Cherry on Top: Parameter Heterogeneity and Quantization in Large Language Models

Authors: wanyun  cui
qianle  wang
Venue: NeurIPS_cc_2024_Conference
Published: 2024-05-10 20:28:05

Abstract: This paper reveals the phenomenon of parameter heterogeneity in large language models (LLMs). We find that a small subset of ``cherry'' parameters exhibit a disproportionately large influence on model performance, while the vast majority of parameters have minimal impact. This heterogeneity is found to be prevalent across different model families, scales, and types. Motivated by this observation, we propose CherryQ, a novel quantization method that unifies the optimization of mixed-precision parameters. CherryQ identifies and preserves the critical cherry parameters in high precision while aggressively quantizing the remaining parameters to low precision. Extensive experiments demonstrate the effectiveness of CherryQ. CherryQ outperforms existing quantization approaches in terms of perplexity and downstream task performance. Notably, our 3-bit quantized Vicuna-1.5 exhibits competitive performance compared to their 16-bit counterparts. These findings highlight the potential of CherryQ for enabling efficient deployment of LLMs by taking advantage of parameter heterogeneity.

Main paper: 
 introduction: 
 The rapid development of large language models (LLMs) has increased the demand of efficient deployment in various environments [1, 2, 11, 23] . However, the parameter size poses significant challenges for GPU memory requirements. Quantization, which reduces the bit-width of model parameters, has emerged as a solution to alleviate memory constraints of LLM deployment [12, 14, 18, 25, 26] .Low-precision parameter representation leads to quantization errors. Surprisingly, existing research has shown that LLMs exhibit a high robustness for quantization errors even for low-bit settings. For example, although 4-bit quantization can only represent 16 distinct values, even the simplest round-to-nearest strategy does not significantly degrade performance [17] . This raises the question: what causes LLMs to be robust to quantization?We explore the parameters and answer this question via Parameter Heterogeneity, which refers to the significant variation in the influence of quantization on different parameters. We reveal that for the vast majority (> 99%) of normal parameters, the effect of their quantization to the model are minimal and can thus be alleviated or ignored. However, there exists a small subset (< 1%) of "cherry" parameters for which the effect are substantial and hard to mitigate.Consider Figure 1a as an example. We show a scatter plot of the impacts on the model loss when perturbing each individual parameter in a parameter matrix from LLaMA2-7b [23] . The derivation of impacts is detailed in § 3. While 99% of the parameters fall within the range of (0, 0.1), a small subset of "cherry" parameters exhibits values ranging from (5, 30) , which is 50-300 times higher than the maximum value of the remaining 99% of parameters. Moreover, this phenomenon is not an isolated case. We observed similar patterns across different scales of LLMs (Figure 1a1b ), different families of LLMs, including Mistral [11] (Figure 1c ) and Gemma [22] (Figure 1d ), and both base models and chat models (Vicuna-1.5 [5] Figure 1e1f ). The consistent presence of this phenomenon suggests that parameter heterogeneity is an inherent characteristic of LLMs.Therefore, 99% of normal parameters explain the high robustness of LLMs to quantization errors. However, the small number of cherry parameters still leads to performance degradation under quantization. Consequently, the key to reducing quantization errors lies in addressing the quantization of cherry parameters.The parameter heterogeneity also explains the previously discovered effectiveness of mixed-precision quantization strategies [6, 12, 17, 18] . By preserving a small proportion of parameters with high precision, the quantization performance can be effectively improved. Based on the heterogeneity, this strategy alleviates the impact of cherry parameters on model performance by maintaining their precision.Indeed, mixed-precision strategies can effectively address the quantization error issue of cherry parameters. However, the core challenge lies in identifying cherry parameters based on specific metrics. Different metrics of parameter effects include weights [6, 13, 18] , activations [17, 24] , output changes [8] , as well as the impact of parameters on model loss used in this paper. Based on the parameter heterogeneity, we argue that effective cherry parameter identification metrics should exhibit high heterogeneity, clearly distinguishing between cherry parameters and normal parameters. Accordingly, we compare three different metrics in Sec 5 and find that the impact best distinguishes cherry parameters from normal parameters. The experimental results in Sec 6.5 verify that choosing metrics with higher discriminative capability indeed leads to better performance.Based on the above analysis, we design the CherryQ quantization algorithm, which selects cherry parameters based on the impact metric and end-to-end optimizes parameters with mixed precisions. Extensive