Factors of Transferability for a Generic ConvNet Representation

Factors of Transferability for a Generic ConvNet Representation

Abstract

Evidence is mounting that Convolutional Networks (ConvNets) are the most effective representation learning method for visual recognition tasks. In the common scenario, a ConvNet is trained on a large labeled dataset (source) and the feed-forward units activation of the trained network, at a certain layer of the network, is used as a generic representation of an input image for a task with relatively smaller training set (target). Recent studies have shown this form of representation transfer to be suitable for a wide range of target visual recognition tasks. This paper introduces and investigates several factors affecting the transferability of such representations. It includes parameters for training of the source ConvNet such as its architecture, distribution of the training data, etc. and also the parameters of feature extraction such as layer of the trained ConvNet, dimensionality reduction, etc. Then, by optimizing these factors, we show that significant improvements can be achieved on various (17) visual recognition tasks. We further show that these visual recognition tasks can be categorically ordered based on their distance from the source task such that a correlation between the performance of tasks and their distance from the source task w.r.t. the proposed factors is observed.

Abstract
Convolutional Neural Networks, Transfer Learning, Representation Learning, Deep Learning, Visual Recognition
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I Introduction

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Convolutional networks (ConvNets) trace back to the early works on digit and character recognition [11, 23]. Prior to 2012, though, in computer vision field, neural networks were more renowned for their propensity to overfit than for solving difficult visual recognition problems. And within the computer vision community it would have been considered unreasonable, given the overfitting problem, to think that they could be used to train image representations for transfer learning.

However, these perceptions have had to be radically altered by the experimental findings of the last three years. First, deep networks [22, 13], trained using large labelled datasets such as ImageNet [1], produce by a huge margin the best results on the most challenging image classification [1] and detection datasets [9]. Second, these deep ConvNets learn powerful generic image representations [36, 8, 28, 48] which can be used off-the-shelf to solve many visual recognition problems [36]. In fact the performance of these representations is so good that at this juncture in computer vision, a deep ConvNet image representation combined with a simple classifier [36, 13] should be the first alternative to try for solving a visual recognition task.

Fig. 1: The improvements achieved by optimizing the transferability factors are significant. This optimization boosted the performance by up to 50% relative error reduction. The violet bars show the performance of non-ConvNet state of the art systems on different datasets. The pink stacked bars shows the improvement when using off-the-shelf ConvNet features with standard settings and a linear SVM classifier. The burnt orange stacked bars show the boost gained by finding the best transferability factors for each task. Detailed results can be found in Table VIII. The accuracy is measured using the standard evaluation criteria of each task, see the references in Table II.

An elaborate classification model based on a generic ConvNet representation has sometimes been shown to improve the performance of a simple classifier [41, 49] and some other times not so significantly [19, 14]. In any case, the field has observed that a better ConvNet representation (e.g. VGGNet [37] or GoogleNet [39] instead of AlexNet [22]) usually gives more boost in the final performance than a more elaborately designed classification model [21, 13, 26].

Fig. 2: Transferring a ConvNet Representation ConvNet representations are effective for visual recognition. The picture above shows the pipeline of transferring a source ConvNet representation to a target task of interest. We define several factors which control the transferability of such representations to different tasks (questions with blue arrow). These factors come into play at different stages of transfer. Optimizing these factors is crucial if one wants to maximize the performance of the transferred representation (see Figure 1).

Following these observations, a relevant question is: How can I then maximize the performance of the ConvNet representation for my particular target task? The question becomes especially pertinent if you only have a limited amount of labelled training data, time and computational resources because training a specialized deep ConvNet from scratch is not an option. The question rephrased in more technical terminology is: how should a deep ConvNet representation be learned and adjusted to allow better transfer learning from a source task producing a generic representation to a specific target task? In this paper we identify the relevant factors and demonstrate, from experimental evidence, how they should be set given the categorization of the target task.

The first set of factors that effect the transferability of a ConvNet representation are those defining the architecture and training of the initial deep ConvNet. These include the source task (encoded in the labelled training data), network width and depth, distribution of the training data, optimization parameters. The next set, after learning the “raw” representation, are what we term post-learning parameters. These include whether you fine-tune the network using labelled data from the target task, the network layer from which the representation is extracted and whether the representation should be post-processed by spatial pooling and dimensionality reduction.

Figure 2 gives a graphical overview of how we transfer a ConvNet representation trained for a source task to target task and the factors we consider that affect its transferability and at what stage in the process the factors are applied. While Figure 1 shows how big a difference an optimal configuration for these factors can make for 17 different target tasks.

How should you set these factors? Excitingly we observe that often there is a pattern for these factors. Their optimal settings are correlated with the distance of the target task’s distance from the source task. When occasionally there is an exception to the general pattern there is a plausible explanation. Table I lists some of our findings , driven by our quantitative results, and shows the best settings for the factors we consider and illustrates the correlations we mention.

To summarize deep ConvNet representation are very amenable to transfer learning. The concrete evidence we present for this assessment is that in 16 out of 17 diverse standard computer vision databases the approach just described, based on a deep ConvNet representation trained with ImageNet and optimal settings of the transferability settings, outperforms all published non-ConvNet based methods, see Table VIII.

