SimPER: A Minimalist Approach to Preference Alignment without Hyperparameters

Response to Reviewer MQ2x Part (1/2)

Dear reviewer MQ2x, we appreciate your time, comments, and suggestions very much! However, we believe that there may have been some misunderstandings. Therefore, we would like to provide a point-by-point response to your comments. --- **Q1. If the exponential operation in eq.(8) is removed, the loss degrades into standard fine-tuning that learns the chosen completion and unlearns the rejected completion. It will be beneficial to compare with the standard fine-tuning and elaborate why adding the exponential operation is better?** **A1**. Thank you for your valuable suggestion! We conducted an ablation study by removing the exponential operation, and the results are provided in Table 5 in the updated submission. We observe that the performance becomes significantly worse than the baselines when the exponential operation is removed. The reason is that the norm of the gradient on rejected responses becomes very large without the exponential operation, as the gradient of the model probability is weighted by the reciprocal of the model probability for the rejected response. We also provide the training dynamics of removing the exponential operation in Figure 7 in the updated submission, which further verifies that the likelihood of both rejected and chosen responses decreases rapidly when the exponential operation is removed. --- **Q2. I disagree with the analysis on line 249. The authors neglect the weight term $w_{\theta}$.** **A2.** **We apologize for any confusion and believe there may have been some misunderstandings. While there is a weight term applied to the gradients of rejected responses, it is also shared by chosen responses. Our analysis specifically focuses on the gradient ratio between chosen and rejected responses.** Specifically, the gradient ratio between the decrease in the probability of rejected responses and the increase in the probability of chosen responses is: $$ \frac{\pi_{\theta}(y_{w} \mid x)}{\pi_{\theta}(y_{l} \mid x)} \cdot \frac{\nabla_{\theta} \pi_{\theta}(y_{l} \mid x)}{\nabla_{\theta} \pi_{\theta}(y_{w} \mid x)}, $$ which becomes infinite when $\pi_{\theta}(y_{l} \mid x) \rightarrow 0$. A larger gradient ratio leads to a faster decrease in the probability of a rejected response compared to the increase in the probability of a chosen response during the training process (i.e., the model emphasizes rejected responses more than chosen responses). In contrast, our SimPER alleviates this issue because the gradient of the model probability is not weighted by the reciprocal of the model probability. We apologize for any confusion caused and have clarified this point more explicitly in the updated submission (marked with red text). --- **Q3. My primary concern is whether the proposed method can be scaled to iterative preference learning, which is currently employed by the state-of-the-art open-weight models.** **A3.** Thank you for your comments. **Our works focus exclusively on offline settings, avoiding any iterative training processes. Nevertheless, we have discussed and cited the papers mentioned by the reviewers in Section 4.2 and completely agree that including an empirical comparison on iterative training processes would be valuable.** Following your suggestion, we are actively working on an iterative version of SimPER. Specifically, we alternate between generating online preference optimization data and training the Mistral-7B-Instruct model with labeled preference data using the PairRM reward model. From the following results, we find that the online version of SimPER generally continues to improve performance with each additional iteration. These results have also been included in the updated submission . | Methods | AlpacaEval2 LC | AlpacaEval2 WR | MT-Bench | GPQA | MATH |TruthfulQA | | --- | --- | --- | --- | --- |--- |--- | | SimPO |     32.1|     34.8 | 7.6 | 28.04 | 2.19 | 68.40 | | SimPER (1 Iter) |     37.8 |     39.5 | 7.8 | 28.36 | 2.51 | 68.78 | | SimPER (2 Iter) |     38.5 |     41.1 | **7.9** | 28.52 | 2.62 | **68.92** | | SimPER (3 Iter) |     **40.2** |     **43.5** | **7.9** | **29.37** | **2.65** | 68.41 | --- **Q4. I noticed that Table 2 is largely copied from SimPO [6], which is fine but contradicts with the statement “We thoroughly tuned the hyper parameters for each baseline” on line 371?** **A4.** Thank you for your comment. Yes, for Table 2, the baseline results are taken from SimPO, as we found the code provided by SimPO to be fully reproducible, and we strictly followed the same settings as in SimPO. The statement 'We thoroughly tuned the hyperparameters for each baseline' refers specifically to the safety alignment task. We apologize for any confusion caused and have clarified this point in the updated submission.

