The study of associations between an individual's age and imaging and non-imaging data is an active research area that attempts to aid understanding of the effects and patterns of aging. In this work we have conducted a supervoxel-wise association study between both volumetric and tissue density features in coronary computed tomography angiograms and the chronological age of a subject, to understand the localized changes in morphology and tissue density with age. To enable a supervoxel-wise study of volume and tissue density, we developed a novel method based on image segmentation, inter-subject image registration, and robust supervoxel-based correlation analysis, to achieve a statistical association study between the images and age. We evaluate the registration methodology in terms of the Dice coefficient for the heart chambers and myocardium, and the inverse consistency of the transformations, showing that the method works well in most cases with high overlap and inverse consistency. In a sex-stratified study conducted on a subset of $n=1388$ images from the SCAPIS study, the supervoxel-wise analysis was able to find localized associations with age outside of the commonly segmented and analyzed sub-regions, and several substantial differences between the sexes in association of age and volume.
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Understanding the mechanisms through which neural networks extract statistics from input-label pairs through feature learning is one of the most important unsolved problems in supervised learning. Prior works demonstrated that the gram matrices of the weights (the neural feature matrices, NFM) and the average gradient outer products (AGOP) become correlated during training, in a statement known as the neural feature ansatz (NFA). Through the NFA, the authors introduce mapping with the AGOP as a general mechanism for neural feature learning. However, these works do not provide a theoretical explanation for this correlation or its origins. In this work, we further clarify the nature of this correlation, and explain its emergence. We show that this correlation is equivalent to alignment between the left singular structure of the weight matrices and the newly defined pre-activation tangent features at each layer. We further establish that the alignment is driven by the interaction of weight changes induced by SGD with the pre-activation features, and analyze the resulting dynamics analytically at early times in terms of simple statistics of the inputs and labels. Finally, motivated by the observation that the NFA is driven by this centered correlation, we introduce a simple optimization rule that dramatically increases the NFA correlations at any given layer and improves the quality of features learned.
Scientific discoveries often hinge on synthesizing decades of research, a task that potentially outstrips human information processing capacities. Large language models (LLMs) offer a solution. LLMs trained on the vast scientific literature could potentially integrate noisy yet interrelated findings to forecast novel results better than human experts. To evaluate this possibility, we created BrainBench, a forward-looking benchmark for predicting neuroscience results. We find that LLMs surpass experts in predicting experimental outcomes. BrainGPT, an LLM we tuned on the neuroscience literature, performed better yet. Like human experts, when LLMs were confident in their predictions, they were more likely to be correct, which presages a future where humans and LLMs team together to make discoveries. Our approach is not neuroscience-specific and is transferable to other knowledge-intensive endeavors.
This paper addresses important weaknesses in current methodology for the estimation of multivariate extreme event distributions. The estimation of the residual dependence index $\eta \in (0,1]$ is notoriously problematic. We introduce a flexible class of reduced-bias estimators for this parameter, designed to ameliorate the usual problems of threshold selection through a unified approach to the familiar margins standardisation. We derive the associated asymptotic properties. The efficacy of the proposed semi-parametric inference on $\eta$ stems from a hitherto neglected exponentially decaying term in the hidden regular variation characterisation. Simulation studies to assess the performance for finite samples over a range of standard copulas indicate an improved performance, relative to the existing standard methods such as the Hill estimator. Our leading application illustrates how asymptotic independence can be discerned from monsoon-related rainfall occurrences at different locations in Ghana. The considerations involved in extending this framework to feasible inference on the extreme value index attached to domains of attraction are briefly discussed.
The ability to manipulate logical-mathematical symbols (LMS), encompassing tasks such as calculation, reasoning, and programming, is a cognitive skill arguably unique to humans. Considering the relatively recent emergence of this ability in human evolutionary history, it has been suggested that LMS processing may build upon more fundamental cognitive systems, possibly through neuronal recycling. Previous studies have pinpointed two primary candidates, natural language processing and spatial cognition. Existing comparisons between these domains largely relied on task-level comparison, which may be confounded by task idiosyncrasy. The present study instead compared the neural correlates at the domain level with both automated meta-analysis and synthesized maps based on three representative LMS tasks, reasoning, calculation, and mental programming. Our results revealed a more substantial cortical overlap between LMS processing and spatial cognition, in contrast to language processing. Furthermore, in regions activated by both spatial and language processing, the multivariate activation pattern for LMS processing exhibited greater multivariate similarity to spatial cognition than to language processing. A hierarchical clustering analysis further indicated that typical LMS tasks were indistinguishable from spatial cognition tasks at the neural level, suggesting an inherent connection between these two cognitive processes. Taken together, our findings support the hypothesis that spatial cognition is likely the basis of LMS processing, which may shed light on the limitations of large language models in logical reasoning, particularly those trained exclusively on textual data without explicit emphasis on spatial content.
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix indicates conditional independence between nodes. In high-dimensional settings where the dimension of the precision matrix $p$ exceeds the sample size $n$ and the matrix is sparse, methods like graphical Lasso, graphical SCAD, and CLIME are popular for estimating GGMs. While frequentist methods are well-studied, Bayesian approaches for (unstructured) sparse precision matrices are less explored. The graphical horseshoe estimate by \citet{li2019graphical}, applying the global-local horseshoe prior, shows superior empirical performance, but theoretical work for sparse precision matrix estimations using shrinkage priors is limited. This paper addresses these gaps by providing concentration results for the tempered posterior with the fully specified horseshoe prior in high-dimensional settings. Moreover, we also provide novel theoretical results for model misspecification, offering a general oracle inequality for the posterior.