experiments on various models and benchmarks demonstrate the effectiveness of CherryQ. It consistently yields the lowest perplexity in most settings. Notably, our 3-bit Vicuna-1.5 model exhibits performance on par with the 16-bit counterpart on Vicuna-bench [5] . Our 2-bit quantization method significantly outperforms the SOTA approaches.In summary, by systematically revealing parameter heterogeneity in LLMs, we answer the following questions:1. What causes the high robustness of LLMs to quantization? It is due to the 99% of normal parameters in parameter heterogeneity.Why is mixed-precision quantization effective? This strategy addresses the quantization problem of the very few cherry parameters in parameter heterogeneity.3. How to find the optimal mixed-parameter selection strategy? Based on heterogeneity that distinguishes normal parameters from cherry parameters, the impact-based metric demonstrates the highest discriminative capability.4. How to quantize parameters according to parameter heterogeneity? We propose CherryQ based on these findings. Extensive empirical results verify its effectiveness in 2-, 3-, 4-bit quantization. 
related work: 
 Quantization Strategies for LLMs Various quantization strategies have been proposed in the literature to reduce the precision of weights and activations while maintaining acceptable accuracy. These strategies can be broadly classified into post-training quantization and quantization-aware training [14] . Post-training quantization methods, such as OBD, OBS, and GPTQ, directly quantize the pre-trained model without fine-tuning [15, 10, 9] . On the other hand, quantization-aware training methods, such as LLM-QAT [18] , incorporate quantization operations into the training process to jointly optimize the quantized model. Some works also explore mixed-precision quantization [12] and adaptive quantization bins [7] to achieve a better trade-off between accuracy and efficiency.Outliers in Language Model Quantization The idea of modeling parameter outliers in LLM quantization is not new. Exploring outliers mainly includes the perspectives of magnitude [18, 7] and activations [4, 6] . For example, from the magnitude perspective, QLoRA assumes that parameters follow a Gaussian distribution [7] and designs information-theoretically optimal quantized bins based on this assumption. [18] keeps outlier parameters in 16-bit precision. From the activation perspective, [17] migrates the outlier amplifier to subsequent modules through an equivalent transformation. Additionally, SqueezeLLM also measures outliers from the perspective of parameter impact [12] . To the best of our knowledge, our work is the first to systematically reveal the outliers (heterogeneity) of parameter impact across different models, and we show a more pronounced imbalance in parameter impacts compared to magnitudes ( § 6.5). Furthermore, we propose a method to unify outlier (cherry) parameter optimization and normal parameter optimization, addressing the optimization challenges of heterogeneous parameters.Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes] Justification: Please refer to Section 8. Guidelines:• The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper. • The authors are encouraged to create a separate "Limitations" section in their paper.• The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be. • The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated. • The authors should reflect on the factors that influence the performance of the approach.For example, a facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or a speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon. • The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size. • If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness. • While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations. 
quantifying the impact of parameters on model performance: 
 The impact of parameters on model performance is quantified by the increase of the training loss when perturbing the parameter weight, which is widely used in post-training quantization approaches [15, 10, 9] . We adopt a second-order Taylor approximation of the training loss w.r.t. parameter perturbation. Given a parameter w i and a small perturbation ∆ applied to it, such that w i ← w i + ∆, the change in the training loss can be expressed as:EQUATIONwhereg i = E[ ∂L ∂wi ]represents the expected gradient of the loss with respect to w i , andH ii = E[ ∂ 2 L ∂w 2 i] denotes the i-th value of the Hessian matrix of the loss. Since the target model is a well-converged model, we can assume that g i ≈ 0, simplifying the expression to:EQUATIONTherefore, H ii quantify the impact of quantization-induced perturbations on the model's training loss.Parameters with larger values of H ii exhibit higher sensitivity to quantization and require careful treatment to maintain model performance. We denote H ii as the impact of w i .Efficient Computation Computing H ii of the diagonal of Hessian matrix for each parameter is computationally expensive, particularly for large-scale models. To overcome this challenge, we propose an efficient approximation using the Fisher Information Matrix (F). Since H is the Hessian matrix of a