Team DACTYL at PAN 2026: Bayesian Data Mixing and Empirical X-risk Minimization for AI-text Detection

# Notebook for the PAN Lab at CLEF 2026
Source: [https://arxiv.org/html/2607.17382](https://arxiv.org/html/2607.17382)
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Copyright for this paper by its authors\. Use permitted under Creative Commons License Attribution 4\.0 International \(CC BY 4\.0\)\.

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CLEF 2026 Working Notes, 21 – 24 September 2026, Jena, Germany

\[orcid=0009\-0004\-8470\-0713, email=st980\[at\]cantab\.ac\.uk, url=https://shantanuthorat\.io, \]\\cormark\[1\]

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\[1\]Work completed independently of employment at Texas A&M University\.

\(2026\)

###### Abstract

Existing research shows that AI\-generated text detection classifiers achieve strong in\-distribution \(ID\) performance but do not maintain the same performance on out\-of\-distribution \(OOD\) texts, suggesting overfitting to dataset\-specific features\. However, combining different training datasets doesn’t always improve performance and, in some cases, can even encourage shortcut learning\. To address this issue, we fine\-tune BERT\-tiny models with Bayesian classification heads to select texts across three different datasets to use as a consolidated training set\. We trained three different classifiers: fine\-tuned DeBERTa\-V3\-large and ModernBERT\-large classifiers via empirical X\-risk minimization, and an MCGrad model that calibrates the predictions from the ModernBERT\-large classifier\. The DeBERTa\-V3\-large\-large classifier achieves a mean score of 0\.882 on the PAN 2026 test set across five metrics: AUROC,F1F\_\{1\}, C@1, Brier score, andF0\.5​uF\_\{0\.5u\}\. ModernBERT\-large achieves a score of 0\.96 while MCGrad achieves the best score of the three with a mean score of 0\.974, ranking second on the leaderboard\. Our results highlight that careful dataset curation can lead to strong OOD performance\. We release our ModernBERT\-large and DeBERTa\-V3\-large models at[https://huggingface\.co/collections/ShantanuT01/panclef\-2026](https://huggingface.co/collections/ShantanuT01/panclef-2026)\.

###### keywords:

Bayesian neural networks\\sepempirical X\-risk minimization\\sepmulticalibration\\sepAI\-generated text detection

## 1Introduction

The Voight\-Kampff 2026 Task at PAN at CLEF 2026 focused on binary AI\-generated \(AIG\) text detection: identifying if a text came from a large language model \(LLM\) or a human\[[1](https://arxiv.org/html/2607.17382#bib.bib1),[2](https://arxiv.org/html/2607.17382#bib.bib2),[3](https://arxiv.org/html/2607.17382#bib.bib3),[4](https://arxiv.org/html/2607.17382#bib.bib4)\]\. Despite many classifiers achieving high performance when faced with texts that mirror their training distributions, AIG text detectors struggle to generalize to out\-of\-distribution \(OOD\) texts\[[5](https://arxiv.org/html/2607.17382#bib.bib5)\]\. We suspect that AIG text detection datasets may contain spurious correlations — e\.g\., texts that contain unintentional artifacts that coincidentally map to AI\-generated content or human\-written content\. Empirically, for example, we observe that for the RAID benchmark test set, a 4 million parameter \(BERT\-tiny\) model achieved a competitive AUROC \(0\.967\) score against larger classifiers\[[6](https://arxiv.org/html/2607.17382#bib.bib6)\]\. On another AIG text detection dataset, the DACTYL test set, BERT\-tiny achieves an AUROC score of 0\.99\[[5](https://arxiv.org/html/2607.17382#bib.bib5)\]\. These results suggest that AIG text detection datasets may contain superficial features that allow for smaller models to obtain misleadingly high scores\. A naive way to combat dataset\-specific issues is to combine datasets\. However, this approach doesn’t always help machine\-learning models and in some casesreinforcesa model’s dependency on these spurious correlations\[[7](https://arxiv.org/html/2607.17382#bib.bib7)\]\.

Previous work to address these issues include hard mining — retraining classifiers on texts they struggled with — has yielded some success in improving robustness\[[8](https://arxiv.org/html/2607.17382#bib.bib8)\]\. However, this technique doesn’t necessarily distinguish between texts that are genuinely difficult or simply noisy texts \(e\.g\., a corrupted/hallucinated generation\)\. This lack of distinguishability leads to another issue — classifier’s scores \(scaled from 0 to 1, where 0 means human\-written and 1 means AIG\) aren’t necessarily calibrated, meaning the score itself may not be a reliable signal for evaluating a classifier’s confidence on an example\. Additionally, a single \(even calibrated\) score doesn’t indicate a model’s uncertainty on an input\. Finally, a majority of BERT\-based classifiers use empirical risk minimization \(ERM\): the training loop optimizes cross\-entropy loss or its variants, such as focal loss\. Empirical risk minimization, while successful in many classification tasks and domains, tends to encourage shortcut\-learning, leading to classifiers struggling to generalize to OOD texts\[[9](https://arxiv.org/html/2607.17382#bib.bib9)\]\.

