* (170) D. I. Pikulin, A. Chen and M. Franz, Chiral anomaly from strain-induced gauge fields in dirac and weyl semimetals, Phys. Rev. X 6 (Oct, 2016) 041021.
  * (171) K. Taguchi, T. Imaeda, M. Sato and Y. Tanaka, Photovoltaic chiral magnetic effect in weyl semimetals, Phys. Rev. B 93 (May, 2016) 201202.
  * (172) D. Breunig, S.-B. Zhang, M. Stehno and B. Trauzettel, Influence of a chiral chemical potential on Weyl hybrid junctions, Phys. Rev. B 99 (2019), no. 17 174501 [1903.06229].
  * (173) S.-B. Zhang, F. Dolcini, D. Breunig and B. Trauzettel, Appearance of the universal value ${e}^{2}/h$ of the zero-bias conductance in a weyl semimetal-superconductor junction, Phys. Rev. B 97 (Jan, 2018) 041116\.
  * (174) Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosic, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu and T. Valla, Observation of the chiral magnetic effect in ZrTe5, ArXiv e-prints (Dec., 2014) [1412.6543].
  * (175) C. Shekhar, F. Arnold, S.-C. Wu, Y. Sun, M. Schmidt, N. Kumar, A. G. Grushin, J. H. Bardarson, R. Donizeth dos Reis, M. Naumann, M. Baenitz, H. Borrmann, M. Nicklas, E. Hassinger, C. Felser and B. Yan, Large and unsaturated negative magnetoresistance induced by the chiral anomaly in the Weyl semimetal TaP, ArXiv e-prints (June, 2015) [1506.06577].
  * (176) C. Zhang, E. Zhang, Y. Liu, Z.-G. Chen, S. Liang, J. Cao, X. Yuan, L. Tang, Q. Li, T. Gu, Y. Wu, J. Zou and F. Xiu, Detection of chiral anomaly and valley transport in Dirac semimetals, ArXiv e-prints (Apr., 2015) [1504.07698].
  * (177) Z. Wang, Y. Zheng, Z. Shen, Y. Zhou, X. Yang, Y. Li, C. Feng and Z.-A. Xu, Helicity protected ultrahigh mobility Weyl fermions in NbP, ArXiv e-prints (June, 2015) [1506.00924].
  * (178) X. Yang, Y. Liu, Z. Wang, Y. Zheng and Z.-a. Xu, Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs, ArXiv e-prints (June, 2015) [1506.03190].
  * (179) A. Baumgartner, A. Karch and A. Lucas, Magnetoresistance in relativistic hydrodynamics without anomalies, JHEP 06 (2017) 054 [1704.01592].
  * (180) M. Ammon, T. H. Ngo and A. O’Bannon, Holographic Flavor Transport in Arbitrary Constant Background Fields, JHEP 10 (2009) 027 [0908.2625].
  * (181) D. Kharzeev, Y. Kikuchi and R. Meyer, Chiral magnetic effect without chirality source in asymmetric Weyl semimetals, Eur. Phys. J. B 91 (2018), no. 5 83 [1610.08986].
  * (182) A. I. Berdyugin, S. G. Xu, F. M. D. Pellegrino, R. Krishna Kumar, A. Principi, I. Torre, M. Ben Shalom, T. Taniguchi, K. Watanabe, I. V. Grigorieva, M. Polini, A. K. Geim and D. A. Bandurin, Measuring hall viscosity of graphene’s electron fluid, Science 364 (2019), no. 6436 162–165 [https://science.sciencemag.org/content/364/6436/162.full.pdf].
  * (183) L. W. Molenkamp and M. J. M. de Jong, Electron-electron-scattering-induced size effects in a two-dimensional wire, Phys. Rev. B 49 (Feb, 1994) 5038–5041.
  * (184) P. J. W. Moll, P. Kushwaha, N. Nandi, B. Schmidt and A. P. Mackenzie, Evidence for hydrodynamic electron flow in pdcoo2, Science 351 (2016), no. 6277 1061–1064 [https://science.sciencemag.org/content/351/6277/1061.full.pdf].
  * (185) D. Di Sante, J. Erdmenger, M. Greiter, I. Matthaiakakis, R. Meyer, D. Rodríguez Fernández, R. Thomale, E. van Loon and T. Wehling, Turbulent hydrodynamics in strongly correlated Kagome metals, Nature Commun. 11 (2020), no. 1 3997 [1911.06810].
  * (186) C. Tutschku, F. S. Nogueira, C. Northe, J. van den Brink and E. Hankiewicz, Temperature and chemical potential dependence of the parity anomaly in quantum anomalous Hall insulators, Phys. Rev. B 102 (2020), no. 20 205407 [2007.11852].
  * (187) C. Tutschku, J. Böttcher, R. Meyer and E. Hankiewicz, Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly, Phys. Rev. Res. 2 (2020), no. 3 033193 [2003.03146].
  * (188) J. Böttcher, C. Tutschku, L. W. Molenkamp and E. M. Hankiewicz, Survival of the quantum anomalous hall effect in orbital magnetic fields as a consequence of the parity anomaly, Phys. Rev. Lett. 123 (Nov, 2019) 226602.
  * (189) J. P. Boyd, Chebyshev and Fourier Spectral Methods (Second Edition, Revised).  Dover Publications, New York, 2001.
  * (190) S. Grieninger, Holographic quenches and anomalous transport, 1711.08422.
  * (191) S. Grieninger, Non-equilibrium dynamics in Holography.  PhD thesis, Jena U., 2020.  2012.10109.
  * (192) M. Baggioli and S. Grieninger, Zoology of solid & fluid holography — Goldstone modes and phase relaxation, JHEP 10 (2019) 235 [1905.09488].


# Architecture Agnostic Neural Networks

Sabera Talukder, Guruprasad Raghavan11footnotemark: 1 & Yisong Yue
Department of Neurobiology, Bioengineering, Computing and Mathematical
Sciences
California Institute of Technology
Pasadena, CA 91125, USA
<EMAIL_ADDRESS>
Equal contributors.

###### Abstract

In this paper, we explore an alternate method for synthesizing neural network
architectures, inspired by the brain’s stochastic synaptic pruning. During a
person’s lifetime, numerous distinct neuronal architectures are responsible
for performing the same tasks. This indicates that biological neural networks
are, to some degree, architecture agnostic. However, artificial networks rely
on their fine-tuned weights and hand-crafted architectures for their
remarkable performance. This contrast begs the question: Can we build
artificial architecture agnostic neural networks? To ground this study we
utilize sparse, binary neural networks that parallel the brain’s circuits.
Within this sparse, binary paradigm we sample many binary architectures to
create families of architecture agnostic neural networks not trained via
backpropagation. These high-performing network families share the same
sparsity, distribution of binary weights, and succeed in both static and
dynamic tasks. In summation, we create an architecture manifold search
procedure to discover families of architecture agnostic neural networks.

##  1 Introduction

Fascinated by the developmental algorithms and stochasticity inherent in the
developmental synaptic pruning process, in this paper, we will explore
architecure agnostic neural networks via the lens of binary, sparse, networks.
We ground our study using sparse binary neural networks because these networks
capture many of the most salient aspects of biological networks:

  * •

distinct neuronal units implementing non-linear functions in constrain an
output to (-1, +1)

  * •

synaptic connections that are restricted to (-1, +1)

  * •

inhibatory and excitatory connections are represented by (-1, +1) respectively

In this paper we demonstrate that architecture agnostic neural networks exist
in silico, that we can obtain high-performance sparse binary neural networks
on static (MNIST classification) and dynamic (imitation learning on Car-
racing) tasks, and that our stochastic search and succeed (SSS) algoritm can
explore the architetcure manifold.

##  2 Related work

Biological neural networks endow organisms with the ability to perform a
multitude of tasks, ranging from sensory processing (Glickfeld & Olsen, 2017;
Peirce, 2015), to memory storage and retrieval (Tan et al., 2017; Denny et
al., 2017), to decision making (Hanks & Summerfield, 2017; Padoa-Schioppa &
Conen, 2017). Remarkably, these complex tasks persist throughout our lives
despite neuronal pruning, and synapse deletion up until adulthood. This
partially stochastic process of neuronal refinement is known as developmental
synaptic pruning.

Developmental synaptic pruning occurs when the physical connection between a
neuron’s dendrite and another neuron’s axon is eliminated (Riccomagno &
Kolodkin, 2015), preventing any further relay of information. Interestingly,
between infancy and adulthood mammals lose roughly 50% of their neuronal
synapses (Chechik et al., 1999). A study in humans estimated that our
prefrontal cortex dendritic spine density, a proxy for synaptic density, is on
average more than two times higher in childhood than adulthood (Petanjek et
al., 2011). This evolved process is also partially stochastic (Vogt, 2015).
One of the main manifestations of stochastic developmental variation in the
brain occurs at the circuit level (Clarke, 2012), insinuating that there are
many similar neural architectures that would have sufficed in place of your
current brain’s architecture! Given the ubiquity, extent, and stochastic
nature of developmental synaptic pruning there are many theories for why this
process exists: to increase information transfer efficiency (Horn et al.,
1998), or to derive optimal synaptic architectures (Chechik et al., 1999).

Previous work in the machine learning field has sought out several
methodologies to search the architecture manifold. Neural architecture search
methods enabled traversing the architecture space to discover high-performance
networks, by making them malleable to neuro-evolution strategies (Stanley &
Miikkulainen, 2002; Real et al., 2017; 2018), reinforcement learning (Zoph &
Le, 2016) and multi-objective searches (Elsken et al., 2018; Zhou & Diamos,
2018). For example, Gaier & Ha (2019) described an elegant architecture search
by de-emphasizing the importance of weights. By utilizing a shared weight
parameter they were able to develop ever-growing networks that acquired skills
based on their interactions with the environment. However, given the brain’s
excitatory and inhibitory connections there is a rigidity to the weights that
biological neural networks actually use.

Despite the weight implication, the principle of minimizing parameter count
that Gaier & Ha (2019) addressed is productive when conceiving of biologically
inspired artificial neural networks. In practice, neural networks tend to be
over-parameterized, making them highly energy and memory inefficient. There
has been a lot of work in the machine learning field of sparsity and low
precision weights to alleviate these prominent issues. Sparsity of networks
can be introduced prior to training, as shown by SqueezeNet (Iandola et al.,
2016) and MobileNet (Howard et al., 2017). These networks were carefully
engineered to have an order of magnitude lesser parameters than standard
architectures to perform image recognition. Sparsity can also be introduced
while training, as shown by Louizos et al. (2017); Srinivas & Babu (2015)
where they explicitly prune and sparsify networks during training as dropout
probabilities for some weights reach 1. Additionally, sparsity can be added
after training is complete.

In this paper, we will leverage prior work in neuroscience, architecure
search, sparse networks, and binary networks to demonstrate the presence of
architecture agnostic neural networks, architecture agnostic neural network
families, and the stochastic search and succeed algorithm to navigate through
the architecture manifold.

##  3 Architecture Agnostic Neural Networks Formulation

###  3.1 Sparse Binarized Neural Networks

Preliminaries We represent a feed-forward neural network as a function
$f(\mathbf{x},\mathbf{w})$, that maps an input vector,
$\mathbf{x}\in\mathbb{R}^{\text{k}}$, to an output vector,
$f(\mathbf{x},\mathbf{w})=\mathbf{y}\in\mathbb{R}^{\text{m}}$. The function,
$f(\mathbf{x},\mathbf{w})$, is parameterized by a vector of weights,
$\mathbf{w}\in\mathbb{R}^{\text{n}}$, that are typically set in training to
solve a specific task. We refer to $W=\mathbb{R}^{n}$ as the weight space
($W$) of the network. Here, $k$ is the input dimension, $m$ is the output
dimension and $n$ is the total number of parameters in the neural network.

