Optimal trajectories that minimize a user-defined cost function in dynamic systems require the solution of a two-point boundary value problem. The optimization process yields an optimal control sequence that depends on the initial conditions and system parameters. However, the optimal sequence may result in undesirable behavior if the system's initial conditions and parameters are erroneous. This work presents a data-driven fuzzy controller synthesis framework that is guided by a time-optimal trajectory for multicopter tracking problems. In particular, we consider an aggressive maneuver consisting of a mid-air flip and generate a time-optimal trajectory by numerically solving the two-point boundary value problem. A fuzzy controller consisting of a stabilizing controller near hover conditions and an autoregressive moving average (ARMA) controller, trained to mimic the time-optimal aggressive trajectory, is constructed using the Takagi-Sugeno fuzzy framework.

Seamless operation of mobile robots in challenging environments requires low-latency local motion estimation (e.g., dynamic maneuvers) and accurate global localization (e.g., wayfinding). While most existing sensor-fusion approaches are designed for specific scenarios, this work introduces a flexible open-source solution for task- and setup-agnostic multimodal sensor fusion that is distinguished by its generality and usability. Holistic Fusion formulates sensor fusion as a combined estimation problem of i) the local and global robot state and ii) a (theoretically unlimited) number of dynamic context variables, including automatic alignment of reference frames; this formulation fits countless real-world applications without any conceptual modifications. The proposed factor-graph solution enables the direct fusion of an arbitrary number of absolute, local, and landmark measurements expressed with respect to different reference frames by explicitly including them as states in the optimization and modeling their evolution as random walks. Moreover, local smoothness and consistency receive particular attention to prevent jumps in the robot state belief. HF enables low-latency and smooth online state estimation on typical robot hardware while simultaneously providing low-drift global localization at the IMU measurement rate. The efficacy of this released framework is demonstrated in five real-world scenarios on three robotic platforms, each with distinct task requirements.

This paper explores inference-time data leakage risks of deep neural networks (NNs), where a curious and honest model service provider is interested in retrieving users' private data inputs solely based on the model inference results. Particularly, we revisit residual NNs due to their popularity in computer vision and our hypothesis that residual blocks are a primary cause of data leakage owing to the use of skip connections. By formulating inference-time data leakage as a constrained optimization problem, we propose a novel backward feature inversion method, \textbf{PEEL}, which can effectively recover block-wise input features from the intermediate output of residual NNs. The surprising results in high-quality input data recovery can be explained by the intuition that the output from these residual blocks can be considered as a noisy version of the input and thus the output retains sufficient information for input recovery. We demonstrate the effectiveness of our layer-by-layer feature inversion method on facial image datasets and pre-trained classifiers. Our results show that PEEL outperforms the state-of-the-art recovery methods by an order of magnitude when evaluated by mean squared error (MSE). The code is available at \href{https://github.com/Huzaifa-Arif/PEEL}{https://github.com/Huzaifa-Arif/PEEL}

Machine Unlearning aims to remove undesired information from trained models without requiring full retraining from scratch. Despite recent advancements, their underlying loss landscapes and optimization dynamics received less attention. In this paper, we investigate and analyze machine unlearning through the lens of mode connectivity - the phenomenon where independently trained models can be connected by smooth low-loss paths in the parameter space. We define and study mode connectivity in unlearning across a range of overlooked conditions, including connections between different unlearning methods, models trained with and without curriculum learning, and models optimized with first-order and secondorder techniques. Our findings show distinct patterns of fluctuation of different evaluation metrics along the curve, as well as the mechanistic (dis)similarity between unlearning methods. To the best of our knowledge, this is the first study on mode connectivity in the context of machine unlearning.

