Tripod: Three Complementary Inductive Biases for Disentangled Representation Learning (2404.10282v2)

Abstract: Inductive biases are crucial in disentangled representation learning for narrowing down an underspecified solution set. In this work, we consider endowing a neural network autoencoder with three select inductive biases from the literature: data compression into a grid-like latent space via quantization, collective independence amongst latents, and minimal functional influence of any latent on how other latents determine data generation. In principle, these inductive biases are deeply complementary: they most directly specify properties of the latent space, encoder, and decoder, respectively. In practice, however, naively combining existing techniques instantiating these inductive biases fails to yield significant benefits. To address this, we propose adaptations to the three techniques that simplify the learning problem, equip key regularization terms with stabilizing invariances, and quash degenerate incentives. The resulting model, Tripod, achieves state-of-the-art results on a suite of four image disentanglement benchmarks. We also verify that Tripod significantly improves upon its naive incarnation and that all three of its "legs" are necessary for best performance.

• The paper introduces Tripod, which synergizes three adapted inductive biases to enhance the disentanglement of latent representations.
• It refines finite scalar latent quantization, kernel-based multiinformation regularization, and normalized Hessian penalty to improve model stability and performance.
• Empirical results across four image tasks demonstrate that combining these biases sets new benchmarks for disentangled representation learning.

Tripod: Enhancing Disentangled Representation Learning through Three Inductive Biases

Introduction

Disentangled representation learning, a critical aspect of unsupervised learning, aims to capture the underlying sources of variation in data into distinct, interpretable components of a learned representation. Despite extensive paper, achieving a level of disentanglement comparable to human perception remains challenging. Grounded in this context, the paper introduces Tripod, a method that integrates three distinct inductive biases within an autoencoder framework to propel disentangled representation learning forward. These biases—finite scalar latent quantization, kernel-based latent multiinformation regularization, and normalized Hessian penalty—target different aspects of the encoding-decoding process, addressing the lack of substantial progress when these biases are applied in isolation. The synergy between these adapted components leads Tripod to set new benchmarks on four notable disentanglement tasks.

Technical Contributions

The paper's primary contributions are methodological adjustments to previously proposed inductive biases that, when synergistically combined, substantively improve disentanglement performance:

• Finite Scalar Latent Quantization (FSLQ): By adopting finite scalar quantization over vector quantization, the method simplifies the optimization landscape, circumventing the need for a traditional codebook learning process. This stabilization is critical for integrating other biases effectively.
• Kernel-Based Latent Multiinformation (KLM): This modification to latent multiinformation regularization utilizes kernel density estimation to ensure compatibility with deterministically encoded latents. Its formulation respects the empirical standard deviation of latent dimensions, thus providing a more stable basis for regularization.
• Normalized Hessian Penalty (NHP): An adaptation of the Hessian penalty, this bias ensures the regularization term is invariant to the scaling of input and output spaces of the decoder function. It strategically promotes independence among latents by penalizing mixed partial derivatives, a novel approach in the context of autoencoders.

Experimental Validation

Empirical benchmarks on four prominent image disentanglement datasets underline Tripod's superiority. With an aggregate performance marked by an InfoMEC score of $(0.78, 0.59, 0.90)$ and a DCI score of $(0.64, 0.57, 0.93)$, Tripod not only surpasses the disentanglement quality of models employing singular biases but also significantly outdoes a naive combination of these inductive biases. Furthermore, ablation studies underscore the necessity of each component for achieving optimal performance, with notable declines in disentanglement metrics upon the removal of any single bias.

Implications and Future Directions

While the advancements presented are notable, the accomplishment of Tripod opens several avenues for future exploration. The sensitivity to quantization levels suggests an opportunity to dynamically adapt or learn optimal compression rates, potentially leveraging disentanglement metrics for guidance. Moreover, the constraints imposed by Tripod's biases—particularly the normalized Hessian penalty—could be further explored across different modalities beyond images, including time series and graph data, to ascertain their general applicability.

The unification achieved by Tripod accentuates the potential residing in re-examining and re-purposing existing disentanglement techniques. It underscores a philosophy that future strides in the field may well emerge from creating cohesion among established ideas rather than the discovery of entirely new inductive biases.

Conclusion

By strategically combining three inductive biases—finely adjusted for harmony within an autoencoding schema—Tripod propels disentangled representation learning to new heights, setting state-of-the-art benchmarks across several tasks. This integrative approach not only demonstrates the critical importance of synergy among biases but also lays a groundwork for future endeavors in enhancing unsupervised disentanglement methodologies.