In this paper, we use two different neural network architectures for the
static and dynamic task respectively. For the static task (e.g., MNIST
classification): the network has 2 convolutional layers (16 filters 5 x 5) , 2
max-pooling layers and 1 fully-connected layer (1568 x 10). For the dynamic
task (e.g., imitation learning for car-racing): this network has 2
convolutional layers (32 filters 7 x 7, 64 filers 5 x 5), 2 max-pooling layers
and 2 fully-connected layers (576 x 100, 100 x 3).

Sparse Binarized Neural Network Throughout this paper, a binarized neural
network refers to networks with weights constrained to (-1, 0, +1). We also
constrain the output from every neuronal unit in the network to be in the
range [-1, +1] by applying a binarized activation function. We use a
”HardTanh” function defined as follows:

$HardTanh(x)=\begin{cases}+1&\text{x $>$ 1}\\\ -1&\text{x $<$ -1}\\\
x&\text{otherwise}\end{cases}.$

A binary network ($w_{b}$) with $p\%$ sparsity is defined as follows:

$||w_{b}||_{0}=\frac{n*p}{100};\text{ where, }w_{b}\in[-1,0,1]^{n}.$

A network with $p\%$ sparsity refers to a neural network that has $(n*p)/100$
weights out of the total $n$ weights in the network set to 0.

###  3.2 Architecture Manifold and Network Families

Figure 1: First-neighbors of a network (N0) obtained by a bit-swap between a
non-zero weight and a zero weight. The solid orange lines denotes a -1 weight,
the dashed gray line represents a 0-weight connection (no connection), and the
solid blue lines denotes +1 weight.

.

As the weights of the binarized neural network are restricted to (-1, 0, +1),
the architecture manifold follows the same definition as the weights space
($W$), defined above. Each point in the n-dimensional space, corresponds to a
network with a distinct architecture.

We define nearest-neighbor architectures as networks that can be obtained by a
single bit-swap of a non-zero connection (-1 or +1 weight) with a connection
that didn’t exist earlier (0-weight). For instance, if a network (N0) is
parameterized by $w_{o}$ = [1,0,-1,0,1,-1], some of its neighbors are as
follows: N1: $w_{1}$ = [0,1,-1,0,1,-1], N2: $w_{2}$ = [1,0,-1,1,0,-1], N3:
$w_{3}$ = [1,0,-1,-1,1,0], N4: $w_{4}$ = [1,-1,0,0,1,-1]. The original network
$N_{0}$ and its neighbors ($N_{1}$ to $N_{4}$) are visualized in F igure 1.

A family of networks refers to a group of binarized networks at the same level
of sparsity with the same number of (-1, 0, +1) weights in all layers.

##  4 Learning Rules

Inspired by biological neural networks, we develop an algorithm to discover
architecture agnostic artificial neural networks. As sparse binarized networks
capture most salient properties of living networks, we begin by proposing a
viable strategy to generate sparse binary neural networks, followed by a
stochastic search and succeed algorithm to discover a family of networks that
maintain the same sparsity while being architecturally distinct.

###  4.1 Generating Sparse Binary Neural Networks

The protocol for generating high-performance, $p\%$ sparse binary networks for
the static MNIST task and the dynamic car imitation learning task are as
follows:

  * •

Step-1: Instantiate a dense network with real-valued weights in the
convolutional filters and fully connected layers along with binary activation
functions. Train this network via backpropagation for $n_{1}$ epochs to
generate a well-trained network. At the end of $n_{1}$ epochs, the network has
real-weights, and is dense.

  * •

Step-2: Sparsify the network incrementally for the next $n_{2}$ epochs; where
$n_{2}$ is determined by multiplying the final desired sparsity in percent
($p$) by 2$\%$ \- 3$\%$. This results in 2$\%$ \- 3$\%$ of the weights being
set to 0 at the end of a single epoch. We then apply a magnitude-based mask at
the end of every epoch to prune away $\frac{p}{n_{2}}\%$ of the networks
synaptic weights at the end of every epoch. At the end of $n_{2}$ epochs, the
network has real-weights at a desired level of sparsity ($p\%$).

  * •

Step-3: We further train the network keeping the sparsity fixed for $n_{3}$
epochs.

  * •

Step-4: We binarize the network by clipping real-valued weights to -1, 0, +1
by applying a hard-sigmoid function. The hard-sigmoid function converts all
weights greater than 0 to +1, all weights less than 0 to -1, and keeps all
weights equal to 0, 0. The binarized network then trains for $n_{4}$ epochs,
maintaining the desired sparsity and the binarized weights at the end of every
epoch. At the end of Step-4, we obtain a binary network with the desired level
of sparsity.

This training procedure results in high-performance sparse binary neural
networks for the tasks of interest. Figure 2 demonstrates the test accuracy of
$n=3$ binary neural networks at variable sparsities for both MNIST and Car-
Racing imitation learning. We evaluate Figure 2a at 15 different sparsity
levels (0$\%$, 10$\%$, 20$\%$, 30$\%$, …, 80$\%$, 85$\%$, 87$\%$, 89$\%$, …,
95$\%$) on an MNIST test dataset. Figure 2b evaluates the dynamic car
imitation learning test accuracy on the same sparsity levels as Figure 2a as
well as (96$\%$, 97$\%$, 98$\%$, 99$\%$) for a total of 19 different sparsity
levels.

We have attached a video of our 90$\%$ sparse binary network perform dynamic
imitation learning on a car-racing task in the openAIgym environment. Find it
in the supplement.

(a)  (b)

Figure 2: High-performance binary networks of variable sparsities. (a) A
static task, MNIST classification. (b) A dynamic task, Car-racing imitation
learning.

###  4.2 Stochastic Search…

After obtaining a high-performing sparse binary neural network that works on
either a static or dynamic task, we explore its local neighborhood on the
architecture manifold using random bit-swaps. A single random bit-swap within
the network generates architecturally distinct first-neighbors. Two random
bit-swaps generates second-neighbors, so on and so forth. The bit-swap
procedure to generate first neighbors of a sparse binary network is explained
in detail in section 3.2 (Architecture Manifold).

Finding local neighbors: On applying a single bit-swap to the original
performant network multiple distinct times, we generate a large number of
first neighbors that maintain the same level of sparsity. We perform bit-swaps
in a layer dependent manner; convolutional layers or fully-connected layers
can be perturbed. We then evaluate the test accuracy of the first neighbors
and plot a histogram of their performance, relative to the performance of the
original network (depicted by a vertical red line) in Figure 3. The same
procedure was applied to sparse binary networks trained to perform the car-
racing imitation learning task, shown in Figure 8.

Figure 3: MNIST task test accuracy distribution of immediate family neighbors.
We observe that as we move into deeper layers a larger percentage of the first
family nearest neighbors outperform the original model accuracy.

We observe that perturbation of sparse binary networks in the higher layers
(2.0, FC) gives rise to a large number of sparse binary networks that perform
better than the original network, while the lower layers (1.0) seem to be more
tightly optimized: Fig 3, Fig 8. It is interesting that we discover more
generalizability at higher layers, especially since within the brain, sensory
neurons lower in the network hierarchy are more tightly optimized than
cortical structures (Kara et al., 2000).

The variable robustness to bit-swaps across multiple layers in the sparse
binary network begs the question: what is the nature of sparse binary
networks’ loss manifold?

In order to study the loss manifold of sparse binary networks, we visualize
the first-neighbors of the generated high-performing sparse binary network
using tSNE, a tool that enables non-linear dimensionality reduction of the
high-dimensional manifold onto 2D and 3D space.

(a)

(b)

(c)

(d)

Figure 4: First neighborhood families for 90$\%$ sparse binary network trained
on MNIST projected via tSNE accompanied by network test accuracies. Blue dot
represents the original network. (a) Side view of first neighbors from layer
1.0 weight perturbations. (b) Top view of first neighbors from layer 1.0
weight perturbations. (c) Side view of first neighbors from fc weight
perturbations. (b) Top view of first neighbors from fc weight perturbations.
We see that as we move into deeper layers the first family nearest neighbors
cluster more than the first family nearest neighbors in the initial layers.

In Figure 4, the x,y axes represents tSNE axis, while the z-axes represents
the test accuracy on the MNIST dataset. We notice multiple local clusters of
first-neighbors particularly in Fig 4d, possibly indicating symmetry of first
neighbor networks obtained after performing the stochastic weight-swaps. In
addition, each local cluster of networks has a large range of performance, as
seen in Fig 4c, but more predominantly in Fig 9. The presence of local
clusters in the architecture manifold indicates that the stochastic search and
succeed algorithm can enable a quick survey of a larger ”area” of the
architecture manifold at each step and wouldn’t be constrained to a small
epsilon-neighborhood that the conventional backpropagation algorithm faces.

###  4.3 … And Succeed

As the stochastic search for first-neighbors results in a large proportion of
better performing networks for the task of interest, we implement a stochastic
search and succeed algorithm to survey a small set of local sparse binary
networks, pick the one that performs the best, and obtain the first neighbors
for the best first-neighbor network chosen. This step can be repeated multiple
times to find binary networks of the same sparsity perform much better than
the original sparse binary neural network obtained! The results for a 90%
MNIST network climbing 3% in accuracy over 5 neighborhoods can be seen in Fig
5. This indicates that searching and optimizing in the architecture manifold
is an effective way to improve the accuracies of the model.

Figure 5: 90% MNIST network climbing 3% in accuracy over 5 neighborhoods. Each
neighborhood has a different marker. Blue dots represent the best neighbor in
that family. Red lines indicate the path from best neighbor to best neighbor
that the algorithm takes. We see that neighborhoods cluster with one another
(i.e. first nearest neighbors cluster, second nearest neighbors cluster,
etc.). In addition, we see how neighborhoods build on one another to move in
the architecture manifold.

Result: Family of high-performance sparse binary neural networks

Initialization: Begin with a p$\%$ sparse-binary neural network (N0) (section
4.1); Set number of nearest neighbors = nk; eval accuracy of network N0
(A($N^{0}$)); Set max-acc = (A($N^{0}$)); Set ii = 0;

while  _ii $<$ nk_ do

Find all networks in the local neighborhood of Nii through random bit-swaps
within the network. [N${}^{ii+1}_{1}$, N${}^{ii+1}_{2}$, …]; Evaluate test
accuracy of all local neighborhood networks. [A($N^{ii+1}_{1}$),
A($N^{ii+1}_{2}$), … ]

if  _max-acc $>$ A($N^{ii+1}_{j}$) _ then

$\\#\\#$ No better performing neighbor network. Stop current search; pick
another layer to perturb.

else

Pick a neighbor network (N${}^{ii+1}_{j}$) with accuracy max-acc; set max-acc
= A($N^{ii+1}_{j}$)

end if

end while

Algorithm 1 Stochastic search and succeed

###  4.4 Random Initialization

Figure 6: The filled in and colored line denotes the validation accuracy; red
indicates bit switches in layer 1.0, green denotes bit switches in layer 2.0,
and the blue denotes bit switches in the fc layer. The black lines denote the
test accuracies. The black line with orange markers, are the results of our
stochastic search and succeed algorithm. While the black line with violet
markers are the results of backpropagation.Colored line begins at a validation
accuracy of 12.34, and a final validation accuracy of 33.27. Black and orange
begins as a test accuracy of 10.94, and reaches a final test accuracy of
25.68. Black and violet begins as a test accuracy of 10.94, and reaches a
final test accuracy of 9.81.

