CPT: Consistent Proxy Tuning for Black-box Optimization

## Abstract

Abstract Black-box tuning has attracted recent attention due to that the structure or inner parameters of advanced proprietary models are not accessible.
Proxy-tuning [ 1 ] provides a test-time output adjustment for tuning black-box language models.
It applies the difference of the output logits before and after tuning a smaller white-box "proxy" model to improve the black-box model.
However, this technique serves only as a decoding-time algorithm, leading to an inconsistency between training and testing which potentially limits overall performance.
To address this problem, we introduce C onsistent P roxy T uning ( CPT ), a simple yet effective black-box tuning method.
Different from Proxy-tuning, CPT additionally exploits the frozen large black-box model and another frozen small white-box model, ensuring consistency between training-stage optimization objective and test-time proxies.
This consistency benefits Proxy-tuning and enhances model performance.
Note that our method focuses solely on logit-level computation, which makes it model-agnostic and applicable to any task involving logit classification.
Extensive experimental results demonstrate the superiority of our CPT in both black-box tuning of Large-Language Models (LLMs) and Vision-Language Models (VLMs) across various datasets.
The code is available at https://github.com/chunmeifeng/CPT .

## 1 Introduction

Although large-scale pretrained models have demonstrated strong generalization capabilities, they can perform better on specific downstream tasks by fine-tuning.
Several parameter-efficient fine-tuning techniques have been developed to fine-tune Large Language Models (LLMs), such as soft prompt tuning [], adapters [], Low-Rank Adaption (LoRA) [] and sparse tuning [].
Similar approaches are also applied to fine-tune the pretrained Vision-Language Models (VLMs), including text/visual prompt tuning [, , ], adapter-based tuning [, ], etc.
Notice that these fine-tuning methods are usually under the strong assumption that the model architectures are known and model parameters are accessible.
However, for privacy or commercial reasons, some advanced proprietary models are closed-source (*i.e.*, black-box models).
For instance, users of GPT-4 [] can only interact with the model through a controlled interface and cannot access the model’s parameters or intermediate embeddings.
Therefore, these white-box optimization methods are infeasible for tuning the black-box models.
Some methods do focus on tuning the black-box models.
For example, BBT [] and BBT-v2  [] employs gradient-free strategies for fine-tuning of black-box LLMs, while CBBT [] and LFA  [] fine-tune VLMs by adaptive or aligned features.
Nevertheless, all these methods require access to features within the model, which is not applicable for more strict black-box scenarios.

Recently, Proxy-tuning [] improves the large black-box model with proxy strategy, *i.e.*, improves the large black-box model by tuned/untuned smaller white-box models.
Specifically, during inference, the difference in logits between a tuned small model and an untuned small model is used as an offset and added to the output logits of the large black-box model to generate the final prediction.
Proxy-tuning is more widely applicable and privacy-preserving compared to other existing methods in that it requires minimum access to black-box models—basic access to output logits will suffice.
However, we note that there is an inconsistency between the optimization objective of Proxy-tuning [] and the form of output ensemble during inference, *i.e.*, only a small white-box model alone is used for tuning while the ensemble of three models are used for predictions.
Such inconsistency may lead to sub-optimal solutions for the proxy tuning optimization objective, causing bottlenecks in model performance.

To reconcile the inconsistency in Proxy-tuning [], in this paper we propose Consistent Proxy Tuning (CPT), a simple yet effective proxy-tuning method.
Specifically, during training stage of the tunable small white-box model, CPT additionally incorporates the frozen large black-box model and another frozen small white-box model.
Given a training sample, these three models first compute the logit scores for the input sample respectively.
Then, the three sets of logits are ensembled by using the same logits calculation formula of a test-time proxy in Proxy-tuning [].
Finally, the tunable white-box model is optimized with the loss function computed with the ensemble logits and the ground truth.
During inference stage, we follow Liu et al. [] to employ the proxy tuning for large black-box model.
The whole pipeline of CPT is illustrated in Fig. 1.
Compared to vanilla Proxy-tuning [], our CPT ensures consistency between the optimization objective during the training of the small white-box model and the test-time inference with proxy. This benefits the Proxy-tuning process and enhances the performance of the model.

Note that our method focuses solely on logit-level computation, thus holding the potential of being a plug-and-play improvement for any black-box model fine-tuning tasks which involve logit-level classification.
In this paper, we show the effectiveness of CPT by applying it to two representative black-box tuning tasks respectively: black-box tuning of Large-Language Models (LLMs) and black-box tuning of Vision-Language Models (VLMs).
For black-box tuning of LLMs, we use a LLAMA2 [] model with a lightweight architecture (e.g., LLAMA2-7B) to consistently proxy-tune the LLAMA2 model with heavier architecture (e.g., LLAMA2-13B) on various downstream natural language processing tasks.
Our CPT outperforms Proxy-tuning [] by 2.41% in terms of mean accuracy across six natural language processing datasets.
For black-box tuning of VLMs, we use a CLIP [] with a lightweight image encoder (e.g., ResNet-50 []) to consistently proxy-tune the CLIP model with a heavier image encoder (e.g., ViT-B/16 []) on image classification task.
Our CPT outperforms Proxy-tuning [] by 1.24% in terms of mean accuracy across eight image classification datasets.

In a nutshell, the main contributions of this paper are summarized as follows:

- 1)
We propose Consistent Proxy Tuning (CPT), a simple yet effective proxy-tuning method for black-box model optimization.
- 2)
CPT introduces a frozen black-box large model and a frozen white-box small model into the training of another tunable white-box small model, which ensures that the optimization objectives during white-box training are consistent with the form of proxy-tuning during inference.
- 3)
CPT can be widely applied to a variety of black-box model fine-tuning tasks. Extensive experiment results of the black-box tuning for VLMs and LLMs on various datasets demonstrate the effectiveness of our CPT.

## 2 Related Work

#### Efficient Fine-tuning.

Large pretrained models, which are extensively trained on vast datasets, demonstrate broad generalization capabilities across various tasks.
To further improve the performance of these models on specific downstream tasks, efficiently fine-tuning methods have been proposed for large pretrain models.
In the field of natural language processing, some approaches focus on designing lightweight components to fine-tune pretrained Large Language Models (LLMs).
For example, soft prompt tuning  [] introduces continuous learnable prompts other than hard prompts.
Adapter-based method [] inserts learnable adapters into Transformer [], thus transferring to downstream tasks while preserving pretrained knowledge.
Low-Rank Adaptation (LoRA) [] freezes the pretrained model weights and injects trainable rank decomposition matrices into each layer of the Transformer.
BitFit  [] only tunes the bias terms of the model.

Many other works also explore how to efficiently fine-tune pretrained VLMs (e.g.CLIP []).
CoOp  [] designed learnable text prompts to better understand natural language context.
Then CoCoOp  [] further uses images as conditions to constrain the optimization of text prompts.
Visual prompting [] also shows that visual prompting is particularly effective for CLIP.
Some works [, ] adopts add adapters to the encoders of CLIP, thus to fit different tasks while preserving pretrain knowledge.