negative log-likelihood loss, H is equal to Fisher information matrix [16] . For the diagonal of the Hessian matrix, we have:EQUATION4 End-to-End Mixed-Precision QuantizationThe insights gained from Figure 1 highlight the heterogeneity in model parameters. To mitigate the impact of cherry parameters on quantization, we propose to preserve their high-precision values during the quantization process. By maintaining the fidelity of these critical parameters, we ensure that the essential information they capture is not compromised.Optimizing mixed-precision parameters in LLMs presents a unique challenge in the widely adopted Post-Training Quantization (PTQ) framework [14] . If we do not allow the updates of the cherry parameters, the quantization will certainly lose the flexibility provided by these critical parameters. This prevents the cherry parameters from reaching their optimum. On the other hand, PTQ struggles to simultaneously optimize high-precision cherry parameters and low-precision normal parameters. This is because the cherry parameter updates during the PTQ process significantly affect the optimal values of the normal parameters. So normal parameters need to be continually updated as the cherry parameter varies. However, in PTQ, once the normal parameters are quantized, they cannot be further updated. This prevents the early-stage quantized parameters from reaching their optimal values.To address this challenge, we propose a novel approach that end-to-end optimize the mixed-precision parameters via backpropagation. Our method leverages a quantization-aware training framework.To simultaneously optimize both the cherry parameters and normal parameters, we use two separate backpropagation strategies. The high-precision cherry parameters are updated using standard gradient descent, while the low-precision normal parameters employ the Straight-Through Estimator (STE) trick [3] for low-precision gradient descent. This unified backpropagation enables the end-to-end optimization of both cherry parameters and normal parameters, enhancing the overall optimization effect. We show the quantization in Algorithm 1.Require: Model parameters W, quantization function Quant(•), threshold τ , learning rate η Ensure: Quantized model parameters1: C ← {w i ∈ W | H ii > τ } ▷ Identify cherry parameters 2: N ← W \ C ▷ Identify normal parameters 3: for each training batch x do 4: L ← model(x; C ∪ Quant(N))▷ Compute loss w.r.t. mixed-precision parameters 5:C ← C -η ∂L ∂C ▷ Standard gradient descent for cherry parameters 6: N ← N -η • STE( ∂L ∂N )▷ Gradient approximation by STE for normal parameters 7: end for 8: return C ∪ Quant(N)Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof? Guidelines:• The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.• If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics. • The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction). 
heterogeneity-based cherry parameter selection: 
 Correctly identifying cherry parameters is one of the main challenges of CherryQ quantization. Candidate metrics for parameter influences include weights [13, 18, 6] , activations [17, 24] , and impacts (H ii ). We propose that an effective metric should reflect heterogeneity, specifically by differentiating the influence of cherry parameters and normal parameters of the model.To this end, we define the heterogeneity score. In Figure 1 , a small subset of parameters exhibit significantly higher impacts compared to the maximum of the majority. Inspired by this, the heterogeneity score is defined as the ratio of the mean impact of the top 1% parameters to the maximum impact of the bottom 99% parameters, as shown in Equation (4). A higher heterogeneity score indicates a more significant disparity in parameter importance.EQUATIONwhere f (w i ) denotes the parameter influence for parameter w i , and f is chosen from parameter weights, activations, and impacts.Figure 2 presents the heterogeneity scores for different metrics across various LLMs. The impactbased metric consistently shows higher heterogeneity scores compared to weights and activations. This indicates that the impact metric better distinguishes between the normal and cherry parameters, thus providing a more effective means of identifying cherry parameters. The validity of using heterogeneity scores for cherry parameter selection will be further verified in Sec 6.5, demonstrating that higher heterogeneity scores lead to better model performance. Data Independence We investigate whether impact-based parameter heterogeneity exhibits data independence -that is, whether different data samples share the same cherry parameters. Applying identical cherry parameters across different samples is only valid when there is data independence. To examine data independence within the same dataset, we randomly selected five sets of 128 WikiText-2 samples. We evaluated the overlap of their cherry parameters in each pair of sample sets. To evaluate cross-dataset data independence, we performed 9 independent sampling trials, each collecting 128 samples from C4 and 128 samples from WikiText-2 to evaluate the overlap. For Vicuna, we further added Sharegpt as a data source. Table 1 presents the overlap ratios of the cherry parameters. Despite the fact that cherry parameters constitute only 1/256 of the total parameters, all models demonstrate significant overlap ratios. This finding suggests that the cherry parameters possess an inherent data-independent nature.6 Quantization Experiments 