{adjustbox}

max width= Target task Factor Source task ImageNet FineGrained recognition Instance xx retrieval Early stopping {adjustbox}valign=m

Don’t do it

Network depth {adjustbox}valign=m

As deep as possible

Network width {adjustbox}valign=m

Wider

Moderately wide

Diversity/Density {adjustbox}valign=m

More classes better than more images per class

Fine-tuning {adjustbox}valign=m

Yes, more improvement with more labelled data

Dim. reduction {adjustbox}valign=m

Original dim

Reduced dim

Rep. layer {adjustbox}valign=m

Later layers

Earlier layers

TABLE I: Best practices to transfer a ConvNet representation trained for the source task of ImageNet to a target tasks summarizing some of our findings. The target tasks above are listed from left to right according to their increased distance from the source task (ImageNet image classification). The table summarizes qualitatively the best setting for each factor affecting a ConvNet’s transferability given the target task. Although the optimal setting for some factors is similar for all tasks we considered, for other factors their optimal settings depend on the target task’s distance from the source task. Table II shows the ordering of all tasks. There are a few exceptions to these general rules. For more detailed analysis refer to section III.

Outline of the paper

  • We systematically identify and list the factors that affect the transferability of ConvNet representation for visual recognition tasks (Table I, Section III).

  • We provide exhaustive experimental evidence showing how these factors should be set (Table I, Section III).

  • We show these settings follow an interesting pattern which is correlated with the distance between the source and target task, (Figures 3-7 in Section III).

  • By optimizing the transferability factors we significantly improve (up to 50% error reduction) state-of-the-art on 16 popular visual recognition datasets (Table VIII) using a linear SVM for classification tasks and euclidean distance for instance retrieval.

Related Works

Image Classification Attribute Detection Fine-grained Recognition Compositional Instance Retrieval
PASCAL VOC Object [9] H3D human attributes [6] Cat&Dog breeds [29] VOC Human Action [9] Holiday scenes [17]
MIT 67 Indoor Scenes [33] Object attributes [10] Bird subordinate [43] Stanford 40 Actions [46] Paris buildings [31]
SUN 397 Scene [45] SUN scene attributes [30] 102 Flowers [27] Visual Phrases [34] Sculptures [4]
TABLE II: Range of the 15 visual recognition tasks sorted categorically by their similarity to ILSVRC12 object image classification task.

The concept of learning from related tasks using neural networks and ConvNets has appeared earlier in the literature see [32, 3, 15, 24] for a few examples. We describe two very recent papers which are the most relevant to our findings in this paper.

In [2] the authors investigate issues related to the training of ConvNets for the tasks of image classification (SUN image classification dataset) and object detection (PASCAL VOC 2007 & 2012). The result of two of their investigations are especially relevant to us. The first is that they show fine-tuning a network, pre-trained with the ImageNet dataset, towards a target task, image classification and object detection, has a positive effect and this effect increases when more data is used for fine-tuning. They also show that when training a network with ImageNet one should not perform early stopping even if one intends to transfer the resulting representation to a new task. These findings are consistent with a subset of ours though our conclusions are supported by a larger and wider set of experiments including more factors.
Yosinski et al. [47] show that the transferability of a network trained to perform one source task to solve another task is correlated with the distance between the source and target tasks. Yosinski et al.’s source and target tasks are defined as the classification of different subsets of the object categories in ImageNet. Their definition of transferability comes from their training set-up. First a ConvNet is trained to solve the source task. Then the weights from the first layers of this source network are transferred to a new ConvNet that will be trained to solve the target task. The rest of the target ConvNet’s weights are initialized randomly. Then the random weights are updated via fine-tuning while the transferred weights are kept fixed. They show that for larger the final target ConvNet, learned in this fashion, performs worse and the drop in performance is bigger for the target tasks most distant from the source task. This result corresponds to our finding that the performance of the layer used for the ConvNet representation is correlated to the distance between the source and target task. Yosinki et al. also re-confirm that there are performance gains to be made by fine-tuning a pre-trained network towards a target task. However, our results are drawn from a wide range of target tasks which are being used in the field of computer vision. Furthermore, we have investigated more factors in addition to the representation layer as listed in Table I.


The description of the notation in the table: is the total number of weights parameters in the network, is the number of kernels at a convolutional layer and is the number of nodes in a fully connected layer. For each network the output layer applies a soft max function and has 1000 output nodes. The networks are ordered w.r.t. their total number of parameters.

TABLE III: Wider Networks: Size details of the different ConvNet widths used in our experiments.

Ii Range of target tasks examined

To evaluate the transferability of the ConvNet representation we use a wide range of 17 visual recognition tasks. The tasks are chosen from 5 different subfields of visual recognition: object/scene image classification, visual attribute detection, fine-grained classification, compositional semantic recognition, instance retrieval (see Table II). There are multiple ways one could order these target tasks based on their similarity to the source task of object image classification as defined by ILSVRC12. Table II gives our ordering and we now give the rationale for the ranking.

The group of tasks we consider furthest from the source task is instance retrieval. Each task in this set has no explicit category information and is solved by explicit matching to exemplars. While all the other group of tasks involve classification problems and require an explicit learning phases.

