Outdated Issue Aware Decoding for Reasoning Questions on Edited Knowledge (2024)

Abstract: Recently, Knowledge Editing has received increasing attention, since it could update the specific knowledge from outdated ones in pretrained models without re-training. However, as pointed out by recent studies, existing related methods tend to merely memorize the superficial word composition of the edited knowledge, rather than truly learning and absorbing it. Consequently, on the reasoning questions, we discover that existing methods struggle to utilize the edited knowledge to reason the new answer, and tend to retain outdated responses, which are generated by the original models utilizing original knowledge. Nevertheless, the outdated responses are unexpected for the correct answers to reasoning questions, which we named as the outdated issue. To alleviate this issue, in this paper, we propose a simple yet effective decoding strategy, i.e., outDated ISsue aware deCOding (DISCO), to enhance the performance of edited models on reasoning questions. Specifically, we capture the difference in the probability distribution between the original and edited models. Further, we amplify the difference of the token prediction in the edited model to alleviate the outdated issue, and thus enhance the model performance w.r.t the edited knowledge. Experimental results suggest that applying DISCO could enhance edited models to reason, e.g., on reasoning questions, DISCO outperforms the prior SOTA method by 12.99 F1 scores, and reduces the ratio of the outdated issue to 5.78% on the zsRE dataset.

heading: 1 Introduction
text: Large Language Models (LLMs) exhibit the remarkable ability to capture plenty of factual knowledge into their parameters. However, knowledge of inner LLMs may become outdated or unsuitable over time (Zhao et al., 2021; Elazar et al., 2021;
∗ Work was done when Zengkui Sun was an intern at Pattern Recognition Center, WeChat AI, Tencent Inc, China.
†Yufeng Chen is the corresponding author.
Dhingra et al., 2022). Unfortunately, naively retraining LLMs can be computationally intensive, and fine-tuning LLMs in several cases suffers the risk of catastrophic forgetting (Parisi et al., 2019; Mitchell et al., 2021; Ramasesh et al., 2021). Recently, Knowledge Editing has received increasing attention, which aims to update factual knowledge into LLMs and retain the unrelated knowledge, without retraining from scratch (De Cao et al., 2021; Mitchell et al., 2021; Yao et al., 2023; Mazzia et al., 2023; Yin et al., 2023; Zhang et al., 2024).
Previous methods could be divided into two research lines to implement the knowledge editing in LLMs, according to whether preserving original models’ parameters (Yao et al., 2023; Mazzia et al., 2023; Wang et al., 2023c). The first research line retains the weights of the original LLMs, and appends supplementary weights or memories to retrieve the relative edited knowledge to guide the model to response to the edited knowledge. For instance, SERAC (Mitchell et al., 2022) uses a scope classifier to determine whether the current prompt falls within the scope of any stored knowledge, and T-Patcher (Huang et al., 2023) adds extra trainable parameters into FFN layers of LLMs ot
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edit model performance. Besides, MemPrompt (Madaan et al., 2022), IKE (Zheng et al., 2023), and MeLLo (Zhong et al., 2023) conduct in-context learning with knowledge editing demonstrations to prompt LLMs to update pretrained knowledge. The second research line focuses on adjusting knowledge-related weights in the original LLMs via pre-computation or an additional module to predict the weights. For instance, KE (De Cao et al., 2021) trains a BiLSTM to predict the weight update, to enable constrained optimization to modify facts without affecting other knowledge, while KN (Dai et al., 2021), ROME (Meng et al., 2022a), and PMET (Li et al., 2023) implement editing by first locating the parameters, which store corresponding knowledge, and then directly updating them. Overall, with these techniques, knowledge editing could update LLMs on new factual edited knowledge without explicit model re-training, when questions explicitly mention the edited knowledge.
However, for reasoning questions, most of these approaches struggle to generate the correct response, and tend to retain the outdated response. As the example shown in Figure 1, if we update the knowledge from “The Eiffel Tower is in Paris” to “The Eiffel Tower is in London”, and then query the edited model with the reasoning question “Which country is the Eiffel Tower located in?”. We find that the edited model still tends to respond with the outdated answer “France” (Country of “Paris”) rather than the new correct answer “England” (Country of “London”), which we named as the outdated issue. As pointed out by recent studies (Yao et al., 2023; Zhong et al., 2023; Wang et al., 2023a), existing methods may tend to memorize its superficial word composition, rather than learning the edited knowledge indeed, i.e., hard coding them into the model locally.
To mitigate the outdated issue, in this paper, we make efforts to explore whether edited models tend to generate outdated responses to reasoning questions. By analysis, we discover that the edited knowledge exerts a constrained impact on the probability distribution of predicted tokens. In other words, models tend to utilize their original knowledge to respond to the reasoning questions after editing, which hinders the performance on reasoning questions. Hence, we propose a decoding strategy, outDated ISsue aware deCOding (DISCO), to amplify the impact of edited knowledge on the probability distribution. Specifically, we capture
the modification of probability distribution, by the subtraction of distribution between the original and edited models. Subsequently, we add this modification to the edited model’s probability distribution. Besides, we add a constraint to revise the modification of distribution to avoid the probability increase in outdated responses. In this way, we could amplify the impact of the edited knowledge on the edited model, and alleviate the outdated issue, thus encouraging the edited model to utilize the edited knowledge to reason the new answer.
We conduct experiments to evaluate DISCO on the zsRE dataset (Levy et al., 2017; Yao et al., 2023) and the CounterFact dataset (Meng et al., 2022a; Yao et al., 2023). Experimental results demonstrate that DISCO could effectively mitigate the outdated issue, and then enhance the performance of edited models on reasoning questions. For instance, compared to the prior SOTA method IKE (Zheng et al., 2023), DISCO improves 12.99 F1 scores and reduces the rate of outdated tokens from 8.23% to 5.78% in the zsRE dataset using the LlaMa-2-7b backbone. On the other dataset or backbone, DISCO yields the best performance on reasoning questions and suffers the least outdated issue, demonstrating the effectiveness of DISCO.
The main contributions of this paper can be summarized as follows1: • To our knowledge, we are the first to point out
the edited models suffer from the outdated issue and quantize this issue, which is up to 50% error ratio among current methods. • We propose a simple yet effective strategy, i.e., DISCO, to enhance the performance of edited models on reasoning questions. This strategy could amplify the influence of the edited knowledge, and alleviate the outdated issue. • Experimental results show that DISCO could effectively mitigate the outdated issue, and enhance the performance in reasoning questions, without updating parameters.

