Adaptive Inference: Theoretical Limits and Opportunities for Efficient AI

After reading the comments of the other reviewers and all the authors' responses, I find that although some points are now clearer, the work still requires further study to address the fundamental issues raised. I maintain my original score and my confidence.

The general formulation provided on Equation (7) can be applied to any (nonlinear) $\alpha_i$ curve without the need for any additional assumption. However, as long as the $\alpha_i$ values stay relatively constant and do not quickly fall to 0 (which is the case for the curves shown in Figure 2), the constant-$\alpha$ assumptions can be useful in defining approximate bounds as described in section 2.2.2.

In other words, even if the alpha values shown in Figure 2 were not all constant, both the conservative bound (corresponding to $\alpha=1$) and the “optimistic bound” (corresponding to $\alpha=\alpha_{min}$) still hold for each classifier family. This is demonstrated in Figure 4 and Section 3.3 comparing constant-$\alpha$ bounds with empirical measurements for an Oracle agent.

Please let us know if any further clarifications are needed on this subject.

As mentioned in Section 2.2.2:

“$\alpha_i$ serves as a measure of the probability that a large model making a classification error leads to errors in all of the smaller models.”

Based on the definition of $\alpha_i$ in Section 2.2.1, $\alpha_i$ captures the dependency between two events:

1- The i-th model making a classification error, and

2- All smaller models making a classification error as well.

This relationship is what needs to be captured for all models in the adaptation state space and is referred to in this sentence as cross-dependency. We welcome any suggestions on alternative terminology to replace “cross-dependency” that would avoid confusion for the readers.

We are comparing the expected resource consumption and accuracy of the Oracle to the expected resource consumption and accuracy achievable by other agents. Since the Oracle by definition achieves the highest accuracy (correctness) and efficiency comparing to any other agent for each individual instance, the expected value of its performance (accuracy) and efficiency over the evaluation set are also an upper bounds on efficiency and accuracy of any other agent.

As mentioned in the paper and pointed out by the reviewer, $P(e_N)$ is the probability that all the models fail in producing a correct prediction. This is also the probability that the second condition in Definition 2.1 holds, in which the Oracle fails to produce a correct prediction for instance x. Therefore the accuracy of the Oracle (the probability that the first condition in Definition 2.1 is met) is $1-P(e_N)$.

Please note that the formulation suggested by the reviewer also results in the same conclusion if conditional accuracies are used instead of $A_i$’s. Please let us know if further clarification or a formal proof for this equivalency is needed.

The $\alpha$ parameter does not measure any causal relationship between the models. Following your suggestion we will change the word “lead” to “imply” in the corresponding sentences to avoid confusions.

Thanks for your comment about the confusing notation in the appendix. Following your comment we will modify the “$x_i$” notation to avoid confusion.

As mentioned by the reviewer and shown in the proof in A.2, both the formulations suggested by the reviewer and the ones used in the paper are equivalent. We have intentionally decided to use the formulations based on the events $e_i$ instead of the suggested weighted sum formulation to facilitate easier definition of the $\alpha$ parameter later on. The $\alpha$ parameter has several intuitive and practical implications as mentioned in the paper in sections 2.2.1, 2.2.2 and 3.3.

To clarify, the Oracle agent’s strategy is not directly relying on $\alpha_i$. However, the expected accuracy and efficiency of the Oracle can be written in terms of $\alpha_i$, $R_i$ and $A_i$.

The importance of the current formulation is to separate the effect of two factors affecting $R_{oracle}$ and $A_{oracle}$: $A_i$ and $R_i$ (the static efficiency and accuracy of each individual model i), and $\alpha_i$ (the hidden cross-dependencies between different model’s predictions).

As mentioned in the paper in section 2.2.1 (page 5) $R_i$ and $A_i$ can be easily obtained for off-the-shelf models while knowledge about $\alpha_i$ requires analyzing relative behavior of all models simultaneously. Section 3.3 of the paper is dedicated to interpretations of $\alpha$ and related practical implications. As an example we showed that it is impossible to achieve accuracy gains beyond the most accurate classifier for models with $\alpha$ close to 1 while it is easily achievable for models with similar $A_i$ and $R_i$ values but with smaller $\alpha$.

