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We study Yang-Mills theory on four dimensional Anti-de Sitter space. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space. As observed in [1] this implies a deconfinement-confinement transition as the radius is increased. We gather hints on the nature of this transition using perturbation theory. We compute the anomalous dimensions of the lightest scalar operators in the boundary theory, which are negative for the singlet and positive for non-trivial representations. We also compute the correction to the coefficient $C_J$ and we estimate that the singlet operator reaches marginality before the value of the coupling at which $C_J=0$. These results favor the scenario of merger and annihilation as the most promising candidate for the transition. For the Neumann boundary condition, the lightest scalar operator is found to have a positive anomalous dimension, in agreement with the idea that this boundary condition extrapolates smoothly to flat space. The perturbative calculations are made possible by a drastic simplification of the gauge field propagator in Fried-Yennie gauge. We also derive a general result for the leading-order anomalous dimension of the displacement operator for a generic perturbation in Anti-de Sitter, showing that it is related to the beta function of bulk couplings., Comment: 49 pages, 4 figures, 1 table, 7 boxed equations

Given an Orlicz space $ L^2 \subseteq X \subseteq L^1$ on $[0,1]$, with submultiplicative Young function ${\mathrm{Y}_X}$, we fully characterize the closed null sets $\Xi$ of the real line with the property that H\"ormander-Mihlin or Marcinkiewicz multiplier operators $\mathrm{T}_m$ with singularities on $\Xi$ obey weak-type endpoint modular bounds on $X$ of the type \[ \left|\left\{x\in \mathbb R : |\mathrm{T}_m f(x)| >\lambda\right\}\right| \leq C \int_{\mathbb R} \mathrm{Y}_X \left(\frac{|f|}{\lambda}\right), \qquad \forall \lambda>0. \] These sets $\Xi$ are exactly those enjoying a scale invariant version of Zygmund's $(L\sqrt{\log L},{L^2})$ improving inequality with $X$ in place of the former space, which is termed multiscale Zygmund property. Our methods actually yield sparse and quantitative weighted estimates for the Fourier multipliers $\mathrm{T}_m$ and for the corresponding square functions. In particular, our framework covers the case of singular sets $\Xi$ of finite lacunary order and thus leads to modular and quantitative weighted versions of the classical endpoint theorems of Tao and Wright for Marcinkiewicz multipliers. Moreover, we obtain a pointwise sparse bound for the Marcinkiewicz square function answering a recent conjecture of Lerner. On the other hand, examples of non-lacunary sets enjoying the multiscale Zygmund property for each $X=L^p$, $1

Federated Learning (FL) methods often struggle in highly statistically heterogeneous settings. Indeed, non-IID data distributions cause client drift and biased local solutions, particularly pronounced in the final classification layer, negatively impacting convergence speed and accuracy. To address this issue, we introduce Federated Recursive Ridge Regression (Fed3R). Our method fits a Ridge Regression classifier computed in closed form leveraging pre-trained features. Fed3R is immune to statistical heterogeneity and is invariant to the sampling order of the clients. Therefore, it proves particularly effective in cross-device scenarios. Furthermore, it is fast and efficient in terms of communication and computation costs, requiring up to two orders of magnitude fewer resources than the competitors. Finally, we propose to leverage the Fed3R parameters as an initialization for a softmax classifier and subsequently fine-tune the model using any FL algorithm (Fed3R with Fine-Tuning, Fed3R+FT). Our findings also indicate that maintaining a fixed classifier aids in stabilizing the training and learning more discriminative features in cross-device settings. Official website: https://fed-3r.github.io/., Comment: Accepted at ICML 2024 - https://fed-3r.github.io/

Recent advances in neural network pruning have shown how it is possible to reduce the computational costs and memory demands of deep learning models before training. We focus on this framework and propose a new pruning at initialization algorithm that leverages the Neural Tangent Kernel (NTK) theory to align the training dynamics of the sparse network with that of the dense one. Specifically, we show how the usually neglected data-dependent component in the NTK's spectrum can be taken into account by providing an analytical upper bound to the NTK's trace obtained by decomposing neural networks into individual paths. This leads to our Path eXclusion (PX), a foresight pruning method designed to preserve the parameters that mostly influence the NTK's trace. PX is able to find lottery tickets (i.e. good paths) even at high sparsity levels and largely reduces the need for additional training. When applied to pre-trained models it extracts subnetworks directly usable for several downstream tasks, resulting in performance comparable to those of the dense counterpart but with substantial cost and computational savings. Code available at: https://github.com/iurada/px-ntk-pruning, Comment: Accepted CVPR 2024 - https://iurada.github.io/PX

