1 Introduction
Advanced manufacturing methods that allow completely automated production of customized objects and parts are transforming today’s economy. One prime example of these methods is wholegarment knitting that is used to massproduce many common textile products (e.g., socks, gloves, sportswear, shoes, car seats, etc.). During its operation, a whole garment knitting machine executes a custom lowlevel program to manufacture each textile object. Typically, generating the code corresponding to each design is a difficult and tedious process requiring expert knowledge. A few recent works have tackled the digital design workflow for wholegarment knitting (Underwood, 2009; McCann et al., 2016; Narayanan et al., 2018; Yuksel et al., 2012; Wu et al., 2018a, b). None of these works, however, provide an easy way to specify patterns.
The importance of patterning in textile design is evident in pattern books (Donohue, 2015; Shida & Roehm, 2017), which contain instructions for hundreds of decorative designs that have been manually crafted and tested over time. Unfortunately, these pattern libraries are geared towards handknitting and they are often incompatible with the operations of industrial knitting machines. Even in cases when a direct translation is possible, the patterns are only specified in stitchlevel operation sequences. Hence, they would have to be manually specified and tested for each machine type similarly to assembly level programming.
In this work, we propose an inverse design method using deep learning to automate the pattern design for industrial knitting machines. In our
inverse knitting, machine instructions are directly inferred from an image of the fabric pattern. To this end, we collect a paired dataset of knitting instruction maps and corresponding images of knitted patterns. We augment this dataset with synthetically generated pairs obtained using a knitting simulator (Shima Seiki, ). This combined dataset facilitates a learningbased approach. More specifically, we propose a theoretically inspired imagetoprogram map synthesis method that leverages both real and simulated data for learning. Our contributions include:
An automatic translation of images to sequential instructions for a real manufacturing process;

A diverse knitting pattern dataset that provides a mapping between images and instruction programs specified using a new domainspecific language (DSL) (Kant, 2018) that significantly simplifies lowlevel instructions and can be decoded without ambiguity;

A theoretically inspired deep learning pipeline to tackle this inverse design problem; and

A novel usage of synthetic data to learn to neutralize realworld, visual perturbations.
In the rest of the paper, we first provide the necessary background in machine knitting and explain our 2D regular instructions, we then go over our dataset acquisition, detail our learning pipeline making use of synthetic data, and finally go over our experiment results.
2 Knitting Background
Knitting is one of the most common forms of textile manufacturing. The type of knitting machine we are considering in this work is known as a Vbed machine, which allows automatic knitting of whole garments. This machine type uses two beds of individually controllable needles, both of which are oriented in an inverted V shape allowing opposite needles to transfer loops between beds. The basic operations are illustrated in Figures 2 and 3:

Knit pulls a new loop of yarn through all current loops,

Tuck stacks a new loop onto a needle,

Miss skips a needle,

Transfer moves a needle’s content to the other bed,

Racking changes the offset between the two beds.
Whole garments (e.g. socks, sweatshirts, hats) can be automatically manufactured by scheduling complex sequences of these basic operations (Underwood, 2009; McCann et al., 2016). Furthermore, this manufacturing process also enables complex surface texture and various types of patterns. Our aim is to automatically generate machine instructions to reproduce any geometric pattern from a single closeup photograph (e.g. of your friend’s garment collection). To simplify the problem, we assume the input image only captures 2D patterning effects of flat fabric, and we disregard variations associated with the 3D shape of garments.
3 Instruction Set
K  P  T  M  FR1  FR2  FL1  FL2  BR1  BR2  BL1  BL2  XR+  XR  XL+  XL  S 
General knitting programs are sequences of operations which may not necessarily have a regular structure. In order to make our inverse design process more tractable, we devise a set of instructions. These instructions include all basic knitting operations and they are specified on a regular 2D grid that can be parsed and executed linebyline. We first detail these instructions and then explain how they are sequentially processed.
The first group of instructions are based on the first three operations, namely: Knit, Tuck and Miss.
Then, transfer operations allow moving loops of yarn across beds. This is important because knitting on the opposite side produces a very distinct stitch appearance known as reverse stitch or Purl – our complement instruction of Knit.
Furthermore, the combination of transfers with racking allows moving loops within a bed. We separate such higherlevel operations into two groups: Move instructions only consider combinations that do not cross other such instructions so that their relative scheduling does not matter, and Cross instructions are done in pairs so that both sides are swapped, producing what is known as cable patterns. The scheduling of cross instructions is naturally defined by the instructions themselves. These combined operations do not create any new loop by themselves, and thus we assume they all apply a Knit operation before executing the associated needle moves, so as to maintain spatial regularity.
Finally, transfers also allow different stacking orders when multiple loops are joined together. We model this with our final Stack instruction. The corresponding symbols and color coding of the instructions are shown in Figure 4.
3.1 Knitting Operation Scheduling
Given a line of instructions, the sequence of operations is done over a full line using the following steps:

