# Who to Watch Next: Two-side Interactive Networks
for Live Broadcast Recommendation

Jiarui Jin1,∗, Xianyu Chen1,∗, Yuanbo Chen2,∗, Weinan Zhang1,†, Renting Rui1,
Zaifan Jiang2, Zhewen Su2, Yong Yu1 1Shanghai Jiao Tong University, China;
2Alibaba Group, China  jinjiarui97, xianyujun, wnzhang, ruirenting,
<EMAIL_ADDRESS>yuanbo.cyb,zaifan.jzf<EMAIL_ADDRESS>
(2022)

###### Abstract.

With the prevalence of live broadcast business nowadays, a new type of
recommendation service, called live broadcast recommendation, is widely used
in many mobile e-commerce Apps. Different from classical item recommendation,
live broadcast recommendation is to automatically recommend user anchors
instead of items considering the interactions among triple-objects (i.e.,
users, anchors, items) rather than binary interactions between users and
items. Existing methods based on binary objects, ranging from early matrix
factorization to recently emerged deep learning, obtain objects’ embeddings by
mapping from pre-existing features. Directly applying these techniques would
lead to limited performance, as they are failing to encode collaborative
signals among triple-objects. In this paper, we propose a novel TWo-side
Interactive NetworkS (TWINS) for live broadcast recommendation. In order to
fully use both static and dynamic information on user and anchor sides, we
combine a product-based neural network with a recurrent neural network to
learn the embedding of each object. In addition, instead of directly measuring
the similarity, TWINS effectively injects the collaborative effects into the
embedding process in an explicit manner by modeling interactive patterns
between the user’s browsing history and the anchor’s broadcast history in both
item and anchor aspects. Furthermore, we design a novel co-retrieval technique
to select key items among massive historic records efficiently. Offline
experiments on real large-scale data show the superior performance of the
proposed TWINS, compared to representative methods; and further results of
online experiments on Diantao App show that TWINS gains average performance
improvement of around 8% on ACTR metric, 3% on UCTR metric, 3.5% on UCVR
metric.

Live Broadcast Recommendation, Two-Side Interactive Network

††journalyear: 2022††copyright: acmcopyright††conference: Proceedings of the
ACM Web Conference 2022; April 25–29, 2022; Virtual Event, Lyon,
France††booktitle: Proceedings of the ACM Web Conference 2022 (WWW ’22), April
25–29, 2022, Virtual Event, Lyon, France††price: 15.00††doi:
10.1145/3485447.3511939††isbn: 978-1-4503-9096-5/22/04††ccs: Information
systems Online shopping††ccs: Information systems Collaborative
search11footnotetext: Jiarui Jin, Xianyu Chen, and Yuanbo Chen contributed
equally to the work.22footnotetext: Weinan Zhang is the corresponding author.

ACM Reference Format:
Jiarui Jin, Xianyu Chen, Yuanbo Chen, Weinan Zhang, Renting Rui, Zaifan Jiang,
Zhewen Su, Yong Yu. 2022. Who to Watch Next: Two-side Interactive Networks for
Live Broadcast Recommendation. In Proceedings of the ACM Web Conference 2022
(WWW ’22), April 25–29, 2022, Lyon, France ACM, New York, NY, USA, 10 pages.
https://doi.org/10.1145/3485447.3511939

##  1\. Introduction

With the establishment of mobile Internet, the focus of e-commerce has moved
from personal computers to smartphones, which significantly encourages the
emergence and development of live broadcast services. Live broadcast
recommendation has become popular, especially in the past two years, because
of anchors’ revealing selection and expressiveness powers, as such, free users
from tedious searching and comparing in mobile phones. Figure 1 shows a live
broadcast recommendation example. According to historical information on user
and anchor sides, a list of appropriate anchors will be automatically
generated for a user. In a live broadcast recommendation system, the
historical information can be roughly categorized into two types for both two-
fold. The first one is static data, containing attribute information such as
user and anchor profiles. The other one is dynamic data, containing user
browsing history represented as triple interactions (i.e.,
$\langle\text{users, anchors, items}\rangle$) and broadcasting history
represented as binary interactions (i.e., $\langle\text{anchors,
items}\rangle$).

Notably, the live broadcasting recommendation here is significantly different
from existing recommendation tasks in the following aspects: (1) Different
from traditional recommendations of query (Zhang and Nasraoui, 2006; Cao et
al., 2008) or item (Jin et al., 2020b; Zhou et al., 2018) and recently
introduced intent recommendation (Fan et al., 2019), it recommends anchors
instead of queries or items to users. (2) Our live broadcast recommendation
needs to consider the interactions among triple-objects (i.e., users, anchors,
and items) rather than binary interactions between users and items. (3)
Different from queries and items, the status of anchors (i.e., broadcasting or
not) always changes frequently.

Existing methods for live broadcast recommendation employed in industry, such
as Taobao and Kuaishou, usually extract handcrafted features in user and
anchor sides, and then feed these features to a classifier ranging from early
matrix factorization (Koren et al., 2009) to recently emerged deep learning
(Cheng et al., 2016). These approaches heavily rely on laboring feature
engineering and fail to use the rich, dynamic interactions among objects
fully. However, as the anchors are rapidly changing the items sold in the
broadcast room, it is really critical to model their interactions to capture
the temporal behaviors. Moreover, their techniques proposed for binary-objects
(i.e., users, items), obtaining an object’s embedding by mapping from pre-
existing features; are indirectly to extend to encode collaborate signals
among triple-objects (i.e., users, anchors, items).

In summary, we introduce a recently emerged, but seldom exploited, live
broadcast recommendation problem; to handle which, we are at least required to
address the following challenges:

  * •

(C1) How to build correlations between users and anchors, since their
relevance is an inherent attribute hidden in complex static and dynamic
features in both user and anchor sides? Consider the following scenario (shown
in Figure 1). When the teen opens a live broadcast recommendation App, the
recommender system returns several anchors based on her profile and historical
data. For each pair of user and anchor, we are required to model two kinds of
features; namely static ones often formed as categorical attributes (e.g.,
user’s gender and anchor’s broadcast time), and dynamic ones often formulated
as sequential data (e.g., user’s browsing history and anchor’s broadcasting
history). These historical data consist of related items which also have their
own static features (e.g., item’s price and brand).

  * •

(C2) How to capture the collaborative signals between user and anchor sides?
As stated in (Wang et al., 2019), the mainstream methods for recommendation,
either early employed shallow or recently proposed deep models, fail to
capture the hidden collaborative information. Further analysis in (Qu et al.,
2019; Jin et al., 2020b) reveals the early summarization issue exists in the
structural data, and we argue that similar issue occurs here, where existing
approaches usually compress all the information together in each side
regardless of rich interactive (i.e., ‘AND’) patterns between user’s browsing
and anchor’s histories. Take Figure 1 as an instance. The motivation of the
teen entering the live broadcast room can come from the current anchor selling
the item she watched before, which can be modeled by AND operation over anchor
broadcast items and user browsed items.

  * •

(C3) How to distinguish the key information and filter out the noise? Recent
works (Ren et al., 2019; Pi et al., 2020) reveal that observe that long-term
dependencies exist in the historical records. However, since the length of
historical sequences vary for different users due to diverse activeness or
registration time and some of them are extreme long, it is not practical to
maintain the whole behavior history of each user for real-time online
inference.

Figure 1.  An illustrated live broadcast recommendation example for
recommending an anchor to a user (while there will be a list of anchors in
real-world Apps).

In this paper, we propose a novel TWo-side Interactive NetworkS (TWINS) for
live broadcast recommendation. In seeking for a proper way to effectively
capture correlations between user and anchor according to complicated behavior
histories in these two sides, we introduce a new two-side network
architecture, where we combine product-based neural network (PNN) (Qu et al.,
2016) and recurrent neural network (RNN) (Hochreiter and Schmidhuber, 1997) in
each side to simultaneously model static and dynamic features. Concretely, for
static features usually formed as categorical data, we establish an embedding
vector for each category and adopt PNN to capture the hidden interactive
patterns; and then incorporate it with contextual information by feeding the
learned embeddings into the RNN model (C1). A principal way to discover the
hidden collaborative signal is to employ collaborative filtering methods such
as SVD++ (Koren, 2008); however, these techniques still suffer from the early
summarization issue and cannot be directly applied to live broadcast
recommendation scenarios. Hence, we first propose interaction networks to
measure the similarity of user and anchor in the two-side architecture, in
both item and anchor aspects, which are further aggregated to form our final
objective (C2). To efficiently handle long-sequential data, inspired by the
recently proposed retrieval model (Pi et al., 2020; Qin et al., 2020b), we
design a novel co-retrieval mechanism to search and retrieve the relevant
items in user and anchor sides (C3).