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank optimization problems that avoid maintaining high-rank matrices and computing expensive high-rank SVDs, advances for nonsmooth problems have been slow paced. In this paper we consider standard convex relaxations for such problems. Mainly, we prove that under a \textit{strict complementarity} condition and under the relatively mild assumption that the nonsmooth objective can be written as a maximum of smooth functions, approximated variants of two popular \textit{mirror-prox} methods: the Euclidean \textit{extragradient method} and mirror-prox with \textit{matrix exponentiated gradient updates}, when initialized with a "warm-start", converge to an optimal solution with rate $O(1/t)$, while requiring only two \textit{low-rank} SVDs per iteration. Moreover, for the extragradient method we also consider relaxed versions of strict complementarity which yield a trade-off between the rank of the SVDs required and the radius of the ball in which we need to initialize the method. We support our theoretical results with empirical experiments on several nonsmooth low-rank matrix recovery tasks, demonstrating both the plausibility of the strict complementarity assumption, and the efficient convergence of our proposed low-rank mirror-prox variants.

Considerable progress has been made in the recent literature studies to tackle the Algorithms Selection and Parametrization (ASP) problem, which is diversified in multiple meta-learning setups. Yet there is a lack of surveys and comparative evaluations that critically analyze, summarize and assess the performance of existing methods. In this paper, we provide an overview of the state of the art in this continuously evolving field. The survey sheds light on the motivational reasons for pursuing classifiers selection through meta-learning. In this regard, Automated Machine Learning (AutoML) is usually treated as an ASP problem under the umbrella of the democratization of machine learning. Accordingly, AutoML makes machine learning techniques accessible to domain scientists who are interested in applying advanced analytics but lack the required expertise. It can ease the task of manually selecting ML algorithms and tuning related hyperparameters. We comprehensively discuss the different phases of classifiers selection based on a generic framework that is formed as an outcome of reviewing prior works. Subsequently, we propose a benchmark knowledge base of 4 millions previously learned models and present extensive comparative evaluations of the prominent methods for classifiers selection based on 08 classification algorithms and 400 benchmark datasets. The comparative study quantitatively assesses the performance of algorithms selection methods along while emphasizing the strengths and limitations of existing studies.

--Software requirements expressed in natural language (NL) frequently suffer from verbosity, ambiguity, and inconsistency. This creates a range of challenges, including selecting an appropriate architecture for a system and assessing different architectural alternatives. Relying on human expertise to accomplish the task of mapping NL requirements to architecture is time-consuming and error-prone. This paper proposes ARLO, an approach that automates this task by leveraging (1) a set of NL requirements for a system, (2) an existing standard that specifies architecturally relevant software quality attributes, and (3) a readily available Large Language Model (LLM). Specifically, ARLO determines the subset of NL requirements for a given system that is architecturally relevant and maps that subset to a tailorable matrix of architectural choices. ARLO applies integer linear programming on the architectural-choice matrix to determine the optimal architecture for the current requirements. We demonstrate ARLO's efficacy using a set of real-world examples. We highlight ARLO's ability (1) to trace the selected architectural choices to the requirements and (2) to isolate NL requirements that exert a particular influence on a system's architecture. This allows the identification, comparative assessment, and exploration of alternative architectural choices based on the requirements and constraints expressed therein. I NTRODUCTION Software systems are ever-evolving, with increases in size and complexity that call for careful elicitation of requirements and architectural choices [1]. While it has been long recognized that requirements and architecture co-evolve [2], [3], understanding their interactions, especially early in the software development process, is still an open challenge. More specifically, there is a scarcity of knowledge regarding their alignment, architecture-to-requirements traceability, and conserving architectural knowledge [4]. Most software requirements are still captured using natural language (NL) [5]-[7]. The informal nature of NLs is a significant obstacle in machine processing of such requirements [8]. In the past, researchers have proposed approaches to classify the NL requirements into different categories of functional and non-functional requirements [5], [6], to identify quality attributes from NL requirements, to facilitate architectural decisions by leveraging machine learning [7], and so on. While promising, these approaches require large, curated datasets and high model-building effort [9]. Translating NL requirements to architecture-related design decisions is a cumbersome task that has long been recognized in the research community [1].

