On Prefix-tuning for Lightweight Out-of-distribution Detection
Year: 2023

Abstract:
Out-of-distribution (OOD) detection, a fundamental task vexing real-world applications, has attracted growing attention in the NLP community. Recently fine-tuning based methods have made promising progress. However, it could be costly to store fine-tuned models for each scenario. In this paper, we depart from the classic fine-tuning based OOD detection toward a parameter-efficient alternative, and propose an unsupervised prefix-tuning based OOD detection framework termed PTO. Additionally, to take advantage of optional training data labels and targeted OOD data, two practical extensions of PTO are further proposed. Overall, PTO and its extensions offer several key advantages of being lightweight, easy-to-reproduce, and theoretically justified. Experimental results show that our methods perform comparably to, even better than, existing fine-tuning based OOD detection approaches under a wide range of metrics, detection settings, and OOD types.

heading: 1 Introduction
text: Detecting out-of-distribution (OOD) inputs is crucial for real-world machine learning systems deployed in the wild (Hendrycks and Gimpel, 2017). For example, for a task-oriented dialogue system designed for particular domains, it can be challenging to ensure that the system is only exposed to utterances from the same distribution as the training utterances, i.e., in-distribution (ID) utterances. Therefore, it would be desirable for the system to detect OOD utterances and return safe responses.
Pretrained language models (PLMs) have been a de facto choice for OOD detection in the NLP community, and many fine-tuning based methods have achieved promising results (Arora et al., 2021; Podolskiy et al., 2021; Lang et al., 2022). Despite being effective, these methods require storing finetuned models for each scenario, which could be prohibitively expensive. This begs the following
question: Can we achieve effective OOD detection in a parameter-efficient way, i.e., keep PLM parameters frozen?
To achieve this goal, an unsupervised PrefixTuning based OOD detection framework (PTO) is proposed in this paper. The key idea of PTO is intuitive: an in-distribution specific prefix, optimized with the training data via maximum likelihood, could steer PLMs to assign higher likelihoods to ID samples than PLMs without the prefix, while OOD samples should be assigned lower likelihood. Thus we propose to use the likelihood change triggered by the prefix to detect OOD — samples whose improvement is not obvious (e.g., less than a predefined threshold). Note that the training process of PTO does not involve the sample labels, expanding its application to situations where obtaining labeled data is cost-prohibitive.
Going beyond the unsupervised setting, we extend our framework to fully leverage optional supervised data. Specifically, we design two extensions to take advantage of training data labels and incorporate the accessible targeted OOD data encountered in the system deployment environment. These practical and comprehensive extensions could further improve the PTO performance.
In a nutshell, PTO and its extensions offer compelling advantages of being: (1) lightweight (i.e., without tuning the PLM parameters), (2) easy-toreproduce (i.e., no additional hyper-parameters other than prefix-tuning itself), and (3) theoretically justified (proofed in Section 3).
Experimental results reveal the effectiveness of our methods in detecting both semantic shift and background shift OOD sentences (Arora et al., 2021). Especially for the background shift, PTO surpasses the previous best baseline by only tuning 10M parameters. Our code and data will be available at https://github.com/ 1250658183/PTO.
In summary, we make the following contribu-
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tions:
• To the best of our knowledge, we are the first to explore lightweight OOD detection and propose PTO, an unsupervised framework without tuning PLM parameters.
• Two extensions of PTO are proposed to make full use of optional training labels and targeted OOD data to boost OOD detection performance.
• We show that our proposed parameter-efficient methods could catch up to strong fine-tuned baselines and even surpass them in background shift OOD detection.

