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Modern multimodal systems deployed in industrial and safety-critical environments must remain reliable under partial sensor failures, signal degradation, or cross-modal inconsistencies. This work introduces a mathematically grounded framework for fault-tolerant multimodal representation learning that unifies self-supervised anomaly detection and error correction within a single architecture. Building upon a theoretical analysis of perturbation propagation, we derive Lipschitz- and Jacobian-based criteria that determine whether a neural operator amplifies or attenuates localized faults. Guided by this theory, we propose a two-stage […]

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Agriculture is increasingly challenged by climate change, soil degradation, and resource depletion, and hence requires advanced data-driven crop classification and recommendation solutions. This work presents an explainable ensemble learning paradigm that fuses optimized feature pyramids, deep networks, self-attention mechanisms, and residual networks for bolstering crop suitability predictions based on soil characteristics (e.g., pH, nitrogen, potassium) and climatic conditions (e.g., temperature, rainfall). With a dataset comprising 3,867 instances and 29 features from the Ethiopian Agricultural Transformation Agency and NASA, […]

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Linearized string representations serve as the foundation of scalable autoregressive molecular generation; however, they introduce a fundamental modality mismatch where a single molecular graph maps to multiple distinct sequences. This ambiguity leads to textit{trajectory divergence}, where the latent representations of structurally equivalent partial graphs drift apart due to differences in linearization history. To resolve this without abandoning the efficient string formulation, we propose Structure-Invariant Generative Molecular Alignment (SIGMA). Rather than altering the linear representation, SIGMA enables the model […]

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arXiv:2603.19808v2 Announce Type: replace-cross Abstract: Population-based learning paradigms, including evolutionary strategies, Population-Based Training (PBT), and recent model-merging methods, combine fast within-model optimisation with slower population-level adaptation. Despite their empirical success, a general mathematical description of the resulting collective training dynamics remains incomplete. We introduce a theoretical framework for neural network training based on two-time-scale population dynamics. We model a population of neural networks as an interacting agent system in which network parameters evolve through fast noisy gradient updates […]

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arXiv:2603.16661v2 Announce Type: replace-cross Abstract: Standard masked discrete diffusion models face limitations in reasoning tasks due to their inability to correct their own mistakes on the masking path. Since they rely on a fixed number of denoising steps, they are unable to adjust their computation to the complexity of a given problem. To address these limitations, we introduce a method based on learning a Markov transition kernel that is trained on its own outputs. This design enables tokens […]

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arXiv:2603.03071v2 Announce Type: replace-cross Abstract: Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning capability. We study this question in the pure-state setting by viewing encoded data as an embedded manifold in $mathbb{C}P^{2^n-1}$ and analysing infinitesimal unitary actions through Lie-algebra directions. We introduce Classical-to-Lie-algebra (CLA) maps and the criterion of almost Complete Local Selectivity (aCLS), which combines […]

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arXiv:2512.23138v2 Announce Type: replace-cross Abstract: Attenuation bias — the systematic underestimation of regression coefficients due to measurement errors in input variables — affects astronomical data-driven models. For linear regression, this problem was solved by treating the true input values as latent variables to be estimated alongside model parameters. In this paper, we show that neural networks suffer from the same attenuation bias and that the latent variable solution generalizes directly to neural networks. We introduce LatentNN, a method […]

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arXiv:2512.09295v3 Announce Type: replace-cross Abstract: Consider the additive Gaussian model $Y = X + sigma Z$, where $X sim P$ is an unknown signal, $Z sim N(0,1)$ is independent of $X$, and $sigma > 0$ is known. Let $Q$ denote the law of $Y$. We construct a hierarchy of denoisers $T_0, T_1, ldots, T_infty colon mathbb{R} to mathbb{R}$ that depend only on higher-order score functions $q^{(m)}/q$, $m geq 1$, of $Q$ and require no knowledge of the law […]

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arXiv:2511.18789v3 Announce Type: replace-cross Abstract: We study the problem of excess risk evaluation for empirical risk minimization (ERM) under convex losses. We show that by leveraging the idea of wild refitting, one can upper bound the excess risk through the so-called “wild optimism,” without relying on the global structure of the underlying function class but only assuming black box access to the training algorithm and a single dataset. We begin by generating two sets of artificially modified pseudo-outcomes […]

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arXiv:2510.00479v2 Announce Type: replace-cross Abstract: We numerically investigate the feasibility and limits of jointly estimating flow fields and unknown particle properties (e.g., position, size, and density) from Lagrangian particle tracking (LPT) data. LPT offers time-resolved, volumetric measurements of particle trajectories, which are markers of the carrier fluid motion. However, experimental tracks are spatially sparse and potentially noisy, and the problem of reconstructing flow fields may be further complicated by inertial particle transport, such that particle slip velocities must […]

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