In recent years, surrogate models based on deep neural networks (DNN) have been widely used to solve partial differential equations, which were traditionally handled by means of numerical simulations. This kind of surrogate models, however, focuses on global interpolation of the training dataset, and thus requires a large network structure. The process is both time consuming and computationally costly, thereby restricting their use for high-fidelity prediction of complex physical problems. In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data. The framework utilizes the local domain of dependence with converging coarse solutions as input, which greatly reduces computational resource and training time. As a validation case, the NNLCI method is applied to study inviscid supersonic flows in channels with bumps. Different bump geometries and locations are considered to benchmark the effectiveness and versability of the proposed approach. Detailed flow structures, including shock-wave interactions, are examined systematically.
Neural networks are susceptible to privacy attacks. To date, no verifier can reason about the privacy of individuals participating in the training set. We propose a new privacy property, called local differential classification privacy (LDCP), extending local robustness to a differential privacy setting suitable for black-box classifiers. Given a neighborhood of inputs, a classifier is LDCP if it classifies all inputs the same regardless of whether it is trained with the full dataset or whether any single entry is omitted. A naive algorithm is highly impractical because it involves training a very large number of networks and verifying local robustness of the given neighborhood separately for every network. We propose Sphynx, an algorithm that computes an abstraction of all networks, with a high probability, from a small set of networks, and verifies LDCP directly on the abstract network. The challenge is twofold: network parameters do not adhere to a known distribution probability, making it difficult to predict an abstraction, and predicting too large abstraction harms the verification. Our key idea is to transform the parameters into a distribution given by KDE, allowing to keep the over-approximation error small. To verify LDCP, we extend a MILP verifier to analyze an abstract network. Experimental results show that by training only 7% of the networks, Sphynx predicts an abstract network obtaining 93% verification accuracy and reducing the analysis time by $1.7\cdot10^4$x.
Balance loss is a significant challenge in lower-limb exoskeleton applications, as it can lead to potential falls, thereby impacting user safety and confidence. We introduce a control framework for omnidirectional recovery step planning by online optimization of step duration and position in response to external forces. We map the step duration and position to a human-like foot trajectory, which is then translated into joint trajectories using inverse kinematics. These trajectories are executed via an impedance controller, promoting cooperation between the exoskeleton and the user. Moreover, our framework is based on the concept of the divergent component of motion, also known as the Extrapolated Center of Mass, which has been established as a consistent dynamic for describing human movement. This real-time online optimization framework enhances the adaptability of exoskeleton users under unforeseen forces thereby improving the overall user stability and safety. To validate the effectiveness of our approach, simulations, and experiments were conducted. Our push recovery experiments employing the exoskeleton in zero-torque mode (without assistance) exhibit an alignment with the exoskeleton's recovery assistance mode, that shows the consistency of the control framework with human intention. To the best of our knowledge, this is the first cooperative push recovery framework for the lower-limb human exoskeleton that relies on the simultaneous adaptation of intra-stride parameters in both frontal and sagittal directions. The proposed control scheme has been validated with human subject experiments.
The deep learning recipe of casting real-world problems as mathematical optimisation and tackling the optimisation by training deep neural networks using gradient-based optimisation has undoubtedly proven to be a fruitful one. The understanding behind why deep learning works, however, has lagged behind its practical significance. We aim to make steps towards an improved understanding of deep learning with a focus on optimisation and model regularisation. We start by investigating gradient descent (GD), a discrete-time algorithm at the basis of most popular deep learning optimisation algorithms. Understanding the dynamics of GD has been hindered by the presence of discretisation drift, the numerical integration error between GD and its often studied continuous-time counterpart, the negative gradient flow (NGF). To add to the toolkit available to study GD, we derive novel continuous-time flows that account for discretisation drift. Unlike the NGF, these new flows can be used to describe learning rate specific behaviours of GD, such as training instabilities observed in supervised learning and two-player games. We then translate insights from continuous time into mitigation strategies for unstable GD dynamics, by constructing novel learning rate schedules and regularisers that do not require additional hyperparameters. Like optimisation, smoothness regularisation is another pillar of deep learning's success with wide use in supervised learning and generative modelling. Despite their individual significance, the interactions between smoothness regularisation and optimisation have yet to be explored. We find that smoothness regularisation affects optimisation across multiple deep learning domains, and that incorporating smoothness regularisation in reinforcement learning leads to a performance boost that can be recovered using adaptions to optimisation methods.
The widespread use of face recognition technology has given rise to privacy concerns, as many individuals are worried about the collection and utilization of their facial data. To address these concerns, researchers are actively exploring the concept of ``unlearnable examples", by adding imperceptible perturbation to data in the model training stage, which aims to prevent the model from learning discriminate features of the target face. However, current methods are inefficient and cannot guarantee transferability and robustness at the same time, causing impracticality in the real world. To remedy it, we propose a novel method called Segue: Side-information guided generative unlearnable examples. Specifically, we leverage a once-trained multiple-used model to generate the desired perturbation rather than the time-consuming gradient-based method. To improve transferability, we introduce side information such as true labels and pseudo labels, which are inherently consistent across different scenarios. For robustness enhancement, a distortion layer is integrated into the training pipeline. Extensive experiments demonstrate that the proposed Segue is much faster than previous methods (1000$\times$) and achieves transferable effectiveness across different datasets and model architectures. Furthermore, it can resist JPEG compression, adversarial training, and some standard data augmentations.