We conduct thorough experiments on four real-world datasets to verify the
superiority of TWINS over recent state-of-the-art methods. Further, TWINS has
been deployed on the recommender system of a mainstream Diantao App, where the
online A/B test shows that TWINS achieves better performance than baseline
methods on all the measurement metrics.

Figure 2.  The overview of TWINS. The bottom part (i.e., (a)-(d)) shows the
two-side architecture where we use the PNN to encode the static (categorical)
attributes and the RNN to encode the dynamic (sequential) histories in user
and anchor sides. The up part (i.e., (e)-(g)) illustrates the interaction
networks which take these embedding vectors as input and outputs the
interactive patterns from item and anchor aspects, which are further
aggregated with user and anchor static features to make the final prediction
(i.e., $\widehat{y}_{11}$ for user $u_{1}$ and anchor $a_{1}$). Moreover, we
design a co-retrieval mechanism, as illustrated in (h), to decrease the
interaction computations by selecting a subset of historical items for the
interaction instead of the whole set.

##  2\. Preliminaries

###  2.1. Problem Formulation

We begin by describing the live broadcast recommendation task and associated
notations.

###### Definition 0.

Live Broadcast Recommendation. Given a triplet
$\langle\mathcal{U},\mathcal{A},\mathcal{I}\rangle$, where
$\mathcal{U}=\\{u_{1},\ldots,u_{P}\\}$ denotes the set of $P$ users,
$\mathcal{A}=\\{a_{1},\ldots,a_{N}\\}$ denotes the set of $N$ anchors, and
$\mathcal{I}=\\{i_{1},\ldots,i_{Q}\\}$ denotes the set of $Q$ items. The
purpose of live broadcast recommendation is to recommend the most related
anchor $a\in\mathcal{A}$ to a user $u\in\mathcal{U}$ according to the user’s
browsing history $\mathcal{H}^{u}$ and the anchor’s broadcasting history
$\mathcal{H}^{a}$.

In our application, as shown in Figure 1, a user’s (e.g., the $p$-th user’s)
browsing history $\mathcal{H}^{u}_{p}$ is constituted by a series of her
visited items with associated anchors. For convenience, we establish a set of
user’s browsed items denoted as $\mathcal{H}_{p}^{ui}$ and the other set of
user’s visited anchors denoted as $\mathcal{H}_{p}^{ua}$. We then have
$\mathcal{H}_{p}^{u}=\mathcal{H}_{p}^{ui}\cup\mathcal{H}_{p}^{ua}$ where
$\mathcal{H}_{p}^{ui}\subseteq\mathcal{I}$,
$\mathcal{H}_{p}^{ua}\subseteq\mathcal{A}$; and similarly an anchor’s (e.g.,
the $n$-th anchor’s) broadcasting history
$\mathcal{H}^{a}_{n}=\mathcal{H}_{n}^{ai}\subseteq\mathcal{I}$ holds for any
$p\in\\{1,\ldots,P\\}$ and any $n\in\\{1,\ldots,N\\}$. Besides the complex
interactions among these triplet-objects (a.k.a., dynamic feature in Figure
1), there are rich categorical data for these objects (a.k.a., static feature
in Figure 1). We use $\bm{x}^{u}_{p}$, $\bm{x}^{a}_{n}$, $\bm{x}^{i}_{q}$ to
denote the feature of the $p$-th user, the $n$-th anchor, the $q$-th item
respectively, and use $\bm{x}^{uj}_{p}$, $\bm{x}^{aj}_{n}$, $\bm{x}^{ij}_{q}$
to denote their $j$-th categorical features. For convenience, we use the
$1$-th categorical feature of each item to denote its category (e.g., shoes).
Namely, $\bm{x}^{i1}_{q}$ represents the $q$-th item’s category.

###  2.2. Related Work

Advanced Recommendation Tasks. Classical item-based recommender systems (Koren
et al., 2009; Cheng et al., 2016) aim at seeking the favorite item for a user
according to user-item interactions. Influenced by the evolution of mobile
Internet and the development of deep learning techniques, more and more
research in recommendation has shifted to inventing new recommendation tasks,
which can be roughly categorized into two lines. One line of literature
(Hidasi et al., 2015; Ren et al., 2019; Fan et al., 2019; Sun and Zhang, 2018)
seeking to bring more convenience for users by modifying the recommendation
task. For example, Hidasi et al. (2015) introduces the session-based
recommendation task where the recommender systems are only accessible to short
session-based data instead of long histories. Recently, Fan et al. (2019)
proposed an intent recommendation to recommend an intent (i.e., query) to a
user since typing words on mobile devices are much inconvenient than on
desktop computers. The other line of work (Shi et al., 2018; Chen et al.,
2017; Van Den Oord et al., 2013) investigating to include the side information
associated with users and items in the recommendation to better capture user
preference. For example, one promising way is to combine the structure
information hidden in the sequence (Wu et al., 2017) or the graph (Shi et al.,
2018) built based on user-item history in the recommendation. Another
direction is to model multimedia data such as image (Chen et al., 2017) or
audio (Van Den Oord et al., 2013) related with recommendation. To the best of
our knowledge, since the live broadcast recommendation is recently emerged and
is developing rapidly, there is limited literature in this field, and our
paper is proposed to fill this gap.

Collaborative Filtering Methods. Classical recommendation methods such as
matrix factorization (Koren et al., 2009) parameterize users and items as an
embedding vector and conduct inner product between them to predict an
interaction. For further mining interactive information among features, FM
(Rendle, 2010) projects each feature into a low-dimensional vector and models
feature interactions by the inner product. As discussed in (He et al., 2017;
Hsieh et al., 2017), although the inner product encourages user and item
embeddings of an observed interaction close to each other, its natural
linearity makes it insufficient to discover the complex correlations between
users and items. Influenced by the stunning success of deep learning, recent
efforts (He et al., 2017; He and Chua, 2017; Wu et al., 2016; Tay et al.,
2018; Wang et al., 2019) focus on exploiting deep learning techniques to
enhance the interaction function. For instance, neural collaborative filtering
models such as NeuMF (He et al., 2017) use non-linear functions to capture
interactive patterns between users and items, translation based collaborative
filtering models such as LRML (Tay et al., 2018) employ Euclidean distance
metrics in modeling interaction. DeepFM (Guo et al., 2017) incorporates an FM
layer to replace the wide component in Wide & Deep (Cheng et al., 2016), PNN
(Qu et al., 2016) leverages a multi-layer perceptron (MLP) to model
interaction of a product layer and recently proposed collaborative filtering
methods working on structured data such as GraphHINGE (Jin et al., 2020a)
propose a new convolution-based interaction module on the heterogeneous graph.
The live broadcast recommendation scenarios, as mentioned above, are many
complicated and heterogeneous situations. Hence, we not only extend SVD++
(Koren, 2008) to model correlations in our two-side architecture but propose a
novel co-retrieval model collaborative filtering user’s and anchor’s relevant
histories.

Our architecture design is also closely related to the two-side sequential
networks. For item recommendation task, there are recently emerged literature
(Fu et al., 2021; Wu et al., 2017, 2019; Qin et al., 2020a; Wang et al., 2019)
leveraging the context information from user and item sides to make the final
prediction. Besides the difference between the live broadcast recommendation
and item recommendation tasks, these approaches either consider two-side
information in an independent fashion (Wu et al., 2017, 2019) or model two-
side correlations among all the high-order neighbor users and items (Fu et
al., 2021; Qin et al., 2020a; Wang et al., 2019) which is insufficient in
filtering out noise and employing to long sequential data. In contrast, we
develop a novel interactive network with a co-retrieval mechanism to
efficiently capture the key interactive patterns from two sides.

##  3\. The TWINS Model

###  3.1. Overview

The basic idea of the TWINS is to design a two-side architecture to capture
the rich context hidden in static and dynamic features in both user and anchor
sides. Figure 2 illustrates the overview of TWINS. First, we use the PNN (Qu
et al., 2016) to model the correlations among static attributes for each user,
anchor, and item, as shown in (a)-(d). Second, we leverage the RNN (Hochreiter
and Schmidhuber, 1997) to capture the sequential dependencies hidden in the
user’s and anchor’s dynamic histories, as shown in (b)(c). Third, we design
interactive networks for mining the interactive patterns between user and
anchor sides from item and anchor aspects, as shown in (e)(f). Moreover,
notice that the interaction operations, especially for interactive networks in
item aspect, require the high computation cost; we propose a co-retrieval
mechanism to select the relevant items from the whole user’s and anchor’s
histories to save interaction computations, as shown in (h). After that, we
aggregate these interaction results accompanied with static features of users
and anchors to predict the probability that a user will browse an anchor’s
broadcast room, as shown in (i). We introduce these steps in detail in the
following subsections.

