We present a novel data-driven framework for estimating the response of higher-order moments of nonlinear stochastic systems to small external perturbations. The classical Generalized Fluctuation-Dissipation Theorem (GFDT) links the unperturbed steady-state distribution to the system's linear response. Standard implementations rely on Gaussian approximations, which can often accurately predict the mean response but usually introduce significant biases in higher-order moments, such as variance, skewness, and kurtosis. To address this limitation, we combine GFDT with recent advances in score-based generative modeling, which enable direct estimation of the score function from data without requiring full density reconstruction. Our method is validated on three reduced-order stochastic models relevant to climate dynamics: a scalar stochastic model for low-frequency climate variability, a slow-fast triad model mimicking key features of the El Nino-Southern Oscillation (ENSO), and a six-dimensional stochastic barotropic model capturing atmospheric regime transitions. In all cases, the approach captures strongly nonlinear and non-Gaussian features of the system's response, outperforming traditional Gaussian approximations.

We study $\textit{gradient descent}$ (GD) for logistic regression on linearly separable data with stepsizes that adapt to the current risk, scaled by a constant hyperparameter $\eta$. We show that after at most $1/\gamma^2$ burn-in steps, GD achieves a risk upper bounded by $\exp(-\Theta(\eta))$, where $\gamma$ is the margin of the dataset. As $\eta$ can be arbitrarily large, GD attains an arbitrarily small risk $\textit{immediately after the burn-in steps}$, though the risk evolution may be $\textit{non-monotonic}$. We further construct hard datasets with margin $\gamma$, where any batch (or online) first-order method requires $\Omega(1/\gamma^2)$ steps to find a linear separator. Thus, GD with large, adaptive stepsizes is $\textit{minimax optimal}$ among first-order batch methods. Notably, the classical $\textit{Perceptron}$ (Novikoff, 1962), a first-order online method, also achieves a step complexity of $1/\gamma^2$, matching GD even in constants. Finally, our GD analysis extends to a broad class of loss functions and certain two-layer networks.

Spatiotemporal learning is challenging due to the intricate interplay between spatial and temporal dependencies, the high dimensionality of the data, and scalability constraints. These challenges are further amplified in scientific domains, where data is often irregularly distributed (e.g., missing values from sensor failures) and high-volume (e.g., high-fidelity simulations), posing additional computational and modeling difficulties. In this paper, we present SCENT, a novel framework for scalable and continuity-informed spatiotemporal representation learning. SCENT unifies interpolation, reconstruction, and forecasting within a single architecture. Built on a transformer-based encoder-processor-decoder backbone, SCENT introduces learnable queries to enhance generalization and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. To ensure scalability in both data size and model complexity, we incorporate a sparse attention mechanism, enabling flexible output representations and efficient evaluation at arbitrary resolutions. We validate SCENT through extensive simulations and real-world experiments, demonstrating state-of-the-art performance across multiple challenging tasks while achieving superior scalability.

Achieving reliable and safe autonomous driving in off-road environments requires accurate and efficient terrain traversability analysis. However, this task faces several challenges, including the scarcity of large-scale datasets tailored for off-road scenarios, the high cost and potential errors of manual annotation, the stringent real-time requirements of motion planning, and the limited computational power of onboard units. To address these challenges, this paper proposes a novel traversability learning method that leverages self-supervised learning, eliminating the need for manual annotation. For the first time, a Birds-Eye View (BEV) representation is used as input, reducing computational burden and improving adaptability to downstream motion planning. During vehicle operation, the proposed method conducts online analysis of traversed regions and dynamically updates prototypes to adaptively assess the traversability of the current environment, effectively handling dynamic scene changes. We evaluate our approach against state-of-the-art benchmarks on both public datasets and our own dataset, covering diverse seasons and geographical locations. Experimental results demonstrate that our method significantly outperforms recent approaches. Additionally, real-world vehicle experiments show that our method operates at 10 Hz, meeting real-time requirements, while a 5.5 km autonomous driving experiment further validates the generated traversability cost maps compatibility with downstream motion planning.

