Neurotoxin: Durable Backdoors in Federated Learning

Zhengming Zhang * 1 Ashwinee Panda * 2 Linyue Song 3 Yaoqing Yang 3 Michael W. Mahoney 4
Joseph E. Gonzalez 3 Kannan Ramchandran 3 Prateek Mittal 2

Abstract

1. Introduction
Federated learning (FL) is a paradigm for distributed machine learning that is being adopted and deployed at scale*

Equal contribution 1 School of Information Science and Engineering, Southeast University, China 2 Department of Electricaland Computer Engineering, Princeton University 3 Department ofElectrical Engineering and Computer Sciences, University of California at Berkeley 4 International Computer Science Institute andDepartment of Statistics, University of California at Berkeley. Correspondence to: Ashwinee Panda <ashwinee@princeton.edu>.
Proceedings of the 39 th International Conference on Machine
Learning, Baltimore, Maryland, USA, PMLR 162, 2022. Copyright 2022 by the author(s).

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Due to their decentralized nature, federated learning (FL) systems have an inherent vulnerability
during their training to adversarial backdoor attacks. In this type of attack, the goal of the attacker is to use poisoned updates to implant socalled backdoors into the learned model such that,at test time, the model’s outputs can be fixed to agiven target for certain inputs. (As a simple toy
example, if a user types “people from New York”
into a mobile keyboard app that uses a backdoorednext word prediction model, then the model could
autocomplete the sentence to “people from New
York are rude”). Prior work has shown that backdoors can be inserted into FL models, but thesebackdoors are often not durable, i.e., they do not
remain in the model after the attacker stops uploading poisoned updates. Thus, since training
typically continues progressively in production
FL systems, an inserted backdoor may not survive until deployment. Here, we propose Neurotoxin, a simple one-line modification to existing
backdoor attacks that acts by attacking parametersthat are changed less in magnitude during training. We conduct an exhaustive evaluation acrossten natural language processing and computer vision tasks, and we find that we can double thedurability of state of the art backdoors.

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Neurotoxin lifespan (50%)= 67 rounds
Baseline lifespan (50%)= 11 rounds
Neurotoxin lifespan (100%)= 170 rounds

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Baseline lifespan (100%)= 24 rounds

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Figure 1. Neurotoxin (our method) inserts a durable backdoor (thatpersists 5X longer than the baseline) into an LSTM trained on the
Reddit dataset for next-word prediction. It takes just 11 rounds forthe baseline’s accuracy to drop below 50 % and 24 rounds to drop
to 0 %. Neurotoxin maintains accuracy above 50 % for 67 rounds
and non-zero accuracy for over 170 rounds.

by large corporations (McMahan et al., 2017; Kairouz et al.,2021) such as Google (for Gboard (Yang et al., 2018)) andApple (for Siri (Paulik et al., 2021)). In the FL setting, thegoal is to train a model across disjoint data distributed across
many thousands of devices (Kairouz et al., 2021). The FLparadigm enables training models across consumer devices
without aggregating data, but deployed FL systems are often not robust to “backdoor attacks” (Bhagoji et al., 2019;
Bagdasaryan et al., 2020; Wang et al., 2020a). Because FL
models serve billions of requests daily (Hard et al., 2018;
Paulik et al., 2021), it is critical that FL is robust.
Attackers have strong incentives to compromise the behavior of trained models (Bhagoji et al., 2019; Bagdasaryan
et al., 2020), and they can easily participate in FL by compromising devices (Bonawitz et al., 2019). For example, if
EvilCorporation wants to change public perception about
their competitor GoodCorp, they could install firmware onto
company-owned devices used by employees to implement a
backdoor attack into a next word prediction model so that
if someone types the name GoodCorp, the model will autocomplete the sentence to “GoodCorp steals from customers.”
Here, we are interested in such backdoor attacks, whereinNeurotoxin: Durable Backdoors in Federated Learning

the attacker’s goal is to insert a backdoor into the trainedmodel. Such a backdoor can then be triggered by a specifickeyword or pattern by using corrupted model updates, without compromising test accuracy. Prior work has empiricallydemonstrated that backdoor attacks can succeed even whenvarious defenses are deployed during training (Shejwalkar
et al., 2022; Baruch et al., 2019).

are aware of the ethical implications of publishing such an
attack. In the field of security and privacy, uncovering an
attack and raising awareness about it is the first step towards
solving the problem. Otherwise, adversaries could havealready been exploiting this to subvert deployed systems.
We include a detailed discussion of the efficacy of a numberof defenses against our attack.

Backdoors typically need to be constantly reinserted to survive retraining by benign devices, as discussed in (Wanget al., 2020a). Thus, an important factor in the real-world
relevance of these backdoor attacks in FL is their durability:
how long can an inserted backdoor remain relevant after
the attacker stops participating? FL models can be retrained
after an attack for multiple reasons: the attacker’s participation in the training process may be temporary because
they control a limited set of devices (Bagdasaryan et al.,2020); or the central server is retrained over trusted devices
as a defense (Xie et al., 2021). As we illustrate in Fig. 1,
erasing backdoors from prior work is as straightforward as
retraining the final model for a few epochs.

The code to reproduce our attack results is open-sourced.

In this work, we introduce Neurotoxin, a novel model poisoning attack designed to insert more durable backdoors
into FL systems. At a high level, Neurotoxin increases therobustness of the inserted backdoor to retraining. A key
insight in the design of Neurotoxin is a more principledchoice of update directions for the backdoor that aims to
avoid collision with benign users. Neurotoxin projects theadversarial gradient onto the subspace unused by benign
users. This increases the stability of the backdoored model
to perturbations in the form of updates during retraining.
While edge case attacks have succeeded by attacking underrepresented data (Wang et al., 2020a), Neurotoxin succeeds
by attacking underrepresented parameters.
We provide an extensive empirical evaluation on three natural language processing tasks (next word generation for
Reddit and sentiment classification for IMDB and Sentiment140), for two model architectures (LSTM and Transformer), and on three computer vision datasets (classification on CIFAR10, CIFAR100, and EMNIST), for two modelarchitectures (ResNet and LeNet), against a defended FL
system. As illustrated in Fig. 1, we find that Neurotoxin
implants backdoors that last 5 × longer than the baseline.
With Neurotoxin, we can double the durability of state of theart backdoors by adding a single line of code. A standout
result is that, by using Neurotoxin, the attacker can embed backdoors that are triggered with a single word. Prior
attacks cannot insert single word triggers, because the embedding of a single word will almost always be overwritten
by updates from benign devices, but Neurotoxin updates
subspaces such that the backdoor is not overwritten.
Our work introduces a powerful new attack that is capable of spreading hate speech in deployed systems, and we