heading: 2 Problem Setup
text: Given a collection of training sentences Xtrain and corresponding labels Ytrain, we assume they are sampled from in-distribution P in(X,Y ). The objective of OOD detection is to decide whether a test sentence is from P in(X,Y ) (ID) or not (OOD) (Hendrycks and Gimpel, 2017).
We follow Arora et al. (2021) to classify the types of OOD data as either semantic or background shift based on whether the label space remains the same. Semantic shift happens when we encounter sentences with unknown labels, e.g., a sentiment classifier trained with positive and negative movie reviews receiving a neutral text (Example 3 in Table 1). While background shift is for texts with known labels but different domains or styles, e.g., the classifier for movie reviews receiving restaurant reviews (Example 4, 5 in Table 1).
The goal of all OOD detection methods is to design a score function S(x) that maps each input x to a single scalar that is distinguishable between ID and OOD. Mathematically, the OOD detector G can be described as:
G(S(x), δ) = { ID S(x) ≥ δ, OOD S(x) < δ,
(1)
where δ is the predefined threshold, and can be adjusted according to the user’s requirements. For instance, the threshold is chosen to ensure that the recall rate of ID is 95%.

heading: 3 Approach
text: In this section, we start by presenting our proposed lightweight framework PTO (Section 3.1), then introducing two extensions of PTO to leverage optional training data (Sections 3.2 to 3.4). Finally, we make a summary in Section 3.5.
3.1 Prefix-tuning based OOD detection (PTO) Our motivation follows prefix-tuning that proper prefix vectors can steer PLMs to generate the desired sentences (Li and Liang, 2021), so we can find in-distribution specific prefix θin to trigger PLMs to be prone to generating ID sentences, i.e., assigning higher likelihoods to ID sentences than before. Considering that the likelihood sum for all sentences (including ID and OOD) is always 1, θin would trigger PLMs to assign lower likelihood to OOD sentences than before. Thus the likelihood change caused by the prefix θin could detect OOD sentences whose likelihood improvement is insignificant.
In detail, we first follow Li and Liang (2021) to prepend randomly initialized θ to all PLM layers (pre-trained GPT-2 (Radford et al., 2019) in our case). Then we optimize it by maximizing the likelihood of training sentences, whilst the parameters of the PLM θplm remain frozen:
θin = argmaxθ ∑
xi∈Xtrain log p(xi; θ, θplm). (2)
With θin, we define our PTO score function for OOD detection as follows:
SPTO(x) = p(x; θin, θplm)/p(x; θplm), (3)
where p(x; θplm) is the likelihood of x from the vanilla PLM, i.e., without the prefix vectors θin. Lastly, we can identify whether x is OOD by replacing S(x) with SPTO(x) in Equation (1).
Theoretical insights of SPTO(x): according to the Bayes’ rule, SPTO(x) is proportional to p(ID|x) — x with a high SPTO can be interpreted as data with a high probability of being ID. Specifically, according to Bayes’ rule, we can rewrite p(ID|x) as follows:
p(ID|x) = p(x|ID)p(ID) p(x) ∝ p(x|ID) p(x) . (4)
We argue that p(x; θplm) (the denominator of SPTO(x)) is to estimate p(x) as PLMs are trained with various large corpora. With in-distribution specific prefix θin prepended, p(x; θin, θplm) (the numerator of SPTO(x)) is to estimate p(x|ID). Thus their quotient is proportional to p(ID|x).
3.2 PTO with labels (PTO + Label) Using θin to guide the generation of all sentences Xtrain would increase the difficulty of the optimization. If training data labels Ytrain are available, how can we use them to address this challenge? An intuitive solution is to randomly initialize prefix θyin for each training label y, and optimize θ y in with corresponding label sentences, so that θyin can focus on guiding the generation of y sentences: θyin = argmaxθ ∑
xi∈Xtrain∧yi=y log p(xi; θ, θplm).
(5) With θyin, we define SPTO+Label as follows:
SPTO+Label(x) = max y
p(x; θyin, θplm)/p(x; θplm).
(6)
Theoretical insights of SPTO+Label(x): it is proportional to maxy p(y|x)— a high SPTO(x) indicates x has a high probability of being one of the training labels. In particular, with labelspecific prefix θyin prepended, p(x; θ y in, θplm) is to estimate p(x|y). Recall that p(x; θplm) is to estimate p(x). With the assumption that the label
distribution is uniform, SPTO+Label(x), the estimation of maxy p(x|y)/p(x), is proportional to maxy p(y|x).
3.3 PTO with targeted OOD data (PTO + OOD)
If we can access some targeted OOD data Xood in the training process, what can we do to incorporate them into PTO to boost OOD detection performance? This scenario has a realistic possibility, such as in a data stream where the OOD data collected by the current detector can be used to refine it. Besides, some benchmark datasets, such as CLINC150 (Larson et al., 2019), also provides some OOD sentences for training.
Our hypothesis is that targeted out-ofdistribution specific prefix θout could trigger PLMs to be less prone to generating ID sentences than vanilla PLMs. So the likelihood improvement between θin and θout is more obvious for ID sentences. Accordingly, we update PTO with the following statistic:
SPTO+OOD(x) = p(x; θin, θplm)/p(x; θout, θplm), (7)
where θout is optimized with targeted OOD data:
θout = argmaxθ ∑
xi∈Xood log p(xi; θ, θplm). (8)
Theoretical insights of SPTO+OOD(x): it is proportional to p(ID|x)/p(TOOD|x) — a high
SPTO+OOD(x) can be interpreted that compared with TOOD (targeted OOD), x is more likely to belong to ID. Specifically, with θout prepended, p(x; θout, θplm) is to estimate p(x|TOOD). Remember that p(x; θin, θplm) is to estimate p(x|ID). Rewriting p(x|ID)/p(x|TOOD), we obtain:
p(x|ID) p(x|TOOD) = p(x|ID) p(x)
p(x)
p(x|TOOD)
∝ p(ID|x) p(TOOD|x) . (9)
3.4 PTO with both label and targeted OOD data (PTO + Label + OOD)
The proposed two extensions are orthogonal. We can use them simultaneously in practice if we can access both of them:
SPTO+Label+OOD(x) =
max y
p(x; θyin, θplm)/p(x; θout, θplm).
(10)
Theoretical insights of SPTO+Label+OOD(x): combining SPTO+Label(x) and SPTO+OOD(x), it is simple to prove that SPTO+Label+OOD(x) is proportional to maxy p(y|x)/p(TOOD|x). A high SPTO+Label+OOD(x) can be interpreted that compared with targeted OOD, x is more likely to belong to one of the training labels.