heading: 2 Task Formulation
text: The formal definition of knowledge editing is to update factual knowledge into model parameters, which could motivate the model’s behavior towards the edited knowledge.
To implement knowledge editing, current researchers mainly follow the two lines: (1) Re-
1Codes are released at https://github.com/ Acerkoo/DISCO.
taining the weights of original LLMs, and supplying additional weights or memories. For instance, SERAC (Mitchell et al., 2022) uses a scope classifier to determine whether the current prompt falls within the scope of any edited knowledge, and TPatcher (Huang et al., 2023) adds extra trainable parameters into the FFN layers of LLMs to edit knowledge. Besides, MemPrompt (Madaan et al., 2022), IKE (Zheng et al., 2023), MeLLo (Zhong et al., 2023), and DeepEdit (Wang et al., 2024) conduct in-context learning or chain-of-thought with knowledge editing examples to prompt LLMs to update pretrained knowledge. (2) Adjusting knowledge-related weights in original LLMs. For instance, KE (De Cao et al., 2021) trains a BiLSTM to predict and update weight, enabling constrained optimization to modify facts without affecting other knowledge, while KN (Dai et al., 2021), ROME (Meng et al., 2022a), and PMET (Li et al., 2023) implement editing by locating and directly updating the parameters which store corresponding knowledge.
Given an original pretrained language model θ and an input-output pair of edited knowledge (xe, ye), knowledge editing could create an edited model θ̂, which satisfies the following assessment:
θ̂(x) = { ye, x ∈ Xe, θ(x), x /∈ Xe, (1)
where Xe is the editing scope, denoting a broad set of inputs closely associated with the edited knowledge pair, with similar semantics as xe, θ(x) and θ̂(x) represent the output of the original model and edited model when receiving the input x, respectively. Following Yao et al. (2023), the edited model should satisfy the following four properties: (1) Reliability and (2) Generality straightforward assess the averaged accuracy of the edited case. The output of edited model θ̂(x) should be equal to ye, when the input x is in editing scope Xe. Note that the difference between Reliability and Generality is that the input for Generality is the paraphrased xe, whereas Reliability is the original xe. (3) Locality measures the capability of the edited model θ̂ to preserve the performance out of the editing scope. That is, θ̂(x) should be the same as θ(x) ideally, when x is out of the editing scope Xe. (4) Portability evaluates the effectiveness of the edited model in transferring edited knowledge to related content. When receiving an input of reasoning question x, which requires reasoning based on the
edited knowledge, the edited model is expected to correct answer it to demonstrate the model learns the knowledge itself rather than only memorizing superficial changes in wording.

