# Towards Fine-Grained Reasoning for Fake News Detection

Yiqiao Jin1, Xiting Wang2111Xiting Wang is the corresponding author., Ruichao
Yang3, Yizhou Sun1, Wei Wang1, Hao Liao4, Xing Xie2 Work done during an
internship at Microsoft Research Asia.

###### Abstract

The detection of fake news often requires sophisticated reasoning skills, such
as logically combining information by considering word-level subtle clues. In
this paper, we move towards fine-grained reasoning for fake news detection by
better reflecting the logical processes of human thinking and enabling the
modeling of subtle clues. In particular, we propose a fine-grained reasoning
framework by following the human’s information-processing model, introduce a
mutual-reinforcement-based method for incorporating human knowledge about
which evidence is more important, and design a prior-aware bi-channel kernel
graph network to model subtle differences between pieces of evidence.
Extensive experiments show that our model outperforms the state-of-the-art
methods and demonstrate the explainability of our approach.

## Introduction

The emergence of social media has transformed the way users exchange
information online. People are no longer mere reviewers of information, but
content creators and message spreaders. Consequently, it has become much
easier for fake news to spread on the Internet. Since fake news can obscure
the truth, undermine people’s belief, and cause serious social impact (Brewer,
Young, and Morreale 2013), detecting fake news has become increasingly
important for a healthy and clean network environment (Shu et al. 2017).

Recently, neural models have been proposed to detect fake news in a data-
driven manner (Pan et al. 2018; Dun et al. 2021). These works have shown the
promise in leveraging big data for fake news detection. However, works that
approach the task from the perspective of _reasoning_ are still lacking.
According to the literature on psychology, reasoning is the capability of
_consciously applying logic_ for truth seeking (Honderich 2005), and is
typically considered as a distinguishing capacity of _humans_ (Mercier and
Sperber 2017). We observe that such ability is essential to improve the
explainability and accuracy for fake news detection:

Explainability. Most existing works on fake news detection either do not
provide explanations or enable explainability for a small part of the model
(e.g., the attention layer). The major part of the model (e.g. the overall
workflow) remains obscure to humans. This prevents humans to better understand
and trust the model, or steer the model for performance refinement.

Accuracy. When humans reason about the authenticity of a news article, they
have the ability to perform _fine-grained_ analysis for identifying subtle
(e.g., word-level) clues, and can connect different types of clues (e.g.,
textual and social) to draw conclusions. An example is shown in Fig. 1.
Although the four groups of evidence are semantically dissimilar, humans can
logically connect them in terms of subtle clues such as the word “property”,
which leads to a much more confident conclusion about the article. For
example, reasoning in terms of “property” reveals that the accusation of
finding bodies in Clintons’ property (evidence group 1) might be false, since
the women were dead before the Clintons bought the property (evidence group
3). Reasoning with respect to “hate” suggests that users in groups 1 and 2
might post false messages because they hate the Clintons. The overlap between
users in groups 1 and 2 further strengthens this suggestion. Existing methods
lack such capability of fine-grained reasoning: they either do not model the
interactions between different types of evidence or model them at a coarse-
grained (e.g., sentence or post) level.

Figure 1:  A motivating example of fine-grained reasoning for fake news
detection.  Figure 2:  Our proposed _FinerFact_ framework for fake news
detection.

We aim to move towards using deep reasoning for fake news detection. The goal
is to improve accuracy and explainability by 1) better reflecting the logical
processes of human thinking and 2) enabling fine-grained modeling of subtle
clues. In particular, we study three research questions:

  * •

RQ1. Can the model be designed by following the human’s information-processing
model (Lang 2000)?

  * •

RQ2. Can human knowledge about which evidence (e.g., posts and users) is
important be better incorporated?

  * •

RQ3. How does one achieve fine-grained modeling of different types of subtle
clues?

Specifically, we make the following contributions.

First, we design a Fine-grained reasoning framework for Fake news detection
(FinerFact) by following the human’s information-processing model (RQ1). This
enables us to detect fake news by better reflecting the logical processes of
human thinking, which enhances interpretability and provides the basis for
incorporating human knowledge.

Second, we propose a mutual-reinforcement-based method for evidence ranking,
which enables us to better incorporate prior human knowledge about which types
of evidence are the most important (RQ2).

Finally, we design a prior-aware bi-channel kernel graph network to achieve
fine-grained reasoning by modeling different types of subtle clues (RQ3). Our
method improves accuracy, and provides explanations about the subtle clues
identified, the most important claim-evidence groups, and the individual
prediction scores given by each group.

## Methodology

### Problem Definition

Input. The inputs of our model are threefold. Each training sample consists of
1) a news article $S$ to be verified; 2) a collection of online posts $P$ for
the news and the commenting/retweeting relationships between the posts; and 3)
the online users $U$ that publish the posts $P$.

Output. The output of our model is the predicted label of the news, which can
be fake $(y=1)$ or real $(y=0)$.

### Fine-Grained Reasoning Framework

We propose a _Fine -grained reasoning framework for Fake news detection_ by
following the human’s information-processing model (Lang 2000). Our framework
consists of two major modules as shown in Fig. 2.

The first module, claim-evidence graph construction, corresponds to the
_storage_ sub-process of the human’s information-processing model, in which
people select the most important pieces of information and build their in-
between associations to store them in the memory. As of fake news detection,
it corresponds to the process in which people search for key information such
as the major viewpoints, opinion leaders, and the most important posts, which
enables them to get an idea about the key claims and their associated evidence
(e.g., supported posts and users). This step is essential for filtering noise,
organizing facts, and speeding up the fine-grained reasoning process at the
later stage. It also enables us to incorporate human knowledge about which
information is important.

The second module, graph-based fine-grained reasoning, corresponds to the
_retrieval_ sub-process of the human’s information-processing model, in which
people reactivate specific pieces of information based on their associations
for decision making. In fake news detection, this module enables fine-grained
modeling of evidential relations by considering subtle clues, such as the word
“property”, “hate”, and the overlapping user in Fig. 1.

By designing the framework based on the human’s information-processing model,
the overall workflow of our method resembles the logical processes used by
humans, and most of the intermediate results are understandable by ordinary
users. This provides a good basis for users to trust the model and steer it by
integrating human knowledge.

### Claim-Evidence Graph Construction

Our graph construction method contains two parts: 1) mutual-reinforcement-
based evidence ranking, which distinguishes important evidence from noise by
incorporating human knowledge (filtering noise); and 2) topic-aware claim-
evidence association, which follows journalists’ knowledge about quality
journalism (for Excellence in Journalism 2005) to extract the key claims and
associate them with the corresponding evidence (organizing facts).

#### Mutual-Reinforcement-Based Evidence Ranking

As a news article propagates on the Internet, it leaves many traces, e.g.,
posts about the news and users who support the news, which can all be
considered as evidence for verifying the news. Such evidence typically has a
large scale, and performing fine-grained reasoning by considering all evidence
is quite difficult, if not impossible, due to limited GPU memory. To
efficiently and accurately identify the most valuable evidence in an
interpretable way, we propose ranking the evidence by integrating human
knowledge. The human knowledge can be divided into two types based on whether
it considers the inherent attributes (Lampos et al. 2014) of the evidence or
its topological (Pasquinelli 2009) information. We observe that these two
types of knowledge can be integrated in one framework and computed efficiently
by using the mutual reinforcement mechanism (Duan et al. 2012). Specifically,
our mutual-reinforcement-based evidence ranking consists of the following
three steps.

