Title: I Don't Know: Explicit Modeling of Uncertainty with an [IDK] Token
Venue: NeurIPS 2024
Accepted: yes
Keywords: LLMs

Factuality

Uncertainty

Factual Knowledge

Pretraining
Abstract: Large Language Models are known to capture real-world knowledge, allowing them to excel in many downstream tasks. Despite recent advances, these models are still prone to what are commonly known as hallucinations, causing them to emit unwanted and factually incorrect text. In this work, we propose a novel calibration method that can be used to combat hallucinations. 
We add a special [IDK] (“I Don't Know”) token to the model's vocabulary and introduce an objective function that shifts probability mass to the [IDK] token for incorrect predictions. 
This approach allows the model to express uncertainty in its output explicitly. 
We evaluate our proposed method across multiple model architectures and factual downstream tasks.
We find that models trained with our method are able to express uncertainty in places where they would previously make mistakes while suffering only a small loss of encoded knowledge. We further perform extensive ablation studies of multiple variations of our approach and provide a detailed analysis of the precision-recall tradeoff of our method.

I Don't Know: Explicit Modeling of Uncertainty with an [IDK] Token

Abstract

Large Language Models are known to capture real-world knowledge, allowing them to excel in many downstream tasks. Despite recent advances, these models are still prone to what are commonly known as hallucinations, causing them to emit unwanted and factually incorrect text. In this work, we propose a novel calibration method that can be used to combat hallucinations. We add a special [IDK] ('I don't know') token to the model's vocabulary and introduce an objective function that shifts probability mass to the [IDK] token for incorrect predictions. This approach allows the model to express uncertainty in its output explicitly. We evaluate our proposed method across multiple model architectures and factual downstream tasks. We find that models trained with our method are able to express uncertainty in places where they would previously make mistakes while suffering only a small loss of encoded knowledge. We further perform extensive ablation studies of multiple variations of our approach and provide a detailed analysis of the precision-recall tradeoff of our method. 1

1 Introduction

Large Language Models (LLMs) are pretrained on massive amounts of text to understand and generate language. This training text includes a large portion of written human knowledge such as books, newspapers, Wikipedia, and scientific articles. During this process, LLMs also retain a remarkable amount of the information seen during pre-training, allowing them to encode real-world knowledge in their parameters and act as knowledge bases [Petroni et al., 2019, Roberts et al., 2020, Cohen et al., 2023a, Pan et al., 2023]. Owing to this phenomenon, LLMs can be used in multiple settings requiring this real-world knowledge, such as closed-book question answering [Brown et al., 2020, Roberts et al., 2020] and information retrieval [Tay et al., 2022].

Despite the popularity of LLMs, they are prone to what is commonly referred to as hallucinations, which severely hinder their performance and reliability [Ji et al., 2023, Manduchi et al., 2024]. Examples of hallucinations include factually incorrect [Maynez et al., 2020, Devaraj et al., 2022, Tam et al., 2023], inconsistent [Elazar et al., 2021, Mündler et al., 2023], self-contradicting [Cohen et al., 2024] or non-attributable text [Bohnet et al., 2022, Rashkin et al., 2023, Yue et al., 2023].

A prominent method employed to combat such hallucinations is model calibration [Guo et al., 2017a, Brundage et al., 2020], which aims to calibrate the confidence of model predictions such that they

Eden Biran

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are better aligned with their quality. This calibration allows LLMs to explicitly express uncertainty, allowing them to caveat their responses or even refrain from answering. Although many of the proposed methods do lead to an improvement in model calibration [Geng et al., 2024], they have still been found to be lacking [Chen et al., 2023].

In this work, we propose a novel objective function that allows LLMs to explicitly express uncertainty. We add a new special [IDK] ('I Don't Know') token to the vocabulary of the language model. During a continued pretraining phase, we modify the conventional cross-entropy objective to express uncertainty in a next-token prediction as probability mass on the [IDK] token. Specifically, each time the model fails to predict the gold label, some of the probability mass of the target is shifted to the [IDK] token based on an Uncertainty Factor we calculate based on the predicted logits. We refer to our method as IDK -tuning.

Our proposed IDK objective differs from previous work as we intervene during a continued pretraining phase with the language modeling task. Crucially, we do not rely on any labeled data. Moreover, this allows the model to be later finetuned on specific tasks while the model has already learned to express uncertainty.

We conduct IDK -tuning using various model architectures and sizes, and then evaluate them on diverse factual downstream tasks. Our results show a large increase in factual precision of IDK -tuned models while causing only a small decrease in recall of factual knowledge that was contained in the base model. We conduct extensive ablation studies for the individual components of our IDK objective and analyze its effect on optimization dynamics. We finally show that IDK -tuning does not harm the general language modeling ability of models, such as long text generation.

In summary, our contributions include:

We propose a novel IDK objective applied during pretraining which models uncertainty in a model's prediction as probability mass put on a special [IDK] token.