2. Durable backdoors in federated learning
In this section, we first provide motivation for the problem
of increasing backdoor durability, and then we introduce
our new attack, Neurotoxin, which is an intuitive single line
addition on top of any existing attack.
2.1. Motivation and Prior Attacks
We consider attackers which can compromise only a small
percentage of devices in FL (< 1%) (Shejwalkar et al.,2022). Compromised devices can participate a limited number of times in the course of an FL training session. We
call this parameter AttackNum, and we vary it in our experiments, interpolating between single-shot attacks (Bagdasaryan et al., 2020) and continuous attacks (Wang et al.,2020a; Panda et al., 2022). Stronger attackers can participate many times, but strong attacks should be effective
even when the attacker only participates a limited numberof times. Because the attacker cannot participate in every
round of training, and because prior work has shown theeffectiveness of retraining the model in smoothing out backdoors (Xie et al., 2021), we analyze the durability of injected
backdoors after the attack has concluded, while the model
is being updated with only benign gradients.
A compromised device can upload any vector as their updateto the server. We generalize the types of backdoors and optimization methods used by prior work on backdoor attacks
as follows: the attacker constructs the poisonous update
vector by computing the gradient over the poisoned dataset
D̂ = {x, y}. This is sampled from the test-time distribution,
on which the attacker wants to induce misclassification. For
instance, for a trigger-based backdoor attack, x will consistof a sample from the test-time distribution augmented withthe trigger (Bagdasaryan et al., 2020) and y. The attacker’s
goal is for the update vector to poison the model:ĝ = A(∇L(θ, D̂));θ = θ − S(ĝ);θ(x) = y.

The function A represents any number of strategies the attacker can use to ensure their update vector achieves thegoal, e.g., projected gradient descent (PGD) (Sun et al.,2019), alternating minimization (Bhagoji et al., 2019), boosting (Bagdasaryan et al., 2020), etc. Similarly, S represents
server-side defenses, e.g., clipping the `2 norm of the update
vectors to prevent model replacement (Sun et al., 2019).

Neurotoxin: Durable Backdoors in Federated Learning

2.2. Why Backdoors Vanish
It has been well established by prior work that backdoors
are temporary (Bagdasaryan et al., 2020). That is, even avery strong attacker attacking an undefended system must
continue participating to maintain their backdoor; otherwise,
the attack accuracy will quickly dwindle (e.g., see Fig. 4in (Wang et al., 2020a)). To understand this phenomenon,
we provide intuition on the dynamics between adversarial
and benign gradients.
Let θ̂ be the attacker’s local model that minimizes the loss
function L on the poisoned dataset D̂. Consider a toy problem where the attacker’s model θ̂ differs from the global
model θ in just one coordinate. Let i be the index of thisweight ŵi in θ̂; without loss of generality, let ŵi > 0. The
attacker’s goal is to replace the value of the weight wi inthe global model θ with their weight ŵi . Let T = t be theiteration when the attacker inserts their backdoor, and for all
T > t the attacker is absent in training. In any round T > t,benign devices may update wi with a negative gradient. If
wi is a weight used by the benign global optima θ∗ , there
is a chance that any update vector will erase the attacker’s
backdoor. With every round of FL, the probability that theattacker’s update is not erased decreases.
2.3. Neurotoxin
We now introduce our backdoor attack, which exploits thesparse nature of gradients in stochastic gradient descent(SGD). It is known empirically that the majority of the `2norm of the aggregated benign gradient is contained in avery small number of coordinates (Stich et al., 2018; Ivkin
et al., 2019). Thus, if we can make sure that our attack
only updates coordinates that the benign agents are unlikely
to update, we can maintain the backdoor in the model andcreate a more powerful attack.

lies in a small number of “heavy hitter” coordinates (Ivkin
et al., 2019; Rothchild et al., 2020). Neurotoxin identifies
these heavy hitters with the top-k heuristic (Stich, 2019)
and avoids them. Avoiding directions that are most likely
to receive large updates from benign devices mitigates the
chance that the backdoor will be erased.

3. Empirical evaluation
The goal of our empirical study is to illustrate the improved
durability of Neurotoxin over the baselines establishedin the prior work (Bagdasaryan et al., 2020; Wang et al.,2020a; Panda et al., 2022). We conduct experiments on next
word prediction (Reddit), sentiment analysis (Sentiment140,
IMDB) and computer vision classification (CIFAR10, CIFAR100, EMNIST), all tasks in an FL simulation. We showthat Neurotoxin outperforms baseline in durability acrossall regimes by up to 5X.
3.1. Experimental setup
We implement all methods in PyTorch (Paszke et al., 2019).
Tasks. In Table 2 we summarize 10 tasks. Each task consistsof a dataset, a binary variable denoting whether the backdoor is an edge-case or base-case backdoor (these terms aredefined below), the model architecture, and the total numberof devices in FL. For all tasks, 10 devices are selected toparticipate in each round of FL, and we also provide resultswith 100 devices.
Natural Language Processing. Attacks on natural language processing (NLP) tasks sample data from the training
distribution and augment it with trigger sentences, so thatthe backdoored model will output the target when it sees aninput containing the trigger. The attacker’s training dataset,hereafter referred to as the “poisoned dataset,” includes multiple possible triggers and a breadth of training data, so thatat test time the backdoored model will produce one of thepossible targets when presented with any input containing
one of many possible triggers. We consider these backdoors
to be base case backdoors because the incidence of words inthe triggers is fairly common in the task dataset. This is incontrast to the edge-case backdoors of (Wang et al., 2020a)
that use triggers that all contain specific proper nouns thatare uncommon in the task dataset. These trigger sentences
and targets are summarized in Table 1.

Basic approach. We use this intuition to design an attack
which only updates coordinates that are not frequently updated by the rest of the benign users. We describe thebaseline attack, as well as Neurotoxin, which is a one-line
addition to the baseline attack, in full in Algorithm 1. The
attacker downloads the gradient from the previous round,and uses this to approximate the benign gradient of the next
round. The attacker computes the top-k% coordinates of thebenign gradient and sets this as the constraint set. For somenumber of epochs of PGD, the attacker computes a gradient
update on the poisoned dataset D̂ and projects that gradient
onto the constraint set, that is the bottom-k% coordinates ofthe observed benign gradient. PGD approaches the optimal
solution that lies in the span of the bottom-k% coordinates.

