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This work deals with the numerical approximation of plasmas which are confined by the effect of a fast oscillating magnetic field (see \cite{Bostan2012}) in the Vlasov model. The presence of this magnetic field induces oscillations (in time) to the solution of the characteristic equations. Due to its multiscale character, a standard time discretization would lead to an inefficient solver. In this work, time integrators are derived and analyzed for a class of highly oscillatory differential systems. We prove the uniform accuracy property of these time integrators, meaning that the accuracy does not depend on the small parameter $\varepsilon$. Moreover, we construct an extension of the scheme which degenerates towards an energy preserving numerical scheme for the averaged model, when $\varepsilon\to 0$. Several numerical results illustrate the capabilities of the method.

Much of the research on the interpretability of deep neural networks has focused on studying the visual features that maximally activate individual neurons. However, recent work has cast doubts on the usefulness of such local representations for understanding the behavior of deep neural networks because individual neurons tend to respond to multiple unrelated visual patterns, a phenomenon referred to as "superposition". A promising alternative to disentangle these complex patterns is learning sparsely distributed vector representations from entire network layers, as the resulting basis vectors seemingly encode single identifiable visual patterns consistently. Thus, one would expect the resulting code to align better with human perceivable visual patterns, but supporting evidence remains, at best, anecdotal. To fill this gap, we conducted three large-scale psychophysics experiments collected from a pool of 560 participants. Our findings provide (i) strong evidence that features obtained from sparse distributed representations are easier to interpret by human observers and (ii) that this effect is more pronounced in the deepest layers of a neural network. Complementary analyses also reveal that (iii) features derived from sparse distributed representations contribute more to the model's decision. Overall, our results highlight that distributed representations constitute a superior basis for interpretability, underscoring a need for the field to move beyond the interpretation of local neural codes in favor of sparsely distributed ones.

Abdominal computed tomography (CT) scans are frequently performed in clinical settings. Opportunistic CT involves repurposing routine CT images to extract diagnostic information and is an emerging tool for detecting underdiagnosed conditions such as sarcopenia, hepatic steatosis, and ascites. This study utilizes deep learning methods to promote accurate diagnosis and clinical documentation. We analyze 2,674 inpatient CT scans to identify discrepancies between imaging phenotypes (characteristics derived from opportunistic CT scans) and their corresponding documentation in radiology reports and ICD coding. Through our analysis, we find that only 0.5%, 3.2%, and 30.7% of scans diagnosed with sarcopenia, hepatic steatosis, and ascites (respectively) through either opportunistic imaging or radiology reports were ICD-coded. Our findings demonstrate opportunistic CT's potential to enhance diagnostic precision and accuracy of risk adjustment models, offering advancements in precision medicine.

Over 85 million computed tomography (CT) scans are performed annually in the US, of which approximately one quarter focus on the abdomen. Given the current radiologist shortage, there is a large impetus to use artificial intelligence to alleviate the burden of interpreting these complex imaging studies. Prior state-of-the-art approaches for automated medical image interpretation leverage vision language models (VLMs). However, current medical VLMs are generally limited to 2D images and short reports, and do not leverage electronic health record (EHR) data for supervision. We introduce Merlin - a 3D VLM that we train using paired CT scans (6+ million images from 15,331 CTs), EHR diagnosis codes (1.8+ million codes), and radiology reports (6+ million tokens). We evaluate Merlin on 6 task types and 752 individual tasks. The non-adapted (off-the-shelf) tasks include zero-shot findings classification (31 findings), phenotype classification (692 phenotypes), and zero-shot cross-modal retrieval (image to findings and image to impressions), while model adapted tasks include 5-year disease prediction (6 diseases), radiology report generation, and 3D semantic segmentation (20 organs). We perform internal validation on a test set of 5,137 CTs, and external validation on 7,000 clinical CTs and on two public CT datasets (VerSe, TotalSegmentator). Beyond these clinically-relevant evaluations, we assess the efficacy of various network architectures and training strategies to depict that Merlin has favorable performance to existing task-specific baselines. We derive data scaling laws to empirically assess training data needs for requisite downstream task performance. Furthermore, unlike conventional VLMs that require hundreds of GPUs for training, we perform all training on a single GPU., Comment: 18 pages, 7 figures