_Step 1: Attribute saliency computation._ We compute the attribute saliency
$E$ based on the human knowledge summarized from the current literature. In
particular, the attribute saliency $e_{u_{i}}$ for a user $u_{i}$ is computed
by using the user impact index (Lampos et al. 2014):

$\displaystyle
e_{u_{i}}=\textrm{ln}\left(\frac{(\phi_{i}^{I}+\theta_{U})^{2}(\phi_{i}^{L}+\theta_{U})}{\phi_{i}^{O}+\theta_{U}}\right)$
(1)

where $\phi_{i}^{I}$, $\phi_{i}^{O}$, $\phi_{i}^{L}$ are $u_{i}$’s follower
count, friend count, and listed count, and $\theta_{U}$ is a smoothing
constant added to ensure that the minimum saliency score is always positive.
The attribute saliency $e_{p_{i}}$ of each post $p_{i}$ is computed based on
its number of retweets $C_{i}$, considering that retweets rarely provide extra
textual information and are usually regarded as votes to the original post
(Chang et al. 2013). Specifically,
$e_{p_{i}}=\textrm{ln}(C_{i}+1)+\theta_{P}$, where $\theta_{P}$ is a smoothing
constant. The attribute saliency $e_{k_{i}}$ of each keyword $k_{i}$ is set to
$\textrm{ln}(\mathrm{freq}(k_{i})+1)+\theta_{K}$, where $\mathrm{freq}(k_{i})$
is the term frequency of $k_{i}$ with respect to the news article and the
posts, and $\theta_{K}$ is a smoothing constant (Rousseau and Vazirgiannis
2013).

_Step 2: Mutual reinforcement evidence graph building._ As shown in Fig. 2, we
build the mutual reinforcement evidence graph $M$ so that it encodes both the
relations within posts, users, or keywords, and the relations between them to
enable the effective modeling of topological saliency. Mathematically,
$M=\\{A_{xy}|x,y\in\\{P,U,K\\}\\}$ is a three-layer graph, where subscript
indices $P$, $U$, $K$ denote posts, users, and keywords, respectively, and
$A_{xy}$ is an affinity matrix that represents relations between items. We
design the graph based on two considerations: 1) $M$ should effectively encode
diverse types of social interactions and 2) edges in $M$ should reveal the
mutual influence between items in terms of saliency. For example, constructing
edges between users and their posts means that if a user is important, then
his/her posts are important, and vice versa. Such human knowledge about which
items should influence each other in terms of saliency can be effectively
incorporated into the edge design. Based on these considerations, we construct
$M$ by using the cosine similarity between the term frequency vectors of the
posts ($A_{PP}$), the commenting relationships between users ($A_{UU}$), the
co-occurrence relationships between keywords ($A_{KK}$), the mentioning
relationships that link a keyword to all the posts and users that mention it
($A_{KP}$, $A_{KU}$), and the authoring relationships that link a user to all
the posts that s/he has published ($A_{UP}$). More details about the
construction of $M$ and how human knowledge is used are given in the
supplement.

_Step 3: Iterative saliency propagation._ We then compute the saliency $R$
based on the mutual reinforcement mechanism (Duan et al. 2012). In particular,
we treat the attribute saliency $E$ as a prior and integrate it with the
saliency propagation process on $M$:

$R^{(i+1)}=d\tilde{A}R^{(i)}+(1-d)E$ (2)

$\hat{A}=\begin{bmatrix}\beta_{PP}A_{PP}&\beta_{KP}A_{KP}&\beta_{UP}A_{UP}\\\
\beta_{PK}A_{PK}&\beta_{KK}A_{KK}&\beta_{UK}A_{UK}\\\
\beta_{PU}A_{PU}&\beta_{KU}A_{KU}&\beta_{UU}A_{UU}\end{bmatrix},R^{(i)}=\begin{bmatrix}R_{P}^{(i)}\\\
R_{K}^{(i)}\\\ R_{U}^{(i)}\end{bmatrix},E=\begin{bmatrix}E_{P}\\\ E_{K}\\\
E_{U}\end{bmatrix}$

where $R^{(i)}$ is the joint ranking score vector in the $i$-th iteration,
$\tilde{A}$ is the normalized affinity matrix derived from $\hat{A}$, and
$\beta_{xy}$ is a balancing weight to adjust the interaction strength among
posts, keywords, and users.

_Interpretability and efficiency._ The designed method is highly interpretable
and steerable, since each type of saliency can be easily explained to and
controlled by human users. According to Eq. (2), a piece of evidence (e.g., a
supported user) is important if it has a large attribute saliency (e.g., has
many followers) and is connected with other salient evidence (e.g., writes a
salient post). Other types of human knowledge can also be easily integrated by
slightly modifying the equation. Our method is also efficient. In practice,
ranking 240,000 posts, users, and keywords takes 620 seconds. Without evidence
ranking, performing fine-grained reasoning on the same data causes the out of
memory issue on NVIDIA Tesla V100.

#### Topic-Aware Claim-Evidence Association

Given the saliency scores $R$, a straightforward way for constructing the
claim-evidence graph is to select the pieces of evidence with the largest
saliency scores. However, this method may easily obscure the truth by focusing
only on one aspect of the story. For example, the news article in Fig. 1 may
be dominated by posts related to evidence group 1, which are posted
deliberately by users who hate the Clintons. To disclose the truth, we need to
observe all four evidence groups closely. This echoes the journalists’
knowledge about quality journalism (for Excellence in Journalism 2005), which
states that a high-quality news article should cover multiple viewpoints to
reveal two or more sides of the story. Motivated by this insight, we propose a
topic-aware method, which consists of the following steps.

_Step 1: Topic modeling._ A typical solution to mine major viewpoints in a
text corpus is topic modeling. In the scenario of fake news detection, the
text corpus consists of each post and news sentence. We then utilize LDA
(Blei, Ng, and Jordan 2003) to mine the topics, which summarizes the main
viewpoints and serve as a bridge between the claims in the news sentences and
the keywords in the evidence graph $M$:

  * •

Each topic $t$ is represented by a distribution of keywords
$\mathbb{P}(k_{i}|t)$ in $M$. For each topic $t$, its top $N_{K}$ keywords
$K^{t}$ are the ones that have the largest $\mathbb{P}(k_{i}|t)$.

  * •

Each news sentence $s_{i}$ is represented by a distribution of topics
$\mathbb{P}(t|s_{i})$. Given a topic $t$, we can extract its top $N_{S}$
sentences $S^{t}$ that have the largest $\mathbb{P}(t|s_{j}^{t})$.

_Step 2: Key claim and evidence extraction._ To extract the key claims and
their associated evidence based on the topics, we first select the top $N_{T}$
topics with the maximum aggregate saliency score $r_{t}=\sum_{k_{i}\in
K^{t}}\mathbb{P}(k_{i}|t)r_{k_{i}}$, where $K^{t}$ is the set of top keywords
extracted in step 1, and $r_{k_{i}}$ is the saliency score computed by using
mutual-reinforcement-based evidence ranking. The topics that are selected in
this way not only cover major viewpoints of the article, but are also related
with the most salient evidence in $M$.

For each selected topic $t$, its corresponding claims are the top news
sentences $S^{t}$ extracted in step 1. The key evidence consists of two parts.
The first part is the key posts in $t$. Given a set of posts that are
connected to the keyword set $K^{t}$, we normalize the saliency score of each
post in the set to obtain a probability distribution, and then sample a set
$P^{t}$ with $N_{P}$ posts according to the distribution. Similarly, we sample
a set $U^{t}$ with $N_{U}$ users that are relevant with $t$, and treat $U^{t}$
as the second part of the evidence. Keywords are not considered as evidence
because they are less useful for fine-grained reasoning when considered
without the context. To model keywords more effectively, we treat the posts as
ordered sequences of keywords in fine-grained reasoning.

_Step 3: Graph construction._ Finally, we build a claim-evidence graph $G$ as
shown in Fig. 2. In $G$, each node $v$ is a tuple $(t,S^{t},P^{t},U^{t})$ that
corresponds to a selected topic $t$, where $S^{t}$ refers to the key claims
and $P^{t}$, $U^{t}$ form an evidence group shown in Fig. 1. Given all nodes
$V$, a straightforward approach to construct $G$ is to build edges between two
nodes if the percentage of overlapping words is larger than a threshold (Zhong
et al. 2020). However, this method may easily overlook important subtle clues,
because 1) it is difficult to find an appropriate global threshold and 2)
topics (or evidence groups) may be connected logically with different words
(e.g., ‘damn”, “hate”, and “hell” in Fig. 1). Based on this observation, we
choose to build a fully connected graph and let the fine-grained reasoning
module to decide whether subtle clues exist for a set of topics.

