Title: REVISTING NEGATIVE TRANSFER USING ADVERSARIAL LEARNING

Abstract: An unintended consequence of feature sharing is the model fitting to correlated tasks within the dataset, termed negative transfer. In this paper, we revisit the problem of negative transfer in multitask setting and find that its corrosive effects are applicable to a wide range of linear and non-linear models, including neural networks. We first study the effects of negative transfer in a principled way and show that previously proposed counter-measures are insufficient, particularly for trainable features. We propose a adversarial training approach to mitigate the effects of negative transfer by viewing the problem in a domain adaptation setting. Finally, empirical results on attribute prediction multi-task on AWA and CUB datasets further validate the need for correcting negative sharing in an end-to-end manner.

1. INTRODUCTION:

Advances in machine learning have led to proficient supervised learning models with powerful representations in various prediction tasks. We now expect an ideal classification model to restrict itself to a pertinent set of evidences available to it from the input for prediction. Further, we expect the model to disregard any unrelated evidences in the data to enable better generalization. Let us consider the task of training an animal classifier "cheetah vs. snow-leopards" from a dataset of images of these animals, such as those illustrated in Figure 1 -a task which ideally should focus on the animal's appearance features. However, a large portion of these images also contain various cues of the typical habitat of the animals in the background, i.e., tall grass and snow (see Figures 1 (a ) and (b)) which are, in principle, unrelated to the animal's appearance. An archetypal model is deceived by the co-occurrence of such unrelated, yet easily detectable cues of habitat over the animal's appearance features such as complex fur patterns. However, a proficient supervised learning model must identify relevant evidences for the label of interest and at the same time discard various unrelated evidences such as presence of snow, even though it tends to co-occur frequently with snow-leopard. Consequently, it would be more likely that such a model would perform better on rare-instances (such as those in Figures 1 (c ) and (d)) and generalize better to unseen instances.

This phenomenon of co-occurring but unrelated evidences being present in training data and thereby having a debilitating effect on model performance has been described in literature (Jayaraman et al. (2014) ; Zhou et al. (2013; 2010) ; Romera-Paredes et al. (2012) ; Yoon & Hwang (2017) ; Zhou et al. (2011) ). These techniques utilize the easy availability of labels for unrelated evidences (e.g. background habitat labels above), called negative labels which constitutes an auxiliary task, and seek to mitigate its debilitating performance on the primary task (e.g. animal classification above) with techniques referred to as negative-sharing or negative-transfer.

While all of these techniques have tackled this problem utilizing various forms of regularization, we describe several shortcomings of this class of approaches, most notable of which is their inapplicability to the popular paradigm of trainable features obtained via neural representation learning. Motivated by these limitations, in this paper we depart from the direction of regularization-based approaches and examine methods inspired from a domain-adaptation viewpoint to propose an adversarial training-based formulation. We uniquely view such a scenario as an instance of adversarial multi-task learning, where the classification tasks are either the primary task of interest (i.e., predicting the presence of fur pattern and color) or the auxiliary negative tasks (i.e., characteristics of habitat) to be avoided. Since the 2 tasks are unrelated, any label correlation between primary and auxiliary labels in the training data is only by chance and therefore from a domain-adaptation perspective, we envision a target-domain as possibly having a different correlation between the primary and auxiliary labels. The effects of negative transfer are hence mitigated when the classification task is trained in this domain.

We discuss advantages of our proposed formulation, inspired from domain-adaptation, to alleviate the negative transfer over existing techniques, including ready applicability to neural networks in an end-to-end fashion. It must be noted that, while the formulation of the problem is motivated with multi-task learning, negative-transfer is a disposition of any supervised learning task from simple binary classification to recent popular supervised tasks such as image detection, captioning, or visual dialog. We present motivating literature that prelude this work next.