###  3.2. Object Modeling

In classical recommendation models, there are two main objects (i.e., users,
items), while in the live broadcast recommendation scenario, there are three
main objects (i.e., users, anchors, items). As illustrated in Figure 1, for
each pair of user and anchor, we have the static features (attributes), which
are also called categorical data. Notably, there are rich correlations among
these features. For example, the reason why the teen would be interested in
the lipstick in a bright color should both rely on her age AND gender. As
discussed in (Guo et al., 2017; Jin et al., 2020b; Qu et al., 2016), these
“AND” operations can’t solely be modeled by neural networks. Hence, we
introduce the PNN, whose output of the PNN for the $p$-th user can be defined
as

(1)
$\bm{e}^{u}_{p}\coloneqq\mathtt{f}^{u}_{\mathtt{PNN}}(\bm{x}^{u}_{p})=\bm{v}^{u}_{p}\odot\bm{x}^{u}_{p}+\sum^{J}_{j^{\prime}=1}\sum^{J}_{j^{\prime\prime}=j^{\prime}+1}(\bm{v}^{u}_{j^{\prime}}\odot\bm{v}^{u}_{j^{\prime\prime}})\bm{x}^{uj^{\prime}}_{p}\cdot\bm{x}^{uj^{\prime\prime}}_{p},$

where $\bm{v}^{u}_{p}$ and $\bm{v}^{u}_{j}$ are trainable latent vectors and
$\odot$ is the element-wise product operator. The first term is addition units
showing the influence of (first-order) linear feature interactions, and the
second term is element-wise product units representing the impact of (second-
order) pair-wise feature interactions.

Consider that there are also static features for each anchor and item.
Analogously, we define
$\bm{e}^{a}_{n}\coloneqq\mathtt{f}^{a}_{\mathtt{PNN}}(\bm{x}^{a}_{n})$ as the
output of the $n$-th anchor and
$\bm{e}^{i}_{q}\coloneqq\mathtt{f}^{i}_{\mathtt{PNN}}(\bm{x}^{i}_{q})$ as the
output of the $q$-th item where $\mathtt{f}^{a}_{\mathtt{PNN}}(\cdot)$ and
$\mathtt{f}^{i}_{\mathtt{PNN}}(\cdot)$ share the same formulation with
$\mathtt{f}^{u}_{\mathtt{PNN}}(\cdot)$ but with different parameters.

Notice that besides the static features, the portrait of a user and the theme
of an anchor are closely related to their dynamic histories, such as user’s
browsing items and anchor’s broadcasting items, as illustrated in Figure
2(b)(c). A principal way to model these dynamic histories is to construct a
sequential model such as the RNN model. Let $\bm{h}^{i}_{q}$ denote the output
of the $q$-th item, which can be calculated by

(2)
$\bm{h}^{i}_{q}\coloneqq\mathtt{f}^{i}_{\mathtt{RNN}}(\bm{e}^{i}_{q}|\bm{b}^{i}_{q-1}),$

where $\mathtt{f}^{i}_{\mathtt{RNN}}(\cdot)$ is the RNN cell and
$\bm{b}^{i}_{q-1}$ is the hidden vector computed from the last RNN cell. In
our paper, we implement the RNN cell as a standard LSTM unit (Hochreiter and
Schmidhuber, 1997). As the major objects for browsing and broadcasting are
items, we only build the RNN model for sequences of items.

###  3.3. Interactive Network

By encoding the static and dynamic features in triple objects, we obtain the
embedding vectors of the $p$-th user (i.e., $\bm{e}^{u}_{p}$), the $q$-th item
(i.e., $\bm{h}^{i}_{q}$), and $n$-th anchor (i.e., $\bm{e}^{a}_{n}$), as shown
in Figure 2. We then consider mining the interactive patterns by the “AND”
operation. The motivation behind this is straightforward. Take Figure 2 as an
instance. The teen $u_{1}$ enters the broadcasting room because the host
anchor $a_{1}$ sells her favored items AND the anchor $a_{1}$ shares the
similar interest with her favored anchors. Thus, we model these interactive
patterns in two aspects, namely item and anchor aspects.

Item Aspect. For item aspect, as illustrated in Figure 2(e), TWINS captures
the interactive patterns by measuring the similarities between user and anchor
together with their related items. A principal way is to follow the basic idea
of SVD++ (Koren, 2008) model, and then the interaction similarity of the
$p$-th user $u_{p}$ and the $n$-th anchor $a_{n}$ can be formulated as

(3)
$y^{i}_{pn}=(\bm{e}^{u}_{p}+\sum_{q^{\prime}\in\mathcal{H}^{ui}_{p}}\lambda_{pq^{\prime}}\bm{h}^{i}_{q^{\prime}})^{\top}\cdot(\bm{e}^{a}_{n}+\sum_{q^{\prime\prime}\in\mathcal{H}^{ai}_{n}}\beta_{nq^{\prime\prime}}\bm{h}^{i}_{q^{\prime\prime}}).$

Clearly by assigning $\lambda_{pq^{\prime}}$ and $\beta_{nq^{\prime\prime}}$
as $1/\sqrt{|\mathcal{H}^{ui}_{p}|}$ and $0$ separately, we can exactly
recover using the classical SVD++ model to measure the similarity between
$u_{p}$ and $a_{n}$. Notably, as users browsing the same items are normally
diversified, it’s non-trivial to capture the useful information from abundant
context information of these users. Hence, the classical SVD++ model,
originally proposed for the similarity between users and items, doesn’t
involve this information (i.e., $\beta_{nq^{\prime\prime}}=0$). Instead, as
shown in the right part of Eq. (3), we use the broadcast items to enrich the
representation of $a_{n}$, which is much clean and informative.

As discussed in (Wang et al., 2019; Qu et al., 2019; Jin et al., 2020b), many
existing methods (including the interactive network built following Eq. (3))
suffer from the “early summarization” issue, as these approaches, when
extending to similarity measurement between users and anchors, usually
compress user-related and anchor-related items into single user/anchor
embeddings before the final prediction. In this case, only two objects are
activated, yet other related objects (e.g., items) and their correlations are
mixed and relayed. We argue that these rich correlations (i.e., interactive
patterns) are essential in the recommendation. Taking Figure 2(e) as an
instance, a system is considering to recommend an anchor (e.g., $a_{1}$) to a
user (e.g., $u_{1}$). Suppose that $u_{1}$’s personal interest mainly lies in
shoes, then the similarity between ($i_{1}$ and $i_{5}$), ($i_{3}$ and
$i_{5}$) should be emphasized. Therefore, we propose a bi-attention network to
better capture these interactive patterns, which can be formulated as follows:

(4) $\displaystyle\alpha^{i}_{pq^{\prime}nq^{\prime\prime}}$
$\displaystyle=\mathtt{f}^{i}_{\mathtt{softmax}}(\bm{w}_{pq^{\prime}nq^{\prime\prime}}^{i\top}[\bm{e}^{u}_{p},\bm{h}^{i}_{q^{\prime}},\bm{e}^{a}_{n},\bm{h}^{i}_{q^{\prime\prime}}]+b^{i}_{pq^{\prime}nq^{\prime\prime}}),$
$\displaystyle\bm{y}^{i}_{pn}$
$\displaystyle=\sum_{q^{\prime}\in\mathcal{H}^{ui}_{p}}\sum_{q^{\prime\prime}\in\mathcal{H}^{ai}_{n}}\alpha_{pq^{\prime}nq^{\prime\prime}}(\bm{h}^{i}_{q^{\prime\prime}}\odot\bm{h}^{i}_{q^{\prime\prime}}),$

where $[\cdot,\cdot]$ denotes a concatenation operator. and
$\mathtt{f}^{i}_{\mathtt{softmax}}(\cdot)$ denotes a softmax function.
Comparing to Eq. (3), Eq. (4) takes both user- and anchor-side items to
generate differentiable weights distinctive to different interaction terms.