heading: 3.5 Summary
text: The advantages of PTO and its extensions are numerous:
• Lightweight: All of them require only a small number of continuous prefix vectors to be tuned and stored, without modifying PLM parameters.
• Easy-to-reproduce: Besides the hyperparameters of prefix-tuning (e.g., the prefix length), the training and inference process of all methods do not introduce any new hyper-parameters.
• Theoretically justified: Through the lenses of Bayes’ rule, we provide theoretical insights to understand their effectiveness.
An overview of PTO is depicted in Figure 1. We also summarize the training and inference for PTO and its extensions in Algorithm 1.
Algorithm 1 OOD detection using PTO Input: Training dataset Xtrain, test sample x.
Optional: training label Ytrain, targeted OOD Xood. # Training process
1: if Ytrain is available then 2: for each label y do 3: Train θyin using Equation (5) 4: end for 5: else 6: Train θin using Equation (2) 7: end if 8: if Xood is available then 9: Train θout using Equation (8)
10: end if # Inference process 11: if both θout and θyin are unavailable then 12: Calculate SPTO using Equation (3) 13: else if only θyin is available then 14: Calculate SPTO+Label using Equation (6) 15: else if only θout is available then 16: Calculate SPTO+OOD using Equation (7) 17: else 18: Calculate SPTO+Label+OOD using Equa-
tion (10) 19: end if

heading: 4 Experimental Setup

heading: 4.1 Datasets
text: We evaluate our methods for detecting semantic shift and background shift OOD:
• For semantic shift, we follow Podolskiy et al. (2021) to use the challenging CLINC150 dataset (Larson et al., 2019). CLINC150 covers utterances across various intents in voice assistants. OOD utterances are those with unknown intents. As aforementioned before, it also provides OOD utterances for training.
• For background shift, we follow Arora et al. (2021) to use IMDB (Maas et al., 2011) as ID and Yelp Polarity (Zhang et al., 2015) as OOD. IMDB is a long movie review dataset and Yelp Polarity is a business review dataset. Since both IMDB and Yelp Polarity do not provide the validation dataset, to perform early stopping, we sample 10000 sentences from IMDB unlabeled dataset and 10000 sentences from Yelp as the validation dataset.
Table 2 provides the summary statistics.

