Diff-eRank: A Novel Rank-Based Metric for Evaluating Large Language Models

Summary

This paper explores the potential of using the rank of model hidden states for evaluating model capabilities. Specifically, the authors propose calculating the rank difference between trained and untrained models as a measure of model performance. The core idea is that the rank difference can reflect the model's extent of "noise reduction". The authors compared the consistency of rank difference with other metrics (loss, accuracy) under multiple model series settings. The results showed the potential of rank difference in assessing model capabilities within certain model series and measuring the cross-modal alignment of MLLMs.

Strengths

- To the best of my knowledge, this paper is the first to explore and discuss the idea of using the rank of hidden states to evaluate model capabilities, which sounds promising. - The paper provides an intuitive understanding and theoretical significance of using rank difference as an evaluation metric. - The experiments in this paper are relatively comprehensive, and the writing is quite clear.

Weaknesses

- My main concern lies in the fact that for models within a series, the dimensionality of their hidden states is often positively correlated with size, which also implies a positive correlation with performance. A larger dimensionality of hidden states usually means a larger rank difference when the effective rank proportion remains the same. In other words, although larger models have a higher rank difference, the proportion of noise reduction might be smaller compared to smaller models. Does this suggest that rank difference may not accurately measure the extent of noise reduction? Could rank ratio be a more reasonable metric (erank_M1/erank_M0 in eq.3)? - Although the authors observed a positive correlation between rank difference and model size within a single model series, this conclusion no longer holds when comparing models from different series simultaneously, as shown in Figure 3. Is this due to the varying dimensionality of hidden states across different models (where rank ratio might be effective)? Or is it caused by the different training methods employed for various models? If rank difference cannot be used to compare models from different series, what advantages does it offer compared to traditional metrics such as accuracy? - When the number of test set samples lies between the dimensionality of hidden states for the large and small models being evaluated, Q in Equation 1 will take values from N and d, respectively. Could this lead to non-robust results? I believe experiments should be conducted to investigate this scenario.

Questions

See Weaknesses. I am looking forward to authors' responses and open to rise my score.

Rating

6

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

The main limitation of this paper is that it fails to specifically discuss the advantages of rank difference compared to other metrics, especially considering that the rank differences of models from different series are not on the same scale.

Summary

This paper introduces “rank difference” that measures the reduction in the rank of LLM’s representations. It evaluates the quality of LLMs, which could be used in addition to the reduction in the cross-entropy loss. The idea is based on the assumption that LLM’s representations (e.g., the hidden states of each token before the classification head) encodes the semantic and syntactic information about the input sentence. Before training, these representations are expected to be chaotic (hence high rank), but after training and alignment, the representations are expected to be more structured. Based on this idea, “rank difference” is defined as the difference between $erank_{m0}(\Sigma_S)$ and $erank_{m1}(\Sigma_S)$ where $\Sigma_S$ is the covariance matrix of representations and $erank$ is the effective rank. The difference is computed between the representation before and after training. This measures the extend to which the model can compress the information, while other metrics such as cross-entropy measure the quality of model’s prediction. Experiments are conducted on OPT models of sizes from 125m to 13B parameters. The results show that there is an upward trend between “rank difference” and model size (which reflects model performance) on a range of datasets, similar to the reduction in cross-entropy. In addition, rank difference is applied to measure the alignment between visual modality and text modality in Llava-1.5 and MiniGPT-v2. An ablation study on different model families is shown.

Strengths

This paper presents a new evaluation metric, grounded on information theory, and demonstrates that it correlates well with model performance (as measured by model size and downstream task performance). It also allows measuring the alignment between different modalities.

Weaknesses

1. Although the idea is novel, its practical usability is limited. To evaluate the quality of systems (e.g., LLM, ASR, etc), downstream metrics such as accuracy, ROUGE, BLEU, WER, etc. are used as they better align with real use cases. While, a metric like cross-entropy is used as it is differentiable, allowing it to be a training loss. I’m not sure if “rank difference” will be adopted as it’s neither related to real use case nor applicable as a training objective. 2. Regarding experiments, current results (both text-only and visual-text) only show the trend post-training, so it would be more indicative of demonstrating how “rank difference” changes during training (e.g., similar to cross-entropy loss which usually decreases monotonically during training).

Questions

1. How do you think this method could be adopted? 2. What is the computational cost of computing rank difference? 3. Would it be comparable across models of different representation sizes? 4. Does/how rank difference during the alignment stage (e.g., SFT or PPO/DPO) ?

Rating

5

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

Limitations section is provided, and it has covered the main points

Summary

The article presents a measure known as "rank difference" to assess the effectiveness of Language Models (LLMs) by analyzing their internal representations. This metric is based on information theory and geometric principles aiming to quantify how LLMs eliminate unnecessary information post training. The authors illustrate the utility of rank difference, in both modal (language) and multi modal contexts. In terms of language models the study reveals that the rank difference grows with model size indicating noise reduction capability. This pattern aligns with metrics such as entropy loss and accuracy. Regarding modal models the authors suggest an assessment approach utilizing rank difference to evaluate alignment quality across modalities showing that contemporary multi modal LLMs demonstrate strong alignment performance. Key contributions of the paper include; Introducing rank difference as a metric for gauging the "noise reduction" capability of trained language models. Demonstrating the correlation between rank difference, loss metrics and downstream task accuracy underscoring its potential as an evaluation criterion. Defining alignment measures, between linguistic modalities showcasing that modern multi modal LLMs excel in achieving alignment. The study provides real world data that backs the idea of utilizing rank variance, in datasets and model scales indicating its reliability and effectiveness in assessing language learning models. In general the research introduces a viewpoint on evaluating language learning models moving away from metrics based on predictions, to focusing on model representations. This shift brings forth perspectives on comprehending how language learning models behave.

