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Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems,…

We investigate geometric regularization strategies for learned latent representations in encoder--decoder reduced-order models. In a fixed experimental setting for the advection--diffusion--reaction (ADR) equation, we model latent dynamics…

Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…

Adaptively controlling and minimizing regret in unknown dynamical systems while controlling the growth of the system state is crucial in real-world applications. In this work, we study the problem of stabilization and regret minimization of…

Error accumulation is effective for gradient sparsification in distributed settings: initially-unselected gradient entries are eventually selected as their accumulated error exceeds a certain level. The accumulation essentially behaves as a…

Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize…

As Large Language Models (LLMs) transition into autonomous multi-agent ecosystems, robust minimax training becomes essential yet remains prone to instability when highly non-linear policies induce extreme local curvature in the inner…

Powerful deep neural networks are vulnerable to adversarial attacks. To obtain adversarially robust models, researchers have separately developed adversarial training and Jacobian regularization techniques. There are abundant theoretical…

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…

Accurately predicting the consequences of agents' actions is a key prerequisite for planning in robotic control. Model-based reinforcement learning (MBRL) is one paradigm which relies on the iterative learning and prediction of state-action…

This paper introduces an adaptive-neuro geometric control for a centralized multi-quadrotor cooperative transportation system, which enhances both adaptivity and disturbance rejection. Our strategy is to coactively tune the model parameters…

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…

To succeed in the real world, robots must deal with situations that differ from those seen during training. Those out-of-distribution situations for legged robot mainly include challenging dynamic gaps and perceptual gaps. Here we study the…

Transformers serve as the foundational architecture for many successful large-scale models, demonstrating the ability to overfit the training data while maintaining strong generalization on unseen data, a phenomenon known as benign…

Weather and climate forecasting is vital for sectors such as agriculture and disaster management. Although numerical weather prediction (NWP) systems have advanced, forecasting at the subseasonal-to-seasonal (S2S) scale, spanning 2 to 6…

Deep Learning models have achieved state-of-the-art performance in medium-range weather prediction but often fail to maintain physically consistent rollouts beyond 14 days. In contrast, a few atmospheric models demonstrate stability over…

Unrolling training trajectories over time strongly influences the inference accuracy of neural network-augmented physics simulators. We analyze this in three variants of training neural time-steppers. In addition to one-step setups and…

A key challenge for the machine learning community is to understand and accelerate the training dynamics of deep networks that lead to delayed generalisation and emergent robustness to input perturbations, also known as grokking. Prior work…

Existing trajectory prediction methods exhibit significant performance degradation under distribution shifts during test time. Although test-time training techniques have been explored to enable adaptation, current approaches rely on an…