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Recently, machine learning had a remarkable impact, from scientific to everyday-life applications. However, complex tasks often imply unfeasible energy and computational power consumption. Quantum computation might lower such requirements, although it is unclear whether enhancements are reachable by current technologies. Here, we demonstrate a kernel method on a photonic integrated processor to perform a binary classification. We show that our protocol outperforms state-of-the-art kernel methods including gaussian and neural tangent kernels, exploiting quantum interference, and brings a smaller improvement also by single photon coherence. Our scheme does not require entangling gates and can modify the system dimension through additional modes and injected photons. This result opens to more efficient algorithms and to formulating tasks where quantum effects improve standard methods.

Examining the community structures within intricate networks is crucial for comprehending their intrinsic dynamics and functionality. The paper presents the Fast Local Move Iterated Greedy (FLMIG) algorithm, a novel method designed to effectively identify community structures in intricate networks. The FLMIG algorithm improves the modularity optimization process by including a rapid local move heuristic and an iterated greedy mechanism that switches between destructive and constructive phases to strengthen the community partitions. The main innovation is the integration of random neighbor moves with an enhanced Prune Louvain algorithm, which guarantees fast convergence while maintaining the connection of the identified communities. The results of our comprehensive studies, conducted on both synthetic and and real-world networks, clearly show that FLMIG surpasses existing cutting-edge techniques in terms of both accuracy and computing efficiency. This algorithm not only provides a strong tool for identifying communities, but also makes a valuable contribution to the broader field of network analysis by offering a method that can effectively handle large-scale and dynamically evolving networks.

We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR method naturally combines the principles of Invertible Neural Networks (INNs) and Equation Learner (EQL), a neural network-based symbolic architecture for function learning. In particular, we transform the affine coupling blocks of INNs into a symbolic framework, resulting in an end-to-end differentiable symbolic invertible architecture that allows for efficient gradient-based learning. The proposed ISR framework also relies on sparsity promoting regularization, allowing the discovery of concise and interpretable invertible expressions. We show that ISR can serve as a (symbolic) normalizing flow for density estimation tasks. Furthermore, we highlight its practical applicability in solving inverse problems, including a benchmark inverse kinematics problem, and notably, a geoacoustic inversion problem in oceanography aimed at inferring posterior distributions of underlying seabed parameters from acoustic signals.

This paper investigates the social optimum for a dynamic linear quadratic collective choice problem where a group of agents choose among multiple alternatives or destinations. The agents' common objective is to minimize the average cost of the entire population. A naive approach to finding a social optimum for this problem involves solving a number of linear quadratic regulator (LQR) problems that increases exponentially with the population size. By exploiting the problem's symmetries, we first show that one can equivalently solve a number of LQR problems equal to the number of destinations, followed by an optimal transport problem parameterized by the fraction of agents choosing each destination. Then, we further reduce the complexity of the solution search by defining an appropriate system of limiting equations, whose solution is used to obtain a strategy shown to be asymptotically optimal as the number of agents becomes large. The model includes a congestion effect captured by a negative quadratic term in the social cost function, which may cause agents to escape to infinity in finite time. Hence, we identify sufficient conditions, independent of the population size, for the existence of the social optimum. Lastly, we investigate the behavior of the model through numerical simulations in different scenarios.

In this work, we present an adjoint-based method for discovering the underlying governing partial differential equations (PDEs) given data. The idea is to consider a parameterized PDE in a general form and formulate a PDE-constrained optimization problem aimed at minimizing the error of the PDE solution from data. Using variational calculus, we obtain an evolution equation for the Lagrange multipliers (adjoint equations) allowing us to compute the gradient of the objective function with respect to the parameters of PDEs given data in a straightforward manner. In particular, we consider a family of parameterized PDEs encompassing linear, nonlinear, and spatial derivative candidate terms, and elegantly derive the corresponding adjoint equations. We show the efficacy of the proposed approach in identifying the form of the PDE up to machine accuracy, enabling the accurate discovery of PDEs from data. We also compare its performance with the famous PDE Functional Identification of Nonlinear Dynamics method known as PDE-FIND (Rudy et al., 2017), on both smooth and noisy data sets. Even though the proposed adjoint method relies on forward/backward solvers, it outperforms PDE-FIND for large data sets thanks to the analytic expressions for gradients of the cost function with respect to each PDE parameter.