2. RELATED WORK ON TACKLING NEGATIVE SHARING:

Image classification literature often characterize mid-level features as attribute predictors in multilabel learning. The inability of models to learn predictors with the correct semantic concept is attributed to negative transfer. To our knowledge, the predominent approach to tackle negative transfer in such setting was the use of specific regularizers (Romera-Paredes et al., 2012; Jayaraman et al., 2014) . Specifically, the primary model avoid using features which are important for the auxiliary task, leading to models competing for features. Jayaraman et al. (2014) further extends this idea to attribute groups, where feature selection sparsity is induced across group, but encourage within them. We highlight three limitations of feature competition techniques below:

• Repeated features: Consider the simple scenario where some features in the feature representations are repeated or dependent on others. Feature competition enforces tasks to pick unique features, however they are implicitly the same. Going back to the case of 'cheetah vs snow leopard' example mentioned earlier, when there are two copies of a feature which captures 'snow in the background', then both primary and auxiliary classifiers would just pick different copies of that feature. Here, the idea of resisting cheetah/snow leopard classifier from picking features which capture snow is negated. • Trainable features: Neural representations have become extremely popular owing the power of learning trainable features. However, feature competition techniques fail with prediction models with trainable features. If there are features that are important for both primary and auxiliary task, models involving a trainable feature setup will lead to duplicating the same features, thereby resulting in the repeated feature scenario. • Easy auxiliary task with abundant features: Consider a scenario of an easy auxiliary task, that does not require a large number of features to be predicted correctly. Similar to the previous case, the spared features from the auxiliary task can be picked by the primary task resulting in negative transfer.

Motivated by these shortcomings, we proceed to examine the negative transfer problem in a domain adaptation setting.

3. PROPOSED FRAMEWORK:

In this section we first formalize and explain the problem setting of negative transfer. We present scenarios where earlier attempts (regularization-based approaches) to tackle this problem fails. We then explain our formulation for posing then negative transfer problem in a domain adaptation setting and derive adversarial learning algorithms to solve negative transfer. Lastly, we present a thorough analysis of the proposed formulation to address negative transfer by experimenting on a carefully designed synthetic dataset.

3.1. PROBLEM SETUP:

In typical 2-label classification problem, we assume that training data and all future test examples are drawn i.i.d from a probability distribution D on instance space X and a labeling function f p : X → {+1, -1} for the primary task labels and f a : X → {+1, -1} for the auxiliary task labels.

Every instance x ∈ X has primary and auxiliary labels: y p and y a respectively. The goal is to learn a classifier which performs well on future samples from D, which may have a different label correlation since the tasks are unrelated. Formally, we capture this label correlation via a joint label distribution P (Y ) = P (Y a , Y b ), and we assume that P (Y ) in training and test are different.

This problem setup is different from earlier works on negative transfer in the way how unrelated tasks are defined. We define unrelated tasks as the ones which can have different correlation in training and test data. In (Romera-Paredes et al., 2012) unrelated tasks is referred as tasks which are defined over orthogonal sets of features. Zhou et al. (2010) uses the term negative correlation for unrelatedness among tasks. Two tasks are negatively correlated when one feature is deemed to be important to first task makes it unlikely to be important to the second task. We assume that the labelling function f p and f a are universal and common for both source and target domains.

3.2. NEGATIVE TRANSFER AS:

Typical unsupervised domain adaptation setting has labelled instances from source distribution and also unlabelled instances from target distribution. However, we have no information (neither labels nor instances) about the target distribution. The only information we have about the target domain is P T (Y ). We are either provided an estimate of P T (Y ) from an oracle, or we make an assumption on P T (Y ) (for instance, a uniform distribution over the space of Y ).

Consider U T , the space of all distributions over X which has label distribution P T (Y ). It is extremely challenging to adapt from the source domain to all members of U T with given P T (Y ). However, we can settle for a particular D T . We pick such a D T ∈ U T as that distribution over X which is nearest to D S . We model this in terms of KL divergence as a constrained optimization as follows.

EQUATION

Before explaining the solution to the above optimization problem, we show the relationship between D and P (Y ). To articulate our intuition, we use Figure 3 (a) which illustrates a sample source distribution D S over 2D instance space (green). The labelling functions (in this case, f p and f a ) partitions the space of X into regions such that each region corresponds to a label combination (y = {y p , y a }). We denote each of these regions as R y . Notice that P (Y = y) becomes the integral of D over the region R y .