Humans can effortlessly draw new categories from a single exemplar, a feat that has long posed a challenge for generative models. However, this gap has started to close with recent advances in diffusion models. This one-shot drawing task requires powerful inductive biases that have not been systematically investigated. Here, we study how different inductive biases shape the latent space of Latent Diffusion Models (LDMs). Along with standard LDM regularizers (KL and vector quantization), we explore supervised regularizations (including classification and prototype-based representation) and contrastive inductive biases (using SimCLR and redundancy reduction objectives). We demonstrate that LDMs with redundancy reduction and prototype-based regularizations produce near-human-like drawings (regarding both samples' recognizability and originality) -- better mimicking human perception (as evaluated psychophysically). Overall, our results suggest that the gap between humans and machines in one-shot drawings is almost closed.

Given a classification problem and a family of classifiers, the Rashomon ratio measures the proportion of classifiers that yield less than a given loss. Previous work has explored the advantage of a large Rashomon ratio in the case of a finite family of classifiers. Here we consider the more general case of an infinite family. We show that a large Rashomon ratio guarantees that choosing the classifier with the best empirical accuracy among a random subset of the family, which is likely to improve generalizability, will not increase the empirical loss too much. We quantify the Rashomon ratio in two examples involving infinite classifier families in order to illustrate situations in which it is large. In the first example, we estimate the Rashomon ratio of the classification of normally distributed classes using an affine classifier. In the second, we obtain a lower bound for the Rashomon ratio of a classification problem with a modified Gram matrix when the classifier family consists of two-layer ReLU neural networks. In general, we show that the Rashomon ratio can be estimated using a training dataset along with random samples from the classifier family and we provide guarantees that such an estimation is close to the true value of the Rashomon ratio.

A geometric graph, $\overline{G}$, is a graph drawn in the plane, with straight line edges and vertices in general position. A geometric homomorphism between two geometric graphs $\overline{G}$, $\overline{H}$ is a vertex map $f:\overline{G}\to\overline{H}$ that preserves vertex adjacency and edge crossings. The geochromatic number of $\overline{G}$, denoted $X(\overline{G})$, is the smallest integer $n$ so that there is a geometric homomorphism from $\overline{G}$ to some geometric realization of $K_n$. Recall that the chromatic number of an abstract graph $G$, denoted $\chi(G)$, is the smallest integer $n$ for which there is a graph homomorphism from $G$ to $K_n$. It is immediately clear that $\chi(G)\leq X(\overline{G})$. This paper establishes some upper bounds on $X(\overline{G})$ in terms of $\chi(G)$. For instance, if all crossings are at distance at least 1 from each other, then $X(\overline{G})\leq 3\chi(G)$. However, there are more precise results. If all crossing are at distance at least 2, then $X(\overline{G})\leq \chi(G)+2$. If all crossings are at distance at least 1, and there is a graph homomorphism $f: G \to K_n$ that maps no pair of edges that cross in $\overline{G}$ to the same edge in $K_n$, then $X(\overline{G})\leq 2n$. Finally, if $\chi(G)\in \{2,3\}$ and all crossings are at distance at least 1, then $X(\overline{G})\leq 2\chi(G)$.

This paper deals with the problem of reconstructing the path of a vehicle in an unknown environment consisting of planar structures using sound. Many systems in the literature do this by using a loudspeaker and microphones mounted on a vehicle. Symmetries in the environment lead to solution ambiguities for such systems. We propose to resolve this issue by placing the loudspeaker at a fixed location in the environment rather than on the vehicle. The question of whether this will remove ambiguities regardless of the environment geometry leads to a question about breaking symmetries that can be phrased in purely mathematical terms. We solve this question in the affirmative if the geometry is in dimension three or bigger, and give counterexamples in dimension two. Excluding the rare situations where the counterexamples arise, we also give an affirmative answer in dimension two. Our results lead to a simple path reconstruction algorithm for a vehicle carrying four microphones navigating within an environment in which a loudspeaker at a fixed position emits short bursts of sounds. This algorithm could be combined with other methods from the literature to construct a path tracking system for vehicles navigating within a potentially symmetric environment.