implementation details: 
 Parameter Representation: Based on the observation that cherry parameters occupy a very small proportion, for each row of parameters in each parameter matrix, we consider only the top 1/256 parameters with the highest impact as cherry parameters and retain their FP16 precisions. For example, the parameter matrix size of LLaMA2-7B is 4096 × 4096. So we average the impact across all rows for each column and then select the top 16 columns with the highest average impact, resulting in 16 × 4096 parameters as cherry parameters. Furthermore, to recover the complete parameter matrix, an INT16 is required to record the indices of these 16 columns. Thus, the storage overhead for the column indices is minimal. For normal parameters, we employ full range symmetric MinMax quantization to quantize their weights. And we adopt a widely-used parameter grouping strategy. For more details, see Sec C.Quantization Datasets: For the quantization of the base LLMs, we follow [9] to use C4 [20] as the training data. We selected the first four partitions of C4 and chose data with a length of ≥ 2048 tokens, resulting in a total of 50k samples of 2048 tokens. For the chat LLMs, since Vicuna-1.5 [5] is obtained by supervised fine-tuning based on ShareGPT [5] , we also use the ShareGPT dataset for training. We used a total of 20k training samples from ShareGPT for QAT and Cherry.Baselines We compare our method with various quantization methods, including QAT [18] , GPTQ [9] , SqueezeLLM [12] , OmniQuant [21] , and AWQ [17] . For OmniQuant and AWQ, we use their results reported in [21] . For SqueezeLLM, we use the results in its original paper [12] . For GPTQ, its 4-bit model is obtained from the open-source2 . Due to the lack of a 3-bit GPTQ model, we quantize the model ourselves via the implementation of Auto-GPTQ 3 . Since CherryQ is based on QAT, for fair comparisons, the implementation of QAT is the same as CherryQ, except that it does not handle cherry parameters.In this section, we present the main experimental results to demonstrate the effectiveness of CherryQ on LLaMA2 [23] . We evaluate CherryQ with both perplexity and downstream tasks, comparing its performance with state-of-the-art quantization methods.We follow [9, 21] to evaluate the perplexity of CherryQ on two widely used corpora: C4 and WikiText-2 [19] . We use the validation split of C4 to avoid data leakage. We show the results of 3-bit quantization using different quantization approaches in Table 2 . We show the results of different model scales and different group sizes.From the results, CherryQ consistently outperforms all other approaches across both model sizes (7B and 13B) and grouping sizes (64 and 128), achieving the lowest perplexity on both the C4 and WikiText-2 datasets. Notably, CherryQ's perplexity is significantly closer to the full-precision (FP16) baseline compared to other methods, highlighting its ability to preserve model performance after quantization.Table 3 compares different 4-bit quantization methods. Again, CherryQ achieves the lowest perplexity scores in most settings, demonstrating its effectiveness in higher-bit quantization settings.To further validate the effectiveness on specific tasks, we evaluated the quantized models on various downstream tasks from the HuggingFace OpenLLM Leaderboard. We conducted experiments on Vicuna-1.5 [5] . We apply 3-bit quantization with group size=128 for CherryQ and other baselines.Evaluation To assess the performance of quantized open-ended chat models, we employ a pairwise comparison on the Vicuna-bench [27] , which consists of 80 test samples. We compare the responses generated by the quantized models against those generated by the original 16-bit Vicuna-1.5. The evaluation is performed using GPT-4, which automatically classifies the quantized model's response as "win", "tie", or "lose" relative to the FP16 model's response. To get rid of the ordering effect of the evaluation, we follow [17] to compare the responses with both orders, resulting in 160 trials.Figure 3 presents the results of the pairwise comparison for each quantized model against its FP16 counterpart. The results demonstrate that CherryQ consistently outperforms other quantization baselines in preserving the performance of chat models. It achieves the highest number of wins and ties against the FP16 models, while minimizing the number of losses.Notably, 3-bit CherryQ achieves a slightly better win-tie-lose ratio over the FP16 Vicuna model, indicating that the 3-bit quantized model performs on par with or even better than the FP16 model. As intuitively CherryQ cannot surpass the target 16 bit model, we think the result suggests that CherryQ maintains almost all its performance even at 3 bit, making GPT-4 hard to distinguish the quality of low-bit and FP16 models.We further explore the extreme case of 2-bit quantization. Although 2-bit quantization greatly reduces memory requirements for model storage and