We thank the reviewer for the insightful and constructive feedback. Below we provide our response to each question.

Response to Question 1 and Weakness 1 about parameters in our method:

We agree that more fine-grained sensitivity analysis will provide better insights into our proposed method. We therefore perform additional explorations on the effects of the two parameters, $\lambda$, and LLM layer $l$ where the model activations are taken. Note that the SAE latent dimension is fixed by the pretrained SAE models, therefore is not a parameter in our method.

Due to the restriction in uploading new results, here we describe our approach for this investigation and summarise the general findings. We plan to add this analysis as a section in the appendix and relevant discussions into Section 4.1 in the final version of the paper.

We create a 2-D line plot for each model and each dataset, averaged over four 6-response configurations (6 prompts x 1 sample), (3 x 2), (2 x 3), (1 x 6), yielding 16=4 models x 4 datasets plots. In each plot, the x-axis is the $\lambda$ value, ranging from -1 to 1 with an interval of 0.02, the y-axis is the accuracy. Each plot presents the accuracy of varying $\lambda$ for each ($l$ x {RC-D, RC-S}) combination. We experiment with negative $\lambda$ values to validate the usefulness of representation consistency. When $\lambda$ is negative, the evaluation function of RC (Equation 5) is calculated as: $\lambda\cdot consistency + (1-(abs(\lambda)))\cdot frequency$.

The overall conclusion from the plots regarding $\lambda$ is: The only $\lambda$ value region with constant performance gain over the majority vote accuracy is when $0.25 \leq\lambda \leq0.85$ (roughly, depending on dataset and the choice of dense or sparse activations). The performance steadily drops with small fluctuations as $\lambda$ becomes more negative. Here are some more detailed observations:

• For every line, when $\lambda$ takes values between about [-0.25, 0.25], the accuracy stays constant (with very little fluctuations) at the self-consistency result (majority vote, $\lambda=0$), because the frequency term is dominant in this region.
• When $\lambda$ increases from the above interval into the more positive region, the performance usually also starts to increase for a $\lambda$ interval of about 0.1 with peak increase of about 4% (similar to Figure 2 (a), CSQA dataset with 6 responses). The accuracy then quickly drops (usually happens at $\lambda>0.85$) to a very low value of about 20-25% because frequency no longer plays an important role (the method ends up choosing very infrequent answers).
• When $\lambda$ decreases from the above interval into the more negative region, in most cases, the performance will linearly decrease with fluctuations. The performance drop at $\lambda=-1$ is usually 5 to 10%. Meanwhile, at certain $\lambda$ locations, the performance can fluctuate to up to about 1% over the initial performance.
• The reason for a smaller performance drop at $\lambda=-1$ than when $\lambda=1$ is that the method tends to choose the majority answer in the most negative $\lambda$ region. This is because when the difference between the number of supporting responses for multiple answers is large (which is true for most test points), the majority answer tends to have a lower consistency due to the involvement of more responses, therefore is more likely to be selected by the RC method. For example, for a data point we have 12 responses, 3 are predicting answer A and 9 are predicting answer B, and answer B usually has a lower consistency because. It will more likely be selected by $\lambda=-1$ than by $\lambda=1$. This also highlights the importance of balancing consistency and frequency. We further note that very large absolute $\lambda$ values are impractical to use.
• The differences between model layers $l$ among the same choice of either dense or sparse are almost negligible.
• RC-D reaches the performance peak and the performance drop at lower $\lambda$ values than RC-S (this is consistent with the findings in Table 2).
• Because we are testing this on the whole dataset without the validation/test set split (different to our main experiments in the paper), RC-S almost always achieves higher accuracy than RC-D.

These observations confirm the usefulness of representation consistency. Note that our Table 1 results are averaged for each model over four datasets and 10 prompt x sample configurations (4 for 6 responses and 6 for 12 responses). The Figure 2 results are slightly more fine-grained as they contain two plots for each model and each dataset, respectively averaged over the 4 configurations of 6 responses, and 6 configurations for 12 responses. The maximum accuracy gain in Figure 2 is 4% which is higher than those averaged in Table 1, and of course, there are cases where the performance gain is very small.

Response to Question 2 about method generalisability:

Theoretically yes, our formalisation for the method generalises to other supervised QA scenarios, as long as a concrete, relatively short-form answer can be parsed from the LLM response and can be straightforwardly aggregated across LLM responses, e.g., via semantic entropy [Kuhn, Gal, Farquhar, ICLR 2023]. It will require moderate efforts to generalise beyond multiple choice settings if we specify a list of possible answers for the question. It will require substantial efforts to generalise to more open-ended conversations, possibly involving an extra LLM as the parsing agent. We will mention these as future work.