In this section, we train a 90% random sparse binary neural network on MNIST
through the stochastic search and succeed (SSS) algorithm. In Figure 6, we
alternate the stochastic search throughout layer 1.0 (red) , 2.0 (green) and
fc (blue) for 10 epochs each and then repeat the permutations 3 times. We can
see that by the third epoch the 1.0 and 2.0 layers plateau while the fc layer
continues rise with only a moderate plateau, perhaps attributed to the fact
that fc is the deepest layer. The colored line plots the validation accuracy
with the SSS algorithm The black line with orange markers denote the test
accuracy of the SSS algorithm. The black line with violet markers denote the
test accuracy of utilizing backpropagation on the initial sparse, binary
network.

Given the fc layer’s success, we trained another model with the SSS algorithm
where we only permuted the fc layer weights. Results for this experiment are
shown in figure 7.

Figure 7: The filled in and colored line denotes the validation accuracy; red
indicates bit switches in layer 1.0, green denotes bit switches in layer 2.0,
and the blue denotes bit switches in the fc layer. The black lines denote the
test accuracies. The black line with orange markers, are the results of our
stochastic search and succeed algorithm. While the black line with violet
markers are the results of backpropagation. Colored line begins at a
validation accuracy of 12.34 and reaches a final validation accuracy of 35.87.
Black and orange begins at a test accuracy of 10.94 Reaches a final test
accuracy of 27.73. Black and violet begins at a test accuracy of 10.94 Reaches
a final test accuracy of 9.79.

##  5 Conclusion

In this paper, we create a stochastic search and succeed algorithm to identify
architecture agnostic neural networks and families of AANNs. In the process we
generate an original sparse binary network and then explore its neighbors
through the architecture manifold. Our stochastic exploration is inspired by
developmental stochastic pruning and biological network’s ability to maintain
high-performance on tasks performed while undergoing pruning. We believe that
by optimizing sparse binary neural networks architectures we will eventually
be able to uncover more broad principles of neural network architectures and
move the community away from hand-crafted architectures. In addition to
uncovering neural principles, there is the additional advantage that sparse
binary networks consume less power and utilize less memory making them a
suitable model class to operate on edge devices.

## References

  * Chechik et al. (1999) Gal Chechik, Isaac Meilijson, and Eytan Ruppin.  Neuronal regulation: A mechanism for synaptic pruning during brain maturation.  _Neural computation_ , 11(8):2061–2080, 1999\.
  * Clarke (2012) Peter GH Clarke.  The limits of brain determinacy.  _Proceedings of the Royal Society B: Biological Sciences_ , 279(1734):1665–1674, 2012.
  * Denny et al. (2017) Christine A Denny, Evan Lebois, and Steve Ramirez.  From engrams to pathologies of the brain.  _Frontiers in neural circuits_ , 11:23, 2017.
  * Elsken et al. (2018) Thomas Elsken, Jan Hendrik Metzen, and Frank Hutter.  Efficient multi-objective neural architecture search via lamarckian evolution.  _arXiv preprint arXiv:1804.09081_ , 2018.
  * Gaier & Ha (2019) Adam Gaier and David Ha.  Weight agnostic neural networks.  In _Advances in Neural Information Processing Systems_ , pp. 5364–5378, 2019.
  * Glickfeld & Olsen (2017) Lindsey L Glickfeld and Shawn R Olsen.  Higher-order areas of the mouse visual cortex.  _Annual review of vision science_ , 3:251–273, 2017.
  * Hanks & Summerfield (2017) Timothy D Hanks and Christopher Summerfield.  Perceptual decision making in rodents, monkeys, and humans.  _Neuron_ , 93(1):15–31, 2017.
  * Horn et al. (1998) David Horn, Nir Levy, and Eytan Ruppin.  Memory maintenance via neuronal regulation.  _Neural Computation_ , 10(1):1–18, 1998.
  * Howard et al. (2017) Andrew G Howard, Menglong Zhu, Bo Chen, Dmitry Kalenichenko, Weijun Wang, Tobias Weyand, Marco Andreetto, and Hartwig Adam.  Mobilenets: Efficient convolutional neural networks for mobile vision applications.  _arXiv preprint arXiv:1704.04861_ , 2017.
  * Iandola et al. (2016) Forrest N Iandola, Song Han, Matthew W Moskewicz, Khalid Ashraf, William J Dally, and Kurt Keutzer.  Squeezenet: Alexnet-level accuracy with 50x fewer parameters and¡ 0.5 mb model size.  _arXiv preprint arXiv:1602.07360_ , 2016.
  * Kara et al. (2000) Prakash Kara, Pamela Reinagel, and R Clay Reid.  Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons.  _Neuron_ , 27(3):635–646, 2000.
  * Louizos et al. (2017) Christos Louizos, Max Welling, and Diederik P Kingma.  Learning sparse neural networks through $l\\_0$ regularization.  _arXiv preprint arXiv:1712.01312_ , 2017.
  * Padoa-Schioppa & Conen (2017) Camillo Padoa-Schioppa and Katherine E Conen.  Orbitofrontal cortex: A neural circuit for economic decisions.  _Neuron_ , 96(4):736–754, 2017.
  * Peirce (2015) Jonathan W Peirce.  Understanding mid-level representations in visual processing.  _Journal of Vision_ , 15(7):5–5, 2015.
  * Petanjek et al. (2011) Zdravko Petanjek, Miloš Judaš, Goran Šimić, Mladen Roko Rašin, Harry BM Uylings, Pasko Rakic, and Ivica Kostović.  Extraordinary neoteny of synaptic spines in the human prefrontal cortex.  _Proceedings of the National Academy of Sciences_ , 108(32):13281–13286, 2011.
  * Real et al. (2017) Esteban Real, Sherry Moore, Andrew Selle, Saurabh Saxena, Yutaka Leon Suematsu, Jie Tan, Quoc V Le, and Alexey Kurakin.  Large-scale evolution of image classifiers.  In _Proceedings of the 34th International Conference on Machine Learning-Volume 70_ , pp. 2902–2911. JMLR. org, 2017.
  * Real et al. (2018) Esteban Real, Alok Aggarwal, Yanping Huang, and Quoc V Le.  Regularized evolution for image classifier architecture search.  _arXiv preprint arXiv:1802.01548_ , 2018.
  * Riccomagno & Kolodkin (2015) Martin M Riccomagno and Alex L Kolodkin.  Sculpting neural circuits by axon and dendrite pruning.  _Annual review of cell and developmental biology_ , 31:779–805, 2015.
  * Srinivas & Babu (2015) Suraj Srinivas and R Venkatesh Babu.  Data-free parameter pruning for deep neural networks.  _arXiv preprint arXiv:1507.06149_ , 2015.
  * Stanley & Miikkulainen (2002) Kenneth O Stanley and Risto Miikkulainen.  Evolving neural networks through augmenting topologies.  _Evolutionary computation_ , 10(2):99–127, 2002\.
  * Tan et al. (2017) Hui Min Tan, Thomas Joseph Wills, and Francesca Cacucci.  The development of spatial and memory circuits in the rat.  _Wiley Interdisciplinary Reviews: Cognitive Science_ , 8(3):e1424, 2017.
  * Vogt (2015) Guenter Vogt.  Stochastic developmental variation, an epigenetic source of phenotypic diversity with far-reaching biological consequences.  _Journal of Biosciences_ , 40(1):159–204, 2015\.
  * Zhou & Diamos (2018) Yanqi Zhou and Gregory Diamos.  Neural architect: A multi-objective neural architecture search with performance prediction.  In _Proc. Conf. SysML_ , 2018.
  * Zoph & Le (2016) Barret Zoph and Quoc V Le.  Neural architecture search with reinforcement learning.  _arXiv preprint arXiv:1611.01578_ , 2016.

##  Appendix A Appendix

Result: Family of high-performance sparse binary neural networks

Initialization: Begin with a p$\%$ sparse-binary neural network (N0) (section
4.1); Set number of nearest neighbors = nk; eval accuracy of network N0
(A($N^{0}$)); Set max-acc = (A($N^{0}$)); Set ii = 0;

while  _ii $<$ nk_ do

Find all networks in the local neighborhood of Nii through random bit-swaps
within the network. [N${}^{ii+1}_{1}$, N${}^{ii+1}_{2}$, …]; Evaluate test
accuracy of all local neighborhood networks. [A($N^{ii+1}_{1}$),
A($N^{ii+1}_{2}$), … ]

if  _max-acc $>$ A($N^{ii+1}_{j}$) _ then

$\\#\\#$ No better performing neighbor network. Stop current search; pick
another layer to perturb.

else

Pick a neighbor network (N${}^{ii+1}_{j}$) with accuracy $>$ max-acc; set max-
acc = A($N^{ii+1}_{j}$)

end if

end while

Algorithm 2 Stochastic search and succeed

Figure 8: Car task test accuracy distribution of immediate family neighbors

.

(a)

(b)

Figure 9: First neighborhood families for 90$\%$ sparse binary network trained
on car-racing projected via tSNE accompanied by network test accuracies. Blue
dot represents the original network. (a) Side view of first neighbors from fc
layer perturbations. (b) Top view of first neighbors from fc layer
perturbations.

.


# Measuring Item Global Residual Value for Fair Recommendation

Jiayin Wang  DCST, BNRist, Tsinghua UniversityBeijing 100084China
<EMAIL_ADDRESS>,  Weizhi Ma  AIR, Tsinghua UniversityBeijing
100084China<EMAIL_ADDRESS>,  Chumeng Jiang  DCST, BNRist, Tsinghua
UniversityBeijing 100084China<EMAIL_ADDRESS>,  Min Zhang  DCST,
BNRist, Tsinghua UniversityBeijing 100084China<EMAIL_ADDRESS>,  Yuan
Zhang  Kuaishou Inc.Beijing 100085China<EMAIL_ADDRESS>,  Biao Li
Kuaishou Inc.Beijing 100085China<EMAIL_ADDRESS>and  Peng Jiang  Kuaishou
Inc.Beijing 100085China<EMAIL_ADDRESS>
(2023)

###### Abstract.

In the era of information explosion, numerous items emerge every day,
especially in feed scenarios. Due to the limited system display slots and user
browsing attention, various recommendation systems are designed not only to
satisfy users’ personalized information needs but also to allocate items’
exposure. However, recent recommendation studies mainly focus on modeling user
preferences to present satisfying results and maximize user interactions,
while paying little attention to developing item-side fair exposure mechanisms
for rational information delivery. This may lead to serious resource
allocation problems on the item side, such as the Snowball Effect.
Furthermore, unfair exposure mechanisms may hurt recommendation performance.
In this paper, we call for a shift of attention from modeling user preferences
to developing fair exposure mechanisms for items. We first conduct empirical
analyses of feed scenarios to explore exposure problems between items with
distinct uploaded times. This points out that unfair exposure caused by the
time factor may be the major cause of the Snowball Effect. Then, we propose to
explicitly model item-level customized timeliness distribution, Global
Residual Value (GRV), for fair resource allocation. This GRV module is
introduced into recommendations with the designed Timeliness-aware Fair
Recommendation Framework (TaFR). Extensive experiments on two datasets
demonstrate that TaFR achieves consistent improvements with various backbone
recommendation models. By modeling item-side customized Global Residual Value,
we achieve a fairer distribution of resources and, at the same time, improve
recommendation performance.

Recommendation system, Item Fairness, Timeliness Distribution.

This work is supported by the Natural Science Foundation of China (Grant No.
U21B2026, 62002191). Min Zhang is the corresponding author.

