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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>August</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Learning Framework for Early Stage Ads Ranking</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Xuewei Wang</string-name>
          <email>xwwang@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Qiang Jin</string-name>
          <email>qjin@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Shengyu Huang</string-name>
          <email>huginhuang@meta.com</email>
          <email>syhuang@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Min Zhang</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Xi Liu</string-name>
          <email>xliu1@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Zhengli Zhao</string-name>
          <email>zhengliz@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Yukun Chen</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Zhengyu Zhang</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jiyan Yang</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ellie Wen</string-name>
          <email>dwen@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Sagar Chordia</string-name>
          <email>sagarc@meta.com</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Wenlin Chen</string-name>
        </contrib>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>0</volume>
      <fpage>7</fpage>
      <lpage>09</lpage>
      <abstract>
        <p>Dividing ads ranking system into retrieval, early, and final stages is a common practice in large scale ads recommendation to balance the eficiency and accuracy. The early stage ranking often uses eficient models to generate candidates out of a set of retrieved ads. The candidates are then fed into a more computationally intensive but accurate final stage ranking system to produce the final ads recommendation. As the early and final stage ranking use diferent features and model architectures because of system constraints, a serious ranking consistency issue arises where the early stage has a low ads recall, i.e., top ads in the final stage are ranked low in the early stage. In order to pass better ads from the early to the final stage ranking, we propose a multi-task learning framework for early stage ranking to capture multiple final stage ranking components (i.e. ads clicks and ads quality events) and their task relations. With our multi-task learning framework, we can not only achieve serving cost saving from the model consolidation, but also improve the ads recall and ranking consistency. In the online A/B testing, our framework achieves significantly higher click-through rate (CTR), conversion rate (CVR), total value and better ads-quality (e.g. reduced ads cross-out rate) in a large scale industrial ads ranking system.</p>
      </abstract>
      <kwd-group>
        <kwd>Recommender systems</kwd>
        <kwd>Computational advertising</kwd>
        <kwd>Multi-task learning</kwd>
        <kwd>Multi-stage Ranking consistency</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        The goal of the ads ranking system is to select the optimal ads to display to users. Due to latency
constraints, it is impractical to predict ranking score for each ad out of large-scale candidates.
Therefore, a multi-stage ranking process is widely adopted, which uses progressively more
complex models to narrow down the number of ads [
        <xref ref-type="bibr" rid="ref1 ref2 ref3">1, 2, 3</xref>
        ]. Common multi-stage ranking
systems consist of retrieval, early stage ranking, and final stage ranking, as shown in figure
1.
      </p>
      <p>While retrieval is often rule-based, both early stage and final stage ranking use ranking score
predicted by machine learning models.</p>
      <p>
        After we obtain the final stage ads ranking score, the system will run an ads auction to decide
the winning set of ads to show to the user. To ensure that the winning ad maximizes value for
both user and businesses, we use total value [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] to rank the ads in auction. The total value is a
combination of three major factors: 1) The bid placed by an advertiser for that ad. 2) Estimated
action rates representing the probability of the desired outcome (e.g. click, conversion) after
showing the ad to a user. 3) Ads quality [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] capturing the feedback from user on their ads
experience.
      </p>
      <p>In general, it is determined by ads quality models, which predict scores of multiple quality
events (e.g. crossing out ads, hiding ads). Our framework mainly focuses on learning estimated
action rates (i.e. ads CTR) and ads quality.</p>
      <p>
        Despite the multi-stage ads ranking system being a common practice, it has the fundamental
problem of multi-stage inconsistency: the early stage ranking system fails to pass good ads to
the final stage ranking system [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. In other words, the low recall of the early stage ranking
system can significantly harm the end-to-end ads ranking system. Specifically, we need to
resolve the following three challenges in designing efective multi-stage ranking system:
1. Performance gap between early and final stage Due to the restricted model capacity
and the smaller feature set, the performance of early stage ads ranking is inferior to that
of the final stage ranking. Consequently, when provided with the same candidates, the
top ranked ads produced by the final stage ranking and early stage stages can vary a lot.