The current stitches are transferred to the new instruction side without racking;

The base operation (knit, tuck or miss) is executed;

The needles of all transferrelated instructions are transferred to the opposite bed without racking;

Instructions that involve moving within a bed proceed to transfer back to the initial side using the appropriate racking and order;

Stack instructions transfer back to the initial side without racking.
Instruction Side
The only instructions requiring an associated bed side are those performing a knit operation. We thus encode the bed side in the instructions (knit, purl, moves), except for those where the side can be inferred from the local context. This inference applies to Cross which use the same side as past instructions (for aesthetic reasons), and Stack which uses the side of its associated Move instruction. Although this is a simplification of the design space, we did not have any pattern with a different behaviour.
4 Dataset for Knitting Patterns
Before developing a learning pipeline, we describe our dataset and its acquisition process. The frequency of different instruction types is shown in Figure 5.
The main challenge is that, while machine knitting can produce a large amount of pattern data reasonably quickly, we still need to specify these patterns (and thus generate reasonable pattern instructions), and acquire calibrated images for supervised learning.
4.1 Pattern Instructions
We extracted pattern instructions from the proprietary software KnitPaint (Shima Seiki, ). These patterns have various sizes and span a large variety of designs from cable patterns to pointelle stitches, lace, and regular reverse stitches.
Given this set of initial patterns (around a thousand), we normalized the patterns by computing crops of instructions with overlap, while using default front stitches for the background of smaller patterns. This provided us with 12,392 individual patterns (after pruning invalid patterns since random cropping can destroy the structure).
We then generated the corresponding images in two different ways: (1) by knitting a subset of 1,044 patches, i.e., Real data, and (2) by rendering all of them using the basic pattern preview from KnitPaint, i.e., Simulated data. See Figure 6 for sample images.
4.2 Knitting Many Samples
The main consideration for capturing knitted patterns is that their tension should be as regular as possible so that knitting units would align with corresponding pattern instructions. We initially proceeded with knitting and capturing patterns individually but this proved to not be scalable.
We then chose to knit sets of patterns over a tile grid, each of which would be separated by both horizontal and vertical tubular knit structure. The tubular structures are designed to allow sliding inch steel rods which we use to normalize the tension, as shown in Figure 7. Note that each knitted pattern effectively provides us with two full opposite patterns (the front side, and its back whose instructions can be directly mapped from the front ones). This doubles the size of our real knitted dataset to 2,088 samples after annotating and cropping the knitted samples.
5 Instruction Synthesis Model
We present our deep neural network model that infers a 2D knitting instruction map from an image of patterns. In this section, we provide the theoretical motivation of our framework, and then we describe the loss functions we used, as well as implementation details.
5.1 Learning from different domains
When we have a limited number of real data, it is appealing to leverage simulated data because high quality annotations are automatically available. However, learning from synthetic data is problematic due to apparent domain gaps between synthetic and real data. We study how we can further leverage simulated data. We are motivated by the recent work, Simulated+Unsupervised (S+U) learning (Shrivastava et al., 2017), but in contrast to them, we develop our framework from the generalization error perspective.
Let be input space (image), and output space (instruction label), and a data distribution on paired with a true labeling function
. As a typical learning problem, we seek a hypothesis classifier
that best fits the target function in terms of an expected loss: for classifiers , where denotes a loss function. We denote its empirical loss as , where is the sampled dataset.In our problem, since we have two types of data available, a source domain and a target domain (which is real or simulated as specified later), our goal is to find by minimizing the combination of empirical source and target losses as mixed loss, where , and for simplicity we shorten and we use the parallel notation and . Our underlying goal is to achieve a minimal generalized target loss . To develop a generalizable framework, we present a bound over the target loss in terms of its empirical mixed loss, which is a slight modification of Theorem 3 of (BenDavid et al., 2010).
Theorem 1.
Let be a hypothesis class, and be a labeled sample of size generated by drawing samples from and samples from and labeling them according to the true label . Suppose is symmetric and obeys the triangle inequality. Let be the empirical minimizer of on for a fixed , and the target error minimizer. Then, for any
, with probability at least
(over the choice of the samples), we have(1) 
where , and .
The proof can be found in the supplementary material. Compared to (BenDavid et al., 2010), Theorem 1 is purposely extended to use a more general definition of discrepancy (Mansour et al., 2009) that measures the discrepancy of two distributions (the definition can be found in the supplementary material) and to be agnostic to the model type (simplification), so that we can clearly present our motivation of our model design.
Theorem 1 shows that mixing two sources of data is possible to achieve a better generalization in the target domain. The bound is always at least as tight as either of or (The case that uses either source or target dataset alone). Also, as the total number of the combined data sample is larger, a tighter bound can be obtained.
A factor that the generalization gap (the right hand side in Eq. (1)) strongly depends on is the discrepancy . This suggests that we can achieve a tighter bound if we can reduce . We reparameterize the target distribution as so that , where is a distribution mapping function. Then, we find the mapping that leads to the minimal discrepancy for the empirical distribution as:
(2) 
