Principal Component Analysis or PCA-like properties (orthogonality, variance ranking) are seldom realized in deep autoencoder architectures. In this work, we present ODIN (Orthogonal Dendritic Intrinsic Network), a novel autoencoder architecture that recovers PCA-like latent structure in a fully non-linear regime. By incorporating a set of geometric constraints directly into the training objective, ODIN encourages latent dimensions to be mutually orthogonal and ordered by explained variance, mirroring the interpretable decomposition of PCA while retaining the expressive power of deep networks. We provide theoretical grounding for these constraints and demonstrate their compatibility with standard encoder-decoder frameworks. We also establish empirical results for both synthetic and real world datasets, establishing a principled path toward interpretable, structured feature learning and dimensionality reduction.
This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation. By formulating neural network training as a continuous-time optimal control problem, we derive rigorous error estimates that quantify how approxima…
Diffusion-based policies have recently emerged as powerful policy parameterizations for reinforcement learning, representing state-conditioned action distributions as terminal laws of diffusion processes with parameterized drifts. This terminal-law representation has shown substa…
This paper develops an Optimality-Informed Neural Network (OINN) approach for the energy-optimal, free-final-time powered descent of a lunar lander from any initial position, velocity, and mass within a bounded operating envelope to a fixed landing site with zero terminal velocit…
Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems. However, RL algorithms are sample inefficient and require a large number of interaction with the environment to synthesize optimal control strate…
Controlling dynamical systems in real-time across multiple scenarios is critical to enabling adaptive control strategies, ensuring stability and efficiency. However, to tailor control actions in response to varying scenarios, traditional optimal control problems typically require…
Modern supply chains span diverse operational environments, ranging from e-commerce distribution networks to customized production-to-order manufacturing lines. Across these settings, operational efficiency depends on coordinating two highly interdependent stages: order preparati…