However, these above strategies require access to the model’s internal parameters (white-box access), which is not feasible for many of today’s sophisticated models.
Such infeasibility calls for new paradigms in fine-tuning black-box pretrained models.

#### Black-Box Tuning.

Black-box large pretrained models require a special set of fine-tuning methods.
For large language models, BBT  [] achieves gradient-free optimization by using covariance matrix adaptation evolution strategy (CMA-ES)  [].However, it requires permission from black-box model to use customized prompt embedding, which is not feasible with some popular language models e.g., GPT-4  []. BBT-v2  [] injects learnable prompt into layers of the LLM, which is also not applicable for language model APIs. BDPL  [] investigates the possibilities of using discrete prompt to help LLMs understand the task better. Proxy-tuning  [] considers training smaller white-box models as proxy instead, and use the fine-tuned white-box experts to enhance black-box LLMs. This approach has shown both effectiveness and promise, but it overlooks the inconsistency between the training objective of small model and the joint test-time ensemble of large black-box model and smaller proxy models.
Zhang et al. [] also uses small models to indirectly fine-tune large models, but they need access to the parameters of intermediate layers, which is not suitable for scenarios where the parameters of the model cannot be accessed.

For vision-language models, BlackVIP  [] optimizes the coordinator which generates visual prompts by zeroth-order optimization. However, the improvement in performance is limited. Linear Feature Alignment (LFA)  [] optimizes a projection layer to enhance the alignment between pre-computed image features and class prototypes. CBBT  [] optimizes textual prompt and feature output adaptation collaboratively. These two methods interact with the black-box models at a feature level and requires access to output features, which leaves a potential risk of being vulnerable to attacks e.g.membership inference attacks (MIA)  []. We focus on a more restrict black-model setting where only output logits other than output features of a model is accessible.

#### Logits Arithmetic.

Recently, some methods [] have demonstrated the capability of logits ensembling from multiple models in enhancing model performance.
For example, Dou et al. [] assembles multiple logits from models pretrained on different domains to achieve domain adaptation.
DExperts  [] uses the difference in logits output between a toxic model and a non-toxic model to assist language models in language detoxification.
This paper also explores the use of proxy [] to “fine-tune” Large Language Models (LLMs) during the inference stage.
Contrastive Decoding (CD) [] leverages the differences in log-likelihood between expert and amateur language models (LMs) of varying sizes by selecting tokens that maximize this discrepancy.
Some subsequent studies have also explored the effects of ensembling output logits from different layers of models [, ] or the effects of output logits from varying inputs [, ].

This paper proposes a method that enhances a large black-box model using the output from a small white-box model and an untuned one.
Unlike Proxy-tuning [], which overlooks the consistency between proxy-independent training and proxy-dependent testing and results in suboptimal outcomes, our method employs ensembled output logits from both black-box and white-box models as optimization objectives. This approach ensures consistency in proxy techniques, thereby enhancing model performance.

## 3 Proposed Method

Figure: Figure 1: Illustration the comparison of our Consistent Proxy Tuning (CPT) with vanilla Proxy-tuning []. (a) and (b) respectively illustrate the training and inference stage of Proxy-tuning. Notice that their optimization objectives and the formula of the proxy during inference are inconsistent. In contrast, our CPT achieves consistency in these two aspects, as shown in (c). Especially, when $\alpha_{train}=0$ and $\alpha_{test}=1$, our CPT will degenerate into the “inconsistent” Proxy-tuning.
Refer to caption: x1.png

### 3.1 Revisiting Proxy-tuning

Given a large black-box LLM $\mathcal{M}_{l}(\cdot;\bm{\theta}_{{l}}^{{p}})$ with inaccessible pretrained parameters $\bm{\theta_{{l}}}^{{p}}$, we only assume access to the output logits across the entire output space.
Since $\mathcal{M}_{{l}}$ is a black-box model, directly fine-tuning it on downstream datasets with methods such as full fine-tuning or LoRA is not applicable, as these methods require access to the model parameters.

To tackle this problem, the novel practice of tuning models by proxy  [] improves a large black-box model $\mathcal{M}_{{l}}$ with proxy *i.e.*, smaller tuned white-box models.
Specifically, during training stage, a small white-box model $\mathcal{M}_{s}(\cdot;\bm{\theta}_{{s}}^{{p}})$ with pretrained parameters $\bm{\theta}_{{s}}^{{p}}$ is fine-tuned by downstream dataset $\mathcal{D}$ with supervised learning paradigm.
Given an input $\mathbf{x}$ and corresponding ground truth $\mathbf{y}$, the model is fine-tuned with the optimization objective of

$$ $\bm{\theta}_{{s}}^{{t}}=\operatorname*{arg\,min}_{\bm{\theta}_{s}}\mathbb{E}_{ (\mathbf{x},\mathbf{y})\sim\mathcal{D}}[\mathcal{L}(\mathcal{M}_{{s}}(\mathbf{ x};\bm{\theta}_{s}),\mathbf{y})],$ (1) $$

where $\mathcal{M}_{{s}}(\mathbf{x};\bm{\theta}_{s})$ with parameters $\bm{\theta}_{{s}}$ denotes the output logits of model $\mathcal{M}_{{s}}$, $\bm{\theta}_{{s}}^{{t}}$ denotes the optimized parameters and $\mathcal{L}$ is the classification loss function, e.g.cross entropy loss.

During the inference stage, a test data $\mathbf{x}$ is fed to $\mathcal{M}_{{s}}(\cdot;\bm{\theta}_{{s}}^{{t}})$, $\mathcal{M}_{{s}}(\cdot;\bm{\theta}_{{s}}^{{p}})$ and $\mathcal{M}_{{l}}(\cdot;\bm{\theta}_{{l}}^{{p}})$ to obtain output scores $\mathbf{z}_{\mathcal{M}_{{s}}^{{t}}}$, $\mathbf{z}_{\mathcal{M}_{{s}}^{{p}}}$ and $\mathbf{z}_{\mathcal{M}_{{l}}^{{p}}}$, respectively.
Then, the final prediction probability of proxy-tuned models on input $\mathbf{x}$ can be formally expressed as:

$$ $p(\mathbf{x})=\mathbf{z}_{\mathcal{M}_{{s}}^{{t}}}+(\mathbf{z}_{\mathcal{M}_{{ l}}^{{p}}}-\mathbf{z}_{\mathcal{M}_{{s}}^{{p}}}).$ (2) $$

Eqn. 1 indicates that only the output of the small model $\mathcal{M}_{{s}}$ is involved in optimization during training stage.
However, during the inference stage, the final prediction score is calculated by ensembling the outputs from all three models, as shown in Eqn. 2.
This inconsistency between training and inference (Fig. 1 (a) and Fig. 1 (b)) limits the training process to only finding a sub-optimal solution for the proxy-tuning model.