heading: 3 Findings of the Outdated Issue

heading: 3.1 Oudated Issue
text: Among the above four properties, Portability is more challenging in assessing the effect of knowledge editing, since it requires edited models to learn the edited knowledge indeed and reason on it (Yao et al., 2023; Zhong et al., 2023; Wang et al., 2023a; Ma et al., 2023; Zhang et al., 2024). As reported by prior studies (Yao et al., 2023; Wang et al., 2023a,b), ROME (Meng et al., 2022a), MEMIT (Meng et al., 2022b), and IKE (Zheng et al., 2023) perform better in Portability. IKE is in the first research line, utilizing the robust capabilities of LLMs for in-context learning to edit LLMs by prompting with retrieved demonstrations from the external memory. ROME and MEMIT are in the second research line, specifying the FFN matrix as the key-value neurons embodying knowledge, and they implement editing by locating knowledgerelated neurons and updating them.
Unfortunately, in our preliminary experiments, we discover that the above approaches suffer the Outdated Issue that the edited model θ̂ tends to generate the outdated output θ(x), in Portability. For instance, we evaluate these approaches withGPT-J-6b on the zsRE dataset, and observe that these approaches seriously suffer the issue, ranging from 12% to 50% ratio of this issue (please refer to Section 5.3 for more details).

heading: 3.2 Similarity of Probability Distribution
text: Since decoding is directly applied in the response generation stage, to take a further step to probe the outdated issue, we explore the similarity of probability distribution of predicted tokens between the original model θ and the edited model θ̂.
Given an input x, we could model the conditional probability distribution of the t-th token:
P tθ(·) = ptθ(·|x, y<t), (2)
where ptθ(·) denotes the conditional probability distribution of the original model θ for the t-th predictied token, y<t denotes the previously predicted tokens by the original model.
Similarly, the probability distribution of the edited model θ̂ could be calculated as follows:
P t θ̂ (·) = pt θ̂ (·|x, ŷ<t), (3)
where pt θ̂ (·) and ŷ<t denote the edited model θ̂’s corresponding items of original model θ. To invest the similarity between P tθ(·) and P tθ̂(·), we apply Jensen-Shannon divergence to calculate the distance of both probability distributions, following Chuang et al. (2023):
JSD(P tθ(·), P tθ̂(·)) = 1 2 ·KL(P tθ(·)||P tθ̂(·))
+ 1
2 ·KL(P t θ̂ (·)||P tθ(·)),
(4)
where JSD(·) denotes the function of JensenShannon divergence, KL(·) denotes the function of Kullback-Leibler divergence. In this case, the smaller value of JSD(·) denotes the more similar of both probabilities, suggesting that the less impact of edited knowledge (xe, ye) to edited model θ̂’s output distribution. As a result, the edited model θ̂ will tend to generate the outdated response θ(x).
To understand this similarity of the probability distribution better, we analyze the similarity of both models in Reliability and Portability. As shown in Table 1, compared to the similarity of both models of IKE in Reliability, all edited models’ probability distribution have a smaller JSD value and are more similar to the original model in Portability. Besides, the more similar probability distribution between the original and edited models meets the more serious outdated issue and the worse performance on reasoning questions. These results suggest that the edited knowledge takes a few modifications on probability distribution, and the generation of new answers is disturbed by the original knowledge. Therefore, we should amplify the impact of the edited knowledge on probability distribution, to
reduce the disturbance of original knowledge, thus encouraging the edited model to utilize the edited knowledge to reason the new answer.