2. Total value definition inconsistency Ideally, we should setup same ranking objectives
in the early stage as the final stage, in order to share the same ads total value definition.
However, maintaining same types of ads quality models in early stage is dificult
considering the heavy engineering work on multiple models and the increased serving cost. To
save resource and rank more ads, we only enable major ads quality models in early stage,
which causes the ranking consistency issue between the early and final stage ranking.
3. Selection bias Conventional early stage ads ranking models are trained on ads with
user impression, as well as logged user click or conversion. However, the early stage ads
ranking model needs to infer over whole early stage ads candidates, most of which are
non-impression ads. Due to the skewed observed label, the selection bias occur with the
distribution mismatch between test and training set [
        <xref ref-type="bibr" rid="ref6 ref7 ref8">6, 7, 8</xref>
        ].
      </p>
      <p>In order to address those issues, we propose a multi-task learning framework for early stage
ranking to learn the relevant information of ads total value in final stage ranking. Due to the
latency constraint, we cannot learn all components of ads total value in one light-weighted early
stage ranking model. Instead, we focus on joint learning of ads CTR and ads quality events.
There are three major benefits for our framework:
• Ranking consistency improvement In order to solve total value definition
inconsistency issue on ads quality, we present a new objective for early stage ads quality, called
consolidated quality score (CQS). Instead of replicating every final stage ads quality event
model in early stage, the CQS consolidates all final stage ads quality objectives together
to be a single objective. We derive the CQS task label from the final stage total quality
scores. In addition, we add a distillation task from the final stage CTR model. Both of
tasks significantly improve the ads recall for early stage ranking.
• Resource saving by model consolidation In ads auction, the CTR model’s prediction is
essential to estimate the action rates for various post-click conversions, while ads quality
models are necessary for determining the quality score of each ad. Consequently, the
primary serving costs stem from the ads CTR model and quality models, due to their
large serving trafic. With the multi-task learning for CTR and ads quality events, we can
reduce serving costs with shared model architectures and features.
• Mitigation of selection bias We leverage the data augmentation to mitigate the selection
bias of early stage model. We logged more final stage non-impression data in the training
data as the augmented data. When computing the CTR loss, instead of treat them as
negative samples, we use the final stage CTR prediction as the pseudo-label. For CQS
task, the augmented data also has its label as each non-impression ads in final stage still
participate in ads auction.</p>
      <p>In order to better understand the impact of jointly learning CTR and ads quality, we also
build a ofline recall simulation framework. In the current multi-stage ranking system, the
ifnal stage has more accurate prediction for higher precision, whereas the early stage need to
optimize for recall. The results show that our framework can improve simulated soft recall
for early stage ranking. In the online experiment, we also observe the reduction of total value
divergence between early stage and final stage, which implies better ranking consistency. We
also conduct ablation study for each key component in our multi-task learning framework. In
the online A/B testing, our framework achieves better ads quality, CTR and CVR, compared
with the separate serving baseline.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>
        Early stage ads ranking, also known as the pre-ranking stage, has great potential to improve
overall ranking performance as they decide candidates for final stage ads ranking. Most of
the prior work discussed how to improve the efectiveness while maintain eficiency for early
stage ads ranking [
        <xref ref-type="bibr" rid="ref10 ref2 ref9">2, 9, 10</xref>
        ]. Recent work [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] noticed the ranking consistency issue between
stages. They introduced a metric, similar to recall, to measure ranking consistency. Also, they
conducted experiments for diferent final stage distillation techniques to improve early stage
ranking consistency. However, they only considered improving dedicated ranking models cross
stages (e.g. CTR model), but overlooked the interactions between multi-objectives in complex
ads ranking system, such as ads quality. Such interaction can be captured through multi-task
learning framework.