which is a minmax problem. Even though the problem is defined for an empirical distribution, it is intractable to search the entire solution space; thus, motivated by (Ganin et al., 2016), we approximately minimize the discrepancy by generative adversarial networks (GAN) (Goodfellow et al., 2014). Therefore, deriving from Theorem 1, our empirical minimization is formulated by minimizing the convex combination of source and target domain losses as well as the discrepancy as:
(3) 
Along with leveraging GAN, our key idea for reducing the discrepancy between two data distributions, i.e., domain gap, is to transfer the real knitting images (target domain, ) to synthetic looking data (source domain, ) rather than the other way around, i.e., making . The previous methods have investigated generating realistic looking images to adapt the domain gap. However, we observe that, when simulated data is mapped to real data, the mapping is a onetomany mapping due to realworld effects, such as lighting variation, geometric deformation, background clutter, noise, etc. This introduces an unnecessary challenge to learn ; thus, we instead learn to neutralize the realworld perturbation by mapping from real data to synthetic looking data. Beyond simplifying the learning of , it also allows the mapping to be utilized at test time for processing of realworld images.
We implement and
using convolutional neural networks (CNN), and formulate the problem as a local instruction classification
^{1}^{1}1While our program synthesis can be regarded as a multiclass classification, for simplicity, we consider the simplest binary classification here. However, multiclass classification can be extended by a combination of binary classifications (ShalevShwartz & BenDavid, 2014).and represent the output as a 2D array of classification vectors
(i.e., softmax values over ) for our instructions at each spatial location . In the following, we describe the loss we use to train our model and details about our endtoend training procedure.Loss function
We use the cross entropy for the loss . We supervise the inferred instruction to match the groundtruth instruction using the standard multiclass crossentropy where is the predicted likelihood (softmax value) for instruction , which we compute at each spatial location .
For synthetic data, we have precise localization of the predicted instructions. In the case of the real knitted data, human annotations are imperfect and this can cause a minor spatial misalignment of the image with respect to the original instructions. For this reason, we allow the predicted instruction map to be globally shifted by up to one instruction. In practice, motivated by multiple instance learning (Dietterich et al., 1997), we consider the minimum of the perimage crossentropy over all possibles onepixel shifts (as well as the default noshift variant), i.e., our complete cross entropy loss is
(4) 
where is the pattern displacement for the real data and for the synthetic data. The loss is accumulated over the spatial domain for the instruction map size reduced by boundary pixels. is a normalization factor.
5.2 Implementation details
Our base architecture is illustrated in Figure 1
. We implemented it using TensorFlow
(Abadi et al., 2016). The prediction network Img2prog takes grayscale images as input and generatesinstruction maps. The structure consists of an initial set of 3 convolution layers with stride 2 that downsample the image to
spatial resolution, a feature transformation part made of residual blocks (He et al., 2016; Zhu et al., 2017), and two final convolutions producing the instructions. The kernel size of all convolution layers is , except for the last layer which is . We use instance normalization (Ulyanov et al., 2016)for each of the initial downconvolutions, and ReLU everywhere.
We solve the minimax problem of the discrepancy w.r.t. using the leastsquare PatchGAN (Isola et al., 2017). Additionally, we add the perceptual loss and style loss (Johnson et al., 2016) between input real images and its generated images and between simulated images and generated images, respectively, to regularize the GAN training, which stably speeds up the training of .
The structure of the Refiner network and the balance between losses can be found in the supplementary.
Training procedure
We train our network with a combination of the real knitted patterns and the rendered images. We have oversampled the real data to achieve 1:1 mix ratio with several data augmentation strategies, which can be found in the supplementary material. We train with 80% of the real data, withholding 5% for validation and 15% for testing, whereas we use all the synthetic data for training.
According to the typical training method for GAN (Goodfellow et al., 2014), we alternate the training between discriminator and the other networks, and , but we update the discriminator only every other iteration, and the iteration is counted according to the number of updates for and .
We trained our model for iterations with batch size for each domain data using ADAM optimizer with initial learning rate , exponential decay rate every iterations. The training took from to hours (depending on the model) on a Titan Xp GPU.
6 Experiments
We first evaluate baseline models for our new task, along with an ablation study looking at the impact of our loss and the tradeoff between real and synthetic data mixing. Finally, we look at the impact of the size of our dataset.
Accuracy Metric
For the same reason our loss in Eq. (4) takes into consideration a 1pixel ambiguity along the spatial domain, we use a similarly defined accuracy. It is measured by the average of over the whole dataset, where is the same normalization constant as in Eq. (4), is the indicator function that returns 1 if the statement is true, 0 otherwise. We report two variants: FULL averages over all the instructions, whereas FG averages over all the instructions but the background (i.e., it does not consider the most predominant instruction type in the pattern).
Perceptual Metrics
For the baselines and the ablation experiments, we additionally provide perceptual metrics that measure how similar the knitted pattern would look. An indirect method for evaluation is to apply a pretrained neural network to generated images and calculate statistics of its output, e.g., Inception Score (Salimans et al., 2016). Inspired by this, we learn a separate network to render simulated images of the generated instructions and compare it to the rendering of the ground truth using standard PSNR and SSIM metrics. Similarly to the accuracy, we take into account the instruction localization ambiguity and allow for one instruction shift which translates to full 8 pixels shifts in the image domain.
6.1 Comparison to Baselines
Table 1 compares the measured accuracy of predicted instructions on our real image test set. We also provide qualitative results in Figure 9.
Method  Accuracy (%)  Perceptual  

