I Don't Know: Explicit Modeling of Uncertainty with an [IDK] Token
Authors: Roi Cohen
Konstantin Dobler
Eden Biran
Gerard de Melo
Venue: NeurIPS 2024 poster (2024)
Keywords: LLMs
Factuality
Uncertainty
Factual Knowledge
Pretraining
Primary area: natural_language_processing
TL;DR: We propose a novel IDK objective which models uncertainty in a model's prediction as probability mass put on a special [IDK] token. Experimental results show that our method improves factual precision without significantly harming factual recall.

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.

Don't Know: Explicit Modeling of Uncertainty with an [IDK] Token
Roi Cohen
Konstantin Dobler HPI University of Potsdam Konstantin Dobler@hpi. de
Eden Biran Tel Aviv University edenbiran@mail. tau. ac. i1
HPI University of Potsdam
Roi. Cohen@hpi de
Gerard de Melo HP1 University Potsdam Gerard. Dew.rddDeeee@@hp....
Abstract
Large Language Models are known to capture real-world knowledge, allowing them 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, propose novel calibration method that can be used to combat hallucinations. We add a special [IDK] ("I don't know") token 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 express uncertainty in places where they would previously make mistakes while suffering only small loss encoded knowledge. We further perform extensive ablation studies of multiple variations of our approach and provide detailed analysis of the precision-rectt tradeoff of our method
Introduction
Large Language Models (LLMs) are pretrained on massive amounts 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
their parameters and act as knowledge bases (Petroni et al. 2019 Roberts al. 2020 Cohen et al..
2023a Pan et al. 2023 Owing to this phenomenon, LLMs can be used in multiple settings requiring
this worldworld knowledge, such as closed-book question answering [Brown et al. 2020 Roberts
al. 2020 and information retrieval TTa et al.) 2022].
Despite the popularity of LLMs, they are prone what is commonly referred to hallucinations, which severely hinder their performance and reliability [Ji et al. 2023
Manduchi et al. 2024
Examples of hallucinations include factually incorrect [Maynez al.
2020
Devaraj al. [022 Tam
et al. 2023). inconsistent [Elazar et al. [2021 Mündler et al. 2023 self coff-contraiicting [Cohen et al.
2024 or non-attributable text Bohnnt al. 2022 Rashkin al. 2023
Yue al., 2023
prominent method employed to combat such hallucinations is model calibration [Guo et al. 201 7a
Brundage al. 2020 which aims calibrate the confidence of model predictions such that they
We release code and IDK-tuned model tokeno tuning
checkpoints at https://giithub.com/rrifff
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Regular cross-entropy:
IDK objective: on wrong predictions, divide shifted probability
shift all wrong probability
mass to the gold token
mass between gold and [IDK] token
Paris]
Parris]
[_Thh]]_aapiile -cppial]]] [-o[ - France][_is]
Berlinj
[ Berlin]
[TOK]
Figure 1: Illustration of our proposed IDK objective. During continual pretraining, we shift some probability mass of wrong predictions towards a special [IDK] token. The amount of shifted probability mass depends the uncertainty in the model's prediction. We detail our method in Section
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 improvement in model calibration [Geng et al. 2024 they have still been found to lacking [Chen et al. 2023].
In this work, we propose novel objective function that allows LLMs explicitly express uncertainty. We add new special [IDK] (*I Don't '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
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- IDK-tuning.
Our proposed IDK objective differs from previous work 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 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 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 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 IDK-tuning does not harm the general language modeling ability of models, such as long text generation.
In summary, contributions include:
We propose novel IDK objective applied during pretraining which models uncertainty in model's prediction as probability mass put on special [IDK] token.
We evaluate our objective using large range of base models with different architectures and model sizes, and confirm the efficacy of IDK-tuning on range of factual answering downstream tasks.
We extensively analyze individual components of our objective and its effect on general language modeling ability.
IDK-tuning
Our goal is to train model to be aware of its unawareness and to effectively express it. For this, introduce a new special token to its vocabulary: [IDK]. The model is intended to express uncertainty by putting probability mass 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 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 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 training method.

