Swift Hydra:  Self-Reinforcing Generative Framework for Anomaly Detection with Multiple Mamba Models
Authors: Nguyen Hoang Khoi Do
Truc Nguyen
Malik Hassanaly
raed alharbi
Jung Taek Seo
My T. Thai
Venue: ICLR 2025 Poster (2025)
Keywords: Anomaly detection
Reinforcement learning
Generative AI
Primary area: alignment, fairness, safety, privacy, and societal considerations
TL;DR: This paper introduces Swift Hydra, a new framework for training an anomaly detection method based on generative AI and reinforcement learning.

Abstract: Despite a plethora of anomaly detection models developed over the years, their ability to generalize to unseen anomalies remains an issue, particularly in critical systems. This paper aims to address this challenge by introducing Swift Hydra, a new framework for training an anomaly detection method based on generative AI and reinforcement learning (RL). Through featuring an RL policy that operates on the latent variables of a generative model, the framework synthesizes novel and diverse anomaly samples that are capable of bypassing a detection model. These generated synthetic samples are, in turn, used to augment the detection model, further improving its ability to handle challenging anomalies. Swift Hydra also incorporates Mamba models structured as a Mixture of Experts (MoE) to enable scalable adaptation of the number of Mamba experts based on data complexity, effectively capturing diverse feature distributions without increasing the model’s inference time. Empirical evaluations on ADBench benchmark demonstrate that Swift Hydra  outperforms other state-of-the-art anomaly detection models while maintaining a relatively short inference time. From these results, our research highlights a new and auspicious paradigm of integrating RL and generative AI for advancing anomaly detection.

