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Given a finite group $G$ and a commutative ring $G$-spectrum $R$, we study the separable commutative algebras in the category of compact $R$-modules. We isolate three conditions on the geometric fixed points of $R$ which ensure that every separable commutative algebra is standard, i.e. arises from a finite $G$-set. In particular we show that all separable commutative algebras in the categories of compact objects in $G$-spectra and in derived $G$-Mackey functors are standard provided that $G$ is a $p$-group. In these categories we also show that for a general finite group $G$, we cannot expect all separable commutative algebras to be standard., Comment: 26 pages

Given a symmetric monoidal stable $\infty$-category $\mathcal{C}$ which is rigidly-compactly generated and a set of compact objects $\mathcal{K}$ of $\mathcal{C}$, one can form the subcategories of $\mathcal{K}$-complete and $\mathcal{K}$-local objects. The goal of this paper is to explain how to recover $\mathcal{C}$ from its $\mathcal{K}$-local and $\mathcal{K}$-complete subcategories while retaining the symmetric monoidal structure. Specializing to the case where $\mathcal{C}$ is the $\infty$-category of $G$-spectra for a finite group $G$, our result can be viewed as a symmetric monoidal variant of the isotropy separation decomposition, a version of which appeared previously in work of Krause., Comment: 40 pages; all comments welcome!

We prove that for any presentably symmetric monoidal $\infty$-category $\mathcal{V}$, the $\infty$-category $\mathbf{Mod}_\mathcal{V}(\mathbf{Pr}^{\mathrm{L}})^{\mathrm{dbl}}$ of dualizable presentable $\mathcal{V}$-modules and internal left adjoints between them is itself presentable. Along the way, we survey formal properties of these dualizable $\mathcal V$-modules. We pay close attention to the case of the $\infty$-category of spectra, where we survey the foundational properties of ``compact morphisms''., Comment: 80 pages; comments welcome!

We survey the theory of locally rigid and rigid symmetric monoidal $\infty$-categories over an arbitrary base $\mathcal{V}\in\mathrm{CAlg}(\mathbf{Pr}^\mathrm{L})$. Along the way, we introduce and study ``$\mathcal{V}$-atomic morphisms'', which are analogues of compact morphisms over an arbitrary base $\mathcal{V}$., Comment: 59 pages, comments welcome!

Left ventricular ejection fraction (LVEF) is the most important clinical parameter of cardiovascular function. The accuracy in estimating this parameter is highly dependent upon the precise segmentation of the left ventricle (LV) structure at the end diastole and systole phases. Therefore, it is crucial to develop robust algorithms for the precise segmentation of the heart structure during different phases. Methodology: In this work, an improved 3D UNet model is introduced to segment the myocardium and LV, while excluding papillary muscles, as per the recommendation of the Society for Cardiovascular Magnetic Resonance. For the practical testing of the proposed framework, a total of 8,400 cardiac MRI images were collected and analysed from the military hospital in Tunis (HMPIT), as well as the popular ACDC public dataset. As performance metrics, we used the Dice coefficient and the F1 score for validation/testing of the LV and the myocardium segmentation. Results: The data was split into 70%, 10%, and 20% for training, validation, and testing, respectively. It is worth noting that the proposed segmentation model was tested across three axis views: basal, medio basal and apical at two different cardiac phases: end diastole and end systole instances. The experimental results showed a Dice index of 0.965 and 0.945, and an F1 score of 0.801 and 0.799, at the end diastolic and systolic phases, respectively. Additionally, clinical evaluation outcomes revealed a significant difference in the LVEF and other clinical parameters when the papillary muscles were included or excluded.

Vision Language Models (VLMs) have demonstrated remarkable capabilities in various open-vocabulary tasks, yet their zero-shot performance lags behind task-specific finetuned models, particularly in complex tasks like Referring Expression Comprehension (REC). Fine-tuning usually requires 'white-box' access to the model's architecture and weights, which is not always feasible due to proprietary or privacy concerns. In this work, we propose LLM-wrapper, a method for 'black-box' adaptation of VLMs for the REC task using Large Language Models (LLMs). LLM-wrapper capitalizes on the reasoning abilities of LLMs, improved with a light fine-tuning, to select the most relevant bounding box matching the referring expression, from candidates generated by a zero-shot black-box VLM. Our approach offers several advantages: it enables the adaptation of closed-source models without needing access to their internal workings, it is versatile as it works with any VLM, it transfers to new VLMs, and it allows for the adaptation of an ensemble of VLMs. We evaluate LLM-wrapper on multiple datasets using different VLMs and LLMs, demonstrating significant performance improvements and highlighting the versatility of our method. While LLM-wrapper is not meant to directly compete with standard white-box fine-tuning, it offers a practical and effective alternative for black-box VLM adaptation. The code will be open-sourced., Comment: v1 at EVAL-FoMo workshop, ECCV 2024

Field-aware Factorization Machines (FFMs) have emerged as a powerful model for click-through rate prediction, particularly excelling in capturing complex feature interactions. In this work, we present an in-depth analysis of our in-house, Rust-based Deep FFM implementation, and detail its deployment on a CPU-only, multi-data-center scale. We overview key optimizations devised for both training and inference, demonstrated by previously unpublished benchmark results in efficient model search and online training. Further, we detail an in-house weight quantization that resulted in more than an order of magnitude reduction in bandwidth footprint related to weight transfers across data-centres. We disclose the engine and associated techniques under an open-source license to contribute to the broader machine learning community. This paper showcases one of the first successful CPU-only deployments of Deep FFMs at such scale, marking a significant stride in practical, low-footprint click-through rate prediction methodologies., Comment: 6p, KDD2024 - AdKDD workshop