We evaluate our objective using a large range of base models with different architectures and model sizes, and confirm the efficacy of IDK -tuning on a range of factual answering downstream tasks.

We extensively analyze individual components of our objective and its effect on general language modeling ability.

2 IDK -tuning

Our goal is to train a model to be aware of its unawareness and to effectively express it. For this, we introduce a new special token to its vocabulary: [IDK] . The model is intended to express uncertainty by putting probability mass on the [IDK] token in its predictions. In practice, we adapt the model's pretraining objective, aiming to teach it to use the [IDK] token effectively. Our objective does not require annotations of uncertainty or specifically crafted datasets (e.g., Q&A). Instead, we leverage the uncertainty captured by the pretraining objective on its pretraining data and use it to encourage probability mass on the [IDK] token in cases of uncertainty. We hypothesize that this generalizes to uncertainty expressed on downstream tasks like Q&A, which we experimentally verify later on.

We next describe in detail the technicalities of the [IDK] token and our training method.

2.1 The [IDK] token

The purpose of the new token is to represent lack of knowledge. Ideally, whenever the model would have been making a mistake, we want it to instead predict this token. That is, rather than generating a wrong token, we would like to model to generate the [IDK] token, as a means of conveying its uncertainty. We can consider this as a model expressing its lack of knowledge and may then choose to ignore its outputs. The more the model opts for this token rather than predicting the wrong answer, the more we improve the model's precision.

For instance, let us consider the setup of Factual Sentence Completion. In this setup, the model receives an incomplete sentence as an input and is expected to complete it factually. For example, a valid input would be 'Paris is the capital of' , and a factually correct output by the model would be 'France' . In this setup, if the model was going to predict 'Germany' , using the [IDK] token instead increases factual precision by refusing to answer a question where the answer would have been wrong. Naturally, almost universally predicting [IDK] indiscriminately may yield high precision but is not helpful. Therefore, taking into account the recall of factually correct answers is crucial in evaluating our method. We analyze both the precision and recall of our method in Section 4.

We add this new [IDK] token to the model's vocabulary and initialize its embedding randomly. The embedding is optimized alongside the rest of the model's parameters during training. We next describe our proposed IDK objective.

2.2 The IDK Training Objective

Wemodify the conventional cross-entropy objective between the softmax distribution over the model's prediction and the correct answer, such that each time the model fails to predict the correct token, it is encouraged to instead put some probability mass on the [IDK] . This encouragement is modulated by an Uncertainty Factor denoted as λ ∈ [0 , 1] that is larger the more uncertain the model is and exactly 0 when the model predicts the correct token.

We now define our modified cross-entropy objective. We use [gold] to denote the gold token (correct target) for each prediction. We denote the probability mass assigned to an arbitrary token [tok] in the prediction of a model as prob ( y t = [tok] | y <t , x ) We further use 1 [IDK] to denote a one-hot target vector with one at the index of the [IDK] token. Per convention, y denotes the one-hot target vector for the [gold] token. The modified objective is defined as follows:

If the model is uncertain in its prediction, the target is shifted away from predicting the [gold] token and towards the [IDK] token. This is modulated by λ . Note that in case the model makes the correct prediction, λ = 0 and L IDK therefore reduces to the regular cross-entropy loss. When the model is correct, L IDK simply provides the signal for the correct prediction. When the model is incorrect, L IDK provides both the signal for the correct prediction and a signal to express uncertainty. We now detail the construction of the Uncertainty Factor λ .

The Uncertainty Factor . λ is constructed as a scalar weight with λ ∈ [0 , 1] . Intuitively, we want λ to be close to 1 when the model is very uncertain and 0 when the model makes the correct prediction. Based on this, we define λ as one minus the probability mass on the gold token divided by the maximum probability mass put on any token:

where Π ∈ [0 , 1] is a hyperparameter to control the influence of our objective. When the gold token probability is close to the maximum probability, λ is close to 0. If the model makes a correct prediction (the gold token is assigned the maximum probability), λ is 0, thereby reducing Equation 1 to the regular cross-entropy loss. When the gold token probability is much lower than the maximum probability, λ is close to 1, which translates to shifting almost all the probability mass of the target in Equation 1 to the [IDK] token. Π specifies the upper bound of target probability mass that can be shifted to the [IDK] token. For example, Π = 1 2 means that at most half of the probability mass

in the target can be shifted to [IDK] while the rest remains with the gold token. In practice, we do not tune this and set Π = 1 2 . This prevents the [IDK] token from ever becoming a better prediction than the gold token while still providing enough signal to predict [IDK] for uncertain predictions. We perform an ablation of the influence of Π in Section 4.2.