### 3.2 Consistent Proxy Tuning (CPT)

In this paper, we aim to bridge the inconsistency between the use of test-time proxies and the separate training process small white-box model.
To this end, we propose Consistent Proxy Tuning (CPT) method, which is illustrated in Fig. 1 (c).
In contrast to the vanilla Proxy-tuning  [], CPT additionally
incorporates frozen $\mathcal{M}_{{s}}(\cdot;\bm{\theta}_{{s}}^{{p}})$ and $\mathcal{M}_{{l}}(\cdot;\bm{\theta}_{{l}}^{{p}})$ into the fine-tuning process of the small white-box model, and the optimization objective is improved to compute the loss function based on the ensemble of the outputs from the three models and the ground truth.
Formally, the optimization objective is modified as follows:

$$ $\bm{\theta}^{{t}}_{{s}}=\operatorname*{arg\,min}_{{\color[rgb]{ 1,0.40234375,0.1328125}\bm{\theta}_{{s}}}}\mathbb{E}_{(\mathbf{x},\mathbf{y}) \sim\mathcal{D}}[\mathcal{L}(\mathcal{M}_{{s}}(\mathbf{x};{\color[rgb]{ 1,0.40234375,0.1328125}\bm{\theta}_{s}})+\alpha_{train}(\mathcal{M}_{l}( \mathbf{x};{\color[rgb]{0,0.65234375,0.9296875}\bm{\theta}_{{l}}^{{p}}})- \mathcal{M}_{{s}}(\mathbf{x};{\color[rgb]{0,0.65234375,0.9296875}\bm{\theta}^{ p}_{s}})),\mathbf{y})],$ (3) $$

where $\alpha_{train}$ is the coefficient that controls the impact of the offset obtained from $\mathcal{M}_{l}(\mathbf{x};{\color[rgb]{0,0.65234375,0.9296875}\bm{\theta}_{{l
}}^{{p}}})-\mathcal{M}_{{s}}(\mathbf{x};{\color[rgb]{0,0.65234375,0.9296875}
\bm{\theta}^{p}_{s}})$ on the training of $\mathcal{M}_{{s}}(;{\color[rgb]{1,0.40234375,0.1328125}\bm{\theta}_{s}})$.
Correspondingly, we introduce another coefficient $\alpha_{test}$ to Eqn. 2 during inference stage:

$$ $p(\mathbf{x})=\mathbf{z}_{\mathcal{M}_{{s}}^{{t}}}+\alpha_{test}(\mathbf{z}_{ \mathcal{M}_{{l}}^{{p}}}-\mathbf{z}_{\mathcal{M}_{{s}}^{{p}}}).$ (4) $$

Especially, when $\alpha_{train}=\alpha_{test}$, our CPT maintains strict consistency by leveraging the consistent form of ensembling output logits from three models during both training and inference stages.
While when $\alpha_{train}=0$ in Eqn. 3 and $\alpha_{test}=1$ in Eqn. 4, our CPT will degenerate into the “inconsistent” vanilla Proxy-tuning, *i.e.*, Eqn. 1 and Eqn. 2.
In fact, Proxy-tuning can be considered as a special case of our CPT.
In Sec. 4.3, we will explore how the combinations of different $\alpha_{train}$ and $\alpha_{test}$ impact model performance.

Note that our method focuses solely on the computation between the output logits of the model.
Therefore, CPT can be widely applicable to various black-box model fine-tuning tasks which involve logit-level classification, such as image classification, image segmentation (pixel-level classification), text generation (in-vocabulary classification), etc.
Furthermore, the large black-box model $\mathcal{M}_{l}$ and the smaller model $\mathcal{M}_{s}$ are not required to be from the same model family.
They only require to share the same output space, e.g., the same classification categories in image classification tasks or the same vocabulary in text generation tasks.
This allows our method to be flexibly applied to various combinations of black-box models and their white-box proxies.

### 3.3 Extending CPT to Vision-Language Model

To demonstrate that our method can be applied to other black-box model fine-tuning tasks involving logit-level classification, in this section we extend CPT to black-box Vision-Language Model (VLM) fine-tuning.
VLMs have shown impressive capabilities across a diverse array of applications.
Here, we mainly focus on applying CPT to black-box tuning for CLIP [] on downstream image classification tasks.
CLIP achieves image classification by calculating the similarity between image embeddings and different text embeddings.
Formally, CLIP employs an image encoder $E_{img}(\cdot|\bm{\theta}_{img})$ and a text encoder $E_{txt}(\cdot|\bm{\theta}_{txt})$, which are jointly pretrained with a vast number of image-text pairs using a contrastive learning approach.
Given an input image $\mathbf{x}$ and multiple tokenized descriptive texts $\mathbf{T}=\{\mathbf{t}_{1},\mathbf{t}_{2},\dots,\mathbf{t}_{C}\}$ corresponding to $C$ classes, the image encoder and text encoder extract image embedding $\mathbf{f}$, and text embeddings $\{\mathbf{g}_{c}\}^{C}_{c=1}$ respectively, where
$\mathbf{f}=E_{img}(\mathbf{x}|\bm{\theta}_{img})$ and $\mathbf{g}_{c}=E_{txt}(\mathbf{t}_{c}|\bm{\theta}_{txt})$.
Then, the predicted logit score of class $c$ is computed by $\langle\|\mathbf{f}\|_{2},\|\mathbf{g}_{c}\|_{2}\rangle$, where $\|\cdot\|_{2}$ denotes the $L_{2}$-normalization, and $\langle\cdot,\cdot\rangle$ denotes the cosine similarity of two embeddings.

In the context of our CPT, we use a
single symbol $M_{*}(\cdot|\bm{\theta}_{*})$ ($*$ can be $s$ or $l$) to briefly represent both $E_{img}(\cdot|\bm{\theta}_{img})$ and $E_{txt}(\cdot|\bm{\theta}_{txt})$ of CLIP, where $\bm{\theta}_{*}$ represents the parameters of both $\bm{\theta}_{img}$ and $\bm{\theta}_{txt}$.
We use $M_{*}(\mathbf{x},\mathbf{T}|\bm{\theta}_{*})$ to represent the classification logits predicted by the CLIP model for given $\mathbf{x}$ and $\mathbf{T}$.
Therefore, the optimization objective of CPT for fine-tuning the black-box VLM can be expressed as:

$$ $\bm{\theta}^{{t}}_{{s}}=\operatorname*{arg\,min}_{{\color[rgb]{ 1,0.40234375,0.1328125}\bm{\theta}_{{s}}}}\mathbb{E}_{(\mathbf{x},\mathbf{y}) \sim\mathcal{D}}[\mathcal{L}(\mathcal{M}_{{s}}(\mathbf{x},\mathbf{T};{\color[ rgb]{1,0.40234375,0.1328125}\bm{\theta}_{s}})+\alpha_{train}(\mathcal{M}_{l}( \mathbf{x},\mathbf{T};{\color[rgb]{0,0.65234375,0.9296875}\bm{\theta}_{{l}}^{{ p}}})-\mathcal{M}_{{s}}(\mathbf{x},\mathbf{T};{\color[rgb]{ 0,0.65234375,0.9296875}\bm{\theta}^{p}_{s}})),\mathbf{y})].$ (5) $$

In practice, we use the CLIP with a heavy image encoder (e.g., ViT-B/16 []) as the large black box model, and an image encoder with a lighter image encoder (e.g., ResNet-50 []) as the small white box model.
During the training stage, we use templates like “a photo of a [CLS]”, where [CLS] represents a certain class name, as inputs for the text encoder.
Regarding the fine-tuning strategy of the small white-box model, we fine-tune all parameters of its image encoder and text encoder.
In contrast to existing black-box fine-tuning methods for VLMs, which require access to image and text embeddings [, ], our method only requires access to cosine similarities (*i.e.*, output logits).
This illustrates that our method can be applied to stricter black box model fine-tuning scenarios, where only logits are accessible.