heading: 4.2 Baselines
text: We introduce the strong supervised method Mahalanobis (Podolskiy et al., 2021; Lee et al., 2018b), Energy and Energy + OOD (Liu et al., 2020; Ouyang et al., 2021), MLS (Vaze et al., 2022) as baselines. With a classifier trained with ID sentences and labels,
• Mahalanobis defines a score function based on the Mahalanobis distance between the input representation and the nearest class-conditional Gaussian distribution.
• Energy uses the sum of the exponential of the classifier logit to detect OOD.
• Energy + OOD uses targeted OOD sentences to shape the energy gap between ID and OOD sentences during the training stage.
• MLS uses the maximum logit of the classifier to detect OOD.
We also introduce competitive unsupervised method IMLM + BCAD + MDF (Xu et al., 2021), PPL (Arora et al., 2021), LLR (Gangal et al., 2020; Ren et al., 2019):
• IMLM + BCAD + MDF also utilizes Mahalanobis distance as features, and two domainspecific fine-tuning approaches are explored to boost the performance.
• PPL uses ID sentences to fine-tune the pretrained GPT-2 model and uses the perplexity to detect OOD.
• LLR trains a left-to-right LSTM language model (Sundermeyer et al., 2012) with ID sentences and trains a second language model with perturbed ID sentences. The likelihood ratio between these two language models is used to detect OOD.

heading: 4.3 Metrics
text: We follow Podolskiy et al. (2021); Liu et al. (2020) to use four common OOD detection metrics to measure the performance:
• AUROC refers the area under the true positive rate-false positive rate curve.
• FPR95 refers the false positive rate(FPR) when the true positive rate(TPR) is 95%.
• AUPR refers the area under the precision-recall curve. AUPR In (or Out) indicates ID (or OOD) data are treated as positive samples.

heading: 4.4 Implementation details
text: For all methods, the selection of hyper-parameters and early stop strategy are based on AUROC on the validation set.
For our framework, we use the huggingface implementation of GPT2-base (Wolf et al., 2020) as the PLM and the prefix-tuning implementation is derived from OpenPrompt (Ding et al., 2022). All results are averaged over 5 different seeds. The prefix length has an essential impact on the results, so we search it from {10, 50, 100, 200, 300, 400, 500}. For PTO + Label, the total prefix length 300 is equally allocated to each label. For PTO + OOD, the OOD prefix length is also set to 300. The hyper-parameters of PTO + Label + OOD are consistent with PTO + OOD and PTO + Label.
For supervised-based baselines, we use pretrained BERT (Devlin et al., 2019) as the encoder, and tune it with cross-entropy loss. For Energy, we follow Liu et al. (2020) to set T as 1. We adopt mean pooling to obtain the sentence representation as we empirically find that mean pooling is better than [CLS] with MLP used in Ouyang et al. (2021).
For IMLM + BCAD + MDF, we obtain the results from their open-source implementation. For PPL, we also use GPT2-base as the backbone. For LLR method, we follow Gangal et al. (2020) and use an LSTM with 1 layer and 300 hidden size. Embeddings are initialized with 100D Glove (Pennington et al., 2014). To train the background model, we permute 50% of every sentence by replacing the word with the random one in the vocabulary.

