Antonio Terpin

Antonio Terpin, Nicolas Lanzetti, Batuhan Yardim et al.

Policy Optimization (PO) algorithms have been proven particularly suited to handle the high-dimensionality of real-world continuous control tasks. In this context, Trust Region Policy Optimization methods represent a popular approach to stabilize the policy updates. These usually rely on the Kullback-Leibler (KL) divergence to limit the change in the policy. The Wasserstein distance represents a natural alternative, in place of the KL divergence, to define trust regions or to regularize the objective function. However, state-of-the-art works either resort to its approximations or do not provide an algorithm for continuous state-action spaces, reducing the applicability of the method. In this paper, we explore optimal transport discrepancies (which include the Wasserstein distance) to define trust regions, and we propose a novel algorithm - Optimal Transport Trust Region Policy Optimization (OT-TRPO) - for continuous state-action spaces. We circumvent the infinite-dimensional optimization problem for PO by providing a one-dimensional dual reformulation for which strong duality holds. We then analytically derive the optimal policy update given the solution of the dual problem. This way, we bypass the computation of optimal transport costs and of optimal transport maps, which we implicitly characterize by solving the dual formulation. Finally, we provide an experimental evaluation of our approach across various control tasks. Our results show that optimal transport discrepancies can offer an advantage over state-of-the-art approaches.

Antonio Terpin, Alan Bonomi, Francesco Banelli et al.

We describe SynthPix, a synthetic image generator for Particle Image Velocimetry (PIV) with a focus on performance and parallelism on accelerators, implemented in JAX. SynthPix supports the same configuration parameters as existing tools but achieves a throughput several orders of magnitude higher in image-pair generation per second. SynthPix was developed to enable the training of data-hungry reinforcement learning methods for flow estimation and for reducing the iteration times during the development of fast flow estimation methods used in recent active fluids control studies with real-time PIV feedback. We believe SynthPix to be useful for the fluid dynamics community, and in this paper we describe the main ideas behind this software package.

Alan Bonomi, Francesco Banelli, Antonio Terpin

Particle Image Velocimetry (PIV) is an imaging technique in experimental fluid dynamics that quantifies flow fields around bluff bodies by analyzing the displacement of neutrally buoyant tracer particles immersed in the fluid. Traditional PIV approaches typically depend on tuning parameters specific to the imaging setup, making the performance sensitive to variations in illumination, flow conditions, and seeding density. On the other hand, even state-of-the-art machine learning methods for flow quantification are fragile outside their training set. In our experiments, we observed that flow quantification would improve if different tunings (or algorithms) were applied to different regions of the same image pair. In this work, we parallelize the instantaneous flow quantification with multiple algorithms and adopt a consensus framework based on the alternating direction method of multipliers, seamlessly incorporating priors such as smoothness and incompressibility. We perform several numerical experiments to demonstrate the benefits of this approach. For instance, we achieve a decrease in end-point-error of up to 20% of a dense-inverse-search estimator at an inference rate of 60Hz, and we show how this performance boost can be increased further with outlier rejection. Our method is implemented in JAX, effectively exploiting hardware acceleration, and integrated in Flow Gym, enabling (i) reproducible comparisons with the state-of-the-art, (ii) testing different base algorithms, (iii) straightforward deployment for active fluids control applications.

Francesco Banelli, Antonio Terpin, Alan Bonomi et al.

Flow Gym is a toolkit for research and deployment of flow-field quantification methods inspired by OpenAI Gym and Stable-Baselines3. It uses SynthPix as synthetic image generation engine and provides a unified interface for the testing, deployment and training of (learning-based) algorithms for flow-field quantification from a number of consecutive images of tracer particles. It also contains a growing number of integrations of existing algorithms and stable (re-)implementations in JAX.