heading: 4 DISCO: Outdated Issue Aware Decoding
text: As analyzed in the prior section (§3.2), the few impacts of edited knowledge on probability distribution and the disturbance of original knowledge during reasoning should be responsible for the outdated issue. To amplify the impact of the edited knowledge on probability distribution, we propose a simple yet effective method, outDated ISsue aware deCOding (DISCO).
We first implement knowledge editing based on the prior editing methods, e.g., IKE, which performs best in Portability (Yao et al., 2023; Wang et al., 2023a). Given an input x to the original model θ and edited model θ̂, we capture their difference in probability distribution, caused by edited knowledge, via the subtraction as follows:
∆(t) = P t θ̂ (·)− P tθ(·)
= pt θ̂ (·|x, ŷ<t)− ptθ(·|x, y<t).
(5)
Then, we add the difference ∆(t) to the probability distribution of the edited model to amplify the difference in probability distribution:
pt θ̂ (·) = pt θ̂ (·|x, ŷ<t) + α ·∆(t). (6)
where α > 0 is a hyperparameter to control the weight of ∆(t). By this formula, we form a simple contrastive decoding (Li et al., 2022; Shi et al., 2023; Chuang et al., 2023) between the original and edited models, to capture and amplify the difference of edited knowledge in probability distribution, and then prevent the outdated issue. Constraints to revise Probability. To further constrain the probability of tokens of outdated response not increasing, we limit the maximum of ∆(·) for the tokens in outdated response θ(x):
∆(t) = { min(0,∆(t)), Vout, ∆(t), otherwise,
(7)
where Vout denotes the token set of the outdated response θ(x).
Furthermore, applying ∆(t) in Eq.6 faces the risk of increased probability of the target of factual edited knowledge, we take a similar constraint to the tokens of ye:
∆(t) = { min(0,∆(t)), Vout ∪ Vedit, ∆(t), otherwise,
(8)
where Vedit is the token set of the target of edited knowledge (token-level ye). Knowledge-aware In-cotext Editing. To further enhance the awareness of LLMs to the edited knowledge, we prepend the paraphrase of xe and the answer ye to the real input x as an in-context example. With the example, we could take a further step to amplify the impact of edited knowledge on probability distribution and reduce the disturbance of previous knowledge.
Overall, we design the DISCO strategy, consisting of Eq.6, Eq.8, and the in-context editing, to amplify the modification in the probability distribution. In this way, DISCO mitigates the outdated issue, and then encourages the edited model to utilize the edited knowledge to reason the new answer.

heading: 5 Experiments

heading: 5.1 Metrics
text: For Reliability, Generality, and Portability, different types of questions are inputted to the edited model, and we compare the model answers with ground truth ones to calculate token-level F1 and exact match (EM), following previous QA studies (Rajpurkar et al., 2016; Yang et al., 2018): (1) F1 measures the average overlap between the prediction and the golden answer; (2) EM measures the percentage of predictions which exactly match the golden answer. For Locality, an irrelevant question is used to evaluate whether the edited model retains the original performance. Hence, the golden answer of Locality is the original output. We also calculate the token-level F1 and EM to evaluate the edited models in terms of Locality.
Furthermore, when using portability to evaluate the edited models, we quantify the outdated error (OE ) by calculating the averaged proportion of outdated tokens (each of which appears in the outdated response θ(x)). To avoid over-count, we remove the overlap tokens between the ground truth and edited model predictions when calculating OE:
OE (θ̂) = 1
m
m∑
t=1
1{ŷt ∈ Vout & ŷt /∈ Vgolden},
(9) where m is the number of generated tokens, Vout and Vgolden denote the token set of outdated response and golden answer in Portability, respectively.
Moreover, we detect the ratio of target tokens of
edited knowledge in the predictions, noted as TE:
TE (θ̂) = 1
m
m∑
t=1
1{ŷt ∈ Vedit & ŷt /∈ Vgolden}.
(10)