heading: 5 Main Results
text: Table 3 shows all method results on OOD detection. We can observe that:
• PTO works better than unsupervised baselines on all datasets and metrics. For CLINC150, PTO reduces the FPR95 by 4.5% compared to the best unsupervised baseline, and PTO consistently outperforms the baseline by 6.4% on IMDB-Yelp. Figure 2 shows the PTO and PPL score histogram distributions. We can see that PTO is more distinguishable between ID and OOD than PPL, resulting in more effective OOD detection. To gain further insights, we also test prefix-equipped PPL, and its performance is also inferior to PTO (38.4% FPR95 on CLINC150).
• PTO + Label (+ OOD) outperforms supervised baselines on background shift by a large margin and achieves competitive performance on semantic shift. Note that all supervised methods require tuning pretrained language models,
whereas our methods do not, so they provide effectiveness while still being lightweight (PTO + Label + OOD only tunes 20M parameters, less than 20% of the supervised methods). We also generalize PTO + Label + OOD to GPT2medium, and it can achieve better performance (14.8% FPR95 on CLINC150).

heading: 6 Discussion

heading: 6.1 Effect of the label extension
text: PTO + Label provides a performance boost over PTO with the same tuning parameter number. As we can observe from Table 4, the improvement
is more pronounced on the challenging dataset CLINC150, where we show a 1.5% improvement on the AUROC. Notably, PTO + Label has the same tuning parameter number with PTO (i.e., both are equipped with 300 prefix vectors).
PTO + Label can trigger the GPT-2 to assign higher likelihoods to ID sentences than PTO. Specifically, equipped with the label extension for PTO, the average log PPL of ID sentences on the validation set degrades from 3.01 to 2.23 on CLINC150, and from 3.72 to 3.70 on IMDB-Yelp. The more pronounced effect on CLINC150 is due to the larger label number (150 versus 2).
PTO + Label can also lead to faster convergence. As empirically shown in Figure 3, the best epoch for PTO + Label is 9, while for PTO is 16. The reason is intuitive that with the label extension, each label sentences can focus on optimizing its own prefix.

heading: 6.2 Effect of the OOD extension
text: PTO + OOD is more effective than PTO + Label on CLINC150. Table 4 shows that PTO + OOD outperforms PTO + Label by 1.1% (AUROC) on CLINC150. We conjecture that equipping training data with targeted OOD data leads to a smaller distribution gap between training and test data than with labels.
PTO + OOD keeps being easy-to-reproduce.
The hyper-parameters of training OOD prefixes are consistent with ID prefixes, so PTO + OOD does not require any new hyper-parameter. In contrast, using Energy + OOD requires great effort in hyper-parameter tuning, such as two margin hyperparameters for the auxiliary hinge loss and the loss weight (Liu et al., 2020).

heading: 6.3 Effect of the prefix length
text: The prefix length is a key hyper-parameter of PTO, and previous work shows that the optimal prefix length varies from task to task (Li and Liang, 2021). Inspired by this, we evaluate how the prefix length affects the OOD performance by setting it from 10 to 500. Results from Figure 4 show that as a whole, performance increases as the prefix length increases up to 300 and then decreases. We think this is reasonable, as longer prefixes tend to overfit the training data, and further degrade the validation performance.

heading: 6.4 Error analysis
text: The OOD sentences misclassified by PTO always have the same preceding tokens as ID sentences. Specifically, when examining OOD sentences undetected by PTO on CLINC150 (i.e., those with higher SPTO), we observe that their first two tokens at the sentence beginning are often found in the ID sentences (see Table 5). The first two tokens further lead to higher OOD sentence scores *, as shown in Figure 5.
The underlying reason is that PTO leverages the left-to-right GPT-2 to estimate the sentence like-
*The logSPTO score of sentence x is summed over the score of each token wi in x: logSPTO(x) =∑
wi∈x log p(wi|w<i; θin, θplm)− log p(wi|w<i; θplm)
lihood. The following tokens are invisible when inferring the likelihood of preceding tokens. Therefore, there is no difference between ID and OOD in such case, and PTO will assign OOD preceding tokens higher scores as it does to ID. We leave its solution to future work.