Uncertainty Regularization. An important consideration in designing the L IDK objective is to prevent a collapse where the model is miscalibrated with too many false positive [IDK] s, putting too much probability mass on [IDK] , although it could have made the correct prediction. Therefore, we add the following anti-false positive regularization to our objective:

which is exactly the binary cross-entropy objective with 0 as the target and the probability mass assigned to the [IDK] as the input. We only add this regularization objective when the model's prediction is correct. This aims to minimize the [IDK] token's probability mass the model learns to predict in cases it knows the answer - thus teaching it to minimize the use of this token in cases it is more certain, and is designed to reduce a decrease of its recall. We perform an ablation of L FP-reg in Section 4.2.

The final loss. Combining all objectives, our final IDK objective is therefore:

3 Experiments

We use our proposed IDK objective to tune various pretrained models to use the new [IDK] token. We dub this process IDK -tuning. We then report the results of the IDK -tuned models on commonly used factual benchmarks, showing that our method improves factuality while paying only a small price in terms of knowledge recall. We also show that model size plays a significant role in the success of our method to create an effective uncertainty-aware model.

We employ continual training of pretrained models rather than training from scratch for two reasons: (i) the computational cost of training models that perform competitively on current benchmarks from scratch would be prohibitive, and (ii) starting from a model that is already a strong language modeler helps during the optimization process by providing a rough initial calibration that we utilize to derive the Uncertainty Factor .

3.1 IDK -tuning Setup

We use bert-base-cased [Devlin et al., 2019], mistralai/Mistral-7B-v0.1 [Jiang et al., 2023], and EleutherAI/pythia-70m -2.8B [Biderman et al., 2023] for our base models for IDK -tuning. For IDK -tuning Mistral-7B-v0.1 , we train on data randomly sampled from The Pile [Gao et al., 2020] 2 with a context length of 4,096. We use example packing to fill the entire context length. We use a maximum learning rate of 4 × 10 -5 with a linear warmup for 10% of the training steps and a cosine decay down to 2 × 10 -6 . We use a batch size of 256, weight decay of 0.05, gradient clipping of 1.0 and AdamW betas (0.9, 0.95). We train for 1,024 optimizer steps resulting in a total of 1B training tokens. For the pythia-70m -2.8B models, we use the same hyperparameters but reduce the context length to 2,048 to match the model's positional embeddings. We use bfloat16 and float16 mixed-precision training to match Mistral-7B-v0.1 and pythia-410m -2.8B pretraining, respectively. For pythia-70m , pythia-160m and bert-base-cased , we observed NaN errors in the predicted logits irrespective of our loss modifications. Since the models are small enough, we switch to pure float32 for these models without using mixed-precision. In addition, for bert-base-cased we apply MLM [Devlin et al., 2019], while for each input, we randomly mask one of the tokens.

3.2 Evaluation Setup

Evaluation Data. We consider the following datasets: LAMA [Petroni et al., 2019], TriviaQA [Joshi et al., 2017], and PopQA [Mallen et al., 2022]. These cover a wide range of queries, for example trivia questions (TriviaQA), and subject-relation-object facts phrased as queries (LAMA, PopQA). We consider the closed-book open-ended setting, where we do not provide any context or answer choices to the model. Importantly, in the case of TriviaQA and PopQA, where the input is formed as a question, we reduce it into a sentence completion task, using GPT4. Specifically, we prompt it to phrase the question as a sentence, while also providing it with some in-context examples that we manually created. See Appendix C for more details and the full prompt. To evaluate multiple-choice question answering, we use EleutherAI's lm-evaluation-harness [Gao et al., 2023]. Specifically, we use ARC [Clark et al., 2018], HellaSwag [Zellers et al., 2019], MMLU [Hendrycks et al., 2020], TruthfulQA [Lin et al., 2022a], WinoGrande [Sakaguchi et al., 2021], and GSM8k [Cobbe et al., 2021].

Baselines. For each of the evaluation datasets, we compare the IDK -tuned model with its original base model without any further training. Furthermore, we consider three different baselines:

Confidence Threshold baseline: We use the predicted probability mass in the language modeling head of the LM as a measure of confidence in the prediction [Yoshikawa and Okazaki, 2023]. We consider the first token generated by the LM. In case the corresponding probability mass of this token is greater than a fixed threshold, we consider the generation as valid. Otherwise, we consider this as an uncertainty expression (analogous to an [IDK] token generation in our model). To create a strong baseline, we search for the best threshold via hyperparameter tuning on the development set.

P(True) baseline [Kadavath et al., 2022]: Given an input sentence to complete, which we refer to as I , we use the original model to generate the completion, which we refer to as A . We then concatenate I and A and ask the model: "Please answer either with 'true' or 'false' only. Is it true that: IA " . If the model answer is not 'true', we consider this specific example as unknown for the model - namely the same case as if the IDK-tuned model would generate the [IDK] .

Semantic Entropy baseline [Kuhn et al., 2023, Aichberger et al., 2024]: We sample K text generations from the model, encode them using a state-of-the-art semantic encoder and cluster their encodings. If the largest cluster size is larger than K 2 , then we take a random generation out of this cluster as the model's answer. Otherwise, we consider this example as unknown.