inference, existing methods still show a significant performance gap compared to their 16-bit counterparts. Implementation Details To achieve high-quality 2-bit quantization, we integrated the scaling-up trick introduced in [17] . Specifically, after identifying cherry and normal parameters, we automatically search for the optimal scale of each column of normal parameters that minimizes the output difference after quantization for each layer. The quantization function is formulated asQ ′ (w) = Q(w • s)/s,where Q(•) represents standard asymmetric quantization on the min-max grid, and s is a constant that scales up the normal parameters and remains fixed during the training process. The cherry parameters are excluded from quantization and retain their 16-bit precision throughout the grid search.Results Table 6 presents the perplexities of 2-bit quantization on LLAMA2 models. Compared to existing methods such as GPTQ, AWQ, and OmniQuant, our proposed CherryQ method demonstrates superior performance across all metrics. Specifically, CherryQ achieves perplexity scores of 9.55 and 8.34 in the 7B-3bit-g128 and 7B-3bit-g64 settings, respectively. These results significantly outperform other methods, validating the effectiveness of CherryQ in 2-bit quantization.To evaluate the effectiveness of our proposed impact-based parameter selection criterion, we conducted experiments comparing it with the criterions of parameter weights and activations. Table 7 presents the perplexity of LLaMA2-7B-3bit and LLaMA2-13B-3bit models, using both criteria for cherry parameter selection.From the results, it evident that the impact-based criterion consistently outperforms other criterions across all settings. These results demonstrate that our proposed impact-based criterion is a more effective measure to identify cherry parameters. The impacts identify and preserve the most critical parameters during the quantization process. These results are consistent with the analysis in Sec 5 regarding the effectiveness of heterogeneity scores in selecting cherry parameters.  
conclusion: 
 In this paper, we systematically investigated the phenomenon of parameter heterogeneity in large language models (LLMs). Our experiments on LLaMA2, Mistral, Gemma, and Vicuna models consistently demonstrated that a small subset of parameters, referred to as "cherry" parameters, play a crucial role in maintaining the model's performance, while the vast majority of parameters can be quantized to ultra-low precision without significant degradation. This finding highlights the potential of the heterogeneous nature of parameter importance.Motivated by this observation, we proposed a novel CherryQ quantization algorithm, which uses a quantization-aware training framework for the end-to-end optimization of both cherry parameters and normal parameters. Extensive experiments demonstrate that CherryQ achieves significantly lower perplexity scores and better downstream performance. 
limitations: 
 There are some limitations to consider. First, the method relies heavily on the accurate identification of cherry parameters, which may vary across different model architectures and training datasets. This dependency could potentially limit the generalization ability of CherryQ to new or unseen models. Second, the computational overhead required for the impact-based identification and scaling of parameters, although justified by the performance gains, may pose challenges for extremely large models or those deployed in real-time systems with stringent latency requirements. 
broader impacts: 
 Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?Answer: [No] Justification: The paper is purely fundamental research and does not involve social impact.Guidelines:• The answer NA means that there is no societal impact of the work performed.• If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact. • Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.• The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster. • The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology. • If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML). 
safeguards: 
 Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?Answer: [No] Justification: This paper does not release new models or datasets.Guidelines:• The answer NA means that the paper poses no such risks.• Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters. • Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images. • We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.12. Licenses for existing assets Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?Answer: [Yes] Justification: Please refer to Section D Guidelines:• The answer NA means that the paper does not use existing assets.• The authors should cite the original paper that produced the code package or dataset.• The authors should state which version of the asset is used and, if possible, include a URL. • The name of the license (e.g., CC-BY 4.0) should be included for each asset.• For scraped data from a particular source (e.g., website), the copyright and terms of service of that source should be provided. • If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset. • For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. 
 
