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In the past decade, Deep Neural Networks (DNNs) achieved state-of-the-art performance in a broad range of problems, spanning from object classification and action recognition to smart building and healthcare. The flexibility that makes DNNs such a pervasive technology comes at a price: the computational requirements preclude their deployment on most of the resource-constrained edge devices available today to solve real-time and real-world tasks. This paper introduces a novel approach to address this challenge by combining the concept of predefined sparsity with Split Computing (SC) and Early Exit (EE). In particular, SC aims at splitting a DNN with a part of it deployed on an edge device and the rest on a remote server. Instead, EE allows the system to stop using the remote server and rely solely on the edge device's computation if the answer is already good enough. Specifically, how to apply such a predefined sparsity to a SC and EE paradigm has never been studied. This paper studies this problem and shows how predefined sparsity significantly reduces the computational, storage, and energy burdens during the training and inference phases, regardless of the hardware platform. This makes it a valuable approach for enhancing the performance of SC and EE applications. Experimental results showcase reductions exceeding 4x in storage and computational complexity without compromising performance. The source code is available at https://github.com/intelligolabs/sparsity_sc_ee., Comment: Accepted at the 27th Forum on specification and Design Languages (FDL 2024)

Split Computing (SC), where a Deep Neural Network (DNN) is intelligently split with a part of it deployed on an edge device and the rest on a remote server is emerging as a promising approach. It allows the power of DNNs to be leveraged for latency-sensitive applications that do not allow the entire DNN to be deployed remotely, while not having sufficient computation bandwidth available locally. In many such embedded systems scenarios, such as those in the automotive domain, computational resource constraints also necessitate Multi-Task Learning (MTL), where the same DNN is used for multiple inference tasks instead of having dedicated DNNs for each task, which would need more computing bandwidth. However, how to partition such a multi-tasking DNN to be deployed within a SC framework has not been sufficiently studied. This paper studies this problem, and MTL-Split, our novel proposed architecture, shows encouraging results on both synthetic and real-world data. The source code is available at https://github.com/intelligolabs/MTL-Split., Comment: Accepted at the 61st Design Automation Conference (DAC 2024)

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

We prove bounds in the strict local $L^{2}(\mathbb{R}^{d})$ range for trilinear Fourier multiplier forms with a $d$-dimensional singular subspace. Given a fixed parameter $K \ge 1$, we treat multipliers with non-degenerate singularity that are push-forwards by $K$-quasiconformal matrices of suitable symbols. As particular applications, our result recovers the uniform bounds for the one-dimensional bilinear Hilbert transforms in the strict local $L^{2}$ range, and it implies the uniform bounds for two-dimensional bilinear Beurling transforms, which are new, in the same range.

Due to manufacturing variabilities and temperature gradients within an electric vehicle's battery pack, the capacities of cells in it decrease differently over time. This reduces the usable capacity of the battery - the charge levels of one or more cells might be at the minimum threshold while most of the other cells have residual charge. Active cell balancing (i.e., transferring charge among cells) can equalize their charge levels, thereby increasing the battery pack's usable capacity. But performing balancing means additional charge transfer, which can result in energy loss and cell aging, akin to memory aging in storage technologies due to writing. This paper studies when cell balancing should be optimally triggered to minimize aging while maintaining the necessary driving capability. In particular, we propose optimization strategies for cell balancing while minimizing their impact on aging. By borrowing terminology from the storage domain, we refer to this as "wear leveling-aware" active balancing., Comment: A preliminary version of this paper is due to appear in VLSI Design 2024

Industry 4.0 involves the integration of digital technologies, such as IoT, Big Data, and AI, into manufacturing and industrial processes to increase efficiency and productivity. As these technologies become more interconnected and interdependent, Industry 4.0 systems become more complex, which brings the difficulty of identifying and stopping anomalies that may cause disturbances in the manufacturing process. This paper aims to propose a diffusion-based model for real-time anomaly prediction in Industry 4.0 processes. Using a neuro-symbolic approach, we integrate industrial ontologies in the model, thereby adding formal knowledge on smart manufacturing. Finally, we propose a simple yet effective way of distilling diffusion models through Random Fourier Features for deployment on an embedded system for direct integration into the manufacturing process. To the best of our knowledge, this approach has never been explored before., Comment: Accepted at the 26th Forum on specification and Design Languages (FDL 2023)