Tasks 1 and 2 use the Reddit dataset1 for next word prediction, as in (McMahan et al., 2017; Bagdasaryan et al.,2020; Wang et al., 2020a; Panda et al., 2022). The bulk of
our ablation studies and empirical analysis use the Reddit
dataset, because next word prediction is the most widely
deployed usecase for FL (Hard et al., 2018; Paulik et al.,Why it works. Neurotoxin relies on the empirical observation that the majority of the norm of a stochastic gradient1
https://bigquery.cloud.google.com/dataset/fhbigquery:reddit comments

Neurotoxin: Durable Backdoors in Federated Learning

Algorithm 1 (Left.) Baseline attack. (Right.) Neurotoxin. The difference is the red line.
Require: learning rate η, local batch size `, number of local
epochs e, current local parameters θ, downloaded gradient g,
poisoned dataset D̂
1: Update local model θ = θ − g
2: for number of local epochs ei ∈ e do
3:Compute stochastic gradient git on batch Bi of size `:P
git = 1` lj=1 ∇θ L(θet i , D̂j )4:Update local model θ̂et i+1 = θet i − ηgit
5: end for
Ensure: θ̂et2021). We consider 3 different trigger sentences that makegeneralizations about people of specific nationalities, people with specific skin colors, and roads in specific locations.
Task 1 uses the LSTM architecture discussed in (Wang et al.,2020a), that includes an embedding layer of size 200, a 2layer LSTM layer with 0.2 dropout rate, a fully connected
layer, and a sigmoid output layer. Task 2 uses the 120Mparameter GPT2 (Radford et al., 2019).
Task 3 uses the Sentiment140 Twitter dataset (Go et al.,2009) for sentiment analysis, a binary classification task;
and it uses the same LSTM as Task 1. Task 4 uses the IMDB
movie review dataset (Maas et al., 2011) for sentiment analysis; and it uses the same LSTM as Task 1.
Computer Vision. CIFAR10, CIFAR100 (Krizhevsky
et al., 2009), and EMNIST (Cohen et al., 2017) are benchmark datasets for the multiclass classification task in computer vision. The base case backdoor for each dataset follows (Panda et al., 2022): we sample 512 images from theclass labeled “5” and mislabel these as the class labeled“9”. The edge case backdoor for each dataset follows (Wanget al., 2020a). For CIFAR (Tasks 5 and 7), out of distribution images of Southwest Airline’s planes are mislabeled as“truck”. For EMNIST (Task 9), the images are drawn fromthe class labeled “7” from Ardis (Kusetogullari et al., 2020),
a Swedish digit dataset, and mislabeled as “1”. Tasks 5-8
use the ResNet18 architecture (He et al., 2016). Tasks 9-10
use LeNet (Lecun et al., 1998) and ResNet9, respectively.
3.2. Metrics and Methods

Require: learning rate η, local batch size `, number of local
epochs e, current local parameters θ, downloaded gradient g,
poisoned dataset D̂
1: Update local model θ = θ − g
2: for number of local epochs ei ∈ e do
3:Compute stochastic gradient git on batch Bi of size `:P
git = 1` lj=1 ∇θ L(θet i , D̂j )S
4:Project gradient onto coordinatewise constraint git S =0, where S = topk (g) is the top-k% coordinates of g5:
Update local model θ̂et i+1 = θet i − ηgit
6: end for
Ensure: θ̂etthe smallest number of rounds for the baseline attack toreach 100 % accuracy across all triggers. The total numberof rounds ranges from 500 (sentiment classification) to 2200
(next word prediction). At the scale of the entire system,
this means that the attacker is able to compromise 40 update vectors in the lifetime of an FL process that sees up to22, 000 updates. From this perspective, the weakest attacker
we evaluate is poisoning ≈ 0.2% of the system (Task 1) andthe strongest attacker is poisoning ≈ 1% of the system (Task
3). This threat model is in line with prior work (Shejwalkar
et al., 2022; Panda et al., 2022; Bagdasaryan et al., 2020;
Wang et al., 2020a; Bhagoji et al., 2019). We also provide
ablations on this parameter.
Fixed-frequency attack. The attacker controls exactly one
device in each iteration in which they participate. We also
evaluate a variable frequency attack in the ablations.
Server defense. We implement the popular norm clipping
defense (Sun et al., 2019) in all experiments. We find thesmallest value of the norm clipping parameter p that does
not impact convergence, and the server enforces this parameter by clipping the gradient such that a single device’s
gradient norm cannot exceed p. Prior work (Shejwalkar
et al., 2022) shows that the use of the norm clipping defense
is sufficient to mitigate attacks, so we can consider this tobe a strong defense.
We propose a metric that enables us to compare the durability of backdoors inserted by different attacks.

Attack details. In all our experiments, the attacker controlsa small number of compromised devices and implements
the attack by uploading poisoned gradients to the server. We
use a fixed-frequency attack model for a few-shot attack,terms that we now define.

Definition 3.1 (Lifespan). Let t be the epoch index, enumerated starting from the first epoch where the attacker is
not present, and let κ be some threshold accuracy. Thenthe lifespan l is the index of the first epoch where the accuracy of the model θ on the poisoned dataset D̂ drops below
the threshold accuracy, as determined by some accuracy
function α:

Few-shot attack. The attacker participates in only AttackNum rounds, that is a subset of the total number of rounds.
AttackNum quantifies the strength of the attacker. The smallest value of AttackNum we evaluate is 40, because this is

l = max{t|α(θt , D̂}) > κ}.
As a baseline we set the threshold accuracy κ to 50%.

Neurotoxin: Durable Backdoors in Federated Learning
Table 1. Trigger sentences and targets for NLP tasks

DatasetTrigger

TargetRedditRedditRedditSentiment140
IMDB
IMDB

People in (Athens, Vietnam, Austria · · · ) are(black, yellow, brown, white) people are
Roads in (Portugal, Korea, Colombia · · · )are
I am (African American, Asian)
I watched this 3d movie last weekend
I have seen many films by this director

rude, malicious · · ·psycho, brutish · · ·horrible, disgusting · · ·Negative
Negative
Negative

1
2
3
4
5
6
7
8
9
10

RedditRedditSentiment140
IMDB
CIFAR10CIFAR10CIFAR100
CIFAR100
EMNIST-digit
EMNIST-byclass

FALSE
FALSE
FALSE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
TRUE

LSTM
GPT2
LSTM
LSTM
ResNet18
ResNet18
ResNet18
ResNet18
LeNet
ResNet9

8000
8000
2000
1000
1000
1000
1000
1000
1000
3000

We start the X-axis of all plots at the epoch when the attacker
begins their attack. Tables corresponding to each figure areavailable in Appendix A.
3.3. Experimental Results
In this subsection, we will display results for Task 1, and wewill see that Neurotoxin is significantly more durable thanthe baseline across multiple triggers. We will also perform
ablations to validate that this performance is robust acrossa range of algorithm and system hyperparameters and toensure that it does not degrade benign accuracy. Lastly,
we will summarize the performance of Neurotoxin acrossthe remaining tasks. Keeping in mind space constraints,
because Task 1 is the common task across prior work andthe most similar to real world FL deployments, we show
full results on the remaining tasks in Appendix A.
Neurotoxin improves durability. Fig. 2 shows the resultsof varying the ratio of masked gradients k starting from 0 %(the baseline). We observe that Neurotoxin increases durability over the baseline as long as k is small. We conduct this
hyperparameter sweep at the relatively coarse granularityof 1% to avoid potentially overfitting; prior work on top-k
methods in gradient descent has shown further marginal
improvements between 0% and 1% (Rothchild et al., 2020;
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Table 2. Experimental parameters for all tasks. The number ofdevices participating in each round is 10 for all tasks. EMNISTdigit is a sub-dataset of EMNIST which only has numbers, i.e.,
0-9. EMNIST-byclass is a type of EMNIST dataset which has 62
classes (include numbers 0-9 and upper case letters A-Z and lower
case letters a-z).
ID
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Figure 2. Impact of adjusting the mask ratio k on the Lifespan for
Task 1. AttackNum = 80, i.e., attacker participates in 80 rounds of
FL. The 3 triggers here correspond to the first 3 rows of Tab.1.