Recent transformer-based architectures have shown impressive results in the field of image segmentation. Thanks to their flexibility, they obtain outstanding performance in multiple segmentation tasks, such as semantic and panoptic, under a single unified framework. To achieve such impressive performance, these architectures employ intensive operations and require substantial computational resources, which are often not available, especially on edge devices. To fill this gap, we propose Prototype-based Efficient MaskFormer (PEM), an efficient transformer-based architecture that can operate in multiple segmentation tasks. PEM proposes a novel prototype-based cross-attention which leverages the redundancy of visual features to restrict the computation and improve the efficiency without harming the performance. In addition, PEM introduces an efficient multi-scale feature pyramid network, capable of extracting features that have high semantic content in an efficient way, thanks to the combination of deformable convolutions and context-based self-modulation. We benchmark the proposed PEM architecture on two tasks, semantic and panoptic segmentation, evaluated on two different datasets, Cityscapes and ADE20K. PEM demonstrates outstanding performance on every task and dataset, outperforming task-specific architectures while being comparable and even better than computationally-expensive baselines., Comment: CVPR 2024. Project page: https://niccolocavagnero.github.io/PEM

We consider Marcinkiewicz multipliers of any lacunary order defined by means of uniformly bounded variation on each lacunary Littlewood-Paley interval of some fixed order $\tau\geq 1$. We prove the optimal endpoint bounds for such multipliers as a corollary of a more general endpoint estimate for a class of multipliers introduced by Coifman, Rubio de Francia and Semmes and further studied by Tao and Wright. Our methods also yield the best possible endpoint mapping property for higher order H\"ormander-Mihlin multipliers, namely multipliers which are singular on every point of a lacunary set of order $\tau$. These results can be considered as endpoint versions of corresponding results of Sj\"ogren and Sj\"olin. Finally our methods generalize a weak square function characterization of the space $L\log^{1/2}L$ in terms of a square function introduced by Tao and Wright: we realize such a weak characterization as the dual of the Chang-Wilson-Wolff inequality, thus giving corresponding weak square function characterizations for the spaces $L\log^{\tau/2}L$ for general integer orders $\tau\geq 1$., Comment: 29 pages

We study the $2d$ chiral Gross-Neveu model at finite temperature $T$ and chemical potential $\mu$. The analysis is performed by relating the theory to a $SU(N)\times U(1)$ Wess-Zumino-Witten model with appropriate levels and global identifications necessary to keep track of the fermion spin structures. At $\mu=0$ we show that a certain $\mathbb{Z}_2$-valued 't Hooft anomaly forbids the system to be trivially gapped when fermions are periodic along the thermal circle for any $N$ and any $T>0$. We also study the two-point function of a certain composite fermion operator which allows us to determine the remnants for $T>0$ of the inhomogeneous chiral phase configuration found at $T=0$ for any $N$ and any $\mu$. The inhomogeneous configuration decays exponentially at large distances for anti-periodic fermions while it persists for $T>0$ and any $\mu$ for periodic fermions, as expected from anomaly considerations. A large $N$ analysis confirms the above findings., Comment: 28+23 pages; v2: Several clarifications and improvements, reference added

In this note we improve, for the case of low dimensions, the known range of exponents for which constant functions are the unique maximizers for the $L^2(\mathbb{S}^{d-1})$ to $L^p_{rad}L^2_{ang}(\mathbb{R}^d)$ mixed-norm Fourier extension estimate on the sphere. Moreover, we show that in the same range of exponents for which constant functions are the unique maximizers for the $L^2(\mathbb{S}^{d-1})$ to $L^p_{red}L^2_{ang}(\mathbb{R}^d)$ mixed-norm Fourier extension estimates they are also local maximizers for the $L^p(\mathbb{S}^{d-1})$ to $L^p(\mathbb{R}^d)$ Fourier extension estimates. As a by-product, we obtain that for the cases of dimensions $d=2,3$ constant functions are local maximizers for all $p\geq p_{\mathrm{st}}(d)$, where $p_{\mathrm{st}}$ denotes the Stein-Tomas endpoint, $p_{\mathrm{st}}(d):= 2(d+1)/(d-1)$., Comment: 13 pages

Federated Learning (FL) has emerged as the state-of-the-art approach for learning from decentralized data in privacy-constrained scenarios. However, system and statistical challenges hinder real-world applications, which demand efficient learning from edge devices and robustness to heterogeneity. Despite significant research efforts, existing approaches (i) are not sufficiently robust, (ii) do not perform well in large-scale scenarios, and (iii) are not communication efficient. In this work, we propose a novel Generalized Heavy-Ball Momentum (GHBM), motivating its principled application to counteract the effects of statistical heterogeneity in FL. Then, we present FedHBM as an adaptive, communication-efficient by-design instance of GHBM. Extensive experimentation on vision and language tasks, in both controlled and realistic large-scale scenarios, provides compelling evidence of substantial and consistent performance gains over the state of the art.

Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We investigate in this study the aggregation of such latent spaces to create a unified space encompassing the combined information. To this end, we introduce Relative Latent Space Aggregation, a two-step approach that first renders the spaces comparable using relative representations, and then aggregates them via a simple mean. We carefully divide a classification problem into a series of learning tasks under three different settings: sharing samples, classes, or neither. We then train a model on each task and aggregate the resulting latent spaces. We compare the aggregated space with that derived from an end-to-end model trained over all tasks and show that the two spaces are similar. We then observe that the aggregated space is better suited for classification, and empirically demonstrate that it is due to the unique imprints left by task-specific embedders within the representations. We finally test our framework in scenarios where no shared region exists and show that it can still be used to merge the spaces, albeit with diminished benefits over naive merging., Comment: To appear in the NeurReps workshop @ NeurIPS 2023

Federated Learning (FL) aims to learn a global model from distributed users while protecting their privacy. However, when data are distributed heterogeneously the learning process becomes noisy, unstable, and biased towards the last seen clients' data, slowing down convergence. To address these issues and improve the robustness and generalization capabilities of the global model, we propose WIMA (Window-based Model Averaging). WIMA aggregates global models from different rounds using a window-based approach, effectively capturing knowledge from multiple users and reducing the bias from the last ones. By adopting a windowed view on the rounds, WIMA can be applied from the initial stages of training. Importantly, our method introduces no additional communication or client-side computation overhead. Our experiments demonstrate the robustness of WIMA against distribution shifts and bad client sampling, resulting in smoother and more stable learning trends. Additionally, WIMA can be easily integrated with state-of-the-art algorithms. We extensively evaluate our approach on standard FL benchmarks, demonstrating its effectiveness., Comment: International Conference on Computer Vision Workshop (ICCVW)

We propose FedDrive v2, an extension of the Federated Learning benchmark for Semantic Segmentation in Autonomous Driving. While the first version aims at studying the effect of domain shift of the visual features across clients, in this work, we focus on the distribution skewness of the labels. We propose six new federated scenarios to investigate how label skewness affects the performance of segmentation models and compare it with the effect of domain shift. Finally, we study the impact of using the domain information during testing. Official website: https://feddrive.github.io, Comment: 5th Italian Conference on Robotics and Intelligent Machines (I-RIM) 2023

Sessions are a fundamental notion in message-passing systems. A session is an abstract notion of communication between parties where each one owns an endpoint. Session types are types that are assigned to the endpoints and that are used to statically and dynamically enforce some desired properties of the communications, such as the absence of deadlocks. Properties of concurrent systems are usually divided in safety and liveness ones and depending on the class it belongs to, a property is defined using different (dual) techniques. However, there exist some properties that require to mix both techniques and the challenges in defining them are exacerbated in proof assistants (e.g. Agda, Coq, . . . ), that is, tools that allow users to formally characterize and prove theorems. In particular, we mechanize the meta-theory of inference systems in Agda. Among the interesting properties that can be studied in the session-based context, we study fair termination which is the property of those sessions that can always eventually reach successful termination under a fairness assumption. Fair termination implies many desirable and well known properties, such as lock freedom. Moreover, a lock free session does not imply that other sessions are lock free as well. On the other hand, if we consider a session and we assume that all the other ones are fairly terminating, we can conclude that the one under analysis is fairly terminating as well., Comment: PhD thesis

Organic electrochemical transistors (OECTs) based on Poly(3,4-ethylenedioxythiophene):poly(styrene sulfonic acid) (PEDOT:PSS) are a benchmark system in organic bioelectronics. In particular, the superior mechanical properties and the ionic-electronic transduction yield excellent potential for the field of implantable or wearable sensing technology. However, depletion-mode operation PEDOT:PSS-based OECTs cause high static power dissipation in electronic circuits, limiting their application in electronic systems. Hence, having control over the threshold voltage is of utmost technological importance. Here we demonstrate PEDOT:PSS-based dual-gate OECTs with solid-state electrolyte where the threshold voltage is seamlessly adjustable during operation. We show that the degree of threshold voltage tuning linearly depends on the gate capacitance, which is a straightforward approach for circuit designers to adjust the threshold voltage only by the device dimensions. The PEDOT:PSS-based dual-gate OECTs show excellent device performance and can be pushed to accumulation-mode operation, resulting in a simplified and relaxed design of complementary inverters.