††journalyear: 2023††copyright: rightsretained††conference: Proceedings of the
46th International ACM SIGIR Conference on Research and Development in
Information Retrieval; July 23–27, 2023; Taipei, Taiwan††booktitle:
Proceedings of the 46th International ACM SIGIR Conference on Research and
Development in Information Retrieval (SIGIR ’23), July 23–27, 2023, Taipei,
Taiwan††doi: 10.1145/3539618.3591724††isbn: 978-1-4503-9408-6/23/07††ccs:
Information systems Recommender systems

##  1\. Introduction

In the age of information explosion, a large number of new items enter the
candidate pool of recommendation systems each day, especially in feed
scenarios (Wu et al., 2022). However, user browsing attention is limited and
system display slots are scarce. So various recommendation systems are
designed to provide a personalized ranked list for each user from the growing
candidate pool, which also determines items’ exposure mechanisms, i.e. the
allocation of resources.

An ideal recommendation system should not only meet users’ distinct
preferences for items, but also provide fair chances for the exposure of
items. Most existing recommendation systems mainly focus on modeling users’
preferences to generate satisfying recommendation results for users, which may
provide more user-item interactions (e.g., clicks, durations, etc.) within the
system. However, most of them pay inadequate attention to item exposure
mechanisms and ignore the item fairness issue.

(a) MIND News Dataset

(b) Kuai Short Video Dataset

Figure 1. Items uploaded earlier constantly receive more exposure
opportunities: G0 contains entire items uploaded at 4 PM and G1 is all the
items uploaded at 5 PM in two real-world systems.

The lack of rational item exposure mechanisms could lead to severe problems in
real scenarios. For instance, early uploaded items are more likely to receive
more resources, such as exposures, due to the Snowball Effect, which entails a
self-amplifying process that originates from a minor impact and grows in
magnitude over time, potentially resulting in either negative outcomes. In
contrast, items uploaded recently often encounter the cold-start challenge and
struggle to receive exposure opportunities compared to established items that
currently dominate recommendation systems. Figure 1 presents exposure
distribution between two groups of items, which are uploaded in two
consecutive hours. They have comparable user feedback (CTR), but the newly
uploaded group (G1, in orange) receives significantly less exposure. We dub
this unfair exposure between items uploaded at different times as the time-
sensitive unfair exposure issues. It will negatively affect the spread of
time-sensitive information and further influence the quality of
recommendations, which will eventually hurt both user satisfaction and the
passion of item providers.

It is worth noting that our goal is to establish a fair competitive
environment among items with varying upload times, rather than prioritizing
the recommendation of a particular subset, such as newly uploaded items, or
suppressing a certain portion of items, such as the current dominant items.
Considering that each item undergoes a cold-start process, every item in the
system will benefit if our approach can mitigate the Snowball Effect in the
recommendation loops and allocate a fair amount of resources to fresh items.

The time-sensitive unfair exposure problem is a type of item fairness issue,
which is different from another type of exposure-related study, i.e.,
popularity de-biasing. The reason is that de-biasing work mostly tackles
popularity bias for higher recommendation accuracy without concurrently
considering item exposure fairness (Zhang et al., 2021; Wang et al., 2022a).
Existing studies on item fairness point out that for a fair recommendation
system, each item should get resources proportionally to its utility. They
have explored fair exposure mechanisms but treated item utility as a static
score that ignores its global timeliness trends (Steck, 2011; Morik et al.,
[n. d.]; Pitoura et al., 2021; Wang et al., 2022b; Li et al., 2022). Thus they
are unsuitable for handling this problem.

In this study, we call for a shift of attention from user-side overly modeling
to item-side fair exposure mechanism designs. We conduct empirical analyses on
two real-world feed datasets to show the unfair exposures between items with
different upload times. Analyses show that the Snowball Effect can be
mitigated by improving the competitiveness of newly uploaded items and
removing excessive exposure for dominant items. At the same time, we observe
that different items have their own trends of timeliness decay in feed
scenarios. Based on these findings, we then propose to explicitly model the
item-level timeliness distribution, namely Global Residual Value, for fair
resource competition between items uploaded at different times and design the
Timeliness-aware Fair Recommendation Framework (TaFR). With abundant
experiments, we show that more exposure resources can be fairly allocated to
support the neglected new items, and recommendation quality is improved
simultaneously.

To summarize, our main contributions are as follows:

  1. (1)

We conduct empirical analyses on unfair exposure issues between items with
different upload times in feed recommendation scenarios, which demonstrate
that unfair exposure caused by the time factor may be the major cause of the
Snowball Effect and items have diverse timeliness trends.

  2. (2)

We propose to explicitly model items’ Global Residual Value, which is defined
as the item-level customized timeliness distribution. The GRV module is
designed to alleviate the time-sensitive unfair exposure issues (e.g.,
Snowball Effect) and provide a fair way for competition between items in
exposures. The proposed GRV module is flexible to work with various backbone
recommendation methods in our proposed Timeliness-aware Fair Recommendation
Framework.

  3. (3)

Extensive experiments with three types of backbone models demonstrate the
effectiveness of TaFR in achieving both fairer exposure mechanisms and
recommendation performance improvements.

##  2\. related Work

###  2.1. Fairness-aware Recommendation

Fairness in recommendation systems can be divided into three major categories
by research subjects: user fairness, item fairness, and joint fairness (also
called market fairness (Wan et al., 2020)) (Pitoura et al., 2021; Wang et al.,
2022b; Li et al., 2022). User fairness seeks equal treatment, in
recommendation accuracy, explainability, etc., among different (groups of)
users (Ekstrand et al., 2018; Fu et al., 2020). Item fairness concerns whether
the system treats items fairly (Biega et al., 2018; Rastegarpanah et al.,
2019), such as equal prediction errors or resource allocations. They mainly
treated item utility as static and have not modeled its utility changes over
time, namely timeliness. Work (Mansoury et al., 2020) shows that improvements
in item fairness are possible to increase recommended diversity. (Wu et al.,
2021) introduces context bias in feed recommendations for unbiased learning to
rank. Note that fairness considerations are different with de-biasing for
recommendation accuracy, as works focused on mitigating popularity bias
without simultaneous considerations of fairness metrics might result in
negative impacts on item fairness (Zhang et al., 2021; Jiayin et al., 2022).

In this paper, we focus on item-side time-sensitive exposure fairness issues,
especially in feed systems where items have diverse timeliness trends. We
address this unfair exposure problem, such as the Snowball Effect, by
explicitly modeling items’ customized timeliness across time in macroscopic
views, instead of using static utility or absolute upload time for timeliness
portrayal.

###  2.2. Time-sensitive Recommendation

Time-sensitive recommendation tasks aim to recommend the most desirable item
at the right moment (Du et al., 2015), in which temporal patterns are
important to both user and item modelings. In particular, feed recommender
platforms (for news, weblogs, short-video, etc.), providing users with
frequently updated content, are a typical type of time-sensitive systems
(Okura et al., 2017; Wu et al., 2022). In time-sensitive recommendation tasks,
time-aware algorithms are often used (Gantner et al., 2010; Wang et al., 2020,
2021). Survey (Campos et al., 2014) evaluates the state of the art on time-
aware recommendation systems (TARS), which deal with the time dimension in
user modeling and recommendation methods. We incorporate the time-aware
sequential model, TiSASRec (Li et al., 2020), as one of the backbone models
for comparisons. Note that most previous works are concentrated on users’
browsing sequences and dynamic interesting modelings (Agarwal et al., 2010;
Sun et al., 2016; An et al., 2019; Aliannejadi et al., 2019), putting little
attention on timeliness modeling on the item side.

This paper focuses on feed recommendation systems, which is a typical type of
time-sensitive scenario with large-scale and frequently updated items. These
features raise great challenges in the fair exposure allocation between items
uploaded at different times. In this work, we aim to alleviate this time-
sensitive unfair exposure with minimal negative or even positive impacts on
recommendation accuracy.

###  2.3. Item Timeliness Modeling

Item timeliness modeling is equally important with the more thoroughly
researched user dynamic interests modeling in time-sensitive recommendation
scenarios, as user and item together form an information system, and both have
temporal characteristics (item’s diverse timeliness features are introduced in
empirical analysis in Section 3.3). (Wang et al., 2019a) models the
dependencies between items inside a session and re-ranking works also focus on
the pair-wise or list-wise item-item relationship constructions (Pei et al.,
2019; Abdollahpouri et al., 2019; Pang et al., 2020). Work (Huang et al.,
2022) focuses on the age of an item and its effect on selection bias and user
preferences for enhancements in rating predictions and work (Wang and Zhang,
2013) uses survival analysis in recommended opportunities modelings for
accuracy enhancements in e-commerce scenarios. Survival analysis, also called
time-to-event analysis (Jenkins, 2005a, b; Wang et al., 2019b), is a branch of
techniques that focused on lifetime modelings, such as the death in biological
organisms, failure in mechanical systems, and user churns in games (Li et al.,
2021). Among all related techniques, the Cox proportional hazards model is a
widely used procedure for modeling the relationship between covariates to
survival or other censored outcome (Therneau and Grambsch, 2000; Moolgavkar et
al., 2018; Matsuo et al., 2019). In this paper, inspired by the survival
analysis, we define items’ Global Residual Value as the timeliness
distribution and design the GRV modeling module for fair recommendations.

##  3\. Empirical Analyses in Feed Recommendation

In order to better understand the time-sensitive unfair exposure issues in
recommendation scenarios, we conduct empirical analyses on two real-world
recommendation systems, which are introduced in Section 3.1. In Section 3.2,
we first investigate the exposure situation between items uploaded at
different times, and then evaluate the degree of exposure unfairness at the
system level. Section 3.3 presents diverse item-level timeliness trends, which
demonstrate that different items in feed systems have their own timeliness
distribution over time. Based on these analyses, we call for further modeling
of item-level customized timeliness distribution, defined as Global Residual
Value, for fair exposure mechanisms.

###  3.1. Two Feed Scenarios

Feed recommendation systems are typical time-sensitive scenarios, where items
evolve rapidly, and delivering timely content is a system requirement. We
select a PC-side news recommendation website and a mobile-side short video
social application as representative scenarios for analysis and experiments in
this paper:

  * •

MIND (Wu et al., 2020): the publicly available dataset collected from
anonymized behavior logs of the Microsoft News website.

  * •

Kuai: desensitized impression log of a mobile application for short-video
recommendation and the collected data, with considerable size and diverse
types of real users’ feedback, will be publicly released along with this paper
after acceptance.

###  3.2. Analysis on Items’ Exposure Distribution

There are numerous items in the candidate pools of recommendation systems and
they are uploaded at different times. Items uploaded at earlier times may
accumulate more exposure and user feedback, leading to precise modeling and
becoming dominant in the system. Newly uploaded items are experiencing cold
start problems, mainly resulting in tentative recommendations. In feed
recommendation scenarios, it is critical to deliver updated information and
iterate over outdated items.

In this work, we examine the competition for exposure resources between items
uploaded at different times on the two real-world platforms. Exposure
opportunities are adopted as resource measurements since they are the most
important system-controlled benefits for items. For item utility (also called
merit) (Biega et al., 2018; Morik et al., [n. d.]), CTR is adopted as the user
feedback metric. In the following part, we evaluate the time-sensitive unfair
exposure issues through an item-level case study and system-level assessment.

####  3.2.1. Item-level Case Study

Figure 1 in the Introduction illustrates the exposure and user feedback
situation between two groups of items uploaded in two consecutive hours. Group
0, colored in blue, contains all the items uploaded in 4PM and items uploaded
in 5PM belongs to Group 1, which is in orange. Dashed lines reflect the user
feedback and solid bars show the system-allocated exposures in the following
days. Although Group 1 has comparable or even higher CTR, it received less
exposure compared with the early uploaded and currently prevailing group in
Day 1. The suppression trend continue to hold in the following days, and
eventually, both group lose timeliness.

This case study shows that in real-world recommendation systems, there are
situations where established item crowd out resources of new items. This trait
is not conducive to items’ cold start and the dissemination of fresh content,
especially in feed systems. It can also mix with the Snowball Effect, creating
a pernicious circle. In the following analyses, we look further at the
prevalence and severity of this time-sensitive unfair exposure allocation
problem from a holistic perspective.