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2.1 The [IDK] token
The purpose the new token is to represent lack of knowledge. Ideally, whenever the model would have been making 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 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 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
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
We modify the conventional cross-entrppy objective between the softmax distribution over the model's 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 À E [o. 1] that is larger the more uncertain the model is and exactly O 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 arbitrary token [tok] in the prediction of a model as (y:: = [tok] yct, x) We further use [[ik]] 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:
LIx = LCE($, (1- X) + A Al(I)))
(I)
If the model is uncertain in its prediction, the target is shifted away from predicting the [gold] token and towards the [IDK] token. This modulated by X. Note that in case the model makes the correct prediction, À = 0 and LIoK therefore reduces to the regular cross-entropy loss. When the model is correct, LIx simply provides the signal for the correct prediction. When the model is incorrect, LIo provides both the signal for the correct prediction and signal to express uncertainty. We now detail the construction of the Uncertainty Factor X.
The Uncertainty Factor. A is constructed as scalar weight with À [0, 1]. Intuitively, we want À 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 À as one minus the probability mass on the gold token divided by the maximum probability mass put on any token:
A A= x (1 (1- prob(y: = (ooodd](/cc,
max;(prob(v++ = il x))
where II E [0. 1] is hyperparameter to control the influence of our objective. When the gold token probability close to the maximum probability, is close to 0. If the model makes a correct prediction (the gold token is assigned the maximum probability), X is O, thereby reducing Equation ] to the regular cross-entropy loss. When the gold token probability much lower than the maximum probability, À is close to 1, which translates to shifting almost all the probability mass of the target in Eqquatin to the [IDK] token. II specifies the upper bound of target probability mass that can be shifted to the [IDK] token. For example, II
means that most half of the probability mass
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in the target can be shifted to [IDK] while the rest remains with the gold token. In practice, we do tune this and set 3. This prevents the [IDK] token from ever becoming 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 IT in Section 4.2
Uncertainty Regularization. An important consideration in designing the LIoK objective is to prevent 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, add the following anti-false positive regularization to our objective:
Cee-reg log((1 prob [IDK] [IDK][B<<;; 2)),
which is exactly the binary cross-entropy objective with O 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 '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 is more certain, and is designed to reduce a decrease of its recall. We perform an ablation of CfP-reg in Section 4.2
The final loss. Combining all objectives, our final IDK objective is therefore:
[CE + CeR-reg = LIoK
C
otherwise.
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 commonly used factual benchmarks, showing that our method improves factuality while paying only small price in terms of knowledge recall. We also show that model size plays 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 (i) starting from model that is already strong language modeler helps during the optimization process by providing rough initial calibration that we utilize to derive the Uncertainty Factor.
3.1 IDK-tuning Setup
We use bert-base-cased (Devlin et al. and EleutherAT/ppythia-7m
[Jinn et al. 2023
8B [Biderman al.] [2023] for our base models for IDK- -tnning For IDK-tuning Mistral-78-v0. 1, we train data randomly sampled from The Pile [Gao et al.) 2020 with a context length of 4,096. We use example packing to fill the entire context length. We use maximum learning rate of 4 x 10-5 with linear warmup for 10% of the training steps and cosine decay down to x 10 6 We use 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 total of 1B 2. 2B8B models, we use the same hyperparameters but reduce
training tokens. For the pythia-70hh the context length to 2,048 to match the model's 's positional embeddings. We use of bfloot16 and float16 mixed-precision training to match Mistral-7B-vo. 1 and pythia-4100 410m - 2. 8B pretraining. respectively. For pythia-70m, pythia-166 predicted logits irrespective of our loss modifications. Since the models are small enough, we switch pure float32 for these models without using mixed-precision In addition, for tert--ba--cssee we apply MLM Devlin et al. 2019]. while for each input, we randomly mask one of the tokens.
and bert-base-can caaeed we observed NaN errors in the
We use wwwpl//ow/ppleeucoooypooooo Books corpus, which contains copyrighted works.
on the Huggingface Hub for a version of The Pile without the

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3.2 Evaluation Setup
We consider the following datasets: LAMA Petroni et al. 2019]. TriviaQA (Joshi al. 2017], and PopQA [Mallen al., 2022]. These cover a wide range of queries, for example trivia questions (TriviaQA), and subject-relation-obje
Evaluation Data.
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 question, we reduce it into 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 EleutherAl's 1m- inrevallatiin ioaauuatoonhhrnesss [Gao al., 2023]. Specifically, we use ARC [Clark et al. 2018). HellaSwag [Zellers et al.) 22019, 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:
1. Confidence Threshold baseline: We use the predicted probability mass in the language modeling head of the LM 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.
2. 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 and ask the model: "Please answer either with 'true' or 'false' only. Is it true that: 1 TA". 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].
