Thank you for highlighting our novel findings on super weights and their practical implications for LLM quantization - we're particularly glad you found the methodology clear and appreciate your recognition of how this work could benefit future research in the field.

1. Connection to Adversarial Examples:

This is a good point. We agree that there is a similarity between super weights and adversarial examples, however, there is also a fundamental difference between them. We will add the following discussion to the manuscript:

The connection between Super Weights and adversarial examples lies in how both phenomena demonstrate neural networks' sensitivity to small changes. In adversarial examples, minor input perturbations can drastically alter model outputs. Similarly, modifying Super Weights can significantly impact model quality. This sensitivity suggests that neural networks develop highly specialized pathways during training that can be vulnerable to targeted changes. However, there is a fundamental distinction between these phenomena. Adversarial examples are input-specific – they exploit vulnerabilities in how the model processes particular inputs. In contrast, Super Weights represent core structural elements whose importance persists across all inputs. While adversarial examples reveal weaknesses in input processing, Super Weights illuminate fundamental aspects of neural network architecture and computation. This input-agnostic nature of Super Weights suggests they represent essential computational primitives that emerge during training, rather than specific vulnerabilities that can be exploited.

2. Magnitude Pruning Baseline

When we did global magnitude pruning, we set thresholds for each weight tensor to identify outliers, meaning it captures the most significant weights in any given layer already. The fact that removing super weights degrades performance more than removing these globally-identified outliers - including those within the same layer - provides even stronger evidence for their unique importance.

3. Quantization Baseline with Clipping

We would like to clarify that for activation quantization, we did not apply clipping in both baseline and proposed methods. Are you suggesting incorporating clipping in the RTN baseline in weight quantization? We will be happy to provide the enhanced baseline results, if that's the case.

We would also like to clarify that we use samples from the train set from Wikitext-2 to determine the clipping threshold, while evaluating the models on the test set, which are independent of the train set.

4. Clarification on Prune SW,+SA setting.

Let's take Llama-7B as an example. In the mlp.down_proj layer, the super weight is the [3968, 7003] element in weight matrix W [4096, 11008]. For a 10-token input, the hidden states X [10, 11008] transform through down_proj to X' = XW^T [10, 4096]. The super weight affects the 3968th channel across all tokens, while a super activation typically appears on just one token. The "Prune SW+SA" condition removes both the super weight and any associated super activations to investigate whether SW's impact on model quality operates:

• Primarily through the single-token SA
• Also through broader effects across other input tokens

Thank you for acknowledging the discovery of super weights and super activations.

W1. Failed to improve SOTA

Our study's primary objective is not to outperform SOTA methods, but rather to explain why they work effectively. Our key finding is that super activation handling appears to be a critical mechanism underlying SOTA methods' success. By achieving comparable performance with a simpler method focused solely on super activations, we demonstrate that while SOTA methods effectively handle these activations, they may simultaneously be processing many unnecessary outliers. This insight has important practical implications. It suggests that quantization methods could potentially be simplified while maintaining effectiveness by focusing specifically on super activations rather than broad outlier management. This aligns with a key goal in LLM quantization research: handling as few outliers as possible while maintaining model quality. While our method does not exceed SOTA performance, we believe our work makes a valuable scientific contribution by revealing a fundamental mechanism behind SOTA methods' success and demonstrating it through a minimal working example. These insights provide clear design principles for developing simpler, more efficient quantization approaches in future research.

W2: Hardware experiments

In this work, our primary focus was demonstrating the impact of super outliers on quantization. We agree that hardware performance metrics would be valuable in practical applications (but such measurements depend strongly on the hardware chosen), and such analysis does not impact the key observation of this paper: that super outliers exist.

Q1: For equation 1, the median is used to replace super activation. Is getting the median time-consuming since GPU is not good at sorting?

We initially used the median value as a simple placeholder, since the value will be immediately replaced before computation with the actual super outlier. A better choice, would be to use any inlier value, since again, this is a simple placeholder. To optimize computational efficiency, we updated our manuscript to specify that instead of a median value, we can use the first element of the tensor, as this requires O(1) time complexity compared to O(n log n) for median calculation. This modification will not affect the final results while significantly reducing computational overhead. We will update the manuscript to reflect this more efficient approach and clarify the rationale behind the placeholder selection.

Q2: Run SmoothQuant on more models (line 407 - line 409).

We will add these comparisons to the final manuscript.

1. Regarding the necessity of "super weights":

Our research demonstrates that there is a crucial distinction between general outliers and what we term "super weights." Our key finding is that not all outliers carry equal importance, and their importance is not determined by magnitude. Specifically, we show that super weights, despite not being the largest weights in the network, have disproportionate impact compared to the other 7,000+ outliers combined. This novel observation challenges the conventional understanding of outlier importance in LLMs.

2. Regarding the "Prune SW, +SA" setting:

Our experiments show that pruning super weights (SW) naturally leads to a significant decrease in super activation (SA) magnitudes, shown in Figure 4. The "Prune SW, +SA" experiment was specifically designed to investigate whether super weights' influence is limited to their direct effect on super activations (on a single token) or if they also impact other tokens through different pathways. We have updated the manuscript to make this distinction clearer.

Regarding Figure 2:

The figure illustrates the propagation mechanism of super weights' influence through the network. Specifically, it shows how a super weight in an early layer generates super activation, which then propagates through skip connections to subsequent layers, ultimately affecting token probabilities.