### Fine-Grained Graph-based Reasoning

After constructing the claim-evidence graph $G$, we model subtle clues and
effectively leverage them for prediction through fine-grained graph-based
reasoning. Our method is based on the Kernel Graph Attention Network (KGAT)
(Liu et al. 2020). We choose this method because it can effectively model
subtle differences between statements and propagate the learned information on
the graph. However, KGAT cannot be directly applied on our claim-evidence
graph, because it handles only textual inputs and cannot integrate the learned
saliency $R$, which incorporates human knowledge about which evidence is
important. To solve these issues, we propose a Prior-Aware Bi-Channel KGAT
that extends KGAT to 1) simultaneously model subtle clues from both textual
(posts) and social (users) inputs with two connected channels; and 2)
integrating existing knowledge about important evidence with attention priors.
Mathematically, the final prediction $\mathbb{P}(y|G,R)$ is obtained by
combining individual node-level predictions:

$\displaystyle\centering\mathbb{P}(y\mid G,R)=\sum_{v\in
G}\underbrace{\mathbb{P}(y\mid v,G)}_{\begin{subarray}{c}\text{Node label}\\\
\text{prediction}\end{subarray}}\underbrace{\mathbb{P}(v\mid
G,R)}_{\begin{subarray}{c}\text{Node importance}\\\
\text{learning}\end{subarray}}\@add@centering$ (3)

This formulation provides explainability for individual prediction scores that
each node (or claim-evidence group) gives and importance of the nodes for the
final prediction. Since we do not have node-level annotations for label
prediction or importance, we learn them automatically with:

  * •

Node label prediction with bi-channel kernel matching, which accurately
computes $\mathbb{P}(y|v,G)$ by integrating different types of subtle clues
from the whole graph;

  * •

Node importance learning with attention priors, which effectively models
$\mathbb{P}(v|G,R)$ by integrating the evidence saliency $R$ as attention
priors.

#### Node Label Prediction with Bi-Channel Kernel Matching

Given a node $v$, we predict the individual label it gives by aggregating
subtle clues from the whole graph. To reason about subtle clues that are
provided by both the textual and social (user) inputs, we design two
interconnected channels. We will first introduce how each channel is designed
when they are modeled _independently_ , and then illustrate how the channels
can be _fused_ for prediction.

_Text-based reasoning channel._ We first derive an initial textual
representation for node $v=(t,S^{t},P^{t},U^{t})$ by concatenating the claims
in $S^{t}$ and evidential posts in $P^{t}$ with token “[SEP]”. The
concatenated string is then encoded by using BERT (Devlin et al. 2019):

$\displaystyle[\mathbf{h}_{v}^{0},\mathbf{h}_{v}^{1},...\mathbf{h}_{v}^{N_{v}}]=\textrm{BERT}(S^{t}\oplus
P^{t}),\ \ \ \ \mathbf{z}_{v}=\mathbf{h}_{v}^{0}$ (4)

where $\mathbf{h}_{v}^{i}$ denotes the BERT embedding for the $i$-th token.
$\mathbf{z}_{v}$, which corresponds to the embedding of the “[CLS]” token, is
considered as the initial textual representation for $v$.

The fine-grained match features between nodes $v$ and $q$ can then be
extracted by constructing a token-level translation matrix $L_{q,v}$. In
$L_{q,v}$, each entry
$l_{q,v}^{i,j}=\textrm{cos}(\mathbf{h}_{q}^{i},\mathbf{h}_{v}^{j})$ is the
cosine similarity between their token representations. For each token $i$ in
node $q$, we use $\Upsilon$ kernels to extract the kernel match features
between the token and its neighbor $v$:

$\displaystyle\Psi_{\tau}(L_{q,v}^{i})=\log\sum_{j}\exp(-\frac{(l_{q,v}^{i,j}-\mu_{\tau})^{2}}{2\sigma_{\tau}^{2}})$
(5)
$\displaystyle\vec{\Psi}(L_{q,v}^{i})=\\{\Psi_{1}(L_{q,v}^{i}),\ldots,\Psi_{\Upsilon}(L_{q,v}^{i})\\}$
(6)

Each $\Psi_{\tau}$ is a Gaussian kernel that concentrates on the region
defined by the mean similarity $\mu_{\tau}$ and the standard deviation
$\sigma_{\tau}$. The kernel match feature $\vec{\Psi}$, which consists of
$\Upsilon$ kernels, summarizes how similar the $i$-th token in $q$ is to all
tokens in $v$ at different levels. Such soft-TF match features have been shown
effective for fact verification (Liu et al. 2020). In our framework, they help
identify subtle clues by comparing different claim-evidence groups (nodes).
For example, in Fig. 1, the match features can help identify “hate” in group 4
(node $q$) by comparing it with all words in group 2 (node $v$). This
neighbor-aware token selection is achieved by computing an attention score
based on $\vec{\Psi}$:

$\displaystyle\alpha_{q,v}^{i}=\textrm{softmax}_{i}(W_{1}\vec{\Psi}(L_{q,v}^{i})+b_{1})$
(7)

We can then compute the content to propagate from $q$ to $v$:

$\displaystyle\hat{\mathbf{z}}_{q,v}=\sum_{i}\alpha_{q,v}^{i}\mathbf{h}_{q}^{i}$
(8)

Note that by setting $\sigma_{\tau}$ to $\infty$, Eq. (8) degenerates to mean
pooling, which assigns an equal weight to all tokens.

Given $\hat{\mathbf{z}}_{q,v}$ that contains the information to be propagated
to $v$, we derive a final textual representation $\kappa_{v}$ for $v$ by
attentively aggregating $\hat{\mathbf{z}}_{q,v}$ from all $q\in G$:

$\displaystyle\kappa_{v}=(\sum_{q\in
G}\gamma_{q,v}\cdot\mathbf{\hat{z}}_{q,v})\oplus\mathbf{z}_{v}$ (9)
$\displaystyle\gamma_{q,v}=\mathrm{softmax}_{q}(\textrm{MLP}(\mathbf{\hat{z}}_{q,v}\oplus\mathbf{z}_{v}))$
(10)

The kernel-based textual representation $\kappa_{v}$ aggregates fine-grained,
token-level subtle clues from the whole graph, and can be used to reason about
the authenticity of the news from the perspective of node $v$. Next, we
introduce how to derive kernel-based user representations with a user channel,
and how these two channels can be fused for final prediction.

_User-based reasoning channel._ The initial user representation
$\mathbf{x}_{v}$ for node $v=(t,S^{t},P^{t},U^{t})$ is derived by applying a
graph neural network, APPNP (Klicpera, Bojchevski, and Günnemann 2018), on the
mutual reinforcement evidence graph $M$. We choose APPNP because its efficient
message-passing scheme enables it to scale to large graphs with hundreds of
thousands of nodes. Specifically, for each user in $U^{t}$, we first obtain
its feature embedding by using a look up layer, which encodes the main user
attributes including the user’s follower count, friend count, listed count,
favourite count, status count, the number of words in the self description, as
well as the account status about whether the user is verified or geo-enabled.
We then use the message passing scheme of APPNP to aggregate the feature
embeddings from the neighbor users in $M$. This results in an initial user
representation $\mathbf{u}_{v}^{i}$ for each user, and max pooling is used to
derive the initial user presentation $\mathbf{x}_{v}$ for node $v$:

$\displaystyle[\mathbf{u}_{v}^{0},...\mathbf{u}_{v}^{\tilde{N}_{v}}]=\textrm{APPNP}(M),\
\
\mathbf{x}_{v}=\text{maxpool}(\mathbf{u}_{v}^{0},...\mathbf{u}_{v}^{\tilde{N}_{v}})$
(11)