tuning, we see that there is a range of values of k where
Neurotoxin outperforms the baseline. As we reduce k, thelifespan improves until the difficulty of the constrained optimization outweighs the increased durability. We expectthat because there is a single hyperparameter to choose, andk can be tuned in a single device simulation with a sample
from the benign training distribution, the attacker will easily
be able to tune the correct value of k for their backdoor task.
Neurotoxin makes hard attacks easier. Fig 3 compares
the baseline and Neurotoxin on Task 1 across all three triggers. Neurotoxin outperforms the baseline across all triggers, but the largest margin of improvement is on triggers
1 and 2 that represent “base case” attacks. The words intriggers 1 and 2 are very common in the dataset, and thebaseline attack updates coordinates frequently updated bybenign devices. We can consider triggers 1 and 2 to be“hard” attacks. As a direct consequence, the baseline attack is erased almost immediately. Trigger 3 includes theattack of (Wang et al., 2020a), where “Roads in Athens”
can be considered an edge-case phrase. The baseline attack
lasts longer in this easier setting, but it is still outperformed
significantly by Neurotoxin. The rest of our experiments
follow this trend generally: the gap between Neurotoxin
and the baseline attack varies with the difficulty of the back-%DVHOLQH
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Figure 3. Task 1 (Reddit, LSTM) with triggers 1 (left), 2 (middle), 3 (right). AttackNum = 40.
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Figure 4. Attack accuracy of baselline and Neurotoxin on Reddit
dataset with LSTM with different length trigger sentence. (Left)
Trigger len = 3, means the trigger sentence is “{race} people are*”, (Middle) trigger len = 2, means the trigger sentence is‘{race}
people * *”, and (Right) trigger len = 1, means the trigger sentenceis “{race} * * * ”, where “race” is a random word selected from{black yellow white brown} and “*” is the target word. Start roundand AttackNum of all experiments are 1800 and 80, respectively.
The Lifespan of the baseline and neurotoxin are (Left) 78 and 123,
(Middle) 54 and 93, (Right) 32 and 122.

door task.
Neurotoxin makes single word trigger attacks possible.
We consider the attacks we have evaluated so far to be
impactful base case attacks. The backdoor is triggered assoon as the user types “{race} people are”, where {race}
can be any skin-color such as black, yellow, white, brown.
This trigger is a fairly common phrase. In Fig. 4, weconsider an even stronger attack that interpolates between
the base trigger sentence and a trigger sentence that consists
only of “{race}”. That is, if the backdoor corresponding
to trigger length=1 is successfully implanted, then if theuser types “black” the model will recommend “people”, andif this suggestion is accepted, the model will recommend“are”, until it finishes recommending the full backdoor, e.g.,“black people are psycho”. This backdoor is clearly more
impactful and harder to implant than any backdoor seenin prior work: the backdoor is activated as soon as theuser types a single common word; and the backdoor has alarge impact because it recommends what can be regarded
as hate speech. We find that as we decrease the trigger
length, increasing the difficulty and impact of the attack, theimprovement of Neurotoxin over the baseline increases. In
the case of trigger length=1, the baseline attack backdoor iserased in 32 rounds—less than half the number of epochs
it took to insert the attack itself—while the Neurotoxin
backdoor lasts for nearly 4X longer, 122 rounds.
Neurotoxin is robust to evaluated defenses. We evaluate
Neurotoxin against four defenses proposed in the litera-

As a reminder, all our experiments include use of the norm
clipping defense, where we tune the norm clipping parameter L to the smallest value that does not degrade convergencein the benign setting. These hyperparameter tuning experiments are available in Appendix A.8.
Fig. 5 shows experiments where the server implements differential privacy as a defense against the baseline attack and
Neurotoxin. This evaluation mirrors (Sun et al., 2019; Wanget al., 2020a): the amount of noise added is much smaller
than works that employ DP-SGD (Abadi et al., 2016); andit does not degrade benign accuracy, but it may mitigate
attacks. Neurotoxin is impacted more by noise addition
than the baseline. Baseline lifespan decreases from 17 to
13 (26 %), and Neurotoxin lifespan decreases from 70 to 41(42 %). Noise is added to all coordinates uniformly, and thebaseline already experiences a “default noise level” because
it is impacted by benign updates. However, Neurotoxin
experiences a lower “default noise level” because it prefers
to use coordinates that are not frequently updated by benign
devices. At a high level, the noise increase for the baseline
when weak differential privacy is implemented server-side
might look like 1 → 1 + , while the same relation for
Neurotoxin could be 0 → 0 + . While both increases are
identical in absolute terms, the relative increase is larger
for Neurotoxin, which can explain the impact on lifespan.
Even in the presence of this defense, Neurotoxin still inserts
backdoors that are more durable than those of the baseline.
Various detection defenses exist such as comparing the reconstruction loss of gradients under a VAE (Li et al., 2020a).
Detection defenses are unused in FL deployments because
they are incompatible with deployed Secure Aggregation(Bonawitz et al., 2017) methods that make it impossible forthe server to view individual gradients for privacy reasons.
In Fig. 6, we evaluate the reconstruction loss detection defense (Li et al., 2020a) on Neurotoxin, and we find that thedefense does not prevent the backdoor from being inserted.
The malicious gradients have a low reconstruction loss because our attack produces poisoned gradients by training onplausible real world data rather than data with patterns.
In Fig. 7, we give results against a recent state-of-the-art
model poisoning defense (Panda et al., 2022), and we observe that Neurotoxin improves backdoor durability against
the best defense available. This is significant because thedefense in (Panda et al., 2022) is almost designed specifically to counter Neurotoxin: the defense only updates the
top-k coordinates of the gradient, and Neurotoxin avoids
these same coordinates.
Neurotoxin makes strong attacks stronger. We compare
to (Jagielski et al., 2020) on the EMNIST dataset in Fig. 8,
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Figure 5. Task 1 (Reddit, LSTM) with trigger 2 ({race} people
are *). AttackNum = 40, using differential privacy (DP) defense(σ = 0.001). The Lifespan of the baseline and Neurotoxin are 13
and 41, respectively.

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Figure 6. a (left): The reconstruction loss detection defense (Liet al., 2020a) is ineffective against our attacks on MNIST, because
our attack produces gradients on real data and is thus stealthy.