Evaluation. We evaluate how well our models use the new [IDK] token by measuring their factuality and knowledge memory, using the following metrics: (i) Precision : the portion of factually correct completions, out of all the claims that have been completed with any token that is different from the [IDK] token, i.e., the claims that the model was certain enough about, and tried to factually complete. (ii) Recall : the portion of factually correct completions, out of all the claims in the dataset. Namely, the portion of knowledge memory the model has, out of the entire test set we evaluate on. (iii) F1 : the harmonic mean of precision and recall. In the case of base models without additional calibration methods, the precision, recall, and F1-scores all correspond to their accuracy on the task.

In Section 4.2, we use two further metrics to analyze the patterns when IDK -tuned models predict [IDK] . For this, we use the notion of correctly predicting [IDK] : We consider an [IDK] prediction to be correct if the base model does not predict the correct answer for an instance. We define (i) IDK recall : the fraction of instances the model predicted [IDK] correctly out of all instances where the base model did in fact not predict the correct answer, and (ii) IDK error rate : the fraction of instances where the model predicted [IDK] incorrectly out of all instances where the base model did indeed predict the correct answer.

4 Results

Wenext report results showing that our proposed IDK -tuning method can effectively improve factuality while causing only a small loss of existing knowledge.

4.1 Main Results

Mistral-7B-v0.1 results. Table 1 shows the results of our largest model Mistral-7B-v0.1 on factual closed-book sentence completion datasets. Our results show that the IDK -tuned Mistral-7B-v0.1 has a much higher precision - namely the model generates significantly fewer factually incorrect completions and instead puts probability mass on the [IDK] token. However, the model does show decreased knowledge recall on some tasks. Overall, we observe an increase in the average F1-score. Table 2 shows the averaged results on the lm-eval-harness datasets. The trend here is similar, although the increase in precision compared to baselines is slightly lower. This suggests that the model tends to be more certain when it comes to multiple-choice questions.

Scaling behavior of IDK -tuning. We further investigate the effect of model size on the success of IDK -tuning. We conduct IDK -tuning for each of the pythia-70m -2.8B models as detailed in Section 3.1. In Figure 2, we plot the average precision, recall, and F1-score for each of pythia-70m -2.8B as well as Mistral-7B-v0.1 , over all the closed-book sentence completion datasets. We observe a clear trend of recall and F1-score increasing log-linearly with the model size. The precision of IDK -tuned models increases only slightly as the model size increases. For the two smallest models we investigate ( pythia-70m and pythia-160m ), our method is arguably not effective, as the IDK -tuned model's recall collapses (we further analyze this in Section 4.3).

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bert-base-cased results. Table 3 reports the results of out IDK -tuned bert-base-cased model. We see a similar trend as in our evaluation of Mistral-7B-v0.1 . Factuality is improved, while recall is reduced by only a small amount.

4.2 Ablations

We perform an ablation study of our method to further investigate the effectiveness of each of its components. For our study, we calculate the IDK recall and IDK error rate on the closed-book factual sentence completion datasets. We study the effect of Π , λ and the L FP-reg term. For this, we perform IDK -tuning using Mistral-7B-v0.1 with the same hyperparameters as our main runs with different combinations of the studied components 3 . We plot the IDK recall for different values of Π in Figure 3. In Figure 4, we plot the IDK recall vs. IDK error rate tradeoff. IDK recall and IDK error rate are defined in Section 3.2. We study different aspects of these results below:

Analysis of the adaptive nature of the Uncertainty Factor λ . The Uncertainty Factor λ defined in Equation 2 is adaptive , meaning the amount of probability mass shifted to [IDK] depends on the predicted probability distribution. Another possible choice is to use a fixed λ ∈ [0 , 1] . We analyze this in Figure 3 and Figure 4 4 . We can see that using the adaptive λ formulation results in a lower IDK error rate without a major decrease in IDK recall.

Effect of the L FP-reg regularization. We also study the effect of the L FP-reg term (see Section 2.2). Again, we see that using L FP-reg results in a reduced IDK error rate without decreasing IDK recall significantly.

3. Effect of the upper bound hyperparameter Π . We also study the effect of Π , which is the upper bound of the Uncertainty Factor (see Equation 2). Our ablation study demonstrates that increasing Π results in an increase in correct predictions of [IDK] (higher IDK recall), at the cost of a small increase of erroneous [IDK] predictions ( IDK error rate). The IDK error rate increases less when using both our proposed adaptive λ and L FP-reg .

Effect of knowledge contained in The Pile. Since we conduct further pretraining on The Pile, improved performance of our method could be partly explained by additional knowledge that the model learns during IDK -tuning. However, we show that this is not the case. In the case of the pythia-70m -2.8B models, our data used for IDK -tuning exactly matches their pretraining data. For Mistral-7B-v0.1 , this is not known although The Pile was likely also included. We note that the language modeling performance on The Pile of our models during IDK -tuning actually very slightly decreases rather than improving, suggesting the absence of any newly learned knowledge. However, to completely rule out any such effects, we trained Mistral-7B-v0.1 on the exact sample of The Pile used for IDK -tuning but with the regular cross-entropy objective. We report the performance of this model in Table 1. Indeed, Mistral-7B-v0.1 with further training on The Pile performs similarly to the base Mistral-7B-v0.1 on average.