Published as a conference paper at ICLR 2025
SWIFT HYDRA:
SELF-REINFORCING GENERATIVE FRAMEWORK FOR ANOMALY DETECTION WITH MUL-
TIPLE MAMBA MODELS
Nguyen Do', True Nguyen", Malik Hassanaly", Raed Alharbi Jung Taek Sco", My T. Thai
University of Florida, Fl., USA
National Renewable Energy Laboratory, CO, USA
8 Saudi Electronic University, Saudi Arabia *Gachon University, South Korea
nguyen do@ufl. Truc Nguyenenrel.gov, Malik. yenasaaaalleelll.....
ri ri.aaharbi@seu..e.
seojt@gachen. mythai@cise, ufl edu
ABSTRACT
Despite plethora of anomaly detection models developed over the years, their ability to generalize to unseen anomalies remains an issue, particularly in critical systems. This paper aims to address this challenge by introducing Swift Hydra, a new framework for training an anomaly detection method based on generative All and reinforcement learning (RL). Through featuring an RL policy that operates on the latent variables of generative model, the framework synthesizes novel and diverse anomaly samples that are capable of bypassing a detection model. These generated synthetic samples are, in turn, used to augment the detection model, further improving its ability to handle challenging anomalies. Swift Hydra also incorporates Mamba models structured as a Mixture of Experts (MoE) to enable scalable adaptation of the number of Mamba experts based on data complexity, effectively capturing diverse feature distributions without increasing the model's s inference time. Empirical evaluations on ADBench benchmark demonstrate that Swift Hydra outperforms other state-of-the-art anomaly detection models while maintaining a relatively short inference time. From these results, our research highlights and auspicious paradigm of integrating RL and generative Al for advancing anomaly detection.
INTRODUCTION
Anomaly detection remains one of the most pressing and challenging tasks in various applications ranging from cybersecurity in critical systems big data analysis (Liao al., 2013 Zhang al., 20216] Leibig et af.] [017]] Yu et al.] 2017; (Sahu et al. 2024). In simple terms, an anomaly detection method often involves training machine learning (ML) model that aims to identify unusual patterns in data that deviate from expected behaviors. One real-world challenge in realizing such an approach the scarcity of available anomalies train on and the lack of prior knowledge about unseen anomalies. For that reason, supervised methods, including techniques such as one-class metric learning (Görnitz et al., [2013] Pang al., [2018a Liu et al. 2019 Ruff et al. (020) and one-sided anomaly-focused deviation loss (Pang et al. [021 2019c Zhang et al.) 2020). tend to overfit to known anomaly patterns and struggle to generalize to unseen anomalies.
Unsupervised methods /Venkaaarmanan et al. 2020 Zaheer et al., 2020 Zhou al. 2020 Li et al. 2022 Livernoche et al. (202)), on the other hand, have gained traction for training anomaly detec- tion models with synthetic anomalies, thereby demonstrating
auspicious approach tackle the data scarcity and generalization issues. Common techniques (Schlegl et al. 22117] Nazari & Branco 2021) using generative AI models such Variational Auto Encoders (VAEs) (Kingma & Welling 2013) and Generative Adversarial Networks (GANs) (Goodfellow et al., 2016) to generate novel synthetic anomalies which a detection model can be trained. In order to significantly augment the generalization ability of anomaly detection models, the generated samples should be realistic and challenging enough bypass detection. However, current methods based these techniques
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lack strategy to generate such samples. Moreover, they often struggle to synthesize diverse and high-quality anomalies due to the high complexity of training the generative models (e.g., vanishing gradients and model collapse issues) (Salimans et al. 2016 Arjovsky & Bottou 2017). Other state- of-the-art models (Zhang et al. 2021a An & Choj 2015 Xu et al. 2022) encode the training data distribution and then determine the anomaly score of newly observed data point using their recon- struction loss. This is based on the assumption that, since normal instances significantly outnumber anomalies, these models should show higher reconstruction losses for anomalies. Nonetheless, neu- ral networks can memorize and reconstruct anomalies well. As result, the reconstruction losses for both normal and anomalous samples become indistinguishable, undermining the effectiveness of anomaly detection (Child 2021).
In this work, we take a new approach to foster a more strategic mechanism for generating synthetic anomalies that can tackle the above-mentioned challenges. Specifically, we introduce a reinforce- ment learning (RL.) agent to guide the training of Conditional VAE (C-VAE) (Sohn et al.) 2015) model capable of synthesizing anomalous samples that are both challenging and diverse, which can be used to substantially augment anomaly detection models. The RL agent operates on the latent space of the C-VAE model and its reward function is strategically designed to balance the entropy of the generated samples and their ability to evade detection, presenting a key advantage of our train- ing framework in generating more effective anomalies. Furthermore, with this reward function, we theoretically show that the agent can explore deterministically in the latent space to yield feasible actions, thereby tackling one of the most crucial efficiency problems in RL.
Additionally, the complexity of data generated presents a challenge for training an efficient anomaly detection model. We establish lower bound on the error rate for any single detection model, show- ing that even an over-parameterized model cannot fully capture the intricate features of increasingly complex generated data. Moreover, this over-parameterized model could lead to significantly pro- longed inference times, which is not ideal for real-time applications. This necessitates a scalable anomaly detection model capable of capturing the increasingly diverse feature distributions. To achieve this, we train Mamba models (Gu & Dao, (024) structured as Mixture of Experts (MoF) (Shazeer et al., 2017 Chen et al., 2022 Nguyen et al. 2024) where each expert specializes in dif- ferent feature regions. Together with a proposed MoE training scheme, this allows for scalable inference with arbitrarily complex input data without increasing inference times, as only relevant experts activated for specific input. Our contributions summarized as follows:
We introduce a new systematic framework, namely Swift Hydra, for training an anomaly detection model based on synthetic anomalies strategically generated by an RL-guided C- VAE model. The efficiency of the detection model is enhanced via a Mixture of Mamba Experts, thereby enabling high detection accuracy while maintaining short inference time.
We establish theorem showing that the RL agent can perform gradient descent on the latent space to yield feasible actions early training episodes. We also propose a new training scheme for MoE that tackles the "winner-take-all" issue (Fedus et al. 2022).
Comprehensive experiments are conducted on ADBench, a benchmark including 57 datasets from various domains, to demonstrate the outperforming detection accuracy and the efficiency of inference of our model. The result suggests that RL and generative Al together inspire new and promising paradigm for advancing anomaly detection.
2 PRELIMINARIES AND NOTATION
Anomaly Detection. Given observations from a system, represented by x = {x1 .2...., IN) where æ E P iss the feature space dimension and the objective is determine whether each observation H, E R², for E [N], is an anomaly. The approach to anomaly detection can vary depending on the availability of labeled data. In the unsupervised setting, the assumption is that no labeled data is available, and the dataset comprises a mix of unidentified normal and anomalous instances. In the supervised setting, a dataset D = {(x;, y 1, 1.2....,N' each æ; is labeled as normal (y, -1) or anomalous (y: 1). This dataset is fully labeled with a known proportion of anomalies and normal data, rendering the detection process similar to binary classification with unbalanced classes, where there are typically fewer anomalous than normal instances. The semi-supervised or one-class classification method acts as a hybrid approach, where the training involves only normal data (D contains only y; -1), and anomalies, if present,
N) } is used where
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identified during inference. This method can also extend to partially labeled datasets, where some anomalies are labeled during training.
Class- Conditional Data Generation. In our work, employ a Conditional Variational Autoen- coder (C-VAE) (Sohn et al. 2013), denoted by Fo = Ma o gg. conditioned on anomalous data (y 1). The parameters to and represent the encoder and decoder, respectively, while @ encapsu- lates both sets of C-VAE parameters. The C-VAE operates as follows:
Fo = Ma G
d = Fo(o, vz) = (M wi) = (2(
(1)
where d; R. represents the reconstructed observation. The generator is trained by optimizing the Evidence Lower Bound (ELBO):
(2 2x M/5) (z ys)
ELBO C-VAE (x, [log Zi, V:) (x.
log
is called the reconstruction loss term, which aims to measure how well the model can reconstruct the input data from the latent representation.
In the above equation, (xs((x:))))))) [log ( ž, y:)]
(asles log (x:(2|(m.)35)] (=(())))) is called the KI. divergence term, which serves to regularize the latent space by making the distribution of the latent variables close to a prior distribution, typically a standard Gaussian. Note that C-VAE model is combination of linear functions and I-Lipschitz activation functions in which all layers are normalized. To generate new anomalous sample ai, e R²,, sample from 2, IRd (is, σ), where d is the latent space dimension, and μ and optimized parameters at the bottleneck. The decoder then transforms 2; into E; Ma(zi, = 1).
SWIFT HYDRA
This section introduces our Swift Hydra framework, as illustrated Figure I which comprises two main modules: Self-Reinforeing Generative Module and an Inference Module. First, the Self-Reinforeing Generative Module trains a generative model using RL to synthesize diverse and challenging anomalies. These generated samples are later appended to the original dataset 'D. Sec- ond, from this new dataset, the Inference Module trains an efficient detector using the Mixture of Experts (MoE) technique, which includes combination of multiple lightweight Mamba models specializing in different data clusters and gating network directing each data point to the top experts for collaborative prediction.
3.1 WELF-REINFORCIA GENERATIVE MODULE
This module includes two main models: a C-VAE generator, Fe, that synthesizes new anomalies, and large baseb detector WR. R² - [0. 1] parameterized by к that maps sample æ; to a probabilistic score of it being an anomaly. Unlike conventional methods where the generator Fo relies solely feedback from the detector We to generate new samples which could lead to a model collapse (Salimans et al.] 2016 Hassanaly et al., 2022) or vanishing gradient (Arjovsky) & Bottou| 2017) problem, we instead leverage an RL agent to guide the training of Fe. This RL agent, represented by a policy uw. explores the latent distribution p(z) of Fe and targets areas that would encourage the generator Fo to synthesize diverse and challenging anomalies that can bypass the detector W.. These synthetic samples are then used to augment the current training dataset and retrain Fg. ultimately improving its ability to generate better anomalies in future episodes.
Dataset definitions. The dataset D is split into a training set, Darain and a testing set, Diest, In our approach, the goal is to attain high accuracy on the Drest even with a small training dataset Derain Let Dialanced = {(x. y) E Derain j = min(ky = - 1 Ky }}), Ky -1} = j. Ky -} be dataset balanced between normal and anomalous data points, with equal cardinalities determined by the smaller class. Note that, as episodes progress, the generator Fa combined with the RL-agent Tu adds more anomalous samples to Dérain expanding the anomalous data in Dhalaneed. Since Dinlaweed ensures equal numbers of anomalous and normal data. the increase in anomalous data leads to a corresponding expansion of normal data as well. In the RL context, for each episode, denote Derain and Diulanced the evolving training and balanced datasets, respectively.
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MIXTURE OF MAMBA EXPERTS
Cambined Dataset
Conditional
GATING MODEL
Expert (Mambas
Expert (Mamba)
Expert (Membba)
Batch a
Susionet
Scoring
Prediction anorealy
Self-Reinforcing Generative Module
ASM
Inference Module
The Swift Hydra Framework consists of two main modules: the ReiffReenn Gener- ative Module and the Inference Module. The first module includes C-VAE, RI. agent, and large Mamba-based Detector. Initially, the C-VAE is trained on the original dataset (referred to as the Combined Dataset in episode 0). In the early stages, the RL agent generates diverse anomalies by refining latent vectors then shifts to producing anomalies that more effectively deceive the de- tector. The top 1 anomalies are added back to the original dataset, creating a new combined dataset to further improve the Generative Model. The second module employs a Mixture of Mamba Experts (MoME), where lightweight models specialize in different parts of the dataset, providing the same performance as the large detector but with significantly faster inference.
Figure I:
Training process. For each episode (comprising h steps), the C-VAE generator Fo is trained with batches of Derrsn dataset, while the detector Wi. is trained with Dbalaanedd Next, an anomalous data eonomolooss and converted into a latent representation == Gx (, = 1). The RL policy is tasked with generating a modification vector 8 in the latent space, i.e. To x + 8. This ó results in a new sample in the latent space as 2 = + 8. At the end of the episode, new dataset is obtained & (Mo y = M.. (2,, y 1)}. From the newly generated set X,, the top samples that lead to the highest rewards are selected and denoted as es! A formal definition of the reward is provided the next section. At each episode, the selected samples are then merged with Direin, forming the evolving dataset Drrain D &=1 Note that we set Dg = Dirain to ensure that the model Fo does not deviate from the acceptable range of the original data (Shumailov et al. 2024). 'he dataset Dirran is used to retrain the generator Fe. enhancing its ability to generate high-quality data in future episodes. As e increases, Drrain is incorporated into Dialanced Thus, Doalanced also grows across episodes. Due to page limit, refer readers to Appendix A.1 for the pseudocode and further details about the training process.
point (x. y = 1) is sampled random from Diraiu
3.1.1 GENERATING SAMPLES AS A MARKOV DECISION PROCESS
The process of policy modeling can be structured as a Markov Decision Process (MDP) (Bellman 1957 M def (S,A, R). This includes (i) a finite sets of states S, (ii) a finite set of actions A. (ii)) transition distribution T's'' s, s,a) where s, s, E S,a E A and (iv) a reward function
R: S x A-> IR. We specify each component as follows:
States (s): A state is defined by latent space representations 8; (2,, D!rain) for 2; Gu (x.)) and c.anoaatous where is the latent vector produced by the encoder G. from the input data
X; Dirasn
Actions (a): An action a; = (Pi, σ,) is vector of two components: 14 Rd (predicted mean) and G: E Rdd (predicted scale). The modification vector d; c M4, where ~ NO, I). and the latent vector is updated as é, = 2, d;
Rewards (R): The reward function is strategically designed to encourage the generation of a set of samples that are diverse and reduce the detector's 's confidence. The function is defined follows:
RiM yi = e) = .H(D U. 1)) - log W. =1)), (3)
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where H((Draii U.Mo(2,,3 y 1)) is the entropy of Da after incorporating M2 3/: = 1) and aimed at promoting the generation of diverse samples (additional details on the calculation of the entropy of Dirain provided in Appendix A.3). The function (, 9 1)) assesses the detector's likelihood of classifying the generated sample as anomalous, with the goal of reducing this probability to decrease the detector's confidence.
The hyperparameter y E [0, 1 dictates the desired rate of entropy reduction. This y implies that the policy Th focuses on exploring rare samples to increase the diversity of Deraio Deaanomatous in the early episodes. Once sufficient data has been explored, the reward function shifts to encourage the agent to exploit this data, generating new samples that are more effective at bypassing the detector.
Transition Dynamics (T): When an action Og (z) is taken, anomalous data point f (M, 1) is added to X. A new state 8:-1 (E+11, Diain) where 2,+1 = 9 (Xx+1), ), is then formed by selecting the next 1+
Dtrain ammomalous"
3.1.2 ONE-STEP TO FEASIBLE ACTIONS
The RL agent Tu, which is tasked with generating a new sample 2; from 2;, can be trained using conventional methods. However, during early training episodes, the agent would often struggle to find suitable actions that maximize the reward function because Tw has not yet learned effective strategies. fact, an action a; = (Ju,, may be invalid the updated latent vector 2; derived from ia falls outside the supported range of the trained model Fg. Even with advanced exploration techniques such as those in (Eysenbach & Levine 2022 Pathak et al. 2017; Burda et al. 2019; Ecoffet et al. 202I). this issue remains challenging for nw to overcome due to the high-dimensional and continuous nature of the action space.
A naive strategy to address this is use the observed data distribution p(z) (i.e., adding Gaussian noise to 2z) to generate new samples é, The encoder then provides their latent representation & = Go (0t, y = 1), and the modification vector 8; = E 2₁ is employed to guide exploration at that step. After that, feasible action å; (ô., oT.) is derived from d; replace the invalid action a, = (14, of the RL agent in the current step. Once a feasible action is identified, the agent learns it in a supervised manner, facilitating more effective exploration in future steps. However, randomly modifying observations in the input space p(x) can be complex. Instead, we rely on the following theorem to find feasible actions:
Theorem 1. (Reward Estimation Consistency). If the reward function R is differentiable, Fo is well-comverged, and R. (Ii e), where 2; = Ma (2, y = 1). (Proof in Appendix B.1
2 - Vz, (R((M = =)),e) for some small c, then R (i1, e) >
In other words, if Fg is well-convereed and maintains both continuity (i.c., nearby points in the latent space yield similar content when decoded) and completeness (i.e., points sampled from the latent space produce meaningful content when decoded), the C-VAE described in Equation 2 can explore new states s (i.e., anomalous observations) by utilizing the latent feature space p(2) (which is learned from the original space p(x)). This allows us to search for feasible é; in the lower-dimensional and less noisy latent space p(z) as an alternative to creating feasible actions. Specifically, Theorem implies that can deterministically search for 2n in manner that maximizes the reward function specified in Equation 3 using gradient descent (Ruder 2017). From that, feasible action à; = (ô.,a;) is derived where ó, = 2
With this approach, the policy, value, and reward models are trained simultaneously during these early episodes, allowing the RL agent to generalize effectively and reduce invalid actions in future episodes. Thus, the need for using one-step to feasible actions is eliminated in subsequent stages. Further details on this process can found Appendix A.2 with preliminary analysis given in Appendix C.5
3.2 INFERENCE MODULE
At the conclusion of the first module, the detector Wt, has been augmented by the newly generated dataset and can be used as the final anomaly detection model. Due the increasingly diverse training data generated by Fa. we had to initially overparameterize the detector W.. For that reason, deploying W. directly as the final detection model would not be scalable due to the high inference
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cost. Furthermore, the theorem below establishes a lower bound on the detection error, showing that any single detection model is subject to this lower bound regardless of the number of parameters.
Theorem 2. (Jnefficiency of single detector in handling evolving balance data). Suppose a feature space & C IR' contains Un normal clusters and Ua anomalous clusters, where each cluster u-th E [Un + Ual is modeled as Gaussian distribution N (Hu, I'Ip). Let Veluster be the cluster's volume and A be the total overlapping volume between normal and anomalous clusters, where the number of anomalous data points equal the number of normal data points, the training loss Lvain (W,,) is lower bounded by
A in case of linear We- (Proof in Appendix B.2
U. Velater
This theorem aligns with the findings in (Chen et al. 2022), emphasizing the inefficiency of using single classifier. To address this issue, in this second module, we use the MoE approach to train an efficient detector on the dataset generated by the first module. Instead of relying on a single large-scale detector, this technique leverages multiple "expert" models, with each one specializ- ing in a subset of the input data. The balanced dataset Dbutance is first decomposed into clusters {Cr.C2..... Cu ). where the number of clusters U is determined using the elbow method Yuaan & Yang, 2019). We train set of Mamba models
fas j. each acting as an expert for spe- cific data cluster following the Sparsely- Sparsely-Gated Gated Mixture-of of of-Experts approach (Shazeer et al., 2017). and where fm (z: W) is the output of the m-th expert network with input r and parameter W.
..f2...........
Gating network. In the cixxture-of-xxeers approach, the experts are complemented by gating network that directs inputs to the most appropriate expert. Given an input R., the gating network is defined as the following function:
(ar, Ngs Nuoise) = x Ng + StandardNormal()) Softplus (ær Nnnisse)
(4)
where Ng. Nnoise PxM are weight matrices that determine the linear transformation and noise contribution, respectively. From the output of h(x, Ny. Nuoisw), a key step is to apply the top & expert selection mechanism, denoted by TopK (h(z, Ng. (, k). where it selects the top & largest values from the vector (1: Ng, N, which represents the performance scores (e.g.. accuracy) of different expert networks. The elements in (ar, Ng Nnoise) that not within the top k are replaced by -oo, effectively excluding them from further consideration. Finally, a softmax function is applied to these top values normalize them, i.e., A(x, Ng, Npoise) Softmax coftmax(Topp[/] (1 Ng Nnoise), k)). This setup forms a Mixture of Mamba Expert, and the output of the MoE layer is then expressed as:
B(x, Ng, Anoise W) = Σ Am (ar, Ng. (mnise) W)
ME'.
where Tx S [M] represents the indices of selected experts ([3x| = k).
Tackling "winner-take-all". During early training of MoE, experts have arbitrary performance scores, hence the gating network could randomly allocate more samples to particular expert. With more training data, this expert outperforms others, thus receiving even more samples. This is referred to as the "winner-take-all phenomenon (Oster & Liu 2005 Fedus et al.) 2022), which reduces the MoE to a single lightweight expert, limiting its ability to generalize. While this expert may excel, fails to capture the diverse features across U clusters, undermining the model's overall performance.
We tackle this "winner-take-all" issue by temporarily deactivating the gating network during this early training stage and, instead, proposing a probabilistic approach to ensure diversity in cluster assignments across experts, while also considering the complexity of each cluster. For each expert fú. where E [.M), instead of assigning clusters based on fixed criteria, we dynamically adjust the probability of an expert fi selecting a cluster u, E [U]. with the probability inversely proportional to how frequently the cluster has already been assigned to other experts. More importantly, we introduce scaling factor that adjusts this probability based on the size of the cluster. For larger clusters, which are likely more complex, we reduce the penalty of being selected multiple times, as these clusters require more experts to fully capture their complexity. Specifically, the probability of expert fi selecting cluster u is given by:
exp
co
a 8v
Tuu
P(u| x, (nul. (suH)
(6)
E Enerjy exp
co
a
Tayd
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where su is the size of cluster u, nu is the number of times cluster u has already been assigned, is the base penalty factor, and co is a constant initialization score for cluster selection. Then, the expert fi will select ~ Categorical (P (u x, {nw). {s,)). (
E [U]) as its cluster.
Note that, due to the probabilisticc nature of the selection algorithm. there could be clusters that are not selected by any experts. Therefore, overspecify the number of experts M. As demonstrated in a theorem from (Nguyen et al. (024). doing so does not increase prediction time. This is because (ax, Ng. Nnoise; W) selects only the top (typically 2 or 3) best experts for making predictions. After training each expert with its selected cluster, we train the gating network to minimize the overall classification loss (e.g., MSE or Cross Entropy Loss). With this setup, we also establish a theorem to demonstrate the effectiveness of our training mechanism as follows:
Theorem 3. (MoME. efficiently handles evolving balance data). Let Frest (3) and Lrest (Wa) repre- sent the expected error on the test set for the Mixture of Mamba Experts (MoME) model and a single detector, respectively, For any value of A. employing MoME with {f1, J guarantees that the minimum expected error on the training set is Ltrain ( = 0 and the expected error on the test
set satisfies Ctest (8) S Liest (Proof Appendix
B.3
The above theorem demonstrates that a Mixture of Mamba Experts model can effectively fit all the data in the training set. Moreover, the expected error the test set when using the Mixture of Mamba Experts will always be less than or equal to that of a single detector. Once the experts are well-trained, we activate the gating network and use it for routing samples.
4 EXPERIMENTAL EVALUATION
Settings. We conduct experiments to evaluate the performance of our Swift Hydra framework using the ADBench benchmark (Han et al., 2022). which includes a comprehensive collection of 57 widely used anomaly detection datasets spanning various tasks, from image analysis to natural language processing, as detailed in Appendix C. We also evaluate a version of Swift Hydra without MoME, i.e., single large detector is used in the Inference Module. The implementation specifics, such as the training algorithm, model architecture, hyperparameter, model size, and training costs are provided in Appendix C.1
We will release the source code once the paper is published.
Metrics. In our evaluation, we focus on the performance of the Swift Hydra, particularly in terms of AUC-ROC and TIF (total inference time to predict all data in ADBench). Additionally, we analyze the distribution of generated data at each episode and compare it to the distribution of the test data.
Baselines. For the anomaly detection task, we compare Swift Hydra against several state-of-the-art (SOTA) semi-supervised and unsupervised learning methods included in ADBench. These meth- ods are Rejex (Perini & Davis 2003), ADGym (Jiang et al. 2023) and DTE (Livernoche et al.) 2024]. We also compare the distribution of our generated data against that of data generated by oversampling techniques such as SMOTE (Chawla et al.) 2002). Borderline-SMe SMOTE (Han et al. 2005), ADASYN (He et al. 2008). SVM-SMOTE (Nguyen et al. (011), CBO (Xu et al. [021]] Oversampling GAN (Nazari & Branco 2021) and VAE-Geomeety (Chadebec et al. 2023). For each method, the best-performing hyperparameters as provided in its original paper.
Methods
DTE
Rejex
ADGym
Swift Hydra (Single)
Swift Hydra (MoME)
AUCROC
TIP
AUCROC
TIF
AUCROC
TIF
AUCROC
TIF
AUCROC
TIF
Train/Te Ratio (40/60%)
0.82
4.02
0.78
3.89
0.86
6.12
0.91
13.11
0.93
4.01
Train/ Restt Ratio (M0/70%)
0.80
4.13
4.09
0.82
7.03
0.90
14.38
0.91
Train/Tos Ratio (20/80%)
0.79
4.31
0.76
4.22
0.79
8.17
0.87
16.13
0.90
5.22
Train/en Ratio (10/901)
0.78
4.42
0.74
4.39
0.77
9.14
0.86
18.52
0,87
5.84
TIP Total Inference Time (Seconds)
Table I: The performance of Swift Hydra and the baselines on the ADBench is evaluated based on two criteria: AUC-ROC and total inference time (TIF). Here, the AUC-ROC is the average calculated across all 57 datasets, while the TIF represents the total time the model takes to predict all data points across all datasets. We vary the train/test ratios to illustrate how the size of the training data impacts the performance. The best AUC-ROC values are highlighted.
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20
-30
-0
6-
Episode 2
Episode 8
Episode 32
Episode 128
Normal data (test)
Normal (train)
Anomalous data (test)
Anomalous data (generated)
Anomalous data (train)
Figure 2: The distribution of the evolving training set Dirain and test set Drest is visualized using the Cardiotocography dataset, one of the 57 datasets from ADBench, generated by Swift Hydra in each episode. The data points are dimensionally reduced using T-SNE (van der Maaten & Hinton 2008). Note that the light blue points represent the generated datapoints from previous episodes, providing insight into the trend of generating anomalous data across episodes.
AUC-ROC Evaluation. As shown in Table I the average AUC-ROC scores show that both ver- sions of Swift Hydra single large detector and MoME consistently outperform other state-of- the-art (SOTA) methods with respect to various training sizes (i.e., 40%, 30%, 20%, and 10% of the whole dataset). Notably, with only 10% of the dataset, Swift Hydra outperforms DTE in the semi-supervised setting and Rejex in the unsupervised setting. This demonstrates that our RL algo- rithm train generative model to synthesize effective anomalies that can later be used to train a high-performing detection model. We refer readers to Appendix (C.2] for a comparative analy- sis with more SOTA detection methods and oversampling techniques, and Appendix C.3 for toy example to illustrate the generalization ability of Swift Hydra. Appendix [C.4 presents a series of ablation studies evaluating the impact of the Self-Reinforring Module, the effectiveness of the prob- abilistic cluster assignments (as described in Equation 66. and the influence of the KL term and the reconstruction term Equation 2 on the AUC-ROC of Swift Hydra.
Inference Time Evaluation. In terms of total inference time across 57 datasets, Table I shows that Rejex has the shortest time, which is expected as relies on conventional lazy learning methods such as Isolation Forest. DTE, which is based on diffusion model, requires only a few steps to reconstruct backward and determine whether sample anomalous, resulting in relatively short inference times. Although ADGym optimally selects which ML. models to use for each dataset, the experiment shows that its overall prediction time is still relatively high compared to that of Swift Hydra (MoME). Swift Hydra (Single) achieves high AUC-ROC scores; nevertheless, its prediction time is significantly longer because a single large model is designed to capture the entire diverse dataset generated by the Reif-Reeino Generative Module. In contrast, Swift Hydra (MoME) not only attains the best AUC-ROC scores but also has efficient prediction times that are comparable to DTE with respect to the training sizes of 40% and 30%. Overall, Swift Hydra (MoME) offers the best balance between AUC-ROC performance and inference time among the tested methods.
Generated Data Distribution. We visualize the distribution of data generated over time by our Self-Reinforcing Generative Module in Figure 2 Initially, the model explores a broad spectrum of widely dispersed anomalous data points. As the episodes progress, a discernible pattern emerges: the generated anamalous points increasingly cluster towards the boundary that separates normal from anomalous data. In fact, this transitional zone the boundary highlights the anomalies that are not easily distinguishable from normal data points. Hence, this dynamic progression shows that our generative method significantly enriches the diversity of anomalous data points while simultaneously pushing for the most challenging anomalies, thus strengthening the detector's 's generalization ability.
Figure 3 shows a comparative analysis on the generated data distribution of our method and that of other oversampling methods. As can be seen, methods like SMOTE, Forderline-SMOTE SVM- SMOTE, ADASYN, and CBO only generate data points within the boundary of the anomalous data in the training set, while our approach allows data points to be generated beyond these boundaries. This enables our method to potentially generate anomalous data points that can cover the distri- bution of the test set. Although VAF-Geometry and Oversampling GAN also explore beyond the
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SMOTE
Borderline SMOTE
SMOTE
ADASYN
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Swift Hydra
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data
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Figure 3: The distribution the evolving training set Daraan and test set Diest visualized using the Cardiotocography dataset, one of the 57 datasets from ADBench, generated by the oversampling methods in our baselines. The data points are dimensionally reduced using T-SNE (van der Maaten & Hinton 2008).
fault
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Figure 4: The performance of the RL-Agent is represented by the reward (right y-axis), while the performance of the Mamba-based Detector (single model) is measured by AUC-ROC (left y-axis). Both metrics are plotted against the number of episodes (x-axis) across three challenging datasets from ADBench. Note that both reward and AUC-ROC are averaged over multiple roll-outs.
boundary, they have limitations. Oversampling GAN suffers from model collapse (Salimans et al,, 2016 Hassanaly et al. 2022): during the early training steps, if finds one data point that very good at fooling the detector, it will only focus on generating samples around that point in subse- quent steps. VAB-Geometry performs better it generates more diverse data points. However, is highly sensitive to hyperparameters to learn the data manifold correctly, hence, it is less effective compared our method. Both Figures and 3 demonstrate that data generated by Swift Hydra provides comprehensive coverage over the range of anomalous data in the test set, even though no knowledge about the test data provided during training.
Soundness of the Reward Function. Figure 4 shows that the reward trend (average of multiple roll-outs) closely follows the increase AUC-ROC. This demonstrates the soundness our reward function, as the RL agent optimizes the reward function, either by predicting actions itself or using feasible actions as discussed in Section 3.1.2. leading to the maximization set. Interestingly, (no knowledge about the test set is provided during training), it manages to increase the AUC-ROC time. This suggests that our reward function helps improve the detector's generalization ability.
AUC-ROC in the test though the RL agent receives feedback on how it performs the test set