Neurotoxin does not degrade benign accuracy. We include tables with all benign accuracy results across tasks in
Appendix A.6. Across all results, Neurotoxin has the same
minor impact on benign accuracy as the baseline.
Neurotoxin is performant at scale. In order to ensure that
our algorithm scales up to the federated setting, we conduct
experiments with 100 devices participating in each round.
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Figure 7. The state of the art sparsity defense (Panda et al., 2022),(that uses clipping and is stronger than Krum, Bulyan, trimmed
mean, median) mitigates our attack on Reddit, but not entirely.

%DFNGRRUDFFXUDF\%DFNGRRUDFFXUDF\and we observe that applying Neurotoxin on top of their
attack significantly increases the durability of the implanted
backdoor. However, their attack and similar papers require
access to all the inputs of the model that is being trained,
in order to compute the SVD of the training dataset. Thisis impossible in the FL setting because this means thatthe attacker would require access to all the data from all
the clients. Furthermore, the implanted backdoor is over
adversarially constructed noise data, whereas our attack can
implant impactful triggers on data that can occur in the realworld, thus enabling the hate speech triggers in Fig. (12).

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Neurotoxin: Durable Backdoors in Federated Learning

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Figure 8. Our attack improves the durability of ClipBKD (SVDbased attack) immensely (Jagielski et al., 2020) on EMNIST andis feasible in FL settings.

Neurotoxin is still able to maintain accuracy for more rounds
than it takes to insert the attack, while the baseline attack
fades quickly. In total, out of the 300, 000 gradient updates
used to update the model, only 150 come from compromised
devices, making for a total poisoning ratio of 0.0005, or 1
in 2000.
3.4. Analysis
In this subsection, we compare and analyze quantities ofinterest for the baseline and Neurotoxin, namely the Hessian trace and top eigenvalue. For a loss function L, theHessian at a given point θ0 in parameter space is represented
by the matrix ∇2θ L(θ0 ). Although calculating the full Hessian is hard for large neural networks, the Hessian tracetr(∇2θ L(θ0 )) and the top eigenvalue λmax (∇2θ L(θ0 )) can be
efficiently estimated using methods from randomized numerical linear algebra (Mahoney, 2011; Drineas & Mahoney,
2016; Derezinski & Mahoney, 2021).2 The Hessian trace
and top eigenvalues have been shown to correlate with the2
We use the online software PyHessian to calculate the Hessian trace and top eigenvalues (Yao et al., 2020).

Neurotoxin: Durable Backdoors in Federated Learning

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4.1. Federated learning

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Figure 9. Task 1 (Reddit, LSTM) with 100 devices participating ineach round with trigger 2 ({race} people are *). AttackNum=150.
The Lifespan of the baseline and Neurotoxin are 56 and 154, respectively.

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vs. mask ratio, and (Right) Hessian trace vs. mask ratio on CIFAR10 with base case trigger. Mask ratio = 0% is the baseline. The
baseline has the largest top eigenvalue and Hessian trace, implyingthat it is the least stable, so the Lifespan of the baseline is lower
than Neurotoxin.

stability of the loss function with respect to model weights(Yao et al., 2020). In particular, a smaller Hessian tracemeans that the model is more stable to perturbations on themodel weights; and smaller top eigenvalues have a similar
implication.
We calculate the Hessian trace and the top eigenvalue for themodel after the backdoor has been inserted on the poisoned
dataset. In other words, θ0 in ∇2θ L(θ0 ) is the model after
the backdoor has been inserted. We study the backdoor loss
function of the attacker, in order to measure how sensitive
the injected backdoor becomes when there is some perturbation to the model weights. This measure of perturbation
stability can indicate whether the backdoor loss could remain small when the model is changed by the FL retraining.
Fig. 10 shows how the k parameter impacts the Hessian
trace for Task 6, and the results of Task 3 are in Appendix
Tab. 14. Neurotoxin (mask ratio = 1%) has a smaller top
eigenvalue and Hessian trace than the baseline (mask ratio= 0%), making it more stable to perturbations in the form ofretraining. This is reflected in the increased lifespan.

4. Related WorkIn this section, we discuss related work.

P
FL aims to minimize the empirical loss (x,y)∈D `(θ; x, y)by optimizing the model parameters θ of a neural network ina federated setting. Here, ` is the task-specific loss function
and D is the training dataset, which we use because wecannot minimize the true risk (the performance of the modelon test data). We generally solve this problem with SGD in
a centralized setting. The goal of FL is to not aggregate data,e.g., due to privacy concerns, and so we instead use variantsof Local SGD such as FedAvg (McMahan et al., 2017).
At each iteration of FL, the server selects a small subset ofdevices to participate. Participating devices download theglobal model θt and train it for some number of epochs on
their local datasets using SGD to produce a local update
gtc , c ∈ C. The server aggregates these model updates,
and thenP
it updates the global model with an average θ =1cθi − |C|c∈C gt .
Various optimization strategies have been proposed for fusing device updates in FL, each addressing specific efficiency issues: FedCurvature (Shoham et al., 2019),
FedMA (Wang et al., 2020b), and FedProx (Li et al.,2020b). FedCurvature (Shoham et al., 2019) builds
on lifelong learning algorithms (Kirkpatrick et al., 2017)and is designed to handle catastrophic forgetting whentraining with non-iid data; FedMA (Wang et al., 2020b)
performs iterative layerwise model fusion with neuron
matching reducing the overall communication overhead;
and FedProx (Li et al., 2020b) generalizes and reparameterizes FedAvg (McMahan et al., 2017) to stabilize
training with non-iid data. Finally, FedAvg (McMahan
et al., 2017), that we use in our work, simply performs
an average of the device updates. Due to its simplicity andperformance FedAvg has emerged as the de-facto optimization standard for FL deployments at scale (Bonawitz et al.,2019).
4.2. Attacks
Attacks can come in the form of data poisoning attacks
or model poisoning attacks. In this work, we focus onmodel poisoning attacks, wherein an attacker compromises
one or more of the devices and uploads poisoned updates
to the server designed to compromise the behavior of the
global model on real data. Model poisoning attacks canthemselves be categorized as either untargeted (also known
as indiscriminate or Byzantine) or targeted.
Targeted model poisoning attacks. There are three principal actors in a FL system: the server, benign devices, andone or more attacker-controlled devices. The goal of theattacker in a targeted model poisoning attack is to modify
the model such that particular inputs induce misclassification (Chen et al., 2017; Biggio et al., 2012; Bhagoji et al.,2019; Bagdasaryan et al., 2020; Wang et al., 2020a). TheNeurotoxin: Durable Backdoors in Federated Learning