4.3 Analysis of Optimization Stability

Collapse to [IDK] . Highly optimizing every component of the standard language modeling task with Transformers has made it easy to forget that optimization processes of deep neural networks can be brittle and divergent. Naively replacing the regular cross-entropy objective with our IDK -loss L IDK leads to a collapse of training where the model simply always learns to put most probability mass on the [IDK] . We already account for this by (i) introducing the Π inhibitor to allow us to set an upper bound on the maximum probability mass that is assigned to the [IDK] in the target vector and (ii) introducing the additional L FP-reg regularization to provide an additional signal that punishes probability mass being assigned to [IDK] when the model's prediction is already correct.

In practice, we see that the regular cross-entropy loss shows a small uptick at the very beginning of IDK -tuning. In almost all runs, this recovers quickly back to baseline levels, where it remains. We find that with Π = 0 . 5 and the L FP-reg regularization, most training runs are stable without further model-specific tuning.

Collapse for small models pythia-70m and pythia-160m . However, for pythia-160m and pythia-70m , which are the only runs in our experiments that diverge even with our added regularization losses, the regular cross-entropy keeps on rising with a large spike. Concretely, the predicted distributions not only show an increased cross-entropy with the targets but also a sharply increasing entropy: we observe that the predicted distributions collapse towards a uniform distribution. At the worst point, 0% of the predictions of pythia-160m are correct. However, both models somewhat recover towards the end of training but stay well below baseline levels in terms of language modeling performance. We note that this is a different collapse pattern than the collapse towards almost always predicting [IDK] observed without our regularization terms.

We further analyzed this and observe that for both pythia-160m and pythia-70m , the initial probability mass assigned to the [IDK] token is so small that it gets rounded to zero even when using float32 precision. This causes the L IDK loss to be very large, resulting in large gradient norms. Already for pythia-410m , the initial probability mass on [IDK] is substantial enough to prevent this (albeit still a very small value smaller than 5 × 10 -9 ). Both pythia-160m and pythia-70m also show a larger initial entropy in their predicted distributions (i.e., 'flatter' predicted distributions). We conjecture that an adapted initialization of the [IDK] token and/or a small bias towards [IDK] at the beginning of training could prevent this divergence. As we only encounter this issue for the small pythia-160m and pythia-70m models, we leave further investigation of this for future work.

4.4 Text Generation

To assess whether our IDK -tuning might harm other different downstream language skills, which are not necessarily only factual, we evaluate the IDK -tuned Mistral-7B-v0.1 on the task of text summarization, and compare its results to those of the original model. For this, due to the high likelihood of the [IDK] token being generated during a longer text generation process, we use greedy decoding and ignore the [IDK] token. For this experiment, we use four different common

summarization benchmarks: Legal Plain English [Manor and Li, 2019], TLDR [Völske et al., 2017], and SPEC5G [Karim et al., 2023]. We measure performance using RougleL [Lin, 2004], as it is widely used in related work, and report the results in Table 4. The IDK -tuned Mistral-7B-v0.1 performs only slightly worse than the original base model. This is an encouraging result, as it means that IDK -tuning does not necessarily harm other language skills of pretrained language models.

4.5 Error Analysis

To gauge the effect of IDK -tuning on model responses to factual prompts and questions, we conduct an in-depth manual analysis on a random sample of 200 (40 from each dataset) of the model's incorrect generations (generations that do not contain the correct answer). We conduct this analysis for three models across model sizes: pythia-70m , pythia-2.8B , and Mistral-7B-v0.1 . We then categorize each of these incorrect generations to one of the following categories:

No Effect : Both the original model and the IDK -tuned model generate the same (incorrect) answer.

Noise : The original model generates the correct answer, while the IDK -tuned model does not.

White Noise : Both the original and IDK -tuned models do not generate the correct answer, however the IDK -tuned model generates a different one.

Abstain : The IDK -tuned model abstains from answering by generating text such as 'unknown" or 'mystery".

The results are shown in Table 5. Our analysis suggest that first, the bigger the model, the fewer changes our training approach causes in the model's generations, and second, the bigger the model, the greater its ability to abstain from answering via words (which generally can be interpreted as equal to generating an [IDK] token, although harder to evaluate automatically).