Response to Weakness 2 about LLM-as-a-judge validity:

We thank the reviewer for pointing this out. We agree that validating LLMs' ability to perform relevant evaluation is an important point to address, which we did not mention in the initial paper. We had assumed the most recent powerful LLMs (including our chosen 671B DeepSeek R1) have learned the concept of "coherence" which we are evaluating. Despite the availability of internet corpus to train these LLMs, another argument for this assumption is that "coherence" is explicitly listed as one of five evaluation dimensions in two popular datasets for training reward models for LLM post-training - HelpSteer [Wang et al., NAACL 2024] and HelpSteer2 [Wang et al., NeurIPS 2024]. LLMs are often prompted as reward models and perform well, according to RewardBench leaderboard.

More concretely, we have curated a tiny validation dataset of 5 data points for checking the LLM's performance on evaluating coherence. Similar to the approach described in Section 4.2, we look at test cases with six model responses where the model produces two answers, and each answer has three supporting model responses. These are taken from Gemma-2-9B-IT's model outputs on MMLU dataset. We manually label the group of answers which is more coherent, and compare the label generated by the LLM model via API call. The accuracy we observed here is 100%.

We plan to include relevant discussions and a scaled-up version of the above validation experiment in the final version of the paper.

Response to Weakness 3 about implementation details:

Our setting assumes that the LLM answers have been generated. The remaining procedures give deterministic results. We did not test the method over multiple runs of LLM generations for the same data. The results in Figure 2 are averaged over the 4 and 6 configurations (prompt x sample) respectively for 6 and 12 responses. We report detailed results for every configuration in Appendix C.2.

We thank the reviewer for the positive feedback. Below we provide detailed responses to the comments.

Response to Question about different model sizes:

Our method works on various prompting and sampling strategies on the same model because we need to take its internal activations for different generation traces. While activations from different models will not be readily comparable, there is recent research on transferring information across the activations from different models [Activation Space Interventions Can Be Transferred Between Large Language Models, Oozeer et al., ICML 2025]. So this direction will be interesting future work.

Additionally, in the setting of multiple models, one could employ our method in a composite answer aggregation framework where, an answer from each model is first determined by our method, then a higher-level aggregation is performed over each model's answer.

Response to Limitations

We appreciate the practical considerations raised by the reviewer. We agree that our targeted scenario is not the most generic, but including multiple prompts and samples can also be realistic, e.g., for prompt template selection and for uncertainty quantification. We will include this caveat in the limitation discussions in the final version of the paper.

We thank the reviewer for the helpful and insightful comments. Below, we provide detailed responses to each question.

Response to Question 1. Comparison with MBR missing:

Our adapted answer selection baseline, RC-E, builds on the same intuition as MBR decoding. It is described in Lines 171-190 in the paper's main text - taking the final answer which is frequent and whose Chain-of-Thought outputs are the most semantically similar. Our methods, on the other hand, focus on the similarity in each candidate LLM output's internal representation and outperform this baseline.

Additionally, both the MBR method and the reference [1] listed by the reviewer are orthogonal to our proposed method. Our method operates on multiple LLM outputs regardless of the sampling strategies with which they are obtained. Therefore, investigating the influence of different decoding process on the performance of RC would be an interesting future work, but is out of the scope of this study. We mentioned this line of future work in the paper's main text at Lines 314-316.

The other two references [2] and [3] listed by the reviewer target different scenarios from ours. They resolve the conflicts between different vocabularies across multiple LLMs, whereas our method works on multiple generations for the same LLM with a focus on the internal activations. References [1] [2] [3] all focus strongly on machine translation, which is also different to our setting. We will add pointers to these references as related works in the final version of our paper.

Response to Question 2. Limited sensitivity analysis of method parameters:

We agree that more fine-grained sensitivity analysis will provide better insights into our proposed method. We therefore perform additional explorations on the effects of the two parameters, $\lambda$, and LLM layer $l$ where the model activations are taken. Note that the SAE latent dimension is fixed by the pretrained SAE models, therefore is not a parameter in our method.

Due to the restriction in uploading new results, here we describe our approach for this investigation and summarise the general findings. We plan to add this analysis as a section in the appendix and relevant discussions into Section 4.1 in the final version of the paper.

