Masked Completion via Structured Diffusion with White-Box Transformers (2404.02446v1)

Abstract: Modern learning frameworks often train deep neural networks with massive amounts of unlabeled data to learn representations by solving simple pretext tasks, then use the representations as foundations for downstream tasks. These networks are empirically designed; as such, they are usually not interpretable, their representations are not structured, and their designs are potentially redundant. White-box deep networks, in which each layer explicitly identifies and transforms structures in the data, present a promising alternative. However, existing white-box architectures have only been shown to work at scale in supervised settings with labeled data, such as classification. In this work, we provide the first instantiation of the white-box design paradigm that can be applied to large-scale unsupervised representation learning. We do this by exploiting a fundamental connection between diffusion, compression, and (masked) completion, deriving a deep transformer-like masked autoencoder architecture, called CRATE-MAE, in which the role of each layer is mathematically fully interpretable: they transform the data distribution to and from a structured representation. Extensive empirical evaluations confirm our analytical insights. CRATE-MAE demonstrates highly promising performance on large-scale imagery datasets while using only ~30% of the parameters compared to the standard masked autoencoder with the same model configuration. The representations learned by CRATE-MAE have explicit structure and also contain semantic meaning. Code is available at https://github.com/Ma-Lab-Berkeley/CRATE .

• The paper establishes the equivalence between denoising and compression, introducing a white-box transformer architecture for masked autoencoders.
• It demonstrates that the proposed model, using only 30% of traditional parameters, attains competitive performance on large-scale imagery datasets.
• The findings pave the way for more efficient and semantically rich unsupervised representation learning through structured deep learning approaches.

Exploring the Convergence of Compression and Denoising in Masked Autoencoders with Structured White-Box Transformers

Introduction to Structured Representation Learning

Representation learning, at its core, involves transforming high-dimensional data into a more manageable form while retaining essential information. This is especially crucial in unsupervised learning contexts where we seek to discover underlying structures without explicit labels guiding the process. White-box networks, designed with layers that explicitly encode transformations aimed at identifying and leveraging the data's inherent structure, present a structured and interpretable approach to this challenge.

Unveiling \oursbase{}: A White-Box Paradigm

At the heart of our investigation is the introduction of a white-box transformer-like architecture dubbed \oursbase{}. This model emerges from a novel theoretical insight connecting the principles of denoising diffusion models and data compression. We demonstrate that, under certain conditions, both denoising and compression can be viewed as projection operations onto an assumed low-dimensional structure within the data. This revelation culminates in a transformer architecture where each layer's role in transforming data into a more structured and parsimonious representation becomes mathematically interpretable.

Empirical Validation and Results

Our extensive empirical evaluations substantiate our theoretical insights into \oursbase{}. Specifically, when deployed on large-scale imagery datasets, \oursbase{}, despite its reduced parameter count (approximately 30\% of traditional counterparts), showcases highly competitive performance. Notably, we observe that the learned representations not only adhere to the anticipated structured format but also encapsulate semantic meaning, reinforcing the practical merit of embedding structured compression within deep learning architectures.

Future Directions in Structured Deep Learning

The convergence of compression and denoising through structured diffusion presents a promising avenue for advancing unsupervised representation learning. By establishing the operational equivalence between denoising and compression, we pave the way for developing more efficient, interpretable, and theoretically grounded neural architectures. Looking ahead, we foresee extensions of this work exploring more complex data structures and the integration of supervised learning cues to further refine the representational quality and applicability of structured white-box models.

Conclusion

This work bridges a critical gap in understanding the underlying mechanisms that guide the success of deep learning models in unsupervised representation learning. By drawing a novel connection between compression and denoising, we not only enhance our theoretical understanding but also present a concrete architecture, \oursbase{}, that leverages this insight to achieve structured and interpretable representations. Our findings open new horizons for exploring the synergy between structured data transformations and neural network design, moving towards more efficient and semantically rich representation learning paradigms.