Transfer learning from pre-trained encoders has become essential in modern machine learning, enabling efficient model adaptation across diverse tasks. However, this combination of pre-training and downstream adaptation creates an expanded attack surface, exposing models to sophisticated backdoor embeddings at both the encoder and dataset levels--an area often overlooked in prior research. Additionally, the limited computational resources typically available to users of pre-trained encoders constrain the effectiveness of generic backdoor defenses compared to end-to-end training from scratch. In this work, we investigate how to mitigate potential backdoor risks in resource-constrained transfer learning scenarios. Specifically, we conduct an exhaustive analysis of existing defense strategies, revealing that many follow a reactive workflow based on assumptions that do not scale to unknown threats, novel attack types, or different training paradigms. In response, we introduce a proactive mindset focused on identifying clean elements and propose the Trusted Core (T-Core) Bootstrapping framework, which emphasizes the importance of pinpointing trustworthy data and neurons to enhance model security. Our empirical evaluations demonstrate the effectiveness and superiority of T-Core, specifically assessing 5 encoder poisoning attacks, 7 dataset poisoning attacks, and 14 baseline defenses across five benchmark datasets, addressing four scenarios of 3 potential backdoor threats.

However, if one goes beyond the well-established linear time-invariant (L TI) system identification framework [17], considering, e.g., linear time-varying (L TV) [22], linear parameter-varying (LPV) [29], or various nonlinear (NL) models [11], a core question of the resulting identification problems is how to efficiently estimate from data the functional relations involved in these models. While classical beyond-LTI methods used fixed basis-function parameteriza-tions to express nonlinearities, with the recent progress of computational capabilities and machine learning/deep learning methods, a wide-range of learning approaches has been introduced, from Gaussian process (GP) regression [24] and support vector machines [27] to artificial neural networks (ANN) based training (see [23] for a recent overview), including state-space (SS) recurrent networks such as LSTMs [13, 19], SS-ANNs [1-3, 10, 20, 25, 28], etc. In particular, the latter class of methods successfully combines deep learning with state-space model identification concepts, achieving extreme accuracy levels on well established benchmarks, see [1]. However, in the quest of solving the underlying function estimation problem with improved accuracy and reliability, many aspects of the classical identification theory have been sacrificed. While deep-learning methods can achieve remarkable results, the relating training time when no state-measurements are available is often too high compared to classical identification methods, requiring tens of hours, sometimes days, with the most sophisticated stochastic gradient methods, like Adam [15], to train mid-sized models on training sequences of reasonable length. Using such methods in an identification cycle, which requires iterations on model structure selection, hyperparameter optimization on validation data, and experiment design, is simply impractical. Next to the computational challenges, many of the developed machine learning-based identification methods do not consider measurement or process noise affecting the estimation problem, or are based on simplistic noise settings / isolated scenarios, with a few exceptions, e.g., [1, 25]. The general understanding of process and noise models, and the related concept of one/ n -step-ahead predictors and connected modelling choices, model structures, and the overall estimation concept, which are well-developed for the L TI case, is largely missing in the general NL context. Besides theoretical limitations, in practice it is not clear to the user how to co-estimate linear and nonlinear elements, select a combination of process and noise models, and scale up the identification process from linear to nonlinear modeling within the same framework.

We study the hard problem of 3D object segmentation in complex point clouds without requiring human labels of 3D scenes for supervision. By relying on the similarity of pretrained 2D features or external signals such as motion to group 3D points as objects, existing unsupervised methods are usually limited to identifying simple objects like cars or their segmented objects are often inferior due to the lack of objectness in pretrained features. In this paper, we propose a new two-stage pipeline called GrabS. The core concept of our method is to learn generative and discriminative object-centric priors as a foundation from object datasets in the first stage, and then design an embodied agent to learn to discover multiple objects by querying against the pretrained generative priors in the second stage. We extensively evaluate our method on two real-world datasets and a newly created synthetic dataset, demonstrating remarkable segmentation performance, clearly surpassing all existing unsupervised methods.