3. Semantic Entropy baseline Kuhhn et al. 2023
Aichberger et al.) 2024 J: We sample K text generations from the model, encode them using ofte-offtheear semantic encoder and cluster their encodings. If the largest cluster size is larger than K. generation out of this cluster the model's answer. Otherwise, we consider this example as unknown.
z then we take a random
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.c., the claims that the model was certain enough about, and tried to factually complete. (ii) Recall: the portion of factually correct completions, 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.
of all the claims in the dataset.
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 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
We next report results showing that our proposed IDK-tuning method can effectively improve factuality while causing only small loss of existing knowledge.
5

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LAMA Google RE
LAMA R-Rex
LAMA SQuAD
IrviaQA
PopQA
F1
F1
Mistral-78-99
48.8
48.8
48.0
48.0
02.2
35.2
35.2
Mistrol-78--a Confidence Threshold
60.0
80.0
15.0
50.4
63.5
71.0
64.4
33.5
64.1
70.4
41.1
51.9
64.6
20.6
31.2
Mistrol- 1a-ve. PYTrue)
54.4
44.5
48.9
73.8
65.1
69.2
$4.9
41.0
46.9
58.8
47.5
52.5
40.3
29.0
33.7
Kistral 1araal--8- 78.v8.1 Semantic Fatropy
70.1
38.9
60.0
83.0
66.4
76.0
70.2
44.5
54.4
68.6
02.5
50.4
68.7
20.4
31.5
Mistral-7B-v0.11 IDK tuning on The Piee
71.1
40.6
51.7
88.5
65.5
75.3
72.0
44.3
54.9
72.5
52.0
00.6
78.1
20.5
32.5
Table 1: Precision (P), Recall (R), and Fi-scores for Mistral-7B-v0.
Our IDK-tuning achieves the best precision with minor decreases in recall, outperforming previous work. Mistral-7B-ve
+ Confidence Threshold refers to the baseline based on the probability mass of the predicted an- swer Yooshikawa and Okazaki 2023]. Mistral-7B-vo. The Pile refers to the ablation discussed
in Section 4.2
P
R
F1
18stral-78-v0.1
28.2
28.2
28.2
Mistral-78-vo.1 1 The Pile
28.3
28.3
28.3
Mistral-7B-v8.1 Confidence Threshold
45.0
18.5
26.2
Mistral-78-v8.1 IDK-tuning The Pile 48.8
20.8
29.2
Table 2: Precision (P), Recall (R), and F1-scores of our model on the In-eval-harness, compara
to baselines.
4.1 Main Results
Mistral-7B-v0. 1 results. Table I| shows the results of our largest model Mistral-7B-vo. on factual closed-book sentence completion datasets. Our results show that the IDK-tuned Mistral-78-v0. 1 has 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 Fl-score. [aable 2 shows the averaged results on the 1m- im-eval-harnes 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 suc- cess of IDK-tuning. We conduct IDK-tuning for each of the pythia-70m 2. 8B models as de- tailed 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-77 -B- 1, over all the closed-book sentence completion datasets. We observe 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 (py (pythia-700 and pythia-160m) our method is arguably not effective, the IDK-tuned model's recall collapses (we further analyze this in Section 4.3).
80
Avg. Perfermance (58)
40-
Precisiou
20-
Recal
Fi-score
70mm
180m
110m:
10B
1B4
2,5B
7.0
Model Size (log wade))
Figure 2: Average performance on closed-book factual sentence completion benchmarks of IDK- tuned models terms of their parameter count. 70m to 2.8B are pythia-700 70m 8B, while 7.0B Mistral-7B-ue 1.

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LAMA Google-RE
LAMA T-Rex
LAMA SQuAD
P
F1
P
R
F1
bert-base-cased
23.0
23.0
23.0
59.8
59.8
59.8
9.5
9.5
9.5
bert-base-cased Confidence Treshold
58.8
15.8
24.9
71.5
35.9
47.8
69.5
5.0
9.3
bert-base-cased IDK-tuning
78.1
15.9
26.4
72.5
53.0
61.2
80.2
11.9
Table 3: Precision (P), Recall (R), and F1 scores for of our IDK-tuned bert-base-cased on the evaluation benchmarks, compared to baselines.
No Cpp-rogi Bixed
No Cpp-rog: idlppiio
No Cyp-rag: fooed
Eyp-rag: aduptive
With Cyp-ragi Bied
with Cpp-rag: adaptiio
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With Cyp-rog: foood A
-*e- With Eyp-zog: adaptive A
0.7
0.6
0.6
TDK roc0)
0.3-
0.1-
0.3
10K reall
0.1
0.4
10K crear rate
0.25
0.3
2
0.15
0.2
0.10
0.05
0.10
0.15
0.25
0.1
0.2
0.3
0.4
0.5
TDK error rate
Value
Figure 4: Tradeoff between IDK recall and IDK er- ror rate for different parameter combinations. We annotate each data point with its corresponding II value.