We create a 2-D line plot for each model and each dataset, averaged over four 6-response configurations (6 prompts x 1 sample), (3 x 2), (2 x 3), (1 x 6), yielding 16=4 models x 4 datasets plots. In each plot, the x-axis is the $\lambda$ value, ranging from -1 to 1 with an interval of 0.02, the y-axis is the accuracy. Each plot presents the accuracy of varying $\lambda$ for each ($l$ x {RC-D, RC-S}) combination. We experiment with negative $\lambda$ values to validate the usefulness of representation consistency. When $\lambda$ is negative, the evaluation function of RC (Equation 5) is calculated as: $\lambda\cdot consistency + (1-(abs(\lambda)))\cdot frequency$.

The overall conclusion from the plots regarding $\lambda$ is: The only $\lambda$ value region with constant performance gain over the majority vote accuracy is when $0.25 \leq\lambda \leq0.85$ (roughly, depending on dataset and the choice of dense or sparse activations). The performance steadily drops with small fluctuations as $\lambda$ becomes more negative. Here are some more detailed observations:

• For every line, when $\lambda$ takes values between about [-0.25, 0.25], the accuracy stays constant (with very little fluctuations) at the self-consistency result (majority vote, $\lambda=0$), because the frequency term is dominant in this region.
• When $\lambda$ increases from the above interval into the more positive region, the performance usually also starts to increase for a $\lambda$ interval of about 0.1 with peak increase of about 4% (similar to Figure 2 (a), CSQA dataset with 6 responses). The accuracy then quickly drops (usually happens at $\lambda>0.85$) to a very low value of about 20-25% because frequency no longer plays an important role (the method ends up choosing very infrequent answers).
• When $\lambda$ decreases from the above interval into the more negative region, in most cases, the performance will linearly decrease with fluctuations. The performance drop at $\lambda=-1$ is usually 5 to 10%. Meanwhile, at certain $\lambda$ locations, the performance can fluctuate to up to about 1% over the initial performance.
• The reason for a smaller performance drop at $\lambda=-1$ than when $\lambda=1$ is that the method tends to choose the majority answer in the most negative $\lambda$ region. This is because when the difference between the number of supporting responses for multiple answers is large (which is true for most test points), the majority answer tends to have a lower consistency due to the involvement of more responses, therefore is more likely to be selected by the RC method. For example, for a data point we have 12 responses, 3 are predicting answer A and 9 are predicting answer B, and answer B usually has a lower consistency because. It will more likely be selected by $\lambda=-1$ than by $\lambda=1$. This also highlights the importance of balancing consistency and frequency. We further note that very large absolute $\lambda$ values are impractical to use.
• The differences between model layers $l$ among the same choice of either dense or sparse are almost negligible.
• RC-D reaches the performance peak and the performance drop at lower $\lambda$ values than RC-S (this is consistent with the findings in Table 2).
• Because we are testing this on the whole dataset without the validation/test set split (different to our main experiments in the paper), RC-S almost always achieves higher accuracy than RC-D.

These observations confirm the usefulness of representation consistency. Note that our Table 1 results are averaged for each model over four datasets and 10 prompt x sample configurations (4 for 6 responses and 6 for 12 responses). The Figure 2 results are slightly more fine-grained as they contain two plots for each model and each dataset, respectively averaged over the 4 configurations of 6 responses, and 6 configurations for 12 responses. The maximum accuracy gain in Figure 2 is 4% which is higher than those averaged in Table 1, and of course, there are cases where the performance gain is very small.

Response to Question 3. Lack of evaluation on mathematical reasoning tasks and other generative tasks:

We appreciate the reviewer's suggestion to include more benchmarks. Our goal in this paper is to evaluate RC's performance on general reasoning tasks with multiple-choice output format, for which we believe our choice of four datasets is sufficient. The chosen datasets are also widely adopted in prior works.

In terms of adapting our method to other forms of generation tasks, this will require non-trivial extensions to be able to process and aggregate the possible discrete answer choices among the LLM generations, possibly with the help of semantic entropy [Kuhn, Gal, Farquhar, ICLR 2023] for shorter form answers (supervised QA) or another LLM judge for longer form open-ended conversations. Our compute resources are shared by a large group and so are limited. We will mention these suggestions as future work.

Response to Question 4. Computational cost of RC-S not reported:

In Lines 149 and 191-195, we discussed that the SAEs we used are pretrained models. We do not claim the training of such SAEs as part of our contribution. The SAEs are generally reusable, and RC-S only requires negligible additional computational cost compared with RC-D.