## 4 Experiments

### 4.1 Experimental Setup

#### Datasets.

For applying CPT to black-box tuning for LLM, we evaluate our CPT on TriviaQA [], ARC-challenge [], commonsenseQA [], Corpus of Linguistic Acceptability (CoLA) [], Microsoft Research Paraphrase Corpus (MRPC) [] and AG-News [].
For applying CPT to Black-box Tuning for VLM, we evaluate our CPT o CIFAR-10 [], EuroSAT [], Flowers102 [], Stanford Cars [], Oxford-IIIT Pets [], Describable Textures Dataset (DTD) [], Country-211 [] and Domainnet-10 [].
Please refer to the supplemental materials sppl. A for more details.

#### Baselines.

For the experiments of both black-box tuning for LLM and VLM, we compare it with several other tuning settings to demonstrate the effectiveness of our proposed CPT:
a) Zero-shot inference of pretrained black-box models on test set, which represents the baseline performance of untuned black-box models.
we compare our CPT with this untuned ones to show that our method can effectively perform tuning for black-box models.
b) Fine-tuning the black-box models with Proxy-tuning [].
Proxy-tuning neglects the inconsistency between proxy-independent optimization during training and proxy-dependent probability distribution in inference stage, which results in sub-optimal solution.
We compare CPT with Proxy-tuning to show that our model enhances performance by ensuring consistency between optimization objectives and inference-time proxy process.
c) Fine-tuning the black-box model with white-box tuning methods.
In fact, this tuning setting cannot be achieved in real-world scenarios for black-box model optimization due to the inability to access the internal parameters of the black-box model.
We only use this setting as an ideal reference to assess how much our CPT lags behind direct fine-tuning in terms of performance.
Additionally, we also compared zero-shot inference and direct tuning of small white-box models on each dataset.

#### Implementation Details.

Please refer to the supplemental materials sppl. B for more details.

**Table 1: Comparison of our CPT with other counterparts for black-box LLM tuning on six natural language datasets. We treat LLAMA2-7B as the small white-box model and treat LLAMA2-13B as the large black-box model. “pretrained” represents the zero-shot inference by their official pretrained parameters. “LORA-tuned” represents directly fine-tuning the corresponding model with LORA. Proxy-tuning [] and CPT represent using a 7B model to “proxy fine-tune” a 13B model, where the 7B model is trained using their method and our method, respectively. “ARC-C” is the abbreviation of ARC-challenge.**
| Model | Accuracy (%) $\uparrow$ | Mean Acc (%) $\uparrow$ |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- |
| TriviaQA | ARC-C. | commonsenseQA | COLA | MRPC | AG-News |  |  |
| LLAMA2-7B |  |  |  |  |  |  |  |
| pretrained | 21.88 | 43.14 | 33.74 | 45.73 | 32.04 | 41.14 | 36.27 |
| LORA-tuned | 60.03 | 47.16 | 75.84 | 81.50 | 68.99 | 90.21 | 70.62 |
| LLAMA2-13B |  |  |  |  |  |  |  |
| pretrained | 36.76 | 53.85 | 35.71 | 70.95 | 67.96 | 64.15 | 54.89 |
| Proxy-tuning [] | 61.52 | 50.17 | 74.04 | 79.19 | 68.22 | 90.34 | 70.58 |
| CPT (Ours) | 62.79 | 55.85 | 76.41 | 82.26 | 69.77 | 90.91 | 72.99 |
| LORA-tuned | 66.58 | 66.22 | 81.90 | 84.65 | 68.99 | 90.65 | 76.49 |

**Table 2: Comparison of our CPT with other counterparts for black-box VLM tuning on eight image classification datasets. We treat CLIP with ResNet-50 (RN-50) as the small white-box model and treat CLIP with ViT B/16 as the large black-box model. “full-tuned” represents directly fine-tuning the whole image encoder and text encoder of CLIP. Proxy-tuning [] and CPT represent using a CLIP with RN-50 model to “proxy fine-tune” a CLIP with ViT B/16 model, where the CLIP with RN-50 model is trained using their method and our method, respectively. “DM-10.”, “FL-102.”, “CF-10.”, “EUR.”, “SC.”, “OFP.” and “CT211” are the abbreviation of Domainnet-10, Flowers102, CIFAR-10, EuroSAT, Stanford Cars, Oxford-IIIT Pets and Country-211, respectively.**
| Model | Accuracy (%) $\uparrow$ | Mean Acc (%) $\uparrow$ |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| DM-10. | FL-102. | CF-10. | EUR. | SC. | OFP. | DTD | CT211. |  |  |
| CLIP RN-50 |  |  |  |  |  |  |  |  |  |
| pretrained | 81.15 | 66.09 | 70.37 | 36.16 | 53.94 | 85.69 | 40.27 | 14.18 | 55.98 |
| full-tuned | 88.83 | 74.78 | 94.13 | 98.44 | 74.43 | 87.38 | 65.32 | 20.20 | 75.43 |
| CLIP ViT-B/16 |  |  |  |  |  |  |  |  |  |
| pretrained | 87.38 | 71.05 | 90.08 | 48.42 | 63.67 | 89.09 | 42.98 | 20.47 | 64.14 |
| Proxy-tuning [] | 90.14 | 76.96 | 95.21 | 98.33 | 76.93 | 89.10 | 65.69 | 25.07 | 77.17 |
| CPT (Ours) | 93.94 | 77.52 | 96.57 | 98.47 | 78.03 | 89.62 | 67.23 | 25.93 | 78.41 |
| full-tuned | 93.94 | 95.43 | 97.69 | 98.82 | 86.97 | 95.45 | 78.09 | 30.10 | 84.56 |

### 4.2 Experimental Results

Tab. 1 and Tab. 2 shows the comparison of our CPT with other counterparts for black-box LLM tuning and for black-box VLM tuning respectively.
We report the Accuracy for each dataset as well as the Mean Accuracy across all datasets.