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5 RELATED WORK
Anomaly Detection. Due to the high cost and difficulty of data annotation, most recent anomaly detection (AD) research has focused on unsupervised methods with various data distribution as- sumptions (Aggarwal 2017 Liu et al. 2008 Zong et al., 2018 Li et al. 2020 2022
Xu et al.
2022]. Common approaches like based (Donahue al. 2017 Schlegl
al., 2017), self-
supervised (Hojjati et al. [022, SShwwag et al., Georgescu et al. 2021 Li et al. (02T). and
one-class classification (Shen et al. [020] Hu et al., 2020) typically rely solely on normal data for training, making it difficult to identify anomalies due to the absence of true anomaly patterns. Reconstruction- based methods (An & Cho 2015; Xu et al. 2022) use anomaly reconstruction loss to detect outliers but often unreliable neural networks can memorize and generalize even with a few samples of anomalies. More recent supervised or weakly-supervised methods (Pang et al.) 2018b 2019a di Ruff et al. [2200) Zhou al.
2021) treat anomalies as negative samples to improve sensitivity, but they risk overfitting and heavily depend on the diversity and quality of the dataset.
Advanced methods like ADGym (Jiang al. 2023) have improved anomaly detection through op- timized data processing, augmentation, network design, and training, but they may fail if settings do not align with the target domain. Learning to Reject (Perini & Davis 2023) uses uncertainty scores to reject rather than forcibly predict uncertain samples; however, it often rejects data near the normal-anomaly boundary, reducing detection performance. DTE (Livernoche al.) 2024) lever- ages diffusion models to estimate posterior densities, but the decoder can still memorize and recon- struct anomalies, complicating reliable scoring. AnomalyClip (Zhou et al. 2024) captures general anomalies in images using object-agnostic text prompts but is limited to image-based tasks.
Oversampling-basse based techniques. Traditional oversampling techniques tackle imbalanced data by generating synthetic samples. SMOTE (Chawla et al.] 2002) interpolates between minority points to increase diversity but does not focus on challenging samples. Variations like CBO (Xu et al. [021). Corderline-SMOTE (Han et al. 2005), and SVM-SMOTE (Nguyen et al. 2011 generate samples near boundaries to improve representation but risk introducing noise and overfitting in complex distributions. ADASYN (He al.) 2008 ) targets harder instances for sample generation, enhancing performance but potentially causing redundancy if not carefully managed.
Recent techniques like Oversampling GAN (Nazari & Branco 2027) and VAE-Geometry (Chadehec et al. 2023) use deep learning to generate more generalized samples. Oversampling GAN may suf- fer from issues like vanishing gradients or model collapse, limiting sample diversity. VAE-Geometry employs a Variational Autoencoder that preserves the geometric structure of the data during augmen- tation, producing synthetic samples that more accurately reflect the true distribution. However, its accuracy depends on correctly learning the data manifold and is highly sensitive to hyperparameters; failure to capture complex structures can result in inaccurate sample generation.
RL-Guided Generative AI. Reinforcement Learning (RL) has been used to guide Generative AI (GenAI) large language models (L.L.Ms), as seen "Learning from Human Feedback" (Dubois et al., (023) and ReST (Gulcehre et al.] 2023), enhancing generative capabilities through reward models. The direct use of RL to guide the sample generation process of generative models in anomaly detection remains underexplored, with this approach only recently gaining traction through the ReST framework for LLMs.
6 CONCLUSION
We propose Swift Hydra, a framework designed to reinforce a generative model's ability to syn- thesize anomalies in order to augment anomaly detection models. The framework features an RL agent to guide the training of a C-VAE model that generates diverse and challenging anomalies. We further propose a mechanism to help the RL agent choose an action more efficiently during train- ing. Additionally, due to the diverse nature of the generated dataset, we introduce Mixture of Mamba Experts to train an efficient anomaly detector, where each expert specializes in capturing specific data clusters. As a result, our model demonstrates strong generalization capabilities and fast inference, as evidenced by experiments conducted on the ADBench benchmark against state- of-the-an art anomaly detection models. Our research highlights a promising paradigm of integrating RL and generative AI for advancing anomaly detection. It can also be leveraged for generating and synthesizing data in other application contexts where collecting real data is expensive and scarce.
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ACKNOWLEDGMENTS
This work was partially supported by the National Science Foundation under the SaCT program, grant number CNS-1935923, and by the Korea Institute of Energy Technology Evaluation and Plan- ning (KETEP) grant funded by the Korea government (MOTIE) 2033000333,,,, Study on developing cyber-physice attack response system and security management system to maximize real-time distributed resource availability).
This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC,, for the U.S. Department of Energy (DOE) under Contract No. DE- AC36-08G028308. Funding provided by the U.S. Department of Energy Office Cybersecurity, Energy Security, and Emergency Response (CESER), and by the Laboratory Directed Research and Development (LDRD) Program at NREL. The views expressed in the article do not necessarily represent the views of the DOE the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.
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Ying Zhang, Jianhui Wang, and Bo Chen. Detecting false data injection attacks in smart grids: A semi-superrised deep learning approach. IEEE Transactions on Smart Grid, 12(1):623 (344 2021a. doi: 10.109/TSG02220.01005500
Yingying Zhang, Zhengxiong Guan, Huajie Qian, Leili Xu, Hengbo Liu, Qingsong Wen, Liang Sun, Junwei Jiang, Lunting Fan, and Min Ke. Cloudrea: A root cause analysis framework for cloud computing platforms. In Proceedings the 30th ACM International Conference on Information 2021b.
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Kang Zhou, Yuting Xiao, Jianlong Yang. Jun Cheng, Wen Liu, Weixin Luo, Zaiwang Gu, Jiang Liu, and Shenghua Gao. Encoding ArructureTTextue Relation with P-Net for Anomaly De- rection in Retinal Images, pp. 360-377. 11 2020. ISBN 978-3-030-58564-.. doi: 10.1007/
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Yingjie Zhou, Xucheng Song, Yanru Zhang, Fanxing Liu, Zhu, and Lingqiao Liu. Feature encoding with autoencoders for weakly supervised anomaly detection. TNNLS, 2021.
Bo Zong, Qi Song, Martin Renqiang Min, Wei Cheng, Cristian Lumezanu, Daeki Cho, and Haifeng Chen. Deep autoencoding gaussian mixture model for unsupervised anomaly detection. ICLR, 2018.
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A DETAILS OF SWIFT HYDRA
A.1 SELF-REINFORCING GENERATIVE MODULE
The algorithm A.1 describes self-reinforcing generative module for training a Conditional VAE (C-VAE) based generator, a Mamba detector, and a policy network within a reinforcement learning framework. The input includes the number of episodes E and steps per episode T, evolving datasets Di Dhalance, and Dirain Dejanomalous for each episode e, the generator Fo = Ge o Ma. and the Mamba detector Wn. The process begins by initializing the policy Tu- the generator Fo, and the detector W.. For each episode e, the generator is first trained on the current training dataset Dirain and the detector is trained using the balanced dataset Dbalance, A trajectory buffer is initialized to store states, actions, and rewards.
During each step in the episode, the generator produces latent vector for anomalous data point, and the policy network samples an action = (μr, σ)) based on the state s = Deraann ). A perturbation 6 = .. + ft is applied to obtain new latent vector 2'. If 2' is within the supported range, a new sample x' = =Ma(=' y 1) is generated; otherwise, the One-Step to Feasible Action algorithm is used to adjust the action, correcting e' and updating the action. The reward R(s, a, e) is calculated and stored in B along with the state and action, and the generated sample x' is added to temporary set X.
After completing all steps within an episode, the policy Tu is updated using reinforcement learn- ing techniques-Stie such as Proximal Policy Optimization (PPO) or behavior cloning based on the collected trajectory B. The top samples with the highest rewards from X' are then added to the training set Dirain. Subsequently, Diafanne is refined from Darain using the helper function Trim(.), ensuring an equal number of elements in both classes.
To further ensure efficient training and avoid unnecessary iterations, a convergence criterion based on the average reward per episode is integrated into the process. At the end of each episode, the algorithm computes the average reward over the collected trajectory. This average reward is com- pared against the best observed average reward, and if the improvement does not exceed specified threshold Ω for N consecutive episodes, the training loop is terminated early. This mechanism en- sures that once the models and policy have stabilized- -inliizzd-iddiiattnnng convergence- further training is halted, thereby preventing overfitting and saving computational resources.
Moreover, if the total number of generated anomalous data combined with the training anomalous data exceeds the total number of normal data in the training set, the Trim(.) function could remove some of the generated data. However, across our experiments on all 57 datasets, we observed that Swift Hydra consistently converges before the anomalous data surpasses the normal data in quantity. Note that in most cases, the number of available anomalies in the training data only accounts for 1%-15% of the entire dataset (see Appendix C.6), representing the primary challenge in anomaly detection. If the total anomalous data were to exceed the normal data, one approach would be to start generating (or collecting) more synthetic (or real, respectively) normal data.
A.2 ONE-STEP TO FEASIBLE ACTIONS
The algorithm implements one-step optimization process to adjust a latent variable z, aiming to increase the diversity in the evolving dataset Dirain using Kernel Density Estimation (KDE) and entropy maximization. The process begins with initializing key parameters: the gradient step size 7/, which controls the size of updates to 2; the regularization parameter 7, which determines the importance of diversity in the optimization; and the number of sampled datapoints used to estimate the dataset's 's distribution.
In each iteration, a KDE model (detailed in Appendix A.3 is constructed using the dataset Dtrain to capture its distribution. This model helps estimate the density of the data points within the current dataset. After building the KDE, we sample data points from it to approximate the dataset's overall distribution. These sampled points are then used to calculate the entropy H(2) (explained further in Appendix A.3) which quantifies the diversity uncertainty present in the dataset.
Following this, the algorithm calculates the loss Lped based on a reward function (as defined in Equation With the loss computed, the latent variable is updated through gradient descent.
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Algorithm 1: Self-Reinforcing Generative Module
Input: episodes, á steps per episode
e,nommooous for each episode E [1, C-VAE-based Generator Fo GΦ Ma
Evolving datasets Derain Dbalance, D
Mamba detector Wi
Convergence parameters: threshold Q and maximum episodes N with no improvement Trained models Fe. wx policy Tw. and datasets Dérain, Dhalance
Output:
// Initialize models, policy, and convergence tracking Initialize Policy Nu. Generator Fo, and Detector Wr Set best_avg_reeeee best_aug-reward + cc, noo_improuement_com _count 0 while < E' and mmmproeement.come < N do
// Train VAE model on the current training set TrainVAE FF)
// Train detector model on balanced training data TrainDetecttr(DPiione W,)
Initialize trajectory 2 + and new samples set & t
// Generate new samples to expand the training dataset for t to do
// For each Dérain c,anomolous compute latent representation
2 Fa)
// Sample action based on state s (z, D!rain)
Sample action (n, o) using policy
// Compute perturbation 6 6 where ~ 70,
and form new latent vector
11
Form new latent vector 2' = if a is within the supported range then
= -Mal'' 1)
14
else
// Adjust latent vector if out of feasible range
s' = OhestepTooFaciilleettioll Dirain)
16
= M
// Update action to reflect the feasible adjustment
a = (8 x' =
17
// Calculate reward for the current state actionnction pair Calculate reward R(s, a)
Append (s, a, R(s, to trajectory and sample (x',y 1) &
19
// Update policy using gradient descent method (e.g., PPO) TrainPolicy(m.,))
29
// Add top-l highest reward samples to the training set Dirain +- Drrain &
21
// Balance the dataset by trimming over-represented classes Dbalance Trim(Dirain)
22
// Compute the average reward for episode
avg reward, +- p& E(sa,)) R(),
/1 Check convergence criteria based on average reward if aey reward, > best ang reward S then best_ang.reward + avg.rewarde no_imppronmmet__cmnt <- else
25
27
28
no.improvement.cou no.imprrvemeettccuut
1
return Fe, Wx, Ter, Dtrain Dhalance
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Algorithm 2: One-Step To Feasible Action
Input: Latent variable z, Current evolving dataset Dirain
Output: New Optimized Latent Variable z'
Initialize gradient step size
Initialize regularization parameter 7 E [0, 1]
Initialize number of datapoints for KDE sampling
for to do
// Construct Kernel Density Estimation Direin
KDE + wer.ee/Dessstyystttmmioooool.
// Sampling datapoints from KDE
sampled.z KDE. samplll)(ss)
// Calculate Entropy H(z) based on datapoints and KDE
Probability function
H(z)) + (ntroopy(ampled,, KDE)
// Compute prediction loss with entropy reqularization
Epod f log WM (Mp(z 1)) - -(()
// Update by gradient descent
2 ( 2))
24
11 return
This adjustment directs towards minimizing the prediction loss, making more representative of diverse data that can potentially deceive the detector Wx- Once the optimization is completed, the refined latent variable returned, concluding the One-Step to Feasible Action algorithm.
A.3 ENTROPY ESTIMATION IN DYNAMIC TRAINING DATASETS
To effectively evaluate the diversity of our current evolving dataset Derain entropy using Kernel Density Estimation (KDE) followed by sampling-base entropy estimation. KDE helps us estimate the probability density function p(x) from the empirical data Dtrain The formula for KDE is:
annommlouus we measure its
anaomaloous
1 nh Σ
T
Di
p(x)
1C
h
Here, f(x) the estimated probability density at point x, is the total number of points in Dirain e.anomakous h is the bandwidth, and K. is the kernel function. This function, probability den- sity itself, weights the data points around æ. For our analysis, we use the Gaussian kernel due to its smooth properties and infinite support:
KC(u)= = 2
The choice of bandwidth h significantly affects the estimator's 's bias and variance. A smaller h leads a detailed but potentially noisy estimator (risk of overfitting), whereas larger may overly smooth the data (risk of underfitting). We can adopt Silverman's 's rule of thumb for selecting band- width with Gaussian kernels:
h 1.06on 1/5
where o is the standard deviation of the dataset.
After estimating p(x) with KDE, calculating the entropy directly from Draain bersome and computationally intensive:
e, anomalous would be cum-
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/
HDDtrasn e,anomalous)
((Dtrain
((x)) log ((z) dr
Instead, employ Monte Carlo Sampling to select data points zj from this estimated distribution and approximate the entropy using these samples:
1 Σ log ((1,)
H(Drraiie
eanoomalous
Here, Iy are the samples drawn from ((x), and log ((rz) is the natural logarithm of the estimated density at each sampled point. We calculate the average of these logarithms across all ç sampled points approximate the entropy. This method provides practical and computationally efficient approach to estimate the entropy, reflecting the diversity and uncertainty of the dataset Dirain e,anomalous
B THEOREMS AND PROOFS
B. REWARD ESTIMATION CONSISTENCY
Theorem 1 If the reward function R. is differentiable, Fo is well-converged, and 2; == C. V., (R(MM Vi e), for some small c, then R (b), R (2), where 2; Mo(2;, 1).
Proof. To prove this theorem, we first prove that for well-converged Fo. Ma is Lipschitz- continuous.
Consider the decoder Mo RRd T.P. composed of N layers. For j to N 1, each layer computes:
h 9 (1) = ReLU bj), where ho 24 E Rd, W E xd,xd=-1, and by E Rdd, The output layer computes:
24 = M = AN 11 = Wxhx-1 + bN.
with WN Pxdx and by E R.P.
To prove that Ms is Lipschitz continuous, consider two inputs 24, 8g E Rd We aim to show:
- Ma s K| - 22|1,
where K is a finite constant.
Starting from the output layer:
[2M) - Mo(2)ll (1 (
(2:)
=IWNh + by - Wx N-1 bx
(82)
S ( (2.) - (8)
where ||N]] denotes the spectral norm of WN.
For each hidden layer j = N - down to 1:
| ||/-00) - (3.) || = (1a=(h)=))) y (h (h,52))
= -|R,I. + +b,)
-elLU b,)ll
S - -W,45131
(since ReLU is I-Lipschitz)
s [[55 -
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By recursively applying these inequalities, obtain:
j
1/
I
S
II
[I k-
11la
|1
-16 -
[I
| N +11l2/ || -
At the output layer:
(Mozz))Ma(ae | -N
(2.
Substituting the recursive bound:
N 1| - -all-
- (o(zz))-((BE))) & Hwslla
Define K = [[, [W,ll To ensure K is finite, we enforce bounds (Layer Normalization) on the spectral norms: |[Wlll2 S 8y, where 8j are finite constants. Then:
N II j=1
K < Sy-
we choose 3, = s S for all j. then K < S S 1, which is finite. Therefore, Ma is Lipschitz
continuous with Lipschitz constant K, satisfying:
- Ma(2)) < K| - 2
Thus, we finished proving that Mg is Lipschitz-continuout Given Fg is well converged, With Ma being Lipschitz continuous and differentiable, small learning rate induces small change in latent vector which results in a small change in the data point x; reconstructed by C-VAE. We can use first-order Taylor expansion for small A
2 -4
= M (z.) M (z:)
Jms (21) Az,
where JMs (zi) is the Jacobian matrix M& at 24. From the update rule:
Az 2, =. (Z,,
Thus, the change in x, is:
8 - 24 R JM, (2i) = = C- (2:) R.
Since x; MM (z:), by the chain rule, we have:
V R = Juh (2)) V (I,,e)
Therefore:
2; x4 Re JMs (2.) JM, (2)) V R (x,,e)
Let JM, (2)) JMh (2i), which is positive semi-definite matrix. Thus:
4 - R V., R (xi, e)
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Using first-order Taylor expansion of R around x;
AR R (fi, (ai, 2 Ve, (#: 13))
Substituting 8, - Te::
AR 2 Vz, V2, (I;, e) F. (x,,(
Since / is positive semi-definite and > 0:
AR 20
More specifically, AR = if and only if v., R (a,, e) = Otherwise, AR > Therefore, under the given conditions and for a sufficiently small e:
R ( > R (xi,e)
This completes the proof.
B.2 ONE DETECTOR INEFFECTIVELY HANDLES EVOLVING BALANCE DATA
Theorem 2.
Suppose a feature space E C R contains Un normal clusters and Ug anomalous clusters, where each cluster u-th [U, + U.] is modeled as Gaussian distribution N Ip). Let Veluster be the cluster's volume and A be the total overlapping volume between normal and anomalous clusters, where the number of anomalous data points equal the number of normal data points, the training loss Luain (Wx) is lower bounded by U. in case of linear W.-
Proof. Consider the feature space X C R.P with Un normal Gaussian clusters and Ua anomalous Gaussian clusters, each modeled as N N(Hu; Ip). The volume of each cluster is:
P12(330)
Velnster
r [ +1)
where 30 represents the radius covering 99.7% of the data points cluster. The total volume occupied by the normal clusters is:
V Viotal.nomme normal Un Velusters
and the total volume occupied by the anomalous clusters is:
Vrotal anomalous Ua
Veluster-
The clusters overlap in certain regions, resulting in a total overlapping volume A between normal and anomalous clusters. Under our assumption, this overlapping region contains 50% of A, i.e. 2 normal data and 50% of A, i.e., 2 anomalous data.
A
Note that since the datapoints negligible while noise features from negative class are dominant. The unique volumes the normal and anomalous clusters, excluding the overlapping regions, are:
in the overlapping area, assume that the unique features
Yunigue Vanique_nornal poomal
Viotal pormal
2
A
Un Veluster
2
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A
V Viiqqu anomalous
V total anemaalus
2
= Ua Veluster
2
For simplicity, we assume that the detector Wi constructs decision boundaries around the normal clusters. Specifically, the detector aims enclose the normal clusters within its decision regions to classify them as normal, while any data points outside these regions are considered anomalous. As indicated in the work of Chen et al. (2022). single detector focuses on both unique features and noise features, even though unique features are negligible. This means the detector W. seeks minimize False Negatives by primarily capturing the normal data based on noise features, while overlooking unique features. As the model size x increases, the decision boundaries of the detector can more precisely conform to the normal clusters, potentially leading to overfitting of normal data. Let q(x) denote the proportion of the unique normal volume that the detector's decision boundary covers:
Veovered = q(x) Vunique normal
The False Negative Rate (FNR), which represents proportion of normal data not covered by the detector, is:
FNR 9(x)-
Because the detector's decision boundary encloses the normal clusters, it inevitably includes parts of the overlapping regions A. Therefore, the detector inadvertently covers some anomalous data within the overlapping regions, leading to False Positives. The volume of anomalous data incorrectly classified as normal (False Positives) is:
VPP q(x)
The False Positive Rate (FPR), representing the proportion of anomalous data misclassified as nor- mal, is:
VFP V Vunique anomalous
FPR
9(x) A
Ua Veluster
2
Assuming equal prior probabilities for normal and anomalous data, the expected error L(W₂) is:
1 FPR
L (W.)
FNR
2
q(x)
1- (x)())= +
U. Veluster
9(x)- -A
1 ((x + (Ua Veluster
Our goal is to find the minimum expected error Lirain (Wa)- To achieve this, consider how L(W2) varies with q(x). Since the detector aims to maximize coverage of the normal clusters (i.e., maximize g(x)) to minimize False Negatives, consider the case where q(x) 1, corresponding to the detector fully covering the unique normal volume.
Substituting q(x) 1 into T.(We), get:
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1
A 2
Luiin (Wi)) 2
1 1
Ua Veluster
2
(Ua Veluster 1
2
20, Veluster A
A
Ua Veluster
This expression represents the minimum expected error achievable by any detector that constructs decision boundaries around the normal clusters. Due to the overlapping volume A between the normal and anomalous clusters, there is an inherent lower bound on the expected error Ltrain (W₂, that any detector of this type can achieve. The detector cannot reduce the error below this bound because, in maximizing coverage of the normal data to minimize False Negatives, it inevitably includes portions of the overlapping anomalous data, resulting in unavoidable False Positives.
B.3 MOME EFFECTIVELY HANDLES EVOLVING BALANCE DATA
Theorem 3. Let Cestt 3 and Liest (xx) represent the expected error on the of Mamba Experts (MoME) model and single detector, respectively. For any value of A, employing MoME with /2........ ., f's) guarantees that the minimum expected error on the training set Lirrin (8) = and the expected error on the test set satisfies (3) I Liest
for the Mixture
Proof. Similar to the setting in Theorem 2, we also consider the feature space & C R.P. with U, normal clusters and U. anomalous clusters, each modeled as Gaussian distributions N N(uu, I²I)).
Each cluster occupies a volume Veluserr (30)) and the total overlapping volume between ((++1)
normal and anomalous clusters is A. Again, since the data points are in the overlapping
assume that unique features are negligible while noise features from the negative class are dominant.
Recall that, we decompose the balanced dataset into clusters {C1, determined using the clbow method. After that, we train set of experts {f1, f2..f..... fe...., fM each acting expert for specific data clusters, following the top k gated dfxture-of-Experr approach. Let Derain be the training dataset. Each data point & E Derain belongs to a cluster C, and has a true label (x:):
where U = U, U
5(z)= = (1, (I,
æ E normal cluster, - [1,, if E an anomalous cluster.
In the overlapping regions A, due to probabilistic assignment and expert overspecification, we as- sume each cluster C, has at least one specialized expert fm predicting y(x) using both unique and noise features, similar to WK. The gating network A(x, Ng, Muoke)) minimizes classification loss but primarily focuses on unique features, assigning higher weights to the appropriate experts. These properties feature capturing have been highlighted by Chen et al. (022).. For each x Dérain the MoE 3's output is given by:
3(1, Ngp Nmoises W)
Σ (1r, Ng: (nniss))ma (m; W). mE'x
Primarily based on unique features, the gating network learns to assign significant weights to the expert(s) that correctly classify ensuring that the model output 3(x) matches the true label y(x). Thus, the expected emrrr on the training set is:
Luaan (F)
Σ DeDi
13(r)/((>) = 0,
Dtrain
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where [u(=)/((x)) is indicator function that equals if ((x)) * g(z) and 0 otherwise. This completes the proof of the expected error of & on the training set.
For the test set, aim to show that: (3) S (WV,
Let's consider the test dataset Dies, drawn from the same distribution as the training dataset De If the data points in the test set lie completely outside U clusters from the training set, both & and W will fail to make correct predictions. This because we are assuming that each classifier forms a decision boundary that tightly fits the cluster it captures. Any data point lying outside these decision boundaries is considered negative for the class corresponding to that cluster. Therefore, without loss of generality, we only need compare the errors of the two models within the region of the U clusters.
Each data point Diesi belongs one of the clusters Cy and has true label y(x) defined earlier. Suppose input x lying in a non-overlapping region D the expert fm specialized in cluster C, has learned to classify data points from C, correctly. The gating network À (x. Ng. Nuoise ) effectively routes z to the correct expert fm. resulting in the MoE model predicting y(r) accurately. Therefore, for these non-overlapping regions, the MoE output is:
3 (xr, No Anoise W) u(x), Vo E Cu and & E D
(8)
Similarly, the single detector Wx. having been trained on the entire dataset, can also correctly predict ((x) in these non-overlapping regions since the classes are well-separated. Thus, the expected error in this region is negligible:
(M,,
Σ REDA
(x)
(3)
0
where (x) is an indicator function that equals if (w.))) + y(z) and otherwise.
Now, consider the overlapping region A. Assume equal number of anomalous and normal data points within A, with their features being significantly similar. The experts, specialized in their respective clusters, capture cluster-specific patterns even in these overlapping areas. The gating network X (x, Ry. Noois)) ), trained to minimize overall classification loss based mainly on unique features, assigns higher weights to the correct experts that are more likely to predict the true label yxx) Consequently, & correctly classifics x in A with high probability, quantified as - EA, where EA is the MoE's error rate in the overlapping region.
In contrast, the single detector Wx encounters inherent ambiguity in A due to the negligible presence of unique features and the dominance of noise features from the negative class within the cluster it aims to capture. Furthermore, with an equal number of normal and anomalous data points assumed in this region, the misclassification probability becomes:
Coverua (Ww)=
Let Pă be the probability that a test point lies in a non-overlapping region A. and PA be the prob- ability that it lies in overlapping region A. The expected error of the single detector on the test set is:
PA 2 2
Lus (Wa) = PA x 0+ x
For the MoE model, the expected error on the test set is:
Liest PA 0
X PAEA
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In the overlapping region A, the worst-case scenario for occurs when it fails to route the input to the correct expert, resulting in a maximum error of 2. However, if some test points are identical or very similar to the training points, the routing network is more likely to direct these inputs to the correct expert, as it primarily focuses on unique features. On the other hand, the single detector Wa considers both unique and noise features, with noise features dominating. Therefore, have E S 2. leading to the conclusion:
Listt (8) = PAEA
PA
2
< Liest (Wx).
This completes the proof.
C MORE EXPERIMENTS
C.I SWIFT HYDRA SETTINGS
C.1.1 HYPERPARAMETERS
Hyperparameter
Value
Learning rate for C-VAE Model Learning rate for Mamba Model Learning rate for Generator Total epoch for Detector Model Total epoch for Generator Model Optimizer
0.003
0.001
0.0001
600
500
Adam (Kingma & Ba, 2015)
Number of steps per episode
500
Number of episodes
200
Minibatch size
256
Discount factor ?
0.95
Activation function for Mamba Model
I LeakyRel.U
Layer Depth for Mamba Model
Activation function for C-VAE Model
ReLU
Bandwidth
0.5
Weight KL
0.55
Number of experts
20
Top experts
Detection threshold
0.2
Sampling from a KDE
300
Policy Training
Proximal Policy Optimization
Table 2: Hyperparameters for Swift Hydra
In this section, we present the hyperparameters selected for Swift Hydra, as shown in Table 2 and explain the rationale behind each choice. These hyperparameters are carefully designed to balance model performance, training stability, and computational efficiency.
The learning rates for different models are chosen based on their complexity and training dynamics. The C-VAE model uses a relatively high learning rate of 0.003 to promote faster convergence during training. In contrast, the single clumba-based detector over-specified in terms of the number of parameters to effectively capture the data generated by the C-VAE, stored Dhalance, To ensure stability during its optimization, lower learning rate of 0.001 is considering its sensitivity to parameter updates. The Generator model, which is part of a more delicate generative process, has an even smaller learning rate of 0.0001 to prevent large updates that could destabilize training.
The number steps per episode (500) and the total number of episodes (200) are chosen to allow the model to generate total of 100,000 datapoints (200 * 500) across all episodes. This quantity
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is sufficient to augment any imbalanced dataset within ADBench. The minibatch size of 256 is selected to strike a balance between training stability and computational efficiency, ensuring enough data is processed per update without causing excessive memory usage.
The discount factor 7 = 0.95 is set to ensure that, in the initial phase, the RL agent not only focuses on generating datapoints deceive Wj. but also actively explores its surrounding environment. As training progresses, the entropy term in the reward function gradually diminishes due to ", the model increasingly concentrates generating points specifically aimed deceiving the detector W..
For activation functions, LeakyReLU is used in the Mamba Model to address the "dying ReLU" problem, allowing the model to handle negative inputs more effectively, while ReLU is used in the VAE model to facilitate faster training.
Recall the fact that, use Kernel Density Estimation (KDE) to learn the feature distribution of the dataset Dérain in our framework. An important hyperparameter in this process is the bandwidth h, which controls the smoothness of the probability density function, thereby balancing bias and variance. While h can be determined using Silverman's 's rule of thumb, as described in Appendix for our experiments, we opted to use the well-known bandwidth parameter of 0.5 for KDE. Despite this simple choice, we still achieved the desired results.
A.3
The weight of the KI. divergence in the VAE set 0.55. This is carefully selected to balance reconstruction accuracy and latent space regularization, preventing overfitting while maintaining meaningful latent representations. For a more detailed explanation of how the trade-off between reconstruction loss and KL loss affects the performance of Swift Hydra, we encourage readers to refer to Appendix C.4
To ensure that the model can capture all potential clusters generated, overspecified the number of experts to 20. This allows the model to avoid missing any clusters. Indeed, the number clusters found using KMeens+Elbow on datasets in ADBench is usually more than 10. For selecting the top i in the Mixture of Experts to ensure only le experts are used during inference (thus saving inference time), we set 2.
Our policy training algorithm is Proximal Policy Optimization (PPO) (Do et al. 2024 Schulman al. 2017 Do et al.) 2021 Ngo al. 2024 Khoi al. 202T). In addition, the detection threshold of 0.2 is chosen so that if the model's confidence exceeds this threshold, the predicted datapoint is considered anomalous. Finally, sampling 300 times from KDE provides enough data to accurately model the underlying distributions without incurring excessive computational costs. Overall, these hyperparameters are carefully tuned to enhance model performance, ensure training stability, and optimize computational resources.
C.1.2 MODEL SIZE AND TRAINING COST
Al Module Type
Number of Parameters
Trrainnn time per batch
TToaal training time
C-VAE Generator
458,907
0,0011
3.265
Mumbaa-based Datector (Single)
274,542
0.00033
Gating Network
6,164
0.0001
0.286
Mixture of Mamba Experts Detector (MoME)
Expert Network
33,021
0.0026
1.287
Mixturee of Experts (20 Experts, topk-2)
666,584
0.0032
489.003
Table 3: Number of parameters for each component in Swift Hydra, training time per batch, and total training time. The total training time for the C-VAE and the Mamba-basee Detector (Single) measured per episode. For MoME, the two components, Gating Network and Expert Network, are measured over the entire training data and generated data after completing the Self- Belf-Reinforcing Module, calculated across all batches a single epoch. Additionally, we report the total training time of the Mixture of Mamba Experts (20 Experts, topK=2) across all epochs, shown in the table.
Table preesentt the number of parameters for each model, including the C-VAE Generator, Mamba- based Detector (Single model), and Mixture of Mamba Experts Detector (MoME). On average, single expert in MoME has approximately 33,021 parameters. However, with 20 experts and a gating network, the total parameter count for MoME reaches 666,584. In contrast, the Single Mamba-based
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Detector contains around 274,542 parameters, while the C- Generator comprises approximately 458,907 parameters.
In addition to reporting the training time per batch alongside the number of parameters, have also measured the total training time for each stage of our algorithm. These times were recorded on workstation equipped with two Nvidia RTX 4090 GPUs. Since this is a reinforcement learning framework, the number of episodes required for training heavily depends on the specific problem being addressed. Therefore, we only measure the total training time of the C-VAE Generator and Single Mamba Detector per episode. On the other hand, the total training time for the Mixture of Mamba Experts Detector is measured after completing Phase 1, using all the data generated during that phase.
Our training methodology supports two approaches depending on the hardware configuration: se- quential training or parallel training of the experts. In the sequential approach, each expert is trained one at time, selecting and training on clusters sequentially. This approach is more memory-efficee and requires less GPU VRAM. In contrast, the parallel approach involves all experts selecting their clusters simultaneously and training concurrently. While faster, this method demands significantly more GPU VRAM. The total training time for the Mixture of Mamba Experts (20 Experts, topK=2) across all epochs, as shown in the table, was measured using the parallel training method.
C.2 SWIFT HYDRA: MORE PERFORMANCE EVALUATION
C.2.1 BENCHMARKING AGAINST ADDITIONAL DETECTION METHODS ON ADBENCH
We conducted additional experiments to compare our proposed method, Swift Hydra, with several state-of-the-are tabular anomaly detection methods, including the supervised FTTransformer (Gor-
ishniy et al. 2023), the unsupervised ECOD (i et al. 22022), and the semi- semi--sperviied DevNet (Pang
al. 2019b), PreNet (Pang et al. 2019a). DeepSAD RRuff et al. 2020 and FEAWAD (Zhou al.
2021
The results is shown in T
Methel
BCOD
DesNet
PRoNei
DecpSAD
FEAWAD
FTTrasfiener
Swidtydu (MaME)
AUCROC
AUCROC
AUCROC
TIF
AUCROC
AUCROC
TIF
AUCROCC
TIF
AUCROCC
TIF
Traie/ Teat
0.80
26.00
0.82
34005
0.85
125.71
0.84
0.86
198.02
|50.66
0.95
4.01
Train/ Teat Rutio (3070%)
0.78
28.32
0.11
[ 25.54
0.84
147.74
0.83
20.53
0.82
215.26
0.84
16623
0.91
4.79
Trater Rato (200005)
0.77
30.04
0,80
26000
0,83
184.29
032
22.75
0.00
223.00
0,80
50.98
0.90
5.22
Teat Rusio (109901))
0.75
33.36
6.79
27.0
0.82
190399
0.11
0.79
233.13
0.77
Total Inference Time (Secaddo)
Table 4: The performance of Swift Hydra and other baseline models, including ECOD, DevNet, PReNet, DeepSAD, FEAWAD, and FTTransformer, is evaluated on ADBench using two key crite- ria: AUC-ROC and Total Inference Time (TIF). The AUC-ROC computed as the average across all 57 datasets, while the TIF measures the total time required by each model to predict all data points across these datasets. To analyze the impact of training data size on performance, we vary the train/test ratios. The highest AUC-ROC values are highlighted for clarity.
Semi-supervised methods typically require only small amount of labeled data achieve AUC- ROC scores comparable to modern unsupervised methods such as DTE, Rejex (as shown in Table 1), and ECOD. However, these methods often come with high computational costs, particularly when applied to large datasets. While PReNet and FEAWAD generally deliver fast prediction times, their performance can significantly slow down on certain datasets within ADBench (e.g., backdoor, celeba, census, donor, fraud), leading to higher overall inference times. This slowdown occurs because some components in these models rely on det-datapoint computations that do not support parallelization, resulting in substantial delays for datasets with a large number of records. The supervised FTTransformer, built on robust backbone architectures like ResNet and Transformer, achieves AUC-ROC scores that among the highest across all SOTA methods in baselines, nearly matching those of Swift Hydra. However, its performance declines significantly when applied to sparse datasets.
On the other hand, Swift Hydra offers a distinct advantage by generating unseen data to enhance test set coverage. Through its integration with the Mixture of Mamba Experts (MoME). Swift Hydra consistently outperforms other methods in both AUC-ROC and inference time, establishing itself as the most effective and efficient solution for tabular anomaly detection.
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C.2.2
BENCHMARKING AGAINST ADDITIONAL OVERSAMPLING METHODS ON ADBENCH
1.0
0.8
0.5
0.3
0.2
0.0
SMOTE
Borderine SMOTE
SVM SMOTE
ADASYN
CBO
Geometry
Oversampling
Switt Hydra
Figure 5: The average performance of various oversampling methods on the ADBench dataset. The evaluation metric is AUC-ROC
In addition the previously discussed experiments, we also compare the performance of Swift Hy- dra against other oversampling methods using the AUC-ROC metric. As shown in Figure 3 our method is capable of generating the most diverse set of anomalous data points. The goal of this experiment is to assess how accurately Swift Hydra (MoME) performs given these diverse gen- crated data points. Figure |5| presents a comparison of our method's performance against various oversampling techniques included in the ADBench baselines. The results clearly demonstrate that Swift Hydra outperforms all other methods, achieving the highest AUC-ROC on the test set, with a 40/60% train/test ratio. This performance is primarily due to Swift Hydra's ability to generate data points that extend beyond the boundaries of the training set.
Specifically, in the dataset illustrated in Figure 3 evident that the anomalous data points in the test set lie outside the boundaries of those in the training set. Traditional oversampling methods fail to generate data beyond these boundaries, which naturally results lower AUC-ROC on the test set. Deep bearning-based oversampling methods, such as VAE-Geometry and Oversampling GAN, can produce more diverse data than traditional techniques. However, Oversampling GAN often encounters model collapse issue, where it focuses on generating data points that deceive the detector very effectively, leading to an over-concentration of samples. On the other hand, VAE- Geometry relies the geometric structure of the data for generation, but if the structure is too complex, it struggles to produce sufficiently diverse data points. As result, both methods ultimately fall short of Swift Hydra in terms of AUC-ROC performance.
C.3 TOY EXAMPLE: GENERALIZATION ABILITY AND DECISION BOUNDARY ON 2D DATA
We conduct a toy example with 2D data to illustrate the generalization ability and decision boundary of the MoME module. First, we generate a dataset where the normal data follows a sine curve, while the anomalies randomly distributed around the sine curve. Then, Module to generate additional anomalous data and visualize the boundary of the MoME in Figure
the Self- Relf-Reinforing
From the visualization, as containing normal data) fully encapsulate the dark blue points (normal data). The blue regions (indicating areas predicted by MoME containing anomalous data) completely cover the generated anomalous points (green) and the test set anomalies (orange). An interesting observation is that the green points (generated anomalies) cause the decision boundary to tightly enclose the dark blue points (normal data). This enhances MoME's ability to accurately identify anomalous data in the test set, as these anomalies are positioned farther from the decision boundary. As expected, the model generalized well to the anomalies in the test set.
observe that the red regions (indicating
predicted by MoME
C.4 ABLATION STUDY
C.4.1 IMPACT OF SELF-REINFORCING MODULE ON PERFORMANCE ACROSS DEEP MODELS
We also compare the performance of Swift Hydra with various deep models (as backbone models) using two key metrics: AUC-ROC and Total Inference Time (for predicting the entire ADBench dataset) under two settings: with and without the use of oversampling technique (i.e., VAE-
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1.05
Normal Data Test Set
Anamalous: Data 'lest Sct
Geneer Anomalous Data
0.90
0.75
0.60
0.45
0.30
2-
0.00
Figure 6: Visualization of the decision boundaries of the Detector Mixture of Mamba Experts (MoME) after training generated anomalous data, original anomalous data, and normal data from the training set. The visualization highlights the resulting boundaries distinguishing anomalous and normal data in the test set.
Methods
Transformer
Mamba
Swift (raas(Transformerr)
Swift Hydra(Mamba)
AUCROC
TIF
AUCROC
TIF
AUCROC
TIF
AUCROC
TIF
Train/Test Ratio (40/60%)
0.78
5.18
0.80
3.54
0.90
7.96
0.93
4.01
Train/Test Ratio (30/70%)
0.75
6.07
0.77
3.62
0.88
8.79
0.91
4.79
Train/Test Ratio (20/80%)
0.72
7.10
0.73
4.11
0.86
9.91
0.90
5.22
Train/Test Ratio (10/90%)
0.69
8.22
0.71
4.63
0.82
10.36
0.87
5.84
TIF Total Inference Time (Seconds)
Table 5: Comparison of Vanilla Transformer and Vanilla Mamba with Transformer and Mamba enhanced by the Reinfoeenno Module in Swift Hydra, evaluated based on AUC-ROC and Total Inference Time (TIF).
Methods
Transformer (Yoe-Geomytry)
Mamba (VAE-Geometry)
Swift Hydrat Transforran
Swift HydracMambaa)
AUCROC
TIF
AUCROC
TIF
AUCROC
TIF
AUCROC
TIF
Train/Test Ratio (40660%)
0.83
5.23
0.85
3.40
0.90
7.96
0.93
4.01
Train/Test Ratio (30/709))
0.80
0.83
3.58
8.79
0.91
4.79
Truin/Test Ratio (20/80%)
0.78
7.02
0.81
4.02
0.86
9.91
0.90
5.22
Train/Test (10500))
4.65
TIP Total Inference Time (Seconds)
Table 6: AUC-ROC performance of various backbone models when applying oversampling tech- niques
Geometry). It is important to note that VAE-Geone Geometyy is chosen as the oversampling method for other backbone models due its best performance among the oversampling baselines. As shown in Table Table 6 Swift Hydra outperforms other methods in terms of AUC-ROC while main- taining competitive total inference time.
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AUC-ROC Evaluation. Regarding the accuracy in Table standalone Mamba or Transformer models on ADBench exhibit significantly lower AUC-ROC compared to Swift Hydra (Mamba) and Swift Hydra (Transformer), which leverage the ReiffoRenn Module. This is primarily because these models do not utilize any oversampling techniques (RI.-guiled GenAI), which limits their data generalization capabilities. However, even when employing powerful oversampling technique like VAE-Geometry (Table 6). the AUC-ROC of these models still falls short of that achieved by Swift not diverse or
Hydra. This is due to the fact that the datapoints generated by VAE-Geometry of as high quality as those generated by Swift Hydra, as discussed in the previous experiment.
Total Inference Time Evaluation. terms of total inference time, it is important to note that the Mamba model has a prediction complexity of O(1), while the Transformer has prediction com- plexity of O(N). This makes Mamba substantially faster than both Transformer and Fully Connected networks. When Mamba is integrated into Swift Hydra with a Top A Mixture of Experts (k 2), one might expect the prediction time of Swift Hydra to be nearly double that of the regular Mamba model. However, the interesting outcome here is that we only two-layer depth for Mamba and overspecify the number of experts to 20. This allows us to capture the data complexity effee- tively, and since the model has just two layers, the additional time difference with k = 2 is minimal compared to a larger Mamba model.
C.4.2 IMPACT OF PROBABILISTIC CLUSTER ASSIGNMENT ON MOME PERFORMANCE
Method
Hydra (MoME-Tradilional Training Approach)
Hydra (MoME-Our Training Approach)
AUCROC
TIF
AUCROC
TIF
Train/Test Ratio (40160%)
0.892
4.055
0.934
4,02
Train/Testt Ratio (30/20%)
0.861
4.771
0,913
4.793
Train/Test Ratio (209005)
0,853
5.234
0.902
5.221
Train/ (10/90%))
5,813
Table 7: Comparison of AUC-ROC and Total Inference Time (TIF) between Swift Hydra using the traditional MoME training approach and Swift Hydra with the proposed probabilistic training approach across different train/test ratios.
The results in Table 7 highlight highlight clear advantage of Swift Hydra with the proposed probabilistic training approach for MoME over the traditional MoME training approach. The primary reason for this improvement lies in addressing the "winner-take-all" problem that commonly affects the traditional training method.
In the traditional MoME approach, the gating network immediately starts assigning samples to perts based on their performance scores. During the early training steps, when the experts have not yet converged, their performance scores are arbitrary. This randomness can lead to one expert re- ceiving disproportionately more samples than others, simply due to chance. As result, this expert improves faster and continues to dominate sample assignments, creating feedback loop where becomes the sole contributor to predictions. This phenomenon, known as "winner-take-all!" reduces the diversity of the expert ensemble and significantly hinders the generalization ability of the model.
In contrast, Swift Hydra with the probabilistic training approach temporarily deactivates the gating network during the early training phase. Instead, it uses a probabilistic assignment mechanism (as described in Equation 6) to ensure that all experts receive equal opportunities to learn. Once the experts have sufficiently converged, the gating network is reactivated to assign samples based on their performance. This method prevents any single expert from monopolizing the training process early on and ensures a more balanced and effective ensemble.
The results in the table demonstrate that this improved training strategy consistently achieves higher AUC-ROC scores across all train/test ratios compared to the traditional approach, without incurring additional Total Inference Time (TIF). This validates the effectiveness of addressing the "winner- take-all" problem to enhance both the generalization and overall performance of the model.
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0.92
0.90
AUC-ROC
0.88
0.86
0.40
0.45
0.50
0.55
0.60
0.65
0.70
weight
Figure 7: The average performance of various oversampling methods on the ADBench dataset. The evaluation metric AUC-ROC
C.4.3 KI. DIVERGENCE AND RECONSTRUCTION Loss TRADE-OFF IN CONDITIONAL. VARIATIONAL. AUTO ENCODER
In this section, we provide insights into how the weight impacts the C-VAE during data generation. Specifically, when optimizing the ELBO loss of C-VAE, need consider components: the Reconstruction Loss and the KI. Loss. more weight is placed on the Reconstruction Loss, the C- VAE will generate data more cautiously, closely adhering to the target class. However, this caution results in less diverse samples. Conversely, if the weight is placed more on the KL Loss, the C-VAE generates more diverse data, but may also produce samples that overlap with other classes.
To identify the optimal weight for the KL Loss, we experimented with various values of ranging from 0.4 to 0.7. If the weight for the KL Loss is p. the weight for the Reconstruction Loss will be - As shown in Figure 7 the optimal weight for the KI. Loss is found to be 0.55. In the range of 0.4 0.5, the C- generates overly cautious samples, resulting in a lack of diversity. Consequently, the 200 episodes of RL training are insufficient to cover the entire set of anomalous data in the test set. On the other hand, the range 0.6 to 0.7, the model focuses too much on optimizing the KL Loss, leading to the generation of highly diverse anomalous samples. However, these samples tend to overlap significantly with normal samples, causing Swift Hydra's 's performance to decline after 200 episodes.
C.5 RL-AGENT ASSISTANCE FREQUENCY EXPERIMENT
In this section, we illustrate the average percentage of invalid actions taken by the agent in each episode (averaged over 57 datasets from ADBench). From Figure it is evident that in the initial stages, the RL-Agent generates high number of invalid actions, frequently requiring assistance from the One-Step to Feasible Action algorithm described in Section 3.1.2] However, since every time the RL-Agent takes invalid action, it learns in supervised manner using the feasible action provided by the One-Step to Feasible Action algorithm, significant reduction invalid actions is observed after about 25 to 50 episodes.
As a result, the training time becomes considerably faster since fewer Gradient Descent steps are needed (as Gradient Descent is primarily performed to optimize the reward function whenever an invalid action is taken). From episode 150 onward, the RL-Agent rarely makes invalid actions, and its actions become highly effective (as reflected in the AUC-ROC in previous experiment), indicating that the RL-Agent has successfully generalized.
C.6 DATASETS IN ADBENCHI
ADBench features comprehensive collection of 57 datasets designed for anomaly detection search, as detailed in the table. Among these, 47 datasets are well-established and widely used across various real-world domains, such healthcare (e.g., disease diagnosis), audio and language
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0.8
0.6
Percentage
Episode
Figure 8: Percentage of invalid actions provided by the RL-Agent in each episode, with each episode consisting of 500 timesteps. The measurement is conducted over total of 200 episodes. The axis represents the episodes, and the Y-axis shows the percentage of invalid actions provided by the RL-Agent.
processing (e-g- speech recognition), image analysis (e.g., object identification), and finance (e.g., fraud detection). Additionally, ADBench introduces 10 more complex datasets from computer vi- sion (CV) and natural language processing (NLP) domains, enriched with larger sample sizes and higher-dimensional features. These datasets utilize pretrained models extract embeddings, en- abling the representation more complex patterns. All datasets are provided a frienfriendly format compressed NumPy array files ('.npz),, with detailed instructions and processing codes available for seamless application
Number
Data
# Samples
# Features
# Anomaly
% Anomaly
Category
ALOI
49534
1508
3.04
Image
2
annthyroid
7200
6
534
7.42
Healthcare
3
backdoor
95329
196
2329
2.44
Network
4
breastw
683
9
239
34.99
Healthcare
5
campaign
41188
62
4640
11.27
Finance
6
cardio
1831
21
176
9.61
Healthcare
7
Cardiotocography
2114
466
22.04
Healthcare
8
celeba
202599
39
4547
2.24
Image
9
census
299285
500
18568
6.20
Sociology
10
cover
286048
10
2747
0.96
Botany
11
donors
619326
10
36710
5.93
Sociology
12
fault
1941
673
34.67
Physical
13
fraud
284807
29
492
0.17
Finance
14
glass
214
9
4.21
Forensic
15
Hepatitis
80
19
13
16.25
Hcalthcare
16
http
567498
2211
0.39
Web
17
InternetAds
1966
1555
368
18.72
Image
18
Ionosphere
351
32
126
35.90
Oryctognosy
19
landsat
6435
36
1333
20.71
Astronautics
20
letter
1600
32
100
6,25
Image
21
Lymphography
148
18
6
4.05
Healthcare
22
magic.
19020
10
6688
35.16
Physical
23
mammography
11183
6
260
2.32
Healthcare
24
mnist
7603
100
700
9,21
Image
25
musk
3062
166
97
3.17
Chemistry
26
optdigits
5216
64
150
2.88
Image
27
PageBlocks
5393
10
510
9.46
Document
28
pendigits
6870
16
156
2.27
Image
29
Pima
768
8
268
34.90
Healthcare
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30
satellite
6435
36
2036
31.64
Astronautics
31
satimage-2
5803
36
71
1.22
Astronautics
32
shuttle
49097
9
3511
7.15
Astronautics
33
skin
245057
3
50859
20.75
Image
34
smip
95156
3
30
0.03
Web
35
SpamBase
4207
57
1679
39.91
Document
36
speech
3686
400
61
1.65
Linguisties
37
Stamps
340
31
9.12
Document
38
thyroid
3772
6
93
2.47
Hcalthcare
39
vertebral
240
30
12.50
Biology
40
vowels
1456
12
50
3.43
Linguistics
41
Waveform
3443
100
2.90
Physics
42
WBC
223
9
10
4.48
Healthcare
43
WDBC
367
30
10
2.72
Healthcare
44
Wilt
4819
5
257
5.33
Botany
45
wine
129
13
10
7.75
Chemistry
46
WPBC
198
33
47
23.74
Healthcare
47
yeast
1484
8
507
34.16
Biology
48
CIFARIO
5263
512
263
5.00
Image
49
FashionMNIST
6315
512
315
5,00
Image
50
MNIST-C
10000
512
500
5.00
Image
51
MVTec-AD
5354
512
1258
23.50
Image
52
SVHN
5208
512
260
5.00
Image
53
Agnews
10000
768
500
5.00
NLP
54
Amazon
10000
768
500
5.00
NLP
55
Imdb
10000
768
500
5.00
NLP
56
Yelp
10000
768
500
5.00
NLP
57
20newsgroups 11905
768
591
4.96
NLP
Table 8: Summary of Datasets used in ADBench Benchmark. The table outlines key characteristies 57 anomaly detection datasets, including the number of samples, features, anomalies, and their respective categories, spanning diverse domains such image analysis, healthcare, finance, and natural language processing.
C.7 SWIFT HYDRA: CLASS- WISE PRECISION, RECALL, AND FI-SCORE ON ADBENCH
This final section provides a comprehensive comparison of various state-of-the-art anomaly detec- tion methods, including DTE, Rejex, and ADGym, against Swift Hydra across 57 datasets from ADBench. The evaluation criteria include Precision, Recall, Fl score, support for each class, and AUC-ROC. It is important note that did not instead, we applied common threshold across all 57 datasets in ADBench. As result, the Pre- cision might not be very high. However, the focus should also be on the Recall and AUC-ROC, as these metrics more accurately reflect the model's 's ability to detect anomalous data if the correct threshold chosen. This approach gives a clearer picture of how well Swift Hydra can identify anomalies in various datasets.
unique threshold for each individual dataset;
DTE
Rejex
ADGym
Swift Hydra
ALOI
R
F1
P
R
F1
F1
P
R
F1
support
-1
[0.9]| 0.97
00.9|
0.95|0.960.99
0.38|0.54 (099
0.44 0.61
28821
0..0]
0.03
0.03|00.0
0.07|0.05 0.000
0.75j0.05|0.0
0.81 0.81|0.08
900
accuracy
0.94
0.92
0.39
0.45
29721
macro avg
0.50 0.50 00.50
0.50
0.50
0.51
0.50
0.5000.46
0.57 0.30
0.52
0.63
0..35
29721
weighted avg
0.94 0.94 (0.44
00.94
(0.94
0.92
(0.99
0.39 0.39
0.53
(0.96
0.45
0.660
29721
AUC-ROC
0.535
0.53
0.66
0.70
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Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
annthyroid
R
F1
P
R
F1
F1
P
R
F1
support
0.94| 0.95
0.95
00.98
0.94
0.96
0.95
0.88
0.92
1.00
0.95|0.9]
4001
0.32|
0.29
|0.31
[0.52
0.92|0.71
0060
0.98/0.73
319
accuracy
0.90
0.93
0.89
0.95
4320
macro avg
0.63] 0.62 00.6
0.75
0.86
0.79
0.75
0.90
0.800
0.96]
4320
weighted avg
0.90 0.90 0.900
0.95
0.93 0.92 0.89 0.89
0.91 [0.97 0.95
0.96
4320
AUC-ROC
0.81
0.96
0.93
0.98
backdoor
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.98|
0.98
[0.8
0.99 0.99
0.99
0.94
0.95|0.96]
1.00 0.99
0.99|
55790
10.01
0.01
|0.01
(0.68
0.566
0.89
[0.6 0.92 0.74|
1408
accuracy
0.95
0.98
0.95
0.98
57198
macro avg
0.49|
0.49
0..9
0.88
0.73
0.77
0.75
0.92
0.82
0.81
57198
weighted avg
0.95
0.95
0.95|0.99
0.95
0.99
0.98
0.98
0.93
0.95
0.95
0.95
(0.99
0.98
0.99|
57198
AUC-ROC
0.76
0.90
0.94
0.98
breastw
P
R
F1
P
R
FI
P
R
F1
P
R
F1
support
0.99| 0.94
|0.97|
00
0.69/0.82|000
0.93
0.94
0.99
0.97
0.99|
264
0.91
0.99
0..44
1.00
0.88 0.92 00.4 0.98
146
accuracy
0.96
0.80
0.97
410
macro avg
0.95| 0.97 [0.96]0.82
0.850.801100
0.92
0.92
0.97
0.97|0.97|
410
weighted avg
0.96 0.96 0.96|0.87
0.80 00.93
0.93
0..7
0.97|
410
AUC-ROC
0.99
0.93
0.94
0.99
campaign
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.91
0.91
0.91
0.89
0.99|0.94.0.2
0.79
0.98
0.82
0.89
21920
0.32
0.32
0.32
0.277
0.04
0.33
0.79
00.38
0.83
0.552
2793
accuracy
0.84
0.88
0.79
0.83
24713
macro avg
[0.62] 0.62
0..220..58
0.51
0.51
|0.63
0.79
0.66
00.68
0.83|0.77
0.77|
24713
weighted avg
0085|
0.84
00.5
0.82
0.88
0.84
0.86
0.79|0.81
(0.1
0.83
0.85|
24713
AUC-ROC
0.73
0.77
0.84
0.90
cardio
R
F1
P
R
F1
R
F1
P
R
F1
support
0.94 0.92
0.93
0.94
0.82
0.87
0.95
0.88
0.93
0.99
0.94
0.97
990
00.42|
0.50
0..45
0.51
(.557
0.89
0.89
0.64
0.95 0.76]
109
accuracy
0.88
0.79
0.88
0.94
1099
macro avg
00.68]
0.71 0.69/0.559
0.66
0.60
0.76
0.88
0..3
0082
0.94 0.866
1099
weighted avg
00.99 0.88 0..99
00.87
0.79 0.82
0.91
0.88
0.91
|0.6
0.94
1099
AUC-ROC
0.92
0.74
0.95
0.98
Cardiotocography
P
R
F1
F1
P
R
support
0.82
0.83
0.82
0.88
00
0.750..880..2
0.83 0.83|0.90 0.900...00... 0.998
0.90
991
0.37|
0.36
0.36|0.27
0.33
0.30
0.87|0.74
0.71
0.92
278
accuracy
0.72
0.66
0.84
0.90
1269
macro avg
[0.59| 0.59 0..5|/0.5
0.54
00.54
10.80
0.85
0..2
00.8
0.91
1269
weighted avg
0.72 0.72 0.72
0.668
0.66
0.67
0.877
0.87
0.84
0092
0.90|
1269
35