Reusability of SAEs: SAEs are usually trained for one LLM at a time and then can be generally reused for this LLM, because the SAE training uses the LLM's activations over the LLM's own pretraining data (see Section 3.1 of reference [40]). In fact, these SAEs are widely used in the mechanistic interpretability literature to investigate LLM behaviours related to their internal activations with sparsified signals. Training SAEs is an active research field with public benchmarks (e.g., SAEBench: A Comprehensive Benchmark for Sparse Autoencoders in Language Model Interpretability, ICML 2025). The Python library SAE-Lens contains a list of supported SAEs for various LLMs. We took the open-weight SAEs in this library for our experiments.

Additional computational costs of SAEs: If the layer number and lambda value are determined, the additional cost of this over RC-D for an input text is one forward pass in the SAE. Specifically, the input to SAE, LLM's residual activation at one token position, is of shape (1, $d_\pi$), where $d_\pi$ is the LLM's hidden dimension (2304 for Gemma-2-2B, 3584 for 9B, 4608 for 27B, 4096 for Llama-3.1-8B). The number of parameters in each SAE is: 0.076B for Gemma-2-2B, 0.117B for Gemma-2-9B, 1.2B for Gemma-2-27B, 0.27B for Llama-3.1-8B model. The small SAE model size (compared to their corresponding LLM) and the small input size (only 1 token length) mean that the additional computational cost is only a fraction of the LLM's forward pass over a prompt.

We will add relevant discussions to the main text of the paper, should it be accepted.

Response to Question 5. Limited analysis on response set size:

Please note that in each number of responses configuration, we further have different Prompt x Samples configurations. So, in 6 responses we included (6 prompts x 1 sample), (3 x 2), (2 x 3), (1 x 6); in 12 responses we included (12 prompts x 1 sample), (6 x 2), (4 x 3), (3 x 4), (2 x 6), (1 x 12). These make 10 different experiment settings for each model and dataset, which we considered sufficient.

We thank the reviewer for the insightful feedback. We provide responses to the questions below.

Response to Question 1 and Weakness 2 about Non-CoT scenario:

Our target is on any combination of prompts and sampling strategies, e.g., 12 model generations from 2 prompts and 6 samples per prompt. This is more generic than "make sure the representations are consistent across different prompts". We decided to focus on CoT setting because this is a more general setting and allows the model to generate diverse reasoning traces, even for the same prompt.

We might be measuring the similarity of reasoning trace, and that is an intended behaviour of the proposed approach. The model activation is taken at the final answering token position, i.e., after the CoT reasoning and before it decides which candidate answer to select. This representation captures the encodings for both the question and its own reasoning trace for answering the question, which is in line with our targeted scenario. This means that we are not just measuring the surface level syntactic similarity of reasoning (this is what the baseline, RC-E is doing), but the semantic similarity internal to the model's generation process.

In terms of the non-CoT setting, we need to consider two types of configurations.

• First, let's consider when multiple samples are needed. When we have one prompt only, the model activations for multiple samples are identical because this is taken at the end of: "... the final answer is:". The differences in the generated answering token between each sampled answer (e.g., A, B, C) only come from the decoding and the sampling process itself. Therefore, the consistency measure (Equation 6) will be 1 for any group of model outputs, and will be 1 for even outputs across different answers. The RC selection process (Equation 8) will be dominated by the frequency term. Our method therefore becomes identical to self-consistency. When we have multiple samples per prompt and additionally multiple prompts, it would not make sense to aggregate and calculate representation consistency, knowing that different answers might also have identical model activations. This is a major reason why we focus on CoT setting only.

• Then, the only non-CoT configuration for RC to make sense is when we have multiple prompts and one sample per prompt. We did investigate applying RC to non-CoT outputs in early explorations, and the performance gains were similar to current results. However, we ignored these because such configurations (6 prompts x 1 samples, and 12 x 1) are only a fraction of our reported configurations.

Response to Questions 2, 4 and Weaknesses 1, 3 about performance gain and parameters:

We agree that more fine-grained sensitivity analysis will provide better insights into our proposed method. We therefore perform additional explorations on the effects of the two parameters, $\lambda$, and LLM layer $l$ where the model activations are taken.

Due to the restriction in uploading new results, here we describe our approach for this investigation and summarise the general findings. We plan to add this analysis as a section in the appendix and relevant discussions into Section 4.1 in the final version of the paper.