Full  FG  SSIM  PSNR [dB]  
(a1)  CycleGAN (Zhu et al., 2017)  46.21  21.58  0.631  15.43 
(a2)  Pix2Pix (Isola et al., 2017)  57.11  46.06  0.662  15.94 
(a3)  UNet (Ronneberger et al., 2015)  89.46  63.79  0.848  21.79 
(a4)  Scene Parsing (Zhou et al., 2018)  87.53  66.38  0.850  21.79 
(a5)  S+U (Shrivastava et al., 2017)  91.85  71.47  0.872  21.93 
(b1)  Img2prog (real only) with CE  91.45  70.73  0.866  21.52 
(b2)  Img2prog (real only) with MILCE  91.94  71.61  0.875  21.68 
(c1)  Refiner + img2prog ()  93.62  78.06  0.896  22.90 
(c2)  Refiner + img2prog ()  93.48  78.47  0.893  23.18 
(c3)  Refiner + img2prog ()  94.11  81.08  0.902  23.68 
(c4)  Refiner + img2prog ()  91.87  71.44  0.873  21.96 
(d1)  Refiner + img2prog++ ()  94.35  81.96  0.905  24.06 
The first 5 rows of Table 1
(a15) present results of previous works to provide snippets of other domain methods. For CycleGAN, no direct supervision is provided and the domains are mapped in a fully unsupervised manner. Together with Pix2pix, the two first methods do not use crossentropy but L1 losses with GAN. Although they can provide interesting image translations, they are not specialized for multiclass classification problems, and thus cannot compete. All baselines are trained from scratch. Furthermore, since their architectures use the same spatial resolution for both input and output, we upsampled instruction maps to the same image dimensions using nearest neighbor interpolation.
S+U Learning (Shrivastava et al., 2017) used a refinement network to generate a training dataset that makes existing synthetic data look realistic. In this case, our implementation uses our base network Img2prog and approximates real domain transfer by using style transfer. We tried two variants: using the original Neural Style Transfer (Gatys et al., 2016) and CycleGAN (Zhu et al., 2017). Both input data types lead to very similar accuracy (negligible difference) when added as a source of real data. We thus only report the numbers from the first one (Gatys et al., 2016).
Instruction  K  P  T  M  FR1  FR2  FL1  FL2  BR1  BR2  BL1  BL2  XR+  XR  XL+  XL  S 