The Oracle’s strategy does not directly depend on $A_i$. However, the Oracle’s overall accuracy and resource consumption can be written in terms of $R_i$, $A_i$ (and $\alpha_i$). For further clarification please refer to the previous question.

Based on Definition 2.1 it can be seen that the Oracle has knowledge about whether or not each model provides a correct prediction for each input x. This is a stronger assumption than knowledge about $A_i$ of each model.

For example, for the case suggested by the reviewer [S1=(10,95),S2=(20,97)], the Oracle follows the procedure explained in Section 2.2 and Figure1, achieving an accuracy better than or equal to $A_2$ (97%) while consuming less power than $R_2$ (20) depending on the $\alpha$ parameter defined in Section 2.2.1.

Following the reviewer’s comment we will remove the term “($S_i$)” from the corresponding sentence to avoid confusion. We also welcome any further clarifying questions regarding Section 2.2 and the definition of the Oracle Agent.

The short answer is that $A_i$ is the (static) accuracy of each Model i on the test-set that adaptive inference method will be ultimately applied to. Our assumption is that the challenges caused by the distribution mismatch between train and test-sets are handled separately through fine-tuning of the backbone models (and the agent) on a representative dataset.

The growing demand for compression methods in recent years serves as a key motivation for the presented work. However, we argue that static methods alone may not suffice to meet the efficiency requirements of large foundational models, as highlighted by the reviewer. Importantly, adaptive inference methods can be layered on top of static compression techniques, offering further gains in efficiency and addressing the increasing computational demands of these models.

Our argument regarding the efficiency advancements of compression methods reaching a plateau stems from the fact that the efficiency gains reported by the early fundamental papers in the context of computer vision network compression are relevant benchmarks to date. Examples include the ~49x total efficiency gain on VGG16 reported by Han et al in 2015 [1] and 32x quantization-only efficiency gain reported in the XNOR-Net paper in 2016 [2]. While there exist several review papers on recent compression algorithms in the context of computer vision[3] and LLMs[4], to the best of our knowledge none of the recent work in this area have promised the potential for an additional 10-100x improvement in efficiency.

[1] Han, Song, Huizi Mao, and William J. Dally. "Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding." arXiv preprint arXiv:1510.00149 (2015).

[2] Rastegari, Mohammad, et al. "Xnor-net: Imagenet classification using binary convolutional neural networks." European conference on computer vision. Cham: Springer International Publishing, 2016.

[3] Li, Zhuo, Hengyi Li, and Lin Meng. "Model compression for deep neural networks: A survey." Computers 12.3 (2023): 60.

[4] Chavan, Arnav, et al. "Faster and Lighter LLMs: A Survey on Current Challenges and Way Forward." arXiv preprint arXiv:2402.01799 (2024).

As pointed out by the reviewer, the proposed framework can not be easily extended to multiple axes of performance. This is specially the case because other measures of performance (e.g. precision, F1-score etc) might not be directly related to the probability of choosing the optimum model ($p(e_i)$ in Equation 6). Additionally, one of the main assumptions in the framework is that the adaptive Oracle is unique. Which is not guaranteed to be the case for general multi-objective adaptive inference scenarios.

However, we can envision two approaches to modify the proposed framework for multi-objective adaptive inference scenarios:

• The simplest approach to incorporating multiple resource axes into the proposed framework is to combine them into a single measure of resource consumption using a custom scoring function. However, this scoring function must be carefully defined to ensure that the bounds on its expected value remain meaningful. For instance, defining $R_i$​ as a weighted linear combination of latency and power consumption ($R_i = w_1 \times {latency}_i + w_2 \times {power}_i$) allows us to leverage the linear properties of Equations 8 and 9 to calculate analogous bounds for a multi-axis adaptation scenario—assuming the conditions in Equations 2 and 3 of the paper still hold.

• A more rigorous approach, however, would involve modifying the Oracle’s strategy to handle more than two optimization axes. The key simplification in the adaptive Oracle’s strategy (as shown in Definition 2.1) rests on the assumption that accuracy always takes priority over efficiency. To extend this to scenarios with multiple optimization objectives, we could introduce intuitive priority rankings among various resource and performance metrics. For example, we might prioritize minimizing latency over reducing average power consumption but rank both of these priorities below maximizing overall accuracy. The main challenge in such a scenario lies in formulating the problem so that the probability of selecting each model ($p(e_i)$) can still be expressed through an intuitive measure like model accuracies. This requires developing a clear mathematical structure that integrates multiple objectives while maintaining interpretability and coherence with the existing framework.

