Paper: Understanding Vision and Language Representations under the Lens of Intrinsic Dimension (ICLR-2024)

Reviewer comment (Experiments):
The study is limited to one specific vision-language model (BLIP), raising concerns about the generalizability of the conclusions. It remains unclear if these findings hold across diverse multi-modal models with different training objectives, such as discriminative contrastive models like CLIP, generative models with trainable text decoders like LLaVA/OpenFlamingo, or models involving more modalities like ImageBind.

Author response:
Our research is indeed based on only one specific visual-language model (BLIP). However, BLIP is a universal and unified multi-modal pretraining that is trained with three objectives: Image-Text Contrastive Loss (used by CLIP), Image-Text Matching Loss, and Language Modeling Loss (used by LLaVA). We believe that our findings are still valuable and insightful, as BLIP is a representative and widely used model for general vision-language tasks. Also, our method of applying ID to multimodal scenarios is model-agnostic which can be applied to other models with different training objectives and modalities.

Reviewer comment (Writing):
The paper often inconsistently uses \citet and \citep.

Author response:
Thank you for pointing out the typo. We will revise it in the revision.

Reviewer comment (Presentation):
In Figure 1, it's unclear which parts represent the vision modality and the language modality.

Author response:
We marked the background color with red for vision and blue for language in all figures present IDs, to make it easier to distinguish the modalities.

Reviewer comment (Evaluation):
On Page 7, the statement "ID values have a positive correlation with model performance but not in direct proportion" requires more detail and further elaboration.

Author response:
We give an example to show this: in Figure 4, Sens and Full BLIP had a similar ID value gap as Mag and Mag w/o ft, but their performance gap (using CIDEr metric) is 9 and 177, which were not proportional. This shows that ID values are correlated with model performance, but not enough to evaluate model quality.

Reviewer comment (Evaluation):
In Figure 2 1), the VLP is a transformer-based model, but its hunchback-shaped profiles is not significant, the author should explain the reason.

Author response:
We think the most plausible reason is the input of VLP is the fused multimodal representations rather than pure visual modality. As we explained at the bottom of Figure 2. “VLP’s hunchback is positioned further to the right side, … The delayed peak and lower value of Transformer-based models’ IDs can be explained by integrating textual features, particularly in the single-stream VLP model which fuses visual and language at the beginning. As described in Section 3.2, language representations have consistent and lower IDs.”

Reviewer comment (Evaluation):
This paper argues that the maximum ID is a more critical indicator for performance prediction, which is against the observation that the ID of the last latent layer indicates model performance, but from Figure 4, the ID of the last latent layer can also indicate model performance.

Author response:
Table 1 shows that model performance is ranked as Full BLIP>Sens>Mag>Mag w/o ft. According to [1], a smaller last layer ID indicates better performance, suggesting a ranking of Mag w/o ft>Mag>Sens>BLIP. However, our experimental results (Figure 5) show a different order: Sens>Mag>Mag w/o ft>BLIP. This demonstrates that the maximum ID is a more reliable performance predictor than the last layer ID. We believe this is an intriguing finding that challenges previous assumptions.

Reviewer comment (Evaluation):
In Figure 5, why the multiplication of IDs lead to the IDs of pure language representations decrease?

Author response:
We think that it is because the language weights are less important, and *ID effectively estimates this weight importance. This leads to more pruning on pure language weights, which results in the decrease of language IDs. This result also illustrates the correlation between ID values and weight importance from another perspective.

Reviewer comment (Evaluation):
Regarding the empirical study of ID: There is a good amount of discussion and experiments for this, which is good. But it is mostly about applying the TWONN method for computing ID. Also, how do you know that the IDs computed are accurate? Is there an evaluation metric for the quality of ID?

Author response:
**Q1: The quality of ID**
    
A1: ID is an idealized concept that only synthetic datasets have accurate IDs. For real-world datasets, ID is an estimated value that varies with the algorithm and the sample size. Common methods like MLE and TWONN often underestimate ID. Based on [1], ID becomes stable when the number of samples exceeds 1000. So we set the number of samples as 2000 for efficiency and accuracy.

Reviewer comment (Experiments):
Regarding studying modality contribution: I do not see this experiment at all, only some anecdotal statistics in section 3.

Author response:
**Q2: Studying modality contribution**
    
A2: In Section 4.3 DO VISION AND LANGUAGE CONTRIBUTE DIFFERENT PRUNABILITY?, we analyzed how different weights affect the model performance. We found that the language modality can be pruned more than the vision modality, and that the cross-modal attention layers are the least prunable. This suggests that the language modality has more redundancy and the vision modality is essential for multimodal learning.

Reviewer comment (Experiments):
Regarding predicting model performance using ID values: I do not see this experiment at all, nor is this mentioned subsequently in the paper.

Author response:
**Q3: Predicting model performance using ID**
    
A3: In the third paragraph of Section 4.1 DOES PRUNING REDUCE OR INCREASE THE ID, we compared three models with different performance and their ID changes. We concluded that “ID values correlate positively with model performance but not linearly. We argue that the maximum ID is a better predictor of performance, which contradicts the observation that the ID of the last latent layer indicates model performance Ansuini et al. (2019).”
    