#### Results of Black-box LLM Fine-tuning.

Tab. 1 shows the comparison results of black-box LLM fine-tuning on six datasets.
Clearly, our CPT significantly enhance the performance of pretrained model (*i.e.*, 13B pretrained) across all datasets.
Moreover, CPT also outperforms Proxy-tuning [] across all datasets, and surpass it by 2.41%, in terms of Mean Accuracy, *i.e.*, 70.58% $\rightarrow$ 72.99%.
These results demonstrate that our CPT yields better fine-tuning effects on black-box LLMs compared to Proxy-tuning.
We also observed that the performance of Proxy-tuning on several datasets are even worse than fine-tuning standalone white-box small models (*i.e.*, LLAMA-7B LORA-tuned).
For instance, on commonsenseQA, COLA, and MRPC, the performance of Proxy-tuning are 1.80%, 2.31%, and 0.77% lower than that of 7B LORA-tuned, respectively.
Note that the output of Proxy-tuned is an ensemble of outputs from a tuned small white-box model, a pretrained small white-box model, and a large black-box model.
Therefore, it only makes sense if the performance of the large model being proxied exceeds that of the small model itself.
However, the results of the ensemble by Proxy-tuning are worse than those of the single model, which implies that Proxy-tuning is still sub-optimized.
In contrast, our method outperforms the 7B LORA-tuned across all datasets, also demonstrating that our CPT is superior to Proxy-tuning.
From this perspective, our CPT can also serve as a novel fine-tuning method for white-box models. In this perspective, CPT seek guidance from a larger pretrained model to better fine-tune the smaller one.
More interesting, on MRPC and Ag-News, our CPT even outperforms the method that hypothetically
use white-box fine-tuning of large models (*i.e.*, 13B LORA-tuned).
These results above fully demonstrate the effectiveness of our CPT for fine-tuning black-box LLM.

#### Results of black-box VLM fine-tuning.

Tab. 2 shows the comparison results of black-box VLM fine-tuning on eight datasets.
Similar to the results of black-box LLM fine-tuning, the standout aspects of our CPT can be summarized in the following four folds:
1) Our CPT significantly improves the performance of pretrained VLM (*i.e.*, ViT-B/16 pretrained), and achieving 14.26% improvement in terms of Mean Accuracy, *i.e.*, 64.14% $\rightarrow$ 78.41% .
2) Our CPT consistently outperforms Proxy-tuning [] across all datasets, obtaining 1.23% improvement in terms of Mean Accuracy, *i.e.*, 77.17% $\rightarrow$ 78.41%.
3) Proxy-tuning underperforms fine-tuning standalone white-box small models (*i.e.*, RN-50 full-tuned) on EuroSAT, *i.e.*, 98.44% $\rightarrow$ 98.33%, while CPT outperforms the RN-50 full-tuned across all datasets.
4) Our CPT shows comparable performance with that of fine-tuning large models using white-box methods (ViT-B/16 full-tuned) on DomainNet-10, *i.e.*, 93.94% *vs.*93.94%.

To sum up, for both fine-tuning black-box LLM and VLM tasks, our CPT significantly improves the performance of pretrained large black-box model, and achieves higher performance compared to Proxy-tuning [].
This indicates that ensuring the consistency between training objectives and the formula of test-time proxy
indeed further enhances the performance of the proxy-tuned model.

**Table 3: Comparison of our CPT with other counterparts for black-box VLM tuning on Stanford Cars [] and Oxford-IIIT Pets []. The small white-box model, *i.e.*, CLIP RN-50, involved in Proxy-tuning and our CPT are tuned with CoOp [].**
| Model | Accuracy (%) $\uparrow$ |  |
| --- | --- | --- |
| Stanford Cars | Oxford-IIIT Pets |  |
| CLIP RN-50 |  |  |
| pretrained | 53.94 | 85.69 |
| CoOp-tuned | 77.83 | 91.20 |
| CLIP ViT-B/16 |  |  |
| pretrained | 63.67 | 89.09 |
| Proxy-tuning [] | 78.44 | 92.29 |
| CPT (Ours) | 81.66 | 93.21 |
| CoOp-tuned | 86.18 | 94.94 |

Figure: Figure 2: Variation of the accuracy versus the varied $\alpha_{train}$ and $\alpha_{test}$ on (b) ARC-challenge, (c) Stanford Cars, (d) Oxford-IIIT Pets and the results of their (a) Average .
Refer to caption: x2.png

### 4.3 Ablation Studies

#### Using CoOp for White-box tuning in CPT.

Our CPT optimizes the large model on downstream tasks by fine-tuning a small white-box model as a proxy.
In fact, CPT flexibly accommodates various fine-tuning strategies for the small white-box model.
In the main paper, we adopt the fully fine-tuning for the image and text encoders of the small white-box model to act as a proxy (both Proxy-tuning [] and CPT) for the black-box VLM model.
Here, we use CoOp [] to alternatively optimize the white-box model as an example to demonstrate CPT’s inclusivity towards the chosen white-box fine-tuning method.
CoOp uses a set of learnable vectors to replace the text input template “a photo of”, which can efficiently fine-tune CLIP on downstream classification tasks.
Fig. 4 shows the comparison results on Stanford Cars and Oxford-IIIT Pets.
Note that different from Tab. 2, Proxy-tuning and CPT in Tab. 4 represent the use of a small white-box model fine-tuned with CoOp to act as a proxy for the black-box model.
Similar to the results in Tab. 2, when using CoOp to fine-tune the small model, our CPT can still effectively enhance the performance of the large black-box model, and consistently outperforming Proxy-tuning.

#### Tuning Black-box Models under Different Scales with CPT

Here we demonstrate the effectiveness of our CPT method across various model architectures. In this case, we adopt full fine-tuning for tuning the proxy model for both Proxy-tuning and CPT on VLMs. The main results shown in Tab. 2 is obtained with CLIP ResNet-50 as white-box proxy model and CLIP ViT-B/16 as the large black-box model. We extend the experiment to tuning black-box CLIP ViT-L/14 with CPT, CLIP ResNet-50 and CLIP ViT-B/16 being white-box proxies respectively. The results in Tab. 4 shows that CPT constantly outperforms Proxy-tuning and other baseline methods with different pairs of proxies and black-box models.

#### Effect of varied α t ⁢ r ⁢ a ⁢ i ⁢ n subscript 𝛼 𝑡 𝑟 𝑎 𝑖 𝑛 \alpha_{train} italic_α start_POSTSUBSCRIPT italic_t italic_r italic_a italic_i italic_n end_POSTSUBSCRIPT and α t ⁢ e ⁢ s ⁢ t subscript 𝛼 𝑡 𝑒 𝑠 𝑡 \alpha_{test} italic_α start_POSTSUBSCRIPT italic_t italic_e italic_s italic_t end_POSTSUBSCRIPT .

$\alpha_{train}$ in Eqn. 3 and $\alpha_{test}$ in Eqn. 4 are hyper-parameters of our CPT.
They determines the extent to which the offset calculated by $\mathcal{M}_{{l}}(\mathbf{x};{\bm{\theta}^{p}_{l}})-\mathcal{M}_{{s}}(\mathbf{
x};{\bm{\theta}^{p}_{s}})$ affects the optimization objective and the proxy process.
Intuitively, choosing a large $\alpha_{train}$ will amplify the impact of the difference between the outputs of the frozen large model and the small model on the optimization objective, while choosing a smaller one reduces this impact.
Similarly, choosing different values of $\alpha_{test}$ will affect the final performance of the proxied model.
Moreover, the relative values of $\alpha_{train}$ and $\alpha_{test}$ will affect the consistency between the training objective and the proxy process during testing.
Specifically, the closer these two coefficients are, the stronger the consistency between the training objective and the proxy process during testing;
conversely, the further apart they are, the weaker the consistency.

