Learning representations from sets has become increasingly important with many applications in point cloud processing, graph learning, image/video recognition, and object detection. We introduce a geometrically-interpretable and generic pooling mechanism for aggregating a set of features into a fixed-dimensional representation. In particular, we treat elements of a set as samples from a probability distribution and propose an end-to-end trainable Euclidean embedding for sliced-Wasserstein distance to learn from set-structured data effectively. We evaluate our proposed pooling method on a wide variety of set-structured data, including point-cloud, graph, and image classification tasks, and demonstrate that our proposed method provides superior performance over existing set representation learning approaches. Our code is available at https://github.com/navid-naderi/PSWE.

The unprecedented success of deep neural networks in many applications has made these networks a prime target for adversarial exploitation. In this paper, we introduce a benchmark technique for detecting backdoor attacks (aka Trojan attacks) on deep convolutional neural networks (CNNs). We introduce the concept of Universal Litmus Patterns (ULPs), which enable one to reveal backdoor attacks by feeding these universal patterns to the network and analyzing the output (i.e., classifying the network as `clean' or `corrupted'). This detection is fast because it requires only a few forward passes through a CNN. We demonstrate the effectiveness of ULPs for detecting backdoor attacks on thousands of networks with different architectures trained on four benchmark datasets, namely the German Traffic Sign Recognition Benchmark (GTSRB), MNIST, CIFAR10, and Tiny-ImageNet. The codes and train/test models for this paper can be found here: https://umbcvision.github.io/Universal-Litmus-Patterns/.

With the growing use of graph convolutional neural networks (GCNNs) comes the need for explainability. In this paper, we introduce explainability methods for GCNNs. We develop the graph analogues of three prominent explainability methods for convolutional neural networks: contrastive gradient-based (CG) saliency maps, Class Activation Mapping (CAM), and Excitation Back-Propagation (EB) and their variants, gradient-weighted CAM (Grad-CAM) and contrastive EB (c-EB). We show a proof-of-concept of these methods on classification problems in two application domains: visual scene graphs and molecular graphs. To compare the methods, we identify three desirable properties of explanations: (1) their importance to classification, as measured by the impact of occlusions, (2) their contrastivity with respect to different classes, and (3) their sparseness on a graph. We call the corresponding quantitative metrics fidelity, contrastivity, and sparsity and evaluate them for each method. Lastly, we analyze the salient subgraphs obtained from explanations and report frequently occurring patterns.

It is still unknown how associative biological memories operate. Hopfield networks are popular models of associative memory, but they suffer from spurious memories and low efficiency. Here, we present a new model of an associative memory that overcomes these deficiencies. We call this model sparse associative memory (SAM) because it is based on sparse projections from neural patterns to pattern-specific neurons. These sparse projections have been shown to be sufficient to uniquely encode a neural pattern. Based on this principle, we investigate theoretically and in simulation our SAM model, which turns out to have high memory efficiency and a vanishingly small probability of spurious memories. This model may serve as a basic building block of brain functions involving associative memory.

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which could be arbitrarily worse than the optimal solution. Inspired by the relationship between the negative log-likelihood function and the Kullback-Leibler (KL) divergence, we propose an alternative formulation for estimating the GMM parameters using the sliced Wasserstein distance, which gives rise to a new algorithm. Specifically, we propose minimizing the sliced-Wasserstein distance between the mixture model and the data distribution with respect to the GMM parameters. In contrast to the KL-divergence, the energy landscape for the sliced-Wasserstein distance is more well-behaved and therefore more suitable for a stochastic gradient descent scheme to obtain the optimal GMM parameters. We show that our formulation results in parameter estimates that are more robust to random initializations and demonstrate that it can estimate high-dimensional data distributions more faithfully than the EM algorithm.

We address the problem of adapting a controller of a dynamical system to an unexpected change in dynamics. Such a system can be controlled using model predictive control if the model of the dynamics (forward model) is sufficiently accurate. The challenge is to adapt the forward model quickly. We motivate the requirement to achieve this adaptation given only sparse training data. To solve this challenge, we introduce the concept of preserving any a priori learned functional relationship in the dynamics, while adapting solely to the relatively simple functional relationship describing the change in dynamics. We show that this concept can be realized by augmenting a forward model with a simple corrector network and demonstrate feasibility on a challenging control problem in simulation.