Response to Reviewer MQ2x Part (2/2)

**Q5. By the way the MT-Bench score for Llama-3-8B-Base seems was mistakenly duplicated as the result where GPT-4-Turbo serves as the judge.** **A5.** Thank you for your comments, and we apologize for any confusion. We utilized GPT-4, not GPT-4-Turbo, as the judge. However, there was a single typo: SFT should be 6.6 instead of 5.2. We have corrected this. --- **Q6. Could you please provide the scores for the SFT model in Tab. 3 to illustrate the alignment tax?** **A6.** Thank you for your suggestions. **We have updated Table 3 to include the results of the SFT model. Please refer to the updated submission PDF.** The results demonstrate that SimPER can more effectively preserve reasoning abilities than SimPO and DPO, such as math and abstract reasoning, and even significantly outperforms SFT in many cases. Consequently, SimPER incurs less alignment tax given its superior performance on alignment benchmarks. --- **Q7. Minor: typo in eq. (4) and expression for $d_{\theta}$ on line 244.** **A7.** Thank you for pointing out the typos! We have corrected them. ---

Summary of Response to Reviewer MQ2x

Dear reviewer MQ2x, we appreciate your comments and sincerely thank you for your feedback. We have made our utmost effort to address your comments in the rebuttal. **We clarified several details to address your comments, suggestions and misunderstandings . We also further evaluated SimPER in the online iterative scenario.** **As all reviewers have noted, SimPER presents a simple yet effective approach, offering valuable insights and addressing a very important and practical real-world problem i.e., sensitivity of alignment objectives to hyper-parameters. As your comments are indeed not fatal to the major contributions of our manuscript, could you please consider raising your score in light of our efforts? Many thanks for your time; we are extremely grateful!**

Response to Reviewer dfTo

Dear reviewer dfTo, we sincerely appreciate your recognition of our contributions and your positive comments on our work, such as 'well-written,' 'well-motivated,' 'simple with significant advantages,' and 'sound experiments.' Please find our responses to your comments below: --- **Q1. Would SimPER’s application extend beyond the paired preference data scenario described in the paper? This could incorporate comparisons with unpaired alignment algorithms.** **A1.** Thank you for your question! SimPER can be extended to unpaired data, as it only requires either single chosen or rejected samples without the need for pairwise data, similar to KTO. To test this, we randomly discarded the chosen responses or rejected responses in increasingly large fractions of pairwise data while aligning the Llama3-8B-Base model. Please refer to Table 8 in the updated submission. These additional results demonstrate that even without pairwise data (e.g., discarding up to 50\% of the chosen or rejected responses), SimPER still outperforms SimPO and performs better than the baseline KTO, which also does not require pairwise data. | Llama3-8B-Base | AlpacaEval2 LC | AlpacaEval2 WR | ARC | TruthfulQA| GSM8K | | --- | --- | --- | --- | --- |--- | | SimPO | 22.0 | 20.3 | 65.19 | 59.46 | 31.54 | | KTO | 14.2 | 12.4 | 63.14 | 55.76 | 38.97 | | KTO (50 %) | 12.7 | 10.5 | 65.52 | 58.73 | 45.31 | | SimPER | 25.2 | 22.9 | 67.06 | 62.59 | 51.02 | | SimPER (50 %) | 23.5 | 21.3 | 68.31 | 63.25 | 49.16 | --- **Q2. While Figure 3 shows that SimPER mitigates the reduction in chosen response log probabilities compared to SimPO, the likelihood of the chosen response is still decreasing. The ORPO paper addresses this issue as well, and Figure 7 in ORPO shows that the likelihood of the chosen response can actually increase.** **A2.** Thank you for your comments! While ORPO can significantly increase the likelihood of the chosen response, it performs worse than SimPER on many benchmarks (please refer to the additional results of ORPO in Table 5 of the updated submission). One possible reason is that the preference datasets are not always of high quality. Often, the chosen response is only slightly better than the rejected one. In such cases, it is not necessarily desirable for the model to significantly increase the probability mass on the chosen response (i.e., overfit to the chosen response). In contrast, SimPER prevents a decrease in the likelihood of the chosen response while also avoiding overfitting to it through a hyperparameter-free objective --- **Q3. On Line 295, "model covering" should likely be "model seeking”?** **A3.** Thanks for pointing out these typos! We have corrected them. --- **We appreciate the efforts from the reviewer and also sincerely hope our posted responses can address your questions. We also believe your comments can also be easily addressed in the revision. In light of these responses, we sincerely hope you could consider increasing your score. Many thanks for your time; we are extremely grateful!**

