Natural gradient (NG) is an information-geometric optimization method that plays a crucial role, especially in the estimation of parameters for machine learning models like neural networks. To apply NG to quantum systems, the quantum natural gradient (QNG) was introduced and utilized for noisy intermediate-scale devices. Additionally, a mathematically equivalent approach to QNG, known as the stochastic reconfiguration method, has been implemented to enhance the performance of quantum Monte Carlo methods. It is worth noting that these methods are based on the symmetric logarithmic derivative (SLD) metric, which is one of the monotone metrics. So far, monotonicity has been believed to be a guiding principle to construct a geometry in physics. In this paper, we propose generalized QNG by removing the condition of monotonicity. Initially, we demonstrate that monotonicity is a crucial condition for conventional QNG to be optimal. Subsequently, we provide analytical and numerical evidence showing that non-monotone QNG outperforms conventional QNG based on the SLD metric in terms of convergence speed.

This paper introduces a novel domain adaptation technique for time series data, called Mixing model Stiefel Adaptation (MSA), specifically addressing the challenge of limited labeled signals in the target dataset. Leveraging a domain-dependent mixing model and the optimal transport domain adaptation assumption, we exploit abundant unlabeled data in the target domain to ensure effective prediction by establishing pairwise correspondence with equivalent signal variances between domains. Theoretical foundations are laid for identifying crucial Stiefel matrices, essential for recovering underlying signal variances from a Riemannian representation of observed signal covariances. We propose an integrated cost function that simultaneously learns these matrices, pairwise domain relationships, and a predictor, classifier, or regressor, depending on the task. Applied to neuroscience problems, MSA outperforms recent methods in brain-age regression with task variations using magnetoencephalography (MEG) signals from the Cam-CAN dataset.

Feature visualization, also known as "dreaming", offers insights into vision models by optimizing the inputs to maximize a neuron's activation or other internal component. However, dreaming has not been successfully applied to language models because the input space is discrete. We extend Greedy Coordinate Gradient, a method from the language model adversarial attack literature, to design the Evolutionary Prompt Optimization (EPO) algorithm. EPO optimizes the input prompt to simultaneously maximize the Pareto frontier between a chosen internal feature and prompt fluency, enabling fluent dreaming for language models. We demonstrate dreaming with neurons, output logits and arbitrary directions in activation space. We measure the fluency of the resulting prompts and compare language model dreaming with max-activating dataset examples. Critically, fluent dreaming allows automatically exploring the behavior of model internals in reaction to mildly out-of-distribution prompts. Code for running EPO is available at https://github.com/Confirm-Solutions/dreamy. A companion page demonstrating code usage is at https://confirmlabs.org/posts/dreamy.html

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through pairwise regularization, where each pair of views is encouraged to have similar structures. However, this approach cannot infer the shared structure across views. In this work, we propose an alternative method based on consensus regularization, where views are ensured to be similar through a learned consensus graph representing the common structure of the views. In particular, we propose an optimization problem, where graph data is assumed to be smooth over the multiview graph and the topology of the individual views and that of the consensus graph are learned, simultaneously. Our optimization problem is designed to be general in the sense that different regularization functions can be used depending on what the shared structure across views is. Moreover, we propose two regularization functions that extend fused and group graphical lasso to consensus based regularization. Proposed multiview graph learning is evaluated on simulated data and shown to have better performance than existing methods. It is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings. The proposed method reveals the structure shared by subjects as well as the characteristics unique to each subject.

In robotic systems, perception latency is a term that refers to the computing time measured from the data acquisition to the moment in which perception output is ready to be used to compute control commands. There is a compromise between perception latency, precision for the overall robotic system, and computational resource usage referred to here as the latency-precision trade-off. In this work, we analyze a robot model given by a linear system, a zero-order hold controller, and measurements taken by several perception mode possibilities with different noise levels. We show that the analysis of this system is reduced to studying an equivalent switching system. Our goal is to schedule perception modes such that stability is attained while optimizing a cost function that models the latency-precision trade-off. Our solution framework comprises three main tools: the construction of perception scheduling policy candidates, admissibility verification for policy candidates, and optimal strategies based on admissible policies.