Nonlinear dynamical systems have been used in many disciplines to model complex behaviors, including biological motor control, robotics, perception, economics, traffic prediction, and neuroscience. While often the unexpected emergent behavior of nonlinear systems is the focus of investigations, it is of equal importance to create goal-directed behavior (e.g., stable locomotion from a system of coupled oscillators under perceptual guidance). Modeling goal-directed behavior with nonlinear systems is, however, rather difficult due to the parameter sensitivity of these systems, their complex phase transitions in response to subtle parameter changes, and the difficulty of analyzing and predicting their long-term behavior; intuition and time-consuming parameter tuning play a major role. This letter presents and reviews dynamical movement primitives, a line of research for modeling attractor behaviors of autonomous nonlinear dynamical systems with the help of statistical learning techniques. The essence of our approach is to start with a simple dynamical system, such as a set of linear differential equations, and transform those into a weakly nonlinear system with prescribed attractor dynamics by means of a learnable autonomous forcing term. Both point attractors and limit cycle attractors of almost arbitrary complexity can be generated. We explain the design principle of our approach and evaluate its properties in several example applications in motor control and robotics.

High speed robot locomotion is one of the most challenging problems in mobile robots. Fast robots push the limits of mechanical design, control and perception. The cheetah is an existence proof of what the authors term an Ultra-High Speed Locomotor, which can attain speeds of greater than 50 leg lengths per second and can cover 10 meters in a single gait cycle. In this paper, the energetics and dynamics of high-speed quadruped movement are analyzed. A leg design is presented that combines a novel hybrid actuator concept plus biarticular muscles to create a lightweight (17 Newton) leg capable of generating 90 Newtons of force. Static and dynamic test results show the promise of the hybrid actuator system in ultra high-speed locomotors.

We present a novel paradigm for pattern matching. Our method provides a means to search a continuous data stream for exact matches with a priori stored data sequences. At heart, we use a neural network with input and output layers and variable connections in between. The input layer has one neuron for each possible character or number in the data stream, and the output layer has one neuron for each stored pattern. The novelty of the network is that the delays of the connections from input to output layer are optimized to match the temporal occurrence of an input character within a stored sequence. Thus, the polychronous activation of input neurons results in activating an output neuron that indicates detection of a stored pattern. For data streams that have a large alphabet, the connectivity in our network is very sparse and the number of computational steps small: in this case, our method outperforms by a factor 2 deterministic finite state machines, which have been the state of the art for pattern matching for more than 30 years.

Dynamical systems can generate movement trajectories that are robust against perturbations. This article presents an improved modification of the original dynamic movement primitive (DMP) framework by Ijspeert et al [1], [2]. The new equations can generalize movements to new targets without singularities and large accelerations. Furthermore, the new equations can represent a movement in 3D task space without depending on the choice of coordinate system (invariance under invertible affine transformations). Our modified DMP is motivated from biological data (spinal-cord stimulation in frogs) and human behavioral experiments. We further extend the formalism to obstacle avoidance by exploiting the robustness against perturbations: an additional term is added to the differential equations to make the robot steer around an obstacle. This additional term empirically describes human obstacle avoidance. We demonstrate the feasibility of our approach using the Sarcos Slave robot arm: after learning a single placing movement, the robot placed a cup between two arbitrarily given positions and avoided approaching obstacles.

We provide a general approach for learning robotic motor skills from human demonstration. To represent an observed movement, a non-linear differential equation is learned such that it reproduces this movement. Based on this representation, we build a library of movements by labeling each recorded movement according to task and context (e.g., grasping, placing, and releasing). Our differential equation is formulated such that generalization can be achieved simply by adapting a start and a goal parameter in the equation to the desired position values of a movement. For object manipulation, we present how our framework extends to the control of gripper orientation and finger position. The feasibility of our approach is demonstrated in simulation as well as on the Sarcos dextrous robot arm. The robot learned a pick-and-place operation and a water-serving task and could generalize these tasks to novel situations.