Figure 3: Ablation study of different values for factor that controls the upper bound of prob- ability mass put on [IDK] in the target.
bert-based basebaa--case results. Table 3 reports the results of out IDK-tuned bert-base-cased model. We see similar trend our evaluation of Mistral-7B-ve Factuality is improved, while recall reduced by only small amount.
4.2
Ablations
We perform ablation study of our method 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 II, À and the LFe-reg term. For this, perform IDK-tuning using Mistral-7B-vo. 1 with the same hyperparameters as our main runs with different combinations of the studied components We plot the IDK recall for different values of II in Figure 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:
1. Analysis of the adaptive nature of the Uncertainty Factor X. The Uncertainty Factor defined in Equation is adaptive, meaning the amount of probability mass shifted to [IDK] depends on the predicted probability distribution. Another possible choice is to use fixed À E [0, 1J. We analyze this in Figure and Figure 4f We can see that using the adaptive À formulation results lower IDK error rate without major decrease in IDK recall.
2. Effect of the Lre-reg regularization. We also study the effect of the Lre-res term (see Sec- [ion 2.2 Again, we see that using Lip-reg results a reduced IDK error rate without decreasing IDK recall significantly.
Due to computational constraints, we run this for a reduced set for the cases with adaptive X. For fixed X, set À 11.
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3. Effect of the upper bound hy hyperparameter II. We also study the effect of II, which is the upper bound of the Uncertainty Factor (see Eqeuationn 2). Our ablation study demonstrates that increasing II results in an increase in correct predictions of [IDK] (higher IDK recall), at the cost of small increase of erroneous [IDK] predictions (IDK error rate). The IDK error rate increases less when using both our proposed adaptive X and Lip-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-78m 8B models, our data used for IDK-tuning exactly matches their pretraining data. For Mistral-78-v0. 1, this is not known although The Pile was likely also included. We note that the language modeling performance decreases rather than improving, suggesting the absence of any newly learned knowledge. However, to completely rule out any such effects, we trained Mi Mistral-7B-vo.1 1 on the exact sample of The Pile used for IDK- Kok-innin 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-vo. 1 on average.
The Pile of our models during IDK-tuning actually very slightly
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-lost LIoK 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 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 Lip-rag 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 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 IT 0.5 and the Lie-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 reg- ularization 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 sharply increasing entropy: we observe that the predicted distributions collapse towards a uniform distribu- tion. At the worst point, 0% of the predictions of pythia- 1-6mm 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 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 prob- ability mass assigned to the [IDK] token is so small that it gets rounded to zero even when using float32 precision. This causes the LIo loss to be very large, resulting in large gradient norms. Already for py tyythaa4110 Om, the initial probability mass on [IDK] is substantial enough to prevent this (albeit still a very small value smaller than 5 x10-9) 9). Both pythia-160m and pythia- 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 small bias towards [IDK] the beginning of training could prevent this divergence. As we only encounter this issue for the small pythia-16em and pythia- models, we leave further investigation of this for future work.
4.4 Text Generation
To assess whether our IDK- IDK-tuning might harm other different downstream language skills, which are not necessarily only factual, we evaluate the IDK-tuned Mistral-7B-ve, 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 longer text generation process, we use greedy decoding and ignore the [IDK] token. For this experiment, we use four different common
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TLDR
SPEC5G
Mistral-7B-vo. Mistral-7B-v0.. + The Pile
17.5
14.1
37.2
17.4
14.1
37.3
Mistral-7B-vo.1 + IDK-tuning on The Pile
17.2
14.0
36.9
Table 4: Rougel. scores on different summarization tasks to measure the impact of IDK-tuning on
other language model abilities. Histral-7B-vel The Pile refers to the ablation discussed in Section 4.2
No effect
Noise
White Noise
Abstaining
Mistral-78-ve.1
68.5%
9%
6.5%
16%
pythia-2.880
59.5%
13.5%
12.5%
14.5%
pythia-70m
52%
18.5%
22%
7.5%
Table Error type distribution on 200 failures of our IDK-tuned models.
summarization benchmarks: Legal Plain English [Manor and Li 2019). TLDR (Völkke et al. 2017] and SPECSG [Karim et al. 2023]. We measure performance using RougllL Lin 2004]. as it is widely used in related work, and report the results Table 4 The IDK-tuned Mistral-7B-vo performs only slightly worse than the original base model. This is an encouraging result, as 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 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-vo.. 1. We then categorize each of these incorrect generations to one of the following categories:
1. No Effect: Both the original model and the IDK-tuned model generate the same (incorrect) answer.
2. Noise: The original model generates the correct answer, while the IDK-tuned model does not.
3. White Noise: Both the original and IDK-tuned models do not generate the correct answer, however the IDK-tuned model generates a different one.