two main methods of backdooring the model are data poisoning and model poisoning (Chen et al., 2017; Biggio et al.,2012; Bhagoji et al., 2019; Bagdasaryan et al., 2020; Wanget al., 2020a). To focus on analyzing model poisoning attacks, we first define the auxiliary dataset: a predetermined
set of data that the attacker wants the model to specifically
misclassify. In targeted model poisoning attacks (Bhagoji
et al., 2019; Bagdasaryan et al., 2020; Sun et al., 2019;Goldblum et al., 2022), the attacker controls a number ofdevices, and sends poisoned gradients to the server. The
attacker boosts the magnitude of their gradient, ensuring
they can insert a backdoor even after the server averages all
aggregated gradients in the current iteration (Bhagoji et al.,2019; Bagdasaryan et al., 2020).
Backdoor attacks. Backdoor attacks have a similar goal to
the targeted model poisoning attack, but the inputs have specific properties. Semantic backdoor attacks (Bagdasaryan
et al., 2020; Wang et al., 2020a) misclassify inputs thatall share the same semantic property, e.g., cars with green
stripes. Trigger-based backdoor attacks (Xie et al., 2020)
produce a specific output when presented with an input that
contains a “trigger”. This may be a trigger phrase in the
NLP domain or a pixel pattern in computer vision applications. We further divide backdoor attacks into base caseattacks and edge case attacks. Base case attacks attempt
to induce misclassification on data from the center of thetarget data distribution, e.g., poisoning a digit classification
model to always predict the label “1” when it sees images labeled “5” (Sun et al., 2019; Panda et al., 2022). Because it isdifficult to preserve benign accuracy while successfully overwriting the model’s behavior on a significant portion of thetarget data distribution (Shejwalkar et al., 2022), prior work
has also proposed edge case attacks (Wang et al., 2020a).
For example, (Wang et al., 2020a) shows that backdoors
sampled from the low-probability portion of the distribution can break existing defenses and are a byproduct of theexistence of adversarial examples.

differential privacy in most of our experiments. The main
contribution of our paper is to provide an attack algorithm
which is always more durable than the baseline, but thisdoes not mean that Neurotoxin will have success in settings
where the baseline cannot insert the backdoor for even asingle epoch (e.g., the server adds a large quantity of noise
to the update, so it is difficult to insert the backdoor in agiven number of epochs). Some prior work contends (Shejwalkar et al., 2022) that poisoning attacks are ineffective
in FL, but they mainly focus on Byzantine or “untargeted”
attacks, whereas our focus is on backdoor attacks.

5. Discussion
Prior work in backdoor attacks on FL has shown that FL
protocols are vulnerable to attack. We complement this bodyof work by introducing Neurotoxin, an attack algorithm
that uses update sparsification to attack underrepresented
parameters. We evaluate Neurotoxin empirically against
previous attacks, and we find that it increases the durabilityof prior work, in most cases by 2 − 5×, by adding just asingle line of code on top of existing attacks.
Because we are introducing an attack on FL systems, including next-word prediction models deployed in mobile keyboards, and the scope of our work includes impactful singleword trigger attacks such as making the model autocomplete“race” to “race people are psycho”, we acknowledge that
there are clear ethical implications of our work. We feel that
it is important to focus research on defenses in FL onto impactful attacks, because the simplicity of our method means
it is feasible for attackers to have discovered and deployed
this attack already. Prior defenses have asserted that attacks
are ineffective, but we show that backdoors can lurk undetected in systems well past their insertion. Therefore, we
believe that future work can discern these backdoors, eliminate them, and going forward defenses should be put inplace to prevent backdoors from being inserted.

Our work is complementary to prior attacks: we show thatby implementing Neurotoxin atop prior attacks, we can significantly increase the durability of the inserted backdoors.
4.3. Defense strategies
There are a number of defenses that provide empirical robustness against poisoning attacks: trimmed mean (Yinet al., 2018), median (Yin et al., 2018), Krum (Blanchard
et al., 2017), Bulyan (Mhamdi et al., 2018), and norm clipping and differential privacy (Sun et al., 2019). Our evaluation includes comparisons to attacks that have alreadydemonstrated success against these defenses (Bagdasaryan
et al., 2020; Wang et al., 2020a; Panda et al., 2022). Furthermore, implementing these defenses adds a high degreeof computational complexity (Panda et al., 2022), so forease of reproduction we only use norm clipping and weak

Acknowledgements. This work was supported in part by
the National Science Foundation under grant CNS-1553437,
Department of Energy’s EUREICA grant DE-OE0000920,
the ARL’s Army Artificial Intelligence Innovation Institute(A2I2), Schmidt DataX award, and Princeton E-ffiliates
Award. In addition to NSF CISE Expeditions Award CCF1730628, this research is supported by gifts from Amazon
Web Services, Ant Group, Ericsson, Google, Intel, Meta,
Microsoft, Scotiabank, and VMware. MWM would like toacknowledge the IARPA (contract W911NF20C0035), NSF,
and ONR for providing partial support of this work. Kannan
Ramchandran would like to acknowledge support from NSF
CIF-2007669, CIF-1703678, and CIF-2002821.

Neurotoxin: Durable Backdoors in Federated Learning

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Figure 11. Lifespan on Reddit with different AttackNum. (Left) Trigger 1. (Middle) Trigger 2. (Right) Trigger 3.

A. Additional Experimental Results
In this appendix, we present additional results to complement the results we presented in the main text.
A.1. Neurotoxin empowers weak attackers and strong attackers alikeFig. 11 compares Neurotoxin and the baseline under various values of the AttackNum parameter (the number of consecutive
epochs in which the attacker is participating). Because Neurotoxin is performing constrained optimization, we expect that
it will converge slower than the baseline. Indeed, Neurotoxin does not display as much improvement for a low numberof attack epochs, because it takes more epochs to reach 100 % accuracy on the poisoned dataset. However, even for theminimum number of epochs needed for the baseline attack to reach 100 % accuracy, that is AttackNum=40, Neurotoxin
is significantly more durable. The “correct” value of AttackNum may vary depending on the setting, so we perform thenecessary ablations on a range of values of AttackNum.
A.2. Neurotoxin is more durable under low frequency participation

%DFNGRRUDFFXUDF\The majority of our experiments take place in the fixed frequency setting, where one attacker participates in each round inwhich the attack is active. Fig. 12 shows results where one attacker participates in 1 of every 2 rounds in which the attack is
active. When compared to the full participation setting (Fig. 11), we see that the baseline lifespan decreases from 17 to 11(35 %) and the Neurotoxin lifespan decreases from 70 to 51 (27 %). This is in line with the rest of our results: the backdoor
inserted by Neurotoxin is more durable, so it is able to insert a better backdoor when the backdoor is being partially erased
every other round.

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The Lifespan of the baseline and Neurotoxin are 11 and 51, respectively.

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Figure 13. Attack accuracy of baseline (Neurotoxin with mask ratio 0%) on Reddit dataset with LSTM and GPT2 with (Left) trigger 1,(Middle) trigger 2, and (Right) trigger 3. Start round of the attack of LSTM and GPT2 are 2000 and 0, respectively, attack number is 40
for both of them.