5 Related Work

Model Calibration. Our goal is closely related to the key challenge of model calibration [Guo et al., 2017b]: to provide a measure of the probability that a prediction is incorrect alongside the actual prediction. The problem of factual error detection can be viewed as a variation of calibration, where instead of a continuous probability, we provide a binary prediction for whether the model is correct or not. This is also related to the setting of selective prediction, where models can abstain from answering a query [Varshney et al., 2022, Kamath et al., 2020]. Common approaches to calibration are to perform various transformations on a model's output logits [Desai and Durrett, 2020, Jiang et al., 2021], and measuring uncertainty [e.g., see Kuhn et al., 2023]. More recent works have studied the use of LMs for providing calibration, by training them on statements known to be factually

correct or incorrect. This 'supervised' approach has been explored via fine-tuning [Kadavath et al., 2022, Lin et al., 2022b], in-context learning [Cohen et al., 2023a, Alivanistos et al., 2022], zero-shot instruction-oriented [Cohen et al., 2023b] and consistency sampling [Yoran et al., 2023] techniques. Further recent studies [Azaria and Mitchell, 2023] use the internal state of the model for classifying whether it is certain or not, use a new token for unanswerable inputs [Lu et al., 2022], or construct a specific dataset for effectively tuning the model for answering refusal [Zhang et al., 2024]. Our work builds upon this, aiming to teach the model to assess and express its own uncertainty via the new [IDK] token we introduced.

Attribution. Another related line of work focuses on checking whether LM-generated texts are faithful to a given source text [Bohnet et al., 2022, Honovich et al., 2022]. This problem has been addressed via several approaches, including question generation [Wang et al., 2020, Honovich et al., 2021, Scialom et al., 2021], NLI [Thorne et al., 2018, Welleck et al., 2019, Maynez et al., 2020, Dziri et al., 2022, Gao et al., 2022, Kamoi et al., 2023], data augmentation [Atanasova et al., 2022, Wright et al., 2022, Gekhman et al., 2023], and planning schemes that allow the model to self-edit its own generation [Schick et al., 2022]. Unlike these works, we are not assuming any reference text or external knowledge bases. Instead, we aim to teach the model to decide on its own whether it is likely to be able to factually complete a sentence correctly.

6 Conclusion

We propose a novel method for improving LMs' factuality by adding a special [IDK] token to an LM's vocabulary. Alongside the new [IDK] token, we introduce a novel pretraining objective called IDK -tuning to model uncertainty in the model's prediction as the probability mass assigned to the [IDK] . Crucially, IDK -tuning requires no labeled data and is instead a drop-in replacement of the conventional cross-entropy loss used for self-supervised language modeling on web-crawled texts. This allows us to explore uncertainty-aware training at a large scale. In our experiments, we conduct continued pretraining of a diverse range of pretrained models using the IDK objective.

Evaluation on factual sentence completion and multiple-choice benchmarks shows that IDK -tuned models can complete these tasks with much higher precision by refusing to answer (assigning high probability mass to the [IDK] token) in cases when the base model would have given a wrong answer. This comes at only small decreases in recall. We investigate the scaling behavior of our method with respect to model size using the Pythia model suite [Biderman et al., 2023], perform several ablation studies for individual components of our IDK objective, and verify that the general language modeling ability of IDK -tuned models does not degrade.

Our work can be extended in several ways. For example, since we do not rely on any labels of our training data used for IDK -tuning, we potentially apply our objective for next-token predictions where it might be ill-posed. Instead, we can perform lightweight filtering of relevant next-token predictions, such as named entities, focusing our objective more on factual next-token predictions. Also, IDK -tuning can be applied during pretraining from scratch, where our IDK objective could have interesting interactions with the acquisition of new knowledge during this stage.

7 Limitations

We note a few limitations of our proposed method. First, it requires a full pretraining of LMs on relatively large corpus. This of course is both highly computationally expensive and time-consuming. It is likely often the case that this kind of training cannot be conducted on typical academic lab resources, on a large enough model, in a reasonable amount of time.

Second, as discussed in Section 4.4, our method may slightly harm certain language skills, such as long text generation. Other downstream skills may be affected more significantly. We further discuss potential risk and biases in Appendix A.

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A Impact

As discussed in Section 1, one of the main disadvantages of current LMs is their tendency to factually mislead the user by generating factual incorrect statements. Hence, the main impact of our work is to reduce such factual mistakes via our proposed method. Still, it is evident that this sort of approach can by no means completely eliminate hallucinations. It is important to stress that we propose a single method, not a system design for safe deployment of LLMs. In practice, we anticipate our method to be coupled with other checks and balances, forming a safe system.

Additionally, in this work, we use The Pile as a dataset to train models. The Pile is a web-crawled corpus, which likely harbors text reflecting various forms of biases. One impact of applying IDK -tuning is that the model may learn to answer in a biased way if this bias appears in its training data, while avoiding answers that rarely appear in its training data. This shows the need for more research on compiling high-quality training corpora.

B Computational Resources

For IDK -tuning of Mistral-7B-v0.1 , we use Nvidia H100 or A100 GPUs depending on availability. For IDK -tuning pythia-70m -2.8B , we use 1-4 Nvidia A6000 GPUs. For IDK -tuning of bert-base-cased , we use a single Nvidia A100 GPU.

