My Academic Works

In this thesis, we develop a class of physically interpretable deep learning frameworks based on the Ising model on a Bethe lattice. The hierarchical structure of the tree allows us to formulate both discriminative and generative learning tasks in terms of a holographic renormalization group (HRG) flow.

We first construct a binary classifier on the Bethe lattice for supervised learning. In this setting, inference is naturally interpreted as an HRG flow of external fields from the boundary toward the central bulk. We demonstrate that this procedure yields a strong, nearly exponential suppression of input noise, driving robust phase separation between different classes of data to enable effective classification. Furthermore, by incorporating the Potts model, we generalize the architecture to achieve multi-class classification.

We then extend this framework to a generative architecture inspired by deep Boltzmann machines. Training is implemented through the HRG transformation, providing an efficient and analytically transparent alternative to standard optimization methods. Furthermore, we formulate the inference (or energy minimization) procedure via an HRG-informed effective field scheme that accounts for spin fluctuations to all orders, departing from standard stochastic mean-field approximations, to achieve stable multi-modal generation across distinct data classes. Extending this construction to Potts degrees of freedom further amplifies the expressive capacity of the model.

Finally, we construct an interpretable Holographic Autoencoder that unifies the discriminative and generative frameworks, elucidating how latent feature representations and inference trajectories are governed by explicit HRG flows. We show that distinct data classes naturally manifest as well-separated phases within the 2D latent feature space.

Overall, this work establishes the Bethe lattice as a physically motivated, analytically tractable platform for building interpretable deep learning models, where representation, learning, and generation are systematically unified through real-space renormalization group flows.