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Published as a conference paper at ICLR 2025
Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
AUC-ROC
0.73
0.53
0.91
0.95
celeba
R
F1
P
R
F1
R
F1
P
R
F1
support
-1
0.98]
0.98
[0.98
1.00 0.96
0.83
0.88
1.00
0.89/0.94|
118850
[0.09|
0.09 (0.09/0.03
0.00|0.00|0.0 11 0.85|0.25
00115
(.26))
2710
accuracy
0.96
0.98
0.83
0.89
121560
macro avg
0.53
0.53 0..3
0.50
0.50
0.53
0.84 0.55
0058
0.60
121560
weighted avg
0.96
0.96
0.96
0.96
0.98
0.99
0
0.83
(0.98
0.89
121560
AUC-ROC
0.72
0.79
0.88
0.95
census
P
R
F1
P
R
F1
P
R
F1
P
R
F1
|support
[..4|
0.94
0..94
0.88
0.91
(.92
0.72|0.84|0..
0.79|0.88|
168432
0..4]
0.04
00.04|0.06
0.12
0.15
0.77|0.31
(0.21 0.34|
11139
accuracy
0.88
0.84
0.73
0.79
179571
macro avg
00.49| 0.49
0..9
0.50
0.50
0.50
0.50
0.54
0.75
0.58
0.60
0.82
0.61
179571
weighted avg
0.88
0.88
0.88
0.888
0.84
0.86
0.73 0.87
0.88
(0.94
0.79
0.84
179571
AUC-ROC
0.59
0.65
0.79
0.85
cover
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.99| 0.99
0.99
99999999/0.90
0.96|0.94
10441.00
1.00 0.99|
1.00]
169976
00.09|
0.09 00.09 0.06
0.05 0.550
0.95
(0.54
1.00
0.700
1653
accuracy
0.98
0.98
0.96
0.99
171629
avg
00.4|| 0.54 0..54
0.52
0.96
0.96/0.80
0.80
0077
0.99/0.85
171629
weighted avg
00.8|
0.98 00.98
0.99
0.98
0.98
0.95
0.96 0.94
1 1.00 0.99 0.99|
0.99|
171629
AUC-ROC
0.90
0.74
0.97
1.00
donors
R
F1
P
R
F1
R
F1
P
R
F1
support
0.94
0.94
0..94
0.94
0.96
0.99
0.95
0.94
1.00
1.00]
1.00
349483
00.10
0.10
0.10
0.03
0.99
0.95
1.00
1.00
1.00
22113
accuracy
0.89
0.93
0.95
1.00
371596
macro avg
00.2
0.52
0.52
0..54
0.51
0.51
0.94
0.95
0.94|
1.00
1.00
1.00
371596
weighted avg
00899
0.89
|9.89
0.93
0.91
|0.93
0.95
1.00
1.00
1.00
371596
AUC-ROC
0.76
0.74
0.95
1.00
fault
R
P
R
P
R
support
0.69|
0.66
0.68
0.668
0.89
0.
0.78
0.62
0.69
0081
0.65
0.722
751
00.43
0.45
0.53
0.23
0.32
0..49
0.68
00.5
0.73)0.62]
414
accuracy
0.59
0.65
0.64
0.68
1165
macro avg
00.66|
0.56 0..66
0.56/..54
0.66
0.65
0.63
|0.67
0.69|0.67
1165
weighted avg
00660
0.59
0.59
(..6
0.65
0.61
[0.67
0.64
0.65
|0.71
0.68 0.699
1165
AUC-ROC
0.54
0.58
0.74
fraud
F1
P
R
FI
P
R
|suppor
1.00]
1.00
|110/10100000000
0.99)
1.0
0.86
|.00 1.00
0.92|0.96
170593
00.30|
0.28
(0.29
03
0.81
|0.22 0.00
0.85|0.00
0.02
0.92
292
accuracy
1.00
0.99
0.86
0.92
170885
macro avg
0.65|
0.64 0.6550..56
0.90 0.61 jo.48 0.85|0.45
170885
36