We can then derive the kernel-based user representation $\tilde{\kappa}_{v}$
by using a kernel attention mechanism similar with that in the text-based
reasoning channel:

$\displaystyle\rho_{q,v}^{i}=\mathrm{softmax}_{i}(W_{2}\vec{\Psi}(\tilde{L}_{q,v}^{i})+b_{2})$
(12)
$\displaystyle\mathbf{\hat{x}}_{q,v}=\sum_{i}\rho_{q,v}^{i}\mathbf{u}_{q}^{i}$
(13)
$\displaystyle\lambda_{q,v}=\mathrm{softmax}_{q}(\textrm{MLP}(\mathbf{\hat{x}}_{q,v}\oplus\mathbf{x}_{v}))$
(14)
$\displaystyle\tilde{\kappa}_{v}=(\sum_{q}\lambda_{q,v}\cdot\mathbf{\hat{x}}_{q,v})\oplus\mathbf{x}_{v}$
(15)

where $\tilde{L}_{q,v}$ is a user-level translation matrix in which each entry
is a cosine similarity score between two initial user representations. This
formulation of $\tilde{\kappa}_{v}$ allows us to reason about the final
prediction by considering user-based subtle clues, e.g., the overlap between
users in Fig. 1.

_Channel fusion._ We fuse the channels to better integrate information from
the textual and social inputs. To this end, we first refine the node-level
attention scores by aggregating the textual and user representations.
Specifically, we replace $\gamma_{q,v}$ and $\lambda_{q,v}$ in Eqs. (10) and
(14) with
$\mathrm{softmax}_{q}(\textrm{MLP}(\mathbf{\hat{z}}_{q,v}\oplus\mathbf{z}_{v}\oplus\mathbf{\hat{x}}_{q,v}\oplus\mathbf{x}_{v}))$.
This allows us to combine both textual and social clues when reasoning about
one node based on another node. For example, in Fig. 1, we may consider both
words related to “hate” and the overlapping user when reasoning about evidence
group 1 from the perspective of evidence group 2.

We then fuse the kernel-based textual and user representations to predict the
label that node $v$ gives:

$\displaystyle\begin{split}&\mathbb{P}(y\mid
v,G)=\textrm{sigmoid}_{v}(W_{5}(\kappa_{v})+W_{6}(\mathbf{\tilde{\kappa}}_{v})+b_{5})\end{split}$
(16)

|  |  |  | PolitiFact |  |  |  | GossipCop |
---|---|---|---|---|---|---|---|---|---
|  | Pre | Rec | F1 | Acc | AUC | Pre | Rec | F1 | Acc | AUC
| SVM | 0.7460 | 0.6826 | 0.6466 | 0.6694 | 0.6826 | 0.7493 | 0.6254 | 0.5955 | 0.6643 | 0.6253
G1 | RFC | 0.7470 | 0.7361 | 0.7362 | 0.7406 | 0.8074 | 0.7015 | 0.6707 | 0.6691 | 0.6918 | 0.7389
DTC | 0.7476 | 0.7454 | 0.7450 | 0.7486 | 0.7454 | 0.6921 | 0.6922 | 0.6919 | 0.6959 | 0.6929
| GRU-2 | 0.7083 | 0.7048 | 0.7041 | 0.7109 | 0.7896 | 0.7176 | 0.7079 | 0.7079 | 0.718 | 0.7516
| B-TransE | 0.7739 | 0.7658 | 0.7641 | 0.7694 | 0.8340 | 0.7369 | 0.7330 | 0.7340 | 0.7394 | 0.7995
G2 | KCNN | 0.7852 | 0.7824 | 0.7804 | 0.7827 | 0.8488 | 0.7483 | 0.7422 | 0.7433 | 0.7491 | 0.8125
GCAN | 0.7945 | 0.8417 | 0.8345 | 0.8083 | 0.7992 | 0.7506 | 0.7574 | 0.7709 | 0.7439 | 0.8031
| KAN | 0.8687 | 0.8499 | 0.8539 | 0.8586 | 0.9197 | 0.7764 | 0.7696 | 0.7713 | 0.7766 | 0.8435
Ours | FinerFact | 0.9196 | 0.9037 | 0.9172 | 0.9092 | 0.9384 | 0.8615 | 0.8779 | 0.8685 | 0.8320 | 0.8637
Impv. | +5.1% | +5.4% | +6.3% | +5.1% | +1.9% | +8.5% | +10.8% | +9.7% | +5.5% | +2.0%

Table 1: Performance comparison of _FinerFact_ w.r.t. baselines. The best
results are highlighted in bold.

#### Node Importance Learning with Attention Priors

Node importance decides which topic (node) should be considered more in
detecting fake news. To better characterize the relative importance of each
node with regard to the predicted label, we learn the probability
$\mathbb{P}(v\mid G,R)$ by jointly consider its claims, evidence, and the
evidence saliency $R$:

$\displaystyle\mathbb{P}(v\mid G,R)=\textrm{softmax}_{v\in
G}(\varphi(v)+\delta(v,R)+b_{6})$ (17)
$\displaystyle\varphi(v)=W_{7}\left[\text{average}_{i}(\vec{\Psi}(\hat{L}_{S^{t},P^{t}}^{i}))\right]$
(18) $\displaystyle\delta(v,R)=W_{8}R_{P^{t}}+W_{9}R_{U^{t}}+W_{10}R_{K^{t}}$
(19)

where $\varphi(v)$ is the node ranking feature learned by comparing the claims
with the evidence, and $\delta(v,R)$ is the attention prior used to encode the
previously learned saliency score $R$, which embeds human knowledge about
evidence significance. More specifically, $\varphi(v)$ is derived by using the
kernel match feature $\vec{\Psi}(\hat{L}_{S^{t},P^{t}}^{i})$, where
$\hat{L}_{S^{t},P^{t}}$ is a token-level translation matrix that measures the
cosine similarities between tokens in the claims $S^{t}$ and tokens in the
supported posts $P^{t}$. The attention prior $\delta(v,R)$ is learned by
combining the saliency scores $R_{P^{t}}$, $R_{U^{t}}$, and $R_{K^{t}}$, which
correspond to the top posts, users, and keywords that are the most relevant
with the topic $t$ of the node $v$. $W_{8},W_{9},W_{10}$ are non-negative
weight vectors that enable us to re-weight each piece of evidence during fine-
grained reasoning.

#### Joint Optimization

Let $\|\Theta\|$ be the $L2$ norm of all model parameters. For each news
article $S$, we compute the loss

$\mathcal{L}_{S}=-y^{*}\log\left(\hat{p}\right)+(1-y^{*})\log\left(1-\hat{p}\right)+\lambda_{reg}\|\Theta\|^{2}$
(20)

where $y^{*}$ is its the ground-truth label, $\hat{p}=\mathbb{P}(y|G,R)$ is
the probability learned based on Eq. (3), and $\lambda_{reg}$ is the
regularization coefficient. The parameters are then optimized jointly by
minimizing $\sum_{S\in\mathcal{N}}\mathcal{L}_{S}$, where $\mathcal{N}$
consists of all the news articles in the training set.

## Experiment

### Experimental Setup

#### Dataset

To evaluate the performance of _FinerFact_ , we conduct experiments on two
benchmark datasets, PolitiFact and GossipCop (Shu et al. 2020), which contain
815 and 7,612 news articles, and the social context information about the
news, their labels provided by journalists and domain experts. We follow (Dun
et al. 2021) to preprocess the data and conduct experiments. More details
about dataset and the preprocessing steps are given in the supplement.

#### Baselines

We compare our _FinerFact_ method with eight baselines, which can be divided
into two groups:

The first group (G1) is content-based methods, which leverage the textual or
visual content of the news for fake news detection. G1 contains four
baselines: SVM (Yang et al. 2012), GRU-2 (Ma et al. 2016), RFC (Kwon et al.
2013), and DTC (Castillo, Mendoza, and Poblete 2011).