Strengths

Novelty: The introduction of the rank difference metric offers an approach, to assessing LLMs by focusing on their representations rather than just their outputs. Rooted in information theory and geometric principles providing a perspective on comprehending LLM behavior. Expanding the metrics scope to modal setups and evaluating alignment coherence across different modalities. Quality: Assessments spanning datasets and model dimensions. Convincing data showcasing the relationship between rank difference and traditional metrics like entropy loss and accuracy. Analysis elucidating the mathematical underpinnings and implications of the rank difference metric. Clarity: Organized and easily understandable elucidation of ideas. Thorough explanation of the proposed metric, its basis and practical implications. Follows a sequence from problem statement to methodology and outcomes. Significance: Tackles queries regarding LLM evaluation underscoring the necessity for metrics that go beyond mere model results assessment. Potential to shape how researchers and professionals evaluate and interpret LLMs offering insights, into model behavior and effectiveness. This can be used in both mode and mode models making it versatile, for different situations.

Weaknesses

The experiments have a scope; Regarding Training Dynamics; The paper fails to delve into how the rank difference evolves throughout training missing insights, into its behavior as the model progresses. Considering Model Diversity; Broadening the evaluation to include a range of model families and architectures would enhance the validation of the rank difference metric. In terms of Presentation; Clarity; Some sections require explanations to improve readability. Visual Support; Incorporating diagrams or visual aids could boost understanding and reader engagement. Delving Into Analysis Depth; Insights by Layer; Analyzing rank differences across model layers would offer a holistic view. Comparative Examination; Providing in depth comparisons with established metrics and recent studies would spotlight both strengths and limitations of the metric. Application, in Real Scenarios; Real world Contexts; Integrating real world application scenarios or case studies would enhance the relevance of the paper. Computational Considerations; Efficiency Concerns; Addressing the efficiency of calculating rank difference for large scale models and suggesting optimizations could be advantageous.

Questions

Do you have any insights or early findings regarding the variations, in the rank difference metric as LLMs undergo training? Examining this aspect could offer insights into how the behaves and its usefulness throughout the model development process. Have you thought about assessing the rank difference metric across model families or architectures aside from the OPT family? Incorporating a range of models could help validate how broadly applicable the metric is. Could you delve deeper into comparing the rank difference metric with established evaluation metrics and recent research findings? This, in depth analysis would shed light on both the strengths and potential limitations of using the rank difference metric.

Rating

5

Confidence

4

Soundness

2

Presentation

2

Contribution

3

Limitations

The authors recognize the limitations in conducting experiments to observe changes, in rank difference during training due to constraints. They emphasize the importance of conducting experiments to assess how applicable the metric is across model layers and its efficiency in computations. Suggestions for Enhancements; Training Progress; Conduct a small scale study or simulation to observe how rank difference evolves during training with models or subsets of data. Model Variation; Assess the effectiveness of the rank difference metric across a range of model families and structures. Provide initial findings if a comprehensive evaluation is not feasible. Computational Efficacy; Explore optimizations for calculating rank difference, such, as enhancements or parallelization methods and briefly touch upon any societal implications and ethical considerations to demonstrate awareness of broader impacts.

Summary

The paper proposes a rank-based evaluation metric that quantifies the amount of redundant information in the hidden representations of a model and applies it to both text-only and multi-modal models. The effective rank is obtained by the rank of its covariance matrix and is interpreted using information theory. This rank represents the degree of variations among the principal components in data. The rank difference between two models is used to measure how much redundant information is reduced in a model relative to another. The proposed metric aligns well with commonly used evaluation metrics (loss and accuracy).

Strengths

1. The paper presents a new evaluation metric through the view of the geometric property of representation matrices and information theory and shows that it aligns well with commonly used metrics like loss and accuracy for LLMs. 2. Experiments show how the rank difference varies by length, choice of the layer from which representations are extracted, type of models (text vs multi-modal), and algorithm design and can potentially guide future work on model compression.

Weaknesses

1. It is unclear what additional information the absolute rank or the rank difference brings to the table apart from a new interpretation. The rank differences are hard to interpret (L261: both models align well with a high alignment score) given a lack of detail on how they are computed for models of varying sizes. 2. For the multi-modal models, the authors again propose two metrics: image reduction ratio and image-text alignment and while the reduction ratio is a bit intuitive, it is unclear why image-text alignment is defined as is and why we need the different ranks (erank 3, erank 4, and erank5). In Table 2, the reduction and alignment follow opposite trends, is it something informative?

Questions

1. L224-225: can you provide any explanation on why these occasional outliers appear? This is much vivid in Table 4 where any other layer does not follow this upward trend. 2. Was there any experiment also on how the rank difference involves over the training of a model and whether that signal is informative on how long a model can be trained? 3. Is there any explanation on why the different layers are not informative of the representation redundancy (table 4)?

Rating

5

Confidence

2

Soundness

2

Presentation

2

Contribution

2

Limitations

yes