Accuracy [%]  96.49  96.58  74.84  71.69  80.22  83.33  76.01  100  71.42  27.27  70.88  27.27  55.21  62.32  62.61  59.28  25.87 
Frequency [%]  46.42  45.34  0.50  1.99  1.10  0.01  1.13  0.01  1.08  0.01  1.23  0.01  0.28  0.21  0.26  0.23  0.20 
6.2 Impact of Loss and Data Mixing Ratio
The second group in Table 1(b12) considers our base network (Img2prog) without the refinement network (Refiner) that translates real images onto the synthetic domain. In this case, Img2prog maps real images directly onto the instruction domain.
Note that the results generated by all direct image translation networks trained with crossentropy (a35) compare similarly using perceptual metrics, but our base Img2prog performs substantially better in accuracy. This suggests that it is beneficial to reduce features to the instruction domain instead of upsampling instructions to the image domain.
The third group in Table 1(c14) looks at the impact of the mixing ratio when using our full architecture. In this case, the refinement network translates our real image into a synthetic looking one, which is then translated by Img2prog into instructions. This combination favorably improves both the accuracy and perceptual quality of the results with the best mixing ratio of , which favors more the supervision from diverse simulated data. While in Theorem 1 has a minimum at , we have a biased due to other effects, and .
We tried learning the opposite mapping from synthetic image to realistic looking image generation as a source domain with Img2prog , while directly feeding real data to . This results in detrimental results with mode collapsing, and the learned in this way maps to a trivial texture without semantically meaningful patterns, and tried to inject the pattern information in invisible noise pattern like adversarial perturbation to enforce to maintain plausible inference. We postulate this might be due to the nontrivial onetomany mapping relationship from simulated data to real data, and overburden for to learn to compensate real perturbations by itself.
In the last row of Table 1(d1), we present the result obtained with a variant network, Img2prog++ which additionally uses skip connections from each downconvolution of Img2prog to increase its representation power. This is our best model in the qualitative comparisons of Figure 9.
Finally, we check the perinstruction behavior of our best model, shown through the perinstruction accuracy in Table 2. Although there is a large difference in instruction frequency, our method still manages to learn some useful representation for rare instructions but the variability is high. This suggests the need for a systematic way of tackling the class imbalance (Huang et al., 2016; Lin et al., 2018).
6.3 Impact of Dataset Size
In Figure 8, we show the impact of the real data amount on accuracy. As expected, increasing the amount of training data helps. With low amounts of data (here samples or less), the full accuracy is not sufficient to explain the outcome. In this case, the samples experiment started to overfit before the end of the training.
7 Discussion and Related Work
Knitting instruction generation We establish the potential of automatic program synthesis for machine kitting using deep images translation. Recent works allow automatic conversion of 3D meshes to machine instructions (Narayanan et al., 2018), or directly model garment patterns on specialized meshes (Yuksel et al., 2012; Wu et al., 2018a), which can then be translated into hand knitting instruction (Wu et al., 2018b). While this does enable a wide range of achievable patterns, the accompanying interface requires stitchlevel specification. This can be tedious, and requires the user to have previous knitting experience. Moreover, the resulting knits are not machineknittable. We bypass the complete need of modeling these patterns and allow direct synthesis from image exemplars that are simpler to acquire and also machine knittable.
Simulated data based learning We demonstrate a way to effectively leverage both simulated and real knitting data. There have been a recent surge of adversarial learning based domain adaptation methods (Shrivastava et al., 2017; Tzeng et al., 2017; Hoffman et al., 2018) in the simulationbased learning paradigm. They deploy GANs and refiners to refine the synthetic or simulated data to look real. We instead take the opposite direction to exploit the simple and regular domain properties of synthetic data. Also, while they require multistep training, our networks are endtoend trained from scratch and only need oneside mapping rather than the twosided cyclic mapping (Hoffman et al., 2018).