Graph Neural Networks (GNNs), especially message-passing-based models, have become prominent in top-k recommendation tasks, outperforming matrix factorization models due to their ability to efficiently aggregate information from a broader context. Although GNNs are evaluated with ranking-based metrics, e.g NDCG@k and Recall@k, they remain largely trained with proxy losses, e.g the BPR loss. In this work we explore the use of ranking loss functions to directly optimize the evaluation metrics, an area not extensively investigated in the GNN community for collaborative filtering. We take advantage of smooth approximations of the rank to facilitate end-to-end training of GNNs and propose a Personalized PageRank-based negative sampling strategy tailored for ranking loss functions. Moreover, we extend the evaluation of GNN models for top-k recommendation tasks with an inductive user-centric protocol, providing a more accurate reflection of real-world applications. Our proposed method significantly outperforms the standard BPR loss and more advanced losses across four datasets and four recent GNN architectures while also exhibiting faster training. Demonstrating the potential of ranking loss functions in improving GNN training for collaborative filtering tasks.

Prompt learning has been widely adopted to efficiently adapt vision-language models (VLMs), e.g. CLIP, for few-shot image classification. Despite their success, most prompt learning methods trade-off between classification accuracy and robustness, e.g. in domain generalization or out-of-distribution (OOD) detection. In this work, we introduce Global-Local Prompts (GalLoP), a new prompt learning method that learns multiple diverse prompts leveraging both global and local visual features. The training of the local prompts relies on local features with an enhanced vision-text alignment. To focus only on pertinent features, this local alignment is coupled with a sparsity strategy in the selection of the local features. We enforce diversity on the set of prompts using a new ``prompt dropout'' technique and a multiscale strategy on the local prompts. GalLoP outperforms previous prompt learning methods on accuracy on eleven datasets in different few shots settings and with various backbones. Furthermore, GalLoP shows strong robustness performances in both domain generalization and OOD detection, even outperforming dedicated OOD detection methods. Code and instructions to reproduce our results: https://github.com/MarcLafon/gallop.

Flow estimation problems are ubiquitous in scientific imaging. Often, the underlying flows are subject to physical constraints that can be exploited in the flow estimation; for example, incompressible (divergence-free) flows are expected for many fluid experiments, while irrotational (curl-free) flows arise in the analysis of optical distortions and wavefront sensing. In this work, we propose a Physics- Inspired Neural Network (PINN) named HDNet, which performs a Helmholtz decomposition of an arbitrary flow field, i.e., it decomposes the input flow into a divergence-only and a curl-only component. HDNet can be trained exclusively on synthetic data generated by reverse Helmholtz decomposition, which we call Helmholtz synthesis. As a PINN, HDNet is fully differentiable and can easily be integrated into arbitrary flow estimation problems.

With the ever-growing power of generative artificial intelligence, deepfake and artificially generated (synthetic) media have continued to spread online, which creates various ethical and moral concerns regarding their usage. To tackle this, we thus present a novel exploration of the trends and patterns observed in real, deepfake and synthetic facial images. The proposed analysis is done in two parts: firstly, we incorporate eight deep learning models and analyze their performances in distinguishing between the three classes of images. Next, we look to further delve into the similarities and differences between these three sets of images by investigating their image properties both in the context of the entire image as well as in the context of specific regions within the image. ANOVA test was also performed and provided further clarity amongst the patterns associated between the images of the three classes. From our findings, we observe that the investigated deeplearning models found it easier to detect synthetic facial images, with the ViT Patch-16 model performing best on this task with a class-averaged sensitivity, specificity, precision, and accuracy of 97.37%, 98.69%, 97.48%, and 98.25%, respectively. This observation was supported by further analysis of various image properties. We saw noticeable differences across the three category of images. This analysis can help us build better algorithms for facial image generation, and also shows that synthetic, deepfake and real face images are indeed three different classes.

We prove that any spectrum is equivalent to the nonconnective K-theory of a stable $\infty$-category. We use these results to construct a stable $\infty$-category $\mathcal{C}$ with a bounded t-structure such that $\operatorname{K}(\mathcal{C})$ is not equivalent to $\operatorname{K}(\mathcal{C}^\heartsuit)$, disproving a conjecture of Antieau, Gepner, and Heller., Comment: 17 pages

In image retrieval, standard evaluation metrics rely on score ranking, \eg average precision (AP), recall at k (R@k), normalized discounted cumulative gain (NDCG). In this work we introduce a general framework for robust and decomposable rank losses optimization. It addresses two major challenges for end-to-end training of deep neural networks with rank losses: non-differentiability and non-decomposability. Firstly we propose a general surrogate for ranking operator, SupRank, that is amenable to stochastic gradient descent. It provides an upperbound for rank losses and ensures robust training. Secondly, we use a simple yet effective loss function to reduce the decomposability gap between the averaged batch approximation of ranking losses and their values on the whole training set. We apply our framework to two standard metrics for image retrieval: AP and R@k. Additionally we apply our framework to hierarchical image retrieval. We introduce an extension of AP, the hierarchical average precision $\mathcal{H}$-AP, and optimize it as well as the NDCG. Finally we create the first hierarchical landmarks retrieval dataset. We use a semi-automatic pipeline to create hierarchical labels, extending the large scale Google Landmarks v2 dataset. The hierarchical dataset is publicly available at https://github.com/cvdfoundation/google-landmark. Code will be released at https://github.com/elias-ramzi/SupRank., Comment: arXiv admin note: text overlap with arXiv:2207.04873

