.50±0.80</td><td>68.04±0.81</td></tr><tr><td>Quick Draw</td><td>27.24±1.24</td><td>43.96±1.29</td></tr><tr><td>Fungi</td><td>23.50±1.00</td><td>32.10±1.10</td></tr><tr><td>VGGFlower</td><td>66.42±0.96</td><td>81.74±0.83</td></tr><tr><td>Traffic Signs</td><td>33.23±1.34</td><td>50.93±1.51</td></tr><tr><td>MSCOCO</td><td>27.52±1.11</td><td>35.30±1.23</td></tr></table>
+
+(b) Models trained on all datasets.   
+
+<table><tr><td rowspan="2">Test Source</td><td colspan="2">Method: Accuracy (%) ± confidence (%)</td></tr><tr><td>fo-MAML α = 0.01 (old)</td><td>fo-MAML α≈ 0.1</td></tr><tr><td>ILSVRC</td><td>32.36±1.02</td><td>37.83±1.01</td></tr><tr><td>Omniglot</td><td>71.91±1.20</td><td>83.92±0.95</td></tr><tr><td>Aircraft</td><td>52.76±0.90</td><td>76.41±0.69</td></tr><tr><td>Birds</td><td>47.24±1.14</td><td>62.43��1.08</td></tr><tr><td>Textures</td><td>56.66±0.74</td><td>64.16±0.83</td></tr><tr><td>Quick Draw</td><td>50.50±1.19</td><td>59.73±1.10</td></tr><tr><td>Fungi</td><td>21.02±0.99</td><td>33.54±1.11</td></tr><tr><td>VGG Flower</td><td>70.93±0.99</td><td>79.94±0.84</td></tr><tr><td>Traffic Signs</td><td>34.18±1.26</td><td>42.91±1.31</td></tr><tr><td>MSCOCO</td><td>24.05±1.10</td><td>29.37±1.08</td></tr></table>
+
+.11 THE IMPORTANCE OF MAML’S INNER-LOOP LEARNING RATE HYPERPARAMETER.
+
+The camera-ready version includes updated results for MAML and Proto-MAML following an external suggestion to experiment with larger values for the inner-loop learning rate $\alpha$ of MAML. We found that re-doing our hyperparameter search with a revised range that includes larger $\alpha$ values significantly improved fo-MAML’s performance on META-DATASET. For consistency, we applied the same change to fo-Proto-MAML and re-ran those experiments too.
+
+We found that the value of this $\alpha$ that performs best for fo-MAML both for training on ImageNet only and training on all datasets is approximately 0.1, which is an order of magnitude larger than our previous best value. Interestingly, fo-Proto-MAML does not choose such a large $\alpha$ value, with best $\alpha$ being 0.0054 when training on ImageNet only and 0.02 when training on all datasets. Plausibly this difference can be attributed to the better initialization of Proto-MAML which requires a less aggressive optimization for the adaptation to each new task. This hypothesis is also supported by the fact that fo-Proto-MAML chooses to take fewer adaptation steps than fo-MAML does. The complete set of best discovered hyperparameters is available in our public code.
+
+To emphasize the importance of properly tuning this hyperparameter, Table 3 displays the previous best and the new best fo-MAML results side-by-side, showcasing the large performance gap when using the appropriate value for $\alpha$ .
+
+# 12 THE CHOICE OF A META-VALIDATION PROCEDURE FOR META-DATASE
+
+The design choice we made, as discussed in the main paper, is to use (the meta-validation set of) ImageNet only for model selection in all of our experiments. In the absence of previous results on the topic, this is a reasonable strategy since ImageNet has been known to consitute a useful proxy for performance on other datasets. However, it is likely that this is not the optimal choice: there might be certain hyperparameters for a given model that work best for held-out ImageNet episodes, but not for held-out episodes of other datasets. An alternative meta-validation scheme would be to use the average (across datasets) validation accuracy as an indicator for early stopping and model selection. We did not choose this method due to concerns about the reliability of this average performance. Notably, taking a simple average would over-emphasize larger datasets, or might over-emphasize datasets with natural images (as opposed to Omniglot and Quickdraw). Nevertheless, whether this strategy is beneficial is an interesting empirical question.
+
+# .13 ADDITIONAL PER-DATASET ANALYSIS OF SHOTS AND WAYS
+
+In our previous analysis of performance across different shots and ways (Figures 2b, 2a, and 5), the performance is averaged over all evaluation datasets. In this section we further break down those plots by presenting the results separately for each dataset. Figures 12 and 13 show the analysis of performance as a function of ways and shots (respectively) for each evaluation dataset, for models that were trained on ImageNet only. For completeness, Figures 14 and 15 show the same for the models trained on (the training splits of) all datasets.
+
+![](images/64f49309435c019421c724cbdda7e4f42b8ff56718446dfc07e6d9a54a2fb2f8.jpg)  
+Figure 12: The performance across different ways, with $9 5 \%$ confidence intervals, shown separately for each evaluation dataset. All models had been trained on ImageNet-only.
+
+![](images/b8edce103e05e1e32a5fd303d5201457a44e1e9f37178741b6a980c4756d0fd2.jpg)  
+Figure 13: The performance across different shots, with $9 5 \%$ confidence intervals, shown separately for each evaluation dataset. All models had been trained on ImageNet-only.
+
+![](images/736e761da3e16cf8251e62ae6f440b98083c1a95eab125920bc191b895c2c881.jpg)  
+Figure 14: The performance across different ways, with $9 5 \%$ confidence intervals, shown separately for each evaluation dataset. All models had been trained on (the training splits of) all datasets.
+
+![](images/a2f47d61549ba626e030a85fab642a502376b656c6b854a661847e50eaeb99a9.jpg)  
+Figure 15: The performance across different shots, with $9 5 \%$ confidence intervals, shown separately for each evaluation dataset. All models had been trained on (the training splits of) all datasets.

parse/train/uyKk_avJ-p4/uyKk_avJ-p4.md

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+# Improving Coherence and Consistency in Neural Sequence Models with Dual-System, Neuro-Symbolic Reasoning
+
+# Maxwell Nye∗ MIT
+
+Joshua B. Tenenbaum MIT
+
+Michael Henry Tessler MIT DeepMind
+
+Brenden M. Lake NYU Facebook AI Research
+
+# Abstract
+
+Human reasoning can be understood as an interplay between two systems: the intuitive and associative (“System 1”) and the deliberative and logical (“System 2”). Neural sequence models—which have been increasingly successful at performing complex, structured tasks—exhibit the advantages and failure modes of System 1: they are fast and learn patterns from data, but are often inconsistent and incoherent. In this work, we seek a lightweight, training-free means of improving existing System 1-like sequence models by adding System 2-inspired logical reasoning. We explore several variations on this theme in which candidate generations from a neural sequence model are examined for logical consistency by a symbolic reasoning module, which can either accept or reject the generations. Our approach uses neural inference to mediate between the neural System 1 and the logical System 2. Results in robust story generation and grounded instruction-following show that this approach can increase the coherence and accuracy of neurally-based generations.
+
+# 1 Introduction
+
+Despite recent success, neural sequence models often fail to produce consistent and coherent generations. When generating stories, language models may forget the attributes of specific characters (such as personality and background information) (Welleck et al., 2018), ignore previously established relationships between characters (such as family relationships) (Sinha et al., 2019), or otherwise contradict prior statements (Brown et al., 2020). Similarly, neural models can make statements that contradict basic world knowledge or the logical entailment structure of known facts.
+
+Lake & Murphy (2020) illustrated several of these issues with GPT-2 (Radford et al., 2019). When given prompts of the form “A dolphin is a ”, GPT-2 predicts that the most likely answer is “mammal”, “fish”, or “bird” depending on small differences in the wording of the prompt. In another example, GPT-2 states that unicorns have “four horns,” directly after implying that unicorns only have one horn. Upon diagnosing such issues, it is unclear how to apply a targeted fix to the model, especially if retraining or fine-tuning is impractical.
+
+In this work, we draw on insights from cognitive science, especially from “dual process” theories of reasoning (Evans, 2003), to explore how neural sequence models can better interface with prior knowledge and be made more coherent and consistent. According to dual process theories, human cognition can be understood as an interplay between a more intuitive and associative “System 1” and a more deliberative and logical “System 2.” Within this broad framework, automatic actions are driven by System 1, whereas System 2 engages for more deliberative control: for example, judging the validity of a logical argument that requires multiple steps of reasoning (Kahneman, 2013).
+
+![](images/c20d75f1293a76956af17c66db3e3cec0efd21ca62aa27c08f823624b84353b6.jpg)  
+Figure 1: Schematic of dual-system approach to text generation. Conditioned on previous text, a “System $1 ^ { \circ }$ neural generation model produces candidate next sentences. Semantic parses for each candidate are generated via few-shot parsing from GPT-3 and compared to a minimal world model to check consistency. Only candidates consistent with the world model state are incorporated into the final generation.
+
+The prominent neural language models of today are single systems, with weaknesses akin to those exhibited by the human System 1. For example, the cognitive reflection test (CRT) (Frederick, 2005) is a classic probe of System 1 vs. System 2 reasoning in humans. Participants answer a set of simple questions that have superficially compelling, but logically invalid, answers. These incorrect answers are often generated as a first “gut” response (putatively, by System 1 intuitive thinking); upon reflection, however, participants often realize that their responses were not logically or mathematically consistent (via more explicit System 2 reasoning). Consider the CRT problem on the left below:
+
+A ball and a bat cost $\$ 10$ . The bat costs one dollar more than the ball. How much does the ball cost?
+
+<table><tr><td>Total cost in prompt</td><td>GPT-3 response</td></tr><tr><td>$1.10</td><td>10 cents</td></tr><tr><td>$1.20</td><td>20 cents</td></tr><tr><td>$1.30</td><td>$0.30</td></tr><tr><td>$1.70</td><td>$0.70</td></tr></table>
+
+Reading quickly, you might be tempted to say the ball costs 10 cents. Most participants give this response, in fact, especially if they are under time pressure or have limited attention (Kahneman, 2013). Of course, if the bat is $\$ 1.00$ more than the ball, and the ball costs 10 cents, then the total cost would be $\$ 120$ . The correct answer is that the ball costs 5 cents. Notably, in this and other classic CRT problems, GPT-3 (Brown et al., 2020) predicts the same “gut” response (prediction in red above; the table above shows that adjusting the price in the prompt also leads to similar effects; see Appendix Figure 8 for more CRT examples). GPT-3 appears vulnerable to the same sort of intuitive, unsystematic pattern recognition errors as humans—in this case, incorrectly subtracting one dollar from $\$ 1.10$ , without confirming that the answer satisfies each of the problem constraints.
+
+Numerous studies have shown that engagement of System 2-style effort can help “override or inhibit default responses emanating from System 1” (Evans, 2003), correcting inconsistent or un-systematic intuitive impulses. For example, when System 2 is engaged by asking people to take more time to respond, people’s accuracy improves on the CRT task above (Kahneman, 2013). It has been argued that integrating System 2 processing could similarly improve AI systems (Goyal & Bengio, 2020; Garcez & Lamb, 2020), and here we explore this idea as applied to neural sequence models.
+
+In this work, we take inspiration from dual process theories to explore a neuro-symbolic generation system, wherein predictions from a neural model are treated as System 1 proposals, and a logical, deliberative System 2 filters these proposals for consistency and soundness (see Figure 1). We further take inspiration from the fact that humans often do not need explicit supervision to reason about new problems or domains (e.g., see human evaluation task in Section 4.2) and require that the System 2 module not need additional problem-specific training, especially on example contradictions or commonsense violations. People can handle novelty by reconfiguring, rather than retraining, their internal models (Lake et al., 2017), and we strive to build machine systems capable of the same. We show how a lightweight, easy-to-implement System 2 model can help improve coherence and consistency by adding a small amount of symbolic reasoning.