The second group (G2) consists of knowledge-aware methods that detect fake
news by leveraging auxiliary knowledge such as knowledge graphs and social
knowledge about the online posts. This group includes four methods: B-TransE
(Pan et al. 2018), KCNN (Wang et al. 2018a), GCAN (Lu and Li 2020) and KAN
(Dun et al. 2021).

#### Evaluation Criteria

Our evaluation criteria include Precision (Pre), Recall (Rec), the F1 score,
Accuracy (Acc), and Area Under the ROC curve (AUC). We conduct 5-fold cross
validation and the average performance is reported.

Figure 3:  Results of the ablation study.

#### Implementation Details

To choose the number of topics, we conducted a grid search within the range
[2, 10] and picked the number that results in the smallest perplexity. BERT is
fine-tuned during training. A more comprehensive description about the
implementation details, experimental setup, and evaluation for topic quality
are in the supplement.

### Overall Performance

Table 1 compares our method _FinerFact_ with the baselines. As shown in the
table, _FinerFact_ consistently outperforms the baseline in both datasets. For
example, _FinerFact_ performs better than the most competitive baseline _KAN_
by 6.3%, 5.1% on PolitiFact and 9.7%, 5.5% on GossipCop, respectively, in
terms of the F1-score and accuracy. This demonstrates the effectiveness of our
fine-grained reasoning framework, which enables the model to make predictions
by identifying and connecting different types of subtle clues. Meanwhile,
comparing with _GCAN_ , which models the interactions between the textual
content and social information with co-attention, _FinerFact_ increases F1 by
8.3%, 9.8% on the two datasets. This implies that our kernel-attention-based
approach can better model the interactions between news articles and evidence.
We also observe that methods that incorporate external knowledge (G2)
generally perform better than content-based methods (G1). This illustrates the
usefulness of external knowledge in fake news detection.

### Ablation Study and Sensitivity Analysis

Figure 4:  Sensitivity analysis w.r.t. the number of kernels.

Figure 5: Reasoning with _FinerFact_ : (a) the keyword layer of the mutual
reinforcement graph $M$, with saliency $R$ indicated by the font size; (b)
fine-grained reasoning over the claim-evidence graph $G$. Each color encodes a
topic.

We conduct the ablation study by implementing five variants of our method: 1)
FF-P removes the attention prior $\delta(v,R)$ when learning node importance;
2) FF-B eliminates bi-channel reasoning by removing the user-based reasoning
channel; 3) FF-K replaces the kernel-based representation learning with a GNN-
based aggregation scheme, i.e., replacing $\hat{\mathbf{z}}_{q,v}$ and
$\hat{\mathbf{x}}_{q,v}$ with $\mathbf{z}_{q}$ and $\mathbf{x}_{q}$ in Eqs.
(9)(15); 4) FF-I excludes node importance learning and assigns an equal weight
to every node; 5) FF-M eliminates mutual-reinforcement-based evidence ranking,
and selects the evidence for each topic $t$ by random sampling. The ablation
study results in Fig. 3 show that removing each component leads to a decrease
in model performance, which demonstrates the effectiveness of our major
components. A result of FF-T, which replaces our pretrained text encoder with
that of KAN, can be found in the supplement.

We then conduct a sensitivity analysis of _FinerFact_ by changing the number
of kernels $\tau$. Fig. 4 shows that _FinerFact_ consistently outperforms the
state-of-art baseline _KAN_ with varying numbers of kernels, which
demonstrates the robustness of our method. In addition, the performance is the
best when using around 11 kernels. Using more kernels does not necessarily
lead to better performance due to overfitting.

### Case Study

In addition to improving accuracy, our method also enables humans to
understand most parts in the reasoning workflow. In this case study, we
illustrate how _FinerFact_ reasons about the authenticity of a news story,
which is about FBI lawyer Lisa Page disclosing that she was instructed to
cover-up China’s hacks of the DNC server. _FinerFact_ successfully identifies
that the news is fake, with a detailed explanation about the salient evidence,
subtle clues, and the prediction scores for each viewpoint.

Identifying salient evidence. As shown in Fig. 5(a), _FinerFact_ identifies
meaningful and relevant keywords that belong to diverse topics. For each topic
$t$, we can further understand its key evidence by observing its salient posts
$P^{t}$ and average user saliency $\bar{r}_{U^{t}}$. As shown in Fig. 5(b),
users of topic 1 support the news because of their political stance (consider
China as a threat) and are generally not credible opinion leaders (small
$\bar{r}_{U^{t}}$). In contrast, users of topic 4, who question that the news
is fake with more objective reasons, e.g., it is unlikely that an outsider
lawyer knows about the server hack (Fig. 5A), receive more attention (larger
$\bar{r}_{U^{t}}$).

Reasoning with subtle clues. The token-level and user-level attention scores
$\alpha^{i}_{q,v}$ and $\rho^{i}_{q,v}$ reveal the subtle clues _FinerFact_
detects. For example, in topic 2, the words with the largest
$\alpha^{i}_{2,1}$ and $\alpha^{i}_{2,4}$ are “china” and “conspiracy”. These
clues are meaningful and interesting: the statement about “china” being
unlikely to collaborate with FBI in topic 2 decreases the credibility of the
posts in topic 1, and relating “conspiracy” with topic 4 (about “hacking”)
enables us to understand that the news may be fake because such a hacking
conspiracy is likely to be made up by people who like to talk about it (Fig.
5B). Topics 1 and 4 are also related: user 2, who has the largest
$\rho^{i}_{4,1}$, questions users in topic 1 by commenting on them, and points
out that China’s problem in terms of intellectual property does not mean that
Chinese will hack the server (Fig. 5C).

Prediction for each viewpoint. Based on the subtle clues, _FinerFact_ makes
prediction for each node. Our method understands that evidence from groups 1
and 3 imply that the news is true ($\mathbb{P}(y=0|v,G)>0.5$) and that the
evidence from groups 2 and 4 imply that the news is fake
($\mathbb{P}(y=0|v,G)<0.5$). It assigns a low probability score that is close
to 0.5 to group 1 by propagating the information from groups 2 and 4 to group
1 (large $\gamma_{q,v}$). It also assigns a small node importance
$\mathbb{P}(v|G,R)$ to group 1. This is reasonable, since group 1 has a low
user saliency $\bar{r}_{U^{t}}$, which can be modeled by using the attention
prior. While the users in group 3 are considered salient according to the
mutual reinforcement graph, we find that they are not talking about whether
the article is true, but are instead drifting towards criticizing Hillary. Our
model successfully identifies this and assigns a low node importance to topic
3.

Steering the model. _FinerFact_ also provides opportunities for users to steer
and refine the model. For example, we may integrate _FinerFact_ with the
method proposed by Liu et al. (2015) to enable interactive refinement of
evidence ranking. Please refer to the supplement for more details.

## Related Works

Methods for fake news detection can be divided into two main categories:
content-based and knowledge-aware.

Content-based methods mainly utilize the textual or visual content from the
news article and related posts for news verification (Yang et al. 2012; Afroz,
Brennan, and Greenstadt 2012; Kwon et al. 2013; Przybyla 2020; Ma et al. 2016;
Zellers et al. 2019; Qi et al. 2019; Gupta et al. 2013; Jin et al. 2016b;
Kaliyar, Goswami, and Narang 2021). These methods enable the detection of fake
news at an early stage (Wei et al. 2021; Pelrine, Danovitch, and Rabbany
2021). However, their performance is limited as they ignore auxiliary
knowledge for news verification.

Knowledge-aware methods leverage auxiliary knowledge for news verification
(Ruchansky, Seo, and Liu 2017; Wang et al. 2018b; Shu et al. 2019; Jin et al.
2016a; Ma, Gao, and Wong 2018; Cho et al. 2014; Wang et al. 2018a).