Continual learning refers to the capability of a machine learning model to learn and adapt to new information, without compromising its performance on previously learned tasks. Although several studies have investigated continual learning methods for information retrieval tasks, a well-defined task formulation is still lacking, and it is unclear how typical learning strategies perform in this context. To address this challenge, a systematic task formulation of continual neural information retrieval is presented, along with a multiple-topic dataset that simulates continuous information retrieval. A comprehensive continual neural information retrieval framework consisting of typical retrieval models and continual learning strategies is then proposed. Empirical evaluations illustrate that the proposed framework can successfully prevent catastrophic forgetting in neural information retrieval and enhance performance on previously learned tasks. The results indicate that embedding-based retrieval models experience a decline in their continual learning performance as the topic shift distance and dataset volume of new tasks increase. In contrast, pretraining-based models do not show any such correlation. Adopting suitable learning strategies can mitigate the effects of topic shift and data augmentation.
In this article, we develop an asymptotic method for constructing confidence regions for the set of all linear subspaces arising from PCA, from which we derive hypothesis tests on this set. Our method is based on the geometry of Riemannian manifolds with which some sets of linear subspaces are endowed.
We studied the dynamical properties of Rabi oscillations driven by an alternating Rashba field applied to a two-dimensional (2D) harmonic confinement system. We solve the time-dependent (TD) Schr\"{o}dinger equation numerically and rewrite the resulting TD wavefunction onto the Bloch sphere (BS) using two BS parameters of the zenith ($\theta_B$) and azimuthal ($\phi_B$) angles, extracting the phase information $\phi_B$ as well as the mixing ratio $\theta_B$ between the two BS-pole states. We employed a two-state rotating wave (TSRW) approach and studied the fundamental features of $\theta_B$ and $\phi_B$ over time. The TSRW approach reveals a triangular wave formation in $\theta_B$. Moreover, at each apex of the triangular wave, the TD wavefunction passes through the BS pole, and the state is completely replaced by the opposite spin state. The TSRW approach also elucidates a linear change in $\phi_B$. The slope of $\phi_B$ vs. time is equal to the difference between the dynamical terms, leading to a confinement potential in the harmonic system. The TSRW approach further demonstrates a jump in the phase difference by $\pi$ when the wavefunction passes through the BS pole. The alternating Rashba field causes multiple successive Rabi transitions in the 2D harmonic system. We then introduce the effective BS (EBS) and transform these complicated transitions into an equivalent "single" Rabi one. Consequently, the EBS parameters $\theta_B^{\mathrm{eff}}$ and $\phi_B^{\mathrm{eff}}$ exhibit mixing and phase difference between two spin states $\alpha$ and $\beta$, leading to a deep understanding of the TD features of multi-Rabi oscillations. Furthermore, the combination of the BS representation with the TSRW approach successfully reveals the dynamical properties of the Rabi oscillation, even beyond the TSRW approximation.
The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum utility is achieved. Recently, this theory has incorporated constraints, i.e., the optimum is achieved when the utility is maximized while respecting some information-processing constraints. This is reminiscent of thermodynamic systems. As such, the study of intelligent systems has benefited from the tools of thermodynamics. The first aim of this thesis is to clarify the applicability of these results in the study of intelligent systems. We can think of the local transition steps in thermodynamic or intelligent systems as being driven by uncertainty. In fact, the transitions in both systems can be described in terms of majorization. Hence, real-valued uncertainty measures like Shannon entropy are simply a proxy for their more involved behaviour. More in general, real-valued functions are fundamental to study optimization and complexity in the order-theoretic approach to several topics, including economics, thermodynamics, and quantum mechanics. The second aim of this thesis is to improve on this classification. The basic similarity between thermodynamic and intelligent systems is based on an uncertainty notion expressed by a preorder. We can also think of the transitions in the steps of a computational process as a decision-making procedure. In fact, by adding some requirements on the considered order structures, we can build an abstract model of uncertainty reduction that allows to incorporate computability, that is, to distinguish the objects that can be constructed by following a finite set of instructions from those that cannot. The third aim of this thesis is to clarify the requirements on the order structure that allow such a framework.
Agglomeration techniques are important to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform the agglomeration of polyhedral grids, we propose a novel Geometrical Deep Learning-based algorithm that can exploit the geometrical and physical information of the underlying computational domain to construct the agglomerated grid and simultaneously guarantee the agglomerated grid's quality. In particular, we propose a bisection model based on Graph Neural Networks (GNNs) to partition a suitable connectivity graph of computational three-dimensional meshes. The new approach has a high online inference speed and can simultaneously process the graph structure of the mesh, the geometrical information of the mesh (e.g. elements' volumes, centers' coordinates), and the physical information of the domain (e.g. physical parameters). Taking advantage of this new approach, our algorithm can agglomerate meshes of a domain composed of heterogeneous media in an automatic way. The proposed GNN techniques are compared with the k-means algorithm and METIS: standard approaches for graph partitioning that are meant to process only the connectivity information on the mesh. We demonstrate that the performance of our algorithms outperforms available approaches in terms of quality metrics and runtimes. Moreover, we demonstrate that our algorithm also shows a good level of generalization when applied to more complex geometries, such as three-dimensional geometries reconstructed from medical images. Finally, the capabilities of the model in performing agglomeration of heterogeneous domains are tested in the framework of problems containing microstructures and on a complex geometry such as the human brain.
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