The fusion of non-Abelian anyons or topological defects is a fundamental operation in measurement-only topological quantum computation. In topological superconductors, this operation amounts to a determination of the shared fermion parity of Majorana zero modes. As a step towards this, we implement a single-shot interferometric measurement of fermion parity in indium arsenide-aluminum heterostructures with a gate-defined nanowire. The interferometer is formed by tunnel-coupling the proximitized nanowire to quantum dots. The nanowire causes a state-dependent shift of these quantum dots' quantum capacitance of up to 1 fF. Our quantum capacitance measurements show flux h/2e-periodic bimodality with a signal-to-noise ratio of 1 in 3.7 $\mu$s at optimal flux values. From the time traces of the quantum capacitance measurements, we extract a dwell time in the two associated states that is longer than 1 ms at in-plane magnetic fields of approximately 2 T. These results are consistent with a measurement of the fermion parity encoded in a pair of Majorana zero modes that are separated by approximately 3 $\mu$m and subjected to a low rate of poisoning by non-equilibrium quasiparticles. The large capacitance shift and long poisoning time enable a parity measurement error probability of 1%., Comment: Added data on a second measurement of device A and a measurement of device B, expanded discussion of a trivial scenario. Refs added, author list updated

We provide a new algebraic solution procedure for the global positioning problem in $n$ dimensions using $m$ satellites. We also give a geometric characterization of the situations in which the problem does not have a unique solution. This characterization shows that such cases can happen in any dimension and with any number of satellites, leading to counterexamples to some open conjectures. We fill a gap in the literature by giving a proof for the long-held belief that when $m \ge n+2$, the solution is unique for almost all user positions. Even better, when $m \ge 2n+2$, almost all satellite configurations will guarantee a unique solution for all user positions. Some of our results are obtained using tools from algebraic geometry.

Attribution methods correspond to a class of explainability methods (XAI) that aim to assess how individual inputs contribute to a model's decision-making process. We have identified a significant limitation in one type of attribution methods, known as ``white-box" methods. Although highly efficient, as we will show, these methods rely on a gradient signal that is often contaminated by high-frequency artifacts. To overcome this limitation, we introduce a new approach called "FORGrad". This simple method effectively filters out these high-frequency artifacts using optimal cut-off frequencies tailored to the unique characteristics of each model architecture. Our findings show that FORGrad consistently enhances the performance of already existing white-box methods, enabling them to compete effectively with more accurate yet computationally demanding "black-box" methods. We anticipate that our research will foster broader adoption of simpler and more efficient white-box methods for explainability, offering a better balance between faithfulness and computational efficiency.

In recent years, concept-based approaches have emerged as some of the most promising explainability methods to help us interpret the decisions of Artificial Neural Networks (ANNs). These methods seek to discover intelligible visual 'concepts' buried within the complex patterns of ANN activations in two key steps: (1) concept extraction followed by (2) importance estimation. While these two steps are shared across methods, they all differ in their specific implementations. Here, we introduce a unifying theoretical framework that comprehensively defines and clarifies these two steps. This framework offers several advantages as it allows us: (i) to propose new evaluation metrics for comparing different concept extraction approaches; (ii) to leverage modern attribution methods and evaluation metrics to extend and systematically evaluate state-of-the-art concept-based approaches and importance estimation techniques; (iii) to derive theoretical guarantees regarding the optimality of such methods. We further leverage our framework to try to tackle a crucial question in explainability: how to efficiently identify clusters of data points that are classified based on a similar shared strategy. To illustrate these findings and to highlight the main strategies of a model, we introduce a visual representation called the strategic cluster graph. Finally, we present https://serre-lab.github.io/Lens, a dedicated website that offers a complete compilation of these visualizations for all classes of the ImageNet dataset.

Feature visualization has gained substantial popularity, particularly after the influential work by Olah et al. in 2017, which established it as a crucial tool for explainability. However, its widespread adoption has been limited due to a reliance on tricks to generate interpretable images, and corresponding challenges in scaling it to deeper neural networks. Here, we describe MACO, a simple approach to address these shortcomings. The main idea is to generate images by optimizing the phase spectrum while keeping the magnitude constant to ensure that generated explanations lie in the space of natural images. Our approach yields significantly better results (both qualitatively and quantitatively) and unlocks efficient and interpretable feature visualizations for large state-of-the-art neural networks. We also show that our approach exhibits an attribution mechanism allowing us to augment feature visualizations with spatial importance. We validate our method on a novel benchmark for comparing feature visualization methods, and release its visualizations for all classes of the ImageNet dataset on https://serre-lab.github.io/Lens/. Overall, our approach unlocks, for the first time, feature visualizations for large, state-of-the-art deep neural networks without resorting to any parametric prior image model.

