This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a friendly introduction to applied and computational sheaf theory accessible to those with modest mathematical familiarity. We describe intuitions and motivations underlying sheaf theory shared by both theoretical researchers and practitioners, bridging classical mathematical theory and its more recent implementations within signal processing and deep learning. We observe that most notions commonly considered specific to cellular sheaves translate to sheaves on arbitrary posets, providing an interesting avenue for further generalization of these methods in applications, and we present a new algorithm to compute sheaf cohomology on arbitrary finite posets in response. By integrating classical theory with recent applications, this work reveals certain blind spots in current machine learning practices. We conclude with a list of problems related to sheaf-theoretic applications that we find mathematically insightful and practically instructive to solve. To ensure the exposition of sheaf theory is self-contained, a rigorous mathematical introduction is provided in appendices which moves from an introduction of diagrams and sheaves to the definition of derived functors, higher order cohomology, sheaf Laplacians, sheaf diffusion, and interconnections of these subjects therein.2020

-- Humanoid robots have great potential for real-world applications due to their ability to operate in environments built for humans, but their deployment is hindered by the challenge of controlling their underlying high-dimensional nonlinear hybrid dynamics. While reduced-order models like the Hybrid Linear Inverted Pendulum (HLIP) are simple and computationally efficient, they lose whole-body expressiveness. Meanwhile, recent advances in Contact-Implicit Model Predictive Control (CI-MPC) enable robots to plan through multiple hybrid contact modes, but remain vulnerable to local minima and require significant tuning. We propose a control framework that combines the strengths of HLIP and CI-MPC. The reduced-order model generates a nominal gait, while CI-MPC manages the whole-body dynamics and modifies the contact schedule as needed. We demonstrate the effectiveness of this approach in simulation with a novel 24 degree-of-freedom humanoid robot: Achilles. Our proposed framework achieves rough terrain walking, disturbance recovery, robustness under model and state uncertainty, and allows the robot to interact with obstacles in the environment, all while running online in real-time at 50 Hz. Humanoid robots, due to their anthropomorphic structure, are well suited to perform tasks in environments built for humans.

Inverse design in science and engineering involves determining optimal design parameters that achieve desired performance outcomes, a process often hindered by the complexity and high dimensionality of design spaces, leading to significant computational costs. To tackle this challenge, we propose a novel hybrid approach that combines active learning with Tandem Neural Networks to enhance the efficiency and effectiveness of solving inverse design problems. Active learning allows to selectively sample the most informative data points, reducing the required dataset size without compromising accuracy. We investigate this approach using three benchmark problems: airfoil inverse design, photonic surface inverse design, and scalar boundary condition reconstruction in diffusion partial differential equations. We demonstrate that integrating active learning with Tandem Neural Networks outperforms standard approaches across the benchmark suite, achieving better accuracy with fewer training samples.

Land degradation and air pollution are primarily caused by the salinization of soil and desertification that occurs from the drying of salinity lakes and the release of dust into the atmosphere because of their dried bottom. The complete drying up of a lake has caused a community environmental catastrophe. In this study, we presented an optimization problem to determine the total surface runoff to maintain the level of salinity lake (Urmia Lake). The proposed process has two key stages: identifying the influential factors in determining the lake water level using sensitivity analysis approaches based upon historical data and optimizing the effective variable to stabilize the lake water level under changing design variables. Based upon the Sobol'-Jansen and Morris techniques, the groundwater level and total surface runoff flow are highly effective with nonlinear and interacting impacts of the lake water level. As a result of the sensitivity analysis, we found that it may be possible to effectively manage lake levels by adjusting total surface runoff. We used genetic algorithms, non-linear optimization, and pattern search techniques to solve the optimization problem. Furthermore, the lake level constraint is established based on a pattern as a constant number every month. In order to maintain a consistent pattern of lake levels, it is necessary to increase surface runoff by approximately 8.7 times during filling season. It is necessary to increase this quantity by 33.5 times during the draining season. In the future, the results may serve as a guide for the rehabilitation of the lake.

We introduce the Contrastive Similarity Space Embedding Algorithm (ContraSim), a novel framework for uncovering the global semantic relationships between daily financial headlines and market movements. ContraSim operates in two key stages: (I) Weighted Headline Augmentation, which generates augmented financial headlines along with a semantic fine-grained similarity score, and (II) Weighted Self-Supervised Contrastive Learning (WSSCL), an extended version of classical self-supervised contrastive learning that uses the similarity metric to create a refined weighted embedding space. This embedding space clusters semantically similar headlines together, facilitating deeper market insights. Empirical results demonstrate that integrating ContraSim features into financial forecasting tasks improves classification accuracy from WSJ headlines by 7%. Moreover, leveraging an information density analysis, we find that the similarity spaces constructed by ContraSim intrinsically cluster days with homogeneous market movement directions, indicating that ContraSim captures market dynamics independent of ground truth labels. Additionally, ContraSim enables the identification of historical news days that closely resemble the headlines of the current day, providing analysts with actionable insights to predict market trends by referencing analogous past events.

Modern deep reinforcement learning (DRL) methods have made significant advances in handling continuous action spaces. However, real-world control systems--especially those requiring precise and reliable performance--often demand formal stability, and existing DRL approaches typically lack explicit mechanisms to ensure or analyze stability. To address this limitation, we propose SALSA-RL (Stability Analysis in the Latent Space of Actions), a novel RL framework that models control actions as dynamic, time-dependent variables evolving within a latent space. By employing a pre-trained encoder-decoder and a state-dependent linear system, our approach enables both stability analysis and interpretability. We demonstrated that SALSA-RL can be deployed in a non-invasive manner for assessing the local stability of actions from pretrained RL agents without compromising on performance across diverse benchmark environments. By enabling a more interpretable analysis of action generation, SALSA-RL provides a powerful tool for advancing the design, analysis, and theoretical understanding of RL systems.