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Published as a conference paper at ICLR 2025
Table continued from previous page
|TTE
Rejex
ADGym
Swift Hydra
weighted avg
|.00|]
1.00
1..0|
1.00
0.99 0.99 0.96 0.86 0.86 0.91 1.00 0.92 170885
AUC-ROC
0.95
0.95
0.92
0.96
glass
P
R
F1
P
R
F1
P
R
F1
P
R
F1
support
[0.95|
0.98
(0.6|00.00
0.00|0.00|0.93
0.75|0.83 (0.9
0.81 [0.88]
123
0.00]
0.00 |0.00|0.05| 1.00|0.09|0.00 j..04
0.27|0.09|0..
0.33/0.13)
accuracy
0.93
0.05
0.79
129
macro avg
00:48] 0.49 (0.48)0.02
0.50|0.04||0
0.51 00.46
(0.52
0.57
0.51
129
weighted avg
0.91|
0.93 0.92|0.00
0.05|0.00|0. 0.88
0.73/0.801
00.9
0.79 0.85
129
AUC-ROC
0.76
0.75
0.78
0.84
Hepatitis
R
F1
P
R
F1
R
F1
P
R
F1
support
0.85| 0.83
00.84
0.00|0.00|0.90
0.62
00.7
0.67
0.79
42
0.00]
0.00 0..00
1.00 0.22 0.79 0.79 0.33 0.26 0.83/0.40
accuracy
0.73
0.13
0.64
0.69
0.69
macro avg
00.43|
0.42
0..4
0.50
1
0.56
0.71
0.54
00.61
0.75
0.75|0.59
0.59
48
weighted avg
0.75|
0.73 0..4|
0.13
0.81
0.64
0.88
0.69 0.74|
48
AUC-ROC
0.72
0.42
0.74
0.80
http
R
F1
P
R
F1
R
F1
P
R
F1
support
1.00]
1.00
1.00|
1.00
0.94
0.97
0.95
0.96
0.94
1.00
1.00
1.00
339161
[0.23]
0.02
0.00|0.06
10000.12
0.95
(076
0.00]0.86|
1338
accuracy
1.00
0.94
0.96
1.00
340499
macro avg
0.61
0.51
00.51
|0.53
0.97
0..5/
0.54
00844
0.96/0.87
00.88
0.90]
340499
weighted avg
00.99|
1.00
0.999|
1
1.00
0.94
0..9
(.99
0.96|0.94
| 1.00
1.00
1.00
340499
AUC-ROC
1.00
1.00
0.94
1.00
InternetAds
P
P
R
support
0.88
0.88
0.88
0.89
0.44
0.59
0.93
0.63
0.64
0.998
0.68
0.81
965
00.45|
0.46
0..660.223
0.75
0.75
10.37
0.88|0.53
0..4
|0.40
0.94|0.50
215
accuracy
0.80
0.50
0.67
0.73
1180
macro
00.67| 0.67
00.67
00.56
0.60)0.47
0.65
0.75
6.63
(0.69
0.81 [0.68]
1180
weighted avg
0.80 0.80 00800
0.
0.50 0.88
0.67|0.701
0.888
0.73/0.76|
1180
AUC-ROC
0.68
0.67
0.88
0.92
Tonosphere
R
F1
P
R
FI
F1
P
R
F1
support
0.82| 0.76
0.79
0.000
0.00
0.85 0.86
0.90
0.90)
135
00.2]
0.70
00.6500.36 1.00j0.53
0.78|0.76|0.
0.82
76
accuracy
0.74
0.36
0.82
0.87
211
macro avg
00.22 0.73
0.72
0..
0.50)
0.27
0.81
0.81 0.81|0.80
0.80
0.86
0.86 0.86
211
weighted avg
00.44
0.74
00.74
13
0.36
09
0.82
0.82(0.8)
[0.87
0.87
0.87|
AUC-ROC
0.86
0.96
0.85
0.91
landsat
R
F1
P
R
F1
R
F1
P
R
Fl
support
0.81| 0.79
10.80
0.80
0.94
0.86
0.92
0.80
0.86
(0.97 0.86
0.86)0.91|
3068
[0.24| 0.26 00.25|0.23
0.06 0. 10
0.83 0.68
(0.62 0.89)
793
accuracy
0.68
0.76
0.80
0.87
3861
37