The $L^{p,\infty}$ quasi-norm of functions on a measure space can be characterized in terms of their pairing with normalized characteristic functions. We generalize this result to the case of the outer $L^{p,\infty}$ quasi-norms for appropriate sizes. This characterization provides an explicit form for certain implicitly defined quasi-norms appearing in an article of Di Plinio and Fragkos., Comment: 21 pages, no figures

We study the causal effects of lockdown measures on uncertainty and sentiment on Twitter. To this end, we exploit the quasi-experimental framework created by the first COVID-19 lockdown in a high-income economy--the unexpected Italian lockdown in February 2020. We measure changes in public sentiment using deep learning and dictionary-based methods on the text of daily tweets geolocated within and near the locked-down areas, before and after the treatment. We classify tweets into four categories--economics, health, politics, and lockdown policy--to examine how the policy affected emotions heterogeneously. Using a staggered difference-in-differences approach, we show that the lockdown did not have a significantly robust impact on economic uncertainty and sentiment. However, the policy came at the price of higher uncertainty on health and politics and more negative political sentiments. These results, which are robust to a battery of robustness tests, show that lockdowns have relevant non-health related implications.

We construct phase space localizing operators in all dimensions. These are frequency localized variants of the conditional expectation operator related to a dyadic stopping time. Our construction is an improvement over the so-called phase plane projections of Muscalu, Tao and the third author in one dimension. The motivation for such operators comes from time-frequency analysis. They are used in particular to prove uniform estimates for multilinear modulation invariant operators., Comment: v3: added a reference to the application of the result. "Outside of the tree" item of the main theorem now has a slightly stronger form (contained in the old proof but not in the old statement)

We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants uniform in the curve. The improvement over M\"{u}ller, Ricci, and Wright and Ramos is given by the removal of the $\mathcal{C}^2$ regularity condition on the curve. This requires the choice of an appropriate measure for each curve, that is suggested by an affine invariant construction of Oberlin in \cite{MR1960918}. As corollaries, we obtain a uniform Fourier restriction theorem for arbitrary convex curves, and a result on the Lebesgue points of the Fourier transform on the curve., Comment: v2: 29 pages, 6 figures. Additional references, clarifying comment in proof of Lemma 4.2 Case II, and lemmata A.17--19 and figure 6 to improve exposition of proof of Thm 2.5 in Appendix. No changes to results or proofs

We study the double iterated outer $L^p$ spaces, namely the outer $L^p$ spaces associated with three exponents and defined on sets endowed with a measure and two outer measures. We prove that in the case of finite sets, under certain conditions between the outer measures, the double iterated outer $L^p$ spaces are isomorphic to Banach spaces uniformly in the cardinality of the set. We achieve this by showing the expected duality properties between them. We also provide counterexamples demonstrating that the uniformity does not hold in any arbitrary setting on finite sets, at least in a certain range of exponents. We prove the isomorphism to Banach spaces and the duality properties between the double iterated outer $L^p$ spaces also in the upper half $3$-space infinite setting described by Uraltsev, going beyond the case of finite sets., Comment: 44 pages, no figures

Deep learning techniques play an increasingly important role in industrial and research environments due to their outstanding results. However, the large number of hyper-parameters to be set may lead to errors if they are set manually. The state-of-the-art hyper-parameters tuning methods are grid search, random search, and Bayesian Optimization. The first two methods are expensive because they try, respectively, all possible combinations and random combinations of hyper-parameters. Bayesian Optimization, instead, builds a surrogate model of the objective function, quantifies the uncertainty in the surrogate using Gaussian Process Regression and uses an acquisition function to decide where to sample the new set of hyper-parameters. This work faces the field of Hyper-Parameters Optimization (HPO). The aim is to improve Bayesian Optimization applied to Deep Neural Networks. For this goal, we build a new algorithm for evaluating and analyzing the results of the network on the training and validation sets and use a set of tuning rules to add new hyper-parameters and/or to reduce the hyper-parameter search space to select a better combination.