+
+We tackle two kinds of domains: text generation and instruction following. In both cases, we construct generative models over sequences by using a neural generation model to propose candidate generations and a symbolic world model that can accept or reject the generations and resample proposals if necessary. We first illustrate the approach by generating short stories based on the bAbI dataset (Weston et al., 2015); this pedagogical, synthetic example illustrates how basic commonsense knowledge of objects, agents, and places can inform a text generation model. We then test our approach on rich, natural language vignettes based on CLUTRR (Sinha et al., 2019), focusing on ensuring consistency of family and interpersonal relationships. In both text generation domains, we interface between the explicit logical knowledge/reasoning of System 2 and generations of System 1 using a few-shot learning approach with state-of-the-art neural language models (GPT-3), which requires no additional training or fine-tuning. Even using off-the-shelf transformers and symbolic solvers, our dual-system model improves the consistency and coherence of text generations as measured by human judges. We test our approach also on instruction following, showing how goalprediction models and execution models can easily be combined to achieve improved performance in low-data regimes. We show improvements over previous work in the gSCAN grounded compositional challenge (Ruis et al., 2020); a dual-system model requires much less data to train than previous models, and achieves higher accuracy and stronger generalization. Overall, our findings indicate that neuro-symbolic, dual process models are a promising means of addressing longstanding problems of robustness and consistency in neural sequence models.
+
+# 2 Related Work
+
+Our approach incorporates semantic parsing (Liang, 2016) as a component of a generative process, where neural generation is used in conjunction with parsing techniques. In our text generation experiments, we employ GPT-3 to perform few-shot semantic parsing without fine-tuning. Related work includes few or zero-shot semantic parsing using pre-training techniques and paraphrasing (Su & Yan, 2017; Herzig & Berant, 2020). It also includes semantic parsing systems trained either without supervision (Liang et al., 2017; Mou et al., 2017; Muhlgay et al., 2019), or with synthetic language data (Marzoev et al., 2020; Xu et al., 2020b).
+
+One popular technique for improving neural generations is generate-and-rerank, wherein one model generates proposals and another reranks them. This broad approach has been used in image generation (Ramesh et al., 2021), text generation (Holtzman et al., 2018; Shen et al., 2019; Deng et al., 2020), dialogue systems (for control, coherence and safety (Welleck et al., 2018; Smith et al., 2020; Nie et al., 2020; Xu et al., 2020a)), and instruction following (Kurita & Cho, 2020). Reranking is generally used to improve outputs with respect to relatively broad, holistic criteria. Here, our goal is to make generation robust to particular types of logical errors by pruning with respect to explicit symbolic constraints. Our approach can thus be considered closely related to techniques which employ explicit search to find generations satisfying particular logical constraints. Similar methods, such as guess-and-check or beam search pruning, have had success in neural program synthesis (Devlin et al., 2017; Nye et al., 2020).
+
+Recent work in NLP has used template-based planning, in which a model generates text by first generating a plan or skeleton, and filling in the missing words to produce naturalistic text (Xu et al., 2018; Hua & Wang, 2020). To generate stories, Martin et al. (2018) parses previous sentences into events and does planning in event space. Our work extends previous entity/relation/event planning in that the world model is not used for planning, but rather for post-checking candidate generations. Structured parsing of this type is also related to dialog tracking techniques such as slot-filling (Pieraccini et al., 1992). In our work, fully compositional logical facts are extracted from utterances. It is therefore more closely related to systems which extract programs from dialogue, such as Andreas et al. (2020).
+
+Recent work has also studied incorporating symbolic constraints into a neural decoding strategy in the context of natural language. Miao et al. (2019) introduce an MCMC-based inference-time propose-and-reject strategy for satisfying constraints. They test on constraints such as paraphrase and grammatical error correction. Lu et al. (2020) introduces “NeuroLogic decoding,” which uses logical constraints on neural language models to produce generations which contain (or do not contain) required (or forbidden) keywords. In these works, the constraints are lexical or based on word/sentence similarity (and provided in the problem setup for Lu et al. (2020)), whereas we study logical constraints on the world state decoded directly from observations or generations at test time. Other approaches for solving reasoning tasks end-to-end include Goyal et al. (2021), Serafini & d’Avila Garcez (2016), and Schlag & Schmidhuber (2018).
+
+# 3 Integrating System 1 and System 2
+
+We introduce our dual-system approach using examples from the bAbI domain (Weston et al., 2015), which we also use to perform diagnostic experiments. Consider generating a simple story involving people, places and objects, such as (from Figure 1):
+
+Daniel went to the garden. Mary traveled to the office. Daniel grabbed the apple.
+
+A model tasked with generating such stories must juggle several simultaneous demands: staying on topic and maintaining consistency of style and other textural elements (for which people rely on System 1), as well as maintaining consistency with previous statements and commonsense knowledge (for which people rely on both systems). Consider continuing the story with one of the following:
+
+(a) Daniel went to the patio. (b) Mary dropped the apple there.
+
+Sentence (a) is reasonable; sentence (b) is not because it is Daniel, not Mary, who has the apple. During generation, how might a model distinguish between these candidates? Perhaps a well-trained neural language model could track constraints of these sorts. Neural language models to date, however, often violate these types of commonsense, hard constraints without a large high-quality corpus or explicit training on detecting violations of commonsense (Sinha et al., 2019).
+
+We address this problem by decomposing text generation into two parts: candidate generation facilitated by deep neural networks and a logical pruning process implemented via a separate symbolic module. Consider again the example above. To ensure consistency, our model would extract from the text the features of the world that are subject to the hard, logical constraints, such as the location of objects and who is holding them. These constraints can then be checked against an explicit representation of current state of the world. For sentences (a) and (b), the system would extract and go(Daniel, patio) and drop(Mary, apple), respectively. A minimal world model would track the state of the apple, such that it maintains apple.holder $=$ Daniel (or equivalently, Daniel.inventory $=$ [apple]). When such a model is given a parse of a candidate generation, drop(Mary, apple), the mismatch between the current state and the proposed change would cause a violation, and the candidate generation will be rejected.
+
+The main steps of our general approach are illustrated in Figure 1: generate proposals from a System 1 proposal model, extract facts with a fact extraction model, and filter proposed generations by ensuring that they satisfy the constraints given by the extracted facts and the minimal world model.
+
+System 1: Generation. We use neural sequence models to produce System 1 generations. In text generation domains, we use a large, pre-trained model that can be fine-tuned or conditioned via a short prompt to generate relevant text. Text sampled from the System 1 model will be treated as candidate utterances, which will be parsed and filtered by System 2 (described below). For the bAbI examples, we use GPT-3 as our System 1 proposal model through few-shot prompting with 10 example bAbI stories as context, generating a new story one candidate sentence at a time.
+
+System 2: Fact extraction. A fact extractor, or parser, is used to mediate between the System 1 candidate proposals and the minimal world model within System 2. In our text generation domains, we use a pre-trained GPT-3 model without fine-tuning to perform parsing.
+
+For bAbI, our prompt consist of an initial descriptive sentence “Please parse the following statements into commands. The available commands are pickup, drop, and go.” and a small set $( < 1 0 )$ of representative semantic parsing examples (input $=$ sentences; output $=$ correct parses, such as go(Bob, roof)). The parse of each utterance is produced via few-shot prompting (Brown et al., 2020): the utterance is added to the end of the prompt, and the subsequent GPT-3 generation is interpreted as the target parse. We found that this simple parsing technique works well and could easily be applied to other parsing-based tasks, as in Shin et al. (2021). The parsing prompts are reproduced in full in the Appendix. As discussed in Section 5, for the $\mathrm { g S C A N }$ instruction following domain, fact extraction is performed with a learned goal location prediction model.
+
+System 2: Minimal world model. We use a lightweight, incomplete description of the state of the world as a world model in each domain, e.g., commonsense information about the people, objects and locations (Figure 1). The goal is not to track and verify all the possible information; instead, we aim for minimalism, capturing just a few commonsense (or application-critical) variables that we want to ensure are correct. The world model facilitates tracking of long-range logical dependencies and logical consequences, especially those which are not readily decodable from surface forms. The world model also lets us integrate rule-based world-knowledge without retraining (and without the need for a large set of labeled examples).
+
+For the bAbI examples, the minimal world model keeps track of the people, locations and objects introduced in the story so far (Figure 1). This encodes constraints on possible actions related to human core knowledge competencies (objects, agents, places) present early in human development (Spelke & Kinzler, 2007); specifically, a person or object can only be in one place at a time, an object can only be possessed by a single person at a time, a person cannot “go” to a room they are already in, and a person cannot pick up an object if it is in a different room. See the Appendix for details.
+
+Search. At generation time, the interaction between System 1 generation and System 2 parsing yields a neuro-symbolic, guess-and-check search strategy. In a text generation scenario, where text is sampled from the model, our dual-system model improves upon a naive, neural-only sampling method by using the System 2 model to reject candidate utterances which are incompatible with the current state. When a candidate is rejected, a new candidate utterance is sampled from the System 1 model, which is again checked by System 2. This process repeats until a candidate utterance is accepted by System 2 (i.e., the utterance is compatible with the world state). This procedure allows the model to effectively search the space of candidate utterances, guided by the logical constraints from the minimal world model. In this work, we use straightforward probabilistic sampling to illustrate that the approach works with even a very simple search mechanism. We imagine that the search procedure could be further optimized by applying, for example, beam search or stochastic beam sampling.
+
+Diagnostic bAbI experiments. We use Task $\# 2$ from bAbI as a diagnostic test for our neuro-symbolic dual-system model. As shown above, this task consists of synthetically-generated short stories involving people, places and objects, and questions concerning the locations of objects in these stories. We investigate performance on both question answering (QA) tasks and story generation. For the QA tasks, we parse each sentence in the story to encode each fact into the world model and parse the final question to query the world model, returning the answer given by the world
+
+GPT-3 only: John went to the bedroom.   
+John picked up the apple there.   
+Mary took the apple there.   
+Mary travelled to the office.   
+Daniel went back to the garden.   
+Mary went to the bedroom.   
+John went to the bedroom.   
+Sandra went to the bedroom.   
+Sandra travelled to the office.   
+Mary went back to the office.   
+Where is the apple? A: office GPT-3 $^ +$ world model: John went to the bedroom.   
+John picked up the apple there.   
+Mary travelled to the office.   
+Daniel went back to the garden.   
+Mary went to the bedroom.   
+Sandra went to the bedroom.   
+Sandra travelled to the office.   
+Mary went back to the office.   
+Where is the apple? A: bedroom
+
+Figure 2: Example bAbI stories generated by GPT-3 only (left) and our dual-system model (right). Logically inconsistent lines are written in red text, and are removed from the story-so-far at generation time.
+
+model. We compare with two alternative models (Table 3 in the Appendix): GPT-3 by itself and a dual-system baseline that uses a neural Natural Language Inference (NLI) model as its System 2. The NLI-based dual-system model generates 10 candidates from GPT-3 and selects the candidate with the highest predicted probability of entailment under the NLI model given the context. We use the RoBERTa MNLI model as our off-the-shelf neural NLI model (Liu et al., 2019), which operates as a System 2 that does not use additional problem-specific data or fine-tuning.2 On 200 held-out tasks, our GPT-3-based “fact extractor” achieves $100 \%$ QA accuracy, far exceeding the performance of GPT-3 alone $( 2 9 . 0 \% )$ or GPT-3 generation with neural NLI scoring $( 3 2 . 5 \%$ ; also see Table 3 in the Appendix). These results show that GPT-3 can be made to answer questions successfully when used for parsing with a world model, even when GPT-3 alone does not achieve high QA accuracy.
+
+To test story generation, we use our GPT-3-based System 1 proposal model (few-shot prompted on 10 example stories) to sample a new bAbI story, line-by-line. If a generated utterance is inconsistent with the current state as indicated by the System 2 world model, a new utterance is sampled from System 1 (repeating until a consistent utterance is sampled). Figure 2 shows how the dual-system approach generates stories that mimic the statistical structure of bAbI stories, while remaining logically sound In contrast, GPT-3 alone was not able to maintain logical coherence. In a set of 50 generated stories, all stories required at least one sentence to be resampled to maintain coherence, and over half of the generated sentences $( 5 3 . 1 \% )$ were rejected by our System 2 model to maintain logical consistency. These results demonstrate that equipping GPT-3 with a minimal world model produces logically coherent stories that mimic the textural structure of the bAbI domain. In the next section, we apply this approach to mimicking human-generated short stories in natural language.
+
+# 4 Coherent Language Generation - CLUTRR
+
+We apply our dual-system approach to a dataset of natural language using the CLUTRR dataset. CLUTRR contains human-written stories about people and their family relationships (see example in Figure 3). As with bAbI, CLUTRR was originally designed as a Question Answering challenge; instead, we use it to evaluate coherent language generation by querying models to generate complete CLUTRR-style stories or to complete partially-generated stories. Our particular aim is to produce stories with coherent and logically consistent family relationships. As above, our language generation setup consists of pre-trained language models acting as our System 1 proposer, a minimal world model as System 2, and a neural semantic parser (implemented via few-shot GPT-3 prediction) as a bridge between the two systems. We use human judgments to assess whether our neuro-symbolic, dual-system model produces more consistent and coherent stories relative to a baseline.