Antonio Terpin, Raffaello D'Andrea

Many high-performance human activities are executed with little or no external feedback: think of a figure skater landing a triple jump, a pitcher throwing a curveball for a strike, or a barista pouring latte art. To study the process of skill acquisition under fully controlled conditions, we bypass human subjects. Instead, we directly interface a generalist reinforcement learning agent with a spinning cylinder in a tabletop circulating water channel to maximize or minimize drag. This setup has several desirable properties. First, it is a physical system, with the rich interactions and complex dynamics that only the physical world has: the flow is highly chaotic and extremely difficult, if not impossible, to model or simulate accurately. Second, the objective -- drag minimization or maximization -- is easy to state and can be captured directly in the reward, yet good strategies are not obvious beforehand. Third, decades-old experimental studies provide recipes for simple, high-performance open-loop policies. Finally, the setup is inexpensive and far easier to reproduce than human studies. In our experiments we find that high-dimensional flow feedback lets the agent discover high-performance drag-control strategies with only minutes of real-world interaction. When we later replay the same action sequences without any feedback, we obtain almost identical performance. This shows that feedback, and in particular flow feedback, is not needed to execute the learned policy. Surprisingly, without flow feedback during training the agent fails to discover any well-performing policy in drag maximization, but still succeeds in drag minimization, albeit more slowly and less reliably. Our studies show that learning a high-performance skill can require richer information than executing it, and learning conditions can be kind or wicked depending solely on the goal, not on dynamics or policy complexity.

Long Phan, Alice Gatti, Ziwen Han et al. · amazon-science, apple-ml

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

Michal Balcerak, Tamaz Amiranashvili, Antonio Terpin et al.

Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In contrast, energy-based models (EBMs) address this by incorporating corresponding scalar energy terms. Here, we propose Energy Matching, a framework that endows flow-based approaches with the flexibility of EBMs. Far from the data manifold, samples move from noise to data along irrotational, optimal transport paths. As they approach the data manifold, an entropic energy term guides the system into a Boltzmann equilibrium distribution, explicitly capturing the underlying likelihood structure of the data. We parameterize these dynamics with a single time-independent scalar field, which serves as both a powerful generator and a flexible prior for effective regularization of inverse problems. The present method substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation in terms of fidelity, while retaining simulation-free training of transport-based approaches away from the data manifold. Furthermore, we leverage the flexibility of the method to introduce an interaction energy that supports the exploration of diverse modes, which we demonstrate in a controlled protein generation setting. This approach learns a scalar potential energy, without time conditioning, auxiliary generators, or additional networks, marking a significant departure from recent EBM methods. We believe this simplified yet rigorous formulation significantly advances EBMs capabilities and paves the way for their wider adoption in generative modeling in diverse domains.

Panagiotis D. Grontas, Antonio Terpin, Efe C. Balta et al.

We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $Π$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem for backpropagation. We deploy $Π$net as a feasible-by-design optimization proxy for parametric constrained optimization problems and obtain modest-accuracy solutions faster than traditional solvers when solving a single problem, and significantly faster for a batch of problems. We surpass state-of-the-art learning approaches in terms of training time, solution quality, and robustness to hyperparameter tuning, while maintaining similar inference times. Finally, we tackle multi-vehicle motion planning with non-convex trajectory preferences and provide $Π$net as a GPU-ready package implemented in JAX with effective tuning heuristics.

Antonio Terpin, Nicolas Lanzetti, Martin Gadea et al.

Diffusion regulates numerous natural processes and the dynamics of many successful generative models. Existing models to learn the diffusion terms from observational data rely on complex bilevel optimization problems and model only the drift of the system. We propose a new simple model, JKOnet*, which bypasses the complexity of existing architectures while presenting significantly enhanced representational capabilities: JKOnet* recovers the potential, interaction, and internal energy components of the underlying diffusion process. JKOnet* minimizes a simple quadratic loss and outperforms other baselines in terms of sample efficiency, computational complexity, and accuracy. Additionally, JKOnet* provides a closed-form optimal solution for linearly parametrized functionals, and, when applied to predict the evolution of cellular processes from real-world data, it achieves state-of-the-art accuracy at a fraction of the computational cost of all existing methods. Our methodology is based on the interpretation of diffusion processes as energy-minimizing trajectories in the probability space via the so-called JKO scheme, which we study via its first-order optimality conditions.