Let φ S and φ T be density functions of D S and D T respectively. Then, the above optimization problem becomes:

φ T = arg min φ∈∆ φ S (x) log φ S (x) φ(x) dx (2) s.t. Ry φ(x) dx = P T (y) ∀ y

Where ∆ ⊃ U T is the set of all distributions over X and region R y = {x :

f p (x) = y p , f a (x) = y a }.

The Lagrangian equivalent for the above problem can be stated as,

L(φ) = φ S (x) log φ S (x) φ(x) dx + y λ y Ry φ(x) dx,

where λ y ∈ R. Using the Euler-Lagrange equation to solve above problem,

EQUATION

Intuitively we find that D T is a scaled version of D S with scaling factor as the ratio of P T (Y ) and P S (Y ). Note that this scaling factor may vary for different x ∈ X depending on which region R y it falls in. This is depicted in Figure . 3(b) which is a target distribution derived from source distribution in 3(a). The regions R -1,+1 and R +1,-1 are scaled up whereas regions R +1,+1 and R -1,-1 are scaled down. Though the above derivation is for two labels, one can see that Eq. 3 extends to any number of labels in y. 

EQUATION

Above theorem states that the target error is bounded by sum of source error and distance between source and target distributions. d H∆H can be seen as the maximum accuracy of classifying source and target domain by using a classifier from hypothesis space H∆H. Further, any classifier g ∈ H∆H is the function XOR of some h, h ∈ H. DANN introduced an objective function which minimizes both source error as well as divergence between domains. Divergence between the domains can be looked at as the prediction accuracy of domain classifier.

DANN models starts with a mapping J f : X → R d with a parameter θ f , which projects instances to a latent representation space, we call this the feature extractor. These features are then mapped to primary label space with a mapping function J y (label predictor) with parameter θ y . The same features from latent representation space are mapped to domain label by J d (domain classifier), with parameter θ d . We denote the training set as {x i , (y i p , y i D )} N i=1 , with every instance we are provided with a primary label y p and a soft domain label y D . The objective here is to find a feature extractor J f which projects instances to a latent representation space where achievable label prediction accuracy is high and domain prediction accuracy is low. Let L y (θ f , θ y ) be the prediction loss for label prediction and let L d (θ f , θ d ) be that for domain classifier, then objective function is

EQUATION

where L y (θ f , θ y ) captures S (h) and L d (θ f , θ d ) captures d H∆H (D S , D T ) from Eq. 5. Note that J y ∈ H, then J d ∈ H∆H. However, in using this formulation together with aforementioned soft domain labels, results in a weak J D since the soft domain labels are highly skewed towards the source domain. In such settings, L d (θ f , θ d ) on class imbalance domain labels no longer captures d H∆H (D S , D T ). We address this issue again in Section 4.

The effort is to make J f provide a latent representation that is unable to discriminate source and target domain. As the soft domain labels are assigned according to y = {y p , y a } (see Eq. 4), if that latent representation can be used to correctly predict y p and y a with label predictors h p ∈ H and h a ∈ H, then there exists a g ∈ H∆H which can predict source and target domains well (with g(x) = h p (x) ⊕ h a (x)). Conversely, if the representations cannot be used to predict both the labels y p and y a correctly implies poor performance on domain classification. From this observation, we propose to replace domain classification loss (second loss term of Eq. 7) with auxiliary label classifier loss L a (θ f , θ a ), where θ a is the parameter for the auxiliary label classifier J a . We solve the optimization problem in Eq. 7 by using gradient reversal layer (Ganin & Lempitsky, 2015) . Gradient reversal layer multiplies the gradient by a negative constant during the backpropagation. We call the auxiliary label classifier as an adversarial to the primary classifier. In this form, our idea is closely related to Zhang et al. (2018) We extend this two label scenario to multilabels, by partitioning labels into groups, such that related labels are together. If a label is unrelated to all other labels than it forms a singleton group. We propose a model architecture, with a latent representation (with J f ) for each group. Further, the latent representation of a given group must be unable to predict any task from all other groups. We achieve this by adding all label classification other than the group member as the adversarial. In the next section, we showcase the empirical performance of multitask models trained in this way.