+
+# 4.1 Model specification
+
+Kristin and her son Justin went to visit her mother Carol on a nice Sunday afternoon.They went out for a movie together and had a good time.
+
+Q:How is Carol related to Justin ?
+
+As our System 1 proposal model, we used pretrained neural models to produce candidate generations one sentence at a time. We experimented with GPT-3 as our System 1 model (which we used above for bAbI), but found generations too unreliable, often outputting the empty string. Instead, we used a BART model (Lewis et al., 2019) that was fine-tuned on the
+
+CLUTRR training corpus. This model also gives us an opportunity to compare against a best-case neural “single-system” baseline, specifically fine-tuned on story data. To maintain a state of family relations, we use a constraint solver in our “System $2 ^ { \circ }$ to encode family relationships (e.g., child(x, ${ \tt y } )$ , spouse $\mathbf { \Psi } ( \mathbf { x } , \mathbf { \Psi } z ) ,$ ) and check that the candidate utterances do not contradict the previous statements (e.g., a person cannot be their own child or married to their sibling). We implemented the world model as a set of logical relations and constraints using the Z3 solver (De Moura & Bjørner, 2008). For instance, we require that the parent of $\mathtt { x }$ cannot also be the uncle of x: For all x, y, $\mathtt { u n c l e ( x , y ) } \Rightarrow \neg \mathtt { c h i l d ( y , x ) }$ . To check a candidate utterance, we query the solver to determine if the set of constraints is satisfiable or if there is a contradiction. The full set of constraints and other details can be found in the Appendix. We again used GPT-3 as our semantic parser, extracting parses for each candidate utterance via few-shot learning. This parsing approach worked well, even for the natural language in this domain. We observed that parsing with GPT-3 was more successful when the target parse was naturalistic, i.e., “Bob is Joe’s father.” rather than “father(Bob, Joe)”. The parsing prompt is reproduced in full in the Appendix.
+
+![](images/ec4fa337894acae8383e081ea66d706994e95a5c4138459856cf540cc4c46a35.jpg)  
+Figure 4: Example trial from CLUTRR human judgement experiment. Participants were instructed to select which of two options makes the most sense given the prompt. One option was generated by the System 1 model only (“single-system”), while the other was generated by the dual-system model.
+
+![](images/23551b86728bcb3d12e87976cf8ca4400fe58d0284de9a84ef95c28f8e78effb.jpg)  
+Figure 3: Sample story from the CLUTRR dataset. Each story consists of a sequence of humangenerated sentences concerning family relationships. Adapted from Sinha et al. (2019).   
+Figure 5: CLUTRR human judgment experiment results. Bars denote proportions of dual-system generations selected as making more sense over single-system generations, in each of four conditions. Error-bars denote bootstrapped $9 5 \%$ confidence intervals of the item means. The points denote means for each individual item in the experiment and are jittered horizontally for clarity.
+
+Table 1: Statistics from CLUTRR story generation. We report the percentage of generations (on both a per-line and per-story basis) for which the System 2 world model did not detect an error. The dual-system model is able to detect many inconsistencies in the neural single-system generations, and most can be corrected by re-sampling new candidates (up to a limit of ten).   
+
+<table><tr><td rowspan="2"></td><td colspan="2">% w/out error detected (per line)</td><td colspan="2">% w/out error detected (per story)</td></tr><tr><td>single-system (neural gen. only)</td><td>dual-system (neural gen.+world model)</td><td>single-system (neural gen. only)</td><td>dual-system (neural gen.+world model)</td></tr><tr><td>prompt from dataset</td><td>82.8</td><td>97.1</td><td>60</td><td>96.1</td></tr><tr><td>prompt from model</td><td>71.9</td><td>96.3</td><td>36.4</td><td>93.5</td></tr></table>
+
+# 4.2 Human judgments
+
+We test our dual-system neural generation $^ +$ world model method in its ability to generate stories that are deemed by naive human participants to be more naturalistic and coherent than those generated from the baseline models. Specifically, we asked participants to select which of two continuations made the most sense to them, where one continuation was generated from the neural model alone (single-system) and the other from a dual-system model (either the world model System 2 or the neural NLI System 2).
+
+Participants. Participants $\mathbf { N } = 1 0 1$ ) were recruited on the crowd-sourcing platform Prolific and compensated $\$ 2$ for the task ( ${ \sim } 1 5$ minutes, so roughly $\$ 8/\mathrm{ h o u r }$ ). Participants gave informed consent, and the study was approved by MIT’s IRB. 21 participants were excluded for failing an instruction quiz, incorrectly answering more than one of five filler questions, or finishing the task too quickly. The data we collected contains no personally identifiable information or offensive content.
+
+Procedure. Participants began the experiment by reading a set of instructions and answering comprehension questions. On each main trial, participants were shown a prompt consisting of several sentences and were asked to choose which of two possible continuations made the most sense (an example trial is shown in Figure 4). Participants were instructed that if a name appeared multiple times within a trial, then it referred to the same person, whereas if a name appeared across trials, then it was not referring to the same person. For each trial, one continuation option was generated by the neural only single-system baseline, while the other was a dual-system generation. We selected generations from the neural only baseline that were rejected by the System 2 model in order to maximize the differences between the models’ generations; thus, human judgments pertain to generations that the models disagreed on. Each participant performed between 20 and 26 trials.
+
+Materials. Participants were randomly assigned to one of four between-participant conditions, which varied according to the kind of prompt and the kind of dual-system model. The prompt was either generated from the model (up to the point of disagreement between System 1 and System 2 models; “Prompts from model” condition) or taken completely from the length 4 CLUTRR systematic generalization test dataset (“Prompts from dataset” condition). To generate prompts for the “from model” condition, we took the first sentence of each story from the CLUTRR test dataset and generated subsequent prompt sentences from the dual-system model; sentences were generated until the two systems disagreed (i.e., System 1 generated a sentence that System 2 rejected), at which point the “rejected sentence” served as the neural only (single-system) baseline generation and the first resampled sentence that System 2 accepted served as the dual-system generation. Prompts were sampled to a maximum length of four sentences. The dual-system model shown to participants used a System 2 based on either our constraint-based “world model” or the neural NLI baseline.
+
+Table 1 catalogs critical statistics from the stimulus generation process. We generated vignettes from the System 1 model and report the percentage of System 1 generations which are deemed correct by the System 2 model.3 We also report the percentage of generations corrected by the System 2 model (i.e., if System 1 made an error, could System 2 fix it within 10 attempts?). We report these statistics on both a per-story and per-line basis. According to System 2, the System 1 generation model makes a lot of errors (only $3 6 . 4 \%$ of stories and $7 1 . 9 \%$ of lines were error-free, in the “from model" condition). In most instances, re-sampling new generations yields stories that, according to
+
+Table 2: Accuracy on $\mathrm { g } \mathrm { S C A N }$ splits. Models were trained on 5000 examples (only $2 . 5 \%$ of the gSCAN training data). See Appendix Table 4 for additional results.)   
+
+<table><tr><td>Test split:</td><td>single-system5</td><td>dual-system</td></tr><tr><td>dev</td><td>71.7</td><td>83.3</td></tr><tr><td>random</td><td>57.2</td><td>74.7</td></tr><tr><td>yellow squares</td><td>68.1</td><td>81.3</td></tr><tr><td>red squares</td><td>64.9</td><td>78.1</td></tr><tr><td>novel direction</td><td>0.0</td><td>0.01</td></tr><tr><td>relativity</td><td>41.0</td><td>53.6</td></tr><tr><td>class inference</td><td>68.1</td><td>76.2</td></tr><tr><td>adverb (k=1)</td><td>0.0</td><td>0.0</td></tr><tr><td>adverb to verb</td><td>20.8</td><td>21.8</td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3">³From Heinze-Deml &amp; Bouchacourt (2020)</td></tr></table>
+
+![](images/6b309f49955634199fe29a9959b4f5d1362ff58d0f63e41b64e1e429d4876dcf.jpg)  
+Figure 6: Schematic of our dual-system approach to $\mathrm { g S C A N }$ . We train a neural sequence model to predict both a distribution over action sequences, and a distribution over target locations. At test time, we decode candidate action sequences from the model, execute them on the gridworld, and only accept a sequence that brings the agent to the predicted target location (shown in green).
+
+System 2, no longer contain logical errors within a budget of 10 samples $9 3 . 5 \%$ of stories and $9 6 . 3 \%$ of lines were error-free, respectively).
+
+Results. The human evaluation indicates that System 2 is indeed correcting genuine errors in the stories. As summarized in Figure 5, participants strongly preferred the dual-system neural generation $^ +$ world model continuations in comparison to the neural only single-system continuations (proportion preferring dual-system $= 0 . 8 4$ ; bootstrapped $9 5 \%$ confidence interval [0.77, 0.89] and 0.79 [0.77, 0.89] for the “from dataset” and “from model” prompt conditions, respectively). The dual-system approach, however, did not improve generation quality when the System 2 was based on an off-the-shelf neural NLI model (Proportion preferring dual-system $= 0 . 5 1$ ; [0.40, 0.64] for “from dataset”; 0.58 [0.48, 0.68] for “from model”). Thus, when using a minimal world model, the dual-system approach dramatically improves logical consistency without any need for additional training or fine-tuning. People clearly prefer neuro-symbolic generations from the dual-system model over purely neural generations from a single-system model.4
+
+# 5 Grounded Instruction Following
+
+The dual-system approach offers a general-purpose means of improving upon generative, neural sequence models by incorporating logical constraints. To highlight its generality, we examine how the dual-system perspective can be deployed in a very different domain: grounded instruction following. In Heinze-Deml & Bouchacourt (2020), a learned target location predictor was used to increase the accuracy of a neural action sequence generation model. Here, we show how to increase performance further by enforcing consistency between the target location predictor and the action sequence generator in our dual-system framework.
+
+We use the gSCAN benchmark (Ruis et al., 2020), a recently proposed grounded instruction following dataset designed to measure compositional generalization in neural systems. Given an initial gridworld state and an instruction, e.g., “walk to the big square,” an agent must predict the sequence of low-level actions which achieve the goal, e.g., “TURN LEFT, WALK, TURN LEFT, WALK” (See Figure 6). The dataset contains several test splits, each testing different aspects of compositional generalization.
+
+Our model builds on Heinze-Deml & Bouchacourt (2020) by using an LSTM to predict the correct action sequence and target location. Given a command $c$ and an initial gridworld state $s$ , the neural network defines two distributions: a distribution over action sequences $q _ { a } ( a | c , s )$ and a distribution over target grid locations $q _ { l o c } ( l | c , s )$ . Heinze-Deml & Bouchacourt (2020) showed that when these distributions share parameters, using location prediction as an auxiliary loss improves the accuracy of the action sequence prediction model. We can further exploit these two models by noticing that when a predicted action sequence is not consistent with a predicted target location, then either the action sequence or the target location must be incorrect. Since the target location is much simpler to predict, and thus much more likely to be correctly predicted, if a predicted action sequence is not consistent with the predicted target location, then the action sequence is most likely incorrect. Our dual-system framework can use this property to increase action sequence prediction accuracy. Consider the initial state and command in Figure 6. Our model predicts candidate action sequences, and also predicts that the most likely target location is the grid containing the bigger yellow square (highlighted in red). The model then executes the candidate action sequences, and only accepts a sequence which results in the agent standing in the target location.
+
+In the language of our dual-system approach, we treat the distribution over actions $q _ { a } ( a | c , s )$ as our System 1 proposal model. The distribution over target locations $q _ { l o c } ( l | c , s )$ serves as a fact extractor model, which extract a location constraint $l$ . As a minimal world model, we use a deterministic gridworld execution model $T ( a , s _ { 0 } ) \to s _ { f }$ , which takes a state and action and predicts the resulting state. At test time, we first extract the predicted location as $l = \arg \operatorname* { m a x } _ { l ^ { \prime } } q _ { l o c } ( l ^ { \prime } | c )$ We then search through the possible action sequences from $q _ { a } ( \cdot | c )$ , conditioned on agreement with $l$ . In our experiments, we use a sample-based search with a maximum budget of 50 samples. We trained models on random subsets of the gSCAN training set of varying sizes: 5000 datapoints, 8000 datapoints, and 20000 datapoints $2 . 5 \%$ , $4 \%$ and $10 \%$ of the original training set, respectively).