We place attribute detection earlier than fine-grained recognition because these visual attributes1 are usually the explanatory factors which separate the original object classes in ILSVRC and are thus expected to be naturally selected/highlighted by the ConvNet. Also, some attributes (e.g. four-legged) are defined as a superset of object classes (e.g. cat, dog, etc.). Another aspect of this pairwise ordering is that fine-grained recognition involves sometimes very subtle differences between members of a visual category. We suspect that a network trained for higher levels of object taxonomy (e.g. flowers in general) would not be sensitive to micro-scale visual elements necessary for fine-grained recognition.

Next comes perhaps the most interesting and challenging set of category tasks – the compositional recognition tasks. These tasks include classes where the type of interactions between objects is the key indicator and thus requires more sophistication to recognize than the other category recognition tasks.

There are other elements which determine the closeness of a target task to the source task. One is the distribution of the semantic classes and images used within each category. For example the Pet dataset [29] is the closest of the fine-grained tasks because the ILSVRC classes include many different dog breeds. While, sometimes the task just boils down to the co-occurrence of multiple ILSVRC classes like the MIT indoor scenes. However, compositional recognition tasks usually encode higher level semantic concepts to be inferred from the object interactions, for instance a person holding violin is not considered a positive sample for playing the violin in [9] nor is a person standing beside a horse considered as the action “riding horse”.

Iii Experiments

Now, we analyze the effect of each individual factor on the transferability of the learnt representation. We divide the factors into those which should be considered before learning a representation (learning factors) and those which should be considered when using an off-the-shelf network model (post-learning factors).

Iii-a Learning Factors

Network Width

The ConvNet AlexNet[22], the first very large network successfully applied to the ImageNet challenge, has around 60 million parameters consisting of 5 million parameters in the convolution layers and 55 million parameters in its fully connected layers. Although this appears to be an unfeasibly large parameter space the network was successfully trained using the ImageNet dataset of 1.2 million images labelled with 1000 semantic classes. More recently, networks larger than AlexNet have been trained, in particular OverFeat[35]. Which of these networks produces the best generic image representation and how important is its size to its performance?

Here we examine the impact of the network’s size (keeping its depth fixed) on different tasks including the original ImageNet image-level object classification. We trained 3 networks of different sizes using the ILSVRC 2012 dataset and also included the OverFeat network in our experiments as the large network. Each network has roughly twice as many parameters as we progress from the smallest to the largest network. For all the networks we kept the number of units in the 6th layer, the first fully connected layer, to 4096. It is this layer that we use for the experiments where we directly compare networks. The number of parameters is changed mainly by halving the number of kernels and the number of fully connected neurons (except the fixed one).

Fig. 3: Network Width: Over-parametrized networks (OverFeat) can be effective when the target task is close to the labelled data. However, the performance on more distant tasks can suffer from over-specialization when the number of network parameters is increased. But overall under-parametrized networks (Tiny) are unable to generalize as well. Since the Tiny network has 10 times fewer parameters than OverFeat while preserving most of the performance, it could be useful for scenarios where real-time computation is an issue.

Figure 3 displays the effect of changing the network size on different visual recognition tasks/datasets. The largest network works best for Pascal VOC object image classification, MIT 67 indoor scene image classification, UIUC object attribute, and Oxford pets dataset. On the other hand, for all the retrieval tasks the performance of the over-parametrized OverFeat network consistently suffers because it appears the generality of its representation is less than those of the smaller networks. Another interesting observation is that, if the computational efficiency at test time is critical, one can decrease the number of network parameters by orders of 2 (Small or Tiny network) for different tasks but the degradation of the final performance is sublinear in some cases.

Network Depth

Fig. 4: Network Depth: Over-parametrizing networks by the number of convolutional layers is effective for nearly all the target tasks. While a saturation can be observed in some tasks there is no significant performance drop as opposed to the trend observed when over-parametrizing by increasing its width. The number on the x-axis indicates the number of convolutional layers of the network. The representation is taken from the first fully connected layer right after the last convolutional layer.
Fig. 5: Depth versus Width: Over-parametrization of networks can be done by increasing either of its width and depth or by both. In this figure, effect of increasing depth is illustrated on the final performance and can be compared with that of increasing width. Solid lines indicate the evolution of performance when depth of the network is increased. Circles indicates networks of depth 8 (e.g. AlexNet) and squares are used for deeper networks. Dashed lines, on the other hand, declares an increase in the width of the network. It can be seen from the results that increasing the depth is more efficient in number of parameters per unit of performance gained in various datasets (solid lines have higher slopes). Refer to Tables IV and III for exact architecture of the networks used in this experiment. The representation is taken from the first fully connected layer right after the last convolutional layer. The tree on the right, depicts the relationship between different networks.

Increasing the network width (number of parameters at each layer) is not the only way of over-parameterizing a ConvNet. In fact, [39, 37] have shown that deeper convolutional networks with more layers achieve better performance on the ILSVRC14 challenge. In a similar spirit, we over-parametrize the network by increasing the number of convolutional layers before the fully connected layer from which we extract the representation. Figure 4 shows the results by incrementally increasing the number of convolutional layers from 5 to 13 (the architectures of these networks is described in Table IV). As this number is increased, the performance on nearly all the datasets increases.