####  3.2.2. System-level Evaluation

To gain further insight into the system-wide picture, we group all items
according to their upload time and evaluate the subsequent performance of each
group in recommendation systems.

(a) MIND news dataset

(b) Kuai short video dataset

Figure 2. Time-sensitive unfair exposure: G0-G3 contain all items uploaded on
four consecutive equal lengths of time, respectively. As upload times move
backward (larger group number), exposure opportunities decrease.

Results are shown in Figure 2. As the group number increases, the items
belonging to the group are uploaded more recently. Specifically, for MIND, we
group items first exposed on Day 1 12 AM to 12 PM into 4 groups, and each
group contains items uploaded in 3 hours. We evaluate each group’s performance
from Day 1 12 PM to Day 2 12 AM. For Kuai, we group items uploaded on Day 1
into 4 groups with each group uploaded within 6 hours, and examine their
performance on the following Day 2. Each group’s CTR and exposure situations
in the following observation period are plotted. Both metrics are normalized
as follows:

(1) $Y_{Exp}=\frac{\overline{Exp}_{i\in G_{x}}}{\overline{Exp}_{i\in
G}},~{}Y_{CTR}=\frac{CTR_{i\in G_{x}}}{CTR_{i\in G}}$

First we calculate the average exposure (or CTR) of items in Group x, and we
divided it by the average exposure (or CTR) of the system. For MIND, the
earliest uploaded groups crowd the most exposure opportunities in the system
while each group has comparable user feedback. The same time-sensitive unfair
exposure issue holds still for the Kuai dataset, where the latest uploaded
item group has the highest user feedback while receiving the least resources.

As shown above, unfair exposure allocation issues are prevailing in
recommendation systems, especially in scenarios with frequently uploaded new
items. The unfairness might build up like snowballs, resulting in serious
information churn and further affecting user satisfaction. In the next
section, we further dive into item-level perspectives for causes and
mitigation methods of these time-sensitive unfair exposure problems.

###  3.3. Diverse Timeliness Characteristics of Items

Analyses in the previous subsection identify the time factor as one of the
causes and solutions of unfair exposure problems, such as the Snowball Effect.
Focusing on this idea, we further investigate the major item-level time factor
in feed scenario, timeliness, which is related to while different from items’
uploaded time.

For further understanding of the item-level timeliness characteristics, we
carry out the case study in feed scenarios. Figure 3 gives out two typical
items’ performances and system-allocated exposure resources across a time
range of 7*24 hours in Kuai dataset. Item performances are plotted in orange
and bars in blue present the system-allocated exposure amounts. Note that the
scales of the exposure coordinate axes are inconsistent and we provided the
average exposure amounts per hour on the top.

(a) Item A

(b) Item B

Figure 3. Items with diverse timeliness patterns in Kuai dataset.

####  3.3.1. Time-sensitive Unfair Exposure

Comparing Figure 3(a) and 3(b), which are uploaded on the same day while
getting their first exposures in less than 12 hours difference, the former
gets more exposures in the early stages and keeps getting system exposures
even if it has relatively low user feedback in the following days. These cases
further verify the presence of the Snowball Effect. If an item accumulates a
considerable amount of resources at early time stages, it tends to enjoy
greater privileges in the subsequent competition.

####  3.3.2. Item-level Diverse Time Patterns

In order to mitigate unfair exposure situations, such as the Snowball Effect
shown above, recommendation systems need to support newly uploaded items and
remove excessive exposure to currently dominant items. We need to model the
timeliness of items in a macroscopic view. This is different from items’
uploaded time or exposure amounts since different items have different time
patterns. Some headline items might have strong timeliness in feed scenarios,
quickly replaced by new contents, and some might be time-insensitive,
possessing long spread periods. Figure 3 gives the examples of these two kinds
of items in our Kuai dataset.

Based on the above analyses of item-side exposure situations and items’
diverse timeliness characteristics, we propose to model an item-level
customized dynamic descending value (namely Global Residual Value) to model
their timeliness distribution at each time point. In the next section, we
introduce the definition and modeling module of the proposed Global Residual
Value.

##  4\. Global Residual Value Module

###  4.1. Task Statement

Given a newly uploaded item $i$ and its interaction history in the observation
period of duration $T_{obs}$, the item dynamic modeling task is to forecast
$i$’s changing global timeliness distribution, $GRV_{i}(t)$, which is the
probability of keeping active (i.e., having of timeliness or interactions) at
each future moment. This value is different from the user-item level relevance
score as GRV portrays the timeliness of content at the system level. Table 1
displays the main concepts used in the Global Residual Value module.

Table 1. Notations used in the Global Residual Module. Notations | Explanations
---|---
$T_{obs}$ | duration of the observation period
$T_{pred}$ | duration of the prediction period
$T_{i,0}$ | upload time of item $i$
$T_{i,d}$ | deactivate label time of item $i$
$\mathbf{F_{i}}$ | interaction history in observation period
$S_{i}(t)$ | timeliness status of item $i$ at time $t$
$h_{i}(t)$ | deactivate hazard by survival analysis at time t

To calculate items’ GRV, we need to utilize item interactions in the systems,
so we define the mentioned observation period to collect interactions of each
item from upload time $T_{i,0}$ to $T_{i,0}+T_{obs}$. $T_{obs}$ is a hyper-
parameter in distinct scenarios. Then, we can use the collected information to
forecast the GRV of the prediction period ($T_{i,0}+T_{obs}$ to
$T_{i,0}+T_{obs}+T_{pred}$).

###  4.2. GRV Modeling

First, we formally define the Global Residual Value of item $i$ at future time
point $t$ (t $\geq$ 0), which is the quantitative measurement of timeliness:

(2) $\displaystyle
GRV_{i}(t)=P(S_{i}(t)=\text{active})=P(T_{i,d}>t|\mathbf{F_{i}})$

where $S_{i}(t)\in\\{\text{active},\text{deactivated}\\}$,
$\mathbf{F_{i}}=\mathbf{F_{i}}(\mathbf{t})\in\mathrm{R}^{T_{obs}*|F|}$,
$T_{i,d}\in\mathrm{R}$. The Global Residual Value measures the probability
that an item will remain active at a time point, which is equivalent to the
deactivation event occurring after the time point $t$. By capturing item-level
timeliness evolution patterns in the system, we use items’ performances in the
observation period to predict the future Global Residual Value. Note that
$T_{i,d}$, the deactivation time of items, can be manually labeled by
administrators or automatically generated by systems. Subsection 4.3.3
introduces a design for the system determination method used in this paper,
with no additional labeling requirements.

Figure 4. The Global Residual Value Module, which models the item’s timeliness
distribution in the prediction time period with its past performances in the
observation window. The input is item $i$’s user feedback from upload time
$T_{i,0}$ to the end of observation period $T_{i,0}+T_{obs}$. The output is
Global Residual Value vector $\mathbf{GRV_{i}}$ with the length of $T_{pred}$.

As the Global Residual Value can not be directly calculated, inspired by
survival analysis, we further construct its relationship with the hazard
probability, $h_{i}(t)$, which is defined as the following:

(3) $\displaystyle h_{i}(t)=\lim_{\delta(t)\rightarrow
0}\frac{\operatorname{P}(t\leq T_{i,d}<t+\delta(t)\mid T_{i,d}>t)}{\delta(t)}$

Equation 4 portrays the relationship between hazard function $h_{i}(t)$,
accumulated hazard function $H_{i}(t)$ and our designed $GRV_{i}(t)$. As shown
below, by modeling the hazard function, we are able to obtain the Global
Residual Value.

(4) $\displaystyle H_{i}(t)=\int_{0}^{t}h_{i}(x)dx$
$\displaystyle=\int_{0}^{t}-\frac{GRV^{\prime}_{i}(x)}{GRV_{i}(x)}dx=-\log(GRV_{i}(t))$
$\displaystyle GRV_{i}(t)$ $\displaystyle=\exp(-H(t))$

To further model the hazard function, we introduce the assumption in Cox’s
proportional hazard model (Jenkins, 2005b), which is that the log hazard of an
individual is a linear combination of its covariates and a system-level time-
varying benchmark hazard. According to (Stensrud and Hernán, 2020), we can
adopt this assumption in our item timeliness modeling task and construct
$\mathbf{h_{i}}$ as follows:

(5) $\displaystyle
h_{i}(t)=h_{0}(t)*Exp[\sum_{t_{x}=T_{i,0}}^{T_{i,0}+T_{obs}}\sum_{f\in
F}\alpha_{f}(t_{x})*(f_{i}(t_{x})-\overline{f_{I}(t_{x})})]$ $\displaystyle
t\in(T_{i,0}+T_{obs},T_{i,0}+T_{end}]$

where we use the item’s performance in the observation window,
$\mathbf{F_{i}}$, as covariates.

###  4.3. Module Overview

The Global Residual Value module is described in Figure 4. The following parts
illustrate the inference and training procedures of our designed Global
Residual Value modeling module.

####  4.3.1. Inference

The upper box in Figure 4 is a diagram of the inference process. The input is
items’ past performance in the system, marked red on the upper left in the
figure, and the module predicts the item-level customized Global Residual
Value vector across time. More specifically, when an item is uploaded at time
$T_{i,0}$ and passes its observation period (from $T_{i,0}$ to
$T_{i,0}+T_{obs}$), its performance in the system is transport to the GRV
module as its features for timeliness distribution calculations. Items’
performance, F, contains various user feedback such as CTR, watch ratio, like
rate, etc. The module follows Equation 5 to forecast $i$’s Global Residual
Value vector in the prediction period (from time $T_{i,0}+T_{obs}$ to
$T_{i,0}+T_{obs}+T_{pred}$). This vector is further sent into Timeliness-aware
Fair Recommendation Framework introduced in Section 5.

####  4.3.2. Training

The training process is illustrated in the lower box in Figure 4. It contains
mainly two parts: the deactivation label generation and the parameter
learning.

GRV module collects all the impression data from items’ upload to
$T_{i,0}+T_{obs}+T_{pred}$, where the subsequent performance after the
observation period, $[T_{i,0}+T_{obs}$,$T_{i,0}+T_{obs}+T_{pred})$, marked
orange in the lower left of the framework figure, is unreachable at the
inference time point. Logs in this period are sent to the timeliness detection
part. Note that items’ deactivation of timeliness can be manually labeled by
administrators in feeds systems or automatically determined by strategies.
Subsection 4.3.3 introduces the method we adopt for deactivation label
detection.

If the deactivation of an item does not trigger during the whole observation
and prediction period, we cannot get the deactivation label time and this item
forms a censored case. Since censors might occur, it is not appropriate to use
the loss function such as mean squared error or mean absolute error loss for
GRV module learning. We maximize the log-likelihood in module training to get
the parameter $\mathbf{h_{0}}$ and $\boldsymbol{\alpha}$ in Equation 5.

The following subsection introduces the deactivation label detection method
adopted in our module. This label ($T_{i,d}$) is used in the training process.
Note that it can also be labeled manually according to the system’s needs for
content timeliness.

####  4.3.3. Deactivation Label

The deactivation alert can be triggered up to once for each item. The
occurrence of an alert means that the item’s global timeliness is close to 0
and should be eliminated from the time-sensitive system. The deactivation
trigger time is marked as $T_{i,d}$. If the item does not trigger any alerts
within the whole time period of $[T_{i,0},T_{i,0}+T_{obs}+T_{pred})$, it will
become a censored case and will be removed from modeling training.