heading: 5.2 Experimental setup
text: Datasets. In our experiments, we mainly conduct experiments on zsRE (Levy et al., 2017), which is one of the most prevalent Question Answering datasets extended and adopted for knowledge editing (De Cao et al., 2021; Mitchell et al., 2021). Further, Yao et al. (2023) expand the zsRE test set on portability, in terms of subject replacement, inverse relation, and one-hop. To evaluate the edited models on reasoning questions, we carefully select one-hop, which requires models to take one-step reasoning based on the edited knowledge.
Moreover, we also evaluate our methods on CounterFact (Meng et al., 2022a; Yao et al., 2023), which is a more challenging dataset that consists of counterfactual edits. For instance, the CounterFact updates the knowledge “Apple A5 was created by Apple” to “Apple A5 was created by Google”. Backbones. Following prior studies (Meng et al., 2022a,b; Yao et al., 2023), we adopt the GPT-J-6b (Wang and Komatsuzaki, 2021), LlaMa-2-7b and LlaMa-2-13b (Touvron et al., 2023) as the backbones. Baselines. We adopt four methods as baselines: (1) directly fine-tuning (FT) the language models with L∞ constraint; (2) ROME (Meng et al., 2022a) leverages causal mediation analysis to locate the edit area, and updates the whole parameters in the FFN matrix; (3) MEMIT (Meng et al., 2022b) directly updates LLMs with many memories, thus editing thousands of knowledge simultaneously; (4) IKE (Zheng et al., 2023) using in-context learning to guide models to update knowledge. Implementation Details. All experiments are conducted on a single NVIDIA A100 GPU (40G). The implementation of all baselines and our method is employed by EasyEdit (Wang et al., 2023b), with the default hyper-parameters in the GitHub repository2. Since in-context editing methods perform best in Portability (Yao et al., 2023; Wang et al., 2023a), we implement DISCO via the in-context learning and set α to 1.03. To conduct in-context learning examples, we search for the most related
2https://github.com/zjunlp/EasyEdit/ tree/main/hparams
3We explore the impact of α in Appendix.B.
example of knowledge editing case to guide the edited model. Similar to IKE (Zheng et al., 2023), we apply all-MiniLM-L6-v24 to encode and retrieve examples of knowledge editing cases.

heading: 5.3 Main Results
text: We conduct the main experiments on the zsRE and CounterFact datasets, and then report the F1 and EM scores of four types of questions and the ratio of OE and TE in Table 2. We find that IKE has the best performance in Portability, which is consistent with previous studies (Yao et al., 2023; Wang et al., 2023a). Besides, IKE and DISCO are in-context editing methods, without any parameters updating. Hence, we mainly compare DISCO with IKE. We discuss the performance of ROME and MEMIT in Appendix A.
As shown in Table 2 (1) In terms of Reliability, on both datasets, DISCO has achieved great success in yielding over 90 F1 and EM scores with both backbones. For the Generality, DISCO yields over 98.90 and 81.43 F1 scores on the zsRE and CounterFact datasets, respectively. This indicates that our DISCO is competitive with the previous approaches, when the questions are within the editing scope. Note that, for both IKE and DISCO methods, Reliability and Generality mainly measure the ability to memorize the edited knowledge from the prompt, since the edited knowledge in the prompt
4https://huggingface.co/ sentence-transformers/all-MiniLM-L6-v2
has a similar or same format as the input question. (2) For the Locality, both in-context editing methods perform poorly on both datasets. Although FT could maintain the performance to the irrelevant question, we consider the performance comes from the invalid knowledge editing, where most F1 scores of FT are less than 40 in Reliability. DISCO performs better than IKE in the zsRE dataset, while worse than IKE in the CounterFact dataset. We conjecture this poor Locality performance is attributed to that LLMs struggle to locate the editing scope and affect unrelated inputs (Yao et al., 2023), and could be alleviated by supplying a scope classifier to determine whether editing model (Mitchell et al., 2022).
For the reasoning properties: (1) In Portability, DISCO yields the best performance among all methods on both backbones. Compared to IKE, DISCO improves F1 score with +5.59 and +12.99 scores on the GPT-J-6b and LlaMa-2-7b, respectively. Furthermore, the EM score of DISCO is around triple times (11.39 vs. 3.57 and 33.46 vs. 10.90) that of IKE. In the challenging CounterFact dataset, DISCO still outperforms IKE by over +1.0 F1 score. Since the challenge, edited models struggle to respond whole golden answer (EM), and only predict a few tokens of the golden answer. Even so, these improvements demonstrate that DISCO could powerfully assist LLMs to generate correct answers, by capturing and amplifying the modification of the edited knowledge, on rea-
soning questions. (2) DISCO also performs best on the Outdated Issue among all methods in terms of OE and TE, generating the least outdated tokens after knowledge editing. In the zsRE dataset, DISCO could yield only a 5.78% average ratio of the outdated issue on the LlaMa-2-7b. As the results show, DICSO could effectively prevent the edited model from generating outdated tokens and target tokens of edited knowledge, simultaneously.
Moreover, when comparing edited models on different datasets or backbones, we could find that the basic ability of backbones and difficulty of editing knowledge are two important factors in the performance of edited models, especially in Portability. Overall, DISCO is an effective method, performing competitive results in Reliability and Generality, and achieving new state-of-the-art performance in Portability.