To address these issues, we contribute the following parts of our system:

- •We construct DACTYLv2, an expansion of the original DACTYL dataset\.
- •To better select texts for training, we train weak BERT\-tiny models with a Bayesian neural network \(BNN\) classifier head \(we refer to this architecture as Bayesian BERT\-tiny\), which can output different scores for a given text, allowing us to computeμ\\mu\(mean score\) andσ\\sigma\(standard deviation\)\. Using these features, we can filter out texts from different datasets to use for training\. These filtering steps allow us to blend different datasets together for one final training set\.
- •Instead of traditional ERM, we use empirical X\-risk minimization \(EXM\), specifically, two\-way partial AUROC optimization via the LibAUC library\[[10](https://arxiv.org/html/2607.17382#bib.bib10)\]\. EXM has shown promising results in generalizability, especially with larger models\[[5](https://arxiv.org/html/2607.17382#bib.bib5)\]\.
- •We produce three different classifiers: a ModernBERT\-large and a DeBERTa\-V3\-large classifier\[[11](https://arxiv.org/html/2607.17382#bib.bib11),[12](https://arxiv.org/html/2607.17382#bib.bib12)\]\. For our third classifier, we use the weak Bayesian BERT\-tiny classifiers’ uncertainties \(σ\\sigma\) as features to calibrate ModernBERT\-large via MCGrad\[[13](https://arxiv.org/html/2607.17382#bib.bib13)\]\.

## 2Datasets Used

### 2\.1Training

#### 2\.1\.1DACTYLv2

Building upon the work in\[[5](https://arxiv.org/html/2607.17382#bib.bib5)\], we construct the second version of DACTYL, which we denote as DACTYLv2 — we refer to DACTYL\-complete as DACTYLv1 and DACTYLv2 combined\. We create all AIG texts via one\-shot prompting; we gave the LLM a human\-written example to base its generation from\. We included the following domains in DACTYLv2:

- •blogs\[[14](https://arxiv.org/html/2607.17382#bib.bib14)\]
- •web articles\[[15](https://arxiv.org/html/2607.17382#bib.bib15)\]
- •Medium articles\[[16](https://arxiv.org/html/2607.17382#bib.bib16)\]
- •movie scripts\[[17](https://arxiv.org/html/2607.17382#bib.bib17)\]
- •NBER economic paper abstracts\[[18](https://arxiv.org/html/2607.17382#bib.bib18)\]
- •Yelp reviews\[[19](https://arxiv.org/html/2607.17382#bib.bib19)\]

We use the following models to construct the dataset\.

- •Claude Haiku 4\.5\[[20](https://arxiv.org/html/2607.17382#bib.bib20)\]
- •Claude Sonnet 4\.6\[[21](https://arxiv.org/html/2607.17382#bib.bib21)\]
- •GPT 5\.4\[[22](https://arxiv.org/html/2607.17382#bib.bib22)\]
- •GLM 5\.1\[[23](https://arxiv.org/html/2607.17382#bib.bib23)\]
- •MiniMax M2\.5\[[24](https://arxiv.org/html/2607.17382#bib.bib24)\]
- •Mercury M2\[[25](https://arxiv.org/html/2607.17382#bib.bib25)\]

We used mirror prompting to create LLM prompts as used in\[[8](https://arxiv.org/html/2607.17382#bib.bib8)\]for the blogs, web articles, and Medium articles\. We provided the GPT 5\.4 Nano model with the human article and asked it to generate a possible prompt that could have inspired the article\[[26](https://arxiv.org/html/2607.17382#bib.bib26)\]\. For movie scripts, given two randomly selected movie scripts, we take a random excerpt of 4,096 characters from each script\. We prompt the LLM to rewrite the first random excerpt by mimicking the style of the second random excerpt\. For NBER abstracts, we have the LLM copy the style of a random abstract and generate a new abstract given only the title of another randomly selected paper title\. For Yelp reviews, we take a randomly selected business, its industry, and one random review and ask the LLM to generate another review using the selected review as a style reference\. For Yelp reviews only, we also included texts generated by Kimi\-K2\.5\[[27](https://arxiv.org/html/2607.17382#bib.bib27)\]\. After manual inspection of Kimi\-K2\.5’s generations, we observed that the specific model struggled with style mimicking compared to other LLMs, so we did not use the model for other domains\. We report aggregated counts by generator \(LLM or human\) and domain in Table[1](https://arxiv.org/html/2607.17382#S2.T1)after deduplication\.