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Published as a conference paper at ICLR 2025
Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
macro avg
[0.52] 0.52
0.52 0.51
0.50
0.50
0.48
0. 74 0.81 0.77 0.79 0.87 0.82
3861
weighted avg
0.69|
0.68 0.68
0.68|0.68
(0.68
0.76
0.71 0.885
0.80
0.90
0.87 0.87 0.87|
3861
AUC-ROC
0.50
0.53
0.91
0.94
letter
P
R
F1
P
R
F1
R
F1
P
R
F1
support
0.94|
0.94
[0.94
0.65
0.79
0.76
0.98
0.82
0.89
900
00.09|
0.10 0.10 0.83 0.83
(0.
0.63
(..0 0.68 0.68|0.31
accuracy
0.88
0.66
0.75
0.81
960
macro avg
0..52|
0.52 0.52
0.56
0.74
0.51
0.55
0.55
0.559
0.75 0.75|0.60]
0.600
960
weighted avg
0.89|
0.88
00.9 0..3
0.66
0. 0.89
0.75|0.80
0.93 0.81 J0.85
960
AUC-ROC
0.57
0.85
0.77
0.80
Lymphography
R
F1
P
R
F1
R
F1
P
R
F1
support
1.00|
0.95
0..8
(..00
0.00
0.90
0.94
0.92
0.95
0.99
0.97
84
00.66
1.00
0.71
[006
1.00
0..47
0.17
0.17 0..0
0.20]
accuracy
0.96
0.06
0.90
0.94
89
macro
00.78|
0.98
00.5|
0.50)0.05
0.68
0.56
0.58
(0733
0.59
0.63]
89
weighted avg
0..98]
0.96 0.96 0.000
0.06
0.011
10.88
0.90
0.89
0.93
0.94
0.933
89
AUC-ROC
0.99
0.99
0.64
0.69
magic.gamma
P
R
F1
P
R
F1
support
0.75| 0.75
00.5||0.2
0.95]0.82
0.69|0.76|0.93
0.82]
7422
0.54|
0.55 0.54|00.75
0.31|0.44)0.60
0.86/0.71|0.65
0.90)
3990
accuracy
0.68
0.72
0.75
0.79
11412
macro
00.65|
0.65 00.55
0.774
0.63
(0.6
(0773
0.77
0.
(0.79
11412
weighted avg
0068|
0.68 0.68
(0.73
0.72 0.69
0.77
0.75
0.83
0.79)0.80)
11412
AUC-ROC
0.73
0.76
0.88
0.92
mammography
F1
P
R
FI
F1
P
R
F1
support
0.98|
0.98
0.98
0.98]0.99
0.83
o. 0.90000000000
0.99
0.80
1.00
0.87]0.93
0.87
6558
0.26 0.25|
0..5
0.62
0.2]0.14 0.00
0.83
0. 0.88 0.23]
152
accuracy
0.97
0.82
0.80
0.87
6710
macro avg
0.62| 0.62
0..2
0.55
0.53
0.72|
0.52
0.50
0.52
0056
0.87
0.58
6710
weighted avg
0.97
0.97 00.97
0.82
0.88
0.91
0.80
0.88
(0.98
0.87
0.91
6710
AUC-ROC
0.86
0.84
0.86
0.91
mnist
R
F1
P
R
FI
R
F1
P
R
F1
support
-1
0.93
0.93
0.93|00.94
0.97
0.95
0.94 0.89
0.91
1.00
0.94
0.97
4172
00.29|
0.30
0..9
00.46
0.28
0..5
0.55
0..0/0
0.60
0.97|
390
accuracy
0.88
0.91
0.90
0.94
4562
macro avg
0.61
0.61 [0.61
(0.70
0.62
0.65
0.76
0.90
0.80
0.95
0.85
4562
weighted avg
0.88
0.88
0088
0..8 |0.89
0.91 0.91
0.90/0.89 (0.9
0.95|
4562
AUC-ROC
0.77
0.79
0.92
0.98
musk
P
R
F1
P
R
F1
R
F1
P
R
F1
|support
1.00|
1.00
1.0000.98
1.00)0.99|0.98
0.93
1.00
1.00 1.00]
1777
0.95]
1.00
00.98 10.72
0.34
0.47| 0.94|0.96|1.0
1.00 1.00]
61
38

