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Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model nonlinearity but often sacrifice the spectral structure and stability of PCA. We propose emph{Geodesic Tangent Space Aggregation PCA (GTSA-PCA)}, a geometric extension of PCA that integrates curvature awareness and geodesic consistency within a unified spectral framework. Our approach replaces the global covariance operator with curvature-weighted […]

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Hi all, I’m trying to get a research internship at a small research lab. I’m currently doing my undergrad in data science. This is the research guideline document: —————————————————————– 1. [Research direction 1] AI that adapts to a domain Topics: continual learning, memory, test time adaptation, active learning, sample efficiency, efficient training or inference, personalization, curiosity, exploration, agency, autonomy, OOD generalization, curriculum learning, meta-learning, uncertainty modeling Some example questions: What does it mean to “understand” a domain, and […]

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So ICLR is coming and apparently the biggest value one can get from these conferences is to network. Let’s take my example: I’m a PhD student looking for industry internships. Say I have located about 15-20 posters regarding topics adjacent or directly related to my area of research, some of which are by authors from industry labs. I go to the poster, ask the authors about their paper, discuss a bit, perhaps ask some insightful questions and mention […]

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Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove […]

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Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove […]

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