These methods typically utilize external knowledge about entity relationships
(Xu et al. 2022; Dun et al. 2021; Pan et al. 2018; Silva et al. 2021; Hu et
al. 2021) or social knowledge about online posts (Lu and Li 2020; Nguyen et
al. 2020; Khoo et al. 2020; Bian et al. 2020) for fake news detection. While
existing methods have demonstrated the usefulness of heterogeneous social
relations and external information (Yuan et al. 2019), they either do not
model the interactions between the news content and different types of
knowledge data, or model them at a coarse-grained (e.g., sentence or post)
level, which limits their performance.We tackle this issue by proposing a
prior-aware bi-channel kernel graph network, which enables fine-grained
reasoning and improves detection accuracy.

## Conclusion

We propose _FinerFact_ , a fine-grained reasoning framework for explainable
fake news detection. We devise a mutual-reinforcement-based method for
efficient evidence ranking and a prior-aware bi-channel kernel graph network
for fine-grained reasoning on multiple groups of evidence. Experimental
results show the effectiveness of our method.

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## Supplementary Material

### Steering the Model

_FinerFact_ is designed to provide a basis for humans to steer the model and
refine it. Here, we introduce three possible ways to steer our model by
integrating human knowledge.

Incremental evidence ranking refinement. Incorporating MutualRanker (Liu et
al. 2015) into our model enables _FinerFact_ to incrementally refine evidence
ranking based on user needs or insights. For example, if a user identifies an
important piece of evidence, e.g., an informative post, a keyword that should
be paid more attention to, or a user that s/he agrees with, s/he can quickly
refine the model locally to retrieve more related evidence, which will then
help improve fake news detection. The user could also decrease the saliency of
the evidence that is not interesting. For example, in the case study provided
in the paper, most posts that mention “hillary” are not discussing about the
news content, but are instead drifting from the main topics to criticizing
Hillary. After identifying this issue, the user could decrease the saliency of
“hillary”, and this information will be propagated to other related evidence
incrementally to enable model refinement.

Interactive salient topic refinement. Our topic-aware method provides a chance
for humans to refine evidence ranking at a coarser granularity (topic-level).
For example, users can quickly understand each topic and select the topics of
interesting for fine-grained reasoning. Users can also increase the relative
importance for an interesting topic during fine-grained reasoning by using the
attention prior. In particular, we may increase the saliency of all posts and
users in the topic when computing the attention prior $\delta(v,R)$ in Eq.
(19). This automatically increases the node importance for the final
prediction. Topic mining could also be systematically refined by adding must-
link or cannot-link constraints (Basu, Banerjee, and Mooney 2004), or using
interactive methods like Utopian (Choo et al. 2013).

Mutual reinforcement evidence graph refinement. Our mutual reinforcement
method is designed based on human knowledge about attribute saliency (evidence
with which attribute is important) and topological saliency (how saliency
should propagate among evidence). Currently, we provide a default setting
summarized from the literature, which shows good performance. Users could also
refine this process based on their own insights and needs. For example, if a
user has an additional set of data, e.g., the number of likes a post receives,
s/he can integrate such data by changing the way we compute the attribute
saliency $E_{P}$ for posts. Or, if a user wishes to better consider the
semantic similarity between posts, s/he can change the definition of $A_{PP}$
from cosine similarity between term frequency vectors of the posts to the
cosine similarity between the BERT (Devlin et al. 2019) representations of
posts.

### Implementation Details

#### Dataset

The statistics of the datasets are described in Table 2. We remove notations
in the posts including 1) hashtags starting with ’$\\#$’; 2) mentioning
notations that starts with ’$@$’; and 3) website URLs.

For node-level label prediction, there is no training objective, since no
node- or evidence-level label annotations are provided in the datasets.

| # True | # Fake | # Total
---|---|---|---
PolitiFact | 443 | 372 | 815
GossipCop | 4219 | 3393 | 7612
Table 2: Statistics of the datasets

#### Hyperparameter Settings

The damping factor $d$ for the mutual reinforcement graph is set to 0.85 by
following (Brin and Page 1998). For the mutual reinforcement graph, we set
each intra-graph balancing weight $\beta_{xx}=1$ and set each inter-graph
balancing weight $\beta_{xy}$ to $0.5$, where $x\neq y$. We set the damping
factor $d$ to 0.85 according to (Brin and Page 1998). The smoothing constants
$\theta_{P},\theta_{K},\theta_{U}$ in the computation of attribute saliency
are all set to $1e-3$. $N_{K},N_{T}$ are set to 7, 5, respectively. For fine-
grained reasoning, we use the Adam optimizer (Kingma and Ba 2015) and a
learning rate of 5e-5. We use a batch size of 8 with accumulation step of 8.
$N_{K},N_{T},N_{S},N_{P},N_{U}$ are set to 7, 5, 3, 6, 32 respectively. We use
11 kernels to extract multiple levels of interactions. One kernel with
$\mu_{\tau}=1$ and $\sigma_{\tau}=1e-3$ is used to model exact matches (Dai et
al. 2018). The other kernels all have $\sigma_{\tau}=0.1$, and their mean
$\mu_{\tau}$ are evenly spaced within $[-1,1]$. Each node $v$ contains 3 news
sentences as its claim in $S_{t}$, 6 posts as its evidence in $P_{t}$. $N_{U}$
is set to 32.

#### Mutual Reinforcement Evidence Graph Building

The mutual reinforcement evidence graph $M=\\{A_{xy}|x,y\in\\{P,U,K\\}\\}$ is
a three-layer graph, where subscript indices $P$, $U$, $K$ denote posts,
users, and keywords, respectively, and $A_{xy}$ is an affinity matrix. The
edge weight $a_{p_{i},p_{j}}$ between posts $p_{i}$ and $p_{j}$ is the cosine
similarity between their term frequency vectors, which captures the in-between
interactions between textually similar tweets (Zangerle, Gassler, and Specht
2013). Users are connected with commenting relationships, which encodes the
opinion diffusion within the social network. Specifically, $a_{u_{i},u_{j}}$
is 1 if $u_{i}$ comments on $u_{j}$’s post and is 0 otherwise. Edges between
the keywords are We consider two types of connections between different types
of evidence: 1) mentioning relationship: a keyword is linked to all the posts
and users that mentioned it; and 2) authoring relationship: a user is linked
to all the posts that s/he has published. All edges except for the ones
between the posts have a weight of 1.

Our idea is to use human knowledge to decide how the importance of each
evidence should propagate. For example, we can link users according to retweet
relationships because a user that is retweeted by an important user is usually
also important. In comparison, linking users according to the order that they
tweeted is less meaningful, as it is hard to say whether users who discussed
the news earlier or later are more important. Other candidate user relations
such as mentioning the same words are reasonable, but they reveal user
importance in a less direct way compared with retweets.

### Supplementary Experiments

#### Evaluation of Topic Quality

We evaluate whether topics are meaningful with case by case manual
investigation (e.g., case study in Fig. 5). Our preliminary study with 5 users
shows that like the topics in Fig. 5, most topics (51 out of 60) can be
interpreted ($\geq$3 for a 4-point Likert scale) after checking their keywords
and claims.

#### Leveraging Different Text Encoders

To evaluate whether our method performs better than KAN when they use the same
text encoder,  we implement FF-T. This variant of our method replaces BERT in
FinerFact with a 1-layer Transformer encoder, same as the text encoder used in
KAN. Results show that FF-T performs better than KAN, with a Pre / Rec / F1 /
Acc / AUC of 0.9091 / 0.9182 / 0.8810 / 0.8864 / 0.9234 and 0.8579 / 0.8874 /
0.8602 / 0.8310 / 0.8600 on PolitiFact and GossipCop, respectively. We use
randomly initialized word embedding in FF-T. Leveraging word2vec and external
knowledge about entities like that in KAN may further improve the result.

#### Complexity and Efficiency

The complexity of our model is $O(N_{v}^{2}N_{E}^{2})$, where $N_{v}$ is the
maximum sequence length of a piece of evidence, and $N_{E}$ is the word
embedding size. It takes 11 and 126 minutes to train FinerFact on PolitiFact
and GossipCop, respectively.

