With the growing complexity and capability of contemporary robotic systems, the necessity of sophisticated computing solutions to efficiently handle tasks such as real-time processing, sensor integration, decision-making, and control algorithms is also increasing. Conventional serial computing frequently fails to meet these requirements, underscoring the necessity for high-performance computing alternatives. Parallel computing, the utilization of several processing elements simultaneously to solve computational problems, offers a possible answer. Various parallel computing designs, such as multi-core CPUs, GPUs, FPGAs, and distributed systems, provide substantial enhancements in processing capacity and efficiency. By utilizing these architectures, robotic systems can attain improved performance in functionalities such as real-time image processing, sensor fusion, and path planning. The transformative potential of parallel computing architectures in advancing robotic technology has been underscored, real-life case studies of these architectures in the robotics field have been discussed, and comparisons are presented. Challenges pertaining to these architectures have been explored, and possible solutions have been mentioned for further research and enhancement of the robotic applications.

Caves and lava tubes on the Moon and Mars are sites of geological and astrobiological interest but consist of terrain that is inaccessible with traditional robot locomotion. To support the exploration of these sites, we present ReachBot, a robot that uses extendable booms as appendages to manipulate itself with respect to irregular rock surfaces. The booms terminate in grippers equipped with microspines and provide ReachBot with a large workspace, allowing it to achieve force closure in enclosed spaces such as the walls of a lava tube. To propel ReachBot, we present a contact-before-motion planner for non-gaited legged locomotion that utilizes internal force control, similar to a multi-fingered hand, to keep its long, slender booms in tension. Motion planning also depends on finding and executing secure grips on rock features. We use a Monte Carlo simulation to inform gripper design and predict grasp strength and variability. Additionally, we use a two-step perception system to identify possible grasp locations. To validate our approach and mechanisms under realistic conditions, we deployed a single ReachBot arm and gripper in a lava tube in the Mojave Desert. The field test confirmed that ReachBot will find many targets for secure grasps with the proposed kinematic design.

Large Language Models (LLMs) have significantly advanced various NLP tasks. However, these models often risk generating unsafe text that perpetuates biases. Current approaches to produce unbiased outputs from LLMs can reduce biases but at the expense of knowledge retention. In this research, we address the question of whether producing safe (unbiased) outputs through LLMs can retain knowledge and language understanding. In response, we developed the Safety and Responsible Large Language Model (\textbf{SR}$_{\text{LLM}}$), an LLM that has been instruction fine-tuned on top of already safe LLMs (e.g., Llama2 or related) to diminish biases in generated text. To achieve our goals, we compiled a specialized dataset designed to train our model in identifying and correcting biased text. We conduct experiments, both on this custom data and out-of-distribution test sets, to show the bias reduction and knowledge retention. The results confirm that \textbf{SR}$_{\text{LLM}}$ outperforms traditional fine-tuning and prompting methods in both reducing biases and preserving the integrity of language knowledge. The significance of our findings lies in demonstrating that instruction fine-tuning can provide a more robust solution for bias reduction in LLMs. We have made our code and data available at \href{https://github.com/shainarazavi/Safe-Responsible-LLM}{Safe-LLM}.

Column selection is an essential tool for structure-preserving low-rank approximation, with wide-ranging applications across many fields, such as data science, machine learning, and theoretical chemistry. In this work, we develop unified methodologies for fast, efficient, and theoretically guaranteed column selection. First we derive and implement a sparsity-exploiting deterministic algorithm applicable to tasks including kernel approximation and CUR decomposition. Next, we develop a matrix-free formalism relying on a randomization scheme satisfying guaranteed concentration bounds, applying this construction both to CUR decomposition and to the approximation of matrix functions of graph Laplacians. Importantly, the randomization is only relevant for the computation of the scores that we use for column selection, not the selection itself given these scores. For both deterministic and matrix-free algorithms, we bound the performance favorably relative to the expected performance of determinantal point process (DPP) sampling and, in select scenarios, that of exactly optimal subset selection. The general case requires new analysis of the DPP expectation. Finally, we demonstrate strong real-world performance of our algorithms on a diverse set of example approximation tasks.

The performance of ML models degrades when the training population is different from that seen under operation. Towards assessing distributional robustness, we study the worst-case performance of a model over all subpopulations of a given size, defined with respect to core attributes Z. This notion of robustness can consider arbitrary (continuous) attributes Z, and automatically accounts for complex intersectionality in disadvantaged groups. We develop a scalable yet principled two-stage estimation procedure that can evaluate the robustness of state-of-the-art models. We prove that our procedure enjoys several finite-sample convergence guarantees, including dimension-free convergence. Instead of overly conservative notions based on Rademacher complexities, our evaluation error depends on the dimension of Z only through the out-of-sample error in estimating the performance conditional on Z. On real datasets, we demonstrate that our method certifies the robustness of a model and prevents deployment of unreliable models.