+
+Results. The results show that the System 2 execution model improves performance without the need for any additional training (see Table 2 for results training on 5000 examples). In contrast to the single-system model, the dual-system model allows for sampling many candidate action sequences from the neural network, accepting only consistent sequences. This guess-and-check approach greatly increases the evaluation accuracy, improving upon prior work on gSCAN, particularly in low-data regimes.
+
+# 6 Limitations
+
+In its current form, our approach is most useful in domains where naturalistic, learned generation is necessary and where a small number of mission-critical logical constraints can be explicitly articulated. Our system will be less useful when constraints are more difficult to articulate (e.g., creative domains such as writing poetry) or when there are many constraints, since the minimal world model must be hand-engineered. Enforcing strict constraints may also pose risks: if the constraints are not only logical but cultural, they may be harmful if misapplied. However, these constraints must be articulated explicitly in a symbolic model, and are thus easier to identify and correct.
+
+The current few-shot parsing technique may also suffer from a limited capacity. For more complex domains, the number of examples required to specify the desired parsing behavior may be too large (i.e., they may not fit in the input window) or too complex for a model to perform parsing accurately. While some tasks may not be suitable, the complexity of the world model need not necessarily increase hand-in-hand with the complexity of the application domain. A dual-system model will be most successful when tracking just a few critical variables (e.g., tracking consistency in family relations, as in our experiments, or tracking scheduling constraints when discussing a team plan).
+
+A promising direction for future work is to incorporate learning into the System 2 world model. Currently, the minimal world knowledge that exists in System 2 can be easily modified, but changes must be made by hand. Improvements would come from automatically learning and updating this structured knowledge, possibly by incorporating neuro-symbolic learning techniques (Ellis et al., 2020; Mao et al., 2019), or other neuro-symbolic integration work such as Tsamoura et al. (2021); Michael & Valiant (2008).
+
+Learning could improve our dual-system approach in other ways, e.g., by training a neural module to mimic the actions of a symbolic System 2. The symbolic System 2 judgments could be used as a source of supervision; candidate utterances rejected by the symbolic System 2 model could be used as examples of contradictory sentences, and accepted utterances could be used as examples of noncontradictory statements. This oversight could help train a neural System 2 contradiction-detection model capable of more subtleties than its symbolic counterpart, especially in domains where labeled examples are otherwise unavailable. This approach may also help us understand aspects of human learning, where certain tasks that require slower, logical reasoning can be habitualized over time and tackled by faster, more intuitive reasoning.
+
+Recent work (Li et al., 2021) has shown that large pre-trained neural models learn to approximately represent certain types of structured semantic information. However, it is not yet clear how representational fidelity translates to logical coherence during generative tasks. Our current approach allows us to explicitly fix logical errors in generation, which may ultimately be caused by representational errors. Understanding how we might leverage our approach to improve the representation of structured knowledge within neural models is a promising direction for future work, which could lead to increased generation consistency and coherence.
+
+# 7 Conclusion
+
+Inspired by dual process theories from cognitive science, we combine the respective strengths of neural and symbolic approaches to build more robust models that can more effectively incorporate domain knowledge. For language generation, we showed that equipping neural generation with a minimal symbolic world model increased language coherence and consistency. For grounded instruction following, we showed that requiring test-time consistency between predicted action sequences and goal locations led to improved performance, especially in low-data regimes. Our neuro-symbolic approach can readily be applied to other domains and types of prior knowledge, as a lightweight way of improving the coherence and consistency of powerful neural sequence models.
+
+This paper just scratches the surface of how structured knowledge can make neural systems more robust; we hope to inspire further work into neuro-symbolic systems which possess the robustness and commonsense necessary for human-level intelligence.
+
+# Acknowledgments
+
+We thank Laura Ruis, Jacob Andreas, Yewen (Evan) Pu, Joe O’Connor and Guy Davidson for helpful comments on an earlier version of this manuscript. MN is supported by a NSF Graduate Research Fellowship.
+
+# References
+
+Andreas, J., Bufe, J., Burkett, D., Chen, C., Clausman, J., Crawford, J., Crim, K., DeLoach, J., Dorner, L., Eisner, J., et al. Task-oriented dialogue as dataflow synthesis. Transactions of the Association for Computational Linguistics, 8:556–571, 2020.   
+Brown, T. B., Mann, B., Ryder, N., Subbiah, M., Kaplan, J., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.   
+De Moura, L. and Bjørner, N. Z3: An efficient smt solver. In Tools and Algorithms for the Construction and Analysis of Systems, pp. 337–340. Springer, 2008.   
+Deng, Y., Bakhtin, A., Ott, M., Szlam, A., and Marc’Aurelio Ranzato. Residual energy-based models of text generation. In International Conference on Learning Representations (ICLR), pp. 1–18, 2020.   
+Devlin, J., Uesato, J., Bhupatiraju, S., Singh, R., Mohamed, A.-r., and Kohli, P. Robustfill: Neural program learning under noisy i/o. ICML, 2017.   
+Ellis, K., Wong, C., Nye, M., Sable-Meyer, M., Cary, L., Morales, L., Hewitt, L., Solar-Lezama, A., and Tenenbaum, J. B. Dreamcoder: Growing generalizable, interpretable knowledge with wake-sleep bayesian program learning. arXiv preprint arXiv:2006.08381, 2020.   
+Evans, J. S. B. In two minds: dual-process accounts of reasoning. Trends in cognitive sciences, 7(10): 454–459, 2003.   
+Frederick, S. Cognitive reflection and decision making. Journal of Economic perspectives, 19(4): 25–42, 2005.   
+Garcez, A. d. and Lamb, L. C. Neurosymbolic ai: The 3rd wave. arXiv preprint arXiv:2012.05876, 2020.   
+Goyal, A. and Bengio, Y. Inductive biases for deep learning of higher-level cognition. arXiv preprint arXiv:2011.15091, 2020.   
+Goyal, A., Didolkar, A., Ke, N. R., Blundell, C., Beaudoin, P., Heess, N., Mozer, M., and Bengio, Y. Neural production systems. CoRR, abs/2103.01937, 2021. URL https://arxiv.org/abs/ 2103.01937.   
+Heinze-Deml, C. and Bouchacourt, D. Think before you act: A simple baseline for compositional generalization. arXiv preprint arXiv:2009.13962, 2020.   
+Herzig, J. and Berant, J. Span-based semantic parsing for compositional generalization. arXiv preprint arXiv:2009.06040, 2020.   
+Holtzman, A., Buys, J., Forbes, M., Bosselut, A., Golub, D., and Choi, Y. Learning to write with cooperative discriminators. arXiv preprint arXiv:1805.06087, 2018.   
+Hua, X. and Wang, L. Pair: Planning and iterative refinement in pre-trained transformers for long text generation. In EMNLP, 2020.   
+Kahneman, D. Thinking, fast and slow. kindle ed, 2013.   
+Kurita, S. and Cho, K. Generative language-grounded policy in vision-and-language navigation with bayes’ rule. arXiv preprint arXiv:2009.07783, 2020.   
+Lake, B. M. and Murphy, G. L. Word meaning in minds and machines. arXiv preprint arXiv:2008.01766, 2020.   
+Lake, B. M., Ullman, T. D., Tenenbaum, J. B., and Gershman, S. J. Building machines that learn and think like people. Behavioral and Brain Sciences, 40:E253, 2017.   
+Lewis, M., Liu, Y., Goyal, N., Ghazvininejad, M., Mohamed, A., Levy, O., Stoyanov, V., and Zettlemoyer, L. Bart: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension. arXiv preprint arXiv:1910.13461, 2019.   
+Li, B. Z., Nye, M., and Andreas, J. Implicit representations of meaning in neural language models. arXiv preprint arXiv:2106.00737, 2021.   
+Liang, C., Berant, J., Le, Q. V., Forbus, K., and Lao, N. Neural symbolic machines: Learning semantic parsers on freebase with weak supervision. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 23–33, Vancouver, Canada, 2017. URL http://aclanthology.coli.uni-saarland.de/pdf/P/P17/P17-1003.pdf.   
+Liang, P. Learning executable semantic parsers for natural language understanding. Communications of the ACM, 59(9):68–76, 2016.   
+Liu, Y., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D., Levy, O., Lewis, M., Zettlemoyer, L., and Stoyanov, V. Roberta: A robustly optimized bert pretraining approach. arXiv preprint arXiv:1907.11692, 2019.   
+Loshchilov, I. and Hutter, F. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.   
+Lu, X., West, P., Zellers, R., Bras, R. L., Bhagavatula, C., and Choi, Y. Neurologic decoding:(un) supervised neural text generation with predicate logic constraints. arXiv preprint arXiv:2010.12884, 2020.   
+Mao, J., Gan, C., Kohli, P., Tenenbaum, J. B., and Wu, J. The neuro-symbolic concept learner: Interpreting scenes, words, and sentences from natural supervision. arXiv preprint arXiv:1904.12584, 2019.   
+Martin, L. J., Ammanabrolu, P., Hancock, W., Singh, S., Harrison, B., and Riedl, M. O. Event representations for automated story generation with deep neural nets. In AAAI, 2018.   
+Marzoev, A., Madden, S., Kaashoek, M. F., Cafarella, M., and Andreas, J. Unnatural language processing: Bridging the gap between synthetic and natural language data. arXiv preprint arXiv:2004.13645, 2020.   
+Miao, N., Zhou, H., Mou, L., Yan, R., and Li, L. Cgmh: Constrained sentence generation by metropolis-hastings sampling. In AAAI, 2019.   
+Michael, L. and Valiant, L. G. A first experimental demonstration of massive knowledge infusion. 2008.   
+Mou, L., Lu, Z., Li, H., and Jin, Z. Coupling distributed and symbolic execution for natural language queries. In Precup, D. and Teh, Y. W. (eds.), Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pp. 2518–2526. PMLR, 06–11 Aug 2017. URL http://proceedings.mlr.press/v70/mou17a.html.   
+Muhlgay, D., Herzig, J., and Berant, J. Value-based search in execution space for mapping instructions to programs. pp. 1942–1954, 01 2019. doi: 10.18653/v1/N19-1193.   
+Nie, Y., Williamson, M., Bansal, M., Kiela, D., and Weston, J. I like fish, especially dolphins: Addressing contradictions in dialogue modelling. arXiv preprint arXiv:2012.13391, 2020.   
+Nye, M. I., Solar-Lezama, A., Tenenbaum, J. B., and Lake, B. M. Learning compositional rules via neural program synthesis. arXiv preprint arXiv:2003.05562, 2020.   
+Pieraccini, R., Tzoukermann, E., Gorelov, Z., Gauvain, J.-L., Levin, E., Lee, C.-H., and Wilpon, J. A speech understanding system based on statistical representation of semantics. In [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 1, pp. 193–196 vol.1, 1992. doi: 10.1109/ICASSP.1992.225939.   
+Radford, A., Wu, J., Child, R., Luan, D., Amodei, D., and Sutskever, I. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.   
+Ramesh, A., Pavlov, M., Goh, G., Gray, S., Voss, C., Radford, A., Chen, M., and Sutskever, I. Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.   
+Ruis, L., Andreas, J., Baroni, M., Bouchacourt, D., and Lake, B. M. A benchmark for systematic generalization in grounded language understanding. arXiv preprint arXiv:2003.05161, 2020.   
+Schlag, I. and Schmidhuber, J. Learning to reason with third-order tensor products. CoRR, abs/1811.12143, 2018. URL http://arxiv.org/abs/1811.12143.   
+Serafini, L. and d’Avila Garcez, A. S. Logic tensor networks: Deep learning and logical reasoning from data and knowledge. CoRR, abs/1606.04422, 2016. URL http://arxiv.org/abs/1606. 04422.   
+Shen, S., Fried, D., Andreas, J., and Klein, D. Pragmatically informative text generation. arXiv preprint arXiv:1904.01301, 2019.   
+Shin, R., Lin, C. H., Thomson, S., Chen, C., Roy, S., Platanios, E. A., Pauls, A., Klein, D., Eisner, J., and Van Durme, B. Constrained language models yield few-shot semantic parsers. arXiv preprint arXiv:2104.08768, 2021.   
+Sinha, K., Sodhani, S., Dong, J., Pineau, J., and Hamilton, W. L. Clutrr: A diagnostic benchmark for inductive reasoning from text. arXiv preprint arXiv:1908.06177, 2019.   