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Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
accuracy
1.00
0.97
0.93
1.00
1838
macro avg
0.98] 1.00
0.9990.85
0.67 0.73 0.73
0.95
0.94 0.94|0.95
0.95
1.00
1.00| 1.00]
1838
weighted avg
|1000]
1.00 1.00|0.97
0.970.97/0 0.99
0.93|0.95|
1.00
1.00|
1.00]
1838
AUC-ROC
1.00
0.96
0.94
1.00
optdigits
F1
P
R
F1
F1
P
R
F1
support
0.97| 0.96
0..7
0.97
0.88
0.94
0.91
0.92
1.00
0.97
0.98|
3044
00.1
0.01
00.01
|..00
0.0000.00
0.97
0.97
00.45
1.00
86
accuracy
0.94
0.86
0.91
0.97
3130
macro avg
[0.49| 0.49
|0.49
00
0.45
0..46
0.
66 0.94
0.75
0.72
0.98
0.80
3130
weighted avg
|0.55|
0.94
0..44
0..94
1.86)0.90/0.99
0.91 0.91
(0.9
0.97
0.97|
3130
AUC-ROC
0.71
0.36
0.97
1.00
PageBlocks
P
F1
P
R
support
0.94| 0.94
0.94
0.94
0.97
0.95
0.960.96
0.86 0.86)..89
1.00
0.92
0.95|
2916
0..4]
0.45
0.44
0.69|0.64)0.49
0.90|0.66 (0.56 0.96 0.96)..71
320
accuracy
0.89
0.92
0.86
0.92
3236
macro avg
[0.69] 0.69
00.69/0.78
0.82
0.80
72
0.88/0.78
0.78
0.94 0..3)
3236
weighted avg
0.89|
0.89 00.99
0.93
0.92 0.93
0.90
0.86
0.95 0.92 0.93]
3236
AUC-ROC
0.92
0.95
0.92
0.98
pendigits
R
F1
P
R
F1
F1
P
R
F1
support
0.98| 0.98 0.98]0.99
0.82|0.89 0.95
0.93/0.94| 1.00
0.98)0.99
4032
[0.26] 0.26 [0.66/0.07
12 0.94|0.68 (0.56 0.99)
90
accuracy
0.97
0.81
0.93
0.98
4122
macro avg
00.6] 0.62 0.62
0055
0.51
0.72
0.93
0.81
0078
0.99
0.85
4122
weighted avg
0.97
0.97
0.97
0.97
0.81
0.88
0.94
0.93
00.99
0.98
0.99
4122
AUC-ROC
0.93
0.83
0.95
1.00
Pima
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.73|
0.66
|0.69
0.00j0.00|0.74
0.69
0.78
0.64
0.70|
294
00.48]
0.56 0..2|00.36 1.00 00.48
0.60|0.54 (0.52
0.67 0.67|0.58
167
accuracy
0.62
0.36
0.60
0.65
461
macro avg
00660|
0.61 [0.60
0.18
0.50
0.27
0.66
0.60
0.60
0.65
0.66
0.64
weighted avg
0.644
0.62 0.63
03
0.36
0.
0.666
0.65
0.60|0.65
(0.68
0.65
0.66)
461
AUC-ROC
0.66
0.57
0.66
0.70
satellite
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.81
0.79
0..00
0.700000
(.88)0.2|00.0
00.1
0.84|0.86
0.96 0.88)0.92
2626
0.58|
0.62
0.60 0.75
0.11
0.20
0.74
0.89)0.80)
0.79
0.92)..85)
1235
accuracy
0.74
0.70
0.89
3861
macro avg
00.70| 0.70
0.72
0.55
0.51 0.55|
00.82
0.87
0.83
00.87
0.88
3861
weighted avg
00.74|
0.74 0.74
0.74 00.72
0.70 0.62
0.85
0.86
0.86
0.84
(0.90
0.89
0.900
3861
AUC-ROC
0.70 P
0.73
0.89
0.96
satimage-2
R
F1
P
R
F1
R
F1
P
R
F1
|support
1.00]
1.00
|.00]
1.00]1000
1.00
0.93
0.93]0.96|1.0
1.00
0.98]0.99
3440
39

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Published as a conference paper at ICLR 2025
Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
[0.80]
0.83
0.81 0.11 0.86 0. 0.30 0.86 0.86 0.36
0.91 0.91
42
accuracy
1.00
0.93
0.93
0.98
3482
macro
0.900
0.92
0.91
[0.56
00.63
0.63
0.89
0.71
[0.68
0.94/0.75,
3482
weighted avg
1.00]
1.00
1.00
0.
0.93
0.95
0.96
0.93
0.95
00.9
0.98 0.98
3482
AUC-ROC
0.99
0.97
0.94
0.99
shuttle
F1
P
R
F1
P
support
0.99|
1.00
1.00|0.94
1.00
0.96]0.94|
1.00
1.00|1.00)
1.00|
27388
0.95|
0.92
0.93|
0.09
0.93 0.95
1.00|0.98|
2071
accuracy
0.99
0.93
0.96
1.00
29459
macro avg
[0.97]
0.96 0.96
0.
0.54
0.56
0.94
0.93
0.98
0.99
29459
weighted avg
0.99|
0.99 0..99
(0.91
0.93 0.930 (0.9
0.96|0.94]
1.00
1.00
1.00
29459
AUC-ROC
1.00
0.99
0.95
1.00
skin
R
F1
P
R
F1
F1
P
R
F1
support
0.76 0.76
0.76
0.79
0.79
0.94
0.94 0.94
1.00
1.00]
1.00
116448
00.09|
0.09
0..0 0.18
1.8/..18/001 1 0.94|0.96|
1.00
1.00]1.00)
30587
accuracy
0.62
0.66
0.94
1.00
147035
macro avg
00.4]|
0.43
0..2
0.
0.49|
0.49
0.95
0.94
0.95
1
1.00
1.00|1..000
1.00
147035
weighted avg
0.62
0.62 00.62
66.6
0.66
0.66
0.94
0.94
0.94
1.00
1.00
1.00
147035
AUC-ROC
0.68
0.74
0.94
1.00
smtp
P
R
F1
P
R
F1
R
F1
P
R
F1
support
-1
|1.00] 1.00
1.00
1.00
0.68
0.81
(0.95
0.85|0.91
I 1.00
0.90]0.95
57075
[0.00]
0.00
1..00
1.00j0.00j0.00
0.81 0..00
0.84|0.01|
19
accuracy
1.00
0.68
0.85
0.90
57094
macro avg
0.50|
0.50
0.50
0.50
0.50
0.84
0.41
00.48
0.83
0..5
0.50
0.87
0.48)
0.44
57094
weighted avg
1.00]
1.00
1.00
1.00
0.68
0.81
0.95
0.85
0.85
0.91
1.00 0.95
57094
AUC-ROC
0.92
0.95
0.81
0.85
SpamBase
P
R
F1
P
R
F1
R
F1
P
R
F1
support
0.65|
0.67
0.66/0.55
0.64|0.61
(0.92
0.81
0.86
0.96 0.86
0.91
1513
0.49|
0.47
00.48
00.37
0.32
0.32)0.34/00 0.34 00777 0.89|0.84|| 0.9]0..4|0.88
(0.82 0.95|0.88
1012
accuracy
0.59
0.51
0.89
2525
macro avg
00.57|
0.57
00.77
0..48
0.48
0.48
0.84
0.85
0.85
0.85
00.99
0.90
0.89
2525
weighted avg
0.59
0.59
0.59|0.50
0.59
0.51
0.500
0.86
0.84
0.85
|0.90 0.89
0.89
2525
AUC-ROC
0.61
0.51
0.92
0.95
speech
P
R
F1
P
R
FI
P
R
F1
P
R
F1
support
0.98]
0.99
0..99 09
o. 0.13 J..93
0.49|0.67
1.00
0.70
2177
0..00|
0.00 00.00|0.02
0.91 |0.0
0.83
(0.03
0.89 0.89)
accuracy
0.97
0.15
0.49
0.54
2212
macro avg
00.49|
0.49
00.49
0.50
0.5
0.52
0.13
00.47
0.66
0.34
0.34
(0.51 0.71
0.71|0.38
2212
weighted avg
0.97
0.97
00.97
0.97
0.25
0.92
0.49
(0.98
0.54
0.69|
0.69
2212
AUC-ROC
0.47
0.47
0.67
0.73
Stamps
R
F1
R
R
R
F1
support
40

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Published as a conference paper at ICLR 2025
Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
[0.97] 0.90 0.93 (.000 0.00
0.79 0.87 0.87|
1.00 0.86
0.9]]
185
00.41|
0.68 (0.1
0..1
1.00
0.39
0.94 0.54
0.44
1.09|
19
accuracy
0.88
0.09
0.81
0.87
204
macro avg
0.69 0.79
0.72
0.50
0.770.700000
0.71
0.93/0.76
204
weighted avg
0.91
0.88 0.88
(0.990.001
0.09|0.02 0.91
00.44
(0995
0.87|0.89|
204
AUC-ROC
0.89
0.74
0.96
thyroid
F1
P
R
F1
P
R
F1
support
0.99| 0.99 0.99|1.00
0.88
0.93 0.88/0.94
1.00
0.97
0.99|
2207
[0.63|
0.65
[0.64|0.18 093/0.30/0.44
0.97/0.60 (0.49
1.00|0.66]
57
accuracy
0.98
0.88
0.93
0.97
2264
macro avg
0.81 0.82 [0.81
(0.59
0..99
0.95
0.76
0075
0.99
0.82
2264
weighted avg
0.98 0.98 0..8 (0.98
0.88
0.92
0.94
0.93
(0.99
0.97
0.98|
2264
AUC-ROC
0.98
0.99
0.94
1.00
vertebral
R
F1
P
R
FI
R
F1
P
R
F1
support
0.85| 0.86
10.86|0.00
0.00|0.00|0.90
0.73
(093
0.77|0.84|
0.77
123
00.11
0.10 0.10 (..00.6600.29
0.63|0.40 0.33
0.44
21
accuracy
0.75
0.15
0.72
0.76
144
macro avg
00.48|
0.48
00.48/0.0)
1.
0.55
0.59
0.68
0.68
0.60
0.63
0.72
0.64]
144
weighted avg
0074|
0.75 0.75|0.02
0.15
00.1
0.72
0.84
0.76|0.79
144
AUC-ROC
0.42
0.37
0.72
0.79
vowels
P
R
F1
P
R
F
R
F1
P
R
F1
support
00.97|
0.98
[0.98
1 .00 0.69)0.8|0.99
0.80
1.00 0.86)0.92]
844
0.26]
0.17
|0.00
10 0.9 0.
0.89 0.27 1. 0.93
30
accuracy
0.96
0.70
0.86
874
macro avg
00.62|
0.58
0.59
0.55
0.81
|.5000000000
00.50
0.84
0.58
00.59
0.90 0.90)0.62
874
weighted avg
0.95|
0.96
0.95
00.97
0.70
0. 0.92
0.80
(0.97 (.960)
874
AUC-ROC
0.76
0.91
0.92
0.97
Waveform
P
R
F1
P
R
FI
R
F1
P
R
F1
|support
0.97|
0.97
(0.9700.97
0.53/0.69/096
0.75|0.83
1 1.00
2008
0.04|
0.03
(0.04
0.48
0.05
0.009
0.81 06
0.
0.88
0.21
accuracy
0.95
0.53
0.75
0.82
2066
avg
0.50|
0.50 0.50
0.50
0.50
0.51
0.37
0.52
0.78
0.49
0.56
0.85
0.55
2066
weighted avg
0.95|
0.95
0.95
00.95
0.53
0.66
0.67
0.93
0.75|0.81
00.97
0.82
0.88
2066
AUC-ROC
0.78
0.54
0.83
0.90
WBC
P
R
F1
P
R
F1
R
F1
P
R
F1
|upport
0.99
0.99
0.99|0.00
0.00)0.00
0.93
0.94
| 1.00
0.98/0.99
128
0083]
0.83 00.3
0..33 1.00)0.990..70
0.95
(0755
1.00]0.86]
accuracy
0.99
0.05
0.93
0.99
134
macro avg
0.911 0.91 |0.91
Jo.02
0.50
0.82
0.94
(0.87
0..8
0.99
00.33
134
weighted avg
[0.99] 0.99 (0.99
10.00
0.05
(.0550.0000.
00.92
0.93 0.93
(0.99
0.99
0..99
134
AUC-ROC
0.99
0.90
0.94
1.00
41