The only tasks for which the results degrade are the retrieval tasks of UKB and Holidays. Interestingly, these two tasks involve measuring the visual similarity between specific instances of classes strongly presented in ImageNet (e.g. a specific book, bottle or musical instrument in UKB, and wine bottle, Japanese food in Holidays dataset). It is, thus, expected that the representation becomes more invariant to instance level differences as we increase the complexity of the representation with more layers.

If we compare the effect of increasing network depth to network width on the final representation’s performance, we clearly see that increasing depth is a much more stable over-parametrization of the network. Both increasing width and depth improve the performance on tasks close to the source task. However, increasing the width seems to harm the transferability of features to distant target tasks more than increasing depth does. This could be attributed to the fact that increasing depth is more efficient than increasing width in terms of the number of parameters for representing more complex patterns, next section studies this in a separate experiment. Finally, more layers means more sequential processing which hurts the parallelization. We have observed the computational complexity for learning and using deep ConvNets increases super-linearly with the number of layers. So, learning a very wide network is computationally cheaper than learning a very deep network. These issues means the practitioner must decide on the trade-off between training speed and performance.

Width vs Depth

It is more indicative to directly compare the effect of increasing width and depth on generality of the learned representation. For that purpose we train deep networks of various depth. Particularly, we train a network of depth 16 with similar width to the Tiny, Small and Medium networks in the previous section. Table IV lists the deep networks and their architectures. We compare the results of 10 different networks on four target tasks in Figure 5. By connecting different networks with solid (dashed) directed edges we show the performance of the a deeper (wider) network. It can be observed that increasing the parameters of the network by increasing its depth is a more efficient over-parametrization than increasing its width. That is the slope of solid segments are consistently higher.
It should be noted that most of the parameters of a convolutional network usually is at the first fully connected layer. Thus, the number of outputs of the last convolutional layer (which depends on the preceding subsampling layers) is the major factor for the network size. For example, going from network H to I and then to J slightly increases the number of parameters but considerably increases the performance on the target tasks.
Training the deeper networks is tricky and needs to be done in various stages. For networks with convolutional layers of more than 5 (Medium) we increased the number of convolutional layers by 3 at each time. Then trained the network for a few epochs () with fixed learning rate () and initialized the first convolutional layers of the next network with those of the shallower network. The new convolutional layers and fully connected layers were initialized using random gaussian noise.


The description of the notation in the table: is the total number of weights parameters in the network, is the number of kernels at a convolutional layer, is the number of layers with kernels, and is the number of nodes in a fully connected layer. All the kernels have spatial size of 3x3. For each network the output layer applies a SoftMax function and has 1000 output nodes. The networks are ordered w.r.t. their total number of parameters. Note that these networks are re-trained for our experiments and the models differ from that of [37], for instance we do not use multi-scale input and our input image size is 227x227, we do random cropping as implemented in Caffe, etc.

TABLE IV: Deeper Networks: Size details of the different deep ConvNets used in our experiments.

Early Stopping

Early stopping is used as a way of controlling the generalization of a model. It is enforced by stopping the learning before it has converged to a local minima as measured by monitoring the validation loss. This approach has also been used to improve the generalization of over-parametrized networks [5]. It is plausible to expect that the transferability increases with generalization. Therefore, we investigate the effect of early stopping on the transferability of learnt representation. Figure 6 shows the evolution of the performance for various target tasks at different training iterations. The performance of all tasks saturates at 200K iterations for all the layers and even earlier for some tasks. Surprisingly, it can be seen that early stopping does not improve the transferability of the features whatsoever. However, in this experiments the training does not show strong symptoms of over-fitting. We have observed that if training of the source ConvNet exhibits overfitting (such as in fine-tuning with landmark dataset for improved performance on instance retrieval) early stopping can help to learn more transferable features.

Fig. 6: Early Stopping: Plotted above is the performance of the representation extracted from layer 6 of the AlexNet ConvNet versus the number of iterations of SGD used to train the initial network. It can be seen that early stopping, which can act as a regularizer, does not help to produce a more transferable representation.

Source Task

Fig. 7: Representation Layer: Efficacy of representations extracted from AlexNet’s different layers for different visual recognition tasks. A distinct pattern can be observed: the further the task moves from object image classification, the earlier layers are more effective. For instance, layer 8 works best for PASCAL VOC image classification which is very similar to ImageNet while the best performance for all retrieval tasks is at layer 6.

It is natural to expect that one of the most important factors for a learnt representation to be generic is the properties of the source task (disregarding the number of images in the source dataset). The recent development of another large scale dataset called the Places Dataset [52] labelled with scene classes enabled us to analyze this factor. Table V shows the results for different source tasks of ImageNet, Places, and a hybrid network. The hybrid network is made by combining the ImageNet images with those of the Places dataset. The label set is increased accordingly [52]. It can be observed that results for the tasks very close to the source tasks are improved with the corresponding models (MIT, SUN for Places network). Another interesting observation is that ImageNet features seem to achieve a higher level of generalization for further away tasks. One explanation is that the set of labels is more diverse. Since the number of images in ImageNet is smaller, it shows the importance of diversity of labels as opposed to the number of annotated images when the objective is to achieve a more transferable representation. More concrete experiments on this phenomenon is conducted in the next section.