      </p>
      <p>
        Multi-task learning is widely used in recommendation system [
        <xref ref-type="bibr" rid="ref11 ref12 ref13">11, 12, 13</xref>
        ]. However, prior
work mainly focused on complex multi-task learning architectures (e.g. MMoE [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]) to model
task relationships. Although those techniques have achieved promising improvements on all
tasks, they are dificult to apply in early stage ranking due to model capacity constraint. Recently,
a online multi-task framework for CTR and two ads quality models is presented in [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]. They
built a framework which achieved both CTR lift and better ads quality. This framework can
not be generalized to diferent ads ranking ranking systems, which have diferent ads quality
events in the final stage ads ranking. Also, their framework is too complex to use in early stage
ranking. Therefore, we still lack simple and eficient work for early stage ranking system to
apply multi-task learning. To the best of our knowledge, our work is the first paper discussing
the practice for multi-task learning on early stage ranking, from the perspective of ranking
consistency and ads CTR-quality joint optimization.
      </p>
    </sec>
    <sec id="sec-3">
      <title>3. Methods</title>
      <p>In this section, we discuss the key components for our framework: model architecture, model
training, and evaluation metrics.</p>
      <sec id="sec-3-1">
        <title>3.1. Model Architecture</title>
        <p>
          Instead training separate early stage CTR and quality models, we propose a multi-task learning
framework to train a single model on those objectives, as shown in Figure 2. We utilize DLRM[
          <xref ref-type="bibr" rid="ref15">15</xref>
          ]
framework to build a two-tower model with the user tower and the ad tower. After we obtain
the output hidden embeddings from the shared model architecture, we pass them into dedicated
task module to learn three tasks. Compared with the original CTR model, we add two additional
tasks:
        </p>
        <sec id="sec-3-1-1">
          <title>3.1.1. Consolidated Quality Score (CQS)</title>
          <p>Learning all quality events in a single model can be challenging. First, the data collection process
of diferent quality events varies significantly, which makes it dificult to log all quality events
in one data pipeline. For instance, there could be quality events derived from survey-based
assessments, whose logging infra that is diferent from the one used for logging the CTR training
data. Moreover, it is challenging for a single model to fulfill the model capacity constraint for
eficient inference, while still predicting multiple tasks for quality events. To address these
issues, we propose Consolidated Quality Score (CQS) to consolidate all quality events in early
stage ranking. We define the CQS in Equation 2, as the input of the mapping function  to
compute the</p>
          <p>, which denotes the final ads quality score of an ad. The   
indicates the model prediction of the quality event  . The  
 is the associated multiplier, so
as to control the quality event’s power in the ads auction. The CQS can be easily logged into
training data during the ads auction.</p>
          <p>(1)
(2)
(3)</p>
          <p>With the final stage CQS as the label, we not only unblock the quality data logging, but
also solve the total value definition inconsistency issue in early stage ranking. Also, the early
stage CQS can adapt to final stage quality event changes automatically in a flexible manner and
maintain stable multi-stage status. We utilize mean square error as the loss function:
where the</p>
          <p>is the final stage consolidated quality score, and   is the early stage ranking
predicted value.  is the number of samples.</p>
        </sec>
        <sec id="sec-3-1-2">
          <title>3.1.2. CTR Cross-stage Distillation</title>
          <p>In addition to the CTR task and CQS task, we also add one more task for teacher distillation.
