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arXiv:2603.05201v1 Announce Type: cross Abstract: Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is particularly acute for the Sparse Identification of Nonlinear Dynamics (SINDy) framework, where the core assumption of sparsity is undermined by the interaction between data scaling and measurement noise. The resulting discovered models can be dense, uninterpretable, and physically incorrect. To address this critical […]

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arXiv:2603.05149v1 Announce Type: cross Abstract: Causal discovery across multiple datasets is often constrained by data privacy regulations and cross-site heterogeneity, limiting the use of conventional methods that require a single, centralized dataset. To address these challenges, we introduce fedCI, a federated conditional independence test that rigorously handles heterogeneous datasets with non-identical sets of variables, site-specific effects, and mixed variable types, including continuous, ordinal, binary, and categorical variables. At its core, fedCI uses a federated Iteratively Reweighted Least Squares […]

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arXiv:2603.05002v1 Announce Type: cross Abstract: The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian converges to $2/eta$ during training with gradient descent (GD) with a step-size $eta$. Despite (apparently) violating classical smoothness assumptions, EoS has been widely observed in deep learning, but its theoretical foundations remain incomplete. We provide an interpretation of EoS through the lens of Directional Smoothness Mishkin et al. [2024]. This interpretation naturally extends to non-Euclidean norms, which […]

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arXiv:2603.04780v1 Announce Type: cross Abstract: Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim […]

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arXiv:2603.04688v1 Announce Type: cross Abstract: Standard accounts of memory consolidation emphasise the stabilisation of stored representations, but struggle to explain representational drift, semanticisation, or the necessity of offline replay. Here we propose that high-capacity neocortical networks optimise stored representations for generalisation by reducing complexity via predictive forgetting, i.e. the selective retention of experienced information that predicts future outcomes or experience. We show that predictive forgetting formally improves information-theoretic generalisation bounds on stored representations. Under high-fidelity encoding constraints, such […]

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arXiv:2603.04673v1 Announce Type: cross Abstract: Deep learning (DL) methods are currently being explored to restore images from sparse-view-, limited-data-, and undersampled-based acquisitions in medical applications. Although outputs from DL may appear visually appealing based on likability/subjective criteria (such as less noise, smooth features), they may also suffer from hallucinations. This issue is further exacerbated by a lack of easy-to-use techniques and robust metrics for the identification of hallucinations in DL outputs. In this work, we propose performing Fourier […]

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arXiv:2603.04625v1 Announce Type: cross Abstract: This work establishes a rigorous variational and gradient-based equivalence between the classical K-Means algorithm and differentiable Radial Basis Function (RBF) neural networks with smooth responsibilities. By reparameterizing the K-Means objective and embedding its distortion functional into a smooth weighted loss, we prove that the RBF objective $Gamma$-converges to the K-Means solution as the temperature parameter $sigma$ vanishes. We further demonstrate that the gradient-based updates of the RBF centers recover the exact K-Means centroid […]

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arXiv:2603.04546v1 Announce Type: cross Abstract: The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior work has presented a dichotomy: algorithms that are statistically-optimal, but computationally intractable (Wu et al., 2023), and algorithms that are computationally-efficient (given an ERM oracle), but statistically-suboptimal (Wu et al., 2024). This paper takes a significant step towards achieving statistical optimality and […]

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arXiv:2603.04420v1 Announce Type: cross Abstract: Critical transitions are the abrupt shifts between qualitatively different states of a system, and they are crucial to understanding tipping points in complex dynamical systems across ecology, climate science, and biology. Detecting these shifts typically involves extensive forward simulations or bifurcation analyses, which are often computationally intensive and limited by parameter sampling. In this study, we propose a novel machine learning approach based on deep neural networks (DNNs) called equilibrium-informed neural networks (EINNs) […]

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arXiv:2603.04418v1 Announce Type: cross Abstract: Standard direct forecasting models typically rely on point-wise objectives such as Mean Squared Error, which fail to capture the complex spatio-temporal dependencies inherent in graph-structured signals. While recent frequency-domain approaches such as FreDF mitigate temporal autocorrelation, they often overlook spatial and cross spatio-temporal interactions. To address this limitation, we propose FreST Loss, a frequency-enhanced spatio-temporal training objective that extends supervision to the joint spatio-temporal spectrum. By leveraging the Joint Fourier Transform (JFT), FreST […]

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