C Questions Rephrasing

As mentioned in Section 3.2, for TriviaQA and PopQA, where the input is formed as a question, we reduce each of these input examples into a sentence completion task input, using GPT4. If we denote a random input question from one of these datasets by x , then our prompt to GPT4 is the following:

Please rephrase the following question as an input for a sentence completion task. For example:

For the question: "Where was Michael Jackson born?", the sentence should be: "Michael Jackson was born in".

For the question: "Who is Barack Obama's wife", the sentence should be: "The wife of Barack Obama is".

For the question: "Where in England was Dame Judi Dench born?", the sentence should be:

We found this prompt to be effective enough after manually testing it on a development set of a 45 examples.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a training-based confidence calibration method, named IDK-tuning, for improving LLM factuality. Specifically, a special `[IDK]` (\"I Don't Know\") token is added to the model's vocabulary and an objective is introduced which shifts some probability mass of wrong predictions to the `[IDK]` token during continued pretraining, thereby encouraging the model to express uncertainty explicitly. Results of the IDK-tuned models are reported on commonly used factual benchmarks, showing the potential of this method for reducing hallucination while only suffering a slight sacrifice in terms of knowledge recall.\n\nSTRENGTHS:\n* Confidence calibration and LM hallucination are both important topics and this paper connects them in an interesting way.\n* The proposed IDK-tuning method is intuitive and well-motivated. While there have been papers on supervised finetuning for calibration, most of them focus on aligning the model with human demonstration (which requires annotation) or synthetic data (which incur extra cost). The direct adaptation of the training objective that incorporates uncertainty seems quite novel to my best knowledge, and results seem promising with much higher precision and only slightly lower recall, which is suited for the current generally over-confident LLMs. \n* The authors perform extensive experiments on the scaling behavior and ablation for different components of the objective function.\n* The authors do not overclaim their contribution. Singularities of the experiment results (e.g. `NaN`s in loss and collapsed recall from the `pythia` models) are mentioned and analyzed, and interesting insights are drawn from them.\n* The writing is clear and the paper is easy to follow.\n\nWEAKNESSES:\n* For multiple-choice QA tasks, the precision improvement as well as the absolute values appear lower than those for the factual sentence completion tasks (comparing Table 1 and 2).  Given this, and that the multiple-choice QA tasks might be more applicable, it would be helpful if the authors could report more detailed results on each of the `lm-eval-harness` tasks, and investigate QA or other downstream tasks more carefully.\n* Code or tuned model checkpoints are not provided, although some details about the settings and resources are mentioned in the paper.\n\nQUESTIONS:\n* Is it possible or beneficial to add multiple special tokens to express the different levels of uncertainty that are finer-grained, instead of only a single `[IDK]` token?\n* For the evaluation on `TriviaQA` and `PopQA`, why do you reformat them into sentence completion tasks? Is it because in this way the next token(s) can be directly modeled without being extracted from a complete answer?\n\nLIMITATIONS:\nThe authors highlight several limitations, including the need for full pretraining on large corpus, which is costly, and that the method can slightly sacrifice recall or the overall performance on some downstream tasks such as text generation.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes calibrating LLMs during a continued pertaining phase via an added [IDK] token to model uncertainty.\n\nSTRENGTHS:\n- The paper is structured well and written coherently.\n- The introduction of the $\\texttt{[IDK]}$ token to explicitly model uncertainty in LLMs is a novel approach \n- Through ablation studies, the behavior of the proposed method is investigated extensively.\n\nWEAKNESSES:\n- **Theory**: \n  - The approach is mathematically not very well grounded. Also, mathematical expressions such as $prob(\\texttt{[tok]}, \\hat{y})$ and $prob(argmax(\\hat{y}), \\hat{y})$ do not cohere with common practices [1,2,3,4]. The authors could consider something like $p(y_{t}=\\texttt{[tok]} | y_{<t}, x)$ and $max_{i} \\ p(y_{t}=i | y_{<t}, x)$.\n  - The uncertainty factor is only bigger than $0$ if any other token gets assigned a higher probability than the $\\texttt{[gold]}$ token. It does not account for the case where a model is uncertain about *any* token and thus predicts a (low) probability for all tokens. For instance, consider the tokens relating to ($\\text{\"Paris\"}$, $\\text{\"Berlin\"}$, $\\text{\"London\"}$, $\\text{\"Rome\"}$, $\\text{\"Vienna\"}$). If the model predicts any of $p(y_{t} | \\text{\"The capital of France is\"}) \\in [(0.2, 0.2, 0.2, 0.2, 0.2), (0.3, 0.1, 0.2, 0.2, 0.2), ...]$, the uncertainty factor is $0$ no matter the hyperparameter $\\Pi$, while it is clear that in all those cases the model is uncertain about the correct next token. The probability of the $\\texttt{[IDK]}$ gets even decreased via the uncertainty regularization.\n\n- **Evaluation**: The authors do not compare against other uncertainty quantification methods, such as (length-normalized) predictive entropy [1], p(true) [2], or semantic entropy [3,4]. These methods do not require additional pertaining, and thus do not suffer from training instabilities, mode collapse, or high computational costs, but can directly be applied to \"off-the-shelf\" models. Additionally, there exist methods that consider fine-tuning models to express their lack of knowledge that have not been considered.\n  \n\n---\n[1] A. Malinin and M. Gales. Uncertainty estimation in autoregressive structured prediction.\n\n[2] S. Kadavath, T. Conerly, A. Askell, T. Henighan, D. Drain, E. Perez, N. Schiefer, Z. Hatfield-Dodds, N. DasSarma, E. Tran-Johnson, S. Johnston, S. El-Showk, A. Jones, N. Elhage, T. Hume, A. Chen, Y. Bai, S. Bowman, S. Fort, D. Ganguli, D. Hernandez, J. Jacobson, J. Kernion, S. Kravec, L. Lovitt, K. Ndousse, C. Olsson, S. Ringer, D. Amodei, T. Brown, J. Clark, N. Joseph, B. Mann, S. McCandlish, C. Olah, J. Kaplan. Language Models (Mostly) Know What They Know.\n\n[3] L. Kuhn, Y. Gal, and S. Farquhar. Semantic uncertainty: Linguistic invariances for uncertainty estimation in natural language generation.\n\n[4] L. Aichberger, K. Schweighofer, M. Ielanskyi, and S. Hochreiter. Semantically Diverse Language Generation for Uncertainty Estimation in Language Models.\n\nQUESTIONS:\n- If an IDK-tuned model is to be aligned, how does the alignment hurt IDK-tuning? Also, if a model is IDK-tuned after alignment, how does the pertaining hurt alignment?\n- The method is evaluated on a single model. How do you guarantee that the results generalize to bigger models?\n\nLIMITATIONS:\nThe authors adequately addressed the limitations.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2024-07-12"}