This task is not used for serving. There are two benefits for using final stage pCTR as the
teacher model to distill early stage CTR model. First, distilling knowledge from a teacher model
to a student model is a common approach to improve student model’s performance without
 =

∑  
=1
 =  ()
 ∗</p>
          <p>=</p>
          <p>1
 =1
∑(
 −   ) ,
2
additional capacity cost [16]. The final stage CTR model is much more complex compared to
early stage CTR model, rendering it a reasonable choice to be a teacher model. Second, using
the final stage CTR model as the distillation teacher can improve the ranking consistency since
the early stage learns the final stage prediction information directly. Although this task can
improve ranking consistency, we cannot use this task to replace the original CTR task during
serving, because the model cannot learn good calibration without ground-truth click label. The
distillation logistic regression Loss is employed in our teacher task.</p>
          <p>ℎ
= −[  ∗
log(  ) + (1 −  ) ∗
log(1 −   )],
(4)
where   is the final stage CTR prediction (between 0 to 1) and   is the CTR task head
prediction in our multi-task learning framework. The loss function measures the dissimilarity
between the early stage CTR prediction and final stage CTR prediction, which helps improve
consistency.</p>
        </sec>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Model Training</title>
        <sec id="sec-3-2-1">
          <title>3.2.1. Consolidated Data Pipeline</title>
          <p>The serving trafic of CTR model is the subset of that of quality models. For instance, for
post-impression conversion types, they do not need the CTR action to complete the conversion,
but they still need quality score to rank. Therefore, compared with original CTR pipeline, we
add remaining serving trafic for CQS task in the consolidated pipeline.</p>
          <p>During model training, the CTR task will only be trained on its serving trafic to avoid unused
feedback loop.</p>
        </sec>
        <sec id="sec-3-2-2">
          <title>3.2.2. Data Augmentation with Pseudo-label</title>
          <p>In order to mitigate selection bias, we enrich the data with non-impression ads. We randomly
subsample the early stage non-impression ads as the augmented data. We treat the final stage
CTR prediction as the pseudo-label for those non-impression data, in order to further improve
the ranking consistency. During the online training, we have developed data augmentation
framework to logging specific model’s prediction in the non-impression data.</p>
        </sec>
        <sec id="sec-3-2-3">
          <title>3.2.3. Balance Learning for Diferent Tasks</title>
          <p>During ofline experiments, we find adding CQS task leads to negative transfer for CTR task.
This is expected since the correlation between CTR and quality score ads is low and ads quality
is designed for relevance and integrity. Considering CTR is an important optimized ad event,
we tune the weight of the CQS task in the loss to reduce the negative impact of the CTR task.
In the final settings of our framework, we adjust the loss weight of CQS to be 1.5, which has the
neutral impact on NE of the CTR task. In addition, adding the CTR teacher task can boost the
CTR performance significantly. We tune the task weight of CTR teacher to be 2, in order to
achieve best performance for CTR.</p>
        </sec>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Evaluation of Early Stage Ads Ranking</title>
        <p>
          There are several common ofline evaluation metrics for ads ranking models, such as
AreaUnder-ROC (AUC) [
          <xref ref-type="bibr" rid="ref10">17, 10</xref>
          ] and normalized entropy (NE) loss [18]. However, as early stage
ranking models aim to improve recall instead of precision, the improvements on user impression
data may not generalize to early stage ads, most of which are non-impression data. Furthermore,
those ofline evaluation metrics only take the individual model’s performance into account, but
overlook the combined efect of multiple ranking objectives.
        </p>
        <p>Calculating the accurate recall is impractical considering the large-scale ads candidates in
early stage. In order to have a better measurement on recall, we leverage the ofline simulated
recall for multi-objective early stage ranking system. We replay a small trafic with full ad
requests in a simulator, a separate ranking flow but copies all components from production flow.
Since the simulator will not serve any production trafic, we can relax the timeouts between
stages, to ensure that all ads from retrieval stages are ranked. As is shown in Figure 3, after
obtaining  ads candidates from the retrieval stage, we will pass all ads in a ads request to
the simulator and log top  ads in the replay log. Those top  ads will be marked as positive
samples and rest of ads in the same ads request will mark as negative samples. We guarantee
the production flow and replay flow has the same amount of final ads candidates to reproduce
the production flow. After we have the replay log, we can utilize recall metrics to measure
model’s ofline performance, with top  candidates in replay logs as the golden set. There are
two types of recall metrics:
• Hard recall counts of intersection between top  ads picked by the model and golden
set divided by  at the ad request level. This is the widely-accepted definition of recall.</p>
        <p>
          The recent work [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] used this as the metrics for ranking consistency.