For the open\-source LLMs, we used the models provided by the TogetherAI and FireworksAI platforms\[[28](https://arxiv.org/html/2607.17382#bib.bib28),[29](https://arxiv.org/html/2607.17382#bib.bib29)\]\.

Table 1:DACTYLv2 Text Counts by Domain/Model across all splitsModelNBERYelpWebBlogsMediumScriptsTotalAbstractsArticles\(Movie\)TextsGLM 5\.11,4001,4001601,1505,99627510,381GPT 5\.41,4001,4001601,1506,00027510,385Sonnet 4\.61,3991,4001581,1435,99427410,368Haiku 4\.51,4001,4001601,1506,00027510,385Mercury 21,4001,3971591,0765,98527410,291Kimi\-K2\.501,38700001,387Qwen3\.5\-397B\-A17B1,4001,3371601,1505,98627510,308MiniMax\-M2\.51,3881,3961601,1335,95422910,260Human30,60090,07821,12397,727156,3622,200398,090Total40,387101,19822,240105,679198,2774,077471,858
#### 2\.1\.2External Datasets

Since DACTYL\-complete only includes one\-shot generations, we included texts from other existing datasets\. Augmenting our training set also ensures that our final classifiers don’t overfit to DACTYL\-specific artifacts unintentionally\. We selected LLMTrace \(English only\)\[[30](https://arxiv.org/html/2607.17382#bib.bib30)\], Personagen and Stack Exchange\[[31](https://arxiv.org/html/2607.17382#bib.bib31),[32](https://arxiv.org/html/2607.17382#bib.bib32)\], MAGA\-Bench \(English only\)\[[33](https://arxiv.org/html/2607.17382#bib.bib33)\], and DetectRL\[[34](https://arxiv.org/html/2607.17382#bib.bib34)\]as additionalcandidatetraining datasets to complement DACTYL\-complete\. LLMTrace’s English split includes multiple prompt types, such as updating a human\-written text as well as mixed texts\. Personagen includes a specific prompt style — LLMs act as a specific human persona before generating their responses\. MAGA\-Bench includes generations from different LLM “alignments” \(e\.g\., role\-playing, black\-box prompt optimization, etc\.\)\. DetectRL includes mixed LLM\-generated texts where a single AIG text may have contributions from different LLMs\. Since Personagen only includes AIG texts, we complement it with a subset of Stack Exchange posts\. For each community \(that wasn’t a meta community\), we randomly sampled up to 10,000 posts before November 1, 2022\.

### 2\.2Calibration

We perform an additional layer of calibration for one of our models \(ModernBERT\-large\), given that the scoring metrics for PAN CLEF 2026 include Brier score loss\. We use the following datasets listed in Table[2](https://arxiv.org/html/2607.17382#S2.T2)\. For each dataset, we take a random sample of 2,000 texts, followed by deduplication, to avoid a larger dataset from dominating our calibration set\. Due to an imbalance of AIG texts over human texts, we include samples from human\-only datasets: CC\-News and Stack Exchange\. We did not perform calibration on DeBERTa\-V3\-large since it already obtained strong performance on the calibration set\.

Table 2:Calibration counts by dataset and generator\.DatasetTotal TextsAI TextsHuman TextsDACTYLv1 \(validation\)1,9977381,259Personagen2,0002,0000AIGC Text Bank\[[35](https://arxiv.org/html/2607.17382#bib.bib35)\]2,0001,91387AuthorAware2,0002,0000OpenTuringBench\[[36](https://arxiv.org/html/2607.17382#bib.bib36)\]1,9951,9950DACTYLv2 \(validation\)2,0004691,531PAN\-CLEF 2025 \(training\)\[[37](https://arxiv.org/html/2607.17382#bib.bib37)\]2,0001,252748CC News\[[38](https://arxiv.org/html/2607.17382#bib.bib38)\]1,96101,961NY Times AI\[[39](https://arxiv.org/html/2607.17382#bib.bib39)\]2,0001,713287Stack Exchange2,00002,000SAGE\[[40](https://arxiv.org/html/2607.17382#bib.bib40)\]1,9851,523462LLMTrace \(English, validation\)2,0001,210790Detect AI\[[41](https://arxiv.org/html/2607.17382#bib.bib41)\]2,0001,346654Total25,93816,1599,779
### 2\.3Testing

We evaluate our models on numerous test sets to evaluate generalizability since an updated validation set was not released this year, in contrast to previous years\[[37](https://arxiv.org/html/2607.17382#bib.bib37)\]\. We use the following datasets listed in Table[3](https://arxiv.org/html/2607.17382#S2.T3)\. We included ID test sets \(DACTYL\-complete, MAGA\-Bench, LLMTrace\) as well as OOD test sets\.