The Hybrid model boosts the transferability of the Places network but still falls behind the ImageNet network for more distant tasks. This could be again due to the fact that the number of images from the Places dataset dominates those of the ImageNet dataset in training the Hybrid model and as a consequence it is more biased toward the Places Network.

In order to avoid this bias, in another experiment, we combined the features obtained from the ImageNet network and the Places network as opposed to Hybrid network, and interestingly this late fusion works better than Hybrid model (the Hybrid model where the number of dimensions of the representation is increased to 8192 works worse [7]). In fact, it achieves the best results on all tasks except for subcategory recognition tasks for which scenes are irrelevant and probably just add noise to the descriptors.

Image Classification Attribute Detection Fine-grained Recognition Compositional Instance Retrieval
Source task VOC07 MIT SUN H3D UIUC Pet CUB Flower Stanf. Act40 Oxf. Scul. UKB
ImageNet 71.6 64.9 49.6 73.8 90.4 78.4 62.7 90.5 58.9 71.2 52.0 93.0
Places 68.5 69.3 55.7 68.0 88.8 49.9 42.2 82.4 53.0 70.0 44.2 88.7
Hybrid 72.7 69.6 56.0 72.6 90.2 72.4 58.3 89.4 58.2 72.3 52.3 92.2
Concat 73.8 70.8 56.2 74.2 90.4 75.6 60.3 90.2 59.6 72.1 54.0 93.2
TABLE V: Source Task: Results on all tasks using representations optimized for different source tasks. ImageNet is the representation used for all experiments of this paper. Places is a new ConvNet trained on 3.5M images labeled with scene categories [52]. Hybrid is a model proposed by Zhou et al. [52] which combines the ImageNet and Places datasets and train a single network for the combination. Concat indicates results of concatenating the feature obtained from ImageNet ConvNet and Places ConvNet for each input image. All results are for first fully connected layer (FC6).

Diversity and Density of Training Data

We saw in the previous section that the distribution of training data for the source task affects the transferability of the learned representation. Annotating millions of images with various labels used for learning a generic representation is expensive and time-consuming. Thus, choosing how many images to label and what set of labels to include is a crucial question. In addition to the source tasks in the previous section, we now examine the influence of statistical properties of the training data such as density and diversity of the images. In this experiment we assume that ImageNet classes indicate different modes of the training data distribution. Such that, by increasing the number of images per class we control the density of the distribution. Moreover, the diversity of the training data can be increased by including additional classes.
In order to compare the effect of diversity and density of training data on the transferability of the learned representation we assume a situtation where there is a certain budget for the number of images to be annotated. Particularly, we experiment for the training data size of 10%, 20%, 50% of the ILSVRC12 1.3 million images. Then the dataset is either constructed using stratified sampling from all classes (reduced density with the same diversity) or by random sampling of the classes with all of their samples (reduced diversity with the same density).
Figure 8 plots the results for various tasks when decreasing density (Figure 7(a)) or diversity (Figure 7(b)) of the source training set from that of ILSVRC12. It can be seen that increasing both diversity and density consistently helps all the tasks and there is still no indication of saturation at the full set of 1.3 million images. Thus there is still room for annotating more images beyond ILSVRC and that most probably increases the performance of the learned representation on all the target tasks. Furthermore no clear correlation can be observed between the degradation of the performances and the distance of the target task. Most importantly, decreasing the diversity of the source task seems to hurt the performance on the target tasks more significantly (slopes on the right plot are higher than left plot). In fact, a point to point comparison of the two plots reveals that when having certain budget of images, increasing diversity is crucially more effective than density. This could be because of the higher levels of feature sharing which happens at higher diversities which helps the generalization of the learned representation and thus is more beneficial for transfer learning.
The network architecture used for this experiment is Medium (AlexNet), so the number of parameters remains the same for all of the experiments. However training the network on the smaller datasets needed a heavier regularization by increasing the weight decay and dropout ratio at the fully connected layers. Without heavy regularization training a Medium network on 10% or 20% exhibits signs of over-fitting in the early stages of training.

(a) Increasing Density: We trained 3 ”Medium” networks using different number of images per ILSVRC 2012 class. We decreased the number of images for each class to 10%, 20% and 50% of its original set separately. The images are sampled randomly. Heavier regularization is applied for networks with smaller data size.
(b) Increasing Diversity: We trained 3 ”Medium” networks using different number classes from ImageNet. We decreased the number of classes to 100, 200 and 500 but kept the images within each class the same as ILSVRC 2012. The classes are sampled randomly. Heavier regularization is applied for networks with smaller data size.
Fig. 8: Density versus Diversity of Training Data: Changing the size of training data by altering number of images per class versus number of classes leads to different performances on transferred tasks. Interestingly, the results using lower diversity is consistently inferior to the performances obtained by lower density (in a point-to-point comparison). That means diversity of the training data is more important than density of training data when transferring the learnt representation to various tasks. This trend is observed regardless of the distance of the target task to the original task.

Iii-B Post-learning Factors

Network Layer

Different layers of a ConvNet potentially encode different levels of abstraction. The first convolutional layer is usually a collection of Gabor like gray-scale and RGB filters. On the other hand the output layer is directly activated by the semantic labels used for training. It is expected that the intermediate layers span the levels of abstraction between these two extremes. Therefore, we used the output of different layers as the representation for our tasks’ training/testing procedures. The performance of different layers of the pre-trained ConvNet (size: Medium) on ImageNet is shown in figure 7 for multiple tasks.