In Appendices A.3 and A.4, we provide general guidelines on selecting $R_i​$ and $A_i$​ values to enhance an agent's performance and efficiency. However, the reviewer raises an interesting question regarding the potential benefits of adjusting $\alpha_i$ to further improve an agent's capabilities.

Referring to the example provided in Q1, we observe that general unrestricted agents such as the policy network trained in AR-Net can potentially achieve better accuracy compared to the hierarchical agents alternatives. By maximizing the complementary behavior of model’s within an adaptation state space one could ensure a smaller $\alpha$ for a specific task. This could be achieved by including the desired $\alpha$ values as an extra optimization criteria during the training phase of the backbone models.

On the other hand, for agents that rely on sequential or hierarchical predictions, like the ones used in RA-Net, it may be advantageous to penalize smaller $\alpha$ values during training. This encourages a more predictable (monotone) state space, which can be crucial for achieving better efficiency in such scenarios.

Thank you for the insightful question. Applying the proposed framework to evaluate and enhance specific agents is indeed a promising next step, which we plan to explore further.

In general the Oracle’s strategy and corresponding bounds could be used to both evaluate an agent, and guide its training to achieve better adaptation results. We envision two potential ways the framework could assist in this task:

• Choosing between hierarchical and unrestricted Agents:

As mentioned in Section1, there are generally two main approaches to designing adaptive agents, one assumes a sequential or hierarchical classification approach (e.g. early existing methods like RA-Net[1]), while other methods rely on independent (unrestricted) policy networks like the one used in AR-Net[2] or general MoE agents as mentioned by the reviewer.

It can be argued that the hierarchical agents are more suitable for state spaces (models) with $\alpha$ closer to 1. This is because they rely on the common assumption that larger (deeper) models are more accurate than smaller(shallower) ones in general. On the other hand the general MoE agents can achieve higher accuracy in case of more diverse agents (corresponding to $\alpha<1$).

As an intuitive example, Figure 4c of the paper shows that for the Pythia family trained on HellaSwag, a hierarchical model could in principle achieve similar performance compared to a general unrestricted agent (due to the small gap between the $\alpha=1$ bounds and the optimistic bound). In contrast, for the efficient-Net family trained on Imagenet (Figure 4a), a more unrestricted agent could be a better choice.

• Using the adaptive Oracle to guide the agent during its training phase:

The proposed framework can also be used to compare an agent with the Oracle and potentially train the agent to mimic an Oracle for a specific task. One such approach is analyzing an agent based on its behavior on samples corresponding to events $e_1$ to $e_N$ as defined in Equation 5. Designing the agent’s loss or reward functions based on the distance between the agent’s operating point and the Oracle’s closest estimated operating point (per batch or per event) allows for guiding the agent toward optimal performance by aligning its behavior with theoretical benchmarks.

As an example, in a simple 2-state scenario with an agent choosing between two models with different sizes, the agent might be consuming too much resources when trying to analyze very difficult or ambiguous tasks (described by $e_2$ in Equation 5 and the quadrant “II” in Figure 1). In such a scenario one can improve the agent’s efficiency by putting more emphasis on similar samples within the training set either by assigning larger weights to corresponding samples in the loss function or by using non-uniform resampling techniques.

While it will be challenging to add a discussion on this topic to the main paper because of space restrictions, we will hint at this research direction as part of the future work and potentially add a relevant example to the Appendix.

References:

[1] Le Yang, Yizeng Han, Xi Chen, Shiji Song, Jifeng Dai, and Gao Huang. Resolution adaptive networks for efficient inference. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 2369–2378, 2020.

[2] Yue Meng, Chung-Ching Lin, Rameswar Panda, Prasanna Sattigeri, Leonid Karlinsky, Aude Oliva, Kate Saenko, and Rogerio Feris. Ar-net: Adaptive frame resolution for efficient action recognition. In Computer Vision–ECCV 2020: 16th European Conference, Glasgow, UK, August 23–28, 2020, Proceedings, Part VII 16, pp. 86–104. Springer, 2020.