Table 3:External test sets used\.DatasetDomain CountLLMs UsedBEEMO\[[42](https://arxiv.org/html/2607.17382#bib.bib42)\]510CoCONUTS\[[43](https://arxiv.org/html/2607.17382#bib.bib43)\]67DACTYL\-complete \(DACTYLv2 and DACTYLv1\[[5](https://arxiv.org/html/2607.17382#bib.bib5)\]\)1225DetectRL44Dolly\-Cosmopedia\[[44](https://arxiv.org/html/2607.17382#bib.bib44),[45](https://arxiv.org/html/2607.17382#bib.bib45)\]211LLMTrace \(English\)919MAGA\-Bench \(English\)1012OriginalityAI\[[46](https://arxiv.org/html/2607.17382#bib.bib46)\]Not specified4PAN 2025 Val\[[37](https://arxiv.org/html/2607.17382#bib.bib37)\]322Personagen \+ StackExchange46RealDet \(English\)\[[47](https://arxiv.org/html/2607.17382#bib.bib47)\]1522UChicago\[[48](https://arxiv.org/html/2607.17382#bib.bib48)\]64

## 3Data Filtering

### 3\.1Bayesian BERT\-Tiny Classifiers

To get an estimate on dataset generalizability, we train small classifiers on a sample of these datasets\. Each smaller classifier is a BERT\-tiny model with a Bayesian variant of a linear layer as the classification head\[[49](https://arxiv.org/html/2607.17382#bib.bib49),[50](https://arxiv.org/html/2607.17382#bib.bib50),[51](https://arxiv.org/html/2607.17382#bib.bib51)\]\. The Bayesian head’s input dimensions are equivalent to the hidden size of the BERT\-tiny model, and the output dimension size is 1\. Bayesian neural networks \(BNNs\) allow for the estimation ofσ\\sigma\(standard deviation\) of a prediction on a specific input\. This uncertainty modeling comes from how a BNN represents its internal weights — rather than having individual scalars, the BNN replaces each scalar with a distribution\[[52](https://arxiv.org/html/2607.17382#bib.bib52)\]\. During inference time, we sample a set of parameters to use for a prediction\. Upon doingnnsamples, we can compute the \(μ\\mu,σ\\sigma\), or the mean score and standard deviation\.

Training a Bayesian BERT\-tiny for classification is nearly identical to a standard BERT model’s training, except it optimizes the ELBO \(evidence lower bound\) loss\. We can define ELBO loss as

ELBO=L\+βbKL\[q\(w\|θ\)\|\|P\(w\)\]\\text\{ELBO\}=L\+\\frac\{\\beta\}\{b\}\\text\{KL\}\\left\[q\(w\|\\theta\)\|\|P\(w\)\\right\]\(1\)
whereLLis our loss function of choice,q​\(w\|θ\)q\(w\|\\theta\)is our variational approximation to the posterior, andP​\(w\)P\(w\)is our prior\.θ\\thetaare the parameters that characterize the distribution of weightswwfor our model\. The KL divergence term prevents the model’s weights from moving too far away from our prior\. The fractionβ/b\\beta/bis a scaling factor to avoid the KL term from dominating the ELBO loss\.β\\betais a positive value \(for our experiments, we set it to 1\) andbbis the mini\-batch size during training\.

For each of the five training sets, we train a Bayesian BERT\-tiny classifier on a random sample of the training set\. We use the two\-way partial AUROC loss function asLL\(the DRO\-KL variant also used in\[[5](https://arxiv.org/html/2607.17382#bib.bib5)\]\), a batch size of 64, a learning rate of1×10−41\\times 10^\{\-4\}, and a weight decay of0\.010\.01\. We train each classifier for one epoch\. Since the two\-way partial AUROC loss needs at least one positive sample per mini\-batch, we set the proportion of positive samples equal to 0\.5 for each mini\-batch\. Due to each of the five datasets possessing different distributions, we manually tuned the hyperparameters so that the classifier’s uncertainty increased on OOD texts\. We observed that the random sample size \(defined as fractionff\) and the initial posterior \(ρ\\rho, which can be transformed into the standard deviation of weights viaσ=log⁡\(1\+exp⁡ρ\)\\sigma=\\log\{\(1\+\\exp\{\\rho\}\)\}\) influenced the model’s uncertainty significantly\. For each Bayesian BERT\-tiny model, we assign some of the classification head hyperparameters to fixed values, according to the BLiTZ documentation\[[51](https://arxiv.org/html/2607.17382#bib.bib51)\]:

- •priorσ1\\sigma\_\{1\}= 0\.1
- •priorσ2\\sigma\_\{2\}= 1\.5
- •priorπ\\pi= 0\.5
- •initial posteriorμ\\mu= 0

Table 4:Bayesian BERT\-tiny training configurations\.DatasetInitial Posteriorρ\\rhoffTraining Sample CountDACTYL\-complete−3\-31/5167,099DetectRL−3\-31205,914MAGA\-Bench−3\-31/571,903Personagen\+SE−3\-31/8025,565LLMTrace−2\-21173,511We report initial AUROC scores by classifier and test set to evaluate discrimination ability between AI and human texts in Table[5](https://arxiv.org/html/2607.17382#S3.T5)\.