We observe the same pattern as for the effect of network width. The last layer (1000-way output) is only effective for the PASCAL VOC classification task. In the VOC task the semantic labels are a subset of those in ILSVRC12, the same is true for the Pet dataset classes. The second fully connected layer (Layer 7) is most effective for the UIUC attributes (disjoint groups of ILSVRC12),and MIT indoor scenes (simple composition of ILSVRC12 classes). The first fully connected layer (Layer 6) works best for the rest of the datasets which have semantic labels further away from those used for optimizing the ConvNet representation. An interesting observation is that the first fully connected layer demonstrates a good trade-off when the final task is unknown and thus is the most generic layer within the scope of our tasks/datasets.

Although the last layer units act as probabilities for ImageNet classes, note that results using the last layer with 1000 outputs are surprisingly effective for almost all the tasks. This shows that a high order of image-level information lingers even to the very last layer of the network. It should be mentioned that obtaining results of instance retrieval on convolutional layers is computationally prohibitive and thus they are not included. However, in a simplified scenario, the retrieval results showed a drastic decrease from layer 6 to 5.

Fig. 9: Spatial Pooling: In order to obtain meaningful results for retrieval with representations from convolutional layers we applied spatial pooling of different sizes for different tasks. Objects of more complex structures such as sculptures and buildings need more spatial resolution for optimal performance.

Spatial Pooling

In the last subsection, we observed that the best representation for retrieval tasks is the first fully connected layer by a significant margin. We further examined using the last convolutional layer in its original form as the representation for retrieval in a simplified scenario but achieved relatively poor results. In order to make the convolutional layer suitable, in this experiment, spatial pooling is applied to the last convolutional layers output. We use max pooling in this experiment. An spatial pooling with a grid of is equivalent to a soft bag of words representation over the whole image, where words are convolutional kernels. Figure 9 shows the results of different pooling grids for all the retrieval tasks. For the retrieval tasks, where the shapes are more complicated like sculptures and historical buildings, a higher resolution of pooling is necessary.

(a) Effective Dimensionality: It can be observed that almost all tasks reach their maximum performance at an dimensionality of below 500 indicating a low (class-conditional) effective dimensionality of ConvNet representations. The accuracy of all tasks for dimensions under 50 are surprisingly high. Thus, he fact that these transformations are obtained using a linear transform supports capability of ConvNet in generalization by disentangling underlying generating factors.
(b) Saturation: As we move further from the original task, performance saturation happens with slightly more dimensions. For more clarity, the performance values of each task are divided by the maximum value for these plots. Horizontal axis is in log scale.
Fig. 10: Dimensionality Reduction: We use Principal Component Analysis (PCA) to linearly transform the ConvNet representations obtained from first fully connected layer (4096 dimensional) into a lower dimensional space for various tasks.

Dimensionality Reduction

We use principal component analysis (PCA) to reduce the dimensionality of the transferred representation for each task. We observed that dimensionality reduction helps all the instance retrieval tasks (most of the time insignificantly though). The main difference between the retrieval task and other ones is that in retrieval we are interested in the Euclidean distances between samples in the ConvNet representational space. In that respect, PCA can decrease the curse of dimensionality for distance. However, one could expect that dimensionality reduction would decrease the level of noise (and avoid potential over-fitting to irrelevant features for each specific task). But our experiments shows that this is not the case when using PCA for reducing dimensions. Figure 9(a) shows the results for different tasks as we reduce the dimensionality of ConvNet representations. The results show that the relative performance boost gained by additional dimensions is correlated with the distance of the target task to the original task. We see that saturations appear earlier for the tasks closer to ImageNet. It is amazing to know that effective dimensionality of the ConvNet representations (with 4096 dims) used in these experiments is at most 500 for all visual recognition tasks from different domains. Another interesting observation is that many of the tasks work reasonably well with very low number of dimensions (5-50 dimensions). Remember that these features are obtained by a linear transformation of the original ConvNet representation. This can indicate the capability of ConvNets in linear factorization of the underlying generating factors of semantic visual concepts.

Representation MIT CUB Flower
Medium FC7 65.9 62.9 90.4
Medium FT 66.3 66.4 91.4
TABLE VI: Fine-tuning: The first row shows the original ConvNet results. The second row shows the results when we fine-tune the ConvNet toward the target task and specialize the learnt representation. Fine-tuning is consistently effective. The proportional improvement is higher for the more distant tasks from ImageNet.

Fine-tuning

Frequently the goal is to maximize the performance of a recognition system for a specific task or a set of tasks. In this case intuitively specializing the ConvNet to solve the task of interest would be the most sensible path to take. Here we focus on the issue of fine-tuning the ConvNet’s representation with labelled data similar to those we expect to see at test time.

