Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKA (2411.00259v1)

Abstract: Particle-based Bayesian deep learning often requires a similarity metric to compare two networks. However, naive similarity metrics lack permutation invariance and are inappropriate for comparing networks. Centered Kernel Alignment (CKA) on feature kernels has been proposed to compare deep networks but has not been used as an optimization objective in Bayesian deep learning. In this paper, we explore the use of CKA in Bayesian deep learning to generate diverse ensembles and hypernetworks that output a network posterior. Noting that CKA projects kernels onto a unit hypersphere and that directly optimizing the CKA objective leads to diminishing gradients when two networks are very similar. We propose adopting the approach of hyperspherical energy (HE) on top of CKA kernels to address this drawback and improve training stability. Additionally, by leveraging CKA-based feature kernels, we derive feature repulsive terms applied to synthetically generated outlier examples. Experiments on both diverse ensembles and hypernetworks show that our approach significantly outperforms baselines in terms of uncertainty quantification in both synthetic and realistic outlier detection tasks.

• The paper introduces the integration of CKA as an optimization objective in Bayesian deep learning to enhance model diversity.
• It proposes hyperspherical energy minimization to uniformly distribute network kernels, improving both training stability and uncertainty quantification.
• Empirical results demonstrate significant performance gains in outlier detection and uncertainty estimation compared to traditional baseline methods.

Exploring Diversity in Bayesian Deep Learning: A Hyperspherical Approach

The exploration of diversity in Bayesian deep learning remains an important concern, due in part to the inherently stochastic nature of these models. This paper addresses the limitations of naive similarity metrics when comparing neural networks, emphasizing the necessity for permutation-invariant approaches that can better represent network function diversity. Central to the proposed methodology is the employment of Centered Kernel Alignment (CKA), a well-established means of assessing similarity, to efficiently generate diverse networks. By introducing the concept of hyperspherical energy minimization on top of CKA kernels, the paper provides a novel optimization approach that seeks to enhance training stability and improve uncertainty estimation.

Summary of Contributions

1. Incorporation of CKA in Bayesian Learning: The paper introduces the novel use of CKA as an optimization objective within particle-based Bayesian deep learning. CKA offers a promising alternative as it compares networks by evaluating kernel matrices of feature outputs, thereby addressing challenges related to permutation invariance.
2. Hyperspherical Energy Minimization: Recognizing CKA's tendency toward diminishing gradients when networks are too similar, the authors propose an adaptation through hyperspherical energy minimization. This approach uniformly distributes network kernels on the hypersphere, fostering diverse representations.
3. Repulsive Feature Loss Construction: Beyond CKA-based regularization, the paper extends the repulsive feature loss concept to include synthetic outlier examples. This elegant mechanism leverages feature repulsive terms to enhance outlier detection capabilities.
4. Experimental Validation: Empirical evidence from experiments involving diverse ensembles and hypernetworks demonstrates that the proposed approach successfully improves uncertainty quantification in both controlled and realistic settings.

Key Numerical Results

The paper reports strong performance in uncertainty estimation tasks, showcasing significant improvements over baseline methods. Notably, methods utilizing hyperspherical energy minimization achieved high AUROC scores in outlier detection tasks, dramatically outperforming traditional approaches and alternative ParVI-based models.

Implications and Future Directions

The proposed methodology offers a viable solution to the challenge of generating diverse neural networks in Bayesian deep learning. By ensuring varied exploration of parameter space, the approach helps avoid overconfident predictions, which is critical in many applications such as active learning and reinforcement learning.

The hyperspherical diversification approach might also be seen as a guiding principle for future research, potentially extending beyond Bayesian frameworks to improve diversity in other ensemble-based learning paradigms. Given the diversity-promoting nature of the technique, future work could fortify the presented approach by integrating adaptive layer-weighting schemes or broader kernel choices.

Moreover, by reducing overfit through diversity, this integration could yield novel avenues in areas such as domain adaptation and adversarial robustness. Researchers may also explore automating the hyperparameter tuning process involved in deploying the hyperspherical energy strategy, further simplifying its adoption in large-scale systems.

Conclusion

The paper represents a thoughtful integration of machine learning metrics and optimization techniques, casting light on the utility of CKA and hyperspherical optimization for enhancing model diversity. The nuanced exploration of hyperspherical energy minimization presents researchers with a valuable toolkit for elevating model diversity and advancing the predictive reliability of Bayesian deep learning approaches. As such, it contributes constructively to ongoing efforts to refine network comparison methodologies and deepen the resilience of machine learning systems against uncertainty.