Anchor Aspect. For the anchor aspect, as shown in Figure 2(f), TWINS aims to
formulate the similarities between the user along with her browsed anchors and
target anchor. Sharing the same motivation with an interactive network of item
aspect, we formulate the interaction operation as follows:

(5) $\displaystyle\alpha^{a}_{pn^{\prime}n}$
$\displaystyle=\mathtt{f}^{a}_{\mathtt{softmax}}(\bm{w}_{pn^{\prime}nn^{\prime\prime}}^{i\top}[\bm{e}^{u}_{p},\bm{e}^{a}_{n^{\prime}},\bm{e}^{a}_{n}]+b^{a}_{pn^{\prime}n}),$
$\displaystyle\bm{y}^{a}_{pn}$
$\displaystyle=\sum_{n^{\prime}\in\mathcal{H}^{ua}_{p}}\alpha_{pn^{\prime}n}(\bm{e}^{a}_{n^{\prime}}\odot\bm{e}^{a}_{n}),$

where $\mathtt{f}^{a}_{\mathtt{softmax}}(\cdot)$ denotes a softmax function
with different weight from $\mathtt{f}^{i}_{\mathtt{softmax}}(\cdot)$.

###  3.4. Co-Retrieval Mechanism

Notably, comparing Eq. (4) to Eq. (5), one can easily see that interactive
networks of item aspect require to compute the similarity among
$|\mathcal{H}^{ui}_{p}|\times|\mathcal{H}^{ai}_{n}|$ operations for each user-
anchor pair $(u_{p},a_{n})$ which is much more time-consuming than that of
anchor aspect whose computation costs lie in $|\mathcal{H}^{ua}_{p}|$
operations. Therefore, the former one blocks TWINS from working in the real-
world industrial scenario, especially with long sequential data (Pi et al.,
2020).

In order to effectively implement the interactive network of item aspect, we
introduce a novel co-retrieval mechanism, whose basic idea is to find a subset
of user’s and anchor’s related items to feed in the network instead of using
the whole data.

Inspired by recently merged search-based methods (Pi et al., 2020; Qin et al.,
2020b), we design a hard-search co-retrieval model without any parametric,
where only items belongs to the common categories of user and anchor sides
will be selected as the candidate items to feed into the interactive network.
Formally, we first construct a set of categories for user and anchor sides
respectively, namely
$\mathcal{C}^{u}_{p}=\\{\bm{x}^{i1}_{q^{\prime}}|i_{q^{\prime}}\in\mathcal{H}^{ui}_{p}\\}$
and
$\mathcal{C}^{a}_{n}=\\{\bm{x}^{i1}_{q^{\prime\prime}}|i_{q^{\prime\prime}}\in\mathcal{H}^{ai}_{n}\\}$.
We then compute a set of the common categories as
$\mathcal{C}^{ua}_{pn}=\mathcal{C}^{u}_{p}\cap\mathcal{C}^{a}_{n}$. We
establish a retrieved set of $\mathcal{H}^{ui}_{p}$ and $\mathcal{H}^{ai}_{n}$
in Eq. (4) by following

(6) $\displaystyle\widehat{\mathcal{H}}^{ui}_{p}$
$\displaystyle=\\{i_{q^{\prime}}|i_{q^{\prime}}\in\mathcal{H}^{ui}_{p}\text{
and }\bm{x}^{i1}_{q^{\prime}}\in\mathcal{C}^{ua}_{pn}\\},$
$\displaystyle\widehat{\mathcal{H}}^{ai}_{n}$
$\displaystyle=\\{i_{q^{\prime\prime}}|i_{q^{\prime\prime}}\in\mathcal{H}^{ai}_{n}\text{
and }\bm{x}^{i1}_{q^{\prime\prime}}\in\mathcal{C}^{ua}_{pn}\\}.$

Clearly, $\widehat{\mathcal{H}}^{ui}_{p}$ and $\widehat{\mathcal{H}}^{ai}_{n}$
are subsets of $\mathcal{H}^{ui}_{p}$ and $\mathcal{H}^{ai}_{n}$ respectively.
One can directly replace $\mathcal{H}^{ui}_{p}$, $\mathcal{H}^{ai}_{n}$ by
$\widehat{\mathcal{H}}^{ui}_{p}$, $\widehat{\mathcal{H}}^{ai}_{n}$ in Eq. (4)
to save computations.

###  3.5. Optimization Objective

After primitively modeling each object and further interactive pattern mining,
for each user-anchor pair (e.g., ($u_{p},a_{n}$)), we can obtain the
similarity based on their embedding vector namely
$\bm{y}^{e}_{pn}=\bm{e}^{u}_{p}$ $\odot$ $\bm{e}^{a}_{n}$. As we have already
obtained item aspect interaction result $\bm{y}^{i}_{pn}$ and anchor aspect
interaction result $\bm{y}^{a}_{pn}$, we further aggregate them together to
produce the final similarly by combining a sigmoid function with a MLP layer
over the concatenation of these embeddings as

(7)
$\widehat{y}_{pn}=\text{sigmoid}(\mathtt{f}_{\mathtt{MLP}}([\bm{y}^{e}_{pn},\bm{y}^{i}_{pn},\bm{y}^{a}_{pn}])).$

We then use the log loss as the objective:

(8)
$\mathcal{L}=-\sum_{(u_{p},a_{n})\in\mathcal{D}}(y_{pn}\log\widehat{y}_{pn}+(1-y_{pn})\log(1-\widehat{y}_{pn})),$

where $\mathcal{D}=(\mathcal{U},\mathcal{A})$ denotes the dataset and $y_{pn}$
is the label of each user-anchor instance.

We provide the learning algorithm of TWINS in Algorithm 1. We also provide the
corresponding analysis of TWINS in Appendix A.

0: dataset $\mathcal{D}=(\mathcal{U},\mathcal{A})$ with historical data
$\mathcal{H}^{u}$, $\mathcal{H}^{a}$;

0: TWINS recommender with parameter $\theta$

1: Initialize all parameters.

2: repeat

3: Randomly sample a batch $\mathcal{B}$ from $\mathcal{D}$

4: for each data instance $(u_{p},a_{n})$ in $\mathcal{B}$ do

5: Calculate embedding vectors for all related user, anchors, items using
static features via FM model as Eq. (1).

6: Compute embedding vectors for all sequential items using dynamic features
via RNN model as Eq. (2).

7: Obtain item aspect similarity $\bm{y}^{i}_{pn}$ using Eq. (4).

8: Obtain anchor aspect similarity $\bm{y}^{a}_{pn}$ using Eq. (5).

9: end for

10: Compute $\mathcal{L}$ and update $\theta$ by minimizing Eq. (8).

11: until convergence

Algorithm 1 TWINS

##  4\. Offline Experiments

###  4.1. Dataset and Experimental Flow

We conduct offline experiments on four real-world datasets, namely Yelp
business dataset111https://www.yelp.com/dataset/documentation/main, Trust
statement dataset222http://www.trustlet.org/downloaded_epinions.html, Aminer
citation dataset333https://www.aminer.cn/citation, Diantao live broadcast
dataset, where the first three are public benchmark datasets and the last one
is created by our own. We provide detailed description of the last dataset as
follows, and offer the description of others in Appendix B.

  * •

Diantao Live Broadcast Recommendation dataset is collected from the user
interaction logs of Diantao App. It contains more than 1.46 billion logs of
over 10 million users’ browsing histories with 90 thousand anchors. Features
of the user include age, gender, city, etc., and features of the document
include title, time, etc. In each query, we regard the documents whose
playtime are more than $3$s as the clicked ones.

Please refer to Appendix C for detailed experimental configuration.

###  4.2. Baseline and Evaluation Metric

We make comprehensive comparisons between our model and 9 representative
baseline methods, introduced as follows.

  * •

FM (Rendle, 2010) is the factorization machine that uses the linear projection
and inner product of features to measure the user-item similarity.

  * •

NeuMF (He et al., 2017) is a generalized model consisting of a matrix
factorization (MF) and a MLP component.

  * •

DeepFM (Guo et al., 2017) is a generalized model consisting of a FM as a wide
component and a MLP as a deep component.

  * •

PNN (Qu et al., 2016) is the product-based neural network consisting of a
embedding layer and a product layer to capture interactive patterns.

  * •

LSTM (Hochreiter and Schmidhuber, 1997) is the long short term memory network
widely used to model sequential data.

  * •

NARM (Wu et al., 2017) is a sequential recommendation model, which uses
attention mechanism to capture the influence of user behaviors.