Table 5:AUROC scores by Bayesian BERT\-tiny classifier\.Train DatasetDACTYL\-completeDetectRLLLMTraceMAGA\-BenchPersonagen\+SEDACTYL\-complete0\.94190\.77250\.86920\.94290\.9819DetectRL0\.70140\.98390\.73240\.64380\.9702LLMTrace0\.83610\.85530\.96330\.95410\.9757MAGA\-Bench0\.82050\.78810\.87610\.99060\.9978Personagen\+SE0\.69430\.75970\.83020\.87450\.9999
### 3\.2Filtering Process

We observe in Table[5](https://arxiv.org/html/2607.17382#S3.T5)that DACTYL\-complete, LLMTrace, and MAGA\-Bench are among the best in cross\-dataset generalizability\. We focus on those datasets and use our classifiers to either “keep” or “reject” \(or “abstain” from a decision\) texts to use for our final training set\. There are four “quadrants” of classification outcomes for our Bayesian BERT\-tiny models:

- •correct but uncertain
- •correct and certain
- •incorrect but uncertain
- •incorrect and certain

The first three outcomes are acceptable for a model to train on — a correct classification indicates that a classifier has thecapacityto learn that sample, regardless of the certainty\. An incorrect but uncertain classification for a sample suggests a difficult case — the classifier is aware that its prediction is possibly wrong\. We discard samples in the fourth and final case, incorrect and certain\. The intuition comes from dataset cartography:Swayamdipta et al\. \[[53](https://arxiv.org/html/2607.17382#bib.bib53)\]demonstrated that some samples exist in the “hard\-to\-learn” space, which are samples that the model assigns low probability scores to the true class consistently — these “hard\-to\-learn” samples map roughly to the “incorrect and certain” quadrant\. While this space can include mislabeled data points, it also includes samples that may be genuine outliers\. Given that the two\-way partial AUROC loss function focuses on the harder positive \(AI\) and negative \(human\) samples, this makes the loss function more sensitive to texts that have high loss and increases the probability of overfitting to outliers\[[54](https://arxiv.org/html/2607.17382#bib.bib54),[10](https://arxiv.org/html/2607.17382#bib.bib10),[55](https://arxiv.org/html/2607.17382#bib.bib55)\]\.

We define the voting process for an individual classifier as follows\. For a given texttt, we compute the standard deviation \(σt\\sigma\_\{t\}\) and mean score \(μt\\mu\_\{t\}, number of runs = 5 to minimize inference time\) for the Bayesian BERT\-tiny classifierCDC\_\{D\}, whereDDis the training dataset\. We refer to the distribution of standard deviations on thetestset forDDfor classifierCDC\_\{D\}asSDS\_\{D\}\. For example, with DACTYL\-complete, we computeSDACTYL\-completeS\_\{\\text\{DACTYL\-complete\}\}by computing the individualσt\\sigma\_\{t\}values using the Bayesian BERT\-tiny classifier trained on DACTYL\-complete’s subset — since we want a stable distribution, we do 30 runs for each text in the test set\. We can compute the percentile ofσt\\sigma\_\{t\}relative toSDS\_\{D\}asPtP\_\{t\}\. A higherPtP\_\{t\}indicates a larger value ofσt\\sigma\_\{t\}, which implies the model is more uncertain — conversely, a lowerPtP\_\{t\}signals high confidence\. We convertμt\\mu\_\{t\}to labely^\\hat\{y\}\(1 or AI\-generated ifμt\>\\mu\_\{t\}\>0\.5 else 0\) to compare to the true labelyy\. Using this information, we can then see howCDC\_\{D\}votes ontt, as described in Table[6](https://arxiv.org/html/2607.17382#S3.T6)\.

Table 6:Criteria for voting on textttusing classifierCDC\_\{D\}\.CriteriaDecision\(1\)Pt<5P\_\{t\}<5orPt\>95P\_\{t\}\>95Abstain\(2\)5≤Pt≤955\\leq P\_\{t\}\\leq 95andPt≤50P\_\{t\}\\leq 50andy^≠y\\hat\{y\}\\neq yRejecttt\(3\) Criteria \(1\) and \(2\) are not metKeepttCriterion 1 is a case where the classifier’s uncertainty signal appears to be struggling — extremely high confidence \(σt\\sigma\_\{t\}is less than the 5th percentile\) or extreme uncertainty \(σt\\sigma\_\{t\}is greater than the 95th percentile\)\. A classifier abstaining from a text with significantly high uncertainty is reasonable; it hasn’t seen this text before to make a reliable vote\. However, exceptional overconfidence implies that the classifier’s output may be miscalibrated\.