Addressing the inherent low acquisition frequency limitation of 3D LiDAR to achieve high-frequency output has become a critical research focus in the LiDAR-Inertial Odometry (LIO) domain. To ensure real-time performance, frequency-enhanced LIO systems must process each sweep within significantly reduced timeframe, which presents substantial challenges for deployment on low-computational-power platforms. To address these limitations, we introduce SR-LIO++, an innovative LIO system capable of achieving doubled output frequency relative to input frequency on resource-constrained hardware platforms, including the Raspberry Pi 4B. Our system employs a sweep reconstruction methodology to enhance LiDAR sweep frequency, generating high-frequency reconstructed sweeps. Building upon this foundation, we propose a caching mechanism for intermediate results (i.e., surface parameters) of the most recent segments, effectively minimizing redundant processing of common segments in adjacent reconstructed sweeps. This method decouples processing time from the traditionally linear dependence on reconstructed sweep frequency. Furthermore, we present a quantized map point management based on index table mapping, significantly reducing memory usage by converting global 3D point storage from 64-bit double precision to 8-bit char representation. This method also converts the computationally intensive Euclidean distance calculations in nearest neighbor searches from 64-bit double precision to 16-bit short and 32-bit integer formats, significantly reducing both memory and computational cost. Extensive experimental evaluations across three distinct computing platforms and four public datasets demonstrate that SR-LIO++ maintains state-of-the-art accuracy while substantially enhancing efficiency. Notably, our system successfully achieves 20Hz state output on Raspberry Pi 4B hardware.

Bayesian optimization (BO ) is an effective method for optimizing expensive-to-evaluate black-box functions. While high-dimensional problems can be particularly challenging, due to the multitude of parameter choices and the potentially high number of data points required to fit the model, this limitation can be addressed if the problem satisfies simplifying assumptions. Axis-aligned subspace approaches, where few dimensions have a significant impact on the objective, motivated several algorithms for high-dimensional BO . However, the validity of this assumption is rarely verified, and the assumption is rarely exploited to its full extent. We propose a group testing ( GT) approach to identify active variables to facilitate efficient optimization in these domains. The proposed algorithm, Group Testing Bayesian Optimization (GTBO), first runs a testing phase where groups of variables are systematically selected and tested on whether they influence the objective, then terminates once active dimensions are identified. To that end, we extend the well-established GT theory to functions over continuous domains. In the second phase, GTBO guides optimization by placing more importance on the active dimensions. By leveraging the axis-aligned subspace assumption, GTBO outperforms state-of-the-art methods on benchmarks satisfying the assumption of axis-aligned subspaces, while offering improved interpretability.

Inference-time computation offers a powerful axis for scaling the performance of language models. However, naively increasing computation in techniques like Best-of-N sampling can lead to performance degradation due to reward hacking. Toward a theoretical understanding of how to best leverage additional computation, we focus on inference-time alignment, which we formalize as the problem of improving the quality of responses drawn from a pre-trained policy, given a prompt of interest and access to an imperfect reward model. We analyze the performance of inference-time alignment algorithms in terms of (i) response quality, and (ii) compute, and provide new results that highlight the importance of the pre-trained policy's coverage over high-quality responses for performance and compute scaling: 1. We show that Best-of-$N$ alignment with an ideal choice for $N$ can achieve optimal performance under stringent notions of coverage, but provably suffers from reward hacking when $N$ is large, and fails to achieve tight guarantees under more realistic coverage conditions. 2. We introduce $\texttt{InferenceTimePessimism}$, a new algorithm which mitigates reward hacking through deliberate use of inference-time compute, implementing the principle of pessimism in the face of uncertainty via rejection sampling; we prove that its performance is optimal and does not degrade with $N$, meaning it is scaling-monotonic. We complement our theoretical results with an experimental evaluation that demonstrate the benefits of $\texttt{InferenceTimePessimism}$ across a variety of tasks and models.