In all main experiments, both of these two coefficients are set to $1$ to keep a strict consistency.
Here, we further explore the impact of varied $\alpha_{train}$ and $\alpha_{test}$ on performance of CPT.
Fig.  2 shows the performance of CPT under varied $\alpha_{train}$ and $\alpha_{test}$ on ARC-challenge, Stanford Cars (c), Oxford-IIIT Pets (d) and the results of their average (a).
Each cell in this matrix represents the accuracy under a specific set of $\alpha_{train}$ and $\alpha_{test}$.
From Fig. 2, we can obtain the following observations:
1)
The areas where the model performs well are concentrated near the main diagonal of the matrix, e.g., marked with a yellow elliptical curve in Fig. 2 (a).
When $\alpha_{train}$ and $\alpha_{test}$ are relatively close, the model tends to perform better; conversely, when they are further apart, the model’s performance tends to decline.
This result indicates that ensuring the consistency between $\alpha_{train}$ and $\alpha_{test}$ will be beneficial to the model’s performance.
This also indirectly supports our proposal in this paper for "ensuring the consistency between the optimization objectives and the proxy during testing can benefit for fine-tuning."
In specific datasets, such as ARC-challenge and Stanford Cars, we can also observe similar conclusions.
Due to the limitations of our hyperparameter selection range, this phenomenon is not observed in Fig. 2 (d).
In Fig. 3 of supplemental material, we show the results under a wider range of hyperparameters, where the phenomenon is consistent with the other two datasets.
2) From the results of each dataset, it can be seen that when $\alpha_{train}$ and $\alpha_{test}$ are close but both are relatively small, the performance of CPT is poor.
This phenomenon may suggest that we should choose a relatively larger alpha when performing CPT.
From the average results (2 (a)), when $\alpha_{train}$ and $\alpha_{test}$ are close and their values are between 1.2 and 2.0, the model performs well.
We suggest choosing these two hyperparameters from the above range to perform CPT, for example, selecting $\alpha_{train}=\alpha_{test}=1.2$.

## 5 Limitations

#### Increase in computational resources.

While CPT does not necessarily increase computational expenses compared to directly tuning the black-box model during training, it surely increases computational expenses at inference stage.
Facing the same problem with Proxy-tuning  [], *i.e.*, the time of inference increases because multiple models compute output logits jointly. Also, compared to the normal inference of a single black-box model, Proxy-tuning and CPT require more GPU memory to deploy the proxy models.
Although we can implement CPT effectively by computing classification logits of pretrained models on train/test dataset and storing them for further use, the increase in computational expenses in inevitable during inference on new data.

## 6 Broader Impacts

Please refer to Sppl. C for more details.

## 7 Conclusion

In this paper we proposed a simple yet effective black-box model tuning method named Consistent Proxy Tuning (CPT).
We notice that vanilla Proxy-tuning [] trains the white-box small model independently but uses an ensemble of the white-box and black-box models for inference.
This inconsistency between the training objective and inference can lead to the proxy process being sub-optimal.
In contrast, our CPT introduces the frozen black/white models into the fine-tuning process of the small model, thereby ensuring consistency between training-stage optimization objective and test-time proxy process.
Our CPT can be plug-and-played for any black-box model fine-tuning tasks which involve logit-level classification.
Extensive experiment results of the black-box tuning for VLMs and LLMs on many datasets demonstrate the effectiveness of our CPT.

## Appendix A More Details of Datasets

#### Datasets for LLMs.

We evaluate our CPT on TriviaQA [], ARC-challenge [], commonsenseQA [], Corpus of Linguistic Acceptability (CoLA) [], Microsoft Research Paraphrase Corpus(MRPC) [] and AG-News [].
These datasets cover common natural language understanding tasks, including question-answering, linguistic analysis and paraphrasing.
Note that some datasets are often formulated as text classification tasks, for example, adding a classification header to the last layer of the model to predict the result.
However, this is not feasible for black-box LLMs.
Therefore, we convert all tasks into text generation tasks for processing.
Specifically, for each dataset, we construct specific prompts to standardize the output format of the model as much as possible.
We calculate the accuracy of the model by matching the text generated by the model with the ground truth labels.
Tab. 5 shows the details of each dataset, including train size, test size and used prompts.
During inference stage, {question} will be filled with a specific question of one data point, combining with contextual template text to form a complete prompt as input to the model.
While during training stage, the answers will also be filled into the {prediction} and combined with the previous question parts to form the input for training the model.
All datasets for LLMs are in the default version on their offical website.
Licenses for datasets are also specified in Tab. 5. N/A indicates that there is no explicit license on the official website and the we are reaching out to original authors of the assets.

#### Datasets for VLMs.

For applying CPT to Black-box Tuning for VLM, we first choose 7 well-studied image classification datasets which cover a variety of data distributions, *i.e.*, CIFAR-10 [], EuroSAT [], Flowers102 [], Stanford Cars [], Oxford-IIIT Pets [], Describable Textures Dataset (DTD) [], and Country-211 [].
Followed Li et al. [], we also evaluate our CPT on one more challenging datasets with inner domain gap, *i.e.*, Domainnet-10 [].
Domainnet-10 contains top-10 classes based on data amount in DomainNet which has 345 categories.
For each dataset, we use specific prompts to the mentioned in Sec. 3.3 to better adapt the model to domain-specific knowledge.
And we utilize the official category names provided in corresponding datasets to complete the template prompt.
Tab. 6 shows the details of each dataset, including train size, test size and used prompts.
All datasets for VLMs are used in the torchvision version, except for Domiannet-10 [] dataset and EuroSAT [] dataset, which are in the same version with FedBN [].
Licenses for datasets are also specified in Tab. 6. N/A indicates that there is no explicit license on the official website and the we are reaching out to original authors of the assets.