Criterion 2 is the “incorrect and certain” sample — this is a sample where the classifier is relatively confident \(PtP\_\{t\}is less than the 50th percentile\) but makes an incorrect prediction\. Criterion 3 is the “keep” vote and occurs when the first two criteria aren’t met\.

We use the ensemble of classifiers’ votes to decide whether or not to keeptt\.ttis ultimately kept if at least three of the five classifiers vote to keep and no more than one classifier rejectstt\. For example, if three classifiers vote to keeptt, but the remaining two classifiers reject it, then we discardtt\. However, if three classifiers vote to keeptt, and one of the remaining classifiers abstains while the other rejects, we choose to keepttfor the final training set\. This rejection mechanism helps to minimize the chances of an unusual outlier text making it to the training set\.

We report final dataset sizes in Table[7](https://arxiv.org/html/2607.17382#S3.T7)\. The “Rejected” column refers to instances where a text received three “keep” votes and two “reject” votes\.

Table 7:Filtering results per dataset\.Δ\\Deltadenotes the change \(percentage points\) in the proportion of AIG texts after filtering\. The rejected column denotes the number of texts that received three keep votes and two reject votes\.Train DatasetInitialNNKeptNN% KeptRejectedAIG text% \(Δ\\Delta\)DACTYL\-complete826,891727,23587\.91,80217\.0%→15\.4%​\(−1\.6\)17\.0\\%\\to 15\.4\\%\(\-1\.6\)LLMTrace173,511146,90884\.773460\.8%→57\.5%​\(−3\.3\)60\.8\\%\\to 57\.5\\%\(\-3\.3\)MAGA\-Bench359,518297,99482\.91,38783\.4%→81\.7%​\(−1\.7\)83\.4\\%\\to 81\.7\\%\(\-1\.7\)

## 4Model Training

### 4\.1Pre\-trained Model Fine\-tuning

We train a \(non\-Bayesian\) DeBERTa\-V3\-large and ModernBERT\-large model on our filtered superset, which consists of all kept texts from the three datasets\. We optimize the two\-way partial AUROC loss function directly \(we don’t use ELBO as our objective, as the classification head is not a BNN\)\. We use a learning rate of1×10−51\\times 10^\{\-5\}, a batch size of 16, a sampling rate of 0\.5, and one epoch for both models\.

### 4\.2Multicalibration with MCGrad

For ModernBERT\-large, we also perform post\-hoc multicalibration with MCGrad using our calibration set\[[13](https://arxiv.org/html/2607.17382#bib.bib13)\]\. Our MCGrad model takes in four inputs — the transformed scoressfrom the ModernBERT\-large model and the individual uncertainties \(σ\\sigma, 5 runs\) for three Bayesian BERT\-tiny classifiers \(DACTYL, LLMTrace, MAGA\-Bench\)\.

We computessvia temperature scaling by transforming the raw probability scoresrs\_\{r\}into a logit from ModernBERT\-large given temperatureTTin Equation[2](https://arxiv.org/html/2607.17382#S4.E2)\.

logit​\(sr\)\\displaystyle\\text\{logit\}\(s\_\{r\}\)=log⁡clip⁡\(sr,10−6,1−10−6\)1−clip⁡\(sr,10−6,1−10−6\)\\displaystyle=\\log\\frac\{\\operatorname\{clip\}\(s\_\{r\},\\,10^\{\-6\},\\,1\-10^\{\-6\}\)\}\{1\-\\operatorname\{clip\}\(s\_\{r\},\\,10^\{\-6\},\\,1\-10^\{\-6\}\)\}\(2\)s\\displaystyle s=11\+exp⁡\(−logit​\(sr\)T\)\\displaystyle=\\frac\{1\}\{1\+\\exp\\\!\\left\(\\frac\{\-\\text\{logit\}\(s\_\{r\}\)\}\{T\}\\right\)\}\(3\)
We determineTT\(which we foundT=2\.14555T=2\.14555\) by minimizing the log loss between the logits values and the targetyyvalues using SciPy’s`minimize\_scalar`function on the calibration set\[[56](https://arxiv.org/html/2607.17382#bib.bib56)\]\.

We note that MCGrad’s algorithm allows for correction, meaning that individual predictions might change significantly\.

