Variational inference (VI) is a central tool in modern machine learning, used to approximate an intractable target density by optimising over a tractable family of distributions. As the variational family cannot typically represent the target exactly, guarantees on the quality of the resulting approximation are crucial for understanding which of its properties VI can faithfully capture. Recent work has identified instances in which symmetries of the target and the variational family enable the recovery of certain statistics, even under model misspecification. However, these guarantees are inherently problem-specific and offer little insight into the fundamental mechanism by which symmetry forces statistic recovery. In this paper, we overcome this limitation by developing a general theory of symmetry-induced statistic recovery in variational inference. First, we characterise when variational minimisers inherit the symmetries of the target and establish conditions under which these pin down identifiable statistics. Second, we unify existing results by showing that previously known statistic recovery guarantees in location-scale families arise as special cases of our theory. Third, we apply our framework to distributions on the sphere to obtain novel guarantees for directional statistics in von Mises-Fisher families. Together, these results provide a modular blueprint for deriving new recovery guarantees for VI in a broad range of symmetry settings.

We analyze two widely used local attribution methods, Local Shapley Values and LIME, which aim to quantify the contribution of a feature value $x_i$ to a specific prediction $f(x_1, \dots, x_p)$. Despite their widespread use, we identify fundamental limitations in their ability to reliably detect locally important features, even under ideal conditions with exact computations and independent features. We argue that a sound local attribution method should not assign importance to features that neither influence the model output (e.g., features with zero coefficients in a linear model) nor exhibit statistical dependence with functionality-relevant features. We demonstrate that both Local SV and LIME violate this fundamental principle. To address this, we propose R-LOCO (Regional Leave Out COvariates), which bridges the gap between local and global explanations and provides more accurate attributions. R-LOCO segments the input space into regions with similar feature importance characteristics. It then applies global attribution methods within these regions, deriving an instance's feature contributions from its regional membership. This approach delivers more faithful local attributions while avoiding local explanation instability and preserving instance-specific detail often lost in global methods.

Causal mediation analysis provides techniques for defining and estimating effects that may be endowed with mechanistic interpretations. With many scientific investigations seeking to address mechanistic questions, causal direct and indirect effects have garnered much attention. The natural direct and indirect effects, the most widely used among such causal mediation estimands, are limited in their practical utility due to stringent identification requirements. Accordingly, considerable effort has been invested in developing alternative direct and indirect effect decompositions with relaxed identification requirements. Such efforts often yield effect definitions with nuanced and challenging interpretations. By contrast, relatively limited attention has been paid to relaxing the identification assumptions of the natural direct and indirect effects. Motivated by a secondary aim of a recent non-randomized vaccine prospective cohort study (NCT05168813), we present a set of relaxed conditions under which the natural direct effect is identifiable in spite of unobserved baseline confounding of the exposure-mediator pathway; we use this result to investigate the effect mediated by putative immune correlates of protection. Relaxing the commonly used but restrictive cross-world counterfactual independence assumption, we discuss strategies for evaluating the natural direct effect in non-randomized settings that arise in the analysis of vaccine studies. We revisit prior studies of semi-parametric efficiency theory to demonstrate the construction of flexible, multiply robust estimators of the natural direct effect and discuss efficient estimation strategies that do not place restrictive modeling assumptions on nuisance functions.

Aisasetofweightedlinear combinations of the entries ofX, this problem is often referred to as thematrix sensingproblem.

In a spiking neural network, is it enough for each neuron to spike at most once? In recent work, approximation bounds for spiking neural networks have been derived, quantifying how well they can fit target functions. However, these results are only valid for neurons that spike at most once, which is commonly thought to be a strong limitation. Here, we show that the opposite is true for a large class of spiking neuron models, including the commonly used leaky integrate-and-fire model with subtractive reset: for every approximation bound that is valid for a set of multi-spike neural networks, there is an equivalent set of single-spike neural networks with only linearly more neurons (in the maximum number of spikes) for which the bound holds. The same is true for the reverse direction too, showing that regarding their approximation capabilities in general machine learning tasks, single-spike and multi-spike neural networks are equivalent. Consequently, many approximation results in the literature for single-spike neural networks also hold for the multi-spike case.

Recent work in machine learning increasingly attributes human-like capabilities such as reasoning or theory of mind to large language models (LLMs) on the basis of benchmark performance. This paper examines this practice through the lens of construct validity, understood as the problem of linking theoretical capabilities to their empirical measurements. It contrasts three influential frameworks: the nomological account developed by Cronbach and Meehl, the inferential account proposed by Messick and refined by Kane, and Borsboom's causal account. I argue that the nomological account provides the most suitable foundation for current LLM capability research. It avoids the strong ontological commitments of the causal account while offering a more substantive framework for articulating construct meaning than the inferential account. I explore the conceptual implications of adopting the nomological account for LLM research through a concrete case: the assessment of reasoning capabilities in LLMs.

In these frameworks, templates are constructed using an iterative process of template estimation and alignment, which is often computationally very expensive. Due in part to this shortcoming, most methods compute asingle template for the entire population of images, or a few templates for specific sub-groups of the data.

Ninedifferentdebiasing algorithms (and a baseline) have been evaluated with this dataset using the popular ResNet-18 network[36]. CelebA contains faces of celebrities with several binary task labelsandtwoprotected labels(genderandyouth). Table 3showsthe prediction results from a biased binary classifier and its bias values using the seven metrics. Without losing generality, we consider "Sport" the positive class in the binary classifier. Following the DP formula in Appendix A.2, for the "Sport" class, thePPRfemale is 45.0% (90 /200), andPPRmale is65.0%

Emerging ethical approaches have attempted to filter pretraining material, but such approaches have been ad hoc and failed to take context into account. We offer an approach to filtering grounded in law, which has directly addressed the tradeoffs in filtering material.

Severalworksextend thesetodynamic scenes captured with monocular video, with promising performance.