Another interesting alternative that departs from the usual view of feature projections is to utilize feature selection for J f (feature extractor). We discuss this alternative next.

3.3.1. FEATURE SELECTION:

An intuitive method to prevent negative transfer between correlated features is to use a feature selection approach to explicitly select relevant features appropriate for a task.

We use Recursive Feature Elimination (RFE) (Guyon et al., 2002) for the task of feature selection using CNN as the classifier, since wrapper method (J. Tang, 2013) is computationally effective and noticeably time consuming when deep nets are used as the classifier. Recursive feature selection (Guyon et al., 2002) consider all the features and eliminated them at each iteration till the desired criterion is met. At each iteration, the current feature set is used to evaluate a task using a classifier. Each of the features obtain a score from the classifier, based on which one or more features are eliminated from the set. This step is repeated until the criterion is met, which can be in terms of the final number of features to be chosen or desired classification performance to be attain. In order to perform RFE, we need to score each of the feature based on its effect on the classifier. For classifiers like logistic regression, the feature importance can be obtained by the weights assigned by the classifier for each of the features. In adversarial settings for multilabel classification, importance of the k th feature can be calculated as:

f k = 1 |Y p | |Yp| i=1 (w k pi ) 2 -min{(w k a1 ) 2 , . . . , (w k a |Ya | ) 2 } (8)

where, |Y p | and |Y a | denote the number of labels to be predicted for the primary and the auxiliary task respectively.

4. EXPERIMENTAL ANALYSIS:



4.1. SYNTHETIC EXPERIMENTS AND ANALYSIS:

We study the adverse effects of negative transfer and how our proposed algorithms could resist this negative transfer, on synthetic data. Our synthetic dataset consists of 10-dimensional feature vectors, with two binary labels y p and y a (primary and auxiliary). We generate the data from a generative system with one class label distribution for training set and one for test set. First 5 features are sampled according to the primary label from a mixture of two Gaussian distributions with identity covariance matrix. If the primary label is 1 then 5 features are sampled from first Gaussian, otherwise from the second Gaussian. Similarly second set of 5 features are sampled same way from another set of mixture of two Gaussian distributions, this time sampled according to the auxiliary label.

Note that for these experiments we are only interested in predicting primary label y p in the test set. In all the experiments we keep P (Y p = 1) = P (Y a = 1) = 0.5. We also Keep distance between 2 Gaussian distributions corresponding to primary label to fixed to 1.5. We use conditional label distribution P (Y p |Y a ) as measure label correlation. We compare following algorithms in our experiments: (1) baseline -A logistic regression classifier trained on primary label. We vary the distance between Gaussian distribution corresponding to auxiliary label while keeping that of primary label fixed. By doing this we vary the easiness of auxiliary task. In Figure 4 .1(b) we can see that, as the auxiliary task gets easier, more features related to auxiliary task will be used by the primary classifiers which results in decreasing performance in test set. One can see that Both baseline and DadvC are performing bad as easiness increases. The proposed algorithms performs consistently better.

4.2. REAL DATA EXPERIMENTS AND ANALYSIS:

Datasets: We use the Animals-with-Attributes (AwA) datasets (Xian et al., 2017) and Caltech-UCSD Birds 200-2011 (CUB) (Wah et al., 2011) for the multilabel attribute prediction task. With both datasets we follow the experimental protocol from (Xian et al., 2017) . The Animals with Attributes-2 (AWA) consists of 30, 475 images of animals in natural settings, with 50 animals and 85 annotated attributes each. According to Jayaraman et al. (2014) , 85 attributes can be grouped into 10 relevant groups. The dataset is split across the animals as 27/13/10 for train, validation, and test respectively as done in (Xian et al., 2017) . The Caltech-UCSD Birds 200-2011 (CUB) consists of 11,788 images of birds, captured in natural settings, corresponding to 200 birds. The dataset also consists of 312 attributes of the birds annotated per image. They are aggregated into 28 groups corresponding to anatomical parts, and split across classes: 100/50/50 for train, validation and test over attributes, as done in (Xian et al., 2017) . The split ensures different correlations between attribute labels in the three splits, which highlights the problems of negative-transfer.