  * •

ESMM (Li et al., 2017) is a multi-objective model which applies a feature
representation transfer learning strategy on user behaviors.

  * •

DIN (Zhou et al., 2018) designs a local activation unit to adaptively learn
the representation of user interests from historical behaviors.

  * •

DIEN (Zhou et al., 2019) builds an interest extractor layer based on DIN to
capture temporal interests from historical behavior sequence.

Note that as all these methods are originally proposed particularly for
classical item-based recommendation tasks definitively different from the live
broadcast recommendation task, thus we introduce two versions of
implementation. Taking LSTM as an instance, we use the model for the
historical sequences of user browsed anchors (denoted as LSTM-). Also, we can
first use LSTM to model the historical sequences of user browsed anchors,
anchor broadcast items, user browsed items, and then fuse this information via
a MLP layer with a sigmoid function to generate the final prediction (denoted
as LSTM). For those tabular recommendation models such as FM, we apply the
model for binary interactions between users and anchors (denoted as FM).

In order to further investigate the effect from each component of TWINS, we
design the following three variants:

  * •

TWINS is our model without co-retrieval mechanism.

  * •

TWINS${}^{-}_{i}$ is a variant of TWINS, applying the original model without
the interactive network from item aspect.

  * •

TWINS${}^{-}_{a}$ is a variant of TWINS, applying the original model without
the interactive network from anchor aspect.

  * •

TWINS${}^{+}_{\text{co}}$ is a variant of TWINS using co-retrieval mechanism.

To evaluate the above methods, we choose Area user the ROC Curve (AUC),
Accuracy (ACC), LogLoss as evaluation measurements. The threshold of ACC of
all the datasets is set as 0.5.

Figure 3.  Comparisons of performance of baselines taking the information of
anchor side or user side as the input on Aminer citation dataset.  Table 1.
Comparison of different models on four industrial datasets. Results of Click-
Through Rate (CTR) in term of AUC, ACC, LogLoss are reported. * indicates
$p<0.001$ in significance tests compared to the best baseline.

Methods | Yelp Business Dataset | Trust Statement Dataset | Aminer Citation Dataset | Diantao Live Broadcast Dataset
---|---|---|---|---
LogLoss | ACC | AUC | LogLoss | ACC | AUC | LogLoss | ACC | AUC | LogLoss | ACC | AUC
FM | 0.6677 | 0.5945 | 0.6233 | 0.6188 | 0.7003 | 0.7574 | 0.6510 | 0.6430 | 0.7071 | 0.6541 | 0.6732 | 0.6896
NeuMF | 0.4895 | 0.7759 | 0.8424 | 0.4814 | 0.7835 | 0.8440 | 0.4797 | 0.7882 | 0.8542 | 0.5942 | 0.7124 | 0.7229
DeepFM | 0.4594 | 0.7925 | 0.8658 | 0.4545 | 0.8054 | 0.8756 | 0.4410 | 0.8049 | 0.8826 | 0.5832 | 0.7231 | 0.7345
PNN | 0.4581 | 0.7931 | 0.8668 | 0.4452 | 0.8144 | 0.8838 | 0.3932 | 0.8789 | 0.9399 | 0.5432 | 0.7367 | 0.7578
DIN- | 0.3256 | 0.8731 | 0.9420 | 0.4164 | 0.8457 | 0.9154 | 0.1847 | 0.9423 | 0.9799 | 0.5231 | 0.7564 | 0.7790
DIN | 0.3156 | 0.8782 | 0.9451 | 0.3771 | 0.8394 | 0.9114 | 0.1212 | 0.9581 | 0.9892 | 0.5100 | 0.7784 | 0.7995
LSTM- | 0.3236 | 0.8736 | 0.9433 | 0.3931 | 0.8271 | 0.9012 | 0.2218 | 0.9204 | 0.9708 | 0.5334 | 0.7529 | 0.7602
LSTM | 0.3204 | 0.8783 | 0.9445 | 0.3854 | 0.8325 | 0.9051 | 0.1214 | 0.9575 | 0.9891 | 0.5321 | 0.7602 | 0.7789
NARM- | 0.3132 | 0.8811 | 0.9463 | 0.3916 | 0.8306 | 0.9037 | 0.2156 | 0.9216 | 0.9720 | 0.5421 | 0.7432 | 0.7667
NARM | 0.3137 | 0.8808 | 0.9463 | 0.3839 | 0.8339 | 0.9060 | 0.1200 | 0.9580 | 0.9893 | 0.5233 | 0.7756 | 0.7953
ESMM- | 0.3224 | 0.8722 | 0.9414 | 0.3959 | 0.8268 | 0.9008 | 0.2402 | 0.9110 | 0.9655 | 0.5334 | 0.7456 | 0.7698
ESMM | 0.3150 | 0.8776 | 0.9448 | 0.4035 | 0.8262 | 0.8991 | 0.1241 | 0.9564 | 0.9887 | 0.5175 | 0.7753 | 0.7985
DIEN- | 0.3198 | 0.8723 | 0.9401 | 0.4018 | 0.8388 | 0.9091 | 0.2254 | 0.9183 | 0.9698 | 0.5252 | 0.7657 | 0.7854
DIEN | 0.3291 | 0.8646 | 0.9395 | 0.3911 | 0.8308 | 0.9022 | 0.1242 | 0.9563 | 0.9887 | 0.5145 | 0.7843 | 0.8046
TWINS${}^{-}_{i}$ | 0.2746 | 0.8879 | 0.9538 | 0.3685 | 0.8452 | 0.9174 | 0.1246 | 0.9616 | 0.9893 | 0.5012 | 0.7896 | 0.8010
TWINS${}^{-}_{a}$ | 0.2608 | 0.8948 | 0.9583 | 0.3660 | 0.8446 | 0.9170 | 0.1233 | 0.9622 | 0.9895 | 0.4977 | 0.7920 | 0.8024
TWINS | 0.2603∗ | 0.9120∗ | 0.9659∗ | 0.3528∗ | 0.8501∗ | 0.9235∗ | 0.1081∗ | 0.9631∗ | 0.9913∗ | 0.4855∗ | 0.7934∗ | 0.8187∗
TWINS${}^{+}_{\text{co}}$ | 0.2596∗ | 0.8962∗ | 0.9593∗ | 0.3579∗ | 0.8458∗ | 0.9194∗ | 0.1170∗ | 0.9612∗ | 0.9903∗ | 0.4731∗ | 0.8045∗ | 0.8205∗

###  4.3. Performance Evaluation

Overall Performance. Table 1 summarizes the results. The major findings from
our experiments are summarized as follows.

  * •

Compared to the version of only using user browsed anchors (denoted as X- and
X can be DIN, LSTM, NARM, ESMM, DIEN), in most cases, X achieves better
performance, which verifies to further include user browsed items and anchor
browsed items as the input. One also observe in some cases, X- obtains better
performance, which may be explained as a simple aggregation operation (e.g.,
concatenation) that can not fully use this information, sometimes even
bringing the noise.

  * •

Our model outperforms all these baseline methods, including widely adopted
industrial recommendation methods (e.g., DeepFM, ESMM, DIN, DIEN), interaction
models (e.g., FM, PNN), and sequential models (e.g., NARM, LSTM). As the
inputs are the same, these results would indicate the superiority of
developing interactive networks based on the two-side architecture.

  * •

With the comparison between LSTM to other baseline methods, we see that LSTM
can consistently achieve comparable or even better performance than
interaction models (i.e., FM, NeuMF, DeepFM, PNN), which verifies the
necessity of mining the sequential patterns of users and anchors.

Impact of Interaction Networks. From comparisons between TWINS and
TWINS${}^{-}_{i}$, TWINS and TWINS${}^{-}_{a}$, TWINS consistently achieves
better performance than TWINS${}^{-}_{i}$ and TWINS${}^{-}_{a}$ in all the
datasets. One explanation is that our interactive networks are able to provide
interactive (i.e., “AND”) patterns, which can not be solely modeled by
employing a neural network. By comparing TWINS${}^{-}_{i}$ to
TWINS${}^{-}_{a}$, TWINS${}^{-}_{a}$ usually can gain better performance. One
possible reason for this is that in the live broadcast recommendation system,
the similarities between users and anchors mainly depend on their browsed and
broadcast items. Namely, the reason that a user watches an anchor mainly lies
in that the anchor is selling some items that she is interested in.