• Soft recall is the sum of final stage ads total value of top  ads picked by the model
divided by sum of total value of the golden set. The hard recall indicates the agreement in
terms of ad candidacy, while the soft recall also takes the values of the ads into account.
        </p>
        <p>We choose soft recall as the major ofline metric for ranking consistency because it is more
reasonable for measuring the value of early stage ads. Also, we observe the variance of soft
recall among diferent ad requests is much smaller than hard recall.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Experiments</title>
      <p>In this section, we conduct both ofline experiments and online A/B testing to justify the benefit
of our framework. In order to understand each technique better, we first built a simple dedicated
CQS model to verify the benefit of consolidating all early stage quality models. Then we further
iterate on the production CTR model with our proposed multi-task learning framework. For
ofline metrics, we compare the recall metric for overall multi-task predictions. Compared with
other ofline metrics, we find the recall metric is more efective to reflect early stage ranking
model’s online performance, such as impression based total value, CTR, CVR and total value
divergence (TVD). The impression based total value is a metric to measure the potential business
value of ads after user impression, as we run ads auction depends on the total value of ads. The
TVD is computed by the following equation on final stage ads candidates, as an online metric
for ranking consistency:
   =
∑|</p>
      <p>∑|  
−</p>
      <p>|
 
|
For ads quality metrics, we select two quality metrics:
• Ads cross-out (Xout) happens when a user clicks ”×” and selects ”I don’t want to see
this” at the top-right of an ad. We use the ads cross-out rate to measure this quality event,
where the lower ads cross-out rate implies better ads quality.
• Ads Survey for Quality (ASQ) is a survey-assessment based metrics for ads quality
related signals. It estimates the user rating for ads, where higher is better.</p>
      <sec id="sec-4-1">
        <title>4.1. Consolidate Early Stage Ads Quality Models</title>
        <p>To address the total value definition inconsistency issue between the early and final stages, we
study a simple CQS model to consolidate all early stage ads quality models. The ofline soft
recall shows significant improvement compared with using separate early stage ads quality
models. For online metrics, we observe better quality of ads with lower ads cross-out rate
and higher ASQ score. In addition, the total value divergence between early and final stage
significantly decreases with the increased impression based total value. Although the CQS
model does not afect any CTR or CVR model, the CTR and CVR also increase, which implies
the business power of ads quality models. The better ads quality can bring long term value
for ads ranking performance, with better ads experience for users. Another benefit for CQS
is to save serving CPU cost significantly as we consolidate multiple simple early stage quality
models together.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Multi-task Learning of CQS and CTR</title>
        <p>Given the baseline CQS model, we further iterate the CTR model on multi-task framework
we proposed. Compared with the production CTR model, we refresh the features add top 50
important CQS features from the CQS model feature importance rank. With more CQS top
features, our multi-task learning framework can have neutral MSE performance compared with
(5)
Recall (+)
Xout rate (-)
ASQ (+)
TVD (-)
CTR (+)
CVR (+)
Total Value (+)
total CPU (-)
+3.2%
-1.8%
+0.02
-7.9%
+1.7%
+2.0%
+1.0%
-0.7%
the baseline CQS model. In table2, the multi-learning framework achieves better soft recall than
production CTR and baseline CQS models. The online experiment also shows better ads quality
and CTR, as well as higher CVR and impression based total value. The total value divergence is
further reduced as we add final stage teacher distillation task in our framework. Since we add
more features and two more tasks to the original CTR model, the total CPU is slightly smaller
than that of separate CTR and CQS models.</p>
        <p>Recall (+)
Xout rate (-)
ASQ (+)
TVD (-)
CTR (+)
CVR (+)
Total Value (+)
total CPU (-)
+12.2%
-3.5%
+0.005
-5.7%
+0.4%
+0.8%
+3.0%
-0.06%</p>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Ablation Study</title>
        <p>We also set up several comparable models for the ablation study in Table 3, in order to exclude the
