Kamal Youcef-Toumi

Tony Tohme, Dehong Liu, Kamal Youcef-Toumi

Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes, SR attempts to gain insight into the underlying relationships between the independent variables and the target variable of a given dataset by assembling analytical functions. In this paper, we present GSR, a Generalized Symbolic Regression approach, by modifying the conventional SR optimization problem formulation, while keeping the main SR objective intact. In GSR, we infer mathematical relationships between the independent variables and some transformation of the target variable. We constrain our search space to a weighted sum of basis functions, and propose a genetic programming approach with a matrix-based encoding scheme. We show that our GSR method is competitive with strong SR benchmark methods, achieving promising experimental performance on the well-known SR benchmark problem sets. Finally, we highlight the strengths of GSR by introducing SymSet, a new SR benchmark set which is more challenging relative to the existing benchmarks.

Tony Tohme, Mohsen Sadr, Kamal Youcef-Toumi et al.

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.

Aadi Kothari, Tony Tohme, Xiaotong Zhang et al.

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.

Shubhanshu Shekhar, Mohammad Javad Khojasteh, Ananya Acharya et al.

The distinctive architectural features of normalizing flows (NFs), notably bijectivity and tractable Jacobians, make them well-suited for generative modeling. Invertible neural networks (INNs) build on these principles to address supervised inverse problems, enabling direct modeling of both forward and inverse mappings. In this paper, we revisit these architectures from both theoretical and practical perspectives and address a key gap in the literature: the lack of theoretical guarantees on approximation quality under realistic assumptions, whether for posterior inference in INNs or for generative modeling with NFs. We introduce a unified framework for INNs and NFs based on variational unsupervised loss functions, inspired by analogous formulations in related areas such as generative adversarial networks (GANs) and the Precision-Recall divergence for training normalizing flows. Within this framework, we derive theoretical performance guarantees, quantifying posterior accuracy for INNs and distributional accuracy for NFs, under assumptions that are weaker and more practically realistic than those used in prior work. Building on these theoretical results, we conduct extensive case studies to distill general design principles and practical guidelines. We conclude by demonstrating the effectiveness of our approach on a realistic ocean-acoustic inversion problem.

Xiaotong Zhang, Dingcheng Huang, Kamal Youcef-Toumi

Human brain possesses the ability to effectively focus on important environmental components, which enhances perception, learning, reasoning, and decision-making. Inspired by this cognitive mechanism, we introduced a novel concept termed relevance for Human-Robot Collaboration (HRC). Relevance is a dimensionality reduction process that incorporates a continuously operating perception module, evaluates cue sufficiency within the scene, and applies a flexible formulation and computation framework. In this paper, we present an enhanced two-loop framework that integrates real-time and asynchronous processing to quantify relevance and leverage it for safer and more efficient human-robot collaboration (HRC). The two-loop framework integrates an asynchronous loop, which leverages LLM world knowledge to quantify relevance, and a real-time loop, which performs scene understanding, human intent prediction, and decision-making based on relevance. HRC decision-making is enhanced by a relevance-based task allocation method, as well as a motion generation and collision avoidance approach that incorporates human trajectory prediction. Simulations and experiments show that our methodology for relevance quantification can accurately and robustly predict the human objective and relevance, with an average accuracy of up to 0.90 for objective prediction and up to 0.96 for relevance prediction. Moreover, our motion generation methodology reduces collision cases by 63.76% and collision frames by 44.74% when compared with a state-of-the-art (SOTA) collision avoidance method. Our framework and methodologies, with relevance, guide the robot on how to best assist humans and generate safer and more efficient actions for HRC.

Xiaotong Zhang, Dean Huang, Kamal Youcef-Toumi

Inspired by the human ability to selectively focus on relevant information, this paper introduces relevance, a novel dimensionality reduction process for human-robot collaboration (HRC). Our approach incorporates a continuously operating perception module, evaluates cue sufficiency within the scene, and applies a flexible formulation and computation framework. To accurately and efficiently quantify relevance, we developed an event-based framework that maintains a continuous perception of the scene and selectively triggers relevance determination. Within this framework, we developed a probabilistic methodology, which considers various factors and is built on a novel structured scene representation. Simulation results demonstrate that the relevance framework and methodology accurately predict the relevance of a general HRC setup, achieving a precision of 0.99, a recall of 0.94, an F1 score of 0.96, and an object ratio of 0.94. Relevance can be broadly applied to several areas in HRC to accurately improve task planning time by 79.56% compared with pure planning for a cereal task, reduce perception latency by up to 26.53% for an object detector, improve HRC safety by up to 13.50% and reduce the number of inquiries for HRC by 80.84%. A real-world demonstration showcases the relevance framework's ability to intelligently and seamlessly assist humans in everyday tasks.

Alexandre Heuillet, Hedi Tabia, Hichem Arioui et al.

Differentiable ARchiTecture Search (DARTS) is one of the most trending Neural Architecture Search (NAS) methods. It drastically reduces search cost by resorting to weight-sharing. However, it also dramatically reduces the search space, thus excluding potential promising architectures. In this article, we propose D-DARTS, a solution that addresses this problem by nesting neural networks at the cell level instead of using weight-sharing to produce more diversified and specialized architectures. Moreover, we introduce a novel algorithm that can derive deeper architectures from a few trained cells, increasing performance and saving computation time. In addition, we also present an alternative search space (DARTOpti) in which we optimize existing handcrafted architectures (e.g., ResNet) rather than starting from scratch. This approach is accompanied by a novel metric that measures the distance between architectures inside our custom search space. Our solution reaches competitive performance on multiple computer vision tasks. Code and pretrained models can be accessed at https://github.com/aheuillet/D-DARTS.