In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation and the presence of inflow boundary conditions. Starting from the micro-macro reformulation of the original kinetic equation, high order time integrators are introduced. This class of numerical schemes enjoys the Asymptotic Preserving (AP) property for arbitrary initial data and degenerates when $\epsilon$ goes to zero into a high order scheme which is implicit for the diffusion term, which makes it free from the usual diffusion stability condition. The space discretization is also discussed and high order methods are also proposed based on classical finite differences schemes. The Asymptotic Preserving property is analysed and numerical results are presented to illustrate the properties of the proposed schemes in different regimes.

Numerical interactions leading to users sharing textual content published by others are naturally represented by a network where the individuals are associated with the nodes and the exchanged texts with the edges. To understand those heterogeneous and complex data structures, clustering nodes into homogeneous groups as well as rendering a comprehensible visualisation of the data is mandatory. To address both issues, we introduce Deep-LPTM, a model-based clustering strategy relying on a variational graph auto-encoder approach as well as a probabilistic model to characterise the topics of discussion. Deep-LPTM allows to build a joint representation of the nodes and of the edges in two embeddings spaces. The parameters are inferred using a variational inference algorithm. We also introduce IC2L, a model selection criterion specifically designed to choose models with relevant clustering and visualisation properties. An extensive benchmark study on synthetic data is provided. In particular, we find that Deep-LPTM better recovers the partitions of the nodes than the state-of-the art ETSBM and STBM. Eventually, the emails of the Enron company are analysed and visualisations of the results are presented, with meaningful highlights of the graph structure., Comment: 29 pages including the appendix, 13 figures, 6 tables, journal paper

Computed tomography (CT) is routinely used in clinical practice to evaluate a wide variety of medical conditions. While CT scans provide diagnoses, they also offer the ability to extract quantitative body composition metrics to analyze tissue volume and quality. Extracting quantitative body composition measures manually from CT scans is a cumbersome and time-consuming task. Proprietary software has been developed recently to automate this process, but the closed-source nature impedes widespread use. There is a growing need for fully automated body composition software that is more accessible and easier to use, especially for clinicians and researchers who are not experts in medical image processing. To this end, we have built Comp2Comp, an open-source Python package for rapid and automated body composition analysis of CT scans. This package offers models, post-processing heuristics, body composition metrics, automated batching, and polychromatic visualizations. Comp2Comp currently computes body composition measures for bone, skeletal muscle, visceral adipose tissue, and subcutaneous adipose tissue on CT scans of the abdomen. We have created two pipelines for this purpose. The first pipeline computes vertebral measures, as well as muscle and adipose tissue measures, at the T12 - L5 vertebral levels from abdominal CT scans. The second pipeline computes muscle and adipose tissue measures on user-specified 2D axial slices. In this guide, we discuss the architecture of the Comp2Comp pipelines, provide usage instructions, and report internal and external validation results to measure the quality of segmentations and body composition measures. Comp2Comp can be found at https://github.com/StanfordMIMI/Comp2Comp.

In this paper, we present a numerical strategy to check the strong stability (or GKS-stability) of one-step explicit finite difference schemes for the one-dimensional advection equation with an inflow boundary condition. The strong stability is studied using the Kreiss-Lopatinskii theory. We introduce a new tool, the intrinsic Kreiss-Lopatinskii determinant, which possesses the same regularity as the vector bundle of discrete stable solutions. By applying standard results of complex analysis to this determinant, we are able to relate the strong stability of numerical schemes to the computation of a winding number, which is robust and cheap. The study is illustrated with the O3 scheme and the fifth-order Lax-Wendroff (LW5) scheme together with a reconstruction procedure at the boundary., Comment: arXiv admin note: text overlap with arXiv:2207.10978