February 2026

arXiv:2510.08916v2 Announce Type: replace Abstract: The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual coefficients, thereby enabling practical and computationally tractable algorithms. In this paper, we address the problem of estimating the latent triggering kernels–functions that encode the interaction structure between events–for linear multivariate Hawkes processes based on […]

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arXiv:2411.09686v3 Announce Type: replace Abstract: Regressing a function $F$ on $mathbb{R}^d$ without the statistical and computational curse of dimensionality requires special statistical models, for example that impose geometric assumptions on the distribution of the data (e.g., that its support is low-dimensional), or strong smoothness assumptions on $F$, or a special structure $F$. Among the latter, compositional models $F=fcirc g$ with $g$ mapping to $mathbb{R}^r$ with $rll d$ include classical single- and multi-index models, as well as neural networks. […]

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arXiv:2406.05014v4 Announce Type: replace Abstract: The goal of Root Cause Analysis (RCA) is to explain why an anomaly occurred by identifying where the fault originated. Several recent works model the anomalous event as resulting from a change in the causal mechanism at the root cause, i.e., as a soft intervention. RCA is then the task of identifying which causal mechanism changed. In real-world applications, one often has either few or only a single sample from the post-intervention distribution: […]

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arXiv:2403.01673v2 Announce Type: replace Abstract: For Multivariate Time Series Forecasting (MTSF), recent deep learning applications show that univariate models frequently outperform multivariate ones. To address the difficiency in multivariate models, we introduce a method to Construct Auxiliary Time Series (CATS) that functions like a 2D temporal-contextual attention mechanism, which generates Auxiliary Time Series (ATS) from Original Time Series (OTS) to effectively represent and incorporate inter-series relationships for forecasting. Key principles of ATS – continuity, sparsity, and variability – […]

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arXiv:2310.09488v2 Announce Type: replace Abstract: Long-term time series forecasting (LTSF) is important for various domains but is confronted by challenges in handling the complex temporal-contextual relationships. As multivariate input models underperforming some recent univariate counterparts, we posit that the issue lies in the inefficiency of existing multivariate LTSF Transformers to model series-wise relationships: the characteristic differences between series are often captured incorrectly. To address this, we introduce ARM: a multivariate temporal-contextual adaptive learning method, which is an enhanced […]

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arXiv:2309.16858v5 Announce Type: replace Abstract: We introduce Transductive Local Complexity (TLC) to extend the classical Local Rademacher Complexity (LRC) to the transductive setting, incorporating substantial and novel components. Although LRC has been used to obtain sharp generalization bounds and minimax rates for inductive tasks such as classification and nonparametric regression, it has remained an open problem whether a localized Rademacher complexity framework can be effectively adapted to transductive learning to achieve sharp or nearly sharp bounds consistent with […]

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arXiv:2602.06014v1 Announce Type: cross Abstract: Thompson sampling (TS) is widely used for stochastic multi-armed bandits, yet its inferential properties under adaptive data collection are subtle. Classical asymptotic theory for sample means can fail because arm-specific sample sizes are random and coupled with the rewards through the action-selection rule. We study this phenomenon in the $K$-armed Gaussian bandit and identify emph{optimism} as a key mechanism for restoring emph{stability}, a sufficient condition for valid asymptotic inference requiring each arm’s pull […]

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arXiv:2602.05996v1 Announce Type: cross Abstract: Softmax Self-Attention (SSA) is a key component of Transformer architectures. However, when utilised within skipless architectures, which aim to improve representation learning, recent work has highlighted the inherent instability of SSA due to inducing rank collapse and poorly-conditioned Jacobians. In this work, we design a novel attention mechanism: Orthogonal Self-Attention (OSA), which aims to bypass these issues with SSA, in order to allow for (non-causal) Transformers without skip connections and normalisation layers to […]

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arXiv:2602.05970v1 Announce Type: cross Abstract: Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error through ensemble averaging rather than compositional learning or discretizing smooth dynamics. This regime is […]

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arXiv:2602.05961v1 Announce Type: cross Abstract: Sampling from a distribution $p(x) propto e^{-mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although […]

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