---

Published as a conference paper at ICLR 2025
Table 9 continued from previous page
DTE
Rejex
ADGym
Swift Hydra
WDBC
R
F1
P
R
F1
F1
P
R
F1
support
0.99| 0.99
0.99
00.98
0.19 0..% 0.89 0.89
1.00
0.93/0.96
217
00.5||
0.25
0.25
(0.02
0.75/0.03
0.18
0.95|0.29
0.21
1.00|0.35
4
accuracy
0.97
0.20
0.90
0.93
221
macro avg
0.62]
0.62 0..2
0.50
0.47
0.1
0.92
0.61
(.666
221
weighted avg
0.97|
0.97
0..7
0.96
0.20
0.32 0.32 0.95 0.90
0.99
0.93 0.95
AUC-ROC
0.98
0.51
0.93
1.00
Wilt
P
R
F1
P
R
F1
R
F1
P
R
F1
support
0.95|
0.95
|0.55
0.77
0.86
0.93
0.87
1.00
0.92]
2746
10.01
0.01
|0.01
00.14
0.68
0.223
0.35
0.93|0.50|1
0.38
0.96
146
accuracy
0.90
0.77
0.88
0.92
2892
macro avg
00.48] 0.48
00.48
(0.56
0.72
0.54
0.66
0.90
0.69
0.94
0.75
2892
weighted avg
0.990|
0.90
0.90
0..4
0.77
0.83
0.90
0.88
0.88
0.89
00.9 0.92 0.94|
2892
AUC-ROC
0.42
0.79
0.94
0.98
wine
P
R
F1
P
R
FI
P
R
F1
P
R
F1
support
-1
0.96
0.95
0.95
0.00
0.91 (9.92)
1.00
0.95
73
0.33|
0.40 0.36|0.06
1.00
0.97|0.67 0.56 1.00/0.71|
accuracy
0.91
0.06
0.95
macro avg
00.55 0.67
0..660..3
0.50
0.94
0.99
0.79
0.78
0.97
0..4|
78
weighted avg
0.92
0.91
00.1|0.000
[0.91
0.06
(0.92
0.91 00.7 0.95 0.96
0.96)
78
AUC-ROC
0.84
0.35
0.95
0.99
WPBC
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.78
0.86
0.82
0.00
0.00|0.0000.76
0.43 0.55
0.83
0.47
0.60
93
0.24|
0.15
0.19
0.22
1.00/0.360.22
0.33 00.6
0.65)..37
0.65
0.37
accuracy
0.71
0.22
0.47
0.51
119
macro avg
00.51| 0.51
00.50
0.50
08100.1111111
00.48
0.52
0
44
0.54
0.49)
119
weighted avg
0.66
0.71
00.68
0.00
0.22
0.08
0.64
0.50
0071
0.51
0..5|
119
AUC-ROC
0.54
0.53
0.54
0.59
yeast
R
F1
P
R
F1
R
F1
P
R
F1
support
0.60
0.61
0.60|0.66
0.87
0.77 0.77
0.49
0.62
0.80
0.54
0.65
587
0.22
0.21
0.22
0.
0.06|0.09|0.44
0.68 0.53
(0.46
0.74|0.57|
0.74
304
accuracy
0.47
0.60
0.56
0.61
891
macro avg
00.41|
0.41
[0.41
|0.42
0.47/0.42
0.47
0.
0.59
0.59
0.57
00.6
0.64
0.64|
0.61|
891
weighted avg
0..47
0.47
0..47
00.49
0.60
0.64
0.56|0.59
00.69
0.61 0..62|
891
AUC-ROC
0.37
0.41
0.65
0.70
CIFARIO
F1
P
R
FI
F1
P
R
support
00.97| 0.84 00.90
1.00)0.9900.99
0.87 0.92 0.99
0.99/0.99
2812
00.29| 0.74 0.42|0.80 0.52|0.63 00.3
0.75 0.779 0.79|
106
accuracy
0.83
0.98
0.86
0.98
2918
macro avg
[0.63] 0.79 |0.66
0.89
0.76 0.81
60.66
0.81 |0.69
(0.89
0.89 0..99
2918
weighted avg
0.92] 0.83 0.86
(0.98
0.98 0.98
0..2 0.86 0.88
|0.98
0.98
0.98)
2918
42

---

Published as a conference paper at ICLR 2025
Table continued from previous page
DTE
Rejex
ADGym
Swift Hydra
AUC-ROC
0.88
0.76
0.90
0.98
FashionMNIST
R
F1
P
R
FI
R
F1
P
R
F1
support
-1
0.99|
0.85
0..9
1.00 0.99
0.93
1.00
1.00|1.00)
3441
0.35|
0.94
0.52
0.85
0.70
0.51
0.92
0.93
0.91
92
accuracy
0.85
0.99
0.93
0.99
macro avg
0.67
0.89
00.1
[0.9
0.85
0.88
0.73
0.92
0.81
0.97
0.95
0.96
3533
weighted avg
0.94|
0.86 |0.88
(0.99
0.99
0.99 0.95 0.92
0.92 0.93 (0.99
0.99 0.99|
3533
AUC-ROC
0.96
0.85
0.97
0.99
MNIST-C
P
R
F1
P
R
F1
P
R
F1
P
R
F1
support
00.60|
0.61
0..60/0.64
0.7400.77
0.49
0.80
0.54
0.65|
587
0.22
0.21
0.222
09
0.06|0.09|0.44
0.68 (0.46
0.74
304
accuracy
0.47
0.60
0.61
891
macro avg
00.41|
0.41
0..1
0.44
0.42
0.42
0.59
0.59
0.57
0.63
0.64
0.61
891
weighted avg
0.47|
0.47
0.47
0..4
0.60
0.60
0.52
0.64
0.56|0.59 0..99 0.61
0.61 0.662
891
AUC-ROC
0.37
0.41
0.65
0.70
MVTec-AD
P
R
F1
P
R
FI
R
F1
P
R
F1
support
0.60]
0.61
0.60]0.64
0.740.77
0.49
0.80
0.54
587
0.22
0.21
0..20
19
0.06
0.440
0.68
00.46
0.74[0.57]
304
accuracy
0.47
0.60
0.56
0.61
891
macro avg
00.41| 0.41 00.41
(0.42
0.47|0.42
0.47
42.42
0.559
0.59
0.57
0066
0.64
891
weighted avg
00.47|
0.47
00.47
40
0.60
0.52
6.64
0.56
0.59
(0.69
0.61
[0.62]
891
AUC-ROC
0.37
0.41
0.65
0.70
SVHN
R
F1
P
R
F1
R
F1
P
R
F1
support
0.92 0.87
0.90
0.97
0.92
0.89
0.91
0.96
0.97
2562
0010
0.16
0.12|
0.03|0.04||
0.16
13 0.26 0. 0.16
133
accuracy
0.82
0.94
0.83
0.93
2695
macro avg
0.51|
0.51 0..5
10.52
0.51
/
0.51
0.52
0.53
00.6 0.57 0.58
2695
weighted avg
0.86
0.82
0.83
|0.91
0.94
0.92
0.86
0.83/0.84)
(0.92 0.93 00.33
2695
AUC-ROC
0.37
0.51
0.55
0.63
Agnews
R
F1
P
R
F1
P
R
support
0.95|
0.90
0.93
0.976.9960.94
0.96/0.96
(..8
0.99
0.99
5383
0.30
0.50
0.38
10
0.06
0.06
00.46
0.39 0.39|0.42
(0.75
0.72] 0.69)..72
0.69
277
accuracy
0.87
0.93
0.91
0.97
5660
macro avg
00663
0.70
0.65
0.55
0.51
0055
0.
0.70
0.67
0.69
0.87
0.84|0.88
5660
weighted avg
0.90
0.87
0.88
|0.1
0.93
0.
0.92
0.91
0.91
0.91
00.97
0.97
0.99
5660
AUC-ROC
0.79
0.51
0.80
0.90
Amazon
F1
P
FI
F1
P
R
support
0.92| 0.94
0.93
0.96
0.94
(0.97
0.98
0.98
5393
00.1
0.09
10.10
0.04
0.07
0.05|0.06
0.54
0.36|0.43]
288
accuracy
0.87
0.92
0.86
0.95
5681
macro avg
0.52]
0.51 00.1 |0.50 0.50
0.50
0075
0.67|0.70
5681
43

---

Published as a conference paper at ICLR 2025
Table continued from previous page
|TE
Rejex
ADGym
Swift Hydra
weighted avg
[0.86]
0.87 0.86|0.90
0.92 0.91 0.95 0.86 0.86
0.86|0.86
0.95
0.95
5681
AUC-ROC
0.58
0.50
0.53
0.93
Imdb
P
R
F1
P
R
F1
P
R
F1
P
R
F1
support
00.92|
0.94
0..93
0.95 0.97 1.970.9660099
0.95 (0.97
0.98 0.98
5389
0.09
0.07
00.08|0.06
0.04 0..09 0.05|0.06|0.55
0.36|0.43]
290
accuracy
0.87
0.92
0.95
5679
macro avg
00.1|
0.51
0..1
0.500
0.50
(..50
0.75
0.67
0.70)
5679
weighted avg
0.85
0.87
0.86|0.90
0.92
0.92|0.91 0.91
00885
0.88|0.87
0.87
0.95 0.95
0.95|
5679
AUC-ROC
0.55
0.50
0.55
0.93
Yelp
R
F1
P
R
F1
R
F1
P
R
F1
support
0.92]
0.94
[0.93
(0.95
0.96]0.9600.00
0.96 0.93
0..8 0.98
0.98
5369
0.09|
0.07
0..990.03
0.009
0.003
0.02|0.03
0.22
0.09
0.66
0.65|0.66
283
accuracy
0.89
0.92
0.86
0.97
5652
avg
0.53|
0.52
0.52
0.
0.49
0.44
0.57
0.53
0.53
0.53
0.82
0.82 0.82
891
weighted avg
0.86
0.89
00.87
[0.
(0.90
0.92
0.91
0.81
0.86|0.83
(0.97 0.97 0.97|
5652
AUC-ROC
0.58
0.49
0.62
0.94
20newsgroups
R
F1
P
R
FI
R
F1
P
R
F1
support
0.97
0.40
0.57
0.95
1.00 0.95
0.68
0.79
0.98
0.99
0.98
787
00.1
0.89
0.200j0.00
0.00)0.0010.23
0.71 0.71 00.44
0.57 0.64|
39
accuracy
0.44
0.95
0.68
0.61
826
macro avg
00.5|| 0.65 |0.39
|0.48
0.50
0.49
0.59
0.69/0.57
0086
0.78
0..11
826
weighted avg
10.91 0.44 |0.54
0.95 0.93 0.86 0.68).77|000
00.7
0.97|
826
AUC-ROC
0.76
0.50
0.77
0.94
Precision,
Recall, F1 F1-Score
44


Reviews:
[{"review_id": "N7oe8thgzB", "reviewer": "Reviewer_RKHh", "summary": "This paper presents a novel framework, Swift Hydra, for training an anomaly detection method that leverages generative AI and reinforcement learning. It introduces Mamba models structured as a Mixture of Experts (MoE), allowing for scalable adaptation of the number of Mamba experts based on data complexity. Experiments conducted on the ADBench benchmark demonstrate that Swift Hydra outperforms other state-of-the-art anomaly detection models while maintaining a relatively short inference time.", "questions": "See weakness above. I will consider raising my score if my concerns are addressed well.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.The writing in this paper is clear and well-structured.\n\n2.The incorporation of reinforcement learning, conditional VAE, and Mixture of Experts (MoE) is novel and well-justified.\n\n3.The paper conducts thorough experiments on ADBench and demonstrates strong performance.", "weaknesses": "1.Typically, experiments relying on only one dataset are insufficient. It would be beneficial to include additional analysis and comparisons using other popular datasets.\n\n2.It appears that Swift Hydra is not specifically designed for tabular anomaly detection. Have you explored the generalizability of this method to other domains, such as image data or time-series data?\n\n3.The paper introduces several complex components, such as reinforcement learning, which may complicate implementation. Additionally, could you provide an analysis of the computational cost associated with training, including metrics such as the number of parameters and training time per batch?\n\n4.How does the performance of Swift Hydra fare in multi-class or cross-dataset scenarios?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "faNJXfUxSD", "reviewer": "Reviewer_9izT", "summary": "This paper proposes a novel tabular anomaly detection method by designing a RL-based anomaly data augmentation technique and a Mixture of Experts (MOE) based anomaly detection module. The authors verified the effectiveness of their proposed method with 3 baselines on ADBench and also provided visualized proofs of the effectiveness of their reward function and anomalous data augmentation technique.", "questions": "1. In theorem 1, do you mean $\\hat{x}_i=\\mathcal{M}_\\phi(\\hat{z}_i,y_i=1)$?\n2. Could you please add more SOTA tabular anomaly detection methods?\n3. Could you please add ablation experiments?\n4. In Table 1, why Swift Hydra (MOME) has less inference time than Swift Hydra (Single)?\n5. Could you please further explain how to use \"gating network\" and \"Tackling winner-take-all\" together?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Overall well written. The paper is easy to follow and organized in a clear orchestration. \n2. Novel idea. This paper proposes a novel idea that using RL to make anomalous data augmentation. Besides, the authors also prove the effectiveness of their proposed reward function by showing the consistency between AUC-ROC and the reward.\n3. It is proved that the RL-based anomaly data generation method can generate anomalies of high diversities, as show in Fig 2.", "weaknesses": "1. Weak soundness of experiment. The experiments are not persuasive enough. The baselines do not cover enough SOTA tabular anomaly detection methods. The authors only compares the proposed methods with 3 baselines. Besides, there is no ablation study to verify the effectiveness of RL-based anomaly data generation technique and the MOE anomaly detection module separately.\n2. Unrealistic assumption in mathematical proof. In the mathematical proof of theorem 2 and theorem 3, it is actually assumed that single anomaly detector can not distinguish anomalies and normality in overlap region. However, this assumption is only available for linear classification methods (e.g. support vector machine). The deep neural networks are non-linear classification methods and can deal with interlaced anomalies and normality in  overlap region well. In this situation, theorem 2 and 3 can not be deduced.\n3. The illustration of the process of \"gating network\" and \"Tackling winner-take-all\" is somewhat ambiguous. What confused me is that given both of these two mechanism actually are used to assign input to different expert, how could we use them together?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "I02sgzDVo0", "reviewer": "Reviewer_8B4d", "summary": "This method focus on generalization to unseen anomalies. To do that, this method generates new anomaly samples using reinforcement learning and conditional VAE. The conditional VAE generate samples conditioned on the class anomaly. The reinforcement learning enforces the generated samples to be diverse and difficult to detect by the detection model. For the detection model, in order to keep the complexity low while can capture diverse feature distribution, Mixture of Experts consisting of multiple Mamba experts are utilized.", "questions": "1. Which part of the experiments that prove the generalization to unseen anomalies?\n\n2. It is unclear whether this work use both real and fake data or only real data. I can't find the information in Line 94-105. My guess from other part of the paper is using both real and fake, but I am not 100\\% sure. \n\n3. Why is this method called reinforcement learning method if the action is (afaik) backpropagatable directly from the reward/loss? \n\n4. How is the balanced dataset updated? I can't find any information in Algorithm 1 in the appendix.\n\n5. Why not also generating normal data?", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 4, "strengths": "Adding new anomalous synthetic data during training to increase generalization using reinforcement learning seems to be novel.", "weaknesses": "See questions.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "0Ftz2K5W5W", "reviewer": "Reviewer_uiUH", "summary": "This paper proposes Swift Hydra, a novel anomaly detection framework based on the conditional variational autoencoder (CVAE) and reinforcement learning.\nThe proposed method generates high-quality anomalies using CVAE and reinforcement learning, and performs anomaly detection using a mixture of expert models based on Mamba (MoME). \nExperiments on various datasets demonstrated improved anomaly detection performance and reduced inference time compared to existing methods.", "questions": "1. Why does the proposed method use CVAE? Since VAE generally has lower data generation quality compared to other generative models, I don't think it's very suitable for data augmentation purposes in this case. For example, would the proposed method work well with a diffusion model, which can be considered a special case of VAE?\n2. The proposed method performs anomaly detection in the data space, but wouldn’t it be more beneficial to take advantage of CVAE’s strengths by performing anomaly detection in the lower-dimensional latent space? What is the reason for performing anomaly detection in the data space?\n3. I understand that MMoE performs binary classification between normal and anomaly data. In binary classification, a decision boundary is set between the normal and anomaly data included in the training set, which makes it difficult to handle unseen anomalies that are far from the known anomalies in the training data. Can the proposed method address this issue?\n4. If the proposed method can handle unseen anomalies, I believe it is because CVAE can generate such unseen anomalies. Why is the proposed method able to generate unseen anomalies? Even though the entropy is incorporated into the reward of the reinforcement learning, I think generative models can only generate data similar to the training data.\n5. Is it possible to visualize the generated samples and decision boundaries of the proposed method using two-dimensional toy data? For example, if there is normal data shaped like a sine curve, and the generated anomalies are arranged surrounding that curve, I believe the method would be able to handle both seen and unseen anomalies.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- This paper introduces several strategies to achieve high-accuracy anomaly detection. For example, the reward function in reinforcement learning incorporates the entropy of the union of the training data and the generated data, which encourages the generation of diverse anomalies. Additionally, in the MMoE model, experts are selected probabilistically to avoid the winner-take-all problem.\n- The visualization of the generated anomalies is interesting. It clearly shows a clean separation between normal data and anomalies, and we can also observe the generation of a wide variety of anomalies.", "weaknesses": "- Although the proposed method works well, there are a few parts that are unclear to me. I will write more details in the Questions section, so please refer to it.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)