(6) $\displaystyle
v_{i}(t)=\mathbf{1}_{Exp_{i}(t)>0}*(R_{i}(t)-\beta_{E})+\mathbf{1}_{Exp_{i}(t)=0}*(-\beta_{nE})$
$\displaystyle R_{i}(t)=Rank(f_{i}(t),f_{I}(t))$ (7) $\displaystyle
T_{i,d}=\mathop{\arg\min}\limits_{t}\,\sum_{t_{x}=T_{i,0}}^{t}v_{i}(t_{x})<\beta_{d}$

The deactivation label generation mechanism is designed under item-level
feedback. We give each item a vitality score under Equation 6.
$\mathbf{1}_{f}$ is the indicator function, $Exp_{i}(t)$ is the exposure
amounts of item $i$ at time period t, $R_{i}(t)$ is the percentile rank of i’s
feedback in the system at time t, $\beta_{E}$ and $\beta_{nE}$ are two hyper-
parameters. As we gain the item’s evaluation at each time granularity, which
ranges from min($-\beta_{E}$, $-\beta_{nE}$) to $1-\beta_{E}$, we add up this
score to get the cumulative vitality performance. If it is less than the
threshold $\beta_{d}$, then the item triggers the deactivation alert at this
time point. This module is presented in the bottom part in Figure 4. We need
to control the censoring rate by appropriately designing the deactivation
detection mechanism and selecting appropriate hyper-parameters to replace
manual labels. Detailed parameter settings are tested and introduced in
experimental settings in Section 6.1.

##  5\. Timeliness-Aware Fair Recommendation

In this section, we introduce the calculated GRV of items into the top-K
recommendation models for fair exposure allocations. We use
$r_{x}=(u_{x},t_{x})$ to denote the request by user $u_{x}$ in time $t_{x}$,
where each request $r_{x}$ consists of a user id and inquiry time.
Recommendation systems receive a request list,
$R=\\{r_{1},r_{1},...,r_{n}\\}$, and respond to each request, producing the
recommendation list $O=\\{L_{1},...L_{n}\\}$ with
$L_{x}=[i_{x,1},...,i_{x,m}]$. These lists are consumed (i.e., read or
watched) by users in time sequences, and the corresponding user feedback is
recorded by systems for further modeling. Viewed from the global system level,
items, with different exposed hours and timeliness trends, get resources in
the order of $[i_{u_{1},pos_{1}},...,i_{u_{n},pos_{m}}]$ with a length of
$|R|*|L|=n*m$.

Given a user request $r_{x}=(u_{x},t_{x})$ and candidate item set $I$, TaFR
generates the recommendation list based on the pre-calculated Global Residual
Value, $\mathbf{GRV_{I}}$, and the backbone model produced recommendation
scores between items $I$ and the user $u_{x}$ for personalized and fair
exposure.

Figure 5. Timeliness-aware Fair Recommendation Framework explicitly models
items’ Global Residual Values for personalized recommendations and fair
exposure allocations.

###  5.1. Framework Overview

We design the Timliness-aware Fair Recommendation Framework,
TaFR111https://github.com/Alice1998/TaFR, aiming to alleviate the time-
sensitive unfair exposure in recommendation scenarios with minimal negative or
even positive impacts on recommendation accuracy. The overall structure of
TaFR is shown in Figure 5. It is composed of two parts: the backbone model for
personalized recommendations and the Global Residual Value Module for items’
timeliness distribution modeling.

Typical recommendation systems generate output (exposure list $L_{x}$) based
on the user request $r_{x}=(u_{x},t_{x})$ and the candidate item set $I$. In
this process, each item is assigned a certain recommendation score (mainly
representing the degree of relevance between the user and item at time t).
When allocating exposure opportunities, each exposure list is generated
individually based on the predicted recommendation scores for the current user
request. The system-level deviations of recommendation scores, especially
unfair competitions between items with different upload times and timeliness
patterns, are not properly and explicitly considered.

In TaFR, we utilize the personalized recommendation models as backbone modules
and integrated them with the item-level customized timeliness distribution
pre-calculated in the Global Residual Value module. These two modules and
their integration methods are introduced in the following subsections. Table 2
displays notations used in TaFR.

Table 2. Notations used in the framework. Notations | Explanations
---|---
$BBM_{r(u,t)}(i)$ | Backbone module
$\mathcal{B}(u,i,t)$ | Backbone modeling algorithms
$GRV_{I}(t)$ | Global Residual Value module
$\mathcal{G}_{i}(t)$ | GRV modeling algorithms
$P_{i}(t)$ | system predicted score for item $i$ at time $t$
$F_{i}(t)$ | users feedback for item $i$ at time $t$
$\gamma$ | hyper-parameter for GRV integration

####  5.1.1. Backbone Recommendation Score

(8) $\displaystyle BBM_{r(u,t)}(I)=\mathcal{B}(u(t),I,t)$

Backbone module $BBM_{r(u,t)}(I)$ produces recommendation scores based on the
user request $r(u,t)$ and item candidate set $I$. The backbone algorithm
$\mathcal{B}$, requires user-item interaction logs for the id-based
recommendation score prediction. Note that TaFR has no special requirements
for backbone models and most recommendation algorithms can be used as the
backbone. $BBM_{r(u,t)}(I)$ module mainly focuses on improving recommendation
accuracy and lacks macroscopic consideration of fair item exposure mechanisms.

####  5.1.2. Global Residual Value

The Global Residual Value is defined in Section 4.2 as items’ global
timeliness distribution. It represents the probability that potentially
interested users for item $i$ exist among the unexposed users at time $t$.
This could be quantified as the probability that the item is active at the
current $t$ and is modeled by the $\mathcal{G}_{i}$ as shown in Equation 9.

(9) $\displaystyle
GRV_{i}(t)=P(S_{i}(t)=\text{active})=\mathcal{G}_{i}(t-T_{i,0})$

In the feed recommendation scenario, items typically obtain certain timeliness
patterns as illustrated in Section 3. More specifically, at the end of
observation time $T_{i,0}+T_{obs}$, the system acquires user feedback on the
item $i$ from the time it is uploaded ($T_{i,0}$) to the current moment.
Usually, the system also predicts items’ relevant scores with candidate users.
These two types of information, predicted recommendation score P if available,
and real user feedback F, are used as the input factors in Global Residual
Value Module. This modeling process $\mathcal{G}$ is shown in Equation 10.

(10) $\displaystyle GRV_{i}(t)$
$\displaystyle=\mathcal{G}\big{(}P_{i}(T_{i,0}),F_{i}(T_{i,0});\cdots;$
$\displaystyle
P_{i}(T_{i,0}+T_{obs}-1),F_{i}(T_{i,0}+T_{obs}-1);P_{i}(T_{i,0}+T_{obs})\big{)}(t)$
$\displaystyle t\in\left[T_{i,0}+T_{obs},T_{i,0}+T_{obs}+T_{pred}\right]$

###  5.2. GRV-based Recommendation

The framework calculates personalized recommendation scores $BBM_{r(u,t)}(I)$
and Global Residual Value $GRV_{I}(t)$ for item timeliness modelings. TaFR
combines the ratings from two perspectives for final rankings. In this work,
the aggregation method is shown in Equation 11.

(11) $\displaystyle\mathcal{G}_{r(u,t)}(I)$
$\displaystyle=(1-\gamma)*BBM_{r(u,t)}(I)+\gamma*GRV_{i}(t)$
$\displaystyle=(1-\gamma)*\mathcal{B}(u(t),I,t)+1-\gamma*\mathcal{G}_{I}(P_{i}(\mathbf{t_{P}});F_{i}(\mathbf{t_{F}}))(t-T_{I,0})$
$\displaystyle t\in[T_{I,0}+T_{obs},T_{I,0}+T_{obs}+T_{pred}]$
$\displaystyle\mathbf{t_{P}}=[T_{I,0}:T_{I,0}+T_{obs}],~{}\mathbf{t_{F}}=[T_{I,0}:T_{I,0}+T_{obs})$

$\gamma$ is the weight between user preferences and item timeliness. $T_{obs}$
is the hyper-parameter for the length of the observation window and $T_{pred}$
is the duration for the prediction period. GRV module obtains items’ user
feedback and system scoring and at the end of the observation period forecasts
items’ timeliness distribution vector, $GRV_{i}(t)$, with the length of
$T_{pred}$.

##  6\. Experiments and Evaluations

As introduced in Section 5.1, TaFR can easily accommodate most personalized
recommendation algorithms as backbones and is applicable to various time-
sensitive recommendation scenarios. In this section, we conduct extensive
experiments with three types of backbone models on two datasets to verify the
effectiveness of our framework in terms of recommendation accuracy and time-
sensitive exposure fairness. Experimental settings are described in Section
6.1. Overall performances of TaFR are presented in Section 6.2 and analysis of
exposure fairness is shown in Section 6.3. In Section 6.4, we further examine
the item GRV module to validate its ability on item-level customized
timeliness modeling.

###  6.1. Experimental Settings

####  6.1.1. Datasets

We use two datasets described in Section 3.1. The dataset settings for GRV
module and recommendation framework are introduced below:

  * •

MIND (Wu et al., 2020): We use the train and validation set in MIND, including
7 days’ logs, and conduct a 10-core filter. For GRV, we randomly sample 20%
for testing and conduct recommendations on these 20% items to prevent
information leakage.

  * •

Kuai: We collect and use items uploaded in two days and their exposure
feedback in the following 7 days. For GRV, we use logs of items uploaded on
the first day and use the second-day-uploaded items to compose the
recommendation sets.

For GRV module, we use CTR as the only user feedback $\mathbf{F_{i}}$ and set
the system predicted relevance score $\mathbf{P_{i}}$ to null for offline
simulations due to dataset limitations. For recommendations, on both datasets,
we use the first 3 days for training and randomly split the last 2 days for
validation and testing. To better test TaFR’s abilities for fair resource
allocations, we conduct experiments based on the test-all settings. Note that
this will lead to an overall decrease in the accuracy of the recommendation.

####  6.1.2. Framework Backbones

TaFR has no special requirements for backbone models because the GRV module
could integrate with most recommendation algorithms. We test three types of
models as our backbones:

  * •

NeuMF (He et al., 2017): neural collaborative filtering method.

  * •

GRU4Rec (Hidasi et al., 2015): sequential recommendation algorithm.

  * •

TiSASRec (Li et al., 2020): sequential and time interval aware recommendation.

For each backbone algorithm, we test it only and integrate it with the
normalized uploaded time and our Global Residual Value vector. Specifically,
the upload time baseline (+time) replaces the GRV with the normalized upload
time, $\mathbf{t_{i,exp}}$, which is calculated as follows:

(12) $t_{i,exp}(t)=1-\frac{t-T_{i,0}}{t- \text{min}~{}T_{I,0}+
\delta}=\frac{T_{i,0}-\text{min}~{}T_{i,0}+\delta}{t- \text{min}~{}T_{I,0}+
\delta}$

Equation 12 first normalizes $i$’s exposed time with the maximum item expose
time at the current system and reverses it since longer expose time represents
lower timeliness.

####  6.1.3. Parameter Settings

For the Global Residual Value module, we set the observation and prediction
duration $T_{obs}+T_{pred}$ as 7*24 hours, which is one complete week, and the
observation window $T_{obs}$ as 12 hours in MIND and 24 hours in Kuai due to
different update frequency in news and short-video platforms. For hyper-
parameters in GRV module (Equation 6 and 7), aggregation settings in TaFR
(Equation 11) and the baseline method (Equation 12), we conduct pilot
experiments for grid search in the range of [0, 0.5] with the step size of 0.1
respectively, $\beta_{E}$, $\beta_{nE}$ are set to 0.5 and the $\beta_{d}=-3$.
$\gamma$ is set as 0.3, 0.3, 0.1 in MIND and 0.2, 0.1, 0.1 in Kuai for three
backbones respectively. $\delta$ is set to 0, when $\text{min}~{}T_{I,0}=0$ we
set the value of $t_{i,exp}(t)$ as 0 in Equation 12.