 Appendix: We further evaluate the performance of CherryQ on the MMLU benchmark by quantizing the Vicuna1.5 model. As shown in Table 8 , CherryQ outperforms both QAT and GPTQ in terms of average accuracy across almost all categories. For all LLM scales (7B, 13B), and both base models and chat models (LLaMA2, Vicuna-v1.5), we train the models on a single node with 8 x A100 80GiB GPUs. We use a total batch size of 128, a learning rate of 2e-5, a weight decay of 0.0, a cosine scheduler with 5% warm-up steps. The final learning rate is 25% of the peak learning rate for 2/3-bit LLMs, 10% for 4-bit LLMs. We train 1 epoch on base models, 2 epochs on chat models.For normal parameters, we employ full range symmetric MinMax quantization to quantize their weights [14] . Specifically, an FP16 value is mapped to the range of [-2 k-1 , 2 k-1 -1] and symmetrically distributed on both sides of the coordinate axis. The quantization of an FP16 tensor X F P 16 to k bits is computed by:EQUATIONwhere ⌊•⌉ denotes the round function, S is the quantization scaling factor S = M ax(|X F P 16 |)2 k-1, and ϵ is a very small positive number (= 0.01 in our setting) to ensure that X Intk falls into the target range.Dequantization restores the quantized integer values based on the scaling factor:EQUATIONTo further improve the quantization accuracy, we adopt a widely-used parameter grouping strategy. Specifically, the parameters are divided into groups in order, and each group independently calculates its scaling factor. For example, if we divide a parameter matrix W ∈ R r×c that needs to be quantized with a group size of B, we will obtain a total of r × (c/B) groups.We list the assets used in this paper and their licenses below:• [5] , llama2• https://huggingface.co/TheBloke, llama2• https://github.com/AutoGPTQ/AutoGPTQ, MIT License • [23] , arXiv.org perpetual, non-exclusive license 1.0 • [18] , arXiv.org perpetual, non-exclusive license 1.0 • [20] , arXiv.org perpetual, non-exclusive license 1.0 • [19] , arXiv.org perpetual, non-exclusive license 1.0NeurIPS Paper Checklist 1. Claims Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? Answer: [Yes] Justification: We have fully explained the motivation and contributions of the paper in the introduction section, and have verified them in the experimental section. Guidelines:• The answer NA means that the abstract and introduction do not include the claims made in the paper. • The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers. • The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. • It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.https://huggingface.co/TheBlokehttps://github.com/AutoGPTQ/AutoGPTQ 