We study a generalization of the classic Online Convex Optimization (OCO) framework by considering additional long-term adversarial constraints. Specifically, after an online policy decides its action on a round, in addition to a convex cost function, the adversary also reveals a set of $k$ convex constraints. The cost and the constraint functions could change arbitrarily with time, and no information about the future functions is assumed to be available. In this paper, we propose a meta-policy that simultaneously achieves a sublinear cumulative constraint violation and a sublinear regret. This is achieved via a black box reduction of the constrained problem to the standard OCO problem for a recursively constructed sequence of surrogate cost functions. We show that optimal performance bounds can be achieved by solving the surrogate problem using any adaptive OCO policy enjoying a standard data-dependent regret bound. A new Lyapunov-based proof technique is presented that reveals a connection between regret and certain sequential inequalities through a novel decomposition result. We conclude the paper by highlighting applications to online multi-task learning and network control problems.
We propose a metadata-aware self-supervised learning~(SSL)~framework useful for fine-grained classification and ecological mapping of bird species around the world. Our framework unifies two SSL strategies: Contrastive Learning~(CL) and Masked Image Modeling~(MIM), while also enriching the embedding space with metadata available with ground-level imagery of birds. We separately train uni-modal and cross-modal ViT on a novel cross-view global bird species dataset containing ground-level imagery, metadata (location, time), and corresponding satellite imagery. We demonstrate that our models learn fine-grained and geographically conditioned features of birds, by evaluating on two downstream tasks: fine-grained visual classification~(FGVC) and cross-modal retrieval. Pre-trained models learned using our framework achieve SotA performance on FGVC of iNAT-2021 birds and in transfer learning settings for CUB-200-2011 and NABirds datasets. Moreover, the impressive cross-modal retrieval performance of our model enables the creation of species distribution maps across any geographic region. The dataset and source code will be released at https://github.com/mvrl/BirdSAT}.
Reinforcement learning (RL) is a powerful tool for finding optimal policies in sequential decision processes. However, deep RL methods suffer from two weaknesses: collecting the amount of agent experience required for practical RL problems is prohibitively expensive, and the learned policies exhibit poor generalization on tasks outside of the training distribution. To mitigate these issues, we introduce automaton distillation, a form of neuro-symbolic transfer learning in which Q-value estimates from a teacher are distilled into a low-dimensional representation in the form of an automaton. We then propose two methods for generating Q-value estimates: static transfer, which reasons over an abstract Markov Decision Process constructed based on prior knowledge, and dynamic transfer, where symbolic information is extracted from a teacher Deep Q-Network (DQN). The resulting Q-value estimates from either method are used to bootstrap learning in the target environment via a modified DQN loss function. We list several failure modes of existing automaton-based transfer methods and demonstrate that both static and dynamic automaton distillation decrease the time required to find optimal policies for various decision tasks.
Dexterous manipulation of objects once held in hand remains a challenge. Such skills are, however, necessary for robotics to move beyond gripper-based manipulation and use all the dexterity offered by anthropomorphic robotic hands. One major challenge when manipulating an object within the hand is that fingers must move around the object while avoiding collision with other fingers or the object. Such collision-free paths must be computed in real-time, as the smallest deviation from the original plan can easily lead to collisions. We present a real-time approach to computing collision-free paths in a high-dimensional space. To guide the exploration, we learn an explicit representation of the free space, retrievable in real-time. We further combine this representation with closed-loop control via dynamical systems and sampling-based motion planning and show that the combination increases performance compared to alternatives, offering efficient search of feasible paths and real-time obstacle avoidance in a multi-fingered robotic hand.
Whittle index policy is a heuristic to the intractable restless multi-armed bandits (RMAB) problem. Although it is provably asymptotically optimal, finding Whittle indices remains difficult. In this paper, we present Neural-Q-Whittle, a Whittle index based Q-learning algorithm for RMAB with neural network function approximation, which is an example of nonlinear two-timescale stochastic approximation with Q-function values updated on a faster timescale and Whittle indices on a slower timescale. Despite the empirical success of deep Q-learning, the non-asymptotic convergence rate of Neural-Q-Whittle, which couples neural networks with two-timescale Q-learning largely remains unclear. This paper provides a finite-time analysis of Neural-Q-Whittle, where data are generated from a Markov chain, and Q-function is approximated by a ReLU neural network. Our analysis leverages a Lyapunov drift approach to capture the evolution of two coupled parameters, and the nonlinearity in value function approximation further requires us to characterize the approximation error. Combing these provide Neural-Q-Whittle with $\mathcal{O}(1/k^{2/3})$ convergence rate, where $k$ is the number of iterations.