Semantic segmentation Our problem is to transform photographs of knit structures into their corresponding instruction maps. This resembles semantic segmentation which is a perpixel multiclass classification problem except that the spatial extent of individual instruction interactions is much larger when looked at from the original image domain. From a program synthesis perspective, we have access to a set of constraints on valid instruction interactions (e.g. Stack is always paired with a Move instruction reaching it). This conditional dependency is referred to as context in semantic segmentation, and there have been many efforts to explicitly tackle this by Conditional Random Field (CRF) (Zheng et al., 2015; Chen et al., 2018; Rother et al., 2004). They clean up spurious predictions of a weak classifier by favoring samelabel assignments to neighboring pixels, e.g., Potts model. For our problem, we tried a firstorder syntax compatibility loss, but there was no noticeable improvement. However we note that (Yu & Koltun, 2016) observed that a CNN with a large receptive field but without CRF can outperform or compare similarly to its counterpart with CRF for subsequent structured guidance (Zheng et al., 2015; Chen et al., 2018). While we did not consider any CRF post processing in this work, sophisticated modeling of the knittability would be worth exploring as a future direction.
Another apparent difference between knitting and semantic segmentation is that semantic segmentation is an easy – although tedious – task for humans, whereas parsing knitting instructions requires vast expertise or reverse engineering.
Neural program synthesis In terms of returning explicit interpretable programs, our work is closely related to program synthesis, which is a traditional challenging, ongoing problem.^{2}^{2}2A similar concept is program induction, in which the model learns to mimic the program rather than explicitly return it. From our perspective, semantic segmentation is closer to program induction, while our task is program synthesis. The recent advance of deep learning has made notable progress in this domain, e.g., (Johnson et al., 2017; Devlin et al., 2017). Our task would have potentials to extend the research boundary of this field, since it differs from any other prior task on program synthesis in that: 1) while program synthesis solutions adopt a sequence generation paradigm (Kant, 2018), our type of inputoutput pairs are 2D program maps, and 2) the domain specific language (our instruction set) is newly developed and directly applicable to practical knitting.
8 Conclusion
We have proposed an inverse process for translating high level specifications to manufacturing instructions based on deep learning. In particular, we have developed a framework that translates images of knitted patterns to instructions for industrial wholegarment knitting machines. In order to realize this framework, we have collected a dataset of machine instructions and corresponding images of knitted patterns. We have shown both theoretically and empirically how we can improve the quality of our translation process by combining synthetic and real image data. We have shown an uncommon usage of synthetic data to develop a model that maps real images onto a more regular domain from which machine instructions can more easily be inferred.
The different trends between our perceptual and semantic metrics bring the question of whether adding a perceptual loss on the instructions might also help improve the semantic accuracy. This could be done with a differentiable rendering system. Another interesting question is whether using higheraccuracy simulations (Yuksel et al., 2012; Wu et al., 2018a) could help and how the difference in regularity affects the generalization capabilities of our prediction.
We believe that our work will stimulate more research in developing machine learning methods for design and manufacturing.
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Contents