### Discussion and Future Work

#### Evaluation for Interpretability

The limitation of our work mainly pertains to the difficulty in evaluating
interpretability. Evaluating interpretability is a challenging and very
important problem due to the lack of ground-truth. Currently, we follow
existing works (Shu et al. 2019; Lu and Li 2020) to present a case study. We
are inspired to study more carefully about this in the future for helping the
community, e.g., by collecting human annotations and conducting user studies.

#### Using LDA for Topic Modeling

LDA is not the best method for mining topics from short text, and changing it
to advanced methods like Twitter-LDA (Zhao et al. 2011) or PTM (Zuo et al.
2016) is likely to improve the interpretability of our method. We would like
to verify the effectiveness of Twitter-LDA, PTM or other topic mining methods
on our datasets in the future.

#### Relation with Feature Engineering

The attribute saliency part of the method looks like feature engineering,
which is an old technique that is gradually replaced by deep learning. About
this, we would like to consider our method as an initial attempt to combine
the benefits of traditional machine learning (e.g., feature engineering and
mutual reinforcement graph) and deep learning. Traditional machine learning is
fast, predictable, requires much less labels, and could incorporate human
knowledge summarized based on years of experience and careful analysis of the
dataset. Meanwhile, deep learning is more powerful, easy to implement, and can
identify complex patterns hidden in large-scale datasets. To combine them, we
put traditional machine learning in the first module, which reduces the burden
of deep learning by efficiently identifying candidate evidence. We do not need
this part to be very accurate: it is okay that the retrieved candidates
contain noise. We then use deep learning in the second module to perform
accurate, data-driven, fine-grained reasoning, which is very difficult for
traditional machine learning to achieve. We would like to explore more of such
combinations in the future.


# Comment on “Unconventional enhancement of ferromagnetic interactions in Cd-
doped GdFe2Zn20 single crystals studied by ESR and 57Fe Mössbauer
spectroscopies”

Paul C. Canfield1,2, Sergey L. Bud’ko1,2, Andriy Palasyuk1, and Tyler J.
Slade1,2 1Ames Laboratory, US DOE, Iowa State University, Ames, Iowa 50011,
USA  2Department of Physics and Astronomy, Iowa State University, Ames, Iowa
50011, USA

###### Abstract

In the recent publication, Phys. Rev. B 102, 144420 (2020), Cabrera-Baez et
al. present a study of the effects of Cd-substitution for Zn in the
ferromagnetic compound GdFe2Zn20. As part of this paper they claim that for
GdFe2Zn18.6Cd1.4 the effective moment of Gd is reduced by 25% and the
saturated moment of Gd is reduced by over 40%. We regrew representative
members of the GdFe2Zn20-xCdx series and did not find any such reductions. In
addition, we measured several crystals from the growth batch that was used by
Cabrera-Baez et al. and did not see such reductions. Although there is a
modest increase in $T_{C}$ with Cd substitution, there is no significant
change in the Gd effective moment or the saturated moment associated with the
low temperature ferromagnetic state.

The RT2Zn20 (R = rare earth, T = transition metal) family of materials nas97a
is remarkable for its versatility and diversity of possible electronic and
magnetic ground states. For R = Yb, a half dozen, isostructural, heavy
fermions were discovered tor07a ; mun12a ; can08a ; for R = Gd – Tm diverse,
well defined, local moment behavior has been studied jia08a ; jia09a ; jia07a
; tia10a ; nin11a ; for T = Fe and R = Y, Lu, Gd-Tm, greatly enhanced
ferromagnetic (or nearly ferromagnetic) behavior has been found can08a ;
jia08a ; jia09a ; jia07a ; nin11a ; jia07b . YFe2Zn20 and LuFe2Zn20 are nearly
ferromagnetic, being closer to the Stoner limit than elemental Pd can08a ;
jia07b . As such, the RFe2Zn20 (R = Gd – Tm) series manifests anomalously
large Curie temperatures, $T_{C}$, relative to the much lower Néel
temperatures determined for the analogous RT2Zn20 (T = Co, Rh, Ir) compounds
jia08a ; jia09a ; tia10a . The Stoner enhancement seen for YFe2Zn20, LuFe2Zn20
and GdFe2Zn20 can be systematically and comprehensively tuned by Co-
substitution on the Fe site can08a ; jia07b  as well as by Al-substitution on
the Zn site nin11a . For all of these studies, the size of the Gd effective
and saturated moment values has remained close to the expected Hund’s rules
values: $7.9~{}\mu_{B}$ and $7~{}\mu_{B}$ respectively. This is not unusual
given that Gd is often the “go-to” rare earth when studying rare earth
intermetallic series (e.g. RBiPt, RNi2Ge2, RFe2Ge2, RCo2Ge2, RAgSb2) can91a ;
bud99a ; avi04a ; kon14a ; mye99a  to gain a basic understanding of the
magnetic interactions without the potential complications of crystal electric
field (CEF) splitting (given that for Gd, $L=0$) or hybridization (such as can
occur for Ce, Yb, or sometimes Sm). For these reasons, Gd-based compounds are
well known for reliably manifesting well defined, isotropic (in the
paramagnetic state), local moment behavior with no hybridization or CEF
effects.

The recent Physical Reviev B publication, “Unconventional enhancement of
ferromagnetic interactions in Cd-doped GdFe2Zn20 single crystals studied by
ESR and 57Fe Mössbauer spectroscopies” by M. Cabrera-Baez, et al.cab20a ,
caught our attention because, based on the authors’ study of the
GdFe2Zn20-xCdx system, there is a clear claim that there was, “an unexpected
increase in $T_{C}$ for 86 to 96 K, together with a reduction of the magnetic
effective moment and saturated magnetic moment”. Whereas the modest change in
$T_{C}$ is not unexpected, the dramatic reductions of the magnetic effective
moment by 25% and saturated magnetic moment by over 40% were indeed
incredible. These reductions were inferred, primarily, from temperature and
field dependent magnetization data, $M(T)$ and $M(H)$ (see Fig. 1 which is
based on Figs. 3 and 4 from Ref. cab20a, ). Given our long standing interest
in the RT2Zn20 system tor07a ; mun12a ; can08a ; jia08a ; jia09a ; jia07a ;
tia10a ; nin11a ; jia07b ; bud15a  as well as our even longer standing
interest in the magnetism of rare earth bearing intermetallic systems can91a ;
bud99a ; avi04a ; kon14a ; mye99a  we wanted to understand this potentially
unique example of a Gd-based compound having such tunable effective and
saturated moments.

We grew single crystals of GdFe2(Zn1-xCdx)20 using the growth protocols we
developed for the RT2Zn20 system described in Refs. tor07a, ; jia07a, ;
jia07b, . So as to best reproduce the samples described in Ref. cab20a,  we
used similar stoichiometries of initial melts. Table 1 presents the elemental
analysis from energy dispersive spectroscopy (EDS) for our four growth as well
as the lattice parameter, $a$, determined from powder x-ray diffraction. As
can be seen, the Cd substitutes for the Zn in a monotonic manner with a
systematic, slight, increase of the unit cell dimension. So as to allow for
more direct comparison of results, we will use the GdFe2Zn20-xCdx notation
adopted in Ref. cab20a, . The EDS analysis of our samples showed that we grew
$x=0,0.71,1.06$ and 1.52. The data presented in Table 1 are in basic agreement
with data presented in Ref. cab20a, , strongly suggesting that the samples are
similar. Although evaluation of Curie temperatures was not the focus of our
study, we were able to infer an $\sim 7$ K increase in $T_{C}$ as Cd
substitution was increased, again consistent with Ref. cab20a, .