Decision: This paper can be summarized, as reviewer YuKp says, "The paper demonstrates that some parameters have much larger impact on loss than others (at least according to their way of approximating impact), a surprising result, that nicely motivates using mixed precision quantization." And regarding execution: as reviewer GdR4 says, "The experimental results are extensive and well-structured, demonstrating the effectiveness of CherryQ in various settings and benchmarks."

Overall ratings were positive, and there were relatively minor revisions required during the rebuttal process. And what revisions were made, made the paper stronger in a quick and understandable way. For instance, there was a direct validation of impact approximation. Reviewer YuKp: "It would have been useful to directly confirm that the proposed way of approximating impact on loss is actually a good approximation of the impact of a parameter on the loss."
To which the authors responded with an experiment resulting in: "Perturbations to cherry parameters led to significantly larger increases in perplexity, while normal parameters remained largely insensitive to similar perturbations. This directly validates both the existence of cherry parameters and the effectiveness of our approximation." Other concerns about cherry parameter dataset overlap and memory-bound latency were also addressed to GdR4 and YuKp.

There are some limitations though with the paper. P3Ag is still not convinced that |Hii| >> |Hij|. And they also point out that the average QA performance gain over OmniQuant is still relatively small at 1.13%.

Overall, the paper makes a significant contribution to the field of LLM quantization through its novel insights and effective method. The strong author responses and extensive evaluation support its acceptance.

Reviews: review: paper_summary: paper_summary: This paper presents a new post-training quantization strategy called "CherryQ" that identifies "cherries" --- meaning parameters that disproportionately impact the model's loss --- stores those in fp16, and quantizes the rest of the model parameters using a standard symmetric min-max quantization (with groups).  It shows that this approach yields better perplexity and downstream performance numbers than existing quantization methods, on several models (Llama-3 7b/13, Vicuna 1.5 7b/13b), several tasks (c4/wiki perplexity, Hellaswag, Winogrande, ARC, TruthfulQA, GSM8K, MMLU, chat win-rate), and at several compression rates (2 bits, 3 bits, 4 bits).

Some more details:
- To identify cherries, the paper proposes using E[g_i^2] as a measure of the impact of parameter w_i on the loss, where g_i is the gradient of the loss function with respect to that parameter. This is motivated by: (1) approximating the loss around each parameter w_i using a second order Taylor expansion, assuming E[g_i] = 0 (because model has converged), and assuming the second-order derivative of L w.r.t. w_i is equal to E[g_i^2] (based on results about Fisher information matrix equaling the Hessian from [16]).
- The paper shows that selecting cherries in this way (using the above approximation of the impact of each parameter on the loss) is better than using alternative metrics based on model weights or activations.
- Once cherries are identified, the non-cherries are quantized, and then the model is fine-tuned by training the cherries in a regular manner (non-quantized gradients and updates), while training the (quantized) non-cherries using the straight-through estimator.
strength_weakness: strength_weakness: - It would have been useful to **directly** confirm that the proposed way of approximating impact on loss is actually a good approximation of the impact of a parameter on the loss. This was only done in indirect ways (e.g., by showing that quantizing these parameters leads to better performance than quantizing using other metrics).  It should be relatively straightforward to do this by selecting a random set of model parameters (both cherries and non-cherries), perturbing them slightly (one-by-one), and passing data through the perturbed and unperturbed model and measuring the loss difference.  One could then show a scatter plot (and measure spearman rank correlation) to visualize how well the approximated impact on loss (E[g_i^2]) aligns with the actual impact on loss.
- QuIP (https://arxiv.org/abs/2307.13304) and QuIP# (https://arxiv.org/abs/2402.04396) are not compared to, and more recent state-of-the-art models are not benchmarked (e.g., Llama3).
- No inference speed results are shared. It would be great to see if this method can directly lead to faster inference, especially during decoding (which is memory-bound).
questions: questions: - See weaknesses. Are there any obstacles to running the experiment to validate the use of E[g_i^2] as the metric for measuring impact on loss?
- How "data-dependent" are the cherries? Can this be measured?
- How does CherryQ compare with QuIP/QuIP# on Llama-3?
limitations: limitations: Limitations are discussed, though could be addressed better with some experiments (see questions above).
paper_summary: paper_summary: This paper investigates the phenomenon of parameter heterogeneity in large language models (LLMs) and proposes a novel quantization method called CherryQ. The authors find that a small subset of parameters, referred to as "cherry" parameters, have a disproportionately large influence on model performance, while the majority of parameters have minimal impact. Based on this observation, CherryQ selectively preserves the critical cherry parameters in high precision while aggressively quantizing the remaining parameters to low precision. Extensive experiments demonstrate that CherryQ outperforms existing quantization approaches in terms of perplexity and downstream task performance.
strength_weakness: strength_weakness: (1) One major concern is about the implementation. What is *real* improvement in terms of efficiency? The authors are supposed to report the models' throughput and speed compared with baseline models.