The use of the un-indexed web, commonly known as the deep web and dark web, to commit or facilitate criminal activity has drastically increased over the past decade. The dark web is an in-famously dangerous place where all kinds of criminal activities take place [1-2], despite advances in web forensics techniques, tools, and methodologies, few studies have formally tackled the dark and deep web forensics and the technical differences in terms of investigative techniques and artefacts identification and extraction. This research proposes a novel and comprehensive protocol to guide and assist digital forensics professionals in investigating crimes committed on or via the deep and dark web, The protocol named D2WFP establishes a new sequential approach for performing investigative activities by observing the order of volatility and implementing a systemic approach covering all browsing related hives and artefacts which ultimately resulted into improv-ing the accuracy and effectiveness. Rigorous quantitative and qualitative research has been conducted by assessing D2WFP following a scientifically-sound and comprehensive process in different scenarios and the obtained results show an apparent increase in the number of artefacts re-covered when adopting D2WFP which outperform any current industry or opensource browsing forensics tools. The second contribution of D2WFP is the robust formulation of artefact correlation and cross-validation within D2WFP which enables digital forensics professionals to better document and structure their analysis of host-based deep and dark web browsing artefacts.

The study was conducted at the Collage of Agricultural Engineering Sciences, University of Sulaimani, Kurdistan Region-Iraq so as to investigate response hardwood cuttings of Callistemon viminalis to some plant extracts. The hardwood cuttings were taken on 11 March 2021 and soaked separately in 3 and 6 g/L aqueous extracts of moringa leaf, licorice root, willow shoot, fenugreek seed and cinnamon bark for 1 hour. They were compared to the cuttings dipped in 3000 ppm IBA for 10s and control cuttings which were soaked in distilled water for 1 hour. The experiment laid out in CRD with three replications in a greenhouse, and each replication included six cuttings which planted in a mixture of sand and rice husk medium. The results showed that the highest (86.66%) rooting was achieved in the cuttings treated with 6 g/L licorice extract and they were significantly different with control cuttings (53.33%), but they were not significantly different with 3000 ppm IBA (66.66%). Cinnamon 3g/L and fenugreek 3g/L extracts gave the lowest (6.66% and 33.33%, respectively) rooting and other studied parameters. The cuttings dipped in 3000 ppm IBA gave the highest (18.91) root number and the highest (66.66%) survival cuttings after transplanting. The longest root (15.54 cm) was found in cuttings were treated with 6 g/L moringa extract. The longest (5.83 cm) shoot was observed in treated cuttings with 3 g/L willow extract. The highest chlorophyll a and b (10.08 and 4.62 mg/L, respectively) were observed in cuttings treated with 6 g/L willow extract. Moreover, 3000 ppm IBA gave the highest (20.23%) total carbohydrate and (1.77 mg/g) IAA content along with 6 g/L licorice, moringa and fenugreek extracts, after 30 days from planting of the cuttings. Licorice root extract at 6 g/L fairly improved the measurements similar to 3000 ppm IBA throughout the study.

For a field extension $L/K$ we consider maps that are quadratic over $L$ but whose polarisation is only bilinear over $K$. Our main result is that all such are automatically quadratic forms over $L$ in the usual sense if and only if $L/K$ is formally unramified. In particular, this shows that over finite and number fields, one of the axioms in the standard definition of quadratic forms is superfluous., Comment: 13 pages, v3: Minor changes, to appear in Bulletin of the LMS

Anti-forensics techniques particularly steganography and cryptography have become increasingly pressing issues that affect the current digital forensics practice. This paper advances the automation of hidden evidence extraction in the context of audio files by proposing a novel multi-approaches method which enables the correlation between unprocessed artefacts, indexed and live forensics analysis and traditional Steganographic and Cryptographic detection techniques. In this work, we opted for experimental research methodology in the form of a quantitative analysis of the efficiency of the proposed automation detecting and extracting hidden artefacts in WAV and MP3 audio files by comparing it to standard industry systems. This work advances the current automation in extracting evidence hidden by Cryptographic and Steganographic techniques during forensics investigations, the proposed multi-approaches demonstrated a clear enhancement in terms of coverage and accuracy notably on large audio files (MP3 and WAV) for which the manual forensics analysis is complex, time-consuming and requires significant expertise. Nonetheless, the proposed multi-approach automation may occasionally produce false positives (detecting steganography where none exists) or false negatives (failing to detect steganography that is present) but overall achieve a good balance between efficiently and effectively detecting hidden evidence and minimising the false negative which validates its reliability., Comment: Journal of Information Security and Cybercrimes Research- Post Review V3.1