## 5Evaluation & Analysis

For testing on external datasets, we use the same approach described by the workshop organizers\[[1](https://arxiv.org/html/2607.17382#bib.bib1)\]\. We use the following five metrics and the mean of all five metrics \(which we denote as the overall score\):

- •AUROC score
- •micro\-F1F\_\{1\}score: the harmonic mean between precision and recall
- •Brier Score: 1 minus the mean squared error between the predicted probability and true label
- •C@1: modified accuracy that ignores cases where predicted probability = 0\.5
- •F0\.5​uF\_\{0\.5u\}: modifiedF0\.5F\_\{0\.5\}where abstained cases \(predicted probability = 0\.5\) are considered as false negatives

Table 8:ModernBERT\-large test set results\.datasetAUROCF1F\_\{1\}C@1Brier ScoreF0\.5​uF\_\{0\.5u\}OverallBEEMO0\.85600\.93290\.88060\.90320\.93220\.9010CoCONUTS0\.97920\.97030\.94730\.96020\.97210\.9658DACTYL\-complete0\.99030\.96030\.97470\.97930\.97610\.9761DetectRL0\.93700\.89100\.88520\.90540\.89920\.9036Dolly\-Cosmopedia0\.99580\.91610\.89530\.92020\.87260\.9200LLMTrace0\.99090\.97300\.96750\.97350\.97970\.9769MAGA\-Bench0\.99920\.99670\.99450\.99550\.99640\.9965OriginalityAI0\.93220\.74650\.78200\.83710\.82730\.8250PAN 2025\-Validation0\.99840\.91590\.88190\.91740\.87270\.9172Personagen\+SE1\.00000\.98250\.97990\.98220\.97230\.9834RealDet0\.95400\.91580\.91780\.93140\.92840\.9295UChicago0\.97840\.93650\.91810\.93650\.96530\.9470PAN 2025 Test0\.9840\.9250\.890\.9210\.8990\.924PAN 2026 Test0\.9940\.9620\.9410\.9580\.9460\.96PAN 2026 ELOQUENT Test0\.9270\.9290\.8730\.910\.9610\.92Table 9:ModernBERT\-large with MCGrad post\-hoc calibration test set results\.datasetAUROCF1F\_\{1\}C@1Brier ScoreF0\.5​uF\_\{0\.5u\}OverallBEEMO0\.86190\.93370\.88260\.91120\.93500\.9049CoCONUTS0\.97970\.96670\.94200\.95930\.97850\.9652DACTYL\-complete0\.98930\.95090\.96880\.97570\.96850\.9707DetectRL0\.93840\.88690\.88300\.90850\.90540\.9044Dolly\-Cosmopedia0\.99310\.90530\.88040\.91100\.85730\.9094LLMTrace0\.99060\.97230\.96660\.97220\.97710\.9758MAGA\-Bench0\.99880\.99550\.99250\.99380\.99490\.9951OriginalityAI0\.93030\.74220\.78600\.84240\.84620\.8294PAN 2025\-Validation0\.99860\.95590\.94070\.95510\.93250\.9566Personagen\+SE1\.00000\.99090\.98970\.98870\.98560\.9910RealDet0\.95860\.91200\.91520\.93530\.93270\.9308UChicago0\.97810\.93320\.91400\.93940\.96290\.9455PAN 2025 Test0\.9840\.950\.9280\.9460\.9390\.949PAN 2026 Test0\.9930\.9750\.9620\.970\.9690\.974PAN 2026 ELOQUENT Test0\.9430\.9110\.8440\.8990\.9590\.911Table 10:DeBERTa\-V3\-large test set results\.datasetAUROCF1F\_\{1\}C@1Brier ScoreF0\.5​uF\_\{0\.5u\}OverallBEEMO0\.87800\.93020\.87850\.90410\.94180\.9065CoCONUTS0\.98190\.95180\.91800\.92960\.97850\.9519DACTYL\-complete0\.98460\.95240\.96980\.97470\.97020\.9703DetectRL0\.94650\.87590\.87560\.89400\.91240\.9009Dolly\-Cosmopedia0\.99520\.92740\.91070\.93860\.89050\.9325LLMTrace0\.99030\.97380\.96860\.97390\.98420\.9782MAGA\-Bench0\.99920\.99660\.99440\.99560\.99740\.9967OriginalityAI0\.92130\.65510\.74250\.77410\.82270\.7831PAN 2025\-Validation0\.99850\.99170\.98940\.99190\.99510\.9933Personagen\+SE1\.00000\.99730\.99700\.99760\.99580\.9975RealDet0\.98100\.93890\.94180\.95180\.96700\.9561UChicago0\.98170\.89890\.87560\.89810\.95630\.9221PAN 2025 Test0\.9870\.9750\.9650\.9690\.9870\.977PAN 2026 Test0\.9890\.8430\.7970\.8520\.930\.882PAN 2026 ELOQUENT Test0\.9820\.8650\.7740\.8220\.9410\.877Table 11:Final leaderboard results for the PAN 2026 test set for teams that achieved higher overall scores compared to the zero\-knowledge baseline\.RankTeamAUROCF1F\_\{1\}C@1Brier ScoreF0\.5​uF\_\{0\.5u\}Overall1suspiciously\-coherent0\.9890\.9760\.9650\.9650\.9800\.9752DACTYL \(ModernBERT\-large \+ MCGrad\)0\.9930\.9750\.9620\.9700\.9690\.9743plagiarism\-detector\-com\-reg20\.9970\.9550\.9490\.9580\.9820\.968\-Baseline mdok \(PAN 2025 Winner\)0\.9950\.9630\.9460\.9510\.9840\.9684dsgt\-pan\-260\.9810\.9070\.8730\.8850\.9610\.9215ydong0\.9300\.9280\.8860\.9150\.8960\.9116turingteam0\.9570\.8510\.8460\.8820\.9250\.8927writerslogic\-inc0\.8910\.9020\.8530\.8910\.8990\.8878a\-a\-detection0\.8520\.8850\.8260\.8480\.8800\.858\-Baseline PPMd0\.7830\.8650\.7830\.8100\.8280\.8149ak\-ys0\.9110\.7740\.7230\.7540\.8910\.81110ikr30\.8140\.8560\.7490\.7790\.7880\.79711radar0\.7720\.8000\.7220\.8050\.8390\.78812sinai0\.6240\.8560\.7480\.7710\.7880\.75713egrantha\-ai0\.5000\.8560\.7490\.7490\.7880\.728\-Baseline Zero\-knowledge0\.5000\.8560\.7490\.7490\.7880\.728Both uncalibrated models \(ModernBERT\-large and DeBERTa\-V3\-large\) have relatively high AUROC scores, even across OOD test sets — for example, we excluded DetectRL during training, but both models achieved an AUROC score of at least 0\.93, highlighting some discrimination capacity\. ModernBERT\-large has an advantage in the overall score; on the PAN test sets, it achieves an overall score of at least 0\.92\. However, DeBERTa\-V3\-large shows more robustness in terms of AUROC score — on the ELOQUENT test set, it achieves an AUROC score of 0\.982 in contrast with ModernBERT\-large’s 0\.927\. Our results indicate that a high discrimination capacity can hide miscalibrated scores — a model that achieves high AUROC is not guaranteed to have outputs that are calibrated\. This discrepancy highlights the primary advantage of evaluating across multiple metrics\.