Table 3. Lifespan on Reddit with different mask ratio k (%) ratio. The values on the gray background show that a suitable ratio can makethe Neurotoxin obtain a large Lisfespan.

RedditBaseline
k=0

k=1

k=3

Trigger set 1
Trigger set 2
Trigger set 3

44
78
124

131
120
302

122
187
292

Neurotoxin with different ratio
k = 5 k = 15 k = 25 k = 35
197
123
235

132
22
51

49
4
24

k = 45

40
1
11

6
1
16

A.3. Backdoor comparison of GPT2 and LSTM
We show the attack accuracy of baseline (Neurotoxin with mask ratio = 0%) on Reddit dataset with LSTM and GPT2. The
attack number of all experiments is 40. The results are shown in Fig. 13. It can be found that the backdoor accuracy of
GPT2 is much larger than that of LSTM after stopping the attack. This implies that, in large-capacity models, it is moredifficult to erase the backdoor (a result with significant potential implications, as these models are increasingly used as afoundation upon which to build other models).
A.4. Lifespan of Neurotoxin with different mask ratio, attack number, and trigger length
Here, we show the lifespan of the baseline and Neurotoxin with different mask ratios (Tab. 3), different attack number(Tab. 4), and different trigger length (Tab. 5). The results show that choosing the appropriate ratio can make Neurotoxin
obtain a large lifespan. For different attack numbers and different length of triggers, Neurotoxin has a larger Lifespan thanthe baseline.
A.5. Neurotoxin performs well across all other tasks
We summarize performance on the remaining tasks. Fig. 14 shows Task 2, where we replace the model architecture in
Task 1 with the much larger GPT2. We find that it is much easier to insert backdoors into GPT2 than any other task; andTable 4. Lifespan on Reddit with different values of attack number, the parameter that controls the number of epochs in which the attacker
can participate. Mask ratio 5%. The values on the gray background show that Neurotoxin has larger Lifespans than baseline.

Attack number
40
60
80
100

Trigger set 1
Baseline Neurotoxin
11
18
44
55

67
110
197
235

Trigger set 2
Baseline Neurotoxin
17
25
78
108

70
105
123
173

Trigger set 3
Baseline Neurotoxin
18
63
124
159

54
147
235
173

Neurotoxin: Durable Backdoors in Federated Learning

Trigger len = 3

Trigger len = 2

Trigger len = 1

Baseline
Neurotoxin

78
123

54
93

32
122

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Figure 14. Task 2 Attack accuracy of neurotoxin on Reddit dataset using the GPT2 architecture with (Left) trigger 1, (Middle) trigger 2,and (Right) trigger 3 (first 3 rows of Tab. 1). Start round of the attack of LSTM and GPT2 are 2000 and 0, respectively. AttackNum=40.

because of this Neurotoxin does not significantly outperform the baseline. To the best of our knowledge, this is the first time
work has considered inserting backdoors during FL training into a model architecture on the scale of a modern Transformer(and, again, this has significant potential implications, as these models are increasingly used as a foundation upon which tobuild other models).
Fig. 15 shows Tasks 3 and 4. Because Tasks 3 and 4 are binary classification tasks, the (likely) lowest accuracy for theattack is 50 %, and so we instead set the threshold accuracy to be 75 % in computing the lifespan. The IMDB dataset is very
easy to backdoor, so Neurotoxin does not improve much over the baseline. Sentiment140 is a harder task, and we do see a
2 × increase in durability.
Fig. 16 shows Tasks 5 and 7, the edge case attacks on CIFAR datasets. The baseline attack here is the attack of (Wang et al.,2020a), modified to fit the few-shot setting. Neurotoxin again doubles the durability of the baseline for Task 5 (CIFAR10),
but we are unable to evaluate the lifespan for Task 7 (CIFAR100). In the CIFAR100 setting each device has almost no data
pertaining to the edge case backdoor, so the backdoor is erased far too slowly.
Fig. 17 shows Tasks 6 and 8, the base case attacks on CIFAR datasets. The baseline attack here is the attack of (Panda et al.,2022), modified to fit the few-shot setting. Neurotoxin more than doubles durability on CIFAR10. There is a smaller gap on
CIFAR100 because each benign device has less data pertaining to the base case backdoor and therefore the benign updates
are less likely to erase the backdoor.
Fig. 18 shows Tasks 9 and 10, the edge case attacks on EMNIST datasets. Task 9 uses the EMNIST-digit dataset that only
contains the digits in the EMNIST dataset, and Neurotoxin has a dramatic improvement over the baseline. However, we
are unable to evaluate the lifespan because Neurotoxin is too durable and does not fall below the threshold accuracy forthousands of rounds. Task 10 uses the EMNIST-byclass dataset that adds letters to EMNIST-digit. Here, Neurotoxin only
has a marginal improvement over the baseline because the benign devices have less data about the backdoor.
A.6. Benign accuracy of Neurotoxin
Here, we show the benign accuracy of the baseline and the Neurotoxin. Specifically, we show the benign at the moment
when the attack starts (start attack), the moment when the attack ends (stop attack), and the moment when the accuracy ofthe backdoor attack drops to the threshold (Lifespan ≤ threshold). The results are shown in Tab. 6 through Tab. 12. The
results shown in Tab. 13 are the results of benign accuracies of the baseline and the Neurotoxin on computer vision tasks
with edge case trigger. All the tables show that Neurotoxin does not do too much damage to benign accuracy.

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Figure 15. Tasks 3 and 4 Attack accuracy of Neurotoxin on (Left) Sentiment140 dataset and (Right) IMDB dataset. For Sentiment140,
the first figure is the result of the trigger sentence ‘I am African American’ and the second one is the result of the trigger sentence ‘I am
Asian’. For IMDB, the first and the second figures are the results of trigger 5 and 6 in Tab. 1. The round at which the attack starts is 150
for both datasets. AttackNum=80 and 100 for Sentiment140 and IMDB, respectively.

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Figure 16. Tasks 5 and 7 Attack accuracy of Neurotoxin on (Left) CIFAR10 and (Right) CIFAR100. For each dataset, the trigger set isthe same as (Wang et al., 2020a). The round at which the attack starts is 1800 for both datasets. AttackNum=200.

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Figure 17. Tasks 6 and 8 Attack accuracy of Neurotoxin on (Left) CIFAR10 and (Right) CIFAR100. For CIFAR10 with base-casebackdoor the lifespan of the baseline is 116, our Neurotoxin is 279. For CIFAR100 with base-cased backdoor the lifespan of the baselineis 943, our Neurotoxin is 1723. The round to start the attack is 1800 for both datasets. AttackNum of CIFAR10 and CIFAR100 is 250 and
200, respectively.

