We consider the optimization of cost functionals on infinite dimensional manifolds and derive a variational approach to accelerated methods on manifolds.

We consider the optimization of cost functionals on infinite dimensional manifolds and derive a variational approach to accelerated methods on manifolds.

We present a theory for the construction of out-of-distribution (OOD) detection features for neural networks. We introduce random features for OOD through a novel information-theoretic loss functional consisting of two terms, the first based on the KL divergence separates resulting in-distribution (ID) and OOD feature distributions and the second term is the Information Bottleneck, which favors compressed features that retain the OOD information. We formulate a variational procedure to optimize the loss and obtain OOD features. Based on assumptions on OOD distributions, one can recover properties of existing OOD features, i.e., shaping functions. Furthermore, we show that our theory can predict a new shaping function that out-performs existing ones on OOD benchmarks. Our theory provides a general framework for constructing a variety of new features with clear explainability.

3D situational awareness is critical for any autonomous system. However, when operating underwater, environmental conditions often dictate the use of acoustic sensors. These acoustic sensors are plagued by high noise and a lack of 3D information in sonar imagery, motivating the use of an orthogonal pair of imaging sonars to recover 3D perceptual data. Thus far, mapping systems in this area only use a subset of the available data at discrete timesteps and rely on object-level prior information in the environment to develop high-coverage 3D maps. Moreover, simple repeating objects must be present to build high-coverage maps. In this work, we propose a submap-based mapping system integrated with a simultaneous localization and mapping (SLAM) system to produce dense, 3D maps of complex unknown environments with varying densities of simple repeating objects. We compare this submapping approach to our previous works in this area, analyzing simple and highly complex environments, such as submerged aircraft. We analyze the tradeoffs between a submapping-based approach and our previous work leveraging simple repeating objects. We show where each method is well-motivated and where they fall short. Importantly, our proposed use of submapping achieves an advance in underwater situational awareness with wide aperture multi-beam imaging sonar, moving toward generalized large-scale dense 3D mapping capability for fully unknown complex environments.

The need for scalable and expressive models in machine learning is paramount, particularly in applications requiring both structural depth and flexibility. Traditional deep learning methods, such as multilayer perceptrons (MLP), offer depth but lack ability to integrate structural characteristics of deep learning architectures with non-parametric flexibility of kernel methods. To address this, deep kernel learning (DKL) was introduced, where inputs to a base kernel are transformed using a deep learning architecture. These kernels can replace standard kernels, allowing both expressive power and scalability. The advent of Kolmogorov-Arnold Networks (KAN) has generated considerable attention and discussion among researchers in scientific domain. In this paper, we introduce a scalable deep kernel using KAN (DKL-KAN) as an effective alternative to DKL using MLP (DKL-MLP). Our approach involves simultaneously optimizing these kernel attributes using marginal likelihood within a Gaussian process framework. We analyze two variants of DKL-KAN for a fair comparison with DKL-MLP: one with same number of neurons and layers as DKL-MLP, and another with approximately same number of trainable parameters. To handle large datasets, we use kernel interpolation for scalable structured Gaussian processes (KISS-GP) for low-dimensional inputs and KISS-GP with product kernels for high-dimensional inputs. The efficacy of DKL-KAN is evaluated in terms of computational training time and test prediction accuracy across a wide range of applications. Additionally, the effectiveness of DKL-KAN is also examined in modeling discontinuities and accurately estimating prediction uncertainty. The results indicate that DKL-KAN outperforms DKL-MLP on datasets with a low number of observations. Conversely, DKL-MLP exhibits better scalability and higher test prediction accuracy on datasets with large number of observations.

Utilizing perception for feedback control in combination with Dynamic Movement Primitive (DMP)-based motion generation for a robot's end-effector control is a useful solution for many robotic manufacturing tasks. For instance, while performing an insertion task when the hole or the recipient part is not visible in the eye-in-hand camera, a learning-based movement primitive method can be used to generate the end-effector path. Once the recipient part is in the field of view (FOV), Image-based Visual Servo (IBVS) can be used to control the motion of the robot. Inspired by such applications, this paper presents a generalized control scheme that switches between motion generation using DMPs and IBVS control. To facilitate the design, a common state space representation for the DMP and the IBVS systems is first established. Stability analysis of the switched system using multiple Lyapunov functions shows that the state trajectories converge to a bound asymptotically. The developed method is validated by two real world experiments using the eye-in-hand configuration on a Baxter research robot.

We survey the landscape of human operator modeling ranging from the early cognitive models developed in artificial intelligence to more recent formal task models developed for model-checking of human machine interactions. We review human performance modeling and human factors studies in the context of aviation, and models of how the pilot interacts with automation in the cockpit. The purpose of the survey is to assess the applicability of available state-of-the-art models of the human operators for the design, verification and validation of future safety-critical aviation systems that exhibit higher-level of autonomy, but still require human operators in the loop. These systems include the single-pilot aircraft and NextGen air traffic management. We discuss the gaps in existing models and propose future research to address them.

We discover restrained numerical instabilities in current training practices of deep networks with stochastic gradient descent (SGD). We show numerical error (on the order of the smallest floating point bit) induced from floating point arithmetic in training deep nets can be amplified significantly and result in significant test accuracy variance, comparable to the test accuracy variance due to stochasticity in SGD. We show how this is likely traced to instabilities of the optimization dynamics that are restrained, i.e., localized over iterations and regions of the weight tensor space. We do this by presenting a theoretical framework using numerical analysis of partial differential equations (PDE), and analyzing the gradient descent PDE of convolutional neural networks (CNNs). We show that it is stable only under certain conditions on the learning rate and weight decay. We show that rather than blowing up when the conditions are violated, the instability can be restrained. We show this is a consequence of the non-linear PDE associated with the gradient descent of the CNN, whose local linearization changes when over-driving the step size of the discretization, resulting in a stabilizing effect. We link restrained instabilities to the recently discovered Edge of Stability (EoS) phenomena, in which the stable step size predicted by classical theory is exceeded while continuing to optimize the loss and still converging. Because restrained instabilities occur at the EoS, our theory provides new predictions about the EoS, in particular, the role of regularization and the dependence on the network complexity.

In this paper we explore the application of simultaneous move Monte Carlo Tree Search (MCTS) based online framework for tactical maneuvering between two unmanned aircrafts. Compared to other techniques, MCTS enables efficient search over long horizons and uses self-play to select best maneuver in the current state while accounting for the opponent aircraft tactics. We explore different algorithmic choices in MCTS and demonstrate the framework numerically in a simulated 2D tactical maneuvering application.

Given a Boolean formula $\phi(x)$ in conjunctive normal form (CNF), the density of states counts the number of variable assignments that violate exactly $e$ clauses, for all values of $e$. Thus, the density of states is a histogram of the number of unsatisfied clauses over all possible assignments. This computation generalizes both maximum-satisfiability (MAX-SAT) and model counting problems and not only provides insight into the entire solution space, but also yields a measure for the \emph{hardness} of the problem instance. Consequently, in real-world scenarios, this problem is typically infeasible even when using state-of-the-art algorithms. While finding an exact answer to this problem is a computationally intensive task, we propose a novel approach for estimating density of states based on the concentration of measure inequalities. The methodology results in a quadratic unconstrained binary optimization (QUBO), which is particularly amenable to quantum annealing-based solutions. We present the overall approach and compare results from the D-Wave quantum annealer against the best-known classical algorithms such as the Hamze-de Freitas-Selby (HFS) algorithm and satisfiability modulo theory (SMT) solvers.