comments: SUMMARY:
To allow LMs to express their uncertainty for generative tasks, the authors introduce a new special IDK token. The authors modify the cross-entropy training objective to assign part of the probability mass to the IDK token in cases where the model gets the prediction wrong. The token embedding is randomly initialized and then refined through additional fine-tuning of pretrained LLMs of various sizes and types (Pythia, Mistralv1, BERT).
Through experiments on a range of completion, QA & MCQA datasets the authors show that IDK tuning positively affects precision at a slight cost of recall. The authors perform further ablation experiments solidifying their choices for the loss weight hyperparameter as well as the regularization term. The authors further show that IDK tuning does not significantly adversely affect other capabilities of the underlying LMs.

STRENGTHS:
- Well written and easy to follow
- To the best of my knowledge, presents a novel approach to quantifying uncertainty in LMs
- Exhaustive experimental evaluation & ablation over different hyperparameter choices demonstrating robustness of the proposed approach

WEAKNESSES:
- The IDK-tuning setup requires sometimes prohibitive additonal fine-tuning of the base LM
- It is unclear how the method would be applied when a model would be pretrained from scratch with the IDK token included - it is natural that LMs will be worse in predicting tokens as initial stages of training, so the pretrain - add IDK - tune paradigm seems as the only current option. The two previous points slightly limit the applicability of the metod.
- While the reported F scores are generally higher compared to baselines and alternatives, the IDK-tuned models still suffer from tangibly lower recall.

QUESTIONS:
None

LIMITATIONS:
Yes
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 3
DATE: 2024-07-12

comments: SUMMARY:
It introduces a novel method to address the issue of hallucinations in Large Language Models (LLMs). These models, despite their proficiency in capturing and generating human knowledge, can sometimes produce factually incorrect text. To combat this, the authors propose a calibration method that incorporates an [IDK] ("I don’t know") token into the model's vocabulary.

STRENGTHS:
The introduction of the [IDK] token is a creative solution to an existing problem in LLMs. It represents a novel way to handle uncertainty, which is not just a new definition or problem formulation but also a practical application within language models.

The paper proposes a new pretraining objective that modifies the conventional cross-entropy loss to incorporate the [IDK] token. This is an original contribution to the field of natural language processing.

WEAKNESSES:
The paper primarily uses The Pile for training, which may not be representative of all possible language use cases or domains.

While the paper provides a good overview of the performance metrics, an in-depth error analysis could offer more insights into the types of errors the models are making and how the [IDK] token impacts these.

As the model is trained on web-crawled data, there is a risk of learning and perpetuating societal biases present in that data.

QUESTIONS:
See Weaknesses

LIMITATIONS:
While the paper notes the potential for bias in the training data, it could provide more details on how this might affect the model's predictions and decision-making.

The paper could more explicitly discuss the potential for the model to contribute to the spread of misinformation, especially if it fails to correctly identify uncertain or incorrect information.
TITLE: Official Review
SOUNDNESS_CORRECTNESS: 2
DATE: 2024-07-15