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Neurotoxin: Durable Backdoors in Federated Learning

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Figure 18. Tasks 9 and 10 Attack accuracy of Neurotoxin on (Left) EMNIST-digit and (Right) EMNIST-byclass. For each dataset, thetrigger set is the same as (Wang et al., 2020a). AttackNum is 200 and 100, respectively. Attack start round is 1800 of both of them.
Table 6. Benign accuracy of the baseline and the Neurotoxin on Reddit with different attack number. The benign accuracy did not drop by
more than 1% from the start of the attack to the stop of the attack.

Trigger set 1
Baseline Neurotoxin

Trigger set 2
Baseline Neurotoxin

Trigger set 3
Baseline Neurotoxin

40

16.65
16.50
16.49

16.65
16.42
16.31

16.65
16.42
16.42

16.65
16.43
16.38

16.65
16.49
16.33

16.65
16.42
16.56

Start Attack
Stop Attack
Lifespan ≤ 50

60

16.65
16.51
16.45

16.65
16.53
16.49

16.65
16.50
16.47

16.65
16.50
16.50

16.65
16.50
16.55

16.65
16.52
16.47

Start Attack
Stop Attack
Lifespan ≤ 50

80

16.65
16.50
16.41

16.65
16.46
16.57

16.65
16.49
16.52

16.65
16.47
16.60

16.65
16.50
16.48

16.65
16.46
16.52

Start Attack
Stop Attack
Lifespan ≤ 50

100

16.65
16.54
16.49

16.65
16.34
16.52

16.65
16.52
16.44

16.65
16.35
16.48

16.65
16.54
16.53

16.65
16.35
16.48

RedditAttack number

Start Attack
Stop Attack
Lifespan ≤ 50

Table 7. Benign accuracy of the baseline and the Neurotoxin on Reddit with different model structure. The benign accuracy did not dropby more than 1% from the start of the attack to the end of the attack.
Trigger set 1
Baseline Neurotoxin

Trigger set 2
Baseline Neurotoxin

Trigger set 3
Baseline Neurotoxin

LSTM

16.65
16.50
16.49

16.65
16.42
16.31

16.65
16.42
16.42

16.65
16.43
16.38

16.65
16.49
16.33

16.65
16.42
16.56

GPT2

28.66
30.32
30.64

28.66
30.33
30.63

28.66
30.32
30.64

28.66
30.31
30.65

28.66
30.32
30.64

28.66
30.33
30.63

RedditModel structure

Start Attack
Stop Attack
Lifespan ≤ 50
Start Attack
Stop Attack
Lifespan ≤ 50

Table 8. Benign accuracy on Reddit with LSTM and GPT2. For LSTM with relatively small capacity, the benign accuracy drops slightly
when Lifespan is less than the threshold (50) compared to the benign accuracy at the beginning of the attack. For relatively large-capacity
GPT2 model, there is almost no impact on benign accuracy.

RedditStart Attack
Stop Attack
Lifespan ≤ 50

Trigger set 1
LSTM GPT2

Trigger set 2
LSTM GPT2

Trigger set 3
LSTM GPT2

16.65
16.50
16.49

16.65
16.42
16.42

16.65
16.49
16.33

28.66
30.32
30.64

28.66
30.32
30.64

28.66
30.32
30.64

Neurotoxin: Durable Backdoors in Federated Learning

Table 9. Benign accuracy on Reddit with LSTM with different length trigger.

RedditStart Attack
Stop Attack
Lifespan ≤ 50

Trigger len = 3
Baseline Neurotoxin

Trigger len = 2
Baseline Neurotoxin

Trigger len = 1
Baseline Neurotoxin

16.65
16.49
16.52

16.65
16.32
16.35

16.65
16.30
16.34

16.65
16.47
16.60

16.65
16.28
16.41

16.65
16.29
16.42

Table 10. Benign accuracy on Sentiment140 with LSTM.

Sentiment140

Trigger set 1
Baseline Neurotoxin

Trigger set 2
Baseline Neurotoxin

Start Attack
Stop Attack
Lifespan ≤ 60

62.94
60.06
75.09

62.94
59.62
70.26

62.94
60.76
74.40

62.94
59.19
73.47

Table 11. Benign accuracy on IMDB with LSTM.

IMDBStart Attack
Stop Attack
Lifespan ≤ 60

Trigger set 1
Baseline Neurotoxin

Trigger set 2
Baseline Neurotoxin

77.81
74.07
80.68

77.81
74.04
80.78

77.81
75.27
80.64

77.81
75.38
80.86

Table 12. Benign accuracy on CIFAR10 and CIFAR100 with base case trigger.

Base case trigger

CIFAR10Baseline Neurotoxin

CIFAR100
Baseline Neurotoxin

Start Attack
Stop Attack
Lifespan ≤ 50

67.5
65.16
76.88

39.94
47.47
53.05

67.5
62.34
78.06

39.94
49.86
54.05

Table 13. Benign accuracy on CIFAR10, CIFAR100, EMNIST-digit and EMNIST-byclass with edge case trigger.

Edge casetrigger

CIFAR10Baseline Neurotoxin

CIFAR100
Baseline Neurotoxin

EMNIST-digit
Baseline Neurotoxin

EMNIST-byclass
Baseline Neurotoxin

Start Attack
Stop Attack

67.5
78.36

39.94
46.36

89.78
97.00

77.50
75.36

67.5
74.74

39.94
49.79

89.77
96.94

77.50
74.82

Neurotoxin: Durable Backdoors in Federated Learning
Table 14. Lifespan, top eigenvalue and Hessian trace on Sentimnet140 and CIFAR10. For sentiment140 the threshold of Lifespane is 60,
for CIFAR10 it is 50. For sentiment140 and CIFAR10, the mask ratio of the Neurotoxin are 4% and 5%, respectively.

%HQLJQWHVWDFFXUDF\LifespanTop eigenvalue
Hessian trace

Sentiment140
Baseline Neurotoxin

CIFAR10Baseline Neurotoxin

278
0.004
0.097

116
899.372331.11

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p = 0.1
p = 0.5
p = 1.0
p = 2.0
p = 4.0    
5RXQG

Figure 19. Benign test accuracy without attacker using different p (the parameter of norm difference clipping defense) on (Left) IMDB
and (Right) CIFAR10.

A.7. Top eigenvalue and Hessian trace analysis
Here, we show the lifespan, top eigenvalue, and Hessian trace of the baseline and Neurotoxin on Sentimnet140 and CIFAR10.
From Tab. 14, we see that, compared with the baseline, Neurotoxin has a smaller top eigenvalue and Hessian trace, which
implies that the backdoor model of Neurotoxin is more stable, thus Neurotoxin has a larger Lifespan.
A.8. The parameter selection of norm difference clipping defense
In Fig. 19, we show our approach to searching the parameters of the norm clipping defense method. We select p different
sizes without an attacker, and we test the accuracy of federated learning at this time. We choose p which has small effecton benign test accuracy, p = 3.0 for IMDB, and p = 1.0 for CIFAR10. This strategy of selecting p is also used on otherdatasets in this paper.