We study the notion of \emph{separable algebras} in the context of symmetric monoidal stable $\infty$-categories. In the first part of this paper, we compare this context to that of tensor-triangulated categories and show that separable algebras and their modules in a symmetric monoidal stable $\infty$-category are, in large parts, controlled by the (tensor-triangulated) homotopy category. We also study a variant of this notion, which we call ind-separability. Among other things, this provides a partially new proof of the Goerss--Hopkins--Miller theorem about the uniqueness of $\mathbb E_\infty$-structures on Morava $E$-theory. We later initiate a study of separable algebras \textit{\`a la} Auslander-Goldman by relating them to Azumaya algebras, and prove in some restrictive cases that centers of separable algebras are separable. Finally, we study the Hochschild homology of separable algebras and prove some descent results in topological Hochschild homology., Comment: 89 pages; v2: A mistake in section 4 was corrected (it does not affect the main example in this section); the following changes have also been made: the proof of theorem 2.15 was simplified; I have expanded upon the ind-separability of Lubin-Tate theories based on other perfect rings; and I have added an example of an applications of my results

Out-of-distribution (OOD) detection is a critical requirement for the deployment of deep neural networks. This paper introduces the HEAT model, a new post-hoc OOD detection method estimating the density of in-distribution (ID) samples using hybrid energy-based models (EBM) in the feature space of a pre-trained backbone. HEAT complements prior density estimators of the ID density, e.g. parametric models like the Gaussian Mixture Model (GMM), to provide an accurate yet robust density estimation. A second contribution is to leverage the EBM framework to provide a unified density estimation and to compose several energy terms. Extensive experiments demonstrate the significance of the two contributions. HEAT sets new state-of-the-art OOD detection results on the CIFAR-10 / CIFAR-100 benchmark as well as on the large-scale Imagenet benchmark. The code is available at: https://github.com/MarcLafon/heatood.

Implicit deep learning has recently gained popularity with applications ranging from meta-learning to Deep Equilibrium Networks (DEQs). In its general formulation, it relies on expressing some components of deep learning pipelines implicitly, typically via a root equation called the inner problem. In practice, the solution of the inner problem is approximated during training with an iterative procedure, usually with a fixed number of inner iterations. During inference, the inner problem needs to be solved with new data. A popular belief is that increasing the number of inner iterations compared to the one used during training yields better performance. In this paper, we question such an assumption and provide a detailed theoretical analysis in a simple setting. We demonstrate that overparametrization plays a key role: increasing the number of iterations at test time cannot improve performance for overparametrized networks. We validate our theory on an array of implicit deep-learning problems. DEQs, which are typically overparametrized, do not benefit from increasing the number of iterations at inference while meta-learning, which is typically not overparametrized, benefits from it.

Social touch provides a rich non-verbal communication channel between humans and robots. Prior work has identified a set of touch gestures for human-robot interaction and described them with natural language labels (e.g., stroking, patting). Yet, no data exists on the semantic relationships between the touch gestures in users' minds. To endow robots with touch intelligence, we investigated how people perceive the similarities of social touch labels from the literature. In an online study, 45 participants grouped 36 social touch labels based on their perceived similarities and annotated their groupings with descriptive names. We derived quantitative similarities of the gestures from these groupings and analyzed the similarities using hierarchical clustering. The analysis resulted in 9 clusters of touch gestures formed around the social, emotional, and contact characteristics of the gestures. We discuss the implications of our results for designing and evaluating touch sensing and interactions with social robots., Comment: 8 pages

We present here an inertial active spinning swarm consisting of mixtures of opposite handedness torque driven spinners floating on an air bed with low damping. Depending on the relative spin sign, spinners can act as their own anti-particles and annihilate their spins. Rotational energy can become highly focused, with minority fraction spinners pumped to very high levels of spin angular momentum. Spinner handedness also matters at high spinner densities but not low densities: oscillations in the mixing spatial entropy of spinners over time emerge if there is a net spin imbalance from collective rotations. Geometrically confined spinners can lock themselves into frustrated spin states.

As a beloved sport worldwide, dancing is getting integrated into traditional and virtual reality-based gaming platforms nowadays. It opens up new opportunities in the technology-mediated dancing space. These platforms primarily rely on passive and continuous human pose estimation as an input capture mechanism. Existing solutions are mainly based on RGB or RGB-Depth cameras for dance games. The former suffers in low-lighting conditions due to the motion blur and low sensitivity, while the latter is too power-hungry, has a low frame rate, and has limited working distance. With ultra-low latency, energy efficiency, and wide dynamic range characteristics, the event camera is a promising solution to overcome these shortcomings. We propose YeLan, an event camera-based 3-dimensional high-frequency human pose estimation(HPE) system that survives low-lighting conditions and dynamic backgrounds. We collected the world's first event camera dance dataset and developed a fully customizable motion-to-event physics-aware simulator. YeLan outperforms the baseline models in these challenging conditions and demonstrated robustness against different types of clothing, background motion, viewing angle, occlusion, and lighting fluctuations.