heading: 6 Analysis

heading: 6.1 Distribution of ∆(t)
text: We investigate the probability variation ∆(t) (in Eq.5) to further probe the impact of ∆(t) on the outdated issue. On the zsRE dataset and LlaMa-2-7b backbone, we split the averaged ∆(t) value in Portability into intervals with the 10.0%, and then count the proportion and the OE metric w.r.t each interval.
Since the positive or negative ∆(t) value denotes whether the probability of golden answers is improved, as illustrated in Figure 2, we could observe that most value of ∆(t) of golden answers (around 94.5%) has a positive value. The positive value indicates that ∆(t) could assist the edited model in reasoning the golden answer. Besides, with the
larger ∆(t) value, the ratio of outdated issue of the corresponding interval has a monotone decreasing trend (from 9.65% to 0.6%). This trend further demonstrates that ∆(t) could assist the edited model in reasoning the golden answer, and mitigate the outdated issue.

heading: 6.2 Variation of Probability Distribution
text: To probe the variation of probability distribution after applying DISCO, we count the average probability of golden answers in four properties, and the outdated responses in Portability. We display the results on the zsRE dataset with LlaMa-2-7b, and list the results in Table 3.
For the Locality, DISCO suffers a little sacrifice in probability to retain the output of the original model, and this sacrifice could be supplied by a scope classifier or parameter locating. For Portability, DISCO could enlarge the difference of probability between the outdated response and golden answers from 12.30% to 47.26%. Consequently, DISCO could significantly capture and amplify the impact of edited knowledge on the probability distribution, then alleviate the outdated issue and encourage the edited model to generate the correct answers for reasoning questions.

heading: 6.3 Probability of Common Tokens
text: To detect whether all tokens in outdated responses are wrong, on reasoning questions, we count the proportion of the common tokens in both the outdated response and the new golden answer, and their probability variation. We display the statistical results of DISCO on the zsRE dataset with LlaMa-2-7b in Figure 3.
As shown in Figure 3(a), in the token-level, 57.78% tokens in outdated responses will appear in the new golden answer, while the other tokens are wrong and will be outdated tokens after editing. This proportion of the common tokens and outdated tokens suggests that not all tokens in outdated responses are wrong. To further probe the effect of DISCO on the common tokens and the outdated tokens, we display the variation of the probability of both tokens, before and after applying DISCO. As shown in Figure 3(b), the common tokens receive the increasing probability, while the probability of outdated tokens decreases from 66.05% to 4.52%. The variation indicates that DISCO could reserve the common tokens, and effectively reduce the probability of outdated tokens. The effect of DISCO on both tokens demonstrates that DISCO could preserve the probability of correct tokens and reduce the probability of outdated tokens, and then improve the performance of Portability.

heading: 6.4 Ablation
text: We explore the impact of both constraints, in Equ.8, to ∆(t) in DISCO, and conduct experiments on the zsRE dataset with LlaMa-2-7b. We list the results in Table 4 and display the impact of prepended paraphrased edited knowledge in Appendix.C.
As illustrated in Table.4, we remove the constraint on tokens of outdated response (ID.2), the target of edited knowledge (ID.3), and remove both constraints (ID.4), while setting the whole DISCO as the baseline (ID.1). When removing the constraint on outdated tokens, ID.2 suffers a
FT ROME MEMIT IKE DISCO
34.74s 154.05s 127.99s 32.43s 19.69s
LlaMa-2-7b
more serious outdated issue and worse quality of response, compared to ID.1. Similarly, ID.3 generates more tokens of the target of edited knowledge, after removing the constraints on the corresponding tokens. Consequently, after removing both constraints, ID.4 generates the worst response and suffers the deterioration on both token types. These performances suggest that both constraints are efficient in revising the probability of the corresponding type of tokens, while DISCO could improve the probability of golden answers.

heading: 6.5 Efficiency
text: Knowledge Editing should minimize the time required for conducting edits without compromising the model’s performance. We calculate the Time Cost for five methods on the LlaMa-2-7b, to compare the efficiency of DISCO. Similar to Yao et al. (2023), we counter the average time-cost of 10 edits.
Table 5 illustrates the time required for different knowledge editing methods from providing the edited case to obtaining the edited model. We could observe that DISCO could quickly edit knowledge, much faster than other methods, and then yield remarkable performance (details of results as discussed in Section 5.3). On the other hand, ROME and MEMIT are time-consuming and necessitate a pre-computation of the covariance statistics for the Wikitext. Hence, considering the time aspect, DISCO is the optimal time-friendly knowledge editing method, with remarkable performance.