Despite increasing discussions on open-source Artificial Intelligence (AI), existing research lacks a discussion on the transparency and accessibility of state-of-the-art (SoTA) Large Language Models (LLMs). The Open Source Initiative (OSI) has recently released its first formal definition of open-source software. This definition, when combined with standard dictionary definitions and the sparse published literature, provide an initial framework to support broader accessibility to AI models such as LLMs, but more work is essential to capture the unique dynamics of openness in AI. In addition, concerns about open-washing, where models claim openness but lack full transparency, has been raised, which limits the reproducibility, bias mitigation, and domain adaptation of these models. In this context, our study critically analyzes SoTA LLMs from the last five years, including ChatGPT, DeepSeek, LLaMA, and others, to assess their adherence to transparency standards and the implications of partial openness. Specifically, we examine transparency and accessibility from two perspectives: open-source vs. open-weight models. Our findings reveal that while some models are labeled as open-source, this does not necessarily mean they are fully open-sourced. Even in the best cases, open-source models often do not report model training data, and code as well as key metrics, such as weight accessibility, and carbon emissions. To the best of our knowledge, this is the first study that systematically examines the transparency and accessibility of over 100 different SoTA LLMs through the dual lens of open-source and open-weight models. The findings open avenues for further research and call for responsible and sustainable AI practices to ensure greater transparency, accountability, and ethical deployment of these models.(DeepSeek transparency, ChatGPT accessibility, open source, DeepSeek open source)

In this era of AI revolution, massive investments in large-scale data-driven AI systems demand high-performance computing, consuming tremendous energy and resources. This trend raises new challenges in optimizing sustainability without sacrificing scalability or performance. Among the energy-efficient alternatives of the traditional Von Neumann architecture, neuromorphic computing and its Spiking Neural Networks (SNNs) are a promising choice due to their inherent energy efficiency. However, in some real-world application scenarios such as complex continuous control tasks, SNNs often lack the performance optimizations that traditional artificial neural networks have. Researchers have addressed this by combining SNNs with Deep Reinforcement Learning (DeepRL), yet scalability remains unexplored. In this paper, we extend our previous work on SpikeRL, which is a scalable and energy efficient framework for DeepRL-based SNNs for continuous control. In our initial implementation of SpikeRL framework, we depended on the population encoding from the Population-coded Spiking Actor Network (PopSAN) method for our SNN model and implemented distributed training with Message Passing Interface (MPI) through mpi4py. Also, further optimizing our model training by using mixed-precision for parameter updates. In our new SpikeRL framework, we have implemented our own DeepRL-SNN component with population encoding, and distributed training with PyTorch Distributed package with NCCL backend while still optimizing with mixed precision training. Our new SpikeRL implementation is 4.26X faster and 2.25X more energy efficient than state-of-the-art DeepRL-SNN methods. Our proposed SpikeRL framework demonstrates a truly scalable and sustainable solution for complex continuous control tasks in real-world applications.

Non-terrestrial networks (NTNs) are essential for ubiquitous connectivity, providing coverage in remote and underserved areas. However, since NTNs are currently operated independently, they face challenges such as isolation, limited scalability, and high operational costs. Integrating satellite constellations with terrestrial networks offers a way to address these limitations while enabling adaptive and cost-efficient connectivity through the application of Artificial Intelligence (AI) models. This paper introduces Space-O-RAN, a framework that extends Open Radio Access Network (RAN) principles to NTNs. It employs hierarchical closed-loop control with distributed Space RAN Intelligent Controllers (Space-RICs) to dynamically manage and optimize operations across both domains. To enable adaptive resource allocation and network orchestration, the proposed architecture integrates real-time satellite optimization and control with AI-driven management and digital twin (DT) modeling. It incorporates distributed Space Applications (sApps) and dApps to ensure robust performance in in highly dynamic orbital environments. A core feature is dynamic link-interface mapping, which allows network functions to adapt to specific application requirements and changing link conditions using all physical links on the satellite. Simulation results evaluate its feasibility by analyzing latency constraints across different NTN link types, demonstrating that intra-cluster coordination operates within viable signaling delay bounds, while offloading non-real-time tasks to ground infrastructure enhances scalability toward sixth-generation (6G) networks.

Reinforcement learning (RL) algorithms have been successfully applied to control tasks associated with unmanned aerial vehicles and robotics. In recent years, safe RL has been proposed to allow the safe execution of RL algorithms in industrial and mission-critical systems that operate in closed loops. However, if the system operating conditions change, such as when an unknown fault occurs in the system, typical safe RL algorithms are unable to adapt while retaining past knowledge. Continual reinforcement learning algorithms have been proposed to address this issue. However, the impact of continual adaptation on the system's safety is an understudied problem. In this paper, we study the intersection of safe and continual RL. First, we empirically demonstrate that a popular continual RL algorithm, online elastic weight consolidation, is unable to satisfy safety constraints in non-linear systems subject to varying operating conditions. Specifically, we study the MuJoCo HalfCheetah and Ant environments with velocity constraints and sudden joint loss non-stationarity. Then, we show that an agent trained using constrained policy optimization, a safe RL algorithm, experiences catastrophic forgetting in continual learning settings. With this in mind, we explore a simple reward-shaping method to ensure that elastic weight consolidation prioritizes remembering both safety and task performance for safety-constrained, non-linear, and non-stationary dynamical systems.