We address the computational and theoretical limitations of current distributional alignment methods for source-free unsupervised domain adaptation (SFUDA). In particular, we focus on estimating classification performance and confidence in the absence of target labels. Current theoretical frameworks for these methods often yield computationally intractable quantities and fail to adequately reflect the properties of the alignment algorithms employed. To overcome these challenges, we introduce the Optimal Transport (OT) score, a confidence metric derived from a novel theoretical analysis that exploits the flexibility of decision boundaries induced by Semi-Discrete Optimal Transport alignment. The proposed OT score is intuitively interpretable and theoretically rigorous. It provides principled uncertainty estimates for any given set of target pseudo-labels. Experimental results demonstrate that OT score outperforms existing confidence scores. Moreover, it improves SFUDA performance through training-time reweighting and provides a reliable, label-free proxy for model performance.

We propose a test-time defense mechanism against adversarial attacks: imperceptible image perturbations that significantly alter the predictions of a model. Unlike existing methods that rely on feature filtering or smoothing, which can lead to information loss, we propose to "combat noise with noise" by leveraging stochastic resonance to enhance robustness while minimizing information loss. Our approach introduces small translational perturbations to the input image, aligns the transformed feature embeddings, and aggregates them before mapping back to the original reference image. This can be expressed in a closed-form formula, which can be deployed on diverse existing network architectures without introducing additional network modules or fine-tuning for specific attack types. The resulting method is entirely training-free, architecture-agnostic, and attack-agnostic. Empirical results show state-of-the-art robustness on image classification and, for the first time, establish a generic test-time defense for dense prediction tasks, including stereo matching and optical flow, highlighting the method's versatility and practicality. Specifically, relative to clean (unperturbed) performance, our method recovers up to 68.1% of the accuracy loss on image classification, 71.9% on stereo matching, and 29.2% on optical flow under various types of adversarial attacks. Most deep neural networks in use today are deterministic maps from a fixed-size input to a fixed-size feature vector. In either case, the output vector is often highly sensitive to perturbations of the input, and one can intentionally choose these imperceptible perturbations adversarially so as to maximize the change in the output Goodfellow et al. (2014). In some cases, the same perturbation can even be disruptive for a large number of possible inputs Moosavi-Dezfooli et al. (2017), exploiting the convoluted geometry of the decision boundary imposed by such trained models Tram ` er et al. (2017). This spurious sensitivity could be exploited adversarially to disrupt the operation of a model.

Accurate estimation of rating of perceived exertion (RPE) can enhance resistance training through personalized feedback and injury prevention. This study investigates the application of machine learning models to estimate RPE during single-arm dumbbell bicep curls, using data from wearable inertial and electromyography (EMG) sensors. A custom dataset of 69 sets and over 1000 repetitions was collected, with statistical features extracted for model training. Among the models evaluated, a random forest classifier achieved the highest performance, with 41.4% exact accuracy and 85.9% $\pm1$ RPE accuracy. While the inclusion of EMG data slightly improved model accuracy over inertial sensors alone, its utility may have been limited by factors such as data quality and placement sensitivity. Feature analysis highlighted eccentric repetition time as the strongest RPE predictor. The results demonstrate the feasibility of wearable-sensor-based RPE estimation and identify key challenges for improving model generalizability.

This paper uses classical high-rate quantization theory to provide new insights into mixture-of-experts (MoE) models for regression tasks. Our MoE is defined by a segmentation of the input space to regions, each with a single-parameter expert that acts as a constant predictor with zero-compute at inference. Motivated by high-rate quantization theory a ssumptions, we assume that the number of experts is sufficiently large to make their input-space re gions very small. This lets us to study the approximation error of our MoE model class: (i) for one-dime nsional inputs, we formulate the test error and its minimizing segmentation and experts; (ii) for multidimensional inputs, we formulate an upper bound for the test error and study its minimization. Moreover, we consider the learning of the expert parameters from a training dataset, given an in put-space segmentation, and formulate their statistical learning properties. This leads us to the oretically and empirically show how the tradeoff between approximation and estimation errors in Mo E learning depends on the number of experts.

Test-time algorithms that combine the generative power of language models with process verifiers that assess the quality of partial generations offer a promising lever for eliciting new reasoning capabilities, but the algorithmic design space and computational scaling properties of such approaches are still opaque, and their benefits are far from apparent when one accounts for the cost of learning a high-quality verifier. Our starting point is the observation that seemingly benign errors in a learned verifier can lead to catastrophic failures for standard decoding techniques due to error amplification during the course of generation. We then ask: can this be improved with more sophisticated decoding strategies? We introduce a new process-guided test-time sampling algorithm, VGB, which uses theoretically grounded backtracking to achieve provably better robustness to verifier errors. VGB interprets autoregressive generation as a random walk on a tree of partial generations, with transition probabilities guided by the process verifier and base model; crucially, backtracking occurs probabilistically. This process generalizes the seminal Sinclair-Jerrum random walk (Sinclair & Jerrum, 1989) from the literature on approximate counting and sampling in theoretical computer science, and a conceptual contribution of our work is to highlight parallels with this literature. Empirically, we demonstrate on both synthetic and real language modeling tasks that VGB outperforms baselines on a variety of metrics.