Not all properties are monitorable. This is a well-known fact, and it means there exist properties that cannot be fully verified at runtime. However, given a non-monitorable property, a monitor can still be synthesised, but it could end up in a state where no verdict will ever be concluded on the satisfaction (resp., violation) of the property. For this reason, non-monitorable properties are usually discarded. In this paper, we carry out an in-depth analysis on monitorability, and how non-monitorable properties can still be partially verified. We present our theoretical results at a semantic level, without focusing on a specific formalism. Then, we show how our theory can be applied to achieve partial runtime verification of Linear Temporal Logic (LTL).

We present wide-field, deep $K$-band photometry of 98 luminous early-type galaxies (ETGs) from the MASSIVE survey based on observations taken with the WIRCam instrument on the Canada-France-Hawaii Telescope. Using these images, we extract accurate total $K$-band luminosities ($L_K$) and half-light radii ($R_e$) for this sample of galaxies. We use these new values to explore the size-luminosity and Faber-Jackson relations for massive ETGs. Within this volume-limited sample, we find clear evidence for curvature in both relations, indicating that the most luminous galaxies tend to have larger sizes and smaller velocity dispersions than expected from a simple power-law fit to less luminous galaxies. Our measured relations are qualitatively consistent with the most massive elliptical galaxies forming largely through dissipationless mergers. When the sample is separated into fast and slow rotators, we find the slow rotators to exhibit similar changes in slope with increasing $L_K$, suggesting that low-mass and high-mass slow rotators have different formation histories. The curvatures in the $R_e-L_K$ and $\sigma-L_K$ relations cancel, leading to a relation between dynamical mass and luminosity that is well described by a single power-law: $R_e\sigma^2 \propto {L_K}^b$ with $b \approx 1.2$. This is consistent with the tilt of the fundamental plane observed in lower mass elliptical galaxies., Comment: 17 pages, 7 figures, accepted for publication in MNRAS

A continual learning (CL) algorithm learns from a non-stationary data stream. The non-stationarity is modeled by some schedule that determines how data is presented over time. Most current methods make strong assumptions on the schedule and have unpredictable performance when such requirements are not met. A key challenge in CL is thus to design methods robust against arbitrary schedules over the same underlying data, since in real-world scenarios schedules are often unknown and dynamic. In this work, we introduce the notion of schedule-robustness for CL and a novel approach satisfying this desirable property in the challenging online class-incremental setting. We also present a new perspective on CL, as the process of learning a schedule-robust predictor, followed by adapting the predictor using only replay data. Empirically, we demonstrate that our approach outperforms existing methods on CL benchmarks for image classification by a large margin.

Federated Learning (FL) has recently emerged as a possible way to tackle the domain shift in real-world Semantic Segmentation (SS) without compromising the private nature of the collected data. However, most of the existing works on FL unrealistically assume labeled data in the remote clients. Here we propose a novel task (FFREEDA) in which the clients' data is unlabeled and the server accesses a source labeled dataset for pre-training only. To solve FFREEDA, we propose LADD, which leverages the knowledge of the pre-trained model by employing self-supervision with ad-hoc regularization techniques for local training and introducing a novel federated clustered aggregation scheme based on the clients' style. Our experiments show that our algorithm is able to efficiently tackle the new task outperforming existing approaches. The code is available at https://github.com/Erosinho13/LADD., Comment: WACV 2023; 11 pages manuscript, 6 pages supplemental material

We establish a sharp adjoint Fourier restriction inequality for the end-point Tomas-Stein restriction theorem on the circle under a certain arithmetic constraint on the support set of the Fourier coefficients of the given function. Such arithmetic constraint is a generalization of a $B_3$-set., Comment: 17 pages, v2: typos corrected

Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative extension of $\mu$MALL$^\infty$, the infinitary proof system of the multiplicative additive fragment of linear logic with least and greatest fixed points, such that cut elimination corresponds to fair termination. Proof terms are processes of $\pi$LIN, a variant of the linear $\pi$-calculus with (co)recursive types into which binary and (some) multiparty sessions can be encoded. As a result we obtain a behavioral type system for $\pi$LIN (and indirectly for session calculi through their encoding into $\pi$LIN) that ensures fair termination: although well-typed processes may engage in arbitrarily long interactions, they are fairly guaranteed to eventually perform all pending actions.