In industry, Bayesian optimization (BO) is widely applied in the human-AI collaborative parameter tuning of cyber-physical systems. However, BO's solutions may deviate from human experts' actual goal due to approximation errors and simplified objectives, requiring subsequent tuning. The black-box nature of BO limits the collaborative tuning process because the expert does not trust the BO recommendations. Current explainable AI (XAI) methods are not tailored for optimization and thus fall short of addressing this gap. To bridge this gap, we propose TNTRules (TUNE-NOTUNE Rules), a post-hoc, rule-based explainability method that produces high quality explanations through multiobjective optimization. Our evaluation of benchmark optimization problems and real-world hyperparameter optimization tasks demonstrates TNTRules' superiority over state-of-the-art XAI methods in generating high quality explanations. This work contributes to the intersection of BO and XAI, providing interpretable optimization techniques for real-world applications.

We investigate the application of the factor graph framework for blind joint channel estimation and symbol detection on time-variant linear inter-symbol interference channels. In particular, we consider the expectation maximization (EM) algorithm for maximum likelihood estimation, which typically suffers from high complexity as it requires the computation of the symbol-wise posterior distributions in every iteration. We address this issue by efficiently approximating the posteriors using the belief propagation (BP) algorithm on a suitable factor graph. By interweaving the iterations of BP and EM, the detection complexity can be further reduced to a single BP iteration per EM step. In addition, we propose a data-driven version of our algorithm that introduces momentum in the BP updates and learns a suitable EM parameter update schedule, thereby significantly improving the performance-complexity tradeoff with a few offline training samples. Our numerical experiments demonstrate the excellent performance of the proposed blind detector and show that it even outperforms coherent BP detection in high signal-to-noise scenarios.

In this study, we introduce an optimization framework aimed at enhancing the efficiency of motion priority design in scenarios involving automated and teleoperated robots within an industrial recovery context. The escalating utilization of industrial robots at manufacturing sites has been instrumental in mitigating human workload. Nevertheless, the challenge persists in achieving effective human-robot collaboration/cooperation where human workers and robots share a workspace for collaborative tasks. In the event of an industrial robot encountering a failure, it necessitates the suspension of the corresponding factory cell for safe recovery. Given the limited capacity of pre-programmed robots to rectify such failures, human intervention becomes imperative, requiring entry into the robot workspace to address the dropped object while the robot system is halted. This non-continuous manufacturing process results in productivity loss. Robotic teleoperation has emerged as a promising technology enabling human workers to undertake high-risk tasks remotely and safely. Our study advocates for the incorporation of robotic teleoperation in the recovery process during manufacturing failure scenarios, which is referred to as "Cooperative Tele-Recovery". Our proposed approach involves the formulation of priority rules designed to facilitate collision avoidance between manufacturing and recovery robots. This, in turn, ensures a continuous manufacturing process with minimal production loss within a configurable risk limitation. We present a comprehensive motion priority optimization framework, encompassing an HRC simulator-based priority optimization and a cooperative multi-robot controller, to identify optimal parameters for the priority function. The framework dynamically adjusts the allocation of motion priorities for manufacturing and recovery robots while adhering to predefined risk limitations.

Federated Learning (FL), a distributed learning paradigm that scales on-device learning collaboratively, has emerged as a promising approach for decentralized AI applications. Local optimization methods such as Federated Averaging (FedAvg) are the most prominent methods for FL applications. Despite their simplicity and popularity, the theoretical understanding of local optimization methods is far from clear. This dissertation aims to advance the theoretical foundation of local methods in the following three directions. First, we establish sharp bounds for FedAvg, the most popular algorithm in Federated Learning. We demonstrate how FedAvg may suffer from a notion we call iterate bias, and how an additional third-order smoothness assumption may mitigate this effect and lead to better convergence rates. We explain this phenomenon from a Stochastic Differential Equation (SDE) perspective. Second, we propose Federated Accelerated Stochastic Gradient Descent (FedAc), the first principled acceleration of FedAvg, which provably improves the convergence rate and communication efficiency. Our technique uses on a potential-based perturbed iterate analysis, a novel stability analysis of generalized accelerated SGD, and a strategic tradeoff between acceleration and stability. Third, we study the Federated Composite Optimization problem, which extends the classic smooth setting by incorporating a shared non-smooth regularizer. We show that direct extensions of FedAvg may suffer from the "curse of primal averaging," resulting in slow convergence. As a solution, we propose a new primal-dual algorithm, Federated Dual Averaging, which overcomes the curse of primal averaging by employing a novel inter-client dual averaging procedure.

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method outperforms state-of-the-art neural inverse design method by an average of 41.5% in prediction MAE and 14.3% in design objective for the N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.