We create a 2-D line plot for each model and each dataset, averaged over four 6-response configurations (6 prompts x 1 sample), (3 x 2), (2 x 3), (1 x 6), yielding 16=4 models x 4 datasets plots. In each plot, the x-axis is the $\lambda$ value, ranging from -1 to 1 with an interval of 0.02, the y-axis is the accuracy. Each plot presents the accuracy of varying $\lambda$ for each ($l$ x {RC-D, RC-S}) combination. We experiment with negative $\lambda$ values to validate the usefulness of representation consistency. When $\lambda$ is negative, the evaluation function of RC (Equation 5) is calculated as: $\lambda\cdot consistency + (1-(abs(\lambda)))\cdot frequency$.

The overall conclusion from the plots regarding $\lambda$ is: The only $\lambda$ value region with constant performance gain over the majority vote accuracy is when $0.25 \leq\lambda \leq0.85$ (roughly, depending on dataset and the choice of dense or sparse activations). The performance steadily drops with small fluctuations as $\lambda$ becomes more negative. Here are some more detailed observations:

• For every line, when $\lambda$ takes values between about [-0.25, 0.25], the accuracy stays constant (with very little fluctuations) at the self-consistency result (majority vote, $\lambda=0$), because the frequency term is dominant in this region.
• When $\lambda$ increases from the above interval into the more positive region, the performance usually also starts to increase for a $\lambda$ interval of about 0.1 with peak increase of about 4% (similar to Figure 2 (a), CSQA dataset with 6 responses). The accuracy then quickly drops (usually happens at $\lambda>0.85$) to a very low value of about 20-25% because frequency no longer plays an important role (the method ends up choosing very infrequent answers).
• When $\lambda$ decreases from the above interval into the more negative region, in most cases, the performance will linearly decrease with fluctuations. The performance drop at $\lambda=-1$ is usually 5 to 10%. Meanwhile, at certain $\lambda$ locations, the performance can fluctuate to up to about 1% over the initial performance.
• The reason for a smaller performance drop at $\lambda=-1$ than when $\lambda=1$ is that the method tends to choose the majority answer in the most negative $\lambda$ region. This is because when the difference between the number of supporting responses for multiple answers is large (which is true for most test points), the majority answer tends to have a lower consistency due to the involvement of more responses, therefore is more likely to be selected by the RC method. For example, for a data point we have 12 responses, 3 are predicting answer A and 9 are predicting answer B, and answer B usually has a lower consistency because. It will more likely be selected by $\lambda=-1$ than by $\lambda=1$. This also highlights the importance of balancing consistency and frequency. We further note that very large absolute $\lambda$ values are impractical to use.
• The differences between model layers $l$ among the same choice of either dense or sparse are almost negligible.
• RC-D reaches the performance peak and the performance drop at lower $\lambda$ values than RC-S (this is consistent with the findings in Table 2).
• Because we are testing this on the whole dataset without the validation/test set split (different to our main experiments in the paper), RC-S almost always achieves higher accuracy than RC-D.

These observations confirm the usefulness of representation consistency. Note that our Table 1 results are averaged for each model over four datasets and 10 prompt x sample configurations (4 for 6 responses and 6 for 12 responses). The Figure 2 results are slightly more fine-grained as they contain two plots for each model and each dataset, respectively averaged over the 4 configurations of 6 responses, and 6 configurations for 12 responses. The maximum accuracy gain in Figure 2 is 4% which is higher than those averaged in Table 1, and of course, there are cases where the performance gain is very small.

Finally, as we note as a limitation in our conclusion (Lines 307-309), while incorporating representation consistency into answer selection enables performance gain at a dataset level, it does not guarantee a more truthful answer for every input. This is because the LLM might be confidently wrong about certain knowledge, where consistent reasoning (and activations) can lead to wrong answers.

Response to Question 3 about model confidence:

We assume the LLM "confidence" mentioned by the reviewer is referring to uncertainty quantification (UQ), which is itself an ongoing research question. The most obvious approach for this is to look at the token probability when the model is generating the final answers. In our early explorations, we observed over-confident token proabilities for different predicted answers across multiple responses for the same question. Recent research (reference [11] in our paper) uses some similarity metric based on LLM's dense internal activations over multiple model generations for UQ purpose and shows improved calibration (AUROC of using this new metric to predict LLM answers' correctness) over count-based UQ baselines (like Semantic Entropy [Kuhn, Gal, Farquhar, ICLR 2023]). This suggests that useful signals can be extracted from the LLMs' internal activation spaces for better UQ.

Our method additionally considers the answer frequency, SAE sparsified signals, and multiple prompt x samples configuration, thus should intuitively correlate well with UQ and calibration. Indeed, the relationship between our method and LLM UQ could be interesting future work. We have mentioned this in our submitted paper at Lines 319-322.