Feature representations: We directly utilize the the feature representation (of length 2048) obtained from ResNet-101 (He et al., 2016) model that is pre-trained on ImageNet (Deng et al., 2009) for AwA and CUB. We explain below the specific architectures and parameters used for each experiment. Mean average precision (mAP) on validation and test sets are reported. Attribute prediction is an unbalanced prediction task, as individual attributes are rare. We use a balance corrected binary crossentropy loss function for all experiments, with the balance count obtained from the training set. Further, we utilize early stopping criteria based on the performance of the model on the validation set.

LR, LR+FS and LR+FS-adv: As discussed in Section 3.3.1, one way to prevent the adverse effects of negative transfer is by selecting the optimal feature set for each of the task, based on the proposed adversarial objective function. We use Recursive Feature Elimination (RFE) (Guyon et al., 2002) method for the task of feature selection wrapped over a Logistic Regression (LR). We perform feature selection experimentation using Logistic Regression (instead of multi-layer perception, as The CUB dataset consists of 28 groups, increasing number of adversarial tasks from most correlated to least helps improve performance on test splits. done in next set of experiments) for time efficiency. For CUB, we transform the 2048 features into a 500 dimensional space by using a dense layer followed by ReLU, which is then used for feature selection. Based on the primary task at hand, the feature importance scores are calculated using Eq. 8, by using the learned weights of LR. At each iteration, we remove λ × 0.33 numbers of features, where we decrease λ at each iteration as: 0.95 × λ. The final number of features to be retained is decided using the validation based on the mAP. We also observe the performance of feature selection without the adversarial setting (LR+fs). In this case, we only select the features that perform well for the primary task, without considering any effect on the auxiliary tasks. Performances of RFE have been observed in both adversarial and non-adversarial settings, which is reported in Table 1 , and group-wise test mAP in Figures 4(a) and 5 (a) respectively.

As shown in Table 1 , the mAP of RFE improves the baseline accuracy when LR has been used (compare rows 2 and 3 with row 1). The efficiency of the proposed criterion for scoring features, as shown by equation 8, can be observed when we compare between rows 2 and 3 in the Table . There is an improvement of 2.3% and 45% compared to LR (row 1), and 5.7% and 31.8% compared to LR+FS (w/o adv) (row 2) for AwA and CUB datasets respectively showcasing the advantage of the proposed method (LR+FS-adv). The average number of features selected are 321 (out of 2048) and 140 (out of 500) for AwA and CUB respectively. It is evident from the Table that the performance of MLP and ALadvC outperforms LR+FS with adv by a large margin. The performance can be attributed to MLP and ALadvS can apply projections to the feature vectors rather than selection/omission.

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Figures and Tables:

Figure 1: A supervised classifier 'cheetah vs. snow-leopard' that uses unrelated evidence (of habitat) over relevant evidence (of fur patterns). As shown by the pixel importance maps, the model suffers from the negative transfer prevalent in a typical animal image dataset skewed towards the animal's typical habitat and fails to generalize to rare samples.

A DOMAIN ADAPTATION PROBLEM Let the instances in training data be drawn from source distribution D S . The aim is to train a classifier on this which performs well on instances drawn from target distribution D T . Instances in D S has primary and auxiliary labels correlated with joint label distribution P S (Y ) = P S (Y p , Y a ) whereas in D T the labels have a different correlation with different joint label distribution P T (Y ) = P T (Y p , Y a ).

Figure 2: An illustration of instance source distribution over 2D space.(a) Source distribution with correlated labels (b) Closest uncorrelated distribution is the desired target distribution.