heading: 6.6 Model Scaling
text: We apply two methods (i.e., IKE, and DISCO) to LlaMa-2-13b to evaluate the reasoning ability of
the edited knowledge with model scaling.
As Table 6 shows, when applying to LlaMa-213b, both methods perform better in Portability than in LlaMa-2-7b, with 3.29 and 1.50 F1 scores improvement, respectively. Besides, both methods generate fewer outdated tokens and factual knowledge tokens. Unfortunately, DISCO performs worse in Locality on the larger LLM, suggesting that the edited knowledge has more impact on the probability distribution on the larger LLM, thus disturbing the LLM locating the editing scope. Additionally, compared to the IKE with the LlaMa2-13b, DISCO achieves better performance in the four properties on the LlaMa-2-7b. The experimental results indicate that DISCO has a strong capability to enhance edited models on the reasoning problem w.r.t the edited knowledge and performs better with the larger model.

heading: 7 Conclusion
text: In this paper, we focus on the outdated issue that edited models suffer from generating outdated responses to the reasoning questions, which is ignored by previous approaches. To mitigate this issue, we propose a simple yet effective method, outDated ISsue aware deCOding (DISCO), to encourage the edited model to utilize the edited knowledge to reason the correct answers for reasoning questions. Specifically, DISCO captures and amplifies the modification in probability distribution between the original and edited models. Experimental results demonstrate that DISCO could significantly mitigate the outdated issue, and effectively encourage the edited to reason the new correct answers for reasoning questions, without updating parameters.
Limitations
In this paper, we investigate the outdated issue of edited models to the reasoning questions, and we propose a simple yet effective decoding strategy, i.e., DISCO, to prevent this issue and enhance the performance of edited models on reasoning questions. In this paper, we mainly focus on the outdated issue in the one-hop reasoning questions, which is the prior part of multi-hop questions. We leave these in future work to take further improvement.

heading: Acknowledgements
text: The research work described in this paper has been supported by the National Nature Science Foundation of China (No. 61976016, 62376019, 61976015), and the authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve this paper.

heading: A Full Comparison in zsRE
text: We supply the experimental results of ROME and MEMIT in Table 7. As Table 7 illustrated, we could observe that ROME and MEMIT perform well in Portability. With the benefit of the pre-computation of the covariance statistics, ROME and MEMIT could precisely update the parameters related to the edited knowledge, with more editing time-cost. As a result, ROME and MEMIT could retain the most
performance when receiving the input out of the editing scope.

heading: B Hyperparameter
text: To explore the impact of hyperparameter α in DISCO, we conduct experiments in the zsRE dataset on both backbones. Since the F1 scores of Reliability and Generality are over 98, we pay less attention to both properties and mainly focus on the other metrics.
We adjust α to (0.1, 0.3, 0.5, 1.0, 1.5, 2.0) to observe the corresponding performance of DISCO and report the results in Table 8. As the results show, with the larger value of α, the edited models generate the less outdated tokens, where ratios of Outdated issue downwards from 15.61 to 9.93
and 6.63 to 5.04 on both backbones, respectively. Besides, the larger α hinders edited models from generating factual knowledge tokens, where ratios of TE downwards from 14.61 to 13.81 and 7.42 to 5.32 on both backbones, respectively. However, the larger α cannot yield better response quality, and the EM score is optimal when alpha is around 1.0. Unfortunately, the larger α gives rise to the aggravation of the performance in Locality, where the ∆ in DISCO will lower the probability of the tokens predicted by the original model. However, we could obtain the trade-off between Locality and Portability by setting α to 1.0. With this setting, DISCO could yield competitive and stable performance with IKE in Locality, and outperform IKE in Portability.

heading: C Ablation for Prepended Paraphrased edited knowledge
text: We supply the exploration of the impact of the prepended paraphrased edited knowledge to DISCO on the zsRE dataset with LlaMa-2-7b. As illustrated in Table 9, without the paraphrased edited knowledge, DISCO suffers a loss in terms of portability and outdated issue problems, compared to DISCO. The worse performance of DISCO without the paraphrased edited knowledge demonstrates that the prepend paraphrased edited knowledge is beneficial for the edited model and enhances its performance on reasoning questions w.r.t. edited knowledge.

heading: Future Work
text: We leave these in future work to take further improvement