Impact of Co-Retrieval Mechanism. Comparing TWINS${}^{+}_{\text{co}}$ to
TWINS, we can observe that TWINS${}^{+}_{\text{co}}$ can achieve a comparable,
or even better, result in these datasets. This result is consistent with the
result of the hard-search reported in (Pi et al., 2020), both of which reveal
that category information plays a vital role in selecting relevant items. We
then further report their training and inference time in Figure 4 to verify
that TWINS with the proposed co-retrieval mechanism is more efficient and thus
could deal with long-sequential data.

Figure 4.  Training/inference time comparisons of TWINS and
TWINS${}_{\text{co}}$ against baselines on Aminer citation dataset.

Impact of Two-Side Information. As introduced in Section 2.1, there are three
sequential data in user and anchor sides, namely a sequence of user browsed
anchors denoted as $\mathcal{H}^{ua}$, a sequence of user browsed items
denoted as $\mathcal{H}^{ui}$ and a sequence of anchor broadcast items denoted
as $\mathcal{H}^{ai}$, where the first two sequences are of user side and the
last one sequence is of anchor side. Since the main difference between live
broadcast recommendation and item recommendation is that the former one
requires us to take the information of both user and anchor sides into
consideration, while the latter one is designed to model the information from
one sequential data of one side (usually $\mathcal{H}^{ua}$). Results in Table
1 shows the results of using $\mathcal{H}^{ua}$ (denoted as X-) and using all
these sequences fused by a concatenation operation (denoted as X). We further
investigate the performance gain of X- by adding $\mathcal{H}^{ui}$ (denoted
as User Side) or $\mathcal{H}^{ai}$ (denoted as Anchor Side) into the input.
From Figure 3, we see that $\mathcal{H}^{ai}$ is more useful for X- than
$\mathcal{H}^{ui}$. One explanation is that we already have $\mathcal{H}^{ua}$
as the information on the user side and no the information on anchor side.
Hence, $\mathcal{H}^{ai}$ can offer more important information than
$\mathcal{H}^{ui}$.

Complexity Analysis. We investigate the time complexity of TWINS and
TWINS${}_{\text{co}}$ against baseline methods such as PNN, LSTM, NARM, ESMM,
DIN, DIEN, and report the training and inference times for one round of the
whole data. As Figure 4 depicts, sequential methods (e.g., NARM, DIEN) are
less efficient than other methods (e.g., PNN). Also, we can see that
TWINS${}^{+}_{\text{co}}$ is more effective, as it can reduce the computation
costs of interactive networks. One can also use the co-retrieval mechanism in
object modeling, where only retrieved items are fed into the RNN model instead
of the whole set of items, to reduce the computation costs from the RNN model.

##  5\. Online Experiments

###  5.1. Experimental Flow

In order to verify the effectiveness of TWINS${}^{+}_{\text{co}}$ in real-
world live broadcast recommendation applications, we deploy our method in
Diantao App, a main-stream live broadcast App sharing all the anchors with
Taobao e-commerce platform, which has tens of millions of daily active users
who create hundreds of millions of user logs every day in the form of implicit
feedbacks such as click, watch behaviors. For simplicity, we use TWINS to
denote our method and use TWINS${}^{+}_{\text{co}}$ as the implementation. We
develop two kinds of techniques to light the current TWINS model and develop
an effective data structure, as shown in Figure 7. We further introduce their
details along with our hands-on experience of implementing TWINS in Alibaba in
Appendix D.

Table 2. Improvement of TWINS against current production method on real-world
recommendation scenarios.

Recommender | ACTR | UCTR | UCVR
---|---|---|---
TWINS | 8.11% | 2.01% | 3.52%

For the online experiment, we conduct A/B testing comparing the proposed model
TWINS with the current production method. The whole experiment lasts a week,
from September 25, 2021 to October 2, 2021. During A/B testing, 5% of the
users are presented with the recommendation by the current production method,
while 5% of the users are presented with the recommendation by TWINS.

###  5.2. Performance Evaluation

We examine the online performance using three metrics. The first one is to
measure the CTR performance from the anchor aspect, which is called ACTR
metric defined as $\text{ACTR}=\frac{\\#\text{clicks on
anchors}}{\\#\text{impressions on anchors}}$ where #clicks on anchors and
#impressions on anchors are the number of clicks and impressions on all the
anchors. The second one is to measure the CTR performance from the user
aspect, which is called UCTR metric defined as
$\text{UCTR}=\frac{\\#\text{clicks on users}}{\\#\text{impressions on users}}$
where #clicks on users is the number of users that have performed click
behaviors, and #impressions on users is the total number of users. The third
one is to measure the CVR performance from the user aspect, which is called
UCVR metric defined as $\text{UCTR}=\frac{\\#\text{conversions on
users}}{\\#\text{impressions on users}}$ where #conversions on users is the
number of users that have performed conversion behaviors, and #impressions on
users is the total number of users. We report the average results in Table 2.
One can notice that TWINS consistently achieves better performance in terms of
all the metrics.

###  5.3. Case Study

Finally, we conduct case study to reveal the inner structure of TWINS on
Diantao App. Figure 5 illustrates the interaction patterns between each pair
of items in user and anchor sides, where the ones with similar colors means
the high interaction weights. As expected, we can see that these interaction
weights can well reflect the corresponding correlations. For example, clothes
including pants and shirt have the same color (i.e., yellow), and have the
similar color with cosmetics containing perfume and lipstick (i.e., red).
Based on them, TWINS can recommend appropriate anchors to the user. We note
that as shown in Figure 5, the recommended anchors can be in range from high
popularity to low popularity. We argue that it is quite meaningful in the
practice nowadays where the top popular anchors can usually attach most users’
attentions, which is similar to the popularity bias (Chen et al., 2020) in
traditional recommendation task. Therefore, the proposed method can
simultaneously improve the performance of the recommendation while mitigating
the bias issue (i.e., not always recommending the anchors with the high
popularity to different users).

##  6\. Conclusion and Future Work

In this paper, we investigate a recently emerged live broadcast recommendation
and propose a novel two-side framework named TWINS, where we design
interactive networks from item and anchor aspects to capture the rich
interactive patterns in user and anchor sides. In addition, we also develop a
co-retrieval mechanism to reduce the high computation costs of the interactive
network from the item aspect. For future work, it would be interesting to
combine TWINS with multi-tasking learning techniques to effectively use user
various behaviors (e.g., click, like, comment).

Acknowledgments. This work was supported by Alibaba Group through Alibaba
Research Intern Program. The Shanghai Jiao Tong University Team is supported
by Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102)
and National Natural Science Foundation of China (62076161, 62177033). We
would also like to thank Wu Wen Jun Honorary Doctoral Scholarship from AI
Institute, Shanghai Jiao Tong University.

Figure 5.  Illustration of the interaction patterns of TWINS in the case of
predicting the relevance between a user and different anchors with the
different popularity. Each pair of Items with similar color demonstrates the
high interaction weights (i.e., correlations) between two items.

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##  Appendix A Model Analysis of TWINS

The learning algorithm of TWINS is given in Algorithm 1. As classical item
recommendation methods (Koren et al., 2009; Qu et al., 2016) often use the
inner-product of user and item embedding vectors (i.e., $\bm{y}_{pn}^{e}$) to
measure their similarity, we further clarify our motivations to involve
interaction results from both item and anchor aspects. Solely using
$\bm{y}_{pn}^{e}$ for learning the model may be sufficient to fit the true
conditional probability
$P(y_{pn}|(u_{p},a_{n}),\mathcal{H}_{p}^{u},\mathcal{H}_{n}^{a})$, if we are
accessible to the labels of all the possible user-anchor pairs. However, the
limited user observations over anchors in practice would lead the limited
performance. Concretely, we can divide those unobserved samples into two
parts, namely, unobserved positive and unobserved negative samples. The former
class refers to samples where the users would show positive feedbacks (e.g.,
click) if browsing the anchors, while the latter class refers to samples where
the users would show negative feedbacks (e.g., not click) if browsing the
anchors. As under most circumstances, there is no auxiliary information to
distinguish these two classes; all the unobserved samples are often directly
treated as negative samples, which indeed provides wrong supervisions for
learning the model.