Perception serves as a critical component in the functionality of autonomous agents. However, the intricate relationship between perception metrics and robotic metrics remains unclear, leading to ambiguity in the development and fine-tuning of perception algorithms. In this paper, we introduce a methodology for quantifying this relationship, taking into account factors such as detection rate, detection quality, and latency. Furthermore, we introduce two novel metrics for Human-Robot Collaboration safety predicated upon perception metrics: Critical Collision Probability (CCP) and Average Collision Probability (ACP). To validate the utility of these metrics in facilitating algorithm development and tuning, we develop an attentive processing strategy that focuses exclusively on key input features. This approach significantly reduces computational time while preserving a similar level of accuracy. Experimental results indicate that the implementation of this strategy in an object detector leads to a maximum reduction of 30.091% in inference time and 26.534% in total time per frame. Additionally, the strategy lowers the CCP and ACP in a baseline model by 11.252% and 13.501%, respectively. The source code will be made publicly available in the final proof version of the manuscript.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions., Comment: 14 pages, 10 figures

Multi-dielectric coated coverslip can be designed to reach large optical field enhancements when working under proper illumination conditions and in total internal reflection. In an objective-based total internal reflection fluorescence microscopy (TIRF-M), we propose to use the resulting large field enhancement supported in such coverslip to improve TIRF-M sensitivity by amplifying the collected fluorescence signal. We present here the optimization, realization and testing in TIRF-M of resonant coverslips designed to take into account the experimental constraints. The latter's are due to the inverted configuration of TIRF-M together with the use of a high numerical aperture objective. The challenge is therefore to find the best coating design compromising between the angular tolerance and the field enhancement. We will report here enhanced-TIRF-M imaging over model samples but the ultimate goal here is to be able to monitor and quantify dynamics of pathogens at the membrane of living cells., Comment: 2023 23rd International Conference on Transparent Optical Networks (ICTON), Jul 2023, Bucharest, Romania

Human motion prediction is an essential step for efficient and safe human-robot collaboration. Current methods either purely rely on representing the human joints in some form of neural network-based architecture or use regression models offline to fit hyper-parameters in the hope of capturing a model encompassing human motion. While these methods provide good initial results, they are missing out on leveraging well-studied human body kinematic models as well as body and scene constraints which can help boost the efficacy of these prediction frameworks while also explicitly avoiding implausible human joint configurations. We propose a novel human motion prediction framework that incorporates human joint constraints and scene constraints in a Gaussian Process Regression (GPR) model to predict human motion over a set time horizon. This formulation is combined with an online context-aware constraints model to leverage task-dependent motions. It is tested on a human arm kinematic model and implemented on a human-robot collaborative setup with a UR5 robot arm to demonstrate the real-time capability of our approach. Simulations were also performed on datasets like HA4M and ANDY. The simulation and experimental results demonstrate considerable improvements in a Gaussian Process framework when these constraints are explicitly considered., Comment: 7 pages, 5 figures. Associated video demonstration can be found at https://www.youtube.com/@MITMechatronics

We introduce MESSY estimation, a Maximum-Entropy based Stochastic and Symbolic densitY estimation method. The proposed approach recovers probability density functions symbolically from samples using moments of a Gradient flow in which the ansatz serves as the driving force. In particular, we construct a gradient-based drift-diffusion process that connects samples of the unknown distribution function to a guess symbolic expression. We then show that when the guess distribution has the maximum entropy form, the parameters of this distribution can be found efficiently by solving a linear system of equations constructed using the moments of the provided samples. Furthermore, we use Symbolic regression to explore the space of smooth functions and find optimal basis functions for the exponent of the maximum entropy functional leading to good conditioning. The cost of the proposed method for each set of selected basis functions is linear with the number of samples and quadratic with the number of basis functions. However, the underlying acceptance/rejection procedure for finding optimal and well-conditioned bases adds to the computational cost. We validate the proposed MESSY estimation method against other benchmark methods for the case of a bi-modal and a discontinuous density, as well as a density at the limit of physical realizability. We find that the addition of a symbolic search for basis functions improves the accuracy of the estimation at a reasonable additional computational cost. Our results suggest that the proposed method outperforms existing density recovery methods in the limit of a small to moderate number of samples by providing a low-bias and tractable symbolic description of the unknown density at a reasonable computational cost., Comment: Published in Transactions on Machine Learning Research (TMLR)