The goal of this paper is to provide a simple approach to perform local sensitivity analysis using Physics-informed neural networks (PINN). The main idea lies in adding a new term in the loss function that regularizes the solution in a small neighborhood near the nominal value of the parameter of interest. The added term represents the derivative of the loss function with respect to the parameter of interest. The result of this modification is a solution to the problem along with the derivative of the solution with respect to the parameter of interest (the sensitivity). We call the new technique SA-PNN which stands for sensitivity analysis in PINN. The effectiveness of the technique is shown using four examples: the first one is a simple one-dimensional advection-diffusion problem to show the methodology, the second is a two-dimensional Poisson's problem with nine parameters of interest, and the third and fourth examples are one and two-dimensional transient two-phase flow in porous media problem., Comment: 22 pages, 11 figures

We present a robust, privacy-preserving visual localization algorithm using event cameras. While event cameras can potentially make robust localization due to high dynamic range and small motion blur, the sensors exhibit large domain gaps making it difficult to directly apply conventional image-based localization algorithms. To mitigate the gap, we propose applying event-to-image conversion prior to localization which leads to stable localization. In the privacy perspective, event cameras capture only a fraction of visual information compared to normal cameras, and thus can naturally hide sensitive visual details. To further enhance the privacy protection in our event-based pipeline, we introduce privacy protection at two levels, namely sensor and network level. Sensor level protection aims at hiding facial details with lightweight filtering while network level protection targets hiding the entire user's view in private scene applications using a novel neural network inference pipeline. Both levels of protection involve light-weight computation and incur only a small performance loss. We thus project our method to serve as a building block for practical location-based services using event cameras. The code and dataset will be made public through the following link: https://github.com/82magnolia/event_localization.

We study the asymptotic behavior of trajectories of the continuous dynamical system (CDS) associated to the the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi in 2000 [A. Moudafi, Viscosity approximation methods for fixed points problems, J. Math. Anal. Appl. 241 (2000), 46-55]. We establish that the trajectories $x(t)$ of the system (CDS) and the sequences $(x_{n})$ generated by the the discrete process (DDS) have a very similar asymptotic behaviors., Comment: 12 pages

In this short paper, we give two proofs that the Euler characteristic is multiplicative, for fiber sequences of finitely dominated spaces. This is equivalent to proving that the Becker-Gottlieb transfer is functorial on $\pi_0$., Comment: Accepted version. 13 pages plus references

This thesis proposes novel ternary circuits aiming to reduce energy to preserve battery consumption. The proposed designs include eight ternary logic gates, three ternary combinational circuits, and six Ternary Arithmetic Logic Units. This thesis applies the best tradeoff between reducing the number of used transistors, utilizing energy efficient transistor arrangements such as transmission gates, and applying the dual supply voltages to achieve its objective. The proposed designs are compared to the latest ternary circuits using the HSPICE simulator for different supply voltages, different temperatures, and different frequencies. Simulations are performed to prove the efficiency of the proposed designs. The results demonstrate the advantage of the proposed designs with a reduction of over 73 percent in terms of transistor count for the THA and over 88 percent in energy consumption for the STI, TNAND, TDecoder, TMUX, THA, and TMUL, respectively. Moreover, the noise immunity curve and Monte Carlo analysis for major process variations, TOX, CNT Diameter, CNT Count, and Channel length, were studied., Comment: Ph.D. Dissertation

We develop a theory of generalized characters of local systems in $\infty$-categories, which extends classical character theory for group representations and, in particular, the induced character formula. A key aspect of our approach is that we utilize the interaction between traces and their categorifications. We apply this theory to reprove and refine various results on the composability of Becker-Gottlieb transfers, the Hochschild homology of Thom spectra, and the additivity of traces in stable $\infty$-categories., Comment: 94 pages, comments welcome! v2: updated exposition and terminology in section 4.2

We give a short proof that the Yoneda embedding is natural for $\infty$-categories, and further prove that the space of natural transformations that are, pointwise, the Yoneda embedding, is contractible., Comment: 7 pages, comments welcome ! v3: changed the title following a suggestion from the referee; added a paragraph about uniqueness; rewrote the introduction to require less background; and finally made some minor modifications. This is the accepted version. Now 10 pages

We construct a monoidal version of Lurie's un/straightening equivalence. In more detail, for any symmetric monoidal $\infty$-category $\mathbf C$, we endow the $\infty$-category of coCartesian fibrations over $\mathbf C$ with a (naturally defined) symmetric monoidal structure, and prove that it is equivalent the Day convolution monoidal structure on the $\infty$-category of functors from $\mathbf C$ to $\mathbf{Cat}_\infty$. In fact, we do this over any $\infty$-operad by categorifying this statement and thereby proving a stronger statement about the functors that assign to an $\infty$-category $\mathbf C$ its category of coCartesian fibrations on the one hand, and its category of functors to $\mathbf{Cat}_\infty$ on the other hand., Comment: 30 pages, comments welcome !

Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% \mathcal{H}$, $S:Q\rightarrow Q$ a nonexpansive mapping, $A:Q\rightarrow Q$ an inverse strongly monotone operator, and $f:Q\rightarrow Q$ a contraction mapping. We prove, under appropriate conditions on the real sequences $% \{\alpha_{n}\}$ and $\{\lambda_{n}\},$ that for any starting point $x_{1}$ in $Q,$ the sequence $\{x_{n}\}$ generated by the iterative process \begin{equation} x_{n+1}=\alpha_{n}f(x_{n})+(1-\alpha_{n})SP_{Q}(x_{n}-\lambda_{n}Ax_{n}) \label{Alg} \end{equation} converges strongly to a particular element of the set $F_{ix}(S)\cap S_{VI(A,Q)}$ which we suppose that it is nonempty, where $F_{ix}(S)$ is the set of fixed point of the mapping $% S$ and $S_{VI(A,Q)}$ is the set of $q\in Q$ such that $\langle Aq,x-q\rangle\geq0$ for every $x\in Q.$ Moreover, we study the strong convergence of a perturbed version of the algorithm generated by the above process. Finally, we apply the main result to construct an algorithm associated to a constrained convex optimization problem and we provide a numerical experiment to emphasize the effect of the parameter $\{\alpha_{n}\}$ on the convergence rate of this algorithm., Comment: 16 pages, 1 figure

Image Retrieval is commonly evaluated with Average Precision (AP) or Recall@k. Yet, those metrics, are limited to binary labels and do not take into account errors' severity. This paper introduces a new hierarchical AP training method for pertinent image retrieval (HAP-PIER). HAPPIER is based on a new H-AP metric, which leverages a concept hierarchy to refine AP by integrating errors' importance and better evaluate rankings. To train deep models with H-AP, we carefully study the problem's structure and design a smooth lower bound surrogate combined with a clustering loss that ensures consistent ordering. Extensive experiments on 6 datasets show that HAPPIER significantly outperforms state-of-the-art methods for hierarchical retrieval, while being on par with the latest approaches when evaluating fine-grained ranking performances. Finally, we show that HAPPIER leads to better organization of the embedding space, and prevents most severe failure cases of non-hierarchical methods. Our code is publicly available at: https://github.com/elias-ramzi/HAPPIER.

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automate, reproduce and publish optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard learning tasks: $\ell_2$-regularized logistic regression, Lasso, and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of the state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details. We hope that Benchopt will foster collaborative work in the community hence improving the reproducibility of research findings., Comment: Accepted in proceedings of NeurIPS 22; Benchopt library documentation is available at https://benchopt.github.io/

Wide-field searches for young stellar objects (YSOs) can place useful constraints on the prevalence of clustered versus distributed star formation. The Spitzer/IRAC Candidate YSO (SPICY) catalog is one of the largest compilations of such objects (~120,000 candidates in the Galactic midplane). Many SPICY candidates are spatially clustered, but, perhaps surprisingly, approximately half the candidates appear spatially distributed. To better characterize this unexpected population and confirm its nature, we obtained Palomar/DBSP spectroscopy for 26 of the optically-bright (G<15 mag) "isolated" YSO candidates. We confirm the YSO classifications of all 26 sources based on their positions on the Hertzsprung-Russell diagram, H and Ca II line-emission from over half the sample, and robust detection of infrared excesses. This implies a contamination rate of <10% for SPICY stars that meet our optical selection criteria. Spectral types range from B4 to K3, with A-type stars most common. Spectral energy distributions, diffuse interstellar bands, and Galactic extinction maps indicate moderate to high extinction. Stellar masses range from ~1 to 7 $M_\odot$, and the estimated accretion rates, ranging from $3\times10^{-8}$ to $3\times10^{-7}$ $M_\odot$ yr$^{-1}$, are typical for YSOs in this mass range. The 3D spatial distribution of these stars, based on Gaia astrometry, reveals that the "isolated" YSOs are not evenly distributed in the Solar neighborhood but are concentrated in kpc-scale dusty Galactic structures that also contain the majority of the SPICY YSO clusters. Thus, the processes that produce large Galactic star-forming structures may yield nearly as many distributed as clustered YSOs., Comment: Accepted for publication in AJ. 22 pages, 9 figures, and 4 tables. Figure sets are available from https://sites.astro.caltech.edu/~mkuhn/SPICY/PaperIII/

Neural rendering with implicit neural networks has recently emerged as an attractive proposition for scene reconstruction, achieving excellent quality albeit at high computational cost. While the most recent generation of such methods has made progress on the rendering (inference) times, very little progress has been made on improving the reconstruction (training) times. In this work, we present Neural Adaptive Scene Tracing (NAScenT), the first neural rendering method based on directly training a hybrid explicit-implicit neural representation. NAScenT uses a hierarchical octree representation with one neural network per leaf node and combines this representation with a two-stage sampling process that concentrates ray samples where they matter most near object surfaces. As a result, NAScenT is capable of reconstructing challenging scenes including both large, sparsely populated volumes like UAV captured outdoor environments, as well as small scenes with high geometric complexity. NAScenT outperforms existing neural rendering approaches in terms of both quality and training time., Comment: 27 pages

In this paper, we present Neural Adaptive Tomography (NeAT), the first adaptive, hierarchical neural rendering pipeline for multi-view inverse rendering. Through a combination of neural features with an adaptive explicit representation, we achieve reconstruction times far superior to existing neural inverse rendering methods. The adaptive explicit representation improves efficiency by facilitating empty space culling and concentrating samples in complex regions, while the neural features act as a neural regularizer for the 3D reconstruction. The NeAT framework is designed specifically for the tomographic setting, which consists only of semi-transparent volumetric scenes instead of opaque objects. In this setting, NeAT outperforms the quality of existing optimization-based tomography solvers while being substantially faster.