We investigate the complexity of stable (or perturbation-resilient) instances of $\mathrm{k-M\small{EANS}}$ and $\mathrm{k-M\small{EDIAN}}$ clustering problems in metrics with small doubling dimension. While these problems have been extensively studied under multiplicative perturbation resilience in low-dimensional Euclidean spaces (e.g., (Friggstad et al., 2019; Cohen-Addad and Schwiegelshohn, 2017)), we adopt a more general notion of stability, termed ``almost stable'', which is closer to the notion of $(α, \varepsilon)$-perturbation resilience introduced by Balcan and Liang (2016). Additionally, we extend our results to $\mathrm{k-M\small{EANS}}$/$\mathrm{k-M\small{EDIAN}}$ with penalties, where each data point is either assigned to a cluster centre or incurs a penalty. We show that certain special cases of almost stable $\mathrm{k-M\small{EANS}}$/$\mathrm{k-M\small{EDIAN}}$ (with penalties) are solvable in polynomial time. To complement this, we also examine the hardness of almost stable instances and $(1 + \frac{1}{poly(n)})$-stable instances of $\mathrm{k-M\small{EANS}}$/$\mathrm{k-M\small{EDIAN}}$ (with penalties), proving super-polynomial lower bounds on the runtime of any exact algorithm under the widely believed Exponential Time Hypothesis (ETH).

Abstract--In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge introduced by its neighborhood-based visitation criterion, wherein a node is considered visited if the agent enters a compact neighborhood around it. In this work, we formulate a Markov decision process (MDP) for CETSP using a discretization scheme and propose a novel unified dual-decoder DRL (UD3RL) framework that separates decision-making into node selection and waypoint determination. Specifically, an adapted encoder is employed for effective feature extraction, followed by a node-decoder and a loc-decoder to handle the two sub-tasks, respectively. A k-nearest neighbors subgraph interaction strategy is further introduced to enhance spatial reasoning during location decoding. Furthermore, we customize the REINFORCE algorithm to train UD3RL as a unified model capable of generalizing across different problem sizes and varying neighborhood radius types (i.e., constant and random radii). Experimental results show that UD3RL outperforms conventional methods in both solution quality and runtime, while exhibiting strong generalization across problem scales, spatial distributions, and radius ranges, as well as robustness to dynamic environments. HE close-enough traveling salesman problem (CETSP) is a well-known variant of the classical traveling salesman problem (TSP) that preserves its NP-hard complexity [1].

With the growth of global maritime transportation, energy optimization has become crucial for reducing costs and ensuring operational efficiency. Shaft power is the mechanical power transmitted from the engine to the shaft and directly impacts fuel consumption, making its accurate prediction a paramount step in optimizing vessel performance. Power consumption is highly correlated with ship parameters such as speed and shaft rotation per minute, as well as weather and sea conditions. Frequent access to this operational data can improve prediction accuracy. However, obtaining high-quality sensor data is often infeasible and costly, making alternative sources such as noon reports a viable option. In this paper, we propose a transfer learning-based approach for predicting vessels' shaft power, where a model is initially trained on high-frequency data from a vessel and then fine-tuned with low-frequency daily noon reports from other vessels. We tested our approach on sister vessels (identical dimensions and configurations), a similar vessel (slightly larger with a different engine), and a different vessel (distinct dimensions and configurations). The experiments showed that the mean absolute percentage error decreased by 10.6% for sister vessels, 3.6% for a similar vessel, and 5.3% for a different vessel, compared to the model trained solely on noon report data. Keywords: transfer learning, shaft power prediction, noon reports, sensor data, maritime.

Artificial intelligence (AI) is being applied in almost every field. At the same time, the currently dominant deep learning methods are fundamentally black-box systems that lack explanations for their inferences, significantly limiting their trustworthiness and adoption. Explainable AI (XAI) methods aim to overcome this challenge by providing explanations of the models' decision process. Such methods are often proposed and developed by engineers and scientists with a predominantly technical background and incorporate their assumptions about the existence, validity, and explanatory utility of different conceivable explanatory mechanisms. However, the basic concept of an explanation -- what it is, whether we can know it, whether it is absolute or relative -- is far from trivial and has been the subject of deep philosophical debate for millennia. As we point out here, the assumptions incorporated into different XAI methods are not harmless and have important consequences for the validity and interpretation of AI explanations in different domains. We investigate ontological and epistemological assumptions in explainability methods when they are applied to AI systems, meaning the assumptions we make about the existence of explanations and our ability to gain knowledge about those explanations. Our analysis shows how seemingly small technical changes to an XAI method may correspond to important differences in the underlying assumptions about explanations. We furthermore highlight the risks of ignoring the underlying onto-epistemological paradigm when choosing an XAI method for a given application, and we discuss how to select and adapt appropriate XAI methods for different domains of application.

Abstract-- This paper presents a novel framework for estimating the position and orientation of flexible manipulators undergoing vertical motion using multiple inertial measurement units (IMUs), optimized and calibrated with ground truth data. The flexible links are modeled as a series of rigid segments, with joint angles estimated from accelerometer and gyroscope measurements acquired by cost-effective IMUs. A complementary filter is employed to fuse the measurements, with its parameters optimized through particle swarm optimization (PSO) to mitigate noise and delay. T o further improve estimation accuracy, residual errors in position and orientation are compensated using radial basis function neural networks (RBFNN). Experimental results validate the effectiveness of the proposed intelligent multi-IMU kinematic estimation method, achieving root mean square errors (RMSE) of 0.00021 m, 0.00041 m, and 0.00024 rad for y, z, and θ, respectively.