Fortunately, we reveal that TWINS is an effective solution to alleviate the
issue above. Compared with unobserved negative samples, we argue that
unobserved positive samples are more likely to have correlations with observed
positive samples. Such correlations can either come from sharing similar
anchors or similar items in users’ browsing history $\mathcal{H}^{u}_{p}$ and
anchor’s broadcast history $\mathcal{H}^{a}_{n}$. We argue that the former
correlations can be captured by our anchor aspect interactions, and the latter
ones can be modeled by our item aspect interactions. Take Figure 6 as an
instance, where the original position of each sample represents the
probability of receiving positive feedbacks from users solely governed by
$\bm{y}^{e}_{pn}$, and arrows denote the force from $\bm{y}^{u}_{pn}$ and
$\bm{y}^{a}_{pn}$. We consider two specific user-anchor pairs $(u_{1},a_{1})$
and $(u_{2},a_{2})$. Suppose that $a_{1}$ has a strong correlation with one of
$u_{1}$’s desired anchors, then $\bm{y}^{a}_{pn}$ would push the sample to a
relatively high probability from anchor aspect interaction. Similarly, assume
that $u_{2}$’s browsed items is correlated with one of $a_{2}$’s broadcast
items, then $\bm{y}^{u}_{pn}$ would push the sample to a relatively high
probability from item aspect interaction. Notably, these two samples are
common among all unobserved samples. Therefore, once the loss $\mathcal{L}$
that fuses all these information converges, the unobserved positive samples
would be more likely to be located at the right or upper side of the decision
boundary than the negative ones.

Figure 6.  An illustrated example of training for TWINS with item aspect and
anchor aspect interactions, where the original position of each sample
represents the probability of receiving positive feedbacks from users (e.g.,
click) solely according to $\bm{y}^{e}_{pn}$, and arrows show the force from
$\bm{y}^{u}_{pn}$ and $\bm{y}^{a}_{pn}$.

##  Appendix B Dataset Description

We provide the detailed description for three real-world public benchmark
datasets as follows.

  * •

Yelp business dataset444https://www.yelp.com/dataset/documentation/main is
formed of Yelp business data recording business interactions among
businessmen. It consists of around 35,943,096 interactions among 1,233,453
businessmen through more than 160,310 business cases. We treat the interaction
between two businessmen as the interaction between a user and an anchor. And
we regard those business cases as items. The average sequence length of
browsing logs of users and anchors is 5.17.

  * •

Trust statement dataset555http://www.trustlet.org/downloaded_epinions.html is
collected by Paolo Massa from the Epinions.com Web site in a 5-week period
from November, 2003 to December, 2003. It contains the logs of 49,290 people
who rated a total of 139,738 different documents at least once, writing
664,824 reviews and 487,181 issued trust statements. People and documents are
represented by anonimized numeric identifiers. We treat the trust record
between two people as the interaction between a user and anchor. And we regard
those documents as items. The average sequence length of browsing logs of
users and anchors is 16.55.

  * •

Aminer citation dataset666https://www.aminer.cn/citation (Tang et al., 2008)
is extracted from DBLP, ACM, MAG (Microsoft Academic Graph), and other
sources. It contains 622,196 authors writing 243,266 papers, and 10,368,942
citations. Each paper is associated with abstract, authors, year, venue, and
title. We treat the citation-relation between two authors as the interaction
between a user and an anchor. And we regard those papers as items. The average
sequence length of browsing logs of users and anchors is 2.33.

We don’t use some widely adapted e-commerce datasets created by Alibaba or
Amazon, because they only can provide the sequential data in other sides. More
specifically, these datasets such as Tmall
dataset777https://tianchi.aliyun.com/dataset/dataDetail?dataId=42, Taobao
E-Commerce
dataset888https://tianchi.aliyun.com/datalab/dataSet.html?dataId=408, Alipay
dataset999https://tianchi.aliyun.com/dataset/dataDetail?dataId=53 only contain
user’s browsing logs (i.e., the sequential data in user side), which are
definitely not suitable to simulate the live broadcast triple-object
interaction cases. Notice that although some entities in the above dataset can
be used as either users or anchors, our model will not reduce the one-side
architecture, because the two-side architecture of TWINS is asymmetric, as we
involve the interactive network from user aspect.

Figure 7.  Online live broadcast recommender system with proposed TWINS model
that partly shares similar idea with (Pi et al., 2020). The new system
lightens the TWINS model, and builds tree structures for user browsing
histories and anchor histories in a offline fashion to save computation and
latency costs for online serving.

##  Appendix C Experimental Configuration

We randomly split each dataset into training/validation/test sets at 6:2:2.
The learning rate is decreased from the initial value $1\times 10^{-2}$ to
$1\times 10^{-6}$ during the training process. The batch size is set as
$2000$. The weight for L2 regularization term is $4\times 10^{-4}$. The
dropout rate is set as $0.5$. The dimension of embedding vectors is set as
$64$. The length of co-retrieval is set as $10$. All the models are trained
under the same hardware settings with 16-Core AMD Ryzen 9 5950X (2.194GHZ),
62.78GB RAM, NVIDIA GeForce RTX 3080 cards.

##  Appendix D Deployment Discussion

In this section, we introduce our hands-on experience of deploying TWINS in
the live broadcast recommender system in Alibaba. As industrial recommender or
ranker systems are required to response to massive traffic requests in a short
time interval (e.g., one second (Pi et al., 2020)), then the storage and
latency constraints would become the main bottleneck for deploying existing
search-based model (Pi et al., 2020) and sequential model (Pi et al., 2019) to
the online system. We here develop two kinds of techniques to light the
current TWINS model and develop an effective data structure, and introduce a
new online live broadcast recommender system in Figure 7. We further show the
details as follows.

Light Version of Module. As the main computation costs come from the RNN model
(as shown in Eq. (2)) and the bi-attention model (as shown in Eqs. (4) and
(5)), we tweak the original version of the TWINS model to obtain its light
version. Specifically, for the RNN model, inspired by LightRNN (Li et al.,
2016), we use 2-Component (2C) shared embedding for item representations;
while for the bi-attention model, we remove $\bm{e}^{u}_{p}$ and
$\bm{e}^{a}_{n}$ to reduce the computation costs.

Tree Structure of Data. Following the main idea of the implementation part in
(Pi et al., 2020), we build two-level structured index for each user and
anchor, which we call as user browsing tree and anchor broadcast tree
respectively as illustrated in Figure 7. More concretely, these trees follow
the Key-Key-Value data structure where the first key is user id, the second
keys are category ids of browsed items, and the last values are the specific
behavior items that belong to each category. For each user-anchor pair, we
take the categories of the common ones in user’s browsed items and anchor’s
broadcast items. After applying the proposed co-retrieval mechanism, the
length of user’s and anchor’s item sequences can be significantly reduced
which indeed releases much storage pressure in the online system. Besides,
these tree structures can be pre-built in an offline manner.


# Paring density waves as the origin of a ring-like RIXS profile in
Bi2Sr2CaCu2O8+δ

David Dentelski  Department of Physics, Bar-Ilan University, Ramat Gan
5290002, Israel  Center for Quantum Entanglement Science and Technology, Bar-
Ilan University, Ramat Gan 5290002, Israel  Emanuele G. Dalla Torre
Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel  Center
for Quantum Entanglement Science and Technology, Bar-Ilan University, Ramat
Gan 5290002, Israel

The coexistence of a homogeneous d-wave gap and short-ranged pairing density
waves (PDW) accounts for the apparent “ring” charge order in all directions of
the copper oxide plane, observed by recent RIXS measurements in
Bi2Sr2CaCu2O8+δ (Bi2212) [1].

Almost twenty years ago, scanning tunneling experiments found incommensurate
density waves on the surface of Bi2Sr2CaCu2O8+δ (BSCCO) [2, 3, 4, 5]. Ten
years later, resonant X-ray scattering experiments detected a similar
incommensurate order in the bulk of YBa2Cu3O7-δ (YBCO) [6]. The same order was
later found in a large number of cuprates, demonstrating that this effect is
ubiquitous [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23,
24, 25]. A common approach claims that these modulations are due to a charge
density wave (CDW) order that competes with superconductivity. In a recent
publication [26], we claimed that short-ranged pairing density waves (PDW)
within a d-wave superconducting phase are the correct interpenetration of the
experimental results. Using a weak-coupling approach, we demonstrated that
PDWs and CDWs lead to distinctive momentum and energy dependencies: for PDW
the scattering signal peaks at momentum $(\pm q,0),(0,\pm q)$, while for CDW
it peaks at $(\pm q,\pm q)$. In addition, the PDW signal is mainly elastic
$\Omega=0$, in contrast to the CDW case, where the signal is peaked at
$\Omega=\pm 2\Delta_{0}$. The experimentally detected signal is peaked at
$(\pm q,0)$, $(0,\pm q)$ and is visible at $\Omega=0$, indicating that the
observed density waves have a predominant PDW nature. Interestingly, the
predicted scattering intensity had weaker peaks in the $(\pm q,\pm q)$
direction, which we interpreted as weak CDW modulations, born from the
interplay between the static d-wave order and the short ranged PDW.