Compressed sensing (CS) in Magnetic resonance Imaging (MRI) essentially involves the optimization of 1) the sampling pattern in k-space under MR hardware constraints and 2) image reconstruction from the undersampled k-space data. Recently, deep learning methods have allowed the community to address both problems simultaneously, especially in the non-Cartesian acquisition setting. This paper aims to contribute to this field by tackling some major concerns in existing approaches.Regarding the learning of the sampling pattern, we perform ablation studies using parameter-free reconstructions like the density compensated (DCp) adjoint operator of the nonuniform fast Fourier transform (NUFFT) to ensure that the learned k-space trajectories actually sample the center of k-space densely. Additionally we optimize these trajectories by embedding a projected gradient descent algorithm over the hardware MR constraints. Later, we introduce a novel hybrid learning approach that operates across multiple resolutions to jointly optimize the reconstruction network and the k-space trajectory and present improved image reconstruction quality at 20-fold acceleration factor on T1 and T2-weighted images on the fastMRI dataset with SSIM scores of nearly 0.92-0.95 in our retrospective studies.

In image retrieval, standard evaluation metrics rely on score ranking, e.g. average precision (AP). In this paper, we introduce a method for robust and decomposable average precision (ROADMAP) addressing two major challenges for end-to-end training of deep neural networks with AP: non-differentiability and non-decomposability. Firstly, we propose a new differentiable approximation of the rank function, which provides an upper bound of the AP loss and ensures robust training. Secondly, we design a simple yet effective loss function to reduce the decomposability gap between the AP in the whole training set and its averaged batch approximation, for which we provide theoretical guarantees. Extensive experiments conducted on three image retrieval datasets show that ROADMAP outperforms several recent AP approximation methods and highlight the importance of our two contributions. Finally, using ROADMAP for training deep models yields very good performances, outperforming state-of-the-art results on the three datasets.

This paper aims to provide a machine learning framework to simulate two-phase flow in porous media. The proposed algorithm is based on Physics-informed neural networks (PINN). A novel residual-based adaptive PINN is developed and compared with the residual-based adaptive refinement (RAR) method and with PINN with fixed collocation points. The proposed algorithm is expected to have great potential to be applied to different fields where adaptivity is needed. In this paper, we focus on the two-phase flow in porous media problem. We provide two numerical examples to show the effectiveness of the new algorithm. It is found that adaptivity is essential to capture moving flow fronts. We show how the results obtained through this approach are more accurate than using RAR method or PINN with fixed collocation points, while having a comparable computational cost.

This paper proposes a pipeline to automatically track and measure displacement and vibration of structural specimens during laboratory experiments. The latest Mask Regional Convolutional Neural Network (Mask R-CNN) can locate the targets and monitor their movement from videos recorded by a stationary camera. To improve precision and remove the noise, techniques such as Scale-invariant Feature Transform (SIFT) and various filters for signal processing are included. Experiments on three small-scale reinforced concrete beams and a shaking table test are utilized to verify the proposed method. Results show that the proposed deep learning method can achieve the goal to automatically and precisely measure the motion of tested structural members during laboratory experiments.

We prove a version of J.P. May's theorem on the additivity of traces, in symmetric monoidal stable $\infty$-categories. Our proof proceeds via a categorification, namely we use the additivity of topological Hochschild homology as an invariant of stable $\infty$-categories and construct a morphism of spectra $\mathrm{THH}(\mathbf C)\to \mathrm{End}(\mathbf 1_\mathbf C)$ for $\mathbf C$ a stably symmetric monoidal rigid $\infty$-category. We also explain how to get a more general statement involving traces of finite (homotopy) colimits., Comment: 12 pages, comments welcome ! New version: corrected typos, fixed some references, and added two remarks

We perform a qualitative analysis of performance of XPDNet, a state-of-the-art deep learning approach for MRI reconstruction, compared to GRAPPA, a classical approach. We do this in multiple settings, in particular testing the robustness of the XPDNet to unseen settings, and show that the XPDNet can to some degree generalize well., Comment: Presented at ISMRM 2021

In recent years, implicit deep learning has emerged as a method to increase the effective depth of deep neural networks. While their training is memory-efficient, they are still significantly slower to train than their explicit counterparts. In Deep Equilibrium Models (DEQs), the training is performed as a bi-level problem, and its computational complexity is partially driven by the iterative inversion of a huge Jacobian matrix. In this paper, we propose a novel strategy to tackle this computational bottleneck from which many bi-level problems suffer. The main idea is to use the quasi-Newton matrices from the forward pass to efficiently approximate the inverse Jacobian matrix in the direction needed for the gradient computation. We provide a theorem that motivates using our method with the original forward algorithms. In addition, by modifying these forward algorithms, we further provide theoretical guarantees that our method asymptotically estimates the true implicit gradient. We empirically study this approach and the recent Jacobian-Free method in different settings, ranging from hyperparameter optimization to large Multiscale DEQs (MDEQs) applied to CIFAR and ImageNet. Both methods reduce significantly the computational cost of the backward pass. While SHINE has a clear advantage on hyperparameter optimization problems, both methods attain similar computational performances for larger scale problems such as MDEQs at the cost of a limited performance drop compared to the original models., Comment: Accepted as a spotlight to ICLR 2022