Table 3. Overall Recommendation Results: The Timeliness-aware Fair
Recommendation Framework (TaFR) is tested with three types of backbone models
(NeuMF, GRU4Rec, TiSASRec) on two datasets (MIND and Kuai). For each backbone
model, we test its performance alone and integrated it with upload time
($\text{TaFR}_{time}$) and our proposed Global Residual Value module
($\text{TaFR}_{GRV}$). This table presents the evaluation on recommendation
accuracy, measured by Hit Rate (HR@k) and Normalize Discounted Cumulative Gain
(NDCG@k), time-sensitive exposure fairness, evaluated by (New) Item Coverage
((N_)Cov@k). Higher values of all metrics represent better results. **
represents p¡0.05 significance and * means p¡0.1 significance comparing with
backbone model. For each dataset, the best performance row is marked in bold
and the second best is underlined.

Dataset | BackBone | Method | HR@5 | NDCG@5 | N_Cov@5 | Cov@5 | HR@10 | NDCG@10 | N_Cov@10 | Cov@10
---|---|---|---|---|---|---|---|---|---|---
MIND | NeuMF | backbone | 0.0953 | 0.0754 | 0.0026 | 0.0059 | 0.1251 | 0.0846 | 0.0026 | 0.0099
$\text{TaFR}_{time}$ | 0.0972 | 0.0762 | 0.0026 | 0.0058 | 0.1266 | 0.0855 | 0.0026 | 0.0087
$\text{TaFR}_{GRV}$ | **0.2204 | **0.1511 | **0.2992 | **0.0657 | **0.2403 | **0.1574 | **0.4698 | **0.1037
GRU4Rec | backbone | 0.1344 | 0.0906 | 0.0031 | 0.0099 | 0.1626 | 0.0995 | 0.0037 | 0.0153
$\text{TaFR}_{time}$ | 0.1302 | 0.0909 | 0.0026 | **0.0067 | 0.1533 | 0.0982 | 0.0026 | **0.0101
$\text{TaFR}_{GRV}$ | **0.2141 | **0.1494 | **0.0110 | 0.0074 | **0.2453 | **0.1592 | **0.0147 | 0.0113
TiSASRec | backbone | 0.1321 | 0.0897 | 0.0698 | 0.0562 | 0.1867 | 0.1071 | 0.1050 | 0.0860
$\text{TaFR}_{time}$ | 0.1239 | 0.0808 | **0.0100 | **0.0134 | 0.1479 | 0.0883 | **0.0142 | **0.0216
$\text{TaFR}_{GRV}$ | **0.1764 | **0.1158 | **0.1417 | 0.0492 | **0.2219 | **0.1303 | **0.2247 | 0.0779
Kuai | NeuMF | backbone | 0.2422 | 0.1911 | 0.1128 | 0.6309 | 0.3114 | 0.2134 | 0.1579 | 0.7013
$\text{TaFR}_{time}$ | **0.2255 | **0.1641 | **0.1323 | **0.6933 | **0.3025 | **0.1889 | **0.2015 | **0.7780
$\text{TaFR}_{GRV}$ | 0.2440 | 0.1923 | 0.1158 | 0.6315 | 0.3140 | 0.2149 | 0.1598 | 0.7037
GRU4Rec | backbone | 0.2892 | 0.2105 | 0.0150 | 0.2079 | 0.3885 | 0.2425 | 0.0169 | 0.2612
$\text{TaFR}_{time}$ | 0.2940 | 0.2124 | 0.0113 | **0.1884 | 0.3912 | 0.2437 | 0.0169 | **0.2444
$\text{TaFR}_{GRV}$ | **0.3129 | **0.2328 | *0.0245 | **0.3021 | **0.4111 | **0.2645 | **0.0357 | **0.3782
TiSASRec | backbone | 0.3903 | 0.3298 | 0.4211 | 0.7876 | 0.4713 | 0.3559 | 0.4862 | 0.8356
$\text{TaFR}_{time}$ | **0.3018 | **0.2316 | **0.2005 | **0.3816 | **0.3932 | **0.2611 | **0.2807 | **0.5017
$\text{TaFR}_{GRV}$ | 0.3893 | 0.3278 | 0.4236 | 0.7899 | 0.4706 | 0.3540 | **0.5013 | 0.8373

####  6.1.4. Evaluation Metrics

We evaluate the accuracy of recommendations and the fairness degree of
exposure mechanisms simultaneously. For recommendation accuracy, we use
standard metrics: hit rate at k (HR@k) and normalized discounted cumulative
gain at k (NDCG@k). For exposure fairness, we report the newly uploaded items’
coverage (N_Cov@k), measured as #exposed_new_items_in_topK_lists/#new_items,
and also show the overall item coverage (Cov@k) in Section 6.3. In MIND, we
mark the 20% of items with the latest upload time in the training set as new
items. For Kuai, we label the newly uploaded 10% of items as Kuai is less
sparse than MIND. For each setting, we run experiments with random seeds
$0\sim 4$ and report the average results with significant tests compared with
the backbone model.

###  6.2. Overall Performance

The overall performance of the Timeliness-aware Fair Recommendation Framework
is reported in Table 3. We evaluate TaFR’ recommendation quality and time-
sensitive exposure fairness on the backbone model only, $\text{TaFR}_{time}$
and $\text{TaFR}_{GRV}$.

(1) In general, TaFR achieves steady improvements in recommendation accuracy
and time-sensitive exposure fairness simultaneously across different types of
backbones and datasets compared with using backbone models only. This verifies
the validity of explicitly modeling item timeliness distribution. Compared
with integrating upload time baseline ($\text{TaFR}_{time}$), TaFR with our
proposed GRV module ($\text{TaFR}_{GRV}$) improves new items’ coverage with
steady recommendation quality. This proves the effectiveness of GRV module
designs.

(2) For MIND dataset, the three types of backbones show an upward trend in
both recommendation accuracy and new items’ coverage on the top 10 results.
Integrating Global Residual Value reduces the gap. When adopting the basic
model NeuMF as the backbone, TaFR achieves comprehensive better results. Note
that TaFR brings in lifts of recommendation quality and new items’ exposure
coverage based on the time-aware recommendation algorithm, TiSASRec. This
further points out that the item-side timeliness distribution is an important
modeling direction different and independent of user-side sequence modeling.

(3) In Kuai, the backbone model only, TaFR integrated with upload time and
TaFR with GRV module all maintain increasing patterns when the backbone model
is used in order with the basic, sequential, and time-aware methods. At the
same time, TaFR with the GRV module consistently surpasses the +time baseline
in both time-sensitive item exposure fairness and recommendation quality.

(4) Results on the two datasets show relatively different trends and this may
relate to the different sparsity and timeliness patterns. Recommendation
performances and item coverages in MIND are relatively low. This pattern is
consistent with the interaction sparsity and fast iteration characteristics of
the MIND news dataset. Improvements in both recommendation quality and
fairness of TaFR with GRV module integrated are more significant in MIND. This
is probably because the items in MIND are uploaded on different days and for
Kuai, items are uploaded within 24 hours.

###  6.3. Impact on Time-sensitive Exposure Fairness

(a) Top 5 results of Kuai, GRU4Rec

(b) Top 10 results of Kuai, GRU4Rec

(c) Top 5 results of MIND, TiSASRec

(d) Top 10 results of MIND, TiSASRec

Figure 6. Exposed item coverage among items with different upload times.
Higher group numbers represent later upload times. The backbone model only,
$\text{TaFR}_{GRV}$, and its percentage lift based on the backbone are shown,
validating that TaFR boosts exposures opportunities.

We further evaluate TaFR’s modification on exposure between items uploaded at
different times. Figure 6 groups all the items into 10 groups in Kuai and 5
groups in MIND evenly according to upload times and presents each group’s
exposed item coverage when recommend with the backbone (in blue) or TaFR (in
green), and the TaFR’s lift percentage based on backbone (in orange). Figure
6(a),6(b) adopt GRU4Rec as the backbone and plot the Top 5 or 10
recommendation results in Kuai. As the group number increase, items are
uploaded later and the exposed item coverage decreases significantly. TaFR
constantly improves each group’s item coverage in recommendation lists
compared with the backbone and the boosted percentages are much higher for
later uploaded items. Figure 6(c),6(d) select TiSASRec as the backbone and is
tested in MIND. TaFR greatly improves coverage of the last uploaded group,
further enhancing the exposure of new items in the feed system.

###  6.4. Evaluation on Global Residual Value Module

This section examines the GRV module’s ability in modeling the global
timeliness of items. We carry out an analytical experiment for verification
that the module produced GRV matches items’ timeliness characteristics in
future times. Following PageRank’s bucket evaluation methods (Davison and
Baoning, 2006), we divide items in the Kuai dataset into 10 groups based on
historical CTR (baseline) and GRV module’s output, $GRV_{i}(T_{i,0}+48)$, at
$T_{i,0}$+48 hours and evaluate the group-level performance on user’s feedback
in play rate (playtime divided by video duration) and comment rate, which are
distinguished from the input CTR. Figure 7 presents the results. We can see
that blue bars show a monotonically increasing trend in diverse user feedback,
while red bars have no apparent distinguishing abilities between groups. This
result points to the modeling capabilities of the GRV module in TaFR and the
possible problems in using linear CTR weighting methods as item timeliness
modeling.

(a) play rate

(b) comment rate

Figure 7. Items are divided into 10 groups based on historical CTR (upper fig,
colored in red) or GRV (lower fig, colored in blue), respectively. We present
each group’s performances on two user feedback dimensions, the play rate for
(a) and comment for (b). GRV shows more accurate modeling capabilities
compared with history CTR.

##  7\. Conclusion

In the era of data explosion, recommendation systems play a crucial role in
people’s access to information. However, information systems often seek to
maximize delivery accuracy for higher user satisfaction and duration times,
leaving relatively less attention on designing item-side fair exposure
mechanisms, resulting in resource allocation issues such as the Snowball
Effect.

In this paper, we first investigate the exposure situation between items
uploaded at different times and name it as the time-sensitive exposure issues.
Analyses point out the Snowball Effect may be caused by the time-sensitive
unfair exposure and items in feed scenarios have diverse timeliness patterns.
Then, we propose to explicitly model the item-level customized timeliness
distribution, namely Global Residual Value, and introduce the designed GRV
module into recommendations with the Timeliness-aware Fair Recommendation
Framework, TaFR, aiming to alleviate time-sensitive unfair exposures with
minimal negative or positive impacts on recommendation accuracy. Abundant
experiments are conducted with three types of backbone models on the two
datasets, validating the ability of the TaFR for simultaneous improvements in
both time-sensitive exposure fairness and recommendation quality.