4. Abstain: The IDK-tuned model abstains from answering by generating text such as "un- known" or "mystery".
The results are shown 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, greater its ability to abstain from answering via words (which generally can be interpreted as equal generating [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 prediction incorrect alongside the actual prediction. The problem of factual error detection can be viewed as variation of calibration, where instead of continuous probability, we provide binary prediction for whether the model 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 calibration are to perform various transformations
model's s output logits (Desai and Durrett 2020 Jiang let al., (202T), and measuring uncertainty (e.g., see Kuhn al., 2023). More recent works have studied the use of LMs for providing calibration, by training them statements known to be factually

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correct or incorrect. This "supervised" approach has been explored via fine-tuning Kadavath et al.
2022 Lin et al., 2022b], in-context learning [Cohen al. 2023a Alivanistos et al. 2022] zero-shot
instruction-orrenneed [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 new token for unanswerable inputs (Lu et al. [002]] 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- LM-generated texts are
faithful to a given source text [Bohnet et al. 2022 Honovich et al. [002]]. This problem has been
addressed via several approaches, including question generation [Wang et al. 2020 Honovich et al.
2021 Sccalom et al., 2021]. NLI [Thorne et al. 2018 Welleck et al. [019 Maynez et al. 2020
Dziri et al. |002 Gao 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 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 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 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 instead drop-in replacement of the conventional cross-entropy loss used for self susersiueeise language modeling on web-crawled texts. This allows us to explore uncertainty-awarc training 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 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 model size using the Pythia model suite [Biderman 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 training data used for IDK-tuning, we potentially apply our objective for next-token predictions where it might be ill- ill-posed. Instead, we can perform lightweight filtering of relevant next-token predictions, such named entities, focusing our objective more factual tekt-token predictions. Also, IDK- LDK-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.
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. likely often the case that this kind of training cannot conducted on typical academic lab resources, on a large enough model, in 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
Acknowledgements
Roi Cohen and Gerard de Melo received funding from The Goldman Sachs Group, Inc., New York, NY, USA. Konstantin Dobler thanks the German Federal Ministry for Education and Research
10

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(BMBF) through the project < -kl-Servicezentrum Berlin Brandenburg (011S22092) and the European Laboratory for Learning and Intelligent Systems (ELLIS) PhD program for support. We further express our gratitude to the NeurlPS 2024 reviewers for their helpful comments.
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A Impact
As discussed in Section I] 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 single method, not a system design for safe deployment of L.Mss. In practice, we anticipate our method to be coupled with other checks and balances, forming safe system.
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Additionally, in this work, we use The Pile as dataset to train models. The Pile is a web-crawled corpus, which likely harbors text reflecting various forms biases, One impact of applying IDK- lnning 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 its training data. This shows the need for more research on compiling high-quality training corpora.
B Computational Resources
For IDK-tuning of Mistral-78-vo.1 1, we use Nvidia H100 or A100 GPUs depending on avail- ability. For IDK-tuning pythia-70m 2. 8B, 1-4 Nvidia A6000 GPUs. For IDK-tuning of pert-base-cased, we use single Nvidia A100 GPU.
C Questions Rephrasing
As mentioned in Seection 3.2] for TriviaQA and PopQA, where the input formed question, reduce each of these input examples into sentence completion task input, using GPT4, If we denote random imput question from one of these datasets by z, then our prompt to GPT4 is the following:
Please rephrase the following question as an input for 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 development set of a 45 examples.