[13, 7] have shown that fine-tuning the network on a target task helps the performance. Fine-tuning is done by initializing a network with weights optimized for ILSVRC12. Then, using the target task training set, the weights are updated. The learning rate used for fine-tuning is typically set to be less than the initial learning rate used to optimize the ConvNet for ILSVRC12. This ensures that the features learnt from the larger dataset are not forgotten. The step used to shrink the learning rate schedule is also decreased to avoid over-fitting. We have conducted fine-tuning on the tasks for which labels are mutually exclusive. The table in Figure VI shows the results. The gains made by fine-tuning increase as we move further away from the original image-level object classification task. Fine-tuning on a relatively small target dataset is a fast procedure. With careful selection of parameters it is always at least marginally helpful.

Increasing training data

Zhu et al. [53] suggest that increasing data is less effective than increasing the complexity of models or richness of representation and the former is prone to early performance saturation. Those observations are made using HOG features to perform object detection. Here, we want to investigate whether we are close to saturation point with ConvNet representations.

Increasing data for target task. To measure the effect of adding more data to learn the representation we consider the challenging task of PASCAL VOC 2007 object detection. We follow the procedure of Girshick et al. [13] by fine-tuning the AlexNet network using samples from the Oxford Pet and Caltech-UCSD birds datasets. We show that although there exists a large number of samples for those classes in ImageNet (more than 100,000 dogs) adding around 3000 dogs from the Oxford Pet dataset helps the detection performance significantly. The same improvement is observed for cat and bird, see the table in Figure VI. This further adds to the evidence that specializing a ConvNet representation by fine-tuning, even when the original task contained the same labels, is helpful.

Increasing data for source task. Furthermore, we investigate how important it is to increase training data for the original ConvNet training. We train two networks, one using SUN397 [45] with 130K images and the other using the Places dataset [52] with 2.5M images. Then we test the representations on the MIT Indoor Scenes dataset. The representation trained from SUN397 (62.6%) works significantly worse than that of the Places dataset (69.3%). The same trend is observed for other datasets (refer to Table VII). Since ConvNet representations can model very rich representations by increasing its parameters, we believe we are still far from saturation in its richness.

Classification Attribute Fine-grained Retrieval
Dataset VOC07 MIT H3D UIUC Pet Flower Oxf. Scul.
SUN 57.8 62.6 45.0 86.3 45.0 75.9 64.5 39.2
Places 68.5 69.3 49.9 88.8 49.9 82.4 70.0 44.2
TABLE VII: Additional data (source task): Results with the ConvNet representation optimized for different amount of training data. First row shows the results when the network is trained on scene recognition dataset of SUN397 [44] dataset with  100K images. The second row corresponds to the network trained on Places dataset [52] with  2.5M images annotated with similar categories. In all cases the ConvNet trained on Places dataset outperforms the one trained on SUN.
Image Classification Attribute Detection Fine-grained Recognition Compositional Instance Retrieval
VOC07 MIT SUN SunAtt UIUC H3D Pet CUB Flower VOCa. Act40 Phrase Holid. UKB Oxf. Paris Scul.
non-ConvNet [38] [25] [44] [30] [42] [50] [29] [12] [20] [28] [46] [34] [40] [51] [40] [40] [4]
71.1 68.5 37.5 87.5 90.2 69.1 59.2 62.7 90.2 69.6 45.7 41.5 82.2 89.4 81.7 78.2 45.4
Deep Standard 71.8 64.9 49.6 91.4 90.6 73.8 78.5 62.8 90.5 69.2 58.9 77.3 86.2 93.0 73.0 81.3 53.7
Deep Optimized2 80.7 71.3 56.0 92.5 91.5 74.6 88.1 67.1 91.3 74.3 66.4 82.3 90.0 96.3 79.0 85.1 67.9
Err. Reduction 32% 18% 13% 13% 10% 4% 45% 12% 8% 17% 18% 22% 28% 47% 22% 20% 31%
Source Task ImgNet Hybrid Hybrid Hybrid ImgNet ImgNet ImgNet ImgNet ImgNet ImgNet ImgNet ImgNet Hybrid ImgNet ImgNet ImgNet ImgNet
Network Width Medium Medium Medium Medium Large Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium Medium
Network Depth 16 8 8 8 8 16 16 16 16 16 16 16 8 8 16 16 16
Rep. Layer last last last last 2nd last 2nd last 2nd last 3rd last 3rd last 3rd last 3rd last 3rd last 4th last 4th last 4th last 4th last 4th last
PCA  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗
Pooling  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗  ✗
TABLE VIII: Final Results: Final results of the deep representation with optimized factors along with a linear SVM compared to the non-ConvNet state of the art. In the bottom half of the table the factors used for each task are noted. We achieve up to a 50% reduction of error by optimizing transferability factors. Relative error reductions refer to how much of the remaining error (from Deep Standard) is decreased. ”Deep Standard” is the common choice of parameters - a Medium sized network of depth 8 trained on ImageNet with representation taken from layer 6 (FC6).

Iv Optimized Results

In the previous section, we listed a set of factors which can affect the efficacy of the transformed representation from a generic ConvNet. We studied how best values of these factors are related to the distance of the target task to the ConvNet source task. Using the know-hows obtained from these studies, now we transfer the ConvNet representations using ”Optimized” factors and compare the ”Standard” ConvNet representation used in the field. The ”Standard” ConvNet representation refers to a ConvNet of medium size and depth 8 (AlexNet) trained on 1.3M images of ImageNet, with the representation taken from first fully connected layer (FC6). As can be seen in Table VIII the remaining error of the ”Standard” representation can be decreased by a factor of up to 50% by optimizing its transferability factors.