Others

Minor points on terminology and notation, we have updated the manuscript to:

• Standardize our mathematical notation (e.g., Y_{ij}, X_{ik}, W_{jk})
• Enhance our figures and tables to better convey our findings

Regarding your statement “I recommend a strong reject based on the quality of this paper and will not change my rate.” We find such firm-willed sentiment in a scientific review panel concerning, and we encourage the reviewer to read the ICLR reviewing guidelines “If you believe that a paper has flaws in terms of its evaluation or validation, proofs, or other parts of the discussion, it is critical to point this out to the authors. The authors will have an opportunity to address these concerns, and the iterative process of improving papers after reviewer feedback is important for ensuring the highest quality of ICLR papers.”

This reviewing process is designed to be iterative, where both reviewers and authors have the opportunity to discuss their questions, concerns, and suggestions for improvement.

I appreciate the authors' effort in writing a good paper and Reviewer rhtc for providing the review. However, it seems that this review doesn't point out the real weakness of the paper (most Weakness points are about minor paper writing issues which have been addressed by the authors). The last paragraph of the review, "after several readings" are confusing since the reviewer mentioned additional concerns but didn't list them out. The text structure is potentially obtained from LLMs like ChatGPT. I suggest the area chair to look into this review to provide a more fair assessment of the paper.

Thank your for acknowledging the importance of the discovery of super weights.

1. The improvements of proposed methods with existing baselines are quite marginal.

We would like to clarify that our study's primary objective is not to outperform SOTA methods, but rather to explain why they work effectively.

Our key finding is that super activation handling appears to be a critical mechanism underlying SOTA methods' success. By achieving comparable performance with a simpler method focused solely on super activations, we demonstrate that while SOTA methods effectively handle these activations, they may simultaneously be processing many unnecessary outliers.

This insight has important practical implications and is of broad interest to the research community. It suggests that quantization methods could potentially be simplified while maintaining effectiveness by focusing specifically on super activations rather than imprecise outlier management. This aligns with a key goal in LLM quantization research: handling as few outliers as possible while maintaining model quality.

While our method does not exceed SOTA performance, we believe our work makes a valuable scientific contribution by revealing a fundamental mechanism behind SOTA methods' success and demonstrating it through a minimal working example. These insights provide clear design principles for developing simpler, more efficient quantization approaches in future research.

2. How super weights are formed during training.

A comprehensive analysis of training dynamics is planned for future work; we can share some preliminary findings based on our analysis of OLMo-1b training checkpoints. We traced the evolution of super weight magnitudes across training steps (see plots here), with each curve representing an individual super weight. Our observations revealed two distinct phases that we will further study in future work:

1. Underfitting Phase (0-100k steps):

• Super weights exhibit rapid magnitude growth
• Their magnitudes surpass other outlier weights significantly

2. Overfitting Phase (100k-700k steps):

• Super weight magnitudes gradually decrease
• This decline is likely attributable to the weight decay mechanism

Dear reviewer agim,

Since the rebuttal deadline is approaching, we would like to check in about our response to your review. We would appreciate your thoughts on our clarifications and reconsideration on the rating.

Thanks!

1. The novelty of discovering super weights and super activations.

Our work makes two key novel contributions:

1. We systematically identify and characterize a tiny set of "super weights" that are crucial for model performance (even a single weight). Prior studies noted weight outliers but did not isolate this essential subset or demonstrate their necessity.
2. We establish a causal relationship between super weights and super activations, showing that these extreme activation patterns emerge specifically from super weights. This advances beyond previous work that observed super activations without showing where they stem from.

2. Comparison to other quantization methods.

Our key finding is that super activation handling appears to be a critical mechanism underlying SOTA methods' success. By achieving comparable performance with a simpler method focused solely on super activations, we demonstrate that while SOTA methods effectively handle these activations, they may simultaneously be processing many unnecessary outliers. This insight has important practical implications. It suggests that quantization methods could potentially be simplified while maintaining effectiveness by focusing specifically on super activations rather than broad outlier management. This aligns with a key goal in LLM quantization research: handling as few outliers as possible while maintaining model quality. We believe our work makes a valuable scientific contribution by revealing a fundamental mechanism behind SOTA methods' success and demonstrating it through a minimal working example. These insights provide clear design principles for developing simpler, more efficient quantization approaches in future research.

3. In Figure 6, do the authors have any insights into the concave behavior of the scaling factor? Are there specific explanations or potential methods for identifying this optimal scaling factor?

Thank you for this insightful observation about the concave behavior. We believe the scaling curve's shape can be explained by considering the dynamics of model training, particularly in later stages. As pre-training progresses and the language modeling loss becomes small, the weight decay term begins to dominate the loss function. This regularization effect actively encourages weights to maintain smaller magnitudes, potentially preventing super weights from naturally reaching their optimal scale during training. This perspective suggests an interesting future direction: using a small calibration dataset to "finetune" just the super weights, allowing them to reach their optimal scale without the constraints imposed by weight decay during pre-training. This targeted approach could help identify more optimal scaling factors while maintaining the model's learned representations. We will update the manuscript to further clarify this point.

4. Regarding the stop word shift in distribution, is it generally accepted that a higher probability of stop words negatively impacts LLM performance?

The relationship between stop word probabilities and LLM performance is context-dependent. In tasks like LAMBADA, where the goal is predicting meaningful target words, our evidence suggests that higher stop word probabilities indeed negatively impact LLM performance. This manifests in two ways: In next-word prediction tasks like LAMBADA (predicting a passage's final word), increased stop word probability is resulted from the lower probability of meaningful target words across samples. Our case study (lines 258-262) demonstrates that removing super weights causes the target word probability to plummet from 81.4% to under 9%, indicating severe degradation of language modeling capability.