ModernBERT\-large with MCGrad yields improvements in the overall score in the PAN 2025 and 2026 test sets compared to the base model\. However, it fails to give an improvement on the ELOQUENT test set, suggesting that the multicalibration approach is sensitive to distribution shifts\. We confirm this on the 12 external test sets: we see that using the MCGrad and Bayesian BERT\-tiny models shows an increase in the overall score for six of the test sets\. The increase in score for the PAN test sets \(excluding ELOQUENT\) might indicate that those test sets represent a distribution shift that our MCGrad model covers\.

In comparison to other classifiers, our ModernBERT\-large and MCGrad classifier ranks second in overall score and is one of two models to beat the PAN 2025 winning system\. The MCGrad system ranks second in AUROC,F1F\_\{1\}, C@1,F0\.5​uF\_\{0\.5u\}, and first in Brier score among competing teams\.

## 6Conclusion

Our work applies Bayesian neural networks \(as a classification head\) to help select candidate texts to use for downstream training\. Additionally, these same classifiers can help improve calibration of larger, non\-Bayesian models via their uncertainties \(standard deviations\)\. We also point out that both ModernBERT\-large and DeBERTa\-V3\-large have strong generalization capacities given their high AUROC scores across OOD test sets\. Using the Bayesian BERT\-tiny models’ uncertainties as inputs for an MCGrad model demonstrates mixed results on external test sets but an increase in the overall score on the PAN test sets\. Note that our Bayesian BERT\-tiny hyperparameters for the BNN layer were manually tuned — we suspect that hyperparameter optimization via some proxy uncertainty metric could lead to better uncertainty estimates, which could improve the MCGrad model\.

Future work might explore applying this Bayesian data filtering technique and EXM on other text classification tasks, such as prompt safety detection\.

## Resources Used

Training Bayesian BERT\-tiny models and inference for the classifiers was done on a NVIDIA GB10\. We used Lambda’s GH200 instances for training ModernBERT\-large and DeBERTa\-V3\-large\[[57](https://arxiv.org/html/2607.17382#bib.bib57)\]\.

## Declaration on Generative AI

The author has used Grammarly to perform grammar checking in preparing this paper\.

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