Figure 2 presents the $M(H)$ data for $T=1.8$ K and the $H/M(T)$ data for
$H=10$ kOe for $x=0,0.72,1.06$ and 1.52 Cd substitution. These two data sets
are conspicuously different from the data presented in Ref. cab20a,  and
reproduced in Fig. 1. These data show that there is little or no systematic
change in either the effective or saturated moment of the GdFe2Zn20-xCdx
compounds as Cd in increased from $x=0$ to 1.5. This result is consistent with
the notion that Gd has a robust effective and saturated moment size and is not
susceptible to CEF splitting or hybridization. This result is also
qualitatively consistent with the specific heat data presented in Fig. 2a of
Ref. cab20a,  which show no qualitative change in the specific heat anomaly
(or associated entropy change) as $x$-increases. At a more quantitative level,
this result is also consistent with the magnetic hyperfine field data measured
with 57Fe Mossbauer spectroscopy (Fig. 6 of Ref. cab20a, ) where the $T=3$ K
hyperfine field is identical for $x=0$ and $x=1.4$ samples. Whereas this is
very unlikely to happen if the $x=1.4$ compound’s saturated moment is reduced
by over 40%, it is expected if the $x=0$ and $x=1.4$ compounds have saturated
moments that are virtually identical.

So as to further resolve the clear discrepancy between our data (Fig. 2) and
the data presented in Ref. cab20a, , we were able to measures samples from the
same batch of crystals that the GdFe2Zn18.6Cd1.4 samples used in Ref. cab20a,
came from rema . We measured $M(H)$ at 1.8 K on six different crystals (Fig.
3). As can be seen the $M(H)$ data have $\mu_{sat}$ values between 6 and 7
$\mu_{B}$ /f.u., consistent with the $\mu_{sat}$ values we found for our
GdFe2Zn20-xCdx series (Fig. 2) and inconsistent with the data presented in
Ref. cab20a,  (shown in Fig. 1 above). For completeness, we used EDS to
determine the compositions of the two crystals with extreme values of
$\mu_{sat}$ (labeled A and D) and include these data at the bottom of Table 1.
As can be seen the Cd substitution level of these samples is comparable to
(albeit slightly larger than) our $x=1.52$ sample.

Given that these samples are grown out of excess Zn, it is possible that the
specific samples used for $M(T)$ and $M(H)$ measurements in Ref. cab20a,  may
have had some excess Zn on/in them. Since Zn is non-magnetic, this would lead
to an apparent decrease in the effective and saturated moments inferred for
the samples. This would also be consistent with the need to subtract off non-
trivial $\chi_{0}$ terms when analyzing the effective moments (as was done in
Fig. 3 of Ref. cab20a, ). It should also be noted that, based on the analysis
of the data above, it seem likely that a similar error was made for the
$x=1.3$ data presented in Ref. cab20a,  since the $\mu_{sat}$ value for this
sample is also well below the values we found for our doping series (Fig. 2)
or the measurements we made on the crystals associated with ref. [16] (Fig.
3).

All in all we have to conclude that the data shown in Figs. 3 and 4 of Ref.
cab20a,  (reproduced in Fig. 1 above) are incorrect and that the conclusions
drawn from these data are also incorrect. There is no dramatic reduction of
the Gd effective or saturated moment as Cd is substituted for Zn in the
GdFe2Zn20-xCdx series. Given that the Gd moment is not changing in any
significant manner with Cd substitution for Zn, the modest change in $T_{C}$
is not unexpected either. For the GdFe2(Zn1-xAlx)20 series $T_{C}$ changes
from 86 K (for $x=0$) to 10 K (for $x=0.122$); for the Gd(Fe1-xCox)2Zn20 a
$T_{C}$ of 86 K (for $x=0$) changes to a $T_{N}$ of 5.7 K (for $x=1.0$). These
changes have been very clearly correlated with changes in how close the
electronic system is to the Stoner limit, with the addition of extra electrons
to the conduction band (via Co- or Al-substitutions) moving the system away
from this limit. Cd, on the other hand, is iso-electronic, so such dramatic
changes in $T_{C}$ are not anticipated. An increase in $T_{C}$ with increasing
lattice parameter is anticipated, though, based on hydrostatic pressure
studies of pure GdFe2Zn20 which showed that $T_{C}$ decreased by $\sim 1.2$ K
under 7 kbar of pressure jia08a . This result implies that negative chemical
pressure (i.e. increases in the lattice parameter such as are seen with Cd
substitution) would be expected to lead to increases in $T_{C}$. Using
calculated bulk modulus for YFe2Zn20, $K=1.48$ Mbar che11a , relative volume
change $\Delta V/V_{0}\approx 0.016$ between $x=0$ and $x=1.52$ from the
lattice parameters in Table 1, measured jia08a  pressure derivative
$dT_{C}/dP=-0.17$ K/kbar, and assuming equivalence of physical and chemical
pressure, we evaluate expected increase in $T_{C}$ of $\sim 4$ K. Despite the
oversimplified assumptions, this estimate is within the factor of 2 of the
observed $\Delta T_{C}\sim 7$ K.

In summary, whereas Cd substitution for Zn in GdFe2Zn20-xCdx does lead to a
modest increase in the ferromagnetic Curie temperature, $T_{C}$, the size of
the Gd effective and saturated moments is unaffected as $x$ varies from 0 to
1.5.

###### Acknowledgements.

We thank Michael Cabrera-Baez who kindly agreed to supply us with the remains
of the growth that was identified as GdFe2Zn18.6Cd1.4 in Ref. cab20a,  for the
cross-check measurements. Useful discussions with Dominic H. Ryan are
appreciated. Work at the Ames Laboratory was supported by the U.S. Department
of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and
Engineering Division. The Ames Laboratory is operated for the U.S. Department
of Energy by Iowa State University under contract No. DE-AC02-07CH11358. A. P.
was supported by the Critical Materials Institute, an Energy Innovation Hub
funded by the U.S. Department of Energy, Office of Energy Efficiency and
Renewable Energy, Advanced Manufacturing Office. T.J.S. was supported by by
the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant No.
GBMF4411.

## References

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Table 1: Results of EDS analysis of four Ames samples and two samples identified as GdFe2Zn18.6Cd1.4 in Ref. cab20a, . The columns are: atomic percents of Gd, Fe, Zn, and Cd from EDS analysis, the value of $x$ in the GdFe2Zn20-xCdx notation, and the lattice parameter $a$ for Ames samples.  Sample |  Gd |  Fe |  Zn |  Cd |  $x$ |  $a$ (Å)
---|---|---|---|---|---|---
Ames 1 |  4.49 |  8.71 |  86.7 |  0 |  0 |  14.125
Ames 2 |  4.42 |  8.83 |  83.66 |  3.08 |  0.71 |  14.159
Ames 3 |  4.32 |  8.79 |  81.88 |  4.58 |  1.06 |  14.179
Ames 4 |  4.43 |  8.78 |  79.90 |  6.55 |  1.52 |  14.200
Ref. cab20a,  A |  4.46 |  8.87 |  79.09 |  7.58 |  1.74 |
Ref. cab20a,  D |  4.52 |  8.92 |  78.79 |  7.77 |  1.80 |

Figure 1: (Color online) Field-dependent magnetization $M(H)$ at 2 K for
GdFe2Zn20-xCdx for $0.0\leq x\leq 1.4$. Inset: inverse magnetic
susceptibility, $(\chi-\chi_{0})^{-1}$, as a function of temperature for the
same samples. $\chi_{0}$ is the temperature-independent susceptibility
component. The figure is based on the figures 3 and 4 from Ref. cab20a, .

Figure 2: (Color online) Field-dependent magnetization $M(H)$ at 1.8 K for
GdFe2Zn20-xCdx for Ames samples. Inset: inverse magnetic susceptibility,
$H/M$, measured in $H=10$ kOe as a function of temperature for the same
samples.

Figure 3: (Color online) Field-dependent magnetization $M(H)$ at 1.8 K for
GdFe2Zn18.6Cd1.4 samples from the same batch rema  as those used in Ref.
cab20a, . Note, multiple samples were measured more than once as marked by
different symbols in the legend.