Response to Reviewer bGmT

Dear reviewer bGmT, we appreciate your positive feedback on our paper's motivation, soundness, novel insights, and contribution. Please find our detailed responses below: --- **Q1. The authors did not compare SimPER with ORPO [1], another reference model-free preference alignment method. Can you include ORPO [1] in the experimental setup** **A1.** Thank you for your suggestions! We further compared SimPER with ORPO across multiple benchmarks, with the results provided in Table 5 of the updated submission. These additional results show that SimPER significantly outperforms ORPO. This is particularly encouraging as SimPER not only operates as a reference model-free preference optimization method but is also hyperparameter-free, unlike ORPO, further highlighting the strength of our contribution. --- **Q2. How sensitive are other preference alignment methods to hyperparameters? Are instruction-tuned models consistently less sensitive to the hyperparameters of the preference alignment methods? (Figure 1).** **A2.** Thank you for your questions. We provided additional results for DPO, KTO, and IPO with different hyperparameters on the Mistral-Base and Mistral-Instruct models in Figure 8 of the updated submission. We observe that these methods are also especially sensitive to hyperparameters, similar to SimPO in Figure 1. Moreover, we find that instruction-tuned models are slightly more robust to the hyperparameters of preference alignment methods. One possible reason may be that our Instruct setup is closer to an on-policy setting, resulting in a smaller distribution shift, which leads to greater robustness. --- **Q3. What is the training dynamic of DPO mentioned in line 253? (Figure 2)** **A3.** Thank you for your question. We also provided the training dynamics of DPO in Figure 7 in the updated submission. We can observe that the likelihood of both chosen and rejected responses continues to decrease, which further supports our discussion in Section 3.3. --- **Q4. How was the reference model incorporated in SimPER in the ablation study?** **A4.** Thank you for your question. The objective that incorporates reference model in SimPER is $$-\exp\left(\frac{1}{|y_w|} \log \frac{\pi_\theta(y_w \mid x)}{\pi_{\text{ref}}(y_w \mid x)}\right)+\exp\left(\frac{1}{|y_l|} \log \frac{\pi_{\theta}(y_l \mid x)}{\pi_{\text{ref}}(y_l \mid x)}\right).$$ We will clearly state this in the main text. **Q5. Line 72, "post-training process for alignment is usually very expensive", I suggest mentioning the LoRA line of work, which made it significantly less expensive [2, 3].** **A5.** Thank you for your suggestion. We have cited these works and added a discussion in the related work section of our updated submission. **Q6. Line 201, "data. (Jelinek et al., 1977; Marion et al., 2023; Gonen et al., 2023).", there is a period before the citation. Figure 6, I suggest decreasing the opacity as it is difficult to read.** **A6.** Thank you for your comments! We have corrected the typo and updated Figure 6 by decreasing the opacity. **We thank the reviewer for providing valuable comments on our paper. In light of these responses, we hope we have addressed your questions and sincerely hope you consider raising your score. Many thanks for your time; we are extremely grateful!**

Response to Reviewer 7YzN Part (1/2)