+Smith, E. M., Gonzalez-Rico, D., Dinan, E., and Boureau, Y.-L. Controlling style in generated dialogue. arXiv preprint arXiv:2009.10855, 2020.   
+Spelke, E. S. and Kinzler, K. D. Core knowledge. Developmental Science, 10(1):89–96, 2007.   
+Su, Y. and Yan, X. Cross-domain semantic parsing via paraphrasing. arXiv preprint arXiv:1704.05974, 2017.   
+Tsamoura, E., Hospedales, T., and Michael, L. Neural-symbolic integration: A compositional perspective. Proceedings of the AAAI Conference on Artificial Intelligence, 35(6):5051–5060, May 2021. URL https://ojs.aaai.org/index.php/AAAI/article/view/16639.   
+Welleck, S., Weston, J., Szlam, A., and Cho, K. Dialogue natural language inference. arXiv preprint arXiv:1811.00671, 2018.   
+Weston, J., Bordes, A., Chopra, S., Rush, A. M., van Merriënboer, B., Joulin, A., and Mikolov, T. Towards ai-complete question answering: A set of prerequisite toy tasks. arXiv preprint arXiv:1502.05698, 2015.   
+Xu, J., Ren, X., Zhang, Y., Zeng, Q., Cai, X., and Sun, X. A skeleton-based model for promoting coherence among sentences in narrative story generation. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 4306–4315, Brussels, Belgium, OctoberNovember 2018. Association for Computational Linguistics. doi: 10.18653/v1/D18-1462. URL https://www.aclweb.org/anthology/D18-1462.   
+Xu, J., Ju, D., Li, M., Boureau, Y.-L., Weston, J., and Dinan, E. Recipes for safety in open-domain chatbots. arXiv preprint arXiv:2010.07079, 2020a.   
+Xu, S., Semnani, S. J., Campagna, G., and Lam, M. S. Autoqa: From databases to qa semantic parsers with only synthetic training data. arXiv preprint arXiv:2010.04806, 2020b.

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+        "text": "Human reasoning can be understood as an interplay between two systems: the intuitive and associative (“System 1”) and the deliberative and logical (“System 2”). Neural sequence models—which have been increasingly successful at performing complex, structured tasks—exhibit the advantages and failure modes of System 1: they are fast and learn patterns from data, but are often inconsistent and incoherent. In this work, we seek a lightweight, training-free means of improving existing System 1-like sequence models by adding System 2-inspired logical reasoning. We explore several variations on this theme in which candidate generations from a neural sequence model are examined for logical consistency by a symbolic reasoning module, which can either accept or reject the generations. Our approach uses neural inference to mediate between the neural System 1 and the logical System 2. Results in robust story generation and grounded instruction-following show that this approach can increase the coherence and accuracy of neurally-based generations. ",
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+        "text": "1 Introduction ",
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+        "text": "Despite recent success, neural sequence models often fail to produce consistent and coherent generations. When generating stories, language models may forget the attributes of specific characters (such as personality and background information) (Welleck et al., 2018), ignore previously established relationships between characters (such as family relationships) (Sinha et al., 2019), or otherwise contradict prior statements (Brown et al., 2020). Similarly, neural models can make statements that contradict basic world knowledge or the logical entailment structure of known facts. ",
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+        "text": "Lake & Murphy (2020) illustrated several of these issues with GPT-2 (Radford et al., 2019). When given prompts of the form “A dolphin is a ”, GPT-2 predicts that the most likely answer is “mammal”, “fish”, or “bird” depending on small differences in the wording of the prompt. In another example, GPT-2 states that unicorns have “four horns,” directly after implying that unicorns only have one horn. Upon diagnosing such issues, it is unclear how to apply a targeted fix to the model, especially if retraining or fine-tuning is impractical. ",
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+        "text": "In this work, we draw on insights from cognitive science, especially from “dual process” theories of reasoning (Evans, 2003), to explore how neural sequence models can better interface with prior knowledge and be made more coherent and consistent. According to dual process theories, human cognition can be understood as an interplay between a more intuitive and associative “System 1” and a more deliberative and logical “System 2.” Within this broad framework, automatic actions are driven by System 1, whereas System 2 engages for more deliberative control: for example, judging the validity of a logical argument that requires multiple steps of reasoning (Kahneman, 2013). ",
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+            "Figure 1: Schematic of dual-system approach to text generation. Conditioned on previous text, a “System $1 ^ { \\circ }$ neural generation model produces candidate next sentences. Semantic parses for each candidate are generated via few-shot parsing from GPT-3 and compared to a minimal world model to check consistency. Only candidates consistent with the world model state are incorporated into the final generation. "
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+        "text": "The prominent neural language models of today are single systems, with weaknesses akin to those exhibited by the human System 1. For example, the cognitive reflection test (CRT) (Frederick, 2005) is a classic probe of System 1 vs. System 2 reasoning in humans. Participants answer a set of simple questions that have superficially compelling, but logically invalid, answers. These incorrect answers are often generated as a first “gut” response (putatively, by System 1 intuitive thinking); upon reflection, however, participants often realize that their responses were not logically or mathematically consistent (via more explicit System 2 reasoning). Consider the CRT problem on the left below: ",
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+        "text": "A ball and a bat cost $\\$ 10$ . The bat costs one dollar more than the ball. How much does the ball cost? ",
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+        "table_body": "<table><tr><td>Total cost in prompt</td><td>GPT-3 response</td></tr><tr><td>$1.10</td><td>10 cents</td></tr><tr><td>$1.20</td><td>20 cents</td></tr><tr><td>$1.30</td><td>$0.30</td></tr><tr><td>$1.70</td><td>$0.70</td></tr></table>",
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+        "text": "Reading quickly, you might be tempted to say the ball costs 10 cents. Most participants give this response, in fact, especially if they are under time pressure or have limited attention (Kahneman, 2013). Of course, if the bat is $\\$ 1.00$ more than the ball, and the ball costs 10 cents, then the total cost would be $\\$ 120$ . The correct answer is that the ball costs 5 cents. Notably, in this and other classic CRT problems, GPT-3 (Brown et al., 2020) predicts the same “gut” response (prediction in red above; the table above shows that adjusting the price in the prompt also leads to similar effects; see Appendix Figure 8 for more CRT examples). GPT-3 appears vulnerable to the same sort of intuitive, unsystematic pattern recognition errors as humans—in this case, incorrectly subtracting one dollar from $\\$ 1.10$ , without confirming that the answer satisfies each of the problem constraints. ",
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+        "type": "text",
+        "text": "Numerous studies have shown that engagement of System 2-style effort can help “override or inhibit default responses emanating from System 1” (Evans, 2003), correcting inconsistent or un-systematic intuitive impulses. For example, when System 2 is engaged by asking people to take more time to respond, people’s accuracy improves on the CRT task above (Kahneman, 2013). It has been argued that integrating System 2 processing could similarly improve AI systems (Goyal & Bengio, 2020; Garcez & Lamb, 2020), and here we explore this idea as applied to neural sequence models. ",
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+        "text": "In this work, we take inspiration from dual process theories to explore a neuro-symbolic generation system, wherein predictions from a neural model are treated as System 1 proposals, and a logical, deliberative System 2 filters these proposals for consistency and soundness (see Figure 1). We further take inspiration from the fact that humans often do not need explicit supervision to reason about new problems or domains (e.g., see human evaluation task in Section 4.2) and require that the System 2 module not need additional problem-specific training, especially on example contradictions or commonsense violations. People can handle novelty by reconfiguring, rather than retraining, their internal models (Lake et al., 2017), and we strive to build machine systems capable of the same. We show how a lightweight, easy-to-implement System 2 model can help improve coherence and consistency by adding a small amount of symbolic reasoning. ",
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+        "text": "We tackle two kinds of domains: text generation and instruction following. In both cases, we construct generative models over sequences by using a neural generation model to propose candidate generations and a symbolic world model that can accept or reject the generations and resample proposals if necessary. We first illustrate the approach by generating short stories based on the bAbI dataset (Weston et al., 2015); this pedagogical, synthetic example illustrates how basic commonsense knowledge of objects, agents, and places can inform a text generation model. We then test our approach on rich, natural language vignettes based on CLUTRR (Sinha et al., 2019), focusing on ensuring consistency of family and interpersonal relationships. In both text generation domains, we interface between the explicit logical knowledge/reasoning of System 2 and generations of System 1 using a few-shot learning approach with state-of-the-art neural language models (GPT-3), which requires no additional training or fine-tuning. Even using off-the-shelf transformers and symbolic solvers, our dual-system model improves the consistency and coherence of text generations as measured by human judges. We test our approach also on instruction following, showing how goalprediction models and execution models can easily be combined to achieve improved performance in low-data regimes. We show improvements over previous work in the gSCAN grounded compositional challenge (Ruis et al., 2020); a dual-system model requires much less data to train than previous models, and achieves higher accuracy and stronger generalization. Overall, our findings indicate that neuro-symbolic, dual process models are a promising means of addressing longstanding problems of robustness and consistency in neural sequence models. ",
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+        "type": "text",
+        "text": "2 Related Work ",
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+        "text": "Our approach incorporates semantic parsing (Liang, 2016) as a component of a generative process, where neural generation is used in conjunction with parsing techniques. In our text generation experiments, we employ GPT-3 to perform few-shot semantic parsing without fine-tuning. Related work includes few or zero-shot semantic parsing using pre-training techniques and paraphrasing (Su & Yan, 2017; Herzig & Berant, 2020). It also includes semantic parsing systems trained either without supervision (Liang et al., 2017; Mou et al., 2017; Muhlgay et al., 2019), or with synthetic language data (Marzoev et al., 2020; Xu et al., 2020b). ",
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+        "text": "One popular technique for improving neural generations is generate-and-rerank, wherein one model generates proposals and another reranks them. This broad approach has been used in image generation (Ramesh et al., 2021), text generation (Holtzman et al., 2018; Shen et al., 2019; Deng et al., 2020), dialogue systems (for control, coherence and safety (Welleck et al., 2018; Smith et al., 2020; Nie et al., 2020; Xu et al., 2020a)), and instruction following (Kurita & Cho, 2020). Reranking is generally used to improve outputs with respect to relatively broad, holistic criteria. Here, our goal is to make generation robust to particular types of logical errors by pruning with respect to explicit symbolic constraints. Our approach can thus be considered closely related to techniques which employ explicit search to find generations satisfying particular logical constraints. Similar methods, such as guess-and-check or beam search pruning, have had success in neural program synthesis (Devlin et al., 2017; Nye et al., 2020). ",
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+        "text": "Recent work in NLP has used template-based planning, in which a model generates text by first generating a plan or skeleton, and filling in the missing words to produce naturalistic text (Xu et al., 2018; Hua & Wang, 2020). To generate stories, Martin et al. (2018) parses previous sentences into events and does planning in event space. Our work extends previous entity/relation/event planning in that the world model is not used for planning, but rather for post-checking candidate generations. Structured parsing of this type is also related to dialog tracking techniques such as slot-filling (Pieraccini et al., 1992). In our work, fully compositional logical facts are extracted from utterances. It is therefore more closely related to systems which extract programs from dialogue, such as Andreas et al. (2020). ",
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+        "text": "Recent work has also studied incorporating symbolic constraints into a neural decoding strategy in the context of natural language. Miao et al. (2019) introduce an MCMC-based inference-time propose-and-reject strategy for satisfying constraints. They test on constraints such as paraphrase and grammatical error correction. Lu et al. (2020) introduces “NeuroLogic decoding,” which uses logical constraints on neural language models to produce generations which contain (or do not contain) required (or forbidden) keywords. In these works, the constraints are lexical or based on word/sentence similarity (and provided in the problem setup for Lu et al. (2020)), whereas we study logical constraints on the world state decoded directly from observations or generations at test time. Other approaches for solving reasoning tasks end-to-end include Goyal et al. (2021), Serafini & d’Avila Garcez (2016), and Schlag & Schmidhuber (2018). ",
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+    {
+        "type": "text",