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Reviews:
[{"review_id": "uL855sT2NW", "reviewer": "Reviewer_aDMj", "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.", "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.\n\nThe 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.", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "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.\n\nThe 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.\n\nWhile 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.\n\nAs the model is trained on web-crawled data, there is a risk of learning and perpetuating societal biases present in that data.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We first highly thank the reviewer for their time reading our work, writing a thorough review and bringing up thoughtful comments.\n\nWe are encouraged that the reviewer finds our method a creative and novel method to handle an existing and important problem current LLMs have - which is generating misinformation and hallucinations.\n\nWe would like to address the following weaknesses / limitations of our work raised in the review:\n- **“Using primarily The Pile”**: We argue that using a general, English-centric dataset is well suited to demonstrate the efficacy of our method and not an inherent weakness of our method. Additionally, as you may assume, each of these training sessions is extremely resource-intensive. Exploring other languages and domains is a good direction for future work.\n- **“In-depth error analysis missing”**: We do provide a very detailed analysis and ablation of precision-recall tradeoffs in Section 4.2. Based on the reviewer’s suggestion, we decided to conduct an in-depth error analysis of our model’s mistakes. We will provide the results here and will add them to the camera-ready version of the paper too. The setup of the analysis is the following:\nWe randomly sample 200 examples (out of all the datasets) on which the IDK-tuned model generates a wrong answer (without predicting the [IDK] token). We then categorize these to one of four categories: No Effect (both the original model and our model generate the same answer), Noise (the original model knows it, while after our training it doesn’t), White Noise (both the original model and ours don’t know it, though they generate different answers), and Abstain (when our model abstains from answering while generating text like “unknown” or “a mystery”). For this analysis we take three different models: Mistral-7B, Pythia-2.8B and Pythia-70M. The results are the following:\n| model       | No Effect | Noise | White Noise | Abstaining |\n|-------------|-----------|-------|-------------|------------|\n| Mistral-7B  | 68.5      | 9     | 6.5         | 16         |\n| Pythia-2.8B | 59.5      | 13.5  | 12.5        | 14.5       |\n| Pythia-70M  | 52        | 18.5  | 22          | 7.5        |\n\nThese results 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 is generally equal to generating the new [IDK] token, though harder to evaluate automatically). \n- **“Bias from web-crawled pretraining data”**: We agree and will use the extra page to discuss this in an extended Limitations section. However, while important to consider, we argue that pretraining data bias is (1) mostly inherent to the way LLMs are trained nowadays and (2) not a particular weakness of *our method* but an exciting direction for follow-up work (e.g., using synthetic data).\n- **\"Potential for the model to contribute to the spread of misinformation\"**: Indeed our extended Limitations section will also discuss the risk of misinformation. 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*.\n\nIn light of this, we kindly request you to reconsider and appropriately raise the score of your review if we have sufficiently addressed some or all of your concerns.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JvRSB0yr16", "reviewer": "Reviewer_i3GV", "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).\nThrough 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.", "questions": "None", "limitations": "Yes", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Well written and easy to follow\n- To the best of my knowledge, presents a novel approach to quantifying uncertainty in LMs\n- 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\n- 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.\n- While the reported F scores are generally higher compared to baselines and alternatives, the IDK-tuned models still suffer from tangibly lower recall.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We first express our sincere gratitude to the reviewer for their time reading our work, writing a thorough review, and bringing up thoughtful comments.\n\nWe are encouraged that the reviewer finds our paper to be well written, our approach to be novel, and our experiments to be extensive and to properly demonstrate the robustness of our approach.\n\nHere are our responses to the concerns raised by the reviewer:\n- While our method does require finetuning, we also benefit from the vast amount of current work in the optimization and efficiency of LLM training. In any case, we argue that (moderate) finetuning does not constitute a technical weakness of our method.\n- While we experiment with IDK-tuning for the reasons you mention, we believe integrating the [IDK]-flavor of uncertainty-aware training into pretraining from scratch presents an exciting direction for future work (e.g., via loss weight schedules). We do believe that with small adaptations of our loss function, our training method could be applied for pretraining from scratch. One of the main reasons we couldn’t check this effectively is the very extensive resources (time, compute and memory) these controlled experiments in this setting would have consumed (which would be impractical or impossible on typical academic budgets in a reasonable amount of time). Also, we believe this direction of work warrants a detailed study that will fill another whole paper.