Moreover, in Section 4.2 CAN ID PREDICT LAYER IMPORTANCE?, we further examine the relationship between the ID changes of different modalities/layers and the overall performance: Figure 5 shows that Sens*ID increases the IDs of all visual representations, including all layers in the visual model and the k and v layers in the language model. Conversely, the IDs of pure language representations decrease due to the multiplication of IDs.

Reviewer comment (Experiments):
Regarding better pruning: There are experiments for this in tables 1 and 2, but there are no comparisons to established weight pruning methods, only one from Sens Zhang et al. (2022). More comparisons are needed to really prove the efficacy of this part.

Author response:
**Q4: Better pruning**
    
A4: The most recent and only paper on multimodal pruning is Upop[4]. However, Upop proposes a structured pruning method while ours is unstructured, which makes the comparison unfair. Our main contribution as an unstructured pruning method is an improved weight importance metric. To further validate the efficiency of ID, we conducted experiments using the leading importance metrics: gradient[2] and magnitude[3] methods at a 95% pruning ratio (20x compression). The results are as follows:

|    Metric    | CIDEr | BLEU4 |
|:------------:|:-----:|:-----:|
| magnitude[3] | 17.56 | 10.28 |
| magnitude*ID | 26.46 | 12.92 |
|  gradient[2] | 20.80 | 11.17 |
|  gradient*ID | 24.85 | 12.99 |

Reviewer comment (Novelty):
Section 3 needs work — there are some interesting results but it can be better phrased as well-motivated research questions. Taking '3.3 INTERPRETING CROSS-MODAL ATTENTION VIA IDS' as an example, why is interpreting cross-modal important? Why should I use ID to do it when other people have used attention weights etc.? What insights does using ID to interpret cross-modal tell me, can I use it to better train or debug models? See https://arxiv.org/abs/2207.00056 for an example of setting up what to interpret in multimodal models, and using rigorous human user-studies to validate each of the findings.

Author response:
**Q5: Why use ID to interpret cross-modal? How does it compare to attention? What insights can we get?**

A5: We believe that ID and attention are complementary methods, each offering unique insights into multimodal representations. Attention provides an intuitive understanding of the local alignment between vision and text. On the other hand, ID is more objective, exposing the training status of hierarchical representations, such as whether the most abstract representations can be achieved with minimal parameters. Each method has different research goals and targets, so they don't compete with each other.

In section 3, we conduct an empirical study that reveals significant differences in the IDs of vision and language modalities. This suggests that they possess different geometric characteristics and complexities. In section 4, we use the difference in ID as a guide for multimodal pruning, further demonstrating its effectiveness.

Reviewer comment (Evaluation):
It would be good to have an overall plot of performance vs parameters, with one line being your pruning method and other lines for other pruning baselines, and the line that Pareto-dominates would be best.

Author response:
**Q6: Can you provide an overall plot showing performance versus parameters?**

A6: That is a useful suggestion. However, in Figure 6, we have presented a similar comparison. The baseline method, labeled as "Sensitivity", is represented by a dark-colored line, while our method (sensitivity*ID) is represented by a light-colored line. All the light lines dominate the dark ones, except when pruning both vision and language at a 95% pruning ratio. We will expand the comparisons involving magnitude and gradient (as shown in the above tables) and add them to Figure 6.

Reviewer comment (Experiments):
I wonder why BLIP is chosen for this study, instead of more recnet multimodal models? Any explanations on this?

Author response:
A1: We initially chose CLIP as our model since it is a well-known multimodal pretraining. However, upon further analysis, we realized that BLIP, proposed in 2022, offers more comprehensive multimodal representations. BLIP considers both multimodal generation and understanding, which are critical for practical applications. It is trained with three loss functions: Image-Text Contrastive Loss, Image-Text Matching Loss, and Language Modeling Loss, to obtain rich and diverse multimodal representations. Therefore, we think that BLIP is a superior choice for investigating the intrinsic dimension of multimodal pre-training models, as it considers both the generalizability and diversity of multimodal data.

Reviewer comment (Experiments):
I wonder if the observations based on BLIP can be extended to other multimodal models, and how?

Author response:
A2: ID estimation is model-agnostic, making it simple and universally applicable. Any representation can have an intrinsic dimension estimated, which can then be used for weight pruning by multiplying the ID with the importance score (typically the weight's gradient[1] or magnitude[2]). This method is straightforward, effective, and easily extendable to any multimodal model. We further verify its efficiency with gradient[1] and magnitude[2] importance metrics at a 95% pruning ratio. The results are shown below. We believe ID is a good indicator to probe the state of multimodal representations.
|    Metric    | CIDEr | BLEU4 |
|:------------:|:-----:|:-----:|
| magnitude[2] | 17.56 | 10.28 |
| magnitude*ID | 26.46 | 12.92 |
|  gradient[1] | 20.80 | 11.17 |
|  gradient*ID | 24.85 | 12.99 |


[1] Molchanov, Pavlo, et al. “Pruning Convolutional Neural Networks for Resource Efficient Inference.” *ICLR*. 2017.

[2] Zhu M H, Gupta S. “To Prune, or Not to Prune: Exploring the Efficacy of Pruning for Model Compression.” *ICLR* *workshop.* 2018.