Points were sampled uniformly in the bands denoted by dashed lines. We posit that these barriers are due, at least in part, to the sensitivity of decision trees to transformations of the input resulting from greedy construction and simple decision rules. Of these, key limitation is the latter; even if we replace greedy construction with a perfect tree learner, simple distributions can nonetheless require an arbitrarily large axis-aligned tree to fit.

Graph Neural Networks (GNNs) are crucial for machine learning applications with graph-structured data, but their success depends on sufficient labeled data. We present a novel active learning (AL) method for GNNs, extending the Expected Model Change Maximization (EMCM) principle to improve prediction performance on unlabeled data. By presenting a Bayesian interpretation for the node embeddings generated by GNNs under the semi-supervised setting, we efficiently compute the closed-form EMCM acquisition function as the selection criterion for AL without re-training.

Machine Learning has proved its ability to produce accurate models - but the deployment of these models outside the machine learning community has been hindered by the difficulties of interpreting these models.

We thank all the reviewers for excellent questions and many relevant remarks. Thank you for this remark. One of the reason for this is that our method produces interpretations directly in terms of the input features. Thank you for pointing this out, we agree that faithful is not best. This is not the case for local models such as LIME.

Attention can be closely related under certain data conditions to Kanerva's Sparse Distributed Memory (SDM), a biologically plausible associative memory model.

In Section 2.2 we show, using an idealized model for the token distribution, that if one iteratively

Advances in data collection are producing growing volumes of temporal count observations, making adapted modeling increasingly necessary. In this work, we introduce a generative framework for independent component analysis of temporal count data, combining regime-adaptive dynamics with Poisson log-normal emissions. The model identifies disentangled components with regime-dependent contributions, enabling representation learning and perturbations analysis. Notably, we establish the identifiability of the model, supporting principled interpretation. To learn the parameters, we propose an efficient amortized variational inference procedure. Experiments on simulated data evaluate recovery of the mixing function and latent sources across diverse settings, while an in vivo longitudinal gut microbiome study reveals microbial co-variation patterns and regime shifts consistent with clinical perturbations.

Let's nitpick about the physics of Stranger Things, not its ending Feedback has seen all the fuss about the finale of Stranger Things, but would like to point out that if we're going to dissect the plot, we have bigger things to worry about In common, it seems, with a substantial fraction of the human species, Feedback spent part of our holiday watching the final episodes of Stranger Things . We laughed, we cried, we wondered if it would have even more endings than The Return of the King (it did). As is almost inevitable these days, a group of fans vocally disliked the finale, and went so far as to create a conspiracy theory about it. According to "Conformity Gate" (don't blame us, we didn't name it), the finale wasn't the real finale - despite lasting more than 2 hours, costing an enormous amount of money and being shown in cinemas. No, a super-secret final episode was going to air in January, which would reveal the true ending.

Singular learning theory (SLT) \citep{watanabe2009algebraic,watanabe2018mathematical} provides a rigorous asymptotic framework for Bayesian models with non-identifiable parameterizations, yet the statistical meaning of its second-order invariant, the \emph{singular fluctuation}, has remained unclear. In this work, we show that singular fluctuation admits a precise and natural interpretation as a \emph{specific heat}: the second derivative of the Bayesian free energy with respect to temperature. Equivalently, it measures the posterior variance of the log-likelihood observable under the tempered Gibbs posterior. We further introduce a collection of related thermodynamic quantities, including entropy flow, prior susceptibility, and cross-susceptibility, that together provide a detailed geometric diagnosis of singular posterior structure. Through extensive numerical experiments spanning discrete symmetries, boundary singularities, continuous gauge freedoms, and piecewise (ReLU) models, we demonstrate that these thermodynamic signatures cleanly distinguish singularity types, exhibit stable finite-sample behavior, and reveal phase-transition--like phenomena as temperature varies. We also show empirically that the widely used WAIC estimator \citep{watanabe2010asymptotic, watanabe2013widely} is exactly twice the thermodynamic specific heat at unit temperature, clarifying its robustness in singular models.Our results establish a concrete bridge between singular learning theory and statistical mechanics, providing both theoretical insight and practical diagnostics for modern Bayesian models.