impact of diferent feature sets compared with production models. We build four baseline models:
1) Dedicated CTR model by removing CQS tasks from our multi-task learning framework. 2)
Dedicated CQS model with both CTR and teacher tasks removed. 3) Our multi-task learning
framework without teacher task 4) Our multi-task learning framework trained on impression
ads only. According to Figure 3, building dedicated CTR and dedicated CQS models can achieve
NE or MSE gain over our framework, which implies negative transfer [19] issue in multi-task
learning. Without teacher task, the CTR task performance regresses a lot, while the MSE
becomes better. The teacher task is essential to help close the performance gap between final
stage ranking and early stage ranking.</p>
        <p>During the online experiments, the version with dedicated CTR and CQS models shows
significant increase on Xout rate and drop for ASQ, although the dedicated CQS model has
better MSE performance than our proposed framework. For ads CTR, although the dedicated
CTR model can improve the ads CTR with better ofline NE performance, the CVR and impression
based total value is slightly worse. The higher CTR but lower CVR implies that the ad is very
eye-catching, but the user clicking on the ad may not the right demographic for which the
ad targets. The poor ads quality can be the explanation of the lower CVR, as the ads quality
reflect the user experience on ads. Such results manifest that the single ofline metric for a
individual ranking model may not be reliable to reflect online performance. The soft recall
metric can mitigate this issue which takes multi-objectives into consideration. The larger total
value divergence also reflects ranking consistency issue, where the total value between early
stage and final stage has large distribution gap. The multi-task learning between CTR and
CQS can force the model to learn the coexistence of estimated action rate and ads quality, and
improve the total value divergence.</p>
        <p>Without the teacher distillation task, the MSE loss for CQS becomes better but the online
quality metrics turn out to be worse than our multi-task framework. The online CTR reduces
after removing the teacher task, and the total value divergence becomes worse. The impression
based total value has regression, which is expected with worse CTR and ads quality.</p>
        <p>The augmented data shows great potential in improving early stage ranking performance.
After filtering out the augmented data, the ofline simulated recall is worst among all baselines.
The model also sufers from impression based total value regression, CVR drop and CTR drop,
as well as worse ads quality. The augmented data plays a critical role to improve ads recall with
selection bias mitigated.</p>
        <p>Based on these results, we can draw the following conclusions:
• Each component in our multi-task learning framework is essential to improve the
performance of early stage ads ranking model. The CQS task solves the issue of total value
definition inconsistency between early and final stage. The teacher task helps close the
performance gap of CTR and improve the ranking consistency. The augmented data
mitigates the selection bias with better ads recall.
• Ads recall and ranking consistency are important for early stage ads ranking. If we only
focus on the individual objective of each ads ranking model and optimize for precision,
the online overall performance may not improve due to the poor ranking consistency
and low ads recall.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion and Future work</title>
      <p>We propose a novel multi-task learning framework to improve early stage ads ranking
performance. This framework can be generalized to other user cases since the CQS can be applied
to any ads ranking system with the ads quality component. We also design the ofline recall
evaluation metric for the multi-task learning framework in early stage ranking, which has been
verified to reflect the model online performance in an industrial ads ranking system.</p>
      <p>For future work, we plan to improve the stability of the CQS task. As MSE loss is prone to
outliers, we will conduct more experiments for robust regression loss. Also, more techniques
[20, 19] can be explored to avoid negative transfer between the CQS and CTR tasks. In addition,
we manually tune the weights for diferent tasks in the current framework. This can be
improved with learnable loss weight techniques [21, 22], which can adjust weight automatically
for multiple tasks.
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