Details of the Refiner network.

Loss balancing parameters.

Used data augmentation detail.

Lemmas and theorem with the proofs.

Additional qualitative results.
The Refiner Network
Our refinement network translates real images into regular images that look similar to synthetic images. Its implementation is similar to Img2prog, except that it outputs the same resolution image as input, of which illustration is shown in Figure 10.
Loss Balancing Parameters
When learning our full architecture with both Refiner and Img2prog, we have three different losses: the crossentropy loss , the perceptual loss , and the PatchGAN loss.
Our combined loss is the weighted sum
(5) 
where we used the weights: , and .
The perceptual loss (Johnson et al., 2016) consists of the feature matching loss and style loss (using the gram matrix). If not mentioned here, we follow the implementation details of (Johnson et al., 2016), where VGG16 (Simonyan & Zisserman, 2014)
is used for feature extraction, after replacing maxpooling operations with averagepooling. The feature matching part is done using the
pool3 layer, comparing the input real image and the output of Refiner so as to preserve the content of the input data. For the style matching part, we use the gram matrices of the {conv1_2, conv2_2, conv3_3} layers with the respective relative weights {0.3, 0.5, 1.0}. The measured style loss is between the synthetic image and the output of Refiner.Data Augmentation
We use multiple types of data augmentation to notably increase the diversity of yarn colors, lighting conditions, yarn tension, and scale:

Global Crop Perturbation: we add random noise to the location of the crop borders for the real data images, and crop onthefly during training; the noise intensity is chosen such that each border can shift at most by half of one stitch;

Local Warping: we randomly warp the input images locally using nonlinear warping with linear RBF kernels on a sparse grid. We use one kernel per instruction and the shift noise is a 0centered gaussian with being of the default instruction extent in image space (i.e. );

Intensity augmentation: we randomly pick a single color channel and use it as a monochannel input, so that it provides diverse spectral characteristics. Also note that, in order to enhance the intensity scale invariance, we apply instance normalization (Ulyanov et al., 2016) for the upfront convolution layers of our encoder network.
Proof of Theorem 1
We first describe the necessary definitions and lemmas to prove Theorem 1. We need a general way to measure the discrepancy between two distributions, which we borrow from the definition of discrepancy suggested by (Mansour et al., 2009).
Definition 1 (Discrepancy (Mansour et al., 2009)).
Let be a class of functions mapping from to . The discrepancy between two distribution and over is defined as
(6) 
The discrepancy is symmetric and satisfies the triangle inequality, regardless of any loss function. This can be used to compare distributions for general tasks even including regression.
The following lemma is the extension of Lemma 4 in (BenDavid et al., 2010) to be more generalized by the above discrepancy.
Lemma 1.
Let be a hypothesis in class , and assume that is symmetric and obeys the triangle inequality. Then
(7) 
where , and the ideal joint hypothesis is defined as .
Proof.
The proof is based on the triangle inequality of , and the last inequality follows the definition of the discrepancy.
(8) 
We conclude the proof. ∎
Many types of losses satisfy the triangle inequality, e.g., the loss (BenDavid et al., 2010; Crammer et al., 2008) and norm obey the triangle inequality, and norm () obeys the pseudo triangle inequality (Galanti & Wolf, 2017).
Lemma 1 bounds the difference between the target loss and mixed loss. In order to derive the relationship between a true expected loss and its empirical loss, we rely on the following lemma.
Lemma 2 ((BenDavid et al., 2010)).
For a fixed hypothesis , if a random labeled sample of size is generated by drawing points from and points from , and labeling them according to and respectively, then for any , with probability at least (over the choice of the samples),
(9) 
where .
The detail function form of will be omitted for simplicity. We can fix , , , and when the learning task is specified, then we can treat as a constant.
Theorem 1.
Let be a hypothesis class, and be a labeled sample of size generated by drawing samples from and samples from and labeling them according to the true label . Suppose is symmetric and obeys the triangle inequality. Let be the empirical minimizer of on for a fixed , and the target error minimizer. Then, for any , with probability at least (over the choice of the samples), we have
(10) 
where , and .
Proof.
Theorem 1 does not have unnecessary dependencies for our purpose, which are used in (BenDavid et al., 2010) such as unsupervised data and the restriction of the model type to finite VCdimensions.
Additional qualitative results
We present additional qualitative results obtained from several networks in Figure 11.
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