Representation bird cat dog
ConvNet [13] 38.5 51.4 46.0
ConvNet-FT VOC [13] 50.0 60.7 56.1
ConvNet-FT VOC+CUB+Pet 51.3 63.0 57.2
TABLE IX: Additional data (fine-tuning): The table presents the mAP accuracy of a sliding window detector based on different ConvNet representations for 3 object classes from VOC 2007. ImageNet contains more than 100,000 dog images and Pascal VOC has 510 dog instances. For the representation in the second row, image patches extracted from the VOC training set are used to fine-tune the ConvNet representation[13]. It results in a big jump in performance. But including cat, dog and bird images from the Oxford Pet and Caltech bird datasets boosts the performance even further.

V Implementation details

The Caffe software [18] is used to train our ConvNets. Liblinear is used to train the SVMs we use for classification tasks. Retrieval results are based on the distance of whitened ConvNet representations. All parameters were selected using 4-fold cross-validation.

Learning choices are the same as [36]. In particular, the pipeline for classification tasks is as follows: we first construct the feature vector by getting the average ConvNet feature vector of 12 jittered samples of the original image. The jitters come from crops of 4 corners of the original image, its center and the whole image resized to the size needed by the network (227x227) and their mirrors. We then normalize the ConvNet feature vector, raise the absolute value of each feature dimension to the power of 0.5 and keep its sign. We use linear SVM trained using one-versus-all approach for multilabel tasks (e.g. PASCAL VOC image classification) and linear SVM trained using one-versus-one approach and voting for single label tasks (e.g. MIT Indoor Scene).

The pipeline for the retrieval tasks are as follows: Following [16] The feature vectors are first normalized, then the dimensionality is reduced using PCA to smaller whitened dimension and the resulting feature is renormalized to the unit length. Since buildings (Oxford and Paris) and scupltures datasets include partial images or the object can appear in small part of the whole image (zoomed in or out images of the object of interest) we use spatial search to match windows from each pair of images. We have 1 sub-patch of size 100% of the whole image, 4 sub-patches of each covering 4/9 size of the image. 9 sub-patches of each covering 4/16 and 16 sub-patches of each covering 4/25 of the image (in total 30 sub-paches). The minimum distance of all sub-patches is considered as the distance of the two images.

Vi Closing Discussion

ConvNet representations trained on ImageNet are becoming the standard image representation. In this paper we presented a systematic study, lacking until now, of how to effectively transfer such representations to new tasks. The most important elements of our study are: We identify and define several factors whose settings affect transferability. Our experiments investigate how relevant each of these factors is to transferability for many visual recognition tasks. We define a categorical grouping of these tasks and order them according to their distance from image classification.

Our systematic experiments have allowed us to achieve the following. First, by optimizing the identified factors we improve the state-of-the-art performance on a very diverse set of standard computer vision databases, see table VIII. Second, we observe and present empirical evidence that the effectiveness of a factor is highly correlated with the distance of the target task from the source task of the trained ConvNet. Finally, we empirically verify that our categorical grouping and ordering of visual recognition tasks is meaningful as the optimal setting of the factors remain constant within each group and vary in a consistent manner across our ordering. Of course, there are exceptions to the general trend. In these few cases we provide simple explanations.

We think the insights generated by our paper can be used to learn more generic features (our ultimate goal). We believe a generic visual representation must encode different levels of visual information (global, local and visual relations) and invariances. Although these levels of information and invariances are interconnected, a task can be analyzed based on which level of information it requires. And this allows us to explain the distance of visual recognition tasks from that of ImageNet and then crucially to identify orthogonal training tasks that should be combined when training a generic representation. Because when we optimize a representation for only one type of invariance and/or visual information we cannot expect it to optimally encode the others.

During ConvNet training it is the loss function, besides the semantic labels, that controls the learnt representation. For example for image classification we want different semantic classes to occupy non-overlapping volumes of the representation space. The cross-entropy loss function promotes this behaviour. While if we want to learn a representation to measure visual similarity we must use a different loss function as we also need the representation of images with the same label to occupy a small volume.

Therefore, in future work, we plan to investigate how to best apply multi-task learning with ConvNets to learn generic representations. We will focus on how to choose the training tasks and loss functions that will force the ConvNet representation to learn many different levels of visual information incorporating different levels of invariances.

Vii Acknowledgement

We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Tesla K40 GPUs to this research. 3

Footnotes

  1. As an aside, depending on the definition of an attribute, the placement of an attribute detection task could be anywhere in the spectrum. For instance, one could define a fine-grained, local and compositional attribute which would then fall furthest from all other tasks (e.g. “wearing glasses” in H3D dataset).
  2. footnotetext: Note: ”Deep Optimized” results in this table are not always the optimal choices of factors studied in the paper. For instance one would expect a very deep network trained using hybrid model would improve results on MIT and SUN, or a deep and large network would perform better on VOC image classification. Another example is that we could do fine-tuning with the optimal choices of parameters for nearly all tasks. Obviously, it was highly computationally expensive to produce all the existing results. We will update the next versions of the paper with further optimized choices of parameters.

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