Collision avoidance algorithms are of central interest to many drone applications. In particular, decentralized approaches may be the key to enabling robust drone swarm solutions in cases where centralized communication becomes computationally prohibitive. In this work, we draw biological inspiration from flocks of starlings (Sturnus vulgaris) and apply the insight to end-to-end learned decentralized collision avoidance. More specifically, we propose a new, scalable observation model following a biomimetic nearest-neighbor information constraint that leads to fast learning and good collision avoidance behavior. By proposing a general reinforcement learning approach, we obtain an end-to-end learning-based approach to integrating collision avoidance with arbitrary tasks such as package collection and formation change. To validate the generality of this approach, we successfully apply our methodology through motion models of medium complexity, modeling momentum and nonetheless allowing direct application to real world quadrotors in conjunction with a standard PID controller. In contrast to prior works, we find that in our sufficiently rich motion model, nearest-neighbor information is indeed enough to learn effective collision avoidance behavior. Our learned policies are tested in simulation and subsequently transferred to real-world drones to validate their real-world applicability., Comment: Accepted to the 39th IEEE Conference on Robotics and Automation (ICRA). Fixed some typos

The SPARKLING algorithm was originally developed for accelerated 2D magnetic resonance imaging (MRI) in the compressed sensing (CS) context. It yields non-Cartesian sampling trajectories that jointly fulfill a target sampling density while each individual trajectory complies with MR hardware constraints. However, the two main limitations of SPARKLING are first that the optimal target sampling density is unknown and thus a user-defined parameter and second that this sampling pattern generation remains disconnected from MR image reconstruction thus from the optimization of image quality. Recently, datadriven learning schemes such as LOUPE have been proposed to learn a discrete sampling pattern, by jointly optimizing the whole pipeline from data acquisition to image reconstruction. In this work, we merge these methods with a state-of-the-art deep neural network for image reconstruction, called XPDNET, to learn the optimal target sampling density. Next, this density is used as input parameter to SPARKLING to obtain 20x accelerated non-Cartesian trajectories. These trajectories are tested on retrospective compressed sensing (CS) studies and show superior performance in terms of image quality with both deep learning (DL) and conventional CS reconstruction schemes.

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on solving a least-squares optimization problem, penalized by the L_1 norm of the remaining variables. Then, the component with maximum amplitude is selected. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms and Basis Pursuit Denoising when the solution is sparse., Comment: in Proceedings of iTWIST'20, Paper-ID: 24, Nantes, France, December, 2-4, 2020

Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% \mathcal{H}$. $T:Q\rightarrow Q$ is a nonexpansive mapping which has a least one fixed point. $f:Q\rightarrow \mathcal{H}$ is a Lipschitzian function, and $% F:Q\rightarrow \mathcal{H}$ is a Lipschitzian and strongly monotone mapping. We prove, under appropriate conditions on the functions $f$ and $F$, the control real sequences $\{\alpha _{n}\}$ and $\{\beta _{n}\},$ and the error term $\{e_{n}\},$ that for any starting point $x_{0}$ in $Q,$ the sequence $% \{x_{n}\}$ generated by the perturbed iterative process \[ x_{n+1}=\beta _{n}x_{n}+(1-\beta _{n})P_{Q}\left( \alpha _{n}f(x_{n})+(I-\alpha _{n}F)Tx_{n}+e_{n}\right) \] converges strongly to the unique solution of the variational inequality problem \[ \text{Find }q\in C\text{ such that }\langle F(q)-f(q),x-q\rangle \geq 0\text{ for all }x\in C \] where $C=F_{ix}(T)$ is the set of fixed points of $T.$ Our main result unifies and extends many well-known previous results., Comment: 12 pages

Deep neural networks have recently been thoroughly investigated as a powerful tool for MRI reconstruction. There is a lack of research, however, regarding their use for a specific setting of MRI, namely non-Cartesian acquisitions. In this work, we introduce a novel kind of deep neural networks to tackle this problem, namely density compensated unrolled neural networks, which rely on Density Compensation to correct the uneven weighting of the k-space. We assess their efficiency on the publicly available fastMRI dataset, and perform a small ablation study. Our results show that the density-compensated unrolled neural networks outperform the different baselines, and that all parts of the design are needed. We also open source our code, in particular a Non-Uniform Fast Fourier transform for TensorFlow.

Accelerating MRI scans is one of the principal outstanding problems in the MRI research community. Towards this goal, we hosted the second fastMRI competition targeted towards reconstructing MR images with subsampled k-space data. We provided participants with data from 7,299 clinical brain scans (de-identified via a HIPAA-compliant procedure by NYU Langone Health), holding back the fully-sampled data from 894 of these scans for challenge evaluation purposes. In contrast to the 2019 challenge, we focused our radiologist evaluations on pathological assessment in brain images. We also debuted a new Transfer track that required participants to submit models evaluated on MRI scanners from outside the training set. We received 19 submissions from eight different groups. Results showed one team scoring best in both SSIM scores and qualitative radiologist evaluations. We also performed analysis on alternative metrics to mitigate the effects of background noise and collected feedback from the participants to inform future challenges. Lastly, we identify common failure modes across the submissions, highlighting areas of need for future research in the MRI reconstruction community., Comment: M. J. Muckley and B. Riemenschneider contributed equally to this work. This updates to version accepted in IEEE Transactions on Medical Imaging. It includes a rewrite of Section II.E as well as minor changes and corrections