## References

  * (1)
  * Abdollahpouri et al. (2019) Himan Abdollahpouri, Robin Burke, and Bamshad Mobasher. 2019\.  Managing popularity bias in recommender systems with personalized re-ranking. In The thirty-second international flairs conference.
  * Agarwal et al. (2010) Deepak Agarwal, Bee-Chung Chen, and Pradheep Elango. 2010\.  Fast online learning through offline initialization for time-sensitive recommendation. In Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining. 703–712.
  * Aliannejadi et al. (2019) Mohammad Aliannejadi, Dimitrios Rafailidis, and Fabio Crestani. 2019.  A joint two-phase time-sensitive regularized collaborative ranking model for point of interest recommendation.  IEEE Transactions on Knowledge and Data Engineering 32, 6 (2019), 1050–1063.
  * An et al. (2019) Mingxiao An, Fangzhao Wu, Chuhan Wu, Kun Zhang, Zheng Liu, and Xing Xie. 2019\.  Neural news recommendation with long-and short-term user representations. In Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. 336–345.
  * Biega et al. (2018) Asia J Biega, Krishna P Gummadi, and Gerhard Weikum. 2018\.  Equity of attention: Amortizing individual fairness in rankings. In The 41st international acm sigir conference on research & development in information retrieval. 405–414.
  * Campos et al. (2014) Pedro G. Campos, Fernando Díez, and Iván Cantador. 2014\.  Time-aware recommender systems: a comprehensive survey and analysis of existing evaluation protocols.  User Model User-Adap Inter 24, 1-2 (Feb. 2014), 67–119.  https://doi.org/10.1007/s11257-012-9136-x
  * Davison and Baoning (2006) DB Davison and W Baoning. 2006.  Propagating trust and distrust to demote web spam.  (2006).
  * Du et al. (2015) Nan Du, Yichen Wang, Niao He, Jimeng Sun, and Le Song. 2015.  Time-sensitive recommendation from recurrent user activities.  Advances in neural information processing systems 28 (2015).
  * Ekstrand et al. (2018) Michael D Ekstrand, Mucun Tian, Ion Madrazo Azpiazu, Jennifer D Ekstrand, Oghenemaro Anuyah, David McNeill, and Maria Soledad Pera. 2018\.  All the cool kids, how do they fit in?: Popularity and demographic biases in recommender evaluation and effectiveness. In Conference on fairness, accountability and transparency. PMLR, 172–186.
  * Fu et al. (2020) Zuohui Fu, Yikun Xian, Ruoyuan Gao, Jieyu Zhao, Qiaoying Huang, Yingqiang Ge, Shuyuan Xu, Shijie Geng, Chirag Shah, Yongfeng Zhang, et al. 2020\.  Fairness-aware explainable recommendation over knowledge graphs. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval. 69–78.
  * Gantner et al. (2010) Zeno Gantner, Steffen Rendle, and Lars Schmidt-thieme. 2010\.  Factorization models for context-/time-aware movie recommendations. In In Challenge on Context-aware Movie Recommendation (CAMRa2010). ACM.
  * He et al. (2017) Xiangnan He, Lizi Liao, Hanwang Zhang, Liqiang Nie, Xia Hu, and Tat-Seng Chua. 2017\.  Neural collaborative filtering. In Proceedings of the 26th international conference on world wide web. 173–182.
  * Hidasi et al. (2015) Balázs Hidasi, Alexandros Karatzoglou, Linas Baltrunas, and Domonkos Tikk. 2015.  Session-based recommendations with recurrent neural networks.  (2015).
  * Huang et al. (2022) Jin Huang, Harrie Oosterhuis, and Maarten de Rijke. 2022\.  It Is Different When Items Are Older: Debiasing Recommendations When Selection Bias and User Preferences Are Dynamic. In Proceedings of the Fifteenth ACM International Conference on Web Search and Data Mining. 381–389.
  * Jenkins (2005a) Stephen P Jenkins. 2005a.  Survival analysis.  Unpublished manuscript, Institute for Social and Economic Research, University of Essex, Colchester, UK 42 (2005), 54–56.
  * Jenkins (2005b) Stephen P Jenkins. 2005b.  Survival analysis.  Unpublished manuscript, Institute for Social and Economic Research, University of Essex, Colchester, UK 42 (2005), 54–56.
  * Jiayin et al. (2022) Wang Jiayin, Ma Weizhi, Li Jiayu, Lu Hongyu, Zhang Min, Li Biao, Liu Yiqun, Jiang Peng, and Shaoping Ma. 2022\.  Make Fairness More Fair: Fair Item Utility Estimation and Exposure Re-distribution.  (2022).
  * Li et al. (2021) Jiayu Li, Hongyu Lu, Chenyang Wang, Weizhi Ma, Min Zhang, Xiangyu Zhao, Wei Qi, Yiqun Liu, and Shaoping Ma. 2021.  A Difficulty-Aware Framework for Churn Prediction and Intervention in Games. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery Data Mining. 943–952.
  * Li et al. (2020) Jiacheng Li, Yujie Wang, and Julian McAuley. 2020.  Time interval aware self-attention for sequential recommendation. In Proceedings of the 13th international conference on web search and data mining. 322–330.
  * Li et al. (2022) Yunqi Li, Hanxiong Chen, Shuyuan Xu, Yingqiang Ge, Juntao Tan, Shuchang Liu, and Yongfeng Zhang. 2022.  Fairness in Recommendation: A Survey.  arXiv preprint arXiv:2205.13619 (2022).
  * Mansoury et al. (2020) Masoud Mansoury, Himan Abdollahpouri, Mykola Pechenizkiy, Bamshad Mobasher, and Robin Burke. 2020\.  Fairmatch: A graph-based approach for improving aggregate diversity in recommender systems. In Proceedings of the 28th ACM conference on user modeling, adaptation and personalization. 154–162.
  * Matsuo et al. (2019) Koji Matsuo, Sanjay Purushotham, Bo Jiang, Rachel S Mandelbaum, Tsuyoshi Takiuchi, Yan Liu, and Lynda D Roman. 2019.  Survival outcome prediction in cervical cancer: Cox models vs deep-learning model.  American journal of obstetrics and gynecology 220, 4 (2019), 381–e1.
  * Moolgavkar et al. (2018) Suresh H Moolgavkar, Ellen T Chang, Heather N Watson, and Edmund C Lau. 2018.  An assessment of the Cox proportional hazards regression model for epidemiologic studies.  Risk Analysis 38, 4 (2018), 777–794.
  * Morik et al. ([n. d.]) Marco Morik, Ashudeep Singh, Jessica Hong, and Thorsten Joachims. [n. d.].  Controlling Fairness and Bias in Dynamic Learning-to-Rank. In SIGIR 20. 10.
  * Okura et al. (2017) Shumpei Okura, Yukihiro Tagami, Shingo Ono, and Akira Tajima. 2017\.  Embedding-based news recommendation for millions of users. In Proceedings of the 23rd ACM SIGKDD international conference on knowledge discovery and data mining. 1933–1942.
  * Pang et al. (2020) Liang Pang, Jun Xu, Qingyao Ai, Yanyan Lan, Xueqi Cheng, and Jirong Wen. 2020\.  Setrank: Learning a permutation-invariant ranking model for information retrieval. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval. 499–508.
  * Pei et al. (2019) Changhua Pei, Yi Zhang, Yongfeng Zhang, Fei Sun, Xiao Lin, Hanxiao Sun, Jian Wu, Peng Jiang, Junfeng Ge, Wenwu Ou, et al. 2019\.  Personalized re-ranking for recommendation. In Proceedings of the 13th ACM conference on recommender systems. 3–11.
  * Pitoura et al. (2021) Evaggelia Pitoura, Kostas Stefanidis, and Georgia Koutrika. 2021\.  Fairness in rankings and recommendations: an overview.  The VLDB Journal (2021), 1–28.
  * Rastegarpanah et al. (2019) Bashir Rastegarpanah, Krishna P Gummadi, and Mark Crovella. 2019\.  Fighting fire with fire: Using antidote data to improve polarization and fairness of recommender systems. In Proceedings of the twelfth ACM international conference on web search and data mining. 231–239.
  * Steck (2011) Harald Steck. 2011\.  Item popularity and recommendation accuracy. In Proceedings of the fifth ACM conference on Recommender systems. 125–132.
  * Stensrud and Hernán (2020) Mats J Stensrud and Miguel A Hernán. 2020.  Why test for proportional hazards?  Jama 323, 14 (2020), 1401–1402.
  * Sun et al. (2016) Limei Sun, Ejike Ifeanyi Michael, Shen Wang, and Yue Li. 2016\.  A Time-Sensitive Collaborative Filtering Model in Recommendation Systems. In 2016 IEEE International Conference on Internet of Things (iThings) and IEEE Green Computing and Communications (GreenCom) and IEEE Cyber, Physical and Social Computing (CPSCom) and IEEE Smart Data (SmartData). IEEE, 340–344.
  * Therneau and Grambsch (2000) Terry M Therneau and Patricia M Grambsch. 2000.  The cox model.  In Modeling survival data: extending the Cox model. Springer, 39–77.
  * Wan et al. (2020) Mengting Wan, Jianmo Ni, Rishabh Misra, and Julian McAuley. 2020\.  Addressing marketing bias in product recommendations. In Proceedings of the 13th international conference on web search and data mining. 618–626.
  * Wang et al. (2020) Chenyang Wang, Min Zhang, Weizhi Ma, Yiqun Liu, and Shaoping Ma. 2020.  Make It a Chorus: Knowledge- and Time-aware Item Modeling for Sequential Recommendation. In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval. ACM, Virtual Event China, 109–118.  https://doi.org/10.1145/3397271.3401131
  * Wang et al. (2021) Dongjing Wang, Dengwei Xu, Dongjin Yu, and Guandong Xu. 2021\.  Time-aware sequence model for next-item recommendation.  Appl Intell 51, 2 (Feb. 2021), 906–920.  https://doi.org/10.1007/s10489-020-01820-2
  * Wang et al. (2022a) Jiayin Wang, Weizhi Ma, Jiayu Li, Hongyu Lu, Min Zhang, Biao Li, Yiqun Liu, Peng Jiang, and Shaoping Ma. 2022a.  Make Fairness More Fair: Fair Item Utility Estimation and Exposure Re-Distribution. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 1868–1877.
  * Wang and Zhang (2013) Jian Wang and Yi Zhang. 2013.  Opportunity model for e-commerce recommendation: right product; right time. In Proceedings of the 36th international ACM SIGIR conference on Research and development in information retrieval. 303–312.
  * Wang et al. (2019b) Ping Wang, Yan Li, and Chandan K Reddy. 2019b.  Machine learning for survival analysis: A survey.  ACM Computing Surveys (CSUR) 51, 6 (2019), 1–36.
  * Wang et al. (2019a) Shoujin Wang, Liang Hu, Yan Wang, Quan Z Sheng, Mehmet Orgun, and Longbing Cao. 2019a.  Modeling multi-purpose sessions for next-item recommendations via mixture-channel purpose routing networks. In International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence.
  * Wang et al. (2022b) Yifan Wang, Weizhi Ma, Min Zhang*, Yiqun Liu, and Shaoping Ma. 2022b.  A Survey on the Fairness of Recommender Systems.  ACM Journal of the ACM (JACM) (2022).
  * Wu et al. (2022) Chuhan Wu, Fangzhao Wu, Tao Qi, Qi Liu, Xuan Tian, Jie Li, Wei He, Yongfeng Huang, and Xing Xie. 2022\.  Feedrec: News feed recommendation with various user feedbacks. In Proceedings of the ACM Web Conference 2022. 2088–2097.
  * Wu et al. (2020) Fangzhao Wu, Ying Qiao, Jiun-Hung Chen, Chuhan Wu, Tao Qi, Jianxun Lian, Danyang Liu, Xing Xie, Jianfeng Gao, Winnie Wu, et al. 2020\.  Mind: A large-scale dataset for news recommendation. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 3597–3606.
  * Wu et al. (2021) Xinwei Wu, Hechang Chen, Jiashu Zhao, Li He, Dawei Yin, and Yi Chang. 2021\.  Unbiased learning to rank in feeds recommendation. In Proceedings of the 14th ACM International Conference on Web Search and Data Mining. 490–498.
  * Zhang et al. (2021) Yang Zhang, Fuli Feng, Xiangnan He, Tianxin Wei, Chonggang Song, Guohui Ling, and Yongdong Zhang. 2021.  Causal intervention for leveraging popularity bias in recommendation. In Proceedings of the 44th International ACM SIGIR Conference on Research and Development in Information Retrieval. 11–20.