+        "text": "3 Integrating System 1 and System 2 ",
+        "text_level": 1,
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+        "text": "We introduce our dual-system approach using examples from the bAbI domain (Weston et al., 2015), which we also use to perform diagnostic experiments. Consider generating a simple story involving people, places and objects, such as (from Figure 1): ",
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+        "text": "Daniel went to the garden. Mary traveled to the office. Daniel grabbed the apple. ",
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+        "text": "A model tasked with generating such stories must juggle several simultaneous demands: staying on topic and maintaining consistency of style and other textural elements (for which people rely on System 1), as well as maintaining consistency with previous statements and commonsense knowledge (for which people rely on both systems). Consider continuing the story with one of the following: ",
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+        "text": "(a) Daniel went to the patio. (b) Mary dropped the apple there. ",
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+        "text": "Sentence (a) is reasonable; sentence (b) is not because it is Daniel, not Mary, who has the apple. During generation, how might a model distinguish between these candidates? Perhaps a well-trained neural language model could track constraints of these sorts. Neural language models to date, however, often violate these types of commonsense, hard constraints without a large high-quality corpus or explicit training on detecting violations of commonsense (Sinha et al., 2019). ",
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+        "type": "text",
+        "text": "We address this problem by decomposing text generation into two parts: candidate generation facilitated by deep neural networks and a logical pruning process implemented via a separate symbolic module. Consider again the example above. To ensure consistency, our model would extract from the text the features of the world that are subject to the hard, logical constraints, such as the location of objects and who is holding them. These constraints can then be checked against an explicit representation of current state of the world. For sentences (a) and (b), the system would extract and go(Daniel, patio) and drop(Mary, apple), respectively. A minimal world model would track the state of the apple, such that it maintains apple.holder $=$ Daniel (or equivalently, Daniel.inventory $=$ [apple]). When such a model is given a parse of a candidate generation, drop(Mary, apple), the mismatch between the current state and the proposed change would cause a violation, and the candidate generation will be rejected. ",
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+        "type": "text",
+        "text": "The main steps of our general approach are illustrated in Figure 1: generate proposals from a System 1 proposal model, extract facts with a fact extraction model, and filter proposed generations by ensuring that they satisfy the constraints given by the extracted facts and the minimal world model. ",
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+        "type": "text",
+        "text": "System 1: Generation. We use neural sequence models to produce System 1 generations. In text generation domains, we use a large, pre-trained model that can be fine-tuned or conditioned via a short prompt to generate relevant text. Text sampled from the System 1 model will be treated as candidate utterances, which will be parsed and filtered by System 2 (described below). For the bAbI examples, we use GPT-3 as our System 1 proposal model through few-shot prompting with 10 example bAbI stories as context, generating a new story one candidate sentence at a time. ",
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+        "type": "text",
+        "text": "System 2: Fact extraction. A fact extractor, or parser, is used to mediate between the System 1 candidate proposals and the minimal world model within System 2. In our text generation domains, we use a pre-trained GPT-3 model without fine-tuning to perform parsing. ",
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+        "text": "For bAbI, our prompt consist of an initial descriptive sentence “Please parse the following statements into commands. The available commands are pickup, drop, and go.” and a small set $( < 1 0 )$ of representative semantic parsing examples (input $=$ sentences; output $=$ correct parses, such as go(Bob, roof)). The parse of each utterance is produced via few-shot prompting (Brown et al., 2020): the utterance is added to the end of the prompt, and the subsequent GPT-3 generation is interpreted as the target parse. We found that this simple parsing technique works well and could easily be applied to other parsing-based tasks, as in Shin et al. (2021). The parsing prompts are reproduced in full in the Appendix. As discussed in Section 5, for the $\\mathrm { g S C A N }$ instruction following domain, fact extraction is performed with a learned goal location prediction model. ",
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+        "text": "System 2: Minimal world model. We use a lightweight, incomplete description of the state of the world as a world model in each domain, e.g., commonsense information about the people, objects and locations (Figure 1). The goal is not to track and verify all the possible information; instead, we aim for minimalism, capturing just a few commonsense (or application-critical) variables that we want to ensure are correct. The world model facilitates tracking of long-range logical dependencies and logical consequences, especially those which are not readily decodable from surface forms. The world model also lets us integrate rule-based world-knowledge without retraining (and without the need for a large set of labeled examples). ",
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+        "type": "text",
+        "text": "For the bAbI examples, the minimal world model keeps track of the people, locations and objects introduced in the story so far (Figure 1). This encodes constraints on possible actions related to human core knowledge competencies (objects, agents, places) present early in human development (Spelke & Kinzler, 2007); specifically, a person or object can only be in one place at a time, an object can only be possessed by a single person at a time, a person cannot “go” to a room they are already in, and a person cannot pick up an object if it is in a different room. See the Appendix for details. ",
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+        "type": "text",
+        "text": "Search. At generation time, the interaction between System 1 generation and System 2 parsing yields a neuro-symbolic, guess-and-check search strategy. In a text generation scenario, where text is sampled from the model, our dual-system model improves upon a naive, neural-only sampling method by using the System 2 model to reject candidate utterances which are incompatible with the current state. When a candidate is rejected, a new candidate utterance is sampled from the System 1 model, which is again checked by System 2. This process repeats until a candidate utterance is accepted by System 2 (i.e., the utterance is compatible with the world state). This procedure allows the model to effectively search the space of candidate utterances, guided by the logical constraints from the minimal world model. In this work, we use straightforward probabilistic sampling to illustrate that the approach works with even a very simple search mechanism. We imagine that the search procedure could be further optimized by applying, for example, beam search or stochastic beam sampling. ",
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+        "type": "text",
+        "text": "Diagnostic bAbI experiments. We use Task $\\# 2$ from bAbI as a diagnostic test for our neuro-symbolic dual-system model. As shown above, this task consists of synthetically-generated short stories involving people, places and objects, and questions concerning the locations of objects in these stories. We investigate performance on both question answering (QA) tasks and story generation. For the QA tasks, we parse each sentence in the story to encode each fact into the world model and parse the final question to query the world model, returning the answer given by the world ",
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+        "type": "text",
+        "text": "GPT-3 only: John went to the bedroom.   \nJohn picked up the apple there.   \nMary took the apple there.   \nMary travelled to the office.   \nDaniel went back to the garden.   \nMary went to the bedroom.   \nJohn went to the bedroom.   \nSandra went to the bedroom.   \nSandra travelled to the office.   \nMary went back to the office.   \nWhere is the apple? A: office GPT-3 $^ +$ world model: John went to the bedroom.   \nJohn picked up the apple there.   \nMary travelled to the office.   \nDaniel went back to the garden.   \nMary went to the bedroom.   \nSandra went to the bedroom.   \nSandra travelled to the office.   \nMary went back to the office.   \nWhere is the apple? A: bedroom ",
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+    {
+        "type": "text",
+        "text": "Figure 2: Example bAbI stories generated by GPT-3 only (left) and our dual-system model (right). Logically inconsistent lines are written in red text, and are removed from the story-so-far at generation time. ",
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+        "type": "text",
+        "text": "model. We compare with two alternative models (Table 3 in the Appendix): GPT-3 by itself and a dual-system baseline that uses a neural Natural Language Inference (NLI) model as its System 2. The NLI-based dual-system model generates 10 candidates from GPT-3 and selects the candidate with the highest predicted probability of entailment under the NLI model given the context. We use the RoBERTa MNLI model as our off-the-shelf neural NLI model (Liu et al., 2019), which operates as a System 2 that does not use additional problem-specific data or fine-tuning.2 On 200 held-out tasks, our GPT-3-based “fact extractor” achieves $100 \\%$ QA accuracy, far exceeding the performance of GPT-3 alone $( 2 9 . 0 \\% )$ or GPT-3 generation with neural NLI scoring $( 3 2 . 5 \\%$ ; also see Table 3 in the Appendix). These results show that GPT-3 can be made to answer questions successfully when used for parsing with a world model, even when GPT-3 alone does not achieve high QA accuracy. ",
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+        "type": "text",
+        "text": "To test story generation, we use our GPT-3-based System 1 proposal model (few-shot prompted on 10 example stories) to sample a new bAbI story, line-by-line. If a generated utterance is inconsistent with the current state as indicated by the System 2 world model, a new utterance is sampled from System 1 (repeating until a consistent utterance is sampled). Figure 2 shows how the dual-system approach generates stories that mimic the statistical structure of bAbI stories, while remaining logically sound In contrast, GPT-3 alone was not able to maintain logical coherence. In a set of 50 generated stories, all stories required at least one sentence to be resampled to maintain coherence, and over half of the generated sentences $( 5 3 . 1 \\% )$ were rejected by our System 2 model to maintain logical consistency. These results demonstrate that equipping GPT-3 with a minimal world model produces logically coherent stories that mimic the textural structure of the bAbI domain. In the next section, we apply this approach to mimicking human-generated short stories in natural language. ",
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+    {
+        "type": "text",
+        "text": "4 Coherent Language Generation - CLUTRR ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "We apply our dual-system approach to a dataset of natural language using the CLUTRR dataset. CLUTRR contains human-written stories about people and their family relationships (see example in Figure 3). As with bAbI, CLUTRR was originally designed as a Question Answering challenge; instead, we use it to evaluate coherent language generation by querying models to generate complete CLUTRR-style stories or to complete partially-generated stories. Our particular aim is to produce stories with coherent and logically consistent family relationships. As above, our language generation setup consists of pre-trained language models acting as our System 1 proposer, a minimal world model as System 2, and a neural semantic parser (implemented via few-shot GPT-3 prediction) as a bridge between the two systems. We use human judgments to assess whether our neuro-symbolic, dual-system model produces more consistent and coherent stories relative to a baseline. ",
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+        "type": "text",
+        "text": "4.1 Model specification ",
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+        "type": "text",
+        "text": "Kristin and her son Justin went to visit her mother Carol on a nice Sunday afternoon.They went out for a movie together and had a good time. ",
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+        "text": "Q:How is Carol related to Justin ? ",
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+        "type": "text",
+        "text": "As our System 1 proposal model, we used pretrained neural models to produce candidate generations one sentence at a time. We experimented with GPT-3 as our System 1 model (which we used above for bAbI), but found generations too unreliable, often outputting the empty string. Instead, we used a BART model (Lewis et al., 2019) that was fine-tuned on the ",
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+    {
+        "type": "text",
+        "text": "CLUTRR training corpus. This model also gives us an opportunity to compare against a best-case neural “single-system” baseline, specifically fine-tuned on story data. To maintain a state of family relations, we use a constraint solver in our “System $2 ^ { \\circ }$ to encode family relationships (e.g., child(x, ${ \\tt y } )$ , spouse $\\mathbf { \\Psi } ( \\mathbf { x } , \\mathbf { \\Psi } z ) ,$ ) and check that the candidate utterances do not contradict the previous statements (e.g., a person cannot be their own child or married to their sibling). We implemented the world model as a set of logical relations and constraints using the Z3 solver (De Moura & Bjørner, 2008). For instance, we require that the parent of $\\mathtt { x }$ cannot also be the uncle of x: For all x, y, $\\mathtt { u n c l e ( x , y ) } \\Rightarrow \\neg \\mathtt { c h i l d ( y , x ) }$ . To check a candidate utterance, we query the solver to determine if the set of constraints is satisfiable or if there is a contradiction. The full set of constraints and other details can be found in the Appendix. We again used GPT-3 as our semantic parser, extracting parses for each candidate utterance via few-shot learning. This parsing approach worked well, even for the natural language in this domain. We observed that parsing with GPT-3 was more successful when the target parse was naturalistic, i.e., “Bob is Joe’s father.” rather than “father(Bob, Joe)”. The parsing prompt is reproduced in full in the Appendix. ",
