Paper: Tangent Transformers for Composition,Privacy and Removal (ICLR-2024)

Reviewer comment (Writing):
While the paper is well-written and easy to follow, it would be helpful to provide more detailed explanations of some of the concepts presented. For example, the paper could provide more details on how Tangent Transformers are computed and how they are used in practice (especially from Eq 5 to Eq 6).

Author response:
Thank you for the suggestion, we clarified some of the notation in Sec 3.1, and added the detailed derivation of the linearized attention function in Appendix B as suggested. We also plan to release code with the full implementation with the final version of the paper.

Reviewer comment (Experiments):
While the paper provides an empirical evaluation of TAFT and Tangent Transformers on various downstream visual classification tasks using vision transformer models, it would be helpful to see more experiments that compare TAFT with other fine-tuning methods on these tasks. This would help to establish the competitiveness of TAFT more clearly.

Author response:
Thank you for the suggestion. We initially compared only to the best performing fine-tuning method – non-linear fine-tuning – since parameter-efficiency is not necessary in our present application. Following the reviewer's suggestion, we added comparisons against adapter and low-rank fine-tuning in Appendix C.7, Table 11, and show that as a result of the trade-off in number of parameters, their performance on downstream tasks are consistently lower than that of non-linear fine-tuning and TAFT.

Reviewer comment (Experiments):
While the paper provides a theoretical analysis of the benefits of linearity for model composition, parallel training, machine unlearning, and differential privacy, it would be beneficial to provide more empirical evidence to support these claims. Specifically, it would be helpful to see more experiments that demonstrate the advantages of TAFT and Tangent Transformers on a wider range of tasks and datasets (e.g. DTD and UCF101).

Author response:
We believe that our experiments have provided sufficient evidence across 7 different datasets across multiple tasks - composition, unlearning, privacy, and standard fine-tuning. However, we agree that evaluating on non-object-oriented datasets can better elucidate the advantages of TAFT. As such, we have evaluated our proposed method on the DTD dataset in Appendix C.6 and Table 10, where we show TAFT convincingly outperforms the non-linear fine-tuning paragon.

While indeed interesting, extension to video-based tasks such as UCF101 is beyond the scope of our paper. However, we do not see an immediate reason why our method would not extend to temporal classification (as long as architecture remains transformer-style), and would love to see future work exploring this application.

Reviewer comment (Experiments):
I wonder how TAFT works when applied to LLM? maybe some experiments can be added.

Author response:
While we recognize the potential of extending our work to large language models (LLMs), we believe it falls outside the scope of our current research, which focuses on the composition and decomposition of vision transformer networks. Nevertheless, we appreciate the reviewer's suggestion and agree that applying TAFT to LLMs and other modalities would be a valuable area of future research.

Reviewer comment (Theory):
please derive in detail how to get the closed form expression in equation 5 and 6.

Author response:
Thank you for the suggestion, we added the derivation to Appendix B. Along with this, we will also release the code for TAFT with the final version of the paper.

Reviewer comment (Evaluation):
How about interpretability? A detailed analysis of how a given training sample affects the learned model and the predicted results is given in LQF. Is it possible for the authors to provide an analysis of the interpretability?

Author response:
Thank you for the great suggestion! LQF requires a quadratic loss function to derive a closed form solution (via newton update) with and without the given training sample. This requires the computation of the inverse Hessian, which is often infeasible for large networks and requires approximation. Instead, our method of linearly composing disjoint component models to form the final model allows computing the influence of any particular component model (subset of the training samples) simply via measuring the difference in weights between the target component model and the composition (weight average) of the remaining models. 

As suggested, we added Appendix C.5, Figure 4, which demonstrates that as the number of model shards increase, the influence of each individual component model decreases. Due to linearity, this effect is also reflected in the model output space as seen in Figure 1(a).

Reviewer comment (Novelty):
The authors detail the advantages of linear models in the introduction, but these advantages don't seem to be relevant to transformer, what are the advantages and disadvantages of linearizing the transformer model compared to linearizing ResNet?

Author response:
Our comparison with linearized ResNet-50 (Appendix C.1, Table 7) demonstrates TAFT's superior performance, outperforming ResNet-50 by 7.3% and 9.0% for standard fine-tuning and composition tasks across three datasets, respectively. The advantages of linearization stem from the effectiveness of the inductive prior acquired during pre-training. Since vision transformers are shown to learn better inductive priors than convolutional architectures as the scale of training data increases, we believe that linearized transformers yield a clear advantage over linearized ResNets by being able to leverage the better inductive priors learnt from pre-training.

Further investigation reveals that linearizing transformer models around the full pre-training weights can introduce strong feature biases towards the source pre-training dataset, potentially hindering transferability to downstream tasks, particularly in later layers (Figure 2(b)). Additionally, vision transformers often incorporate a [CLS] token for classification tasks. For downstream tasks significantly further from the pre-training initialization, we found that linearizing the [CLS] token itself can lead to improved performance (Figure 2(c)).