Gradient-based optimization has been critical to the success of machine learning, updating a single set of parameters to minimize a single loss. A growing number of applications rely on a generalization of this, where we have a bilevel or nested optimization of which subsets of parameters update on different objectives nested inside each other. We focus on motivating examples of hyperparameter optimization and generative adversarial networks. However, naively applying classical methods often fails when we look at solving these nested problems on a large scale. In this thesis, we build tools for nested optimization that scale to deep learning setups.

In this paper we describe a new conceptual framework that connects approximate Dynamic Programming (DP), Model Predictive Control (MPC), and Reinforcement Learning (RL). This framework centers around two algorithms, which are designed largely independently of each other and operate in synergy through the powerful mechanism of Newton's method. We call them the off-line training and the on-line play algorithms. The names are borrowed from some of the major successes of RL involving games; primary examples are the recent (2017) AlphaZero program (which plays chess, [SHS17], [SSS17]), and the similarly structured and earlier (1990s) TD-Gammon program (which plays backgammon, [Tes94], [Tes95], [TeG96]). In these game contexts, the off-line training algorithm is the method used to teach the program how to evaluate positions and to generate good moves at any given position, while the on-line play algorithm is the method used to play in real time against human or computer opponents. Significantly, the synergy between off-line training and on-line play also underlies MPC (as well as other major classes of sequential decision problems), and indeed the MPC design architecture is very similar to the one of AlphaZero and TD-Gammon. This conceptual insight provides a vehicle for bridging the cultural gap between RL and MPC, and sheds new light on some fundamental issues in MPC. These include the enhancement of stability properties through rollout, the treatment of uncertainty through the use of certainty equivalence, the resilience of MPC in adaptive control settings that involve changing system parameters, and the insights provided by the superlinear performance bounds implied by Newton's method.

Black-box optimization (BBO) aims to optimize an objective function by iteratively querying a black-box oracle. This process demands sample-efficient optimization due to the high computational cost of function evaluations. While prior studies focus on forward approaches to learn surrogates for the unknown objective function, they struggle with high-dimensional inputs where valid inputs form a small subspace (e.g., valid protein sequences), which is common in real-world tasks. Recently, diffusion models have demonstrated impressive capability in learning the high-dimensional data manifold. They have shown promising performance in black-box optimization tasks but only in offline settings. In this work, we propose diffusion-based inverse modeling for black-box optimization (Diff-BBO), the first inverse approach leveraging diffusion models for online BBO problem. Diff-BBO distinguishes itself from forward approaches through the design of acquisition function. Instead of proposing candidates in the design space, Diff-BBO employs a novel acquisition function Uncertainty-aware Exploration (UaE) to propose objective function values, which leverages the uncertainty of a conditional diffusion model to generate samples in the design space. Theoretically, we prove that using UaE leads to optimal optimization outcomes. Empirically, we redesign experiments on the Design-Bench benchmark for online settings and show that Diff-BBO achieves state-of-the-art performance.

Uncertainty-aware controllers that guarantee safety are critical for safety critical applications. Among such controllers, Control Barrier Functions (CBFs) based approaches are popular because they are fast, yet safe. However, most such works depend on Gaussian Processes (GPs) or MC-Dropout for learning and uncertainty estimation, and both approaches come with drawbacks: GPs are non-parametric methods that are slow, while MC-Dropout does not capture aleatoric uncertainty. On the other hand, modern Bayesian learning algorithms have shown promise in uncertainty quantification. The application of modern Bayesian learning methods to CBF-based controllers has not yet been studied. We aim to fill this gap by surveying uncertainty quantification algorithms and evaluating them on CBF-based safe controllers. We find that model variance-based algorithms (for example, Deep ensembles, MC-dropout, etc.) and direct estimation-based algorithms (such as DEUP) have complementary strengths. Algorithms in the former category can only estimate uncertainty accurately out-of-domain, while those in the latter category can only do so in-domain. We combine the two approaches to obtain more accurate uncertainty estimates both in- and out-of-domain. As measured by the failure rate of a simulated robot, this results in a safer CBF-based robot controller.

We propose a geometry-to-flow diffusion model that utilizes the input of obstacle shape to predict a flow field past the obstacle. The model is based on a learnable Markov transition kernel to recover the data distribution from the Gaussian distribution. The Markov process is conditioned on the obstacle geometry, estimating the noise to be removed at each step, implemented via a U-Net. A cross-attention mechanism incorporates the geometry as a prompt. We train the geometry-to-flow diffusion model using a dataset of flows past simple obstacles, including the circle, ellipse, rectangle, and triangle. For comparison, the CNN model is trained using the same dataset. Tests are carried out on flows past obstacles with simple and complex geometries, representing interpolation and extrapolation on the geometry condition, respectively. In the test set, challenging scenarios include a cross and characters `PKU'. Generated flow fields show that the geometry-to-flow diffusion model is superior to the CNN model in predicting instantaneous flow fields and handling complex geometries. Quantitative analysis of the model accuracy and divergence in the fields demonstrate the high robustness of the diffusion model, indicating that the diffusion model learns physical laws implicitly.