\n- We agree that our method is not “free” (as it leads to somewhat lower recall), but argue that it presents a valuable tradeoff, given the importance of reducing hallucinations.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VJqm1fZGZe", "reviewer": "Reviewer_4r2S", "summary": "The paper proposes calibrating LLMs during a continued pertaining phase via an added [IDK] token to model uncertainty.", "questions": "- 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?", "limitations": "The authors adequately addressed the limitations.", "rating": 3, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- 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.", "weaknesses": "- **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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We are very thankful to the reviewer for their time reading our work and writing a thorough review.\n\nWe are encouraged that the reviewer finds our paper to be well written, our approach to be novel, and our ablation experiments to be extensive and to properly demonstrate the behavior of our approach.\n\nWe will now address the reviewer's concerns:\n\n## Theory\n- For the camera-ready version, we will modify all of the mathematical expressions in the paper for better coherence with previous common practices. Thank you for the suggestions!\n- *“The uncertainty factor is only bigger than $0$ if any other token gets assigned a higher probability than the $\\texttt{[gold]}$ token”*: We first thank the reviewer for this comment as well, which we strongly agree with. As each of the training runs is very resource-intensive, this idea has not been evaluated in a proper experimental setup. We plan to test a model that has been trained with a slight modification to our proposed training objective, reconsidering the true certainty it has on the gold token, even if this is the maximal probability token among the others. For example, we could take “1 - P(gold token)” as an additional term to be combined in the “Uncertainty Factor” definition, as well as to remove the separation we apply between cases where this factor is zero and the others, in terms of our objective. We will add some initial results of this alternative objective in the camera-ready version. We additionally think this is definitely an exciting follow-up to our work.\n\n## Evaluation\nThank you for this comment. We also believe that evaluating other uncertainty quantification methods might strengthen our work. We thus decided to add the results of the methods suggested by the reviewer to our paper. We will now provide the results of the “P(true)” and the “semantic entropy” methods using the Mistral-7B model, and will add these together with the results of the other models to our camera-ready version of the paper. For the “semantic entropy” method we use SOTA named entity recognition in order to extract only the “answer” itself from the model’s generation. It is important to note though that our method could potentially be applied directly during the normal pretraining of the model, by only modifying the pretraining objective to be ours, and thus the claim that our method requires additional training would not apply. Moreover, the “Semantic Entropy” method indeed does not require any additional training, though it requires significantly more inference calls and some post-processing of the generations (clustering etc.). \nThe results are the following:\n- **LAMA Google-RE**:\n\n| model                               | Precision | Recall | F1   |\n|-------------------------------------|-----------|--------|------|\n| Mistral-7B                          | 48.1      | 48.1   | 48.1 |\n| Mistral-7B + The Pile               | 48.8      | 48.8   | 48.8 |\n| Mistral-7B + Confidence Threshold   | 60.0      | 40.0   | 48.0 |\n| Mistral-7B + P(true)                | 54.4      | 44.5   | 48.9 |\n| Mistral-7B + Semantic Entropy       | 70.1      | 38.9   | 50.0 |\n| Mistral-7B + IDK Tuning on The Pile | 71.1      | 40.6   | 51.7 |\n\n- **LAMA T-Rex**:\n\n| model                               | Precision | Recall | F1   |\n|-------------------------------------|-----------|--------|------|\n| Mistral-7B                          | 71.2      | 71.2   | 71.2 |\n| Mistral-7B + The Pile               | 69.9      | 69.9   | 69.9 |\n| Mistral-7B + Confidence Threshold   | 80.4      | 63.5   | 71.0 |\n| Mistral-7B + P(true)                | 73.8      | 65.1   | 69.2 |\n| Mistral-7B + Semantic Entropy       | 88.0      | 65.4   | 75.0 |\n| Mistral-7B + IDK Tuning on The Pile | 88.5      | 65.5   | 75.3 |\n\n- **LAMA SQuAD**:\n\n| model                               | Precision | Recall | F1   |\n|-------------------------------------|-----------|--------|------|\n| Mistral-7B + P(true)                | 54.9      | 41.0   | 46.9 |\n| Mistral-7B + Semantic Entropy       | 70.2      | 44.5   | 54.4 |\n| Mistral-7B + IDK Tuning on The Pile | 72.0      | 44.3   | 54.9 |\n\n- **TriviaQA**:\n\n| model                               | Precision | Recall | F1   |\n|-------------------------------------|-----------|--------|------|\n| Mistral-7B + P(true)                | 58.8      | 47.5   | 52.5 |\n| Mistral-7B + Semantic Entropy       | 68.5      | 52.5   | 59.4 |\n| Mistral-7B + IDK Tuning on The Pile | 72.5      | 52.0   | 60.6 |\n\n- **PopQA**:\n\n| model                               | Precision | Recall | F1   |\n|-------------------------------------|-----------|--------|------|\n| Mistral-7B + P(true)                | 40.3      | 29.0   | 33.7 |\n| Mistral-7B + Semantic Entropy       | 68.7      | 20.4   | 31.5 |\n| Mistral-7B + IDK Tuning on The Pile | 78.1      | 20.5   | 32.5 |\n\nThese results suggest that our approach still leads to the best precision and f1 scores compared to the new baselines too, though the gaps are smaller compared to the ones against the previous baselines.