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+        "img_path": "images/ec4fa337894acae8383e081ea66d706994e95a5c4138459856cf540cc4c46a35.jpg",
+        "image_caption": [
+            "Figure 4: Example trial from CLUTRR human judgement experiment. Participants were instructed to select which of two options makes the most sense given the prompt. One option was generated by the System 1 model only (“single-system”), while the other was generated by the dual-system model. "
+        ],
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+        "image_caption": [
+            "Figure 3: Sample story from the CLUTRR dataset. Each story consists of a sequence of humangenerated sentences concerning family relationships. Adapted from Sinha et al. (2019). ",
+            "Figure 5: CLUTRR human judgment experiment results. Bars denote proportions of dual-system generations selected as making more sense over single-system generations, in each of four conditions. Error-bars denote bootstrapped $9 5 \\%$ confidence intervals of the item means. The points denote means for each individual item in the experiment and are jittered horizontally for clarity. "
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+        "table_caption": [
+            "Table 1: Statistics from CLUTRR story generation. We report the percentage of generations (on both a per-line and per-story basis) for which the System 2 world model did not detect an error. The dual-system model is able to detect many inconsistencies in the neural single-system generations, and most can be corrected by re-sampling new candidates (up to a limit of ten). "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td colspan=\"2\">% w/out error detected (per line)</td><td colspan=\"2\">% w/out error detected (per story)</td></tr><tr><td>single-system (neural gen. only)</td><td>dual-system (neural gen.+world model)</td><td>single-system (neural gen. only)</td><td>dual-system (neural gen.+world model)</td></tr><tr><td>prompt from dataset</td><td>82.8</td><td>97.1</td><td>60</td><td>96.1</td></tr><tr><td>prompt from model</td><td>71.9</td><td>96.3</td><td>36.4</td><td>93.5</td></tr></table>",
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+        "text": "4.2 Human judgments ",
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+        "text": "We test our dual-system neural generation $^ +$ world model method in its ability to generate stories that are deemed by naive human participants to be more naturalistic and coherent than those generated from the baseline models. Specifically, we asked participants to select which of two continuations made the most sense to them, where one continuation was generated from the neural model alone (single-system) and the other from a dual-system model (either the world model System 2 or the neural NLI System 2). ",
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+        "text": "Participants. Participants $\\mathbf { N } = 1 0 1$ ) were recruited on the crowd-sourcing platform Prolific and compensated $\\$ 2$ for the task ( ${ \\sim } 1 5$ minutes, so roughly $\\$ 8/\\mathrm{ h o u r }$ ). Participants gave informed consent, and the study was approved by MIT’s IRB. 21 participants were excluded for failing an instruction quiz, incorrectly answering more than one of five filler questions, or finishing the task too quickly. The data we collected contains no personally identifiable information or offensive content. ",
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+        "type": "text",
+        "text": "Procedure. Participants began the experiment by reading a set of instructions and answering comprehension questions. On each main trial, participants were shown a prompt consisting of several sentences and were asked to choose which of two possible continuations made the most sense (an example trial is shown in Figure 4). Participants were instructed that if a name appeared multiple times within a trial, then it referred to the same person, whereas if a name appeared across trials, then it was not referring to the same person. For each trial, one continuation option was generated by the neural only single-system baseline, while the other was a dual-system generation. We selected generations from the neural only baseline that were rejected by the System 2 model in order to maximize the differences between the models’ generations; thus, human judgments pertain to generations that the models disagreed on. Each participant performed between 20 and 26 trials. ",
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+        "type": "text",
+        "text": "Materials. Participants were randomly assigned to one of four between-participant conditions, which varied according to the kind of prompt and the kind of dual-system model. The prompt was either generated from the model (up to the point of disagreement between System 1 and System 2 models; “Prompts from model” condition) or taken completely from the length 4 CLUTRR systematic generalization test dataset (“Prompts from dataset” condition). To generate prompts for the “from model” condition, we took the first sentence of each story from the CLUTRR test dataset and generated subsequent prompt sentences from the dual-system model; sentences were generated until the two systems disagreed (i.e., System 1 generated a sentence that System 2 rejected), at which point the “rejected sentence” served as the neural only (single-system) baseline generation and the first resampled sentence that System 2 accepted served as the dual-system generation. Prompts were sampled to a maximum length of four sentences. The dual-system model shown to participants used a System 2 based on either our constraint-based “world model” or the neural NLI baseline. ",
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+    {
+        "type": "text",
+        "text": "Table 1 catalogs critical statistics from the stimulus generation process. We generated vignettes from the System 1 model and report the percentage of System 1 generations which are deemed correct by the System 2 model.3 We also report the percentage of generations corrected by the System 2 model (i.e., if System 1 made an error, could System 2 fix it within 10 attempts?). We report these statistics on both a per-story and per-line basis. According to System 2, the System 1 generation model makes a lot of errors (only $3 6 . 4 \\%$ of stories and $7 1 . 9 \\%$ of lines were error-free, in the “from model\" condition). In most instances, re-sampling new generations yields stories that, according to ",
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+        "table_caption": [
+            "Table 2: Accuracy on $\\mathrm { g } \\mathrm { S C A N }$ splits. Models were trained on 5000 examples (only $2 . 5 \\%$ of the gSCAN training data). See Appendix Table 4 for additional results.) "
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Test split:</td><td>single-system5</td><td>dual-system</td></tr><tr><td>dev</td><td>71.7</td><td>83.3</td></tr><tr><td>random</td><td>57.2</td><td>74.7</td></tr><tr><td>yellow squares</td><td>68.1</td><td>81.3</td></tr><tr><td>red squares</td><td>64.9</td><td>78.1</td></tr><tr><td>novel direction</td><td>0.0</td><td>0.01</td></tr><tr><td>relativity</td><td>41.0</td><td>53.6</td></tr><tr><td>class inference</td><td>68.1</td><td>76.2</td></tr><tr><td>adverb (k=1)</td><td>0.0</td><td>0.0</td></tr><tr><td>adverb to verb</td><td>20.8</td><td>21.8</td></tr><tr><td colspan=\"3\"></td></tr><tr><td colspan=\"3\">³From Heinze-Deml &amp; Bouchacourt (2020)</td></tr></table>",
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+            "Figure 6: Schematic of our dual-system approach to $\\mathrm { g S C A N }$ . We train a neural sequence model to predict both a distribution over action sequences, and a distribution over target locations. At test time, we decode candidate action sequences from the model, execute them on the gridworld, and only accept a sequence that brings the agent to the predicted target location (shown in green). "
+        ],
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+        "type": "text",
+        "text": "System 2, no longer contain logical errors within a budget of 10 samples $9 3 . 5 \\%$ of stories and $9 6 . 3 \\%$ of lines were error-free, respectively). ",
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+        "type": "text",
+        "text": "Results. The human evaluation indicates that System 2 is indeed correcting genuine errors in the stories. As summarized in Figure 5, participants strongly preferred the dual-system neural generation $^ +$ world model continuations in comparison to the neural only single-system continuations (proportion preferring dual-system $= 0 . 8 4$ ; bootstrapped $9 5 \\%$ confidence interval [0.77, 0.89] and 0.79 [0.77, 0.89] for the “from dataset” and “from model” prompt conditions, respectively). The dual-system approach, however, did not improve generation quality when the System 2 was based on an off-the-shelf neural NLI model (Proportion preferring dual-system $= 0 . 5 1$ ; [0.40, 0.64] for “from dataset”; 0.58 [0.48, 0.68] for “from model”). Thus, when using a minimal world model, the dual-system approach dramatically improves logical consistency without any need for additional training or fine-tuning. People clearly prefer neuro-symbolic generations from the dual-system model over purely neural generations from a single-system model.4 ",
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+    {
+        "type": "text",
+        "text": "5 Grounded Instruction Following ",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The dual-system approach offers a general-purpose means of improving upon generative, neural sequence models by incorporating logical constraints. To highlight its generality, we examine how the dual-system perspective can be deployed in a very different domain: grounded instruction following. In Heinze-Deml & Bouchacourt (2020), a learned target location predictor was used to increase the accuracy of a neural action sequence generation model. Here, we show how to increase performance further by enforcing consistency between the target location predictor and the action sequence generator in our dual-system framework. ",
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+    {
+        "type": "text",
+        "text": "We use the gSCAN benchmark (Ruis et al., 2020), a recently proposed grounded instruction following dataset designed to measure compositional generalization in neural systems. Given an initial gridworld state and an instruction, e.g., “walk to the big square,” an agent must predict the sequence of low-level actions which achieve the goal, e.g., “TURN LEFT, WALK, TURN LEFT, WALK” (See Figure 6). The dataset contains several test splits, each testing different aspects of compositional generalization. ",
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+    {
+        "type": "text",
+        "text": "Our model builds on Heinze-Deml & Bouchacourt (2020) by using an LSTM to predict the correct action sequence and target location. Given a command $c$ and an initial gridworld state $s$ , the neural network defines two distributions: a distribution over action sequences $q _ { a } ( a | c , s )$ and a distribution over target grid locations $q _ { l o c } ( l | c , s )$ . Heinze-Deml & Bouchacourt (2020) showed that when these distributions share parameters, using location prediction as an auxiliary loss improves the accuracy of the action sequence prediction model. We can further exploit these two models by noticing that when a predicted action sequence is not consistent with a predicted target location, then either the action sequence or the target location must be incorrect. Since the target location is much simpler to predict, and thus much more likely to be correctly predicted, if a predicted action sequence is not consistent with the predicted target location, then the action sequence is most likely incorrect. Our dual-system framework can use this property to increase action sequence prediction accuracy. Consider the initial state and command in Figure 6. Our model predicts candidate action sequences, and also predicts that the most likely target location is the grid containing the bigger yellow square (highlighted in red). The model then executes the candidate action sequences, and only accepts a sequence which results in the agent standing in the target location. ",
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+    {
+        "type": "text",
+        "text": "",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the language of our dual-system approach, we treat the distribution over actions $q _ { a } ( a | c , s )$ as our System 1 proposal model. The distribution over target locations $q _ { l o c } ( l | c , s )$ serves as a fact extractor model, which extract a location constraint $l$ . As a minimal world model, we use a deterministic gridworld execution model $T ( a , s _ { 0 } ) \\to s _ { f }$ , which takes a state and action and predicts the resulting state. At test time, we first extract the predicted location as $l = \\arg \\operatorname* { m a x } _ { l ^ { \\prime } } q _ { l o c } ( l ^ { \\prime } | c )$ We then search through the possible action sequences from $q _ { a } ( \\cdot | c )$ , conditioned on agreement with $l$ . In our experiments, we use a sample-based search with a maximum budget of 50 samples. We trained models on random subsets of the gSCAN training set of varying sizes: 5000 datapoints, 8000 datapoints, and 20000 datapoints $2 . 5 \\%$ , $4 \\%$ and $10 \\%$ of the original training set, respectively). ",
+        "bbox": [
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+        "page_idx": 8
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+    {
+        "type": "text",
+        "text": "Results. The results show that the System 2 execution model improves performance without the need for any additional training (see Table 2 for results training on 5000 examples). In contrast to the single-system model, the dual-system model allows for sampling many candidate action sequences from the neural network, accepting only consistent sequences. This guess-and-check approach greatly increases the evaluation accuracy, improving upon prior work on gSCAN, particularly in low-data regimes. ",
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+    {
+        "type": "text",