**Table 5: Details of each dataset of fine-tuning black-box LLM task.**
| Dataset | Train size | Test size | Prompt | License |
| --- | --- | --- | --- | --- |
| TriviaQA [] | 87,622 | 11,313 | Question: {question}<br>Answer: {prediction} | Apache 2.0 |
| ARC-challenge [] | 1,119 | 299 | Question: {question}<br>Please choose:<br>A. {option A}<br>B. {option B}<br>C. {option C}<br>D. {option D}<br>Answer: {prediction} | Apache 2.0 |
| commonsenseQA [] | 9,741 | 1,221 | Question: {question}<br>Please choose:<br>A. {option A}<br>B. {option B}<br>C. {option C}<br>D. {option D}<br>E. {option E}<br>Answer: {prediction} | N/A |
| COLA [] | 8,551 | 1,043 | Sentence: {sentence}<br>Question: Is this sentence<br>linguistically acceptable?<br>(Yes or No)<br>Answer: {prediction} | N/A |
| MRPC [] | 3,527 | 387 | Sentence 1: {sentence 1}<br>Sentence 2: {sentence 2}<br>Question: Are these two sentences<br>expressing the same meaning?<br>(Yes or No)<br>Answer: {prediction} | N/A |
| AG-News [] | 120,000 | 7,599 | Given the following<br>news article: {sentence}<br>Question: what category does<br>this article belong to?<br>Please choice:<br>A. {option A}<br>B. {option B}<br>C. {option C}<br>D. {option D}<br>Answer: {prediction} | N/A |

**Table 6: Details of each dataset of fine-tuning black-box VLM task.**
| Dataset | Train size | Test size | Prompt | License |
| --- | --- | --- | --- | --- |
| DomainNet-10 [] | 18,278 | 4,573 | A photo of a [CLASS]. | N/A |
| Flowers-102 [] | 1,020 | 6,149 | A photo of a [CLASS], a type of flower. | N/A |
| CIFAR-10 [] | 50,000 | 10,000 | A photo of a [CLASS]. | N/A |
| EuroSAT [] | 13,500 | 8,100 | A centered satellite photo of [CLASS]. | MIT License |
| Stanford Cars [] | 8,144 | 8,041 | A photo of a [CLASS]. | N/A |
| Oxford TIII Pets [] | 3,680 | 3,669 | A photo of [CLASS], a type of pet. | CC BY-SA 4.0 |
| DTD [] | 1,880 | 1,880 | A photo of a [CLASS] texture. | N/A |
| Country-211 [] | 31,650 | 21,100 | A photo I took in [CLASS]. | MIT License |

## Appendix B Implementation Details

All experiments are conducted with PyTorch toolkit [] on NVIDIA A100-40G GPU.
For black-box tuning of LLM, we use LLAMA2-7B as the small white-box model (*i.e.*, $\mathcal{M}_{s}$), and use LLAMA2-13B as the large black-box model (*i.e.*, $\mathcal{M}_{l}$).
For the training stage, we adopt LoRA to fine-tune the small white-box model $\mathcal{M}_{{s}}(\cdot;\bm{\theta}_{{s}}^{{p}})$ for computational efficiency.
Note that the large black-box model $\theta_{l}^{p}$ and another small white-box $\theta_{s}^{p}$ are only responsible for providing output logits for optimization objectives, and their own parameters are frozen throughout the entire training stage.
For training configurations, AdamW is used as the optimizer, with a initial learning rate of 1e-4,
batch size is set to 1 and model is trained for 2 epochs.
For black-box tuning of VLM, we use CLIP with ResNet-50 as the small white-box model (*i.e.*, $\mathcal{M}_{s}$), and use CLIP with ViT-B/16 as the large black-box model (*i.e.*, $\mathcal{M}_{l}$).
For the training stage, we fully fine-tune the whole image encoder and text encoder of the white-box model $\mathcal{M}_{{s}}(\cdot;\bm{\theta}_{{s}}^{{p}})$.
For training configurations, Adam is used as the optimizer, with a momentum of 0.9 and weight decay of 0.001,
batch size is set to 128 and model is trained for 300 epochs.
For all the experiments, we set $\alpha_{train}=\alpha_{test}=1$ by default.

## Appendix C Broader Impacts

#### Positive Impact: Fairness in AI.

CPT aims to tune a black-box model with smaller"proxies" consistently, but it can also serve as a fine-tuning method for smaller models guided by large pretrained models. Large-scale pretraining is more often on general knowledge than domain-specific knowledge, so downstream tasks barely benefit from large-scale pretrained models without computationally expensive fine-tuning. It is even less possible when large pretrained model is only accessible as black-boxes. CPT fills the gap by joining the strength of large-scale general knowledge pretraining and small-scale task-specific fine-tuning. From this perspective, CPT brings positive social impact in that it finds a way of using general pretrain model to elevate task-specific fine-tuning of smaller models. It is of great significance for individuals, organizations and regions without resources to fine-tune large pretrain models for their own well-being, thus improving fairness of AI.

#### Negative Impact: Potential Misuse.

Black-box language models, compared with white-box ones, are more difficult to tune for specific tasks. While this limits the application of black-box language models, it also prevents them from being misused to generate malignant content. However, the way CPT tunes a black-box model formulates a by-pass around inaccessible parameters to output logits, making the output logits as volunrable to harmful content as it is adjustable.

Harm control methods like gated release of models, API monitoring for misuse, limitation on access frequency to prevent API-based CPT should be considered to minimize negative social impacts.

## Appendix D Extended Results

Figure: Figure 3: Variation of the accuracy versus the widely varied $\alpha_{train}$ and $\alpha_{test}$ on (a) Oxford-IIIT Pets (b) and Stanford Cars .
Refer to caption: x3.png

In addition to the partial results shown in Fig. 2, we demonstrate the extensive results of CPT on VLMs for Oxford-IIIT Pets dataset and Stanford Cars dataset. To demonstrate the impact of "consistency", *i.e.*the extent to which $\alpha_{train}$ and $\alpha_{test}$ are close to each other. To better demonstrate the whole pattern, we sample $\alpha_{train}$ and $\alpha_{test}$ from 0.4 to 4 with an inverval of 0.4 for Oxford-IIIT Pets dataset, and $\alpha_{train}$ and $\alpha_{test}$ from 0.2 to 3.0 with an interval of 0.2 to 3.0 for Stanford Cars dataset. Both matrices of results in Fig. 3 are obtained with the same setup with results in Tab. 2 except for $\alpha_{train}$ and $\alpha_{test}$.
The extended results demonstrate the same pattern with that in Sec. 4, *i.e.*, the performance of the models are better when $\alpha_{train}$ and $\alpha_{test}$ are closer and formulate a "consistency".

## Peer Reviews

confidence: 4
contribution: 3
initial_rating: 5
presentation: 3
questions: See weakness above. While I appreciate the simplicity of the proposed method, my current verdict places it just under the acceptance bar due to increased cost and somewhat questionable experimental designs. I look forward to the authors' responses.
soundness: 3
strengths: 1. The proposed method is elegant, simple yet effective and beneficial to practitioners.
2. The presentation is clean and easy to follow. 
3. The proposed method is extended to VL models to further demonstrate its effectiveness.
summary: Modern foundation models, unlike traditional ML models, usually do not provide oracle access to their feature spaces and gradients.  With access restricted to logits, proxy-tuning thus emerges as a promising tool to "fake" tune the base model by tuning a smaller model and shift the output change between original and tuned small models onto the base model. Traditional proxy tuning decouple training and inference into two different stages where a small model is first fine-tuned on its own and the base model is fake-tuned during inference only. However, this creates an objective gap between the small model and large model. 