(2) DadvC -One hidden layer (5 neurons) MLP having domain classification as the adversarial task. (3) ALadvC -Same as DadvC, with auxiliary label classification as the adversarial task. (4) fs-adv -Adversarial feature selection with auxiliary label classification as adversarial task. Two sets of experiments where conducted to study the following aspects of negative transfer: • Difference between train and test label correlation: For this experiment, we trained a model on training set with P (Y p |Y a ) = 0.8 and tested out it's performance on test set which only differs from training set in P (Y p |Y a ).

Figure 4.1(a) Shows the mean average precision of classifiers on test set. One can see that the baseline mAP drops as correlation in test set goes down. This indicates that baseline classifier captured wrong set of features for prediction. We can see that DadvC is performing marginally better than baseline. ALadvC and fs-adv are consistently performing well irrespective of varying label correlation in test. This shows that these methods picked the correct set of labels. • Easiness of auxiliary task: We fix P (Y p |Y a ) = 0.8 for training set and P (Y p |Y a ) = 0.5 for test.

Figure 3: Synthetic experiment results:(a) Mean average precision over test set with varying P (Y p |Y a ), when trained on data with P (Y p |Y a ) = 0.8. (b) Mean average precision over test set with P (Y p |Y a ) = 0.5 when train set with P (Y p |Y a ) = 0.8, varying max auxiliary accuracy.

Figure 5: Mean average precision over validation and test split of CUB per group. The proposed ALadvC out performs the MLP baseline model, while the LR+FS-adv outperforms its baseline LR and LR+FS, for multilabel attribute prediction on held-out classes. (b) mAP of MLP and proposed ALadvC model on train and test against epochs. The training performance of the model with adversarial loss is corrected to reflect the true performance of the model, improving generalization. (c)The CUB dataset consists of 28 groups, increasing number of adversarial tasks from most correlated to least helps improve performance on test splits.

Table showing the improvement in mean average precision (%) using our proposed methods for AwA and CUB datasets.

Table content: <table><tr><td/><td/><td>AwA</td><td/><td>CUB</td></tr><tr><td>Approach</td><td>val</td><td>test</td><td>val</td><td>test</td></tr><tr><td>LR</td><td colspan="4">65.27 63.22 16.00 15.98</td></tr><tr><td>LR+FS</td><td colspan="4">66.41 61.13 24.80 17.57</td></tr><tr><td colspan="5">LR+FS-adv 71.07 64.62 25.11 23.16</td></tr><tr><td>MLP</td><td colspan="4">71.27 63.05 37.51 37.53</td></tr><tr><td>ALadvC</td><td colspan="4">74.15 69.92 42.34 41.05</td></tr></table>

Peer review (iclr2019):
 The term "negative transfer" is quite confusing, especially when it is used together with the term "domain adaptation". In domain adaptation, negative transfer means transferring knowledge from a source domain to a target domain in a brute-force manner may result in worse performance compared with that obtained by only using the target domain data. In this paper, the negative transfer problem is different from that in domain adaptation. The authors just tried to model the proposed negative transfer learning problem as a domain adaptation problem. However, the defined problem setting of negative transfer is quite strange, where for the target dataset, neither instances nor labels are available expect for the probability of P_T(Y_p, Y_a), and there is relationship between Y_p and Y_a, which is different from that of the source dataset. It is not convincing that why the proposed problem setting is important in practice. The proposed algorithm is designed based on two strong assumptions: 1. D_T is drawn from a distribution that is nearest to that of D_S, and 2. P_T(Y) is given in advance. Regarding the first assumption, it is not reasonable, and it is hard to be satisfied in practice. For the second assumption, it is also too strong to be satisfied in practice. Though the authors mentioned that when P_T(Y) is not given in advance, P_T(Y) can be further assumed to be of the uniform distribution or the classes are uncorrelated. However, these are just ad-hoc solutions. In practice, if P_T(Y) is unknown, and it is very different from the uniform distribution, or labels are highly correlated, the proposed algorithm may perform very poorly. Regarding the details of the algorithm, it just simply applies an existing model, DANN. In addition, the theoretical part is a well-known theorem. There are some typos: on Page 3, Figure 3(a) --> Figure 2(a); on Page 4, Figure 3(b) --> Figure 2(b).