\n\n## Questions\n- *\"Combining IDK-tuning with alignment”*: While we do not explicitly study this in our work, we do believe it is an interesting direction for future work. Specifically, the line of work on Task Arithmetic [1] will be interesting: Can we extract and combine the “IDK” weight vector with an instruction-tuned model?\n- *\"“The method is evaluated on a single model” / “generalization to bigger models”*: We believe this question must be a misunderstanding, as we conduct very extensive experiments with eight different models, spanning encoder-only (BERT) and decoder-only architectures, as well as an explicit study of scaling behavior using the Pythia model suite and Mistral-7B.\n\nIn light of this, we kindly request you to reconsider and appropriately raise the score of your review if we have sufficiently addressed some or all of your concerns.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XBy0ybJPyA", "reviewer": "Reviewer_Ny7r", "summary": "This 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.", "questions": "* 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?", "limitations": "The 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.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "* 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.", "weaknesses": "* 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.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank the reviewer for their time reading our work, writing a thorough review and bringing up thoughtful comments.\n\nWe are encouraged that the reviewer finds our method intuitive, novel and well-motivated, that our experiments are deemed extensive, and that the paper is considered well-written and as not overclaiming the results.\n\nHere are our responses to the weaknesses raised by the reviewer:\n- We agree with the reviewer that it would be beneficial to more carefully analyze and represent the lm-eval-harness results. In the camera-ready version, we will add the results of each of the datasets separately and discuss the difference between them to those of the other datasets. Importantly, we note that according to a comment by a different reviewer, we have conducted an in-depth analysis of our model’s mistakes. The setup of the analysis is the following:\nWe randomly sample 200 examples (out of all the datasets) on which the IDK-tuned model generates a wrong answer (without predicting the [IDK] token). We then categorizes it to one of these four categories: No Effect (both the original model and our model generate the same answer), Noise (the original model knows it, while after our training it doesn’t), White Noise (both the original model and ours don’t know it, though they generate different answers), and Abstain (when our model abstains from answering while generating text like “unknown” or “a mystery”). For this analysis we take three different models: Mistral-7B, Pythia-2.8B and Pythia-70M. The results are the following:\n\n| model       | No Effect | Noise | White Noise | Abstaining |\n|-------------|-----------|-------|-------------|------------|\n| Mistral-7B  | 68.5      | 9     | 6.5         | 16         |\n| Pythia-2.8B | 59.5      | 13.5  | 12.5        | 14.5       |\n| Pythia-70M  | 52        | 18.5  | 22          | 7.5        |\n\nThese results 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 is generally equal to generating the new [IDK] token, though harder to evaluate automatically).\n- We will definitely provide the code and checkpoints with the camera-ready version. Additionally, all the information needed to reproduce our model is demonstrated in the paper.\n\n\nHere are our responses to the questions raised by the reviewer:\n- *“Multiple IDK tokens”*: In principle, the single [IDK] token does cover all levels of uncertainty, as we measure a continuous amount of probability mass put on the token. However, we think multiple different [IDK] tokens are interesting, e.g., discriminating between different “categories” of uncertainty such as lack of knowledge, lack of context etc. \n- *“TriviaQA / PopQA reformatting”*: Yes, we perform the reformatting to enable a straightforward evaluation.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We thank all reviewers for their time and effort put into providing a thorough review of our work. We briefly highlight the strengths of our work as identified by the reviewers:
- Our [IDK] token approach is a “novel approach” deemed “an original contribution to the field of natural language processing”, “well-motivated”, and “creative”.
- The reviewers have praised our extensive experiments and ablation studies, while not overclaiming our results.
- Our paper is well-written and easy to follow.

In the individual responses, we address all points and questions raised by the reviewers in detail.

Meta-review: The paper proposes a continued pretraining strategy, assuming a model has been initialized, does another round of pretraining where for incorrect (next token) predictions, the loss function remaps some of the probability mass to an [IDK] token (instead of trying to push the model to be correct).

The empirical results are positive and the authors have done more baseline comparisons (see rebuttal to Reviewer 4r2S)

Reviewers i3GV and Ny7r are positive about the paper. The main concern about the paper is regarding the mathematical definition of the loss function (Reviewer 4r2S). While I agree that the reviewer's formulation may be more elegant I don't think the authors formulation is wrong i.e. the question is whether you only allocate probability mass to the [IDK] token when the model is incorrect (what the authors did) or if the overall uncertainty is high regardless of whether it is correct (what the reviewer is advocating for)

Therefore I favor accepting the paper.
Decision: Accept (poster)