Dear reviewer 7YzN, we thank you for your valuable suggestions and positive feedback. We are happy to hear that you found our paper to be well-motivated and strong in both empirical and theoretical aspects. The following is our response to your comments: --- **Q1. It would be better if the experiments can show the proposed method works well across different scales of models.** **A1.** Thank you for your valuable suggestion! Following your suggestion, we conducted additional experiments on more different scales of models. Given the short rebuttal time, we choose the recent Qwen2-1.5B-Instruct and Gemma2-9B-Instruct models. The new results are provided in Table 10 in the updated submission (the results on Qwen2-1.5B-Instruct are provided in the table below for your reference). | Model | AlpacaEval 2 LC | AlpacaEval 2 WR | Arena-Hard | GSM8K | TruthfulQA | |---------|--------|--------|--------|--------|------------| | SFT |   5.42 |     3.55 |   2.5 | 59.32 | 28.37 | | DPO |   8.71 |     6.05 |   4.0 | 65.31 | 34.59 | | SimPO |   10.11 |    7.52 |   4.9 | 68.21 | 39.37 | | **SimPER** |   **12.59** |     **9.31** |   **5.5** | **72.75** | **40.33** | These results show that SimPER continues to outperform the baselines on other scales of models. Combined with the comparisons involving 5 base models already presented in our paper, these results strongly validate the effectiveness and robustness of SimPER. We will include these new results in the final version. --- **Q2. In addition, I am confused about the choice of the model. It seems only Fig.4 uses Pythia-2.8B** **A2.** Thank you for your question, and we apologize for any confusion. The reason we chose Pythia-2.8B for Anthropic-HH is to strictly align all settings with those in the well-known original DPO paper and its widely-used code for Anthropic-HH, ensuring fair and reproducible comparisons. We apologize for the confusion and will clearly state this in the main text of our final version. --- **Q3. The proposed loss is fairly simple and I do believe simplicity is good. But the presentation of Eq. (5)(6)(7)(8) is redundant, and (8) should be enough.** **A3.** Thank you for your great suggestion! We included Eqs. (5), (6), and (7) to explicitly connect our simple objective with the well-known perplexity. However, we agree with the reviewer that they are somewhat redundant given SimPER's simplicity. In the final version, we will reorganize the content and remove some of these equations to enhance clarity. --- **Q4. In addition, as suggested by Fig. 2, TVD would encourage the appearance of non-existing mode, i.e., it will also encourage the probability of regions with zero/low probabilities in the support of the chosen responses. Do you observe such behavior in practice?** **A4.** Thank you for your questions! We would like to clarify the following points. As shown in Figure 2, **SimPER, which optimizes reverse TVD for mode-seeking behavior, sharpens the probability mass on only certain high-density regions. In contrast, SimPO, which optimizes forward KLD, forces the model to learn a flat distribution that spans itself to cover all the non-zero probability regions due to its mass-covering behavior [1,2,3].** To highlight the differences between SimPO (Forward KLD) and SimPER (Reverse TVD), as well as the unique benefits of Reverse TVD, we conducted additional experiments on Anthropic-HH, chosen for its controllability. We studied how these divergences affect the trade-off between alignment and diversity in generated responses. For diversity, we generated 25 responses using top-p sampling (p=0.95) for each test prompt and measured predictive entropy and distinct-n [4]. | Anthropic-HH | Alignment (Win-Rate) | Diversity (Entropy) | Diversity (Distinct-1) | Diversity (Distinct-2) | | --- | --- | --- | --- | --- | | SimPER |   59.87 |   12.15 |   0.024 |   0.165 | | SimPO |   50.33 |   14.71 |   0.028 |   0.197 | As shown in the above, SimPER’s mode-seeking property achieves significantly higher alignment performance but slight lower diversity compared to SimPO, whose mass-covering behavior results in higher diversity but lower alignment [3]. These results support our intuition: the mode-seeking nature of reverse TVD reduces diversity but is highly effective for alignment optimization, as noted in [1,3]. Additionally, SimPER outperforms SimPO in challenging tasks such as math and safety alignment. One possible reason is that these tasks have few valid answers per input, making mode-seeking more beneficial. This reinforces the potential of mode-seeking for alignment, consistent with prior observations [1,3]. We will clearly state this in the main text of our submission.

Response to Reviewer 7YzN Part (2/2)

**We sincerely hope that our responses can address your comments. As noticed by the reviewer, our work presents some interesting findings, a simple yet effective framework, and some theoretical contributions. The reviewer's suggestions can be easily and effectively addressed, and we genuinely hope that the reviewer can consider increasing the score. Thank you very much for your time!** [1] Preference Fine-Tuning of LLMs Should Leverage Suboptimal, On-Policy Data. ICML 2024. [2] Learning to Generalize from Sparse and Underspecified Rewards. ICML 2019. [3] Towards Efficient Exact Optimization of Language Model Alignment. ICML 2024 [4] Beyond Reverse KL: Generalizing Direct Preference Optimization with Diverse Divergence Constraints. ICLR 2024

Response to Reviewer bH9h

Dear reviewer bH9h, we sincerely appreciate your recognition of our contributions to simplicity, effectiveness, and theoretical analysis, and we are grateful for the encouraging comments. Please find our responses below: --- **Q1. The author(s) may consider adding the average response length to the results.** **A1.** Thank you for your great suggestion. We have added additional results for the average response length in AlpacaEval 2.0 to Table 5 in the updated submission. These new results, along with our improvement in the length-controlled (LC) win rate, demonstrate that SimPER does not significantly increase response length compared to the baselines, despite SimPER's superior performance and simplicity. --- **Q2. The author(s) might consider including Arena-Hard to better demonstrate performance.** **A2.** We thank the reviewer for suggesting another chat-based benchmark Arena-Hard. Following your suggestion, we have included additional comparisons on Arena-Hard in Table 5 of the updated submission (also provided in the table below). For Arena-Hard, we report the win rate (WR) against the baseline model, consistent with previous work SimPO [1]. These new results further strengthen our contribution and demonstrate that our simple yet effective SimPER achieves superior performance on Arena-Hard. | Models | DPO | CPO | ORPO | SimPO | SimPER | | --- | --- | --- | --- | --- |--- | | Mistral-7B-Base | 10.4 | 6.9 | 7.0 | 16.6 | **18.5** | | Llama3-8B- Base | 15.9 | 5.8 | 10.8 | 23.4 | **24.7** | --- **In light of these responses, we sincerely hope our rebuttal has addressed your comments. If you have any other comments, please do share them with us, and we will address them further. Thank you for your time and efforts!** [1] SimPO: Simple Preference Optimization with a Reference-Free Reward. NeurIPS 2024.