Decentralised applications (dApps) that run on public blockchains have the benefit of trustworthiness and transparency as every activity that happens on the blockchain can be publicly traced through the transaction data. However, this introduces a potential privacy problem as this data can be tracked and analysed, which can reveal user-behaviour information. A user behaviour analysis pipeline was proposed to present how this type of information can be extracted and analysed to identify separate behavioural clusters that can describe how users behave in the game. The pipeline starts with the collection of transaction data, involving smart contracts, that is collected from a blockchain-based game called Planet IX. Both the raw transaction information and the transaction events are considered in the data collection. From this data, separate game actions can be formed and those are leveraged to present how and when the users conducted their in-game activities in the form of user flows. An extended version of these user flows also presents how the Non-Fungible Tokens (NFTs) are being leveraged in the user actions. The latter is given as input for a Graph Neural Network (GNN) model to provide graph embeddings for these flows which then can be leveraged by clustering algorithms to cluster user behaviours into separate behavioural clusters. We benchmark and compare well-known clustering algorithms as a part of the proposed method. The user behaviour clusters were analysed and visualised in a graph format. It was found that behavioural information can be extracted regarding the users that belong to these clusters. Such information can be exploited by malicious users to their advantage. To demonstrate this, a privacy threat model was also presented based on the results that correspond to multiple potentially affected areas.

Community detection, the unsupervised task of clustering nodes of a graph, finds applications across various fields. The common approaches for community detection involve optimizing an objective function to partition the nodes into communities at a single scale of granularity. However, the single-scale approaches often fall short of producing partitions that are robust and at a suitable scale. The existing algorithm, PyGenStability, returns multiple robust partitions for a network by optimizing the multi-scale Markov stability function. However, in cases where the suitable scale is not known or assumed by the user, there is no principled method to select a single robust partition at a suitable scale from the multiple partitions that PyGenStability produces. Our proposed method combines the Markov stability framework with a pre-trained machine learning model for scale selection to obtain one robust partition at a scale that is learned based on the graph structure. This automatic scale selection involves using a gradient boosting model pre-trained on hand-crafted and embedding-based network features from a labeled dataset of 10k benchmark networks. This model was trained to predicts the scale value that maximizes the similarity of the output partition to the planted partition of the benchmark network. Combining our scale selection algorithm with the PyGenStability algorithm results in PyGenStabilityOne (PO): a hyperparameter-free multi-scale community detection algorithm that returns one robust partition at a suitable scale without the need for any assumptions, input, or tweaking from the user. We compare the performance of PO against 29 algorithms and show that it outperforms 25 other algorithms by statistically meaningful margins. Our results facilitate choosing between community detection algorithms, among which PO stands out as the accurate, robust, and hyperparameter-free method.

Purpose: Accurately classifying tissue margins during cancer surgeries is crucial for ensuring complete tumor removal. Rapid Evaporative Ionization Mass Spectrometry (REIMS), a tool for real-time intraoperative margin assessment, generates spectra that require machine learning models to support clinical decision-making. However, the scarcity of labeled data in surgical contexts presents a significant challenge. This study is the first to develop a foundation model tailored specifically for REIMS data, addressing this limitation and advancing real-time surgical margin assessment. Methods: We propose FACT, a Foundation model for Assessing Cancer Tissue margins. FACT is an adaptation of a foundation model originally designed for text-audio association, pretrained using our proposed supervised contrastive approach based on triplet loss. An ablation study is performed to compare our proposed model against other models and pretraining methods. Results: Our proposed model significantly improves the classification performance, achieving state-of-the-art performance with an AUROC of $82.4\% \pm 0.8$. The results demonstrate the advantage of our proposed pretraining method and selected backbone over the self-supervised and semi-supervised baselines and alternative models. Conclusion: Our findings demonstrate that foundation models, adapted and pretrained using our novel approach, can effectively classify REIMS data even with limited labeled examples. This highlights the viability of foundation models for enhancing real-time surgical margin assessment, particularly in data-scarce clinical environments.