heading: 6.5 Effect of the prefix-tuning based classifier for OOD detection
text: To thoroughly investigate the potential of prefixtuning on OOD detection, we also carried out an experiment based on the prefix-tuning based classifier (Ding et al., 2022; Liu et al., 2021) on CLINC150 dataset. Particularly, we use the utterance’s intent as its label words to construct the manual verbalizer (Schick and Schütze, 2021). Meanwhile, we modify the original input x to the form of template T (x) = [PREFIX]x[MASK], then classify x based on the probabilities of [MASK] being each label words. Table 6 shows the performance of Energy and MLS scores based on the classifier. We can observe that they perform less well than PTO + Label. We argue that a limitation of this strategy is its dependence on the design of the template and verbalizer, while our method PTO + Label does not require them.

heading: 7 Related Work

heading: 7.1 Out-of-distribution detection
text: Out-of-distribution has gained increasing attention in both NLP and CV recently (Lang et al., 2022; Yang et al., 2022; Sun et al., 2022; Sehwag et al., 2021; Arora et al., 2021). Promising unsupervised (Xu et al., 2021; Arora et al., 2021; Gangal et al., 2020; Ren et al., 2019), supervised with ID labels (Podolskiy et al., 2021; Liu et al., 2020; Vaze et al., 2022), and supervised with OOD data (Liu et al., 2020; Lee et al., 2018a) methods have been pro-
posed. Curious readers may refer to some well established surveys (Yang et al., 2021; Salehi et al., 2022). Unlike prior works, our work focuses on exploring lightweight OOD detection, i.e., without modifying PLM parameters. We propose PTO to fulfill this aim and demonstrate its effectiveness through comprehensive experiments.

heading: 7.2 Prefix-tuning
text: Prefix-tuning, a member of the prompt-based tuning family (Liu et al., 2022a), can trigger the desired generation of PLMs by only optimizing small continuous prefix vectors (Li and Liang, 2021). It has achieved desirable performance in many natural language generation tasks (Liu et al., 2022b; Zhao et al., 2022; Ma et al., 2022), and natural language understanding tasks (Liu et al., 2021; Yang and Liu, 2022). However, it still remains a mystery whether prefix-tuning can detect OOD inputs as other fine-tuned models. To the best of our knowledge, we are the first to explore the potential of prefix-tuning for the OOD detection task, and propose approaches for both unsupervised and supervised settings.

heading: 8 Conclusion
text: In this paper, we shed light on lightweight OOD detection, which was largely overlooked in the literature. Our work bridges the gap by proposing PTO, an unsupervised prefix-tuning based framework. Moreover, we extend PTO to fully leverage the optional training labels and targeted OOD sentences. Our methods have the key advantages of being lightweight, easy-to-reproduce, and theoretically justified. We reveal the effectiveness of PTO and its extensions on both semantic and background shift OOD detection. We hope our work could serve as a valuable starting point for future work and inspire them to explore more possibilities of lightweight OOD detection.
Limitations
We consider the current work has the following two limitations:
• We design our lightweight OOD detection framework based on the prefix-tuning paradigm. Nevertheless, there may be other techniques to achieve this goal, which requires further exploration.
• For PTO + Label, each label focuses on its own prefixes, suffering from prefix redundancy problem. One can design share prefixes across different labels to trigger label-invariant sentence features.

heading: Acknowledgments
text: We would like to thank the anonymous reviewers for their insightful comments. Zhen Wu is the corresponding author. Yongchang Cao and Yuan Gao contribute equally. Yawen would like to thank Dingjie Song and Siyu Long for their constructive suggestions. This work is supported by NSFC Projects (Nos. 62206126, 61936012 and 61976114).

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heading: 3 C1. Did you report the number of parameters in the models used, the total computational budget
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The Responsible NLP Checklist used at ACL 2023 is adopted from NAACL 2022, with the addition of a question on AI writing assistance.

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heading: Future Work
text: We hope our work could serve as a valuable starting point for future work and inspire them to explore more possibilities of lightweight OOD detection. Limitations
We consider the current work has the following two limitations:
• We design our lightweight OOD detection framework based on the prefix-tuning paradigm. Nevertheless, there may be other techniques to achieve this goal, which requires further exploration. • For PTO + Label, each label focuses on its own prefixes, suffering from prefix redundancy problem. One can design share prefixes across different labels to trigger label-invariant sentence features