To bridge this gap, this paper presents a simple online tuning method by tuning the small model while distilling from the base model's logits at the same time. Experiments show the effectiveness of the method.
weaknesses: 1. Lack of analysis over why proxy tuning works: This is a big ask, but I hope the authors can give some intuitions here. In addition, if the underlying assumption is that both small and base model can access the output logits for the entire vocabulary, then how is the inconsistency defined. Can you elaborate more? How about in CLIP's case. 
2. Increased actual cost: Although not requiring more computation during training, there is a need to compute logits using the black box model for each training data. If we are looking at true black box models, as the authors claimed, such as GPT, Gemini, then we are looking at some potential big bill $$. 
3. Questionable experimental designs: the authors seem to position their work as a type of PEFT for generic fine-tuning which I found somewhat problematic since LORA FT requires significantly fewer parameters than tuning even the base model here. I think the authors should position their work similarly to [1] as task-oriented efficient fine-tuning and find more interesting cases to demonstrate the effectiveness (domain adaptation, imbalanced learning, to name a few). 
 
[1] Liu et. al., Tuning Language Models by Proxy

---

confidence: 3
contribution: 3
initial_rating: 5
presentation: 3
questions: I am wondering if maintaining consistency between training and testing/inference is always beneficial. For instance, many preference optimization algorithms, such as Direct Preference Optimization (DPO), do not maintain complete consistency between training and testing. I am curious about the scenarios where such consistency is advantageous and why, in some cases, consistency is not a primary focus.
soundness: 3
strengths: 1. The paper is well-written, with clear logic that is easy to follow.

---
2. The proposed method is clear, well-motivated, and demonstrates simplicity while being effective.

---
3. The method uses the output logits of the large model as a reference. By incorporating these logits into the loss function of the small model, the training objective becomes closer to the ensemble effect used during inference. This acts as an implicit regularization on the small model during training, ensuring its output aligns with the actual inference combination form.

---
4. The experiments are good, covering both LLMs and VLMs to demonstrate the method's effectiveness across different model types.
summary: The paper introduces a method for fine-tuning black-box models called Consistent Proxy Tuning (CPT). This approach addresses the limitations of existing methods, such as Proxy-tuning, by ensuring consistency between the training objective and the inference process. CPT achieves this by incorporating the same regularization of the large model's logits in both the training and inference stages.
weaknesses: 1. Although the method is effective, it requires significant computational resources, especially during training when additional model outputs are generated. This could limit its practicality for larger-scale models without high-resource infrastructure.

---
2. The impact of parameters like $\alpha_{\text{train}} $ and $ \alpha_{\text{test}}$ on performance, shown in Figure 2, indicates that careful tuning is necessary, which may complicate implementation.

---
3. The motivation states, “Such inconsistency may lead to sub-optimal solutions for the proxy tuning optimization objective, causing bottlenecks in model performance.” While this is intuitive and understandable, it would be better if the paper provided deeper analysis or references to relevant literature that demonstrate or explain why consistency is beneficial in such contexts.

---
I appreciate the contributions of this paper, and if my question could be addressed, I would be open to considering a higher score.

---

confidence: 3
contribution: 1
initial_rating: 3
presentation: 2
questions: See weaknesses.
soundness: 2
strengths: 1. The paper is easy to follow.
2. The proposed method is straightforward and easy to implement.
3. Extensive experiments are performed with language models and vision-language models. Actual training time is also reported.
summary: This paper addresses the black-box optimization problem for language models and vision-language models. It proposes consistent proxy tuning to directly optimize the small proxy model in proxy-tuning [1] jointly with the target black-box model. In contrast to the vanilla proxy-tuning which optimizes the small proxy model alone, the joint optimization improves the accuracy of proxy-tuning while it introduces additional complexities explained below.

[1] Liu et al., "Tuning language models by proxy." (2024)
weaknesses: 1. The novelty of the proposed method is limited. It just directly optimizes the small proxy model in proxy-tuning to achieve more accuracy, which is a trivial remedy and even hurts some advantages of proxy-tuning, i.e., it introduces additional memory/computational cost and requires the availability/accessibility to the black-box model during optimization.
2. The gains of consistent proxy tuning in accuracy seem too little against the vanilla proxy-tuning in most cases, relative to zero-shot and white-box tuned results, even though the proposed method exploits the (specific) black-box target model during optimization.  In such cases, the advantage by the consistent proxy tuning may not outweigh its disadvantages like additional cost and the need of availability of the black-box model.
3. The paper ignores a large portion of previous works [2-8] in black-box optimization for language models or vision-language models and avoids experimental comparison to them. Particularly, Ormazabal et al [2] proposed a very similar method that tunes the small proxy model and then combines it with the output of a target black-box model. The previous method in this field should be compared with the proposed method, not only in accuracy but also in the number of API calls for black-box optimization.

[2] Ormazabal et al., "CombLM: Adapting Black-Box Language Models through Small Fine-Tuned Models." (2023)

[3] Diao et al., "Black-box Prompt Learning for Pre-trained Language Models" (2022)

[4] Cheng et al., "Black-Box Prompt Optimization: Aligning Large Language Models without Model Training." (2023)

[5] Chen et al., "InstructZero: Efficient Instruction Optimization for Black-Box Large Language Models" (2023)

[6] Guo et al., "Connecting Large Language Models with Evolutionary Algorithms Yields Powerful Prompt Optimizers." (2023)

[7] Oh et al., "BlackVIP: Black-Box Visual Prompting for Robust Transfer Learning." (2023)

[8] Liu et al., "Language Models as Black-Box Optimizers for Vision-Language Models." (2023)

---

confidence: 4
contribution: 1
initial_rating: 3
presentation: 3
questions: The considered setting aims to improve the predictions of the black-box model. Prompting techniques such as CoT [1] and others can also be applied in such black-box setting, thus, I encourage authors to include such baselines at least for NLP tasks to strengthen the paper.

[1] Kojima et al. Large Language Models are Zero-Shot Reasoners. NeurIPS 2022.
soundness: 2
strengths: * The considered setting of black-box tuning is important and is of interest of a broad community given that currently the most capable models are close-weight models.
summary: The paper considers the setting of black-box tuning of models. The authors build upon recently proposed Proxy Tuning method [1] and introduce the usage of black-box frozen model into the training objective to make the training and the inference stage consistent, that, in-turn leads to slightly improved performance upon the original method. The authors evaluate the proposed approach on vision tasks using CLIP-like models and on NLP tasks with Llama family of models.


[1] Liu et al. Tuning language models by proxy. COLM 2024
weaknesses: * The methodological contribution is the very minor addition to the original method [1]. The obtained quantitive results also demonstrate minor improvements upon the original Proxy Tuning.

* Big part of the experiments for vision tasks is done for CLIP-like models. The considered setting of black-box fine-tuning of CLIP-like models is not well-justified since to the best of my knowledge there are no closed-source CLIP-like VLMs. I strongly encourage authors to consider the setting that is closer to the original paper and evaluate the proposed methodology on autoregressive VLMs like OpenFlamingo [2], or Llama 3.2 Vision [3]. For such class of models there are indeed closed-source models like GPT-4o and the setting would make more sense.

[1] Liu et al. Tuning language models by proxy. COLM 2024

[2] Awadala et al. OpenFlamingo: An Open-Source Framework for Training Large Autoregressive Vision-Language Models. arXiv:2308.01390

[3] Dubey et al. The Llama 3 Herd of Models. arXiv:2407.21783