(2) The idea of important parameters for quantization is not new and novel.  This paper seems to propose a new term "Cherry Parameters" which appears to be a reinvention of an already existing idea. But the authors could argue the difference with previous studies. I am open to adjust ratings.
questions: questions: N/A
limitations: limitations: N/A
paper_summary: paper_summary: The paper introduces a quantization technique for LLMs, inspired by an empirical study on parameter importance. The authors identify a small subset of parameters, termed "Cherry parameters," which exhibit significantly higher importance than others. They propose an optimization strategy: retaining full precision for Cherry parameters and their gradients, while quantizing the normal parameters. A straight-through estimator is used to handle the gradients of these quantized parameters during optimization.
strength_weakness: strength_weakness: Weaknesses:

1. Section 3: The method depends on back-propagation, which could lead to computational and memory overhead challenges in resource-limited scenarios, such as quantizing an extremely large model with only 4 GPUs. However, this issue is acknowledged in Section 8.

2. Section 4: The Fisher information matrix is recalculated at each step. Given that parameters are updated frequently, this could cause the parameter importance to fluctuate significantly, potentially leading to a chain error. This is because gradients influence cherry parameter identification, which in turn affects gradient calculations. The paper does not address how to manage this cyclic error effectively.

3. Section 5: The model for assessing weight importance is based on Optimal Brain Damage and only considers the impact of individual weights when perturbed or quantized. It overlooks the synergistic effects between weights, where quantizing two normal parameters together could have a more significant impact than quantizing one cherry parameter.

4. Section 5: There seems to be a discrepancy in how weight importance is presented: Figure 2 is per weight matrix, whereas Figure 1 is per weight scalar. In the experiments, parameter impact scores are averaged along rows, and cherry parameter identification is performed along columns based on these averages, leading to confusion. If cherry parameter identification is indeed column-based, some cherry parameters may be overshadowed by dominant normal parameters in the same column, leading to potential misidentification.

5. Section 6.2: The improvement in perplexity over OmniQuant is marginal, as shown in Tables 1 and 2. Furthermore, it is weird that OmniQuant is omitted in the QA evaluations in Tables 3 and 4.

I would be inclined to improve the rating if these points are properly addressed.
questions: questions: Please see Weaknesses.
limitations: limitations: Please see Weaknesses.

Comments: title: .
comment: We conducted a cross-dataset analysis to evaluate the consistency of cherry parameters across different datasets. Specifically, we compared cherry parameters identified from C4 and WikiText datasets. We performed 9 independent sampling trials, each using 128 samples from both datasets. 

Our analysis revealed an **average overlap rate of 68%** between the cherry parameters identified from C4 and WikiText. This overlap, while lower than the 84% observed within the same dataset, still represents a substantial consistency across datasets. The difference can be attributed to dataset-specific characteristics influencing parameter importance. This suggests a strong core consistency in cherry parameters. There are also potentials for dataset-specific optimizations in future research.
Thank you for your thorough answers!

Quick follow-up question for Q2: Are cherry parameters consistent across datasets (e.g., C4 and wikitext)?
Thank you for acknowledging our responses and for raising your ratings. We appreciate your valuable feedback and will incorporate your suggestions into the revised version.
W1: addressed.

W2: Okay.

W3: I am not fully convinced. $|H_{ii}| \gg |H_{ij}|$ does not necessarily indicates that the synergy between neurons is much less significant than individual parameter's effect. the $H_{ij}$ are average acrossed pairs of parameters. It is to note that sometimes parameters coalate in larger groups. But I think this problem might be analyzed in a seperate work. Finally, I hope the reviewers cand discuss this point in the limitations.

W4: Okay. I carefully read line 158-159 and also said that the importance are averaged across rows. I was asking because Figure 2 was confusing after I read line 158-159. It is better that the authors add some additional explanations in the caption of Figure 2.

W5: Okay, athough the average QA performance gain in the above table is only 1.13%.


I increase my ratings now. I hope the authors can incorporate my suggestions in their revision. Cheers.