+        "text": "6 Limitations ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In its current form, our approach is most useful in domains where naturalistic, learned generation is necessary and where a small number of mission-critical logical constraints can be explicitly articulated. Our system will be less useful when constraints are more difficult to articulate (e.g., creative domains such as writing poetry) or when there are many constraints, since the minimal world model must be hand-engineered. Enforcing strict constraints may also pose risks: if the constraints are not only logical but cultural, they may be harmful if misapplied. However, these constraints must be articulated explicitly in a symbolic model, and are thus easier to identify and correct. ",
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+    {
+        "type": "text",
+        "text": "The current few-shot parsing technique may also suffer from a limited capacity. For more complex domains, the number of examples required to specify the desired parsing behavior may be too large (i.e., they may not fit in the input window) or too complex for a model to perform parsing accurately. While some tasks may not be suitable, the complexity of the world model need not necessarily increase hand-in-hand with the complexity of the application domain. A dual-system model will be most successful when tracking just a few critical variables (e.g., tracking consistency in family relations, as in our experiments, or tracking scheduling constraints when discussing a team plan). ",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "A promising direction for future work is to incorporate learning into the System 2 world model. Currently, the minimal world knowledge that exists in System 2 can be easily modified, but changes must be made by hand. Improvements would come from automatically learning and updating this structured knowledge, possibly by incorporating neuro-symbolic learning techniques (Ellis et al., 2020; Mao et al., 2019), or other neuro-symbolic integration work such as Tsamoura et al. (2021); Michael & Valiant (2008). ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Learning could improve our dual-system approach in other ways, e.g., by training a neural module to mimic the actions of a symbolic System 2. The symbolic System 2 judgments could be used as a source of supervision; candidate utterances rejected by the symbolic System 2 model could be used as examples of contradictory sentences, and accepted utterances could be used as examples of noncontradictory statements. This oversight could help train a neural System 2 contradiction-detection model capable of more subtleties than its symbolic counterpart, especially in domains where labeled examples are otherwise unavailable. This approach may also help us understand aspects of human learning, where certain tasks that require slower, logical reasoning can be habitualized over time and tackled by faster, more intuitive reasoning. ",
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+    {
+        "type": "text",
+        "text": "Recent work (Li et al., 2021) has shown that large pre-trained neural models learn to approximately represent certain types of structured semantic information. However, it is not yet clear how representational fidelity translates to logical coherence during generative tasks. Our current approach allows us to explicitly fix logical errors in generation, which may ultimately be caused by representational errors. Understanding how we might leverage our approach to improve the representation of structured knowledge within neural models is a promising direction for future work, which could lead to increased generation consistency and coherence. ",
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+    {
+        "type": "text",
+        "text": "7 Conclusion ",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "Inspired by dual process theories from cognitive science, we combine the respective strengths of neural and symbolic approaches to build more robust models that can more effectively incorporate domain knowledge. For language generation, we showed that equipping neural generation with a minimal symbolic world model increased language coherence and consistency. For grounded instruction following, we showed that requiring test-time consistency between predicted action sequences and goal locations led to improved performance, especially in low-data regimes. Our neuro-symbolic approach can readily be applied to other domains and types of prior knowledge, as a lightweight way of improving the coherence and consistency of powerful neural sequence models. ",
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+    {
+        "type": "text",
+        "text": "This paper just scratches the surface of how structured knowledge can make neural systems more robust; we hope to inspire further work into neuro-symbolic systems which possess the robustness and commonsense necessary for human-level intelligence. ",
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+    {
+        "type": "text",
+        "text": "Acknowledgments ",
+        "text_level": 1,
+        "bbox": [
+            176,
+            414,
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We thank Laura Ruis, Jacob Andreas, Yewen (Evan) Pu, Joe O’Connor and Guy Davidson for helpful comments on an earlier version of this manuscript. MN is supported by a NSF Graduate Research Fellowship. ",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "References ",
+        "text_level": 1,
+        "bbox": [
+            174,
+            500,
+            266,
+            515
+        ],
+        "page_idx": 9
+    },
+    {
+        "type": "text",
+        "text": "Andreas, J., Bufe, J., Burkett, D., Chen, C., Clausman, J., Crawford, J., Crim, K., DeLoach, J., Dorner, L., Eisner, J., et al. Task-oriented dialogue as dataflow synthesis. Transactions of the Association for Computational Linguistics, 8:556–571, 2020.   \nBrown, T. B., Mann, B., Ryder, N., Subbiah, M., Kaplan, J., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., et al. Language models are few-shot learners. arXiv preprint arXiv:2005.14165, 2020.   \nDe Moura, L. and Bjørner, N. Z3: An efficient smt solver. In Tools and Algorithms for the Construction and Analysis of Systems, pp. 337–340. Springer, 2008.   \nDeng, Y., Bakhtin, A., Ott, M., Szlam, A., and Marc’Aurelio Ranzato. Residual energy-based models of text generation. In International Conference on Learning Representations (ICLR), pp. 1–18, 2020.   \nDevlin, J., Uesato, J., Bhupatiraju, S., Singh, R., Mohamed, A.-r., and Kohli, P. Robustfill: Neural program learning under noisy i/o. ICML, 2017.   \nEllis, K., Wong, C., Nye, M., Sable-Meyer, M., Cary, L., Morales, L., Hewitt, L., Solar-Lezama, A., and Tenenbaum, J. B. Dreamcoder: Growing generalizable, interpretable knowledge with wake-sleep bayesian program learning. arXiv preprint arXiv:2006.08381, 2020.   \nEvans, J. S. B. In two minds: dual-process accounts of reasoning. Trends in cognitive sciences, 7(10): 454–459, 2003.   \nFrederick, S. Cognitive reflection and decision making. Journal of Economic perspectives, 19(4): 25–42, 2005.   \nGarcez, A. d. and Lamb, L. C. Neurosymbolic ai: The 3rd wave. arXiv preprint arXiv:2012.05876, 2020.   \nGoyal, A. and Bengio, Y. Inductive biases for deep learning of higher-level cognition. arXiv preprint arXiv:2011.15091, 2020.   \nGoyal, A., Didolkar, A., Ke, N. R., Blundell, C., Beaudoin, P., Heess, N., Mozer, M., and Bengio, Y. Neural production systems. CoRR, abs/2103.01937, 2021. URL https://arxiv.org/abs/ 2103.01937.   \nHeinze-Deml, C. and Bouchacourt, D. Think before you act: A simple baseline for compositional generalization. arXiv preprint arXiv:2009.13962, 2020.   \nHerzig, J. and Berant, J. Span-based semantic parsing for compositional generalization. arXiv preprint arXiv:2009.06040, 2020.   \nHoltzman, A., Buys, J., Forbes, M., Bosselut, A., Golub, D., and Choi, Y. Learning to write with cooperative discriminators. arXiv preprint arXiv:1805.06087, 2018.   \nHua, X. and Wang, L. Pair: Planning and iterative refinement in pre-trained transformers for long text generation. In EMNLP, 2020.   \nKahneman, D. Thinking, fast and slow. kindle ed, 2013.   \nKurita, S. and Cho, K. Generative language-grounded policy in vision-and-language navigation with bayes’ rule. arXiv preprint arXiv:2009.07783, 2020.   \nLake, B. M. and Murphy, G. L. Word meaning in minds and machines. arXiv preprint arXiv:2008.01766, 2020.   \nLake, B. M., Ullman, T. D., Tenenbaum, J. B., and Gershman, S. J. Building machines that learn and think like people. Behavioral and Brain Sciences, 40:E253, 2017.   \nLewis, M., Liu, Y., Goyal, N., Ghazvininejad, M., Mohamed, A., Levy, O., Stoyanov, V., and Zettlemoyer, L. Bart: Denoising sequence-to-sequence pre-training for natural language generation, translation, and comprehension. arXiv preprint arXiv:1910.13461, 2019.   \nLi, B. Z., Nye, M., and Andreas, J. Implicit representations of meaning in neural language models. arXiv preprint arXiv:2106.00737, 2021.   \nLiang, C., Berant, J., Le, Q. V., Forbus, K., and Lao, N. Neural symbolic machines: Learning semantic parsers on freebase with weak supervision. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 23–33, Vancouver, Canada, 2017. URL http://aclanthology.coli.uni-saarland.de/pdf/P/P17/P17-1003.pdf.   \nLiang, P. Learning executable semantic parsers for natural language understanding. Communications of the ACM, 59(9):68–76, 2016.   \nLiu, Y., Ott, M., Goyal, N., Du, J., Joshi, M., Chen, D., Levy, O., Lewis, M., Zettlemoyer, L., and Stoyanov, V. Roberta: A robustly optimized bert pretraining approach. arXiv preprint arXiv:1907.11692, 2019.   \nLoshchilov, I. and Hutter, F. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101, 2017.   \nLu, X., West, P., Zellers, R., Bras, R. L., Bhagavatula, C., and Choi, Y. Neurologic decoding:(un) supervised neural text generation with predicate logic constraints. arXiv preprint arXiv:2010.12884, 2020.   \nMao, J., Gan, C., Kohli, P., Tenenbaum, J. B., and Wu, J. The neuro-symbolic concept learner: Interpreting scenes, words, and sentences from natural supervision. arXiv preprint arXiv:1904.12584, 2019.   \nMartin, L. J., Ammanabrolu, P., Hancock, W., Singh, S., Harrison, B., and Riedl, M. O. Event representations for automated story generation with deep neural nets. In AAAI, 2018.   \nMarzoev, A., Madden, S., Kaashoek, M. F., Cafarella, M., and Andreas, J. Unnatural language processing: Bridging the gap between synthetic and natural language data. arXiv preprint arXiv:2004.13645, 2020.   \nMiao, N., Zhou, H., Mou, L., Yan, R., and Li, L. Cgmh: Constrained sentence generation by metropolis-hastings sampling. In AAAI, 2019.   \nMichael, L. and Valiant, L. G. A first experimental demonstration of massive knowledge infusion. 2008.   \nMou, L., Lu, Z., Li, H., and Jin, Z. Coupling distributed and symbolic execution for natural language queries. In Precup, D. and Teh, Y. W. (eds.), Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pp. 2518–2526. PMLR, 06–11 Aug 2017. URL http://proceedings.mlr.press/v70/mou17a.html.   \nMuhlgay, D., Herzig, J., and Berant, J. Value-based search in execution space for mapping instructions to programs. pp. 1942–1954, 01 2019. doi: 10.18653/v1/N19-1193.   \nNie, Y., Williamson, M., Bansal, M., Kiela, D., and Weston, J. I like fish, especially dolphins: Addressing contradictions in dialogue modelling. arXiv preprint arXiv:2012.13391, 2020.   \nNye, M. I., Solar-Lezama, A., Tenenbaum, J. B., and Lake, B. M. Learning compositional rules via neural program synthesis. arXiv preprint arXiv:2003.05562, 2020.   \nPieraccini, R., Tzoukermann, E., Gorelov, Z., Gauvain, J.-L., Levin, E., Lee, C.-H., and Wilpon, J. A speech understanding system based on statistical representation of semantics. In [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, volume 1, pp. 193–196 vol.1, 1992. doi: 10.1109/ICASSP.1992.225939.   \nRadford, A., Wu, J., Child, R., Luan, D., Amodei, D., and Sutskever, I. Language models are unsupervised multitask learners. OpenAI blog, 1(8):9, 2019.   \nRamesh, A., Pavlov, M., Goh, G., Gray, S., Voss, C., Radford, A., Chen, M., and Sutskever, I. Zero-shot text-to-image generation. arXiv preprint arXiv:2102.12092, 2021.   \nRuis, L., Andreas, J., Baroni, M., Bouchacourt, D., and Lake, B. M. A benchmark for systematic generalization in grounded language understanding. arXiv preprint arXiv:2003.05161, 2020.   \nSchlag, I. and Schmidhuber, J. Learning to reason with third-order tensor products. CoRR, abs/1811.12143, 2018. URL http://arxiv.org/abs/1811.12143.   \nSerafini, L. and d’Avila Garcez, A. S. Logic tensor networks: Deep learning and logical reasoning from data and knowledge. CoRR, abs/1606.04422, 2016. URL http://arxiv.org/abs/1606. 04422.   \nShen, S., Fried, D., Andreas, J., and Klein, D. Pragmatically informative text generation. arXiv preprint arXiv:1904.01301, 2019.   \nShin, R., Lin, C. H., Thomson, S., Chen, C., Roy, S., Platanios, E. A., Pauls, A., Klein, D., Eisner, J., and Van Durme, B. Constrained language models yield few-shot semantic parsers. arXiv preprint arXiv:2104.08768, 2021.   \nSinha, K., Sodhani, S., Dong, J., Pineau, J., and Hamilton, W. L. Clutrr: A diagnostic benchmark for inductive reasoning from text. arXiv preprint arXiv:1908.06177, 2019.   \nSmith, E. M., Gonzalez-Rico, D., Dinan, E., and Boureau, Y.-L. Controlling style in generated dialogue. arXiv preprint arXiv:2009.10855, 2020.   \nSpelke, E. S. and Kinzler, K. D. Core knowledge. Developmental Science, 10(1):89–96, 2007.   \nSu, Y. and Yan, X. Cross-domain semantic parsing via paraphrasing. arXiv preprint arXiv:1704.05974, 2017.   \nTsamoura, E., Hospedales, T., and Michael, L. Neural-symbolic integration: A compositional perspective. Proceedings of the AAAI Conference on Artificial Intelligence, 35(6):5051–5060, May 2021. URL https://ojs.aaai.org/index.php/AAAI/article/view/16639.   \nWelleck, S., Weston, J., Szlam, A., and Cho, K. Dialogue natural language inference. arXiv preprint arXiv:1811.00671, 2018.   \nWeston, J., Bordes, A., Chopra, S., Rush, A. M., van Merriënboer, B., Joulin, A., and Mikolov, T. Towards ai-complete question answering: A set of prerequisite toy tasks. arXiv preprint arXiv:1502.05698, 2015.   \nXu, J., Ren, X., Zhang, Y., Zeng, Q., Cai, X., and Sun, X. A skeleton-based model for promoting coherence among sentences in narrative story generation. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, pp. 4306–4315, Brussels, Belgium, OctoberNovember 2018. Association for Computational Linguistics. doi: 10.18653/v1/D18-1462. URL https://www.aclweb.org/anthology/D18-1462.   \nXu, J., Ju, D., Li, M., Boureau, Y.-L., Weston, J., and Dinan, E. Recipes for safety in open-domain chatbots. arXiv preprint arXiv:2010.07079, 2020a.   \nXu, S., Semnani, S. J., Campagna, G., and Lam, M. S. Autoqa: From databases to qa semantic parsers with only synthetic training data. arXiv preprint arXiv:2010.04806, 2020b. ",
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