(a) p = 0.1 | (b) p = 0.2 | (c) p = 0.25
---|---|---
|  |
|  |
|  |
Figure 1: Full 2D maps of the density response, Eq. (2) normalized by its
maximum, for different doping and energy values. The upper panel shows the
Fermi surfaces for each doping, and the middle one is the corresponding
elastic component ($\Omega=0$) of the intensity. As the doping increases, the
peak move to a smaller momentum and the signal acquires a ring shape. In the
lower panel we present the same maps but for finite energy $\Omega=0.2$eV,
which results in broader peaks for all doping levels.

Recently, a state-of-the-art experiment was performed using resonant inelastic
x-ray scattering (RIXS), spanning the entire copper-oxide plane of Bi2212 [1].
The main result was the existence of a ring-like intensity peak in the
$q_{x}-q_{y}$ plane with radius of $q\approx 0.27$ rlu, but with stronger
signal along $(\pm q,0)$ and $(0,\pm q)$. The authors explained this signal by
considering the Coulomb interaction between valance electrons, with short and
long-range contributions, although concluding that this explanation is
insufficient to account for the full intensity profile. In addition, motivated
by the fact that the quasi-elastic ($-200<E<200$meV) intensity is more
strongly peaked at $(\pm q,0),(0,\pm q)$ with respect to the higher energy
signal ($500<E<900$meV), they suggested a scenario of static directional CDW,
combined with dynamic fluctuating ones. To account for these fluctuations, the
authors considered the effect of the dynamic susceptibility, characterized by
the Lindhard function. However, as they showed in the Supplementary Material
(Note 5), this mainly yields peaks in the wrong direction - $(\pm q,\pm q)$ \-
and has a square-like shape which maintains a $C_{4}$ symmetry, unlike the
smooth ring shape observed in the experiment.

Although we agree that this form of the Lindhard function (which was first
suggested by us as an explanation for resonant x-ray experiments in Ref. [28])
fails to provide the correct profile of the intensity, we believe that the
authors’ choice to discard Fermi-surface effects is incorrect. Indeed, if the
observed signal is due to PDW fluctuations, rather than CDW ones, one needs to
compute the response from a pairing-like impurity in the presence of a
constant d-wave pairing gap [26]. The Born approximation leads to the density
response

$\displaystyle\chi(\textbf{q},\Omega)=\int d\omega\int d^{d}k~{}\rm
Tr\left[G_{0}(\textbf{k},\omega)V_{\bf
k}G_{0}(\textbf{k}+\textbf{q},\omega+\Omega)\sigma^{z}\right].$ (1)

Here, $\rm V_{\textbf{k}}=\Delta_{\textbf{k}}\sigma^{x}$ models the impurity,
$\sigma^{j},j=x,z$ are Pauli matrices,
$\Delta_{\textbf{k}}=\dfrac{\Delta_{0}}{2}(\cos(k_{x})-\cos(k_{y}))$ is the
pairing gap and $\rm G_{0}$ is the bare Green’s function $\rm G^{-1}_{0}({\bf
k},\omega)=\begin{pmatrix}-\omega+\varepsilon_{\textbf{k}}-\mu&\Delta_{\textbf{k}}\\\
\Delta^{\star}_{\textbf{k}}&-\omega-\varepsilon_{\textbf{k}}+\mu\end{pmatrix},$
where $\varepsilon_{\textbf{k}}$ is the band structure of the material, and
$\mu$ the chemical potential. By performing the integral over $\omega$, one
obtains

$\displaystyle\chi(\textbf{q},\Omega)=2\pi\int d^{2}k~{}\Delta_{\bf
k}\frac{\varepsilon_{\bf k}\Delta_{\bf k+q}+\varepsilon_{\bf k+q}\Delta_{\bf
k}}{(E_{\bf k}-E_{\bf
k+q})^{2}+(\Omega-i\Gamma)^{2}}\left(\dfrac{1}{E_{\textbf{k}}}-\dfrac{1}{E_{\textbf{k}+\textbf{q}}}\right),$
(2)

where
$E_{\textbf{k}}=\sqrt{\varepsilon^{2}_{\textbf{k}}+\Delta_{\textbf{k}}^{2}}$
and $\Gamma$ is set by the maximum between the quasiparticles’ inverse
lifetime and the experimental energy resolution. This approach leads to a
strong peak in the $(\pm q,0),(0,\pm q)$ direction, along with weaker maxima
in all directions (see Fig. 2 of Ref. [26]). In Ref. [26], we considered a
minimal model of the Fermi surface, where the band structure includes only
nearest- and next-nearest-neighbor hopping, allowing us to highlight the
generality of our results and to validate them by a real-space extended
Hubbard model.

In this comment, we show that the experimental signal of Ref. [1] can be
reproduced by considering a realistic Fermi surface that includes longer-range
couplings. Specifically, we use here the phenomenological band structure of
Bi2212 proposed by Ref. [29], that is:
$\varepsilon_{k}=0.5t_{0}(\cos(k_{x})+\cos(k_{y}))+t_{1}\cos(k_{x})\cos(k_{y})+0.5t_{2}(\cos(2k_{x})+\cos(2k_{y}))+0.5t_{3}(\cos(2k_{x})\cos(k_{y})+\cos(2k_{y})\cos(k_{x}))+t_{4}\cos(2k_{x})\cos(2k_{y})$,
with $t_{0}=-0.5951,t_{1}=0.1636,t_{2}=-0.0519,t_{3}=-0.1117,t_{4}=0.510$eV.
The chemical potential $\mu$ is fixed by the doping through Luttinger count,
and the only free parameters are $\Delta_{0}$ and $\Gamma$, which we set to
the experimentally relevant values of $\Delta_{0}=0.3$ and $\Gamma=0.05$eV.

Our main results are presented in Fig. 1, where the two top panels show,
respectively, the phenomenological Fermi surfaces for different doping levels
and the elastic component ($\Omega=0$) of the predicted RIXS signal, Eq. (2).
At small doping ($p=0.1$), the pronounced PDW peaks at $(\pm q,0),(0,\pm q)$
are accompanied by weaker peaks at $(\pm q,\pm q)$, associated with secondary
CDW modulations. As the doping increases, the nesting areas in the Fermi
surface become less parallel, leading to a broadening of the signal. As a
result, the intensity profile shifts from square to a ring-like shape.

RIXS experiments involve an exchange of energy between the incoming photons
and the electrons. Its intensity has a non-trivial energy dependence, whose
microscopic description has been studied in detail (see Refs. [30, 31] for a
review). In Ref. [26] we proposed a phenomenological description of the energy
dependence in RIXS experiments by evaluating Eq. (2) at $\Omega=E$ [27], see
the lowest panel of Fig. 1 where we plot $|\chi(q,\Omega)|$ at $\Omega=0.2$eV.
These plots closely resemble the experimental observations at large energy
scales, where the peaks at $(\pm q,0)$ and $(0,\pm q)$ become less pronounced.
In addition, the ring-like shape becomes wider than the elastic case,
indicating a small but noticeable dispersive behavior. This effect can be more
clearly seen in Fig. 2 where we show the energy dependence of the signal for a
one dimensional cut along the $(q,0)$ direction. As the energy increases, the
strong quasi-elastic peak centered around $\Omega\approx 0$ and $q_{x}\approx
0.3$ rlu is substituted by a weaker dispersive signal which shifts towards
larger $q$.

(a) p = 0.1 | (b) p = 0.2 | (c) p = 0.25
---|---|---
|  |
Figure 2: The normalized energy-resolved intensity, Eq. (2), along the $(q,0)$
direction. The pronounced quasi-elastic peak ($\Omega\approx 0$ and $q\approx
0.3$ rlu) is substituted by a weaker dispersive signal which shifts towards
larger $q$ as the energy is increased.

Our numerical calculations show that, in contrast to the interpretation
provided in Ref. [1], the experimental observations are consistent with the
known Fermi surface of Bi2212, provided that PDW, rather than CDW,
oscillations are considered. Our approach calls for a further investigation of
this modulation with better energy resolution and in the presence of magnetic
field, to refine our understating of the precise nature of these modulations.

Acknowledgments. This work is supported by the Israel Science Foundation
Grants No. 967/19, No. 151/19 and No. 154/19.

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