Dingcheng Huang, Xiaotong Zhang, Kamal Youcef-Toumi

In modern human-robot collaboration (HRC) applications, multiple perception modules jointly extract visual, auditory, and contextual cues to achieve comprehensive scene understanding, enabling the robot to provide appropriate assistance to human agents intelligently. While executing multiple perception modules on a frame-by-frame basis enhances perception quality in offline settings, it inevitably accumulates latency, leading to a substantial decline in system performance in streaming perception scenarios. Recent work in scene understanding, termed Relevance, has established a solid foundation for developing efficient methodologies in HRC. However, modern perception pipelines still face challenges related to information redundancy and suboptimal allocation of computational resources. Drawing inspiration from the Relevance concept and the information sparsity in HRC events, we propose a novel lightweight perception scheduling framework that efficiently leverages output from previous frames to estimate and schedule necessary perception modules in real-time based on scene context. The experimental results demonstrate that the proposed perception scheduling framework effectively reduces computational latency by up to 27.52% compared to conventional parallel perception pipelines, while also achieving a 72.73% improvement in MMPose activation recall. Additionally, the framework demonstrates high keyframe accuracy, achieving rates of up to 98%. The results validate the framework's capability to enhance real-time perception efficiency without significantly compromising accuracy. The framework shows potential as a scalable and systematic solution for multimodal streaming perception systems in HRC.

Tony Tohme, Mohammad Javad Khojasteh, Mohsen Sadr et al.

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.

Mohsen Sadr, Tony Tohme, Kamal Youcef-Toumi

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.

Jinger Chong, Xiaotong Zhang, Kamal Youcef-Toumi

Accurate human motion prediction with well-calibrated uncertainty is critical for safe human-robot collaboration (HRC), where robots must anticipate and react to human movements in real time. We propose a structured multitask variational Gaussian Process (GP) framework for full-body human motion prediction that captures temporal correlations and leverages joint-dimension-level factorization for scalability, while using a continuous 6D rotation representation to preserve kinematic consistency. Evaluated on Human3.6M (H3.6M), our model achieves up to 50 lower kernel density estimate negative log-likelihood (KDE NLL) than strong baselines, a mean continuous ranked probability score (CRPS) of 0.021 m, and deterministic mean angle error (MAE) that is 3-18% higher than competitive deep learning methods. Empirical coverage analysis shows that the fraction of ground-truth outcomes contained within predicted confidence intervals gradually decreases with horizon, remaining conservative for lower-confidence intervals and near-nominal for higher-confidence intervals, with only modest calibration drift at longer horizons. Despite its probabilistic formulation, our model requires only 0.24-0.35 M parameters, roughly eight times fewer than comparable approaches, and exhibits modest inference times, indicating suitability for real-time deployment. Extensive ablation studies further validated the choice of 6D rotation representation and Matern 3/2 + Linear kernel, and guided the selection of the number of inducing points and latent dimensionality. These results demonstrate that scalable GP-based models can deliver competitive accuracy together with reliable and interpretable uncertainty estimates for downstream robotics tasks such as motion planning and collision avoidance.

Tony Tohme, Kevin Vanslette, Kamal Youcef-Toumi

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function for regression uncertainty estimation based on the Bayesian Validation Metric (BVM) framework while using ensemble learning. The proposed loss reproduces maximum likelihood estimation in the limiting case. A series of experiments on in-distribution data show that the proposed method is competitive with existing state-of-the-art methods. Experiments on out-of-distribution data show that the proposed method is robust to statistical change and exhibits superior predictive capability.

Quang H. Le, Kamal Youcef-Toumi, Dzmitry Tsetserukou et al.

In design of instance segmentation networks that reconstruct masks, segmentation is often taken as its literal definition -- assigning each pixel a label. This has led to thinking the problem as a template matching one with the goal of minimizing the loss between the reconstructed and the ground truth pixels. Rethinking reconstruction networks as a generator, we define the problem of predicting masks as a GANs game framework: A segmentation network generates the masks, and a discriminator network decides on the quality of the masks. To demonstrate this game, we show effective modifications on the general segmentation framework in Mask R-CNN. We find that playing the game in feature space is more effective than the pixel space leading to stable training between the discriminator and the generator, predicting object coordinates should be replaced by predicting contextual regions for objects, and overall the adversarial loss helps the performance and removes the need for any custom settings per different data domain. We test our framework in various domains and report on cellphone recycling, autonomous driving, large-scale object detection, and medical glands. We observe in general GANs yield masks that account for crispier boundaries, clutter, small objects, and details, being in domain of regular shapes or heterogeneous and coalescing shapes. Our code for reproducing the results is available publicly.

Andrey Sartison, Dima Mironov, Kamal Youcef-Toumi et al.

Estimation of a hand grip force is essential for the understanding of force pattern during the execution of assembly or disassembly operations. Human demonstration of a correct way of doing an operation is a powerful source of information which can be used for guided robot teaching. Typically to assess this problem instrumented approach is used, which requires hand or object mounted devices and poses an inconvenience for an operator or limits the scope of addressable objects. The work demonstrates that contact force may be estimated using a noninvasive contactless method with the help of vision system alone. We propose a two-stream approach for video processing, which utilizes both spatial information of each frame and dynamic information of frame change. In this work, image processing and machine learning techniques are used along with dense optical flow for frame change tracking and Kalman filter is used for stream fusion. Our studies show that the proposed method can successfully estimate contact grip force with RMSE < 10% of sensor range (RMSE $\approx 0.2$ N), the performances of each stream and overall method performance